Science Publishing Group: Applied and Computational Mathematics: Table of Contents &lt;i&gt; Applied and Computational Mathematics (ACM) &lt;/i&gt; is an applied and computational mathematics journal of high quality, driven by the computational revolution and emphasizing innovative applied mathematics having potential for applicability and practicality. This journal is of interest to a wide audience of applied mathematicians and scientists concerned with the development of mathematical principles and practical issues in computational mathematics. All research articles in &lt;i&gt; ACM &lt;/i&gt; will undergone rigorous peer review, based on initial editor screening and anonymized refereeing by an expert reviewer. http://www.sciencepublishinggroup.com/j/acm Science Publishing Group: Applied and Computational Mathematics: Table of Contents Science Publishing Group en-US Applied and Computational Mathematics Applied and Computational Mathematics http://image.sciencepublishinggroup.com/journal/147.gif http://www.sciencepublishinggroup.com/j/acm Approximate solutionsof Damped Nonlinear Vibrating System with Varying Coefficients under Some Conditions http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20120101.11 Krylov-Bogoliubov-Mitropolskii (KBM) method has been extended to certain damped-oscillatory nonlinear systems with varying coefficients. The solution obtained for different initial conditions for a second order nonlinear system show a good coincidence with those obtained by numerical method. The method is illustrated by an example. Krylov-Bogoliubov-Mitropolskii (KBM) method has been extended to certain damped-oscillatory nonlinear systems with varying coefficients. The solution obtained for different initial conditions for a second order nonlinear system show a good coincidence with those obtained by numerical method. The method is illustrated by an example. Approximate solutionsof Damped Nonlinear Vibrating System with Varying Coefficients under Some Conditions doi:10.11648/j.acm.20120101.11 Applied and Computational Mathematics 2014-01-01 © Science Publishing Group Pinakee Dey Babul Hossain Musa Miah Mohammad Mokaddes Ali Approximate solutionsof Damped Nonlinear Vibrating System with Varying Coefficients under Some Conditions 1 1 5 5 2014-01-01 2014-01-01 10.11648/j.acm.20120101.11 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20120101.11 © Science Publishing Group Investigation of the Channel Flow with Internal Obstacles Using Large Eddy Simulation and Finite-Element Technique http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130201.11 This paper considers the turbulent-flow characteristics and the mechanism of vortex shedding behind one and two square obstacles centered inside a 2-D channel. The investigation was carried out for a range of Reynolds number (Re) from 1 to 300 with a fixed blockage ratio β = 0.25. Comparison of the flow patterns for the single and two obstacles was feasible. The computations were based on the finite-element technique. Large-eddy simulation (LES) with the Smagorinsky method was used to model the turbulent flow. Streamline patterns and velocity contours were visualized to monitor the vortex shedding. The results show that the mechanism of the vortex shedding has different characteristics for the two cases of one and two square obstacles. Interesting findings and useful conclusions were recorded. This paper considers the turbulent-flow characteristics and the mechanism of vortex shedding behind one and two square obstacles centered inside a 2-D channel. The investigation was carried out for a range of Reynolds number (Re) from 1 to 300 with a fixed blockage ratio β = 0.25. Comparison of the flow patterns for the single and two obstacles was feasible. The computations were based on the finite-element technique. Large-eddy simulation (LES) with the Smagorinsky method was used to model the turbulent flow. Streamline patterns and velocity contours were visualized to monitor the vortex shedding. The results show that the mechanism of the vortex shedding has different characteristics for the two cases of one and two square obstacles. Interesting findings and useful conclusions were recorded. Investigation of the Channel Flow with Internal Obstacles Using Large Eddy Simulation and Finite-Element Technique doi:10.11648/j.acm.20130201.11 Applied and Computational Mathematics 2014-01-01 © Science Publishing Group A. F. Abdel Gawad N. A. Mohamed S. A. Mohamed M. S. Matbuly Investigation of the Channel Flow with Internal Obstacles Using Large Eddy Simulation and Finite-Element Technique 2 1 13 13 2014-01-01 2014-01-01 10.11648/j.acm.20130201.11 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130201.11 © Science Publishing Group On Completely Generalized Co-Quasi-Variational Inequalities http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130201.12 In the present work, we introduce and study completely generalized quasi-variational inequality problem for fuzzy mappings. By using the definitions of strongly accretive and retraction mappings, we propose an iterative algorithm for computing the approximate solutions of this class of variational inequalities. We prove that approximate solutions obtained by the proposed algorithm converge to the exact solutions of completely generalized quasi-variational inequality problem. In the present work, we introduce and study completely generalized quasi-variational inequality problem for fuzzy mappings. By using the definitions of strongly accretive and retraction mappings, we propose an iterative algorithm for computing the approximate solutions of this class of variational inequalities. We prove that approximate solutions obtained by the proposed algorithm converge to the exact solutions of completely generalized quasi-variational inequality problem. On Completely Generalized Co-Quasi-Variational Inequalities doi:10.11648/j.acm.20130201.12 Applied and Computational Mathematics 2014-01-01 © Science Publishing Group Syed Shakaib Irfan On Completely Generalized Co-Quasi-Variational Inequalities 2 1 18 18 2014-01-01 2014-01-01 10.11648/j.acm.20130201.12 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130201.12 © Science Publishing Group Numerıcal Approxımatons for Solvıng Partıal Dıfferentıal Equatıons wıth Varıable Coeffıcıents http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130201.13 In this paper, variational iteration method (VIM) and multivariate padé approximaton (MPA) were compared. First, partial differential eqaution has been solved and converted to power series by variational iteration method (VIM), then the numerical solution of partial differential eqauation was put into multivariate padé series. Thus the numerical solutions of the partial differential eqautions were obtained. Numerical solutions of two examples were calculated and results were presented in tables and figures. In this paper, variational iteration method (VIM) and multivariate padé approximaton (MPA) were compared. First, partial differential eqaution has been solved and converted to power series by variational iteration method (VIM), then the numerical solution of partial differential eqauation was put into multivariate padé series. Thus the numerical solutions of the partial differential eqautions were obtained. Numerical solutions of two examples were calculated and results were presented in tables and figures. Numerıcal Approxımatons for Solvıng Partıal Dıfferentıal Equatıons wıth Varıable Coeffıcıents doi:10.11648/j.acm.20130201.13 Applied and Computational Mathematics 2014-01-01 © Science Publishing Group Veyis TURUT Numerıcal Approxımatons for Solvıng Partıal Dıfferentıal Equatıons wıth Varıable Coeffıcıents 2 1 23 23 2014-01-01 2014-01-01 10.11648/j.acm.20130201.13 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130201.13 © Science Publishing Group Theorem on a Matrix of Right-Angled Triangles http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130202.14 The following theorem is proved: All primitive right-angled triangles (primitive Pythagorean triples) may be defined by a pair of positive integer indices (i,j), where i is an uneven number and j is an even number and have no com-mon factor. The sides of every positive integer right angled triangle are then defined by the indices as follows: For hy-potenuse h, uneven leg u and even leg e, h = i2 + ij + j2/2, e = ij + j2/2, u = i2 + ij. This defines an infinite by infinite matrix of right angled triangles with positive integer sides. The following theorem is proved: All primitive right-angled triangles (primitive Pythagorean triples) may be defined by a pair of positive integer indices (i,j), where i is an uneven number and j is an even number and have no com-mon factor. The sides of every positive integer right angled triangle are then defined by the indices as follows: For hy-potenuse h, uneven leg u and even leg e, h = i2 + ij + j2/2, e = ij + j2/2, u = i2 + ij. This defines an infinite by infinite matrix of right angled triangles with positive integer sides. Theorem on a Matrix of Right-Angled Triangles doi:10.11648/j.acm.20130202.14 Applied and Computational Mathematics 2014-01-01 © Science Publishing Group Martin W. Bredenkamp Theorem on a Matrix of Right-Angled Triangles 2 2 41 41 2014-01-01 2014-01-01 10.11648/j.acm.20130202.14 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130202.14 © Science Publishing Group Series of Primitive Right-Angled Triangles http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130202.15 From the infinite matrix of right-angled triangles, series of triangles are found that approach a right-angled triangle that has one irrational side such as the 45 triangle. This allows for the creation of a series of fractions that have as their limit an irrational number. Formulae for finding the next triangle in the triangle series, and thus the next fraction in the fraction series, are also developed. Such a series can be found for the square root of every uneven number that is not a perfect square, and for those of some of the even numbers as well. From the infinite matrix of right-angled triangles, series of triangles are found that approach a right-angled triangle that has one irrational side such as the 45 triangle. This allows for the creation of a series of fractions that have as their limit an irrational number. Formulae for finding the next triangle in the triangle series, and thus the next fraction in the fraction series, are also developed. Such a series can be found for the square root of every uneven number that is not a perfect square, and for those of some of the even numbers as well. Series of Primitive Right-Angled Triangles doi:10.11648/j.acm.20130202.15 Applied and Computational Mathematics 2014-01-01 © Science Publishing Group Martin W. Bredenkamp Series of Primitive Right-Angled Triangles 2 2 53 53 2014-01-01 2014-01-01 10.11648/j.acm.20130202.15 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130202.15 © Science Publishing Group Using Maple to Study the Double Integral Problems http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130202.12 This paper uses the mathematical software Maple as the auxiliary tool to study the evaluation of two types of double integrals. We can find the closed forms of these two types of double integrals by using Euler&apos;s formula and finite geometric series. On the other hand, we propose four examples to do calculation practically. The research methods adopted in this study involved finding solutions through manual calculations and verifying these solutions by using Maple. This type of research method not only allows the discovery of calculation errors, but also helps modify the original directions of thinking from manual and Maple calculations. For this reason, Maple provides insights and guidance regarding prob-lem-solving methods. This paper uses the mathematical software Maple as the auxiliary tool to study the evaluation of two types of double integrals. We can find the closed forms of these two types of double integrals by using Euler&apos;s formula and finite geometric series. On the other hand, we propose four examples to do calculation practically. The research methods adopted in this study involved finding solutions through manual calculations and verifying these solutions by using Maple. This type of research method not only allows the discovery of calculation errors, but also helps modify the original directions of thinking from manual and Maple calculations. For this reason, Maple provides insights and guidance regarding prob-lem-solving methods. Using Maple to Study the Double Integral Problems doi:10.11648/j.acm.20130202.12 Applied and Computational Mathematics 2014-01-01 © Science Publishing Group Chii-Huei Yu Using Maple to Study the Double Integral Problems 2 2 31 31 2014-01-01 2014-01-01 10.11648/j.acm.20130202.12 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130202.12 © Science Publishing Group Solving Boussinesq Equation by Bilinear Bӓcklund Transformation http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130202.13 In this paper Hirota bilinear method is applied to constructing Backlund transformation of the Boussinesq equation. The bilimear Backlund form are used to obtain the soliton solution of the Boussinesq equation. Also as an application for the bilinear Bӓcklund transformation, new classes of wave solutions to the Boussinesq Equation are computed. In this paper Hirota bilinear method is applied to constructing Backlund transformation of the Boussinesq equation. The bilimear Backlund form are used to obtain the soliton solution of the Boussinesq equation. Also as an application for the bilinear Bӓcklund transformation, new classes of wave solutions to the Boussinesq Equation are computed. Solving Boussinesq Equation by Bilinear Bӓcklund Transformation doi:10.11648/j.acm.20130202.13 Applied and Computational Mathematics 2014-01-01 © Science Publishing Group M. Y. Adamu E. Suleiman Solving Boussinesq Equation by Bilinear Bӓcklund Transformation 2 2 35 35 2014-01-01 2014-01-01 10.11648/j.acm.20130202.13 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130202.13 © Science Publishing Group The Effect of Radiation on Natural Convection Flow of Fluid with Variable Viscosity from a Porous Vertical Plate in Presence of Heat Generation http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130202.16 This paper presents a new extension for the effect of radiation on natural convection flow with variable viscosity from a porous vertical plate in presence of heat generation. The governing boundary layer equations are first transformed into a non dimensional form and the resulting non linear system of partial differential equations are then solved numerically using finite difference method together with Keller-Box scheme. The numerical results show that the variable viscosity affects the surface shear stress and the rate of heat transfer, which are here in terms of skin friction coefficient and local Nusselt number. It affects velocity as well as temperature profiles also. These are shown graphically and tabular form for a selection of parameters set of consisting of viscosity variation parameter, heat generation parameter Q, radiation effect Rd , Prandtl number Pr This paper presents a new extension for the effect of radiation on natural convection flow with variable viscosity from a porous vertical plate in presence of heat generation. The governing boundary layer equations are first transformed into a non dimensional form and the resulting non linear system of partial differential equations are then solved numerically using finite difference method together with Keller-Box scheme. The numerical results show that the variable viscosity affects the surface shear stress and the rate of heat transfer, which are here in terms of skin friction coefficient and local Nusselt number. It affects velocity as well as temperature profiles also. These are shown graphically and tabular form for a selection of parameters set of consisting of viscosity variation parameter, heat generation parameter Q, radiation effect Rd , Prandtl number Pr The Effect of Radiation on Natural Convection Flow of Fluid with Variable Viscosity from a Porous Vertical Plate in Presence of Heat Generation doi:10.11648/j.acm.20130202.16 Applied and Computational Mathematics 2014-01-01 © Science Publishing Group Amena Ferdousi M. Mostafizur Rahman Mohammad Salek Parvez M. A. Alim The Effect of Radiation on Natural Convection Flow of Fluid with Variable Viscosity from a Porous Vertical Plate in Presence of Heat Generation 2 2 63 63 2014-01-01 2014-01-01 10.11648/j.acm.20130202.16 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130202.16 © Science Publishing Group A Classic New Method to Solve Quartic Equations http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130202.11 Polynomials of high degrees often appear in many problems such as optimization problems. Equations of the fourth degree or so called quartics are one type of these polynomials. In this paper we give a new Classic method for solving a fourth degree polynomial equation (Quartic). We will show how the quartic formula can be presented easily at the precalculus level. Polynomials of high degrees often appear in many problems such as optimization problems. Equations of the fourth degree or so called quartics are one type of these polynomials. In this paper we give a new Classic method for solving a fourth degree polynomial equation (Quartic). We will show how the quartic formula can be presented easily at the precalculus level. A Classic New Method to Solve Quartic Equations doi:10.11648/j.acm.20130202.11 Applied and Computational Mathematics 2014-01-01 © Science Publishing Group Amir Fathi Nastaran Sharifan A Classic New Method to Solve Quartic Equations 2 2 27 27 2014-01-01 2014-01-01 10.11648/j.acm.20130202.11 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130202.11 © Science Publishing Group Exact and Explicit Approximate Solutions to the Multi-Order Fractional Burgers-Poisson and Fractional Burgers-Poisson Equations http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130203.12 The multi-order fractional Burgers-Poisson (MFBP) equation was introduced, exact as well as approximate solutions to the introduced MFBP, fractional Burgers-Poisson (fBP) and Burgers-Poisson (BP) equations were obtained through the use of the homotopy perturbation method (HPM) and the Adomian decomposition method (ADM) in this paper. The effectiveness and efficiency of the approximate techniques in handling strongly nonlinear multi-order fractional as well as fractional partial differential equations was established in this paper. It was also shown in this paper that the two approximate techniques employed gave similar results to the considered model equations. The multi-order fractional Burgers-Poisson (MFBP) equation was introduced, exact as well as approximate solutions to the introduced MFBP, fractional Burgers-Poisson (fBP) and Burgers-Poisson (BP) equations were obtained through the use of the homotopy perturbation method (HPM) and the Adomian decomposition method (ADM) in this paper. The effectiveness and efficiency of the approximate techniques in handling strongly nonlinear multi-order fractional as well as fractional partial differential equations was established in this paper. It was also shown in this paper that the two approximate techniques employed gave similar results to the considered model equations. Exact and Explicit Approximate Solutions to the Multi-Order Fractional Burgers-Poisson and Fractional Burgers-Poisson Equations doi:10.11648/j.acm.20130203.12 Applied and Computational Mathematics 2014-01-01 © Science Publishing Group Joshua Ikechukwu Nwamba Exact and Explicit Approximate Solutions to the Multi-Order Fractional Burgers-Poisson and Fractional Burgers-Poisson Equations 2 3 85 85 2014-01-01 2014-01-01 10.11648/j.acm.20130203.12 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130203.12 © Science Publishing Group A Note on Self Complementary Brittle and Self Complementary Quasi Chordal Graphs http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130203.13 In this paper we deal with some classes of self-complementary (sc) perfectly orderable graphs namely sc brittle, sc quasi chordal graphs and propose algorithms for these classes. We obtain some results on these classes and an algorithm is proposed based on these results that recognize these classes. We also compile a catalogue for these classes up to 17 vertices. In this paper we deal with some classes of self-complementary (sc) perfectly orderable graphs namely sc brittle, sc quasi chordal graphs and propose algorithms for these classes. We obtain some results on these classes and an algorithm is proposed based on these results that recognize these classes. We also compile a catalogue for these classes up to 17 vertices. A Note on Self Complementary Brittle and Self Complementary Quasi Chordal Graphs doi:10.11648/j.acm.20130203.13 Applied and Computational Mathematics 2014-01-01 © Science Publishing Group Parvez Ali Merajuddin Syed Ajaz Kareem Kirmani A Note on Self Complementary Brittle and Self Complementary Quasi Chordal Graphs 2 3 91 91 2014-01-01 2014-01-01 10.11648/j.acm.20130203.13 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130203.13 © Science Publishing Group Assessment of Earth Surface Pollution due to Residual Rocket Fuel http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130203.14 This paper presents aerohydrodynamic modeling of air and surface pollution caused by toxic rocket fuel components. A numerical algorithm for solving this problem was developed and implemented in a software code in FORTRAN. Modeling of the dissimilation of rocket fuel dynamics for the case of the second-stage rocket &quot;Proton-M&quot; emergency fall was carried out using the developed software package. Finally, the modeling results were compared with a map of vegetation cover contamination in the region of the carrier-rocket second-stage fall. This paper presents aerohydrodynamic modeling of air and surface pollution caused by toxic rocket fuel components. A numerical algorithm for solving this problem was developed and implemented in a software code in FORTRAN. Modeling of the dissimilation of rocket fuel dynamics for the case of the second-stage rocket &quot;Proton-M&quot; emergency fall was carried out using the developed software package. Finally, the modeling results were compared with a map of vegetation cover contamination in the region of the carrier-rocket second-stage fall. Assessment of Earth Surface Pollution due to Residual Rocket Fuel doi:10.11648/j.acm.20130203.14 Applied and Computational Mathematics 2014-01-01 © Science Publishing Group Zhumagulov Bakhytzhan Abdibekov Ualikhan Karzhaubayev Kairzhan Khikmetov Askar Zhubat Kuanysch Assessment of Earth Surface Pollution due to Residual Rocket Fuel 2 3 95 95 2014-01-01 2014-01-01 10.11648/j.acm.20130203.14 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130203.14 © Science Publishing Group Final-Boundary Value Problem in the Non-Classical Treatment for a Sixth Order Pseudoparabolic Equation http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130203.15 In this paper substantiated for a differential equation of pseudoparabolic type with discontinuous coefficients a final-boundary problem with non-classical boundary conditions is considered, which requires no matching conditions. The considered equation as a pseudoparabolic equation generalizes not only classic equations of mathematical physics (heat-conductivity equations, string vibration equation) and also many models differential equations (telegraph equation, Aller&apos;s equation , moisture transfer generalized equation, Manjeron equation, Boussinesq-Love equation and etc.). It is grounded that the final-boundary conditions in the classic and non-classic treatment are equivalent to each other, and such boundary conditions are demonstrated in geometric form. Even from geometric interpretation can see that the grounded non-classic treatment doesn&apos;t require any additional conditions of agreement type. Thus, namely in this paper, the non-classic problem with final-boundary conditions is grounded for a pseudoparabolic equation of sixth order. For simplicity, this was demonstrated for one model case in one of S.L. Sobolev anisotropic space WP(4,2)(G) . In this paper substantiated for a differential equation of pseudoparabolic type with discontinuous coefficients a final-boundary problem with non-classical boundary conditions is considered, which requires no matching conditions. The considered equation as a pseudoparabolic equation generalizes not only classic equations of mathematical physics (heat-conductivity equations, string vibration equation) and also many models differential equations (telegraph equation, Aller&apos;s equation , moisture transfer generalized equation, Manjeron equation, Boussinesq-Love equation and etc.). It is grounded that the final-boundary conditions in the classic and non-classic treatment are equivalent to each other, and such boundary conditions are demonstrated in geometric form. Even from geometric interpretation can see that the grounded non-classic treatment doesn&apos;t require any additional conditions of agreement type. Thus, namely in this paper, the non-classic problem with final-boundary conditions is grounded for a pseudoparabolic equation of sixth order. For simplicity, this was demonstrated for one model case in one of S.L. Sobolev anisotropic space WP(4,2)(G) . Final-Boundary Value Problem in the Non-Classical Treatment for a Sixth Order Pseudoparabolic Equation doi:10.11648/j.acm.20130203.15 Applied and Computational Mathematics 2014-01-01 © Science Publishing Group Ilgar Gurbat oglu Mamedov Final-Boundary Value Problem in the Non-Classical Treatment for a Sixth Order Pseudoparabolic Equation 2 3 99 99 2014-01-01 2014-01-01 10.11648/j.acm.20130203.15 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130203.15 © Science Publishing Group Non-uniform HOC Scheme for the 3D Convection–Diffusion Equation http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130203.11 In this paper, we extend the work of Kalita et al.  to solve the steady 3D convection-diffusion equation with variable coefficients on non-uniform grid. The approach is based on the use of Taylor series expansion, up to the fourth order terms, to approximate the derivatives appearing in the 3D convection diffusion equation. Then the original convection-diffusion equation is used again to replace the resulting higher order derivative terms. This leads to a higher order scheme on a compact stencil (HOC) of nineteen points. Effectiveness of this method is seen from the fact that it can handle the singularity perturbed problems by employing a flexible discretized grid that can be adapted to the singularity in the domain. Four difficult test cases are chosen to demonstrate the accuracy of the present scheme. Numerical results show that the fourth order accuracy is achieved even though the Reynolds number (Re) is high. In this paper, we extend the work of Kalita et al.  to solve the steady 3D convection-diffusion equation with variable coefficients on non-uniform grid. The approach is based on the use of Taylor series expansion, up to the fourth order terms, to approximate the derivatives appearing in the 3D convection diffusion equation. Then the original convection-diffusion equation is used again to replace the resulting higher order derivative terms. This leads to a higher order scheme on a compact stencil (HOC) of nineteen points. Effectiveness of this method is seen from the fact that it can handle the singularity perturbed problems by employing a flexible discretized grid that can be adapted to the singularity in the domain. Four difficult test cases are chosen to demonstrate the accuracy of the present scheme. Numerical results show that the fourth order accuracy is achieved even though the Reynolds number (Re) is high. Non-uniform HOC Scheme for the 3D Convection–Diffusion Equation doi:10.11648/j.acm.20130203.11 Applied and Computational Mathematics 2014-01-01 © Science Publishing Group Rabab Ahmed Shanab Laila Fouad Seddek Salwa Amin Mohamed Non-uniform HOC Scheme for the 3D Convection–Diffusion Equation 2 3 77 77 2014-01-01 2014-01-01 10.11648/j.acm.20130203.11 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130203.11 © Science Publishing Group Consistency of the Douglas – Rachford Splitting Algorithm for the Sum of Three Nonlinear Operators: Application to the Stefan Problem in Permafrost Soils http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130204.11 Consistency of the Douglas – Rachford dimensional splitting scheme is proved for the sum of three nonlinear operators constituting an evolution equation. It is shown that the operators must be densely defined, maximal monotone and single valued on a real Hilbert space in order to satisfy conditions, under which the splitting algorithm can be applied. Numerical experiment conducted for a three-dimensional Stefan problem in permafrost soils suggests that the Douglas – Rachford scheme produces reasonable results, although the convergence rate remains unestablished. Consistency of the Douglas – Rachford dimensional splitting scheme is proved for the sum of three nonlinear operators constituting an evolution equation. It is shown that the operators must be densely defined, maximal monotone and single valued on a real Hilbert space in order to satisfy conditions, under which the splitting algorithm can be applied. Numerical experiment conducted for a three-dimensional Stefan problem in permafrost soils suggests that the Douglas – Rachford scheme produces reasonable results, although the convergence rate remains unestablished. Consistency of the Douglas – Rachford Splitting Algorithm for the Sum of Three Nonlinear Operators: Application to the Stefan Problem in Permafrost Soils doi:10.11648/j.acm.20130204.11 Applied and Computational Mathematics 2014-01-01 © Science Publishing Group Taras A. Dauzhenka Igor A. Gishkeluk Consistency of the Douglas – Rachford Splitting Algorithm for the Sum of Three Nonlinear Operators: Application to the Stefan Problem in Permafrost Soils 2 4 108 108 2014-01-01 2014-01-01 10.11648/j.acm.20130204.11 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130204.11 © Science Publishing Group Analysis of Cracked Plates Using Localized Multi-Domain Differential Quadrature Method http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130204.12 In this paper, A multi-domain differential quadrature method is employed to solve a mode III crack problem. The domain of the problem is assumed to be irregular rather than it possesses discontinuities, (cracks). The entire domain is divided into several subdomains, according to the crack locations. A conformal mapping is applied to transform the irregular subdomains to regular ones. Then the differential quadrature method is employed to solve the problem over the transformed domains. Further, it’s focused on the crack regions by applying the localized version of differential quadrature method. The out of plane deflection is obtained at the immediate vicinity of the crack tips, such that the stress intensity factor can be calculated. The obtained results are compared with the previous analytical ones. Furthermore a parametric study is introduced to investigate the effects of elastic and geometric characteristics on the values of stress intensity factor. In this paper, A multi-domain differential quadrature method is employed to solve a mode III crack problem. The domain of the problem is assumed to be irregular rather than it possesses discontinuities, (cracks). The entire domain is divided into several subdomains, according to the crack locations. A conformal mapping is applied to transform the irregular subdomains to regular ones. Then the differential quadrature method is employed to solve the problem over the transformed domains. Further, it’s focused on the crack regions by applying the localized version of differential quadrature method. The out of plane deflection is obtained at the immediate vicinity of the crack tips, such that the stress intensity factor can be calculated. The obtained results are compared with the previous analytical ones. Furthermore a parametric study is introduced to investigate the effects of elastic and geometric characteristics on the values of stress intensity factor. Analysis of Cracked Plates Using Localized Multi-Domain Differential Quadrature Method doi:10.11648/j.acm.20130204.12 Applied and Computational Mathematics 2014-01-01 © Science Publishing Group Tharwat Osman Mohamed. S. Matbuly Salwa. A. Mohamed Mohamed Nassar Analysis of Cracked Plates Using Localized Multi-Domain Differential Quadrature Method 2 4 114 114 2014-01-01 2014-01-01 10.11648/j.acm.20130204.12 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130204.12 © Science Publishing Group Occurrence of Galilean Geometry http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130205.11 The main difference of Galilean geometry is its relative simplicity, for it enables the student to study it in relative detail without losing a great deal of time and intellectual energy. In this paper, we introduce you with new geometric(non-Euclidean) ideas which exist in affine plane and more simple than Euclidean plane. The main difference of Galilean geometry is its relative simplicity, for it enables the student to study it in relative detail without losing a great deal of time and intellectual energy. In this paper, we introduce you with new geometric(non-Euclidean) ideas which exist in affine plane and more simple than Euclidean plane. Occurrence of Galilean Geometry doi:10.11648/j.acm.20130205.11 Applied and Computational Mathematics 2014-01-01 © Science Publishing Group Abdullaaziz Artıkbayev Abdullah Kurudirek Hüseyin Akça Occurrence of Galilean Geometry 2 5 117 117 2014-01-01 2014-01-01 10.11648/j.acm.20130205.11 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130205.11 © Science Publishing Group An Effective Scheme for Estimating a Smoother Parameter in the Method of Regularization http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130206.11 We had proposed a scheme for the surface approximation which consists of the estimation by the regularization method and the evaluation by generalized CV with an influence function . We have to decide the value of the optimal smoother parameter which can minimize the value of the evaluation function. Among the models which have suitable parameters, we have to choose the best model using information criteria such as CV or generalized CV with an influence function (GCVIF). However, the method of GCVIF is not practical, because it requires the calculation of the inverse matrix of the hat matrix and the influence function . Those calculations take a large amount of time when n increases. An efficient scheme which will take a small amount of time is required. On the other hand, there are many parameters which we have to decide.Those are the coefficients of the spline functions and the total number of knots, and positions of the parameters and a smoother parameter of the penalized term. The range of the total number of knots is decided by the total number of sample points. The range of the positions of the knots is decided by the area of the surface. However, it is difficult to estimate the range of the value of the smoother parameter. Therefore, we have to estimate it quite roughly. In this paper, we propose an effective method to estimate the range of the smoother parameter and consequently obtain the parameter precisely. We can reduce the calculation time which does not contribute to the selection of the optimal model and we can determine a more accurate and smoother parameter in a small amount of time. We had proposed a scheme for the surface approximation which consists of the estimation by the regularization method and the evaluation by generalized CV with an influence function . We have to decide the value of the optimal smoother parameter which can minimize the value of the evaluation function. Among the models which have suitable parameters, we have to choose the best model using information criteria such as CV or generalized CV with an influence function (GCVIF). However, the method of GCVIF is not practical, because it requires the calculation of the inverse matrix of the hat matrix and the influence function . Those calculations take a large amount of time when n increases. An efficient scheme which will take a small amount of time is required. On the other hand, there are many parameters which we have to decide.Those are the coefficients of the spline functions and the total number of knots, and positions of the parameters and a smoother parameter of the penalized term. The range of the total number of knots is decided by the total number of sample points. The range of the positions of the knots is decided by the area of the surface. However, it is difficult to estimate the range of the value of the smoother parameter. Therefore, we have to estimate it quite roughly. In this paper, we propose an effective method to estimate the range of the smoother parameter and consequently obtain the parameter precisely. We can reduce the calculation time which does not contribute to the selection of the optimal model and we can determine a more accurate and smoother parameter in a small amount of time. An Effective Scheme for Estimating a Smoother Parameter in the Method of Regularization doi:10.11648/j.acm.20130206.11 Applied and Computational Mathematics 2014-01-01 © Science Publishing Group Hongmei Bao Kaoru Fueda An Effective Scheme for Estimating a Smoother Parameter in the Method of Regularization 2 6 123 123 2014-01-01 2014-01-01 10.11648/j.acm.20130206.11 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130206.11 © Science Publishing Group Multi Item Inventory Model With Demand Dependent On Unit Cost And Varying Lead Time Under Fuzzy Unit Production Cost; A Karush Kuhn Tucker Conditions Approach http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130206.12 A multi item inventory model with demand dependent on unit price and leading time with limited storage space and set up cost is considered in this paper. The varying production and leading time crashing costs are considered to be continuous functions of unit price and leading time respectively. The model is solved using Karush Kuhn Tucker conditions approach with optimal order quantity, unit price and leading time as decision variables. In most of the real world situations, the cost parameters, the objective functions and constraints of the decision makers are imprecise in nature. In this paper the unit cost has been imposed in fuzzy environment. An optimal total cost is obtained which is illustrated with numerical example for a single item. A multi item inventory model with demand dependent on unit price and leading time with limited storage space and set up cost is considered in this paper. The varying production and leading time crashing costs are considered to be continuous functions of unit price and leading time respectively. The model is solved using Karush Kuhn Tucker conditions approach with optimal order quantity, unit price and leading time as decision variables. In most of the real world situations, the cost parameters, the objective functions and constraints of the decision makers are imprecise in nature. In this paper the unit cost has been imposed in fuzzy environment. An optimal total cost is obtained which is illustrated with numerical example for a single item. Multi Item Inventory Model With Demand Dependent On Unit Cost And Varying Lead Time Under Fuzzy Unit Production Cost; A Karush Kuhn Tucker Conditions Approach doi:10.11648/j.acm.20130206.12 Applied and Computational Mathematics 2014-01-01 © Science Publishing Group P. Vasanthi C. V. Seshaiah Multi Item Inventory Model With Demand Dependent On Unit Cost And Varying Lead Time Under Fuzzy Unit Production Cost; A Karush Kuhn Tucker Conditions Approach 2 6 126 126 2014-01-01 2014-01-01 10.11648/j.acm.20130206.12 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130206.12 © Science Publishing Group On Geometries in Affine Plane http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130206.13 So far, in different articles and books the concepts of modern definition of geometry and Minkowskian, Galilean planes and spaces have been introduced. In this paper, we are going to describe geometry that is improved by W. Thurston and then we are going to introduce you to geometries that are suitable to this description in 2 dimensional planes. So far, in different articles and books the concepts of modern definition of geometry and Minkowskian, Galilean planes and spaces have been introduced. In this paper, we are going to describe geometry that is improved by W. Thurston and then we are going to introduce you to geometries that are suitable to this description in 2 dimensional planes. On Geometries in Affine Plane doi:10.11648/j.acm.20130206.13 Applied and Computational Mathematics 2014-01-01 © Science Publishing Group Abdullah Kurudirek Hüseyin Akça Mehmet Erdoğan On Geometries in Affine Plane 2 6 129 129 2014-01-01 2014-01-01 10.11648/j.acm.20130206.13 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130206.13 © Science Publishing Group Comments on the Adomian Decomposition Methods Applied to the KdV Equation http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130206.15 Based on previous works, especially  and , we try in the present contribution to study some new aspects of the numerical solution of the KdV equation through the standard Adomian Decomposition Method. The use of the multistage Adomian Decomposition Method, applied to this equation, will be presented and discussed. Based on previous works, especially  and , we try in the present contribution to study some new aspects of the numerical solution of the KdV equation through the standard Adomian Decomposition Method. The use of the multistage Adomian Decomposition Method, applied to this equation, will be presented and discussed. Comments on the Adomian Decomposition Methods Applied to the KdV Equation doi:10.11648/j.acm.20130206.15 Applied and Computational Mathematics 2014-01-01 © Science Publishing Group Mahmoud AKDI Moulay Brahim SEDRA Comments on the Adomian Decomposition Methods Applied to the KdV Equation 2 6 142 142 2014-01-01 2014-01-01 10.11648/j.acm.20130206.15 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130206.15 © Science Publishing Group The Synchronization of Identical Memristors Systems Via Lyapunov Direct Method http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130206.14 In this paper, we use Lyapunov direct method to analyze two identical Memristors systems and synchronization phenomena were discussed. The designed controllers were capable of making the time derivative of the Lyapunov’s negative definite functions where these results give guarantees of stability of the error dynamics at the origin and proved the results in form of theoretical and numerical ways. As the result, in both cases, one can see the synchronization phenomena. In this paper, we use Lyapunov direct method to analyze two identical Memristors systems and synchronization phenomena were discussed. The designed controllers were capable of making the time derivative of the Lyapunov’s negative definite functions where these results give guarantees of stability of the error dynamics at the origin and proved the results in form of theoretical and numerical ways. As the result, in both cases, one can see the synchronization phenomena. The Synchronization of Identical Memristors Systems Via Lyapunov Direct Method doi:10.11648/j.acm.20130206.14 Applied and Computational Mathematics 2014-01-01 © Science Publishing Group Shko A. TAHIR The Synchronization of Identical Memristors Systems Via Lyapunov Direct Method 2 6 136 136 2014-01-01 2014-01-01 10.11648/j.acm.20130206.14 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130206.14 © Science Publishing Group The Study of Heat Transfer Phenomena Using PM for Approximate Solution with Dirichlet and Mixed Boundary Conditions http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130206.16 In this paper, we present Perturbation Method (PM) to solve nonlinear problems. As case study PM is employed to obtain approximate solutions for differential equations related with heat transfer phenomena. Comparing figures between approximate and exact solutions, show the effectiveness of the method. In this paper, we present Perturbation Method (PM) to solve nonlinear problems. As case study PM is employed to obtain approximate solutions for differential equations related with heat transfer phenomena. Comparing figures between approximate and exact solutions, show the effectiveness of the method. The Study of Heat Transfer Phenomena Using PM for Approximate Solution with Dirichlet and Mixed Boundary Conditions doi:10.11648/j.acm.20130206.16 Applied and Computational Mathematics 2014-01-01 © Science Publishing Group U. Filobello-Nino H. Vazquez-Leal A. Sarmiento-Reyes A. Perez-Sesma L. Hernandez-Martinez A. Herrera-May V. M. Jimenez-Fernandez A. Marin-Hernandez D. Pereyra-Diaz A. Diaz-Sanchez The Study of Heat Transfer Phenomena Using PM for Approximate Solution with Dirichlet and Mixed Boundary Conditions 2 6 148 148 2014-01-01 2014-01-01 10.11648/j.acm.20130206.16 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130206.16 © Science Publishing Group Multi-Item EOQ Model with Demand Dependent on Unit Price http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130206.17 A multi-item inventory model with demand dependent on unit cost without shortages is discussed in this paper. This paper presents a mathematical model of inventory control problem for determining the minimum total cost with limited storage space and investment. Apart from this, the warehouse space in the selling store is considered in volume. The model is solved using Kuhn-Tucker conditions method. The model is illustrated with a numerical example assuming unit price in fuzzy environment. A multi-item inventory model with demand dependent on unit cost without shortages is discussed in this paper. This paper presents a mathematical model of inventory control problem for determining the minimum total cost with limited storage space and investment. Apart from this, the warehouse space in the selling store is considered in volume. The model is solved using Kuhn-Tucker conditions method. The model is illustrated with a numerical example assuming unit price in fuzzy environment. Multi-Item EOQ Model with Demand Dependent on Unit Price doi:10.11648/j.acm.20130206.17 Applied and Computational Mathematics 2014-01-01 © Science Publishing Group R. Kasthuri C. V. Seshaiah Multi-Item EOQ Model with Demand Dependent on Unit Price 2 6 151 151 2014-01-01 2014-01-01 10.11648/j.acm.20130206.17 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130206.17 © Science Publishing Group Exact Solutions of two-Dimensional Nonlinear Schrödinger Equations with External Potentials http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130206.18 In this paper, exact solutions of two-dimensional nonlinear Schrödinger equation with kerr, saturable and quintic type of nonlinearities are studied by means of the Homotopy analysis method (HAM). Linear stability properties of these solutions are investigated by the linearized eigenvalue problem. We also investigate nonlinear stability properties of the exact solutions obtained by HAM by direct simulations. In this paper, exact solutions of two-dimensional nonlinear Schrödinger equation with kerr, saturable and quintic type of nonlinearities are studied by means of the Homotopy analysis method (HAM). Linear stability properties of these solutions are investigated by the linearized eigenvalue problem. We also investigate nonlinear stability properties of the exact solutions obtained by HAM by direct simulations. Exact Solutions of two-Dimensional Nonlinear Schrödinger Equations with External Potentials doi:10.11648/j.acm.20130206.18 Applied and Computational Mathematics 2014-01-01 © Science Publishing Group Nalan Antar Nevin Pamuk Exact Solutions of two-Dimensional Nonlinear Schrödinger Equations with External Potentials 2 6 158 158 2014-01-01 2014-01-01 10.11648/j.acm.20130206.18 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130206.18 © Science Publishing Group Neural Network Method for Numerical Solution of Initial Value Problems of Fractional Differential Equations http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130206.19 In this paper, the cosine basis neural network algorithm is introduced for the initial value problem of fractional differential equations. By training the neural network algorithm, we get the numerical solution of the initial value problem of fractional differential equations successfully. In this paper, the cosine basis neural network algorithm is introduced for the initial value problem of fractional differential equations. By training the neural network algorithm, we get the numerical solution of the initial value problem of fractional differential equations successfully. Neural Network Method for Numerical Solution of Initial Value Problems of Fractional Differential Equations doi:10.11648/j.acm.20130206.19 Applied and Computational Mathematics 2014-01-01 © Science Publishing Group Luo Xiaodan Junmin Zhang Neural Network Method for Numerical Solution of Initial Value Problems of Fractional Differential Equations 2 6 162 162 2014-01-01 2014-01-01 10.11648/j.acm.20130206.19 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20130206.19 © Science Publishing Group Solution of a Diffusion Problem in a Non-Homogeneous Flow and Diffusion Field by the Integral Representation Method (IRM) http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140301.13 Integral representations are derived from a differential-type boundary value problem using a fundamental solution. A set of integral representations is equivalent to a set of differential equations. If the boundary conditions are substituted into the integral representations, the integral equations are obtained, and the unknown variables are determined by solving the integral equations. In other words, an integral-type boundary value problem is derived from the integral representations. An effective and flexible finite element algorithm is easily obtained from the integral-type boundary value problem. In the present paper, integral representations are obtained for the diffusion of a material or heat in the sea, where the convective velocity and diffusion constant change in space and time. A new numerical solution of an advection-diffusion equation is proposed based integral representations using the fundamental solution of the primary space-differential operator, and the numerical results are shown. An innovative generalization of the integral representation method: generalized integral representation method is also proposed. The numerical examples are given to verify the theory. Integral representations are derived from a differential-type boundary value problem using a fundamental solution. A set of integral representations is equivalent to a set of differential equations. If the boundary conditions are substituted into the integral representations, the integral equations are obtained, and the unknown variables are determined by solving the integral equations. In other words, an integral-type boundary value problem is derived from the integral representations. An effective and flexible finite element algorithm is easily obtained from the integral-type boundary value problem. In the present paper, integral representations are obtained for the diffusion of a material or heat in the sea, where the convective velocity and diffusion constant change in space and time. A new numerical solution of an advection-diffusion equation is proposed based integral representations using the fundamental solution of the primary space-differential operator, and the numerical results are shown. An innovative generalization of the integral representation method: generalized integral representation method is also proposed. The numerical examples are given to verify the theory. Solution of a Diffusion Problem in a Non-Homogeneous Flow and Diffusion Field by the Integral Representation Method (IRM) doi:10.11648/j.acm.20140301.13 Applied and Computational Mathematics 2014-01-01 © Science Publishing Group Hiroshi Isshiki Shuichi Nagata Yasutaka Imai Solution of a Diffusion Problem in a Non-Homogeneous Flow and Diffusion Field by the Integral Representation Method (IRM) 3 1 26 26 2014-01-01 2014-01-01 10.11648/j.acm.20140301.13 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140301.13 © Science Publishing Group Existence and Uniqueness of Mild Solutions for Fractional Integrodifferential Equations http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140301.15 The aim of this paper is to prove the existence and uniqueness of mild solution of a class of l nonlinear fractional integrodifferential equations {█((d^q u(t))/(dt^q )+Au(t)=∫_0^t▒f(t,s,x(s) )ds+∫_0^t▒〖a(t-s)g(s,y(s) )ds, t∈[0,T],〗@u(0)=u_(o.) )┤ in a Banach space X, where 0&lt;q&lt;1. Results are obtained by fixed point theorem. The results are established by using Krasnoselskii’s fixed point theorem and the contraction mapping principle. The aim of this paper is to prove the existence and uniqueness of mild solution of a class of l nonlinear fractional integrodifferential equations {█((d^q u(t))/(dt^q )+Au(t)=∫_0^t▒f(t,s,x(s) )ds+∫_0^t▒〖a(t-s)g(s,y(s) )ds, t∈[0,T],〗@u(0)=u_(o.) )┤ in a Banach space X, where 0&lt;q&lt;1. Results are obtained by fixed point theorem. The results are established by using Krasnoselskii’s fixed point theorem and the contraction mapping principle. Existence and Uniqueness of Mild Solutions for Fractional Integrodifferential Equations doi:10.11648/j.acm.20140301.15 Applied and Computational Mathematics 2014-01-01 © Science Publishing Group V. Dhanapalan M. Thamilselvan M. Chandrasekaran Existence and Uniqueness of Mild Solutions for Fractional Integrodifferential Equations 3 1 37 37 2014-01-01 2014-01-01 10.11648/j.acm.20140301.15 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140301.15 © Science Publishing Group Application of Optimal HAM for Solving the Fractional Order Logistic Equation http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140301.14 In this paper, we use the optimal homotopy analysis method (OHAM) for approximate solutions of the fractional order Logistic equation. The numerical results obtained are compared with the results obtained by using variational iteration method (VIM) and Adomian decomposition method (ADM). The fractional derivatives are described by Caputo&apos;s sense. Exact and/or approximate analytical solutions of these equations are obtained. The results reveal that this method is very effective and powerful to obtain the approximate solutions. In this paper, we use the optimal homotopy analysis method (OHAM) for approximate solutions of the fractional order Logistic equation. The numerical results obtained are compared with the results obtained by using variational iteration method (VIM) and Adomian decomposition method (ADM). The fractional derivatives are described by Caputo&apos;s sense. Exact and/or approximate analytical solutions of these equations are obtained. The results reveal that this method is very effective and powerful to obtain the approximate solutions. Application of Optimal HAM for Solving the Fractional Order Logistic Equation doi:10.11648/j.acm.20140301.14 Applied and Computational Mathematics 2014-01-01 © Science Publishing Group Mohamed S. Mohamed Application of Optimal HAM for Solving the Fractional Order Logistic Equation 3 1 31 31 2014-01-01 2014-01-01 10.11648/j.acm.20140301.14 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140301.14 © Science Publishing Group Thermodynamic Analysis of Variable Viscosity MHD Unsteady Generalized Couette Flow with Permeable Walls http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140301.11 The thermodynamic first and second law analyses of a temperature dependent viscosity hydromagnetic generalized unsteady Couette flow with permeable walls is investigated. The transient model problem for momentum and energy balance is tackled numerically using a semi-discretization method while the steady state boundary value problem is solved by shooting method together with Runge-Kutta-Fehlberg integration scheme. The velocity and the temperature profiles are obtained and are utilized to compute the skin friction coefficient, Nusselt number, entropy generation rate and the Bejan number. Pertinent results are presented graphically and discussed quantitatively. The thermodynamic first and second law analyses of a temperature dependent viscosity hydromagnetic generalized unsteady Couette flow with permeable walls is investigated. The transient model problem for momentum and energy balance is tackled numerically using a semi-discretization method while the steady state boundary value problem is solved by shooting method together with Runge-Kutta-Fehlberg integration scheme. The velocity and the temperature profiles are obtained and are utilized to compute the skin friction coefficient, Nusselt number, entropy generation rate and the Bejan number. Pertinent results are presented graphically and discussed quantitatively. Thermodynamic Analysis of Variable Viscosity MHD Unsteady Generalized Couette Flow with Permeable Walls doi:10.11648/j.acm.20140301.11 Applied and Computational Mathematics 2014-01-01 © Science Publishing Group David Theuri Oluwole Daniel Makinde Thermodynamic Analysis of Variable Viscosity MHD Unsteady Generalized Couette Flow with Permeable Walls 3 1 8 8 2014-01-01 2014-01-01 10.11648/j.acm.20140301.11 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140301.11 © Science Publishing Group An Easy Computable Approximate Solution for a Squeezing Flow between Two Infinite Plates by using of Perturbation Method http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140301.16 This article proposes Perturbation Method (PM) to find an approximate solution for the problem of an axis symmetric Newtonian fluid squeezed between two large parallel plates. After comparing figures between approximate and exact solutions, we will see that the proposed solutions besides of handy, are highly accurate and therefore that PM is efficient. This article proposes Perturbation Method (PM) to find an approximate solution for the problem of an axis symmetric Newtonian fluid squeezed between two large parallel plates. After comparing figures between approximate and exact solutions, we will see that the proposed solutions besides of handy, are highly accurate and therefore that PM is efficient. An Easy Computable Approximate Solution for a Squeezing Flow between Two Infinite Plates by using of Perturbation Method doi:10.11648/j.acm.20140301.16 Applied and Computational Mathematics 2014-01-01 © Science Publishing Group U. Filobello-Nino H. Vazquez-Leal A. Perez-Sesma J. Cervantes-Perez V. M. Jimenez-Fernandez L. Hernandez-Martinez D. Pereyra-Diaz R. Castaneda-Sheissa J. Sanchez-Orea C. Hoyos-Reyes S. F. Hernandez-Machuca J. Huerta-Chua J. L. Rocha-Fernandez A. D. Contreras-Hernandez J. M. Mendez-Perez An Easy Computable Approximate Solution for a Squeezing Flow between Two Infinite Plates by using of Perturbation Method 3 1 42 42 2014-01-01 2014-01-01 10.11648/j.acm.20140301.16 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140301.16 © Science Publishing Group Numerical Solution of Linear Volterra Integro-Differential Equation using Runge-Kutta-Fehlberg Method http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140301.12 In this paper a new fourth and fifth-order numerical solution of linear Volterra integro-differential equation is discussed. One popular technique that uses here for error control is called the Runge-Kutta-Fehlberg method for Ordinary Differential Equation (ODE) part and Newton-Cotes formulae for integral parts. In this paper a new fourth and fifth-order numerical solution of linear Volterra integro-differential equation is discussed. One popular technique that uses here for error control is called the Runge-Kutta-Fehlberg method for Ordinary Differential Equation (ODE) part and Newton-Cotes formulae for integral parts. Numerical Solution of Linear Volterra Integro-Differential Equation using Runge-Kutta-Fehlberg Method doi:10.11648/j.acm.20140301.12 Applied and Computational Mathematics 2014-01-01 © Science Publishing Group Ali Filiz Numerical Solution of Linear Volterra Integro-Differential Equation using Runge-Kutta-Fehlberg Method 3 1 14 14 2014-01-01 2014-01-01 10.11648/j.acm.20140301.12 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140301.12 © Science Publishing Group On Optimization of a Coxian Queueing Model with Two Phases http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140302.11 In this study we have obtained stochastic equation systems of a Coxian queueing model with two phases where arrival stream of this model is according to the exponential distribution with λ parameter. The service time of any customer at server i (i=1,2) is exponential with parameter μ_i. In addition we have obtained state probabilities of this queueing model at any given t moment.Furthermore performance measures of this queueing system are calculated. Various queueing systems are found for some values of α probability and service parameters: if α=1and µ_1=µ_2taken then M/E_2/1/ 0 queueing model is obtained, for α=1it is shown that service time of a customer is according to hypoexponential, if α=0 is taken we have M/ M/1/ 0 queueing system. Lately,an application of this queueing model is done. The optimal value of the mean customer number in the system is found. Finally, optimal ordering according to the loss probability is obtained by changing the service parameters .A numerical example is given on the subject In this study we have obtained stochastic equation systems of a Coxian queueing model with two phases where arrival stream of this model is according to the exponential distribution with λ parameter. The service time of any customer at server i (i=1,2) is exponential with parameter μ_i. In addition we have obtained state probabilities of this queueing model at any given t moment.Furthermore performance measures of this queueing system are calculated. Various queueing systems are found for some values of α probability and service parameters: if α=1and µ_1=µ_2taken then M/E_2/1/ 0 queueing model is obtained, for α=1it is shown that service time of a customer is according to hypoexponential, if α=0 is taken we have M/ M/1/ 0 queueing system. Lately,an application of this queueing model is done. The optimal value of the mean customer number in the system is found. Finally, optimal ordering according to the loss probability is obtained by changing the service parameters .A numerical example is given on the subject On Optimization of a Coxian Queueing Model with Two Phases doi:10.11648/j.acm.20140302.11 Applied and Computational Mathematics 2014-01-01 © Science Publishing Group Vedat Sağlam Merve Uğurlu Erdinç Yücesoy Müjgan Zobu Murat Sağır On Optimization of a Coxian Queueing Model with Two Phases 3 2 47 47 2014-01-01 2014-01-01 10.11648/j.acm.20140302.11 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140302.11 © Science Publishing Group Effect of Variable Thermal Conductivity on Heat and Mass Transfer Flow over a Vertical Channel with Magnetic Field Intensity http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140302.12 The objective of this paper is to study thermal conductivity and magnetic field intensity effects on heat and mass transfer flow over a vertical channel both numerically and analytically. The non-linear partial differential equations governing the flow are non-dimensionalised, simplified and solved using Crank Nicolson type of implicit finite difference method. To check the accuracy of the numerical solution, steady state solutions for velocity, temperature and concentration fields are obtained by using perturbation method. Graphical results for velocity, temperature, concentration, skin friction, Nusselt number and Sherwood number have been obtained, to show the effects of different parameters entering in the problem. Results from these study shows that velocity, temperature and concentration increases with the increase in the dimensionless time until they reach steady state value. Also, it was observed that the analytical and numerical solutions agree very well at large values of time. The objective of this paper is to study thermal conductivity and magnetic field intensity effects on heat and mass transfer flow over a vertical channel both numerically and analytically. The non-linear partial differential equations governing the flow are non-dimensionalised, simplified and solved using Crank Nicolson type of implicit finite difference method. To check the accuracy of the numerical solution, steady state solutions for velocity, temperature and concentration fields are obtained by using perturbation method. Graphical results for velocity, temperature, concentration, skin friction, Nusselt number and Sherwood number have been obtained, to show the effects of different parameters entering in the problem. Results from these study shows that velocity, temperature and concentration increases with the increase in the dimensionless time until they reach steady state value. Also, it was observed that the analytical and numerical solutions agree very well at large values of time. Effect of Variable Thermal Conductivity on Heat and Mass Transfer Flow over a Vertical Channel with Magnetic Field Intensity doi:10.11648/j.acm.20140302.12 Applied and Computational Mathematics 2014-04-29 © Science Publishing Group Ime Jimmy Uwanta Halima Usman Effect of Variable Thermal Conductivity on Heat and Mass Transfer Flow over a Vertical Channel with Magnetic Field Intensity 3 2 56 56 2014-04-29 2014-04-29 10.11648/j.acm.20140302.12 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140302.12 © Science Publishing Group Zeros and Asymptotic Limits of Löwdin Orthogonal Polynomials with a Unified View http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140302.13 The zeros and asymptotic limits of two new classes of orthogonal polynomials, which are derived by applying two orthogonalization procedures due to Löwdin to a set of monomials, are calculated. It is established that they possess all the properties ofthe zeros of a polynomial. Their asymptotic limits are found. A Unified view of all the Löwdin orthogonal polynomials together with the standard classical orthogonal polynomials are presented in a unique graph. The zeros and asymptotic limits of two new classes of orthogonal polynomials, which are derived by applying two orthogonalization procedures due to Löwdin to a set of monomials, are calculated. It is established that they possess all the properties ofthe zeros of a polynomial. Their asymptotic limits are found. A Unified view of all the Löwdin orthogonal polynomials together with the standard classical orthogonal polynomials are presented in a unique graph. Zeros and Asymptotic Limits of Löwdin Orthogonal Polynomials with a Unified View doi:10.11648/j.acm.20140302.13 Applied and Computational Mathematics 2014-05-06 © Science Publishing Group Ramesh Naidu Annavarapu Vipin Srivastava Zeros and Asymptotic Limits of Löwdin Orthogonal Polynomials with a Unified View 3 2 62 62 2014-05-06 2014-05-06 10.11648/j.acm.20140302.13 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140302.13 © Science Publishing Group Method for Integrating Tabular Functions that Considers Errors http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140302.14 If experimental tables are numerically integrated using quadrature formulas, then the measurement errors of the physical instrument is not taken into account. The result of such numerical integration will be inaccurate because of the accumulation of errors due to the summation of random values, and the residual term of the quadrature formula cannot be calculated using solely classical concepts. The traditional approach consists of applying various smoothing algorithms. In this case, methods are used that are unrelated to the problem of integrating itself, which leads to excessive smoothing of the result. The authors propose a method for numerical integration of inaccurate numerical functions that minimizes the residual term of the quadrature formula for the set of unknown values based on the error confidence intervals by using ill-posed problem algorithms. The high level of effectiveness of this new method, for which it is sufficient to know the error level of the signal, is demonstrated through examples. If experimental tables are numerically integrated using quadrature formulas, then the measurement errors of the physical instrument is not taken into account. The result of such numerical integration will be inaccurate because of the accumulation of errors due to the summation of random values, and the residual term of the quadrature formula cannot be calculated using solely classical concepts. The traditional approach consists of applying various smoothing algorithms. In this case, methods are used that are unrelated to the problem of integrating itself, which leads to excessive smoothing of the result. The authors propose a method for numerical integration of inaccurate numerical functions that minimizes the residual term of the quadrature formula for the set of unknown values based on the error confidence intervals by using ill-posed problem algorithms. The high level of effectiveness of this new method, for which it is sufficient to know the error level of the signal, is demonstrated through examples. Method for Integrating Tabular Functions that Considers Errors doi:10.11648/j.acm.20140302.14 Applied and Computational Mathematics 2014-05-19 © Science Publishing Group Vladimir V. Ternovski Mikhail M. Khapaev Method for Integrating Tabular Functions that Considers Errors 3 2 67 67 2014-05-19 2014-05-19 10.11648/j.acm.20140302.14 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140302.14 © Science Publishing Group A Numerical Algorithm for the Resolution of Scalar and Matrix Algebraic Equations Using Runge-Kutta Method http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140303.11 The Runge-Kutta method is an interesting and precise method for the resolution of ordinary differential equations. Fortunately, when supposing the differentiation by any variable that the equation to solve is not variable of, and after iterations, the solution of this equation stretches to the algebraic roots of this equation. This feature of this algorithm, indeed, allows to solve precisely any scalar or matrix equation. The numerical algorithm proposed herein is an iterative procedure of the fourth-order Runge-Kutta method with an adopted precision tolerance of convergence. Also, a method to determine all the roots of the polynomial equations is presented. Some scalar and matrix algebraic equations are resolved using this proposed algorithm, and show how this algorithm featuring with an excellent precision, a good speed and a simplicity for programming to solve equations and deduct the roots. The Runge-Kutta method is an interesting and precise method for the resolution of ordinary differential equations. Fortunately, when supposing the differentiation by any variable that the equation to solve is not variable of, and after iterations, the solution of this equation stretches to the algebraic roots of this equation. This feature of this algorithm, indeed, allows to solve precisely any scalar or matrix equation. The numerical algorithm proposed herein is an iterative procedure of the fourth-order Runge-Kutta method with an adopted precision tolerance of convergence. Also, a method to determine all the roots of the polynomial equations is presented. Some scalar and matrix algebraic equations are resolved using this proposed algorithm, and show how this algorithm featuring with an excellent precision, a good speed and a simplicity for programming to solve equations and deduct the roots. A Numerical Algorithm for the Resolution of Scalar and Matrix Algebraic Equations Using Runge-Kutta Method doi:10.11648/j.acm.20140303.11 Applied and Computational Mathematics 2014-05-27 © Science Publishing Group Tahar Latreche A Numerical Algorithm for the Resolution of Scalar and Matrix Algebraic Equations Using Runge-Kutta Method 3 3 74 74 2014-05-27 2014-05-27 10.11648/j.acm.20140303.11 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140303.11 © Science Publishing Group Modelling the Effects of Variable Viscosity in Unsteady Flow of Nanofluids in a Pipe with Permeable Wall and Convective Cooling http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140303.12 In this paper, the combined effects of variable viscosity, Brownian motion, thermophoresis and convective cooling on unsteady flow of nanofluids in a pipe with permeable wall are investigated. It is assumed that the pipe surface exchange heat with the ambient following the Newton’s law of cooling. Using a semi discretization finite difference method coupled with Runge-Kutta Fehlberg integration scheme, the nonlinear governing equations of momentum and energy balance, and the equation for nanoparticles concentration are tackled numerically. Useful results for the velocity, temperature, nanoparticles concentration profiles, skin friction and Nusselt number are obtained graphically and discussed quantitatively. In this paper, the combined effects of variable viscosity, Brownian motion, thermophoresis and convective cooling on unsteady flow of nanofluids in a pipe with permeable wall are investigated. It is assumed that the pipe surface exchange heat with the ambient following the Newton’s law of cooling. Using a semi discretization finite difference method coupled with Runge-Kutta Fehlberg integration scheme, the nonlinear governing equations of momentum and energy balance, and the equation for nanoparticles concentration are tackled numerically. Useful results for the velocity, temperature, nanoparticles concentration profiles, skin friction and Nusselt number are obtained graphically and discussed quantitatively. Modelling the Effects of Variable Viscosity in Unsteady Flow of Nanofluids in a Pipe with Permeable Wall and Convective Cooling doi:10.11648/j.acm.20140303.12 Applied and Computational Mathematics 2014-05-30 © Science Publishing Group Sara Khamis Oluwole Daniel Makinde Yaw Nkansah-Gyekye Modelling the Effects of Variable Viscosity in Unsteady Flow of Nanofluids in a Pipe with Permeable Wall and Convective Cooling 3 3 84 84 2014-05-30 2014-05-30 10.11648/j.acm.20140303.12 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140303.12 © Science Publishing Group Single Machine Scheduling Problems with Delivery Times under Simple Linear Deterioration http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140303.13 We consider several single machine scheduling problems in which the processing time of a job is a simple linear increasing function of its starting time and each job has a delivery time. The objectives are to minimize the functions about delivery completion times. For the former three problems, we propose polynomial-time algorithms to solve them. For the last problem, we prove that it is NP-hard when all jobs have release dates. We consider several single machine scheduling problems in which the processing time of a job is a simple linear increasing function of its starting time and each job has a delivery time. The objectives are to minimize the functions about delivery completion times. For the former three problems, we propose polynomial-time algorithms to solve them. For the last problem, we prove that it is NP-hard when all jobs have release dates. Single Machine Scheduling Problems with Delivery Times under Simple Linear Deterioration doi:10.11648/j.acm.20140303.13 Applied and Computational Mathematics 2014-06-09 © Science Publishing Group Juan Zou Single Machine Scheduling Problems with Delivery Times under Simple Linear Deterioration 3 3 89 89 2014-06-09 2014-06-09 10.11648/j.acm.20140303.13 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140303.13 © Science Publishing Group Boundary Value Problems on Triangular Domains and MKSOR Methods http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140303.14 The performance of six variants of the successive overrelaxation methods (SOR) are considered for an algebraic system arising from a finite difference treatment of an elliptic equation of Partial Differential Equations (PDEs) on a triangular region. The consistency of the finite difference representation of the system is achieved. In the finite difference method one obtains an algebraic system corresponding to the boundary value problem (BVP). The block structure of the algebraic system corresponding to four different labeling (the natural, the red- black and green (RBG), the electronic and the spiral) of the grid points is considered. Also, algebraic systems obtained from BVP with mixed derivatives are well established. Determination of the optimal relaxation parameters on the bases of the graphical representation of the spectral radius of the iteration matrices for the SOR, the Modified Successive over relaxation (MSOR) and their new variants KSOR, MKSOR, MKSOR1 and MKSOR2 are considered. Application of the treatment to two numerical examples is considered. The performance of six variants of the successive overrelaxation methods (SOR) are considered for an algebraic system arising from a finite difference treatment of an elliptic equation of Partial Differential Equations (PDEs) on a triangular region. The consistency of the finite difference representation of the system is achieved. In the finite difference method one obtains an algebraic system corresponding to the boundary value problem (BVP). The block structure of the algebraic system corresponding to four different labeling (the natural, the red- black and green (RBG), the electronic and the spiral) of the grid points is considered. Also, algebraic systems obtained from BVP with mixed derivatives are well established. Determination of the optimal relaxation parameters on the bases of the graphical representation of the spectral radius of the iteration matrices for the SOR, the Modified Successive over relaxation (MSOR) and their new variants KSOR, MKSOR, MKSOR1 and MKSOR2 are considered. Application of the treatment to two numerical examples is considered. Boundary Value Problems on Triangular Domains and MKSOR Methods doi:10.11648/j.acm.20140303.14 Applied and Computational Mathematics 2014-06-23 © Science Publishing Group I. K. Youssef Sh. A. Meligy Boundary Value Problems on Triangular Domains and MKSOR Methods 3 3 99 99 2014-06-23 2014-06-23 10.11648/j.acm.20140303.14 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140303.14 © Science Publishing Group Analysis of Turbulent Hydromagnetic Flow with Radiative Heat over a Moving Vertical Plate in a Rotating System http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140303.15 In this paper, the combined effects of magnetic fields, buoyancy force, thermal radiation, viscous and Ohmic heating on turbulent hydromagnetic flow of an incompressible electrically conducting fluid over a moving vertical plate in a rotating system is investigated numerically. The governing equations are reduced to non-linear ordinary differential equations using the time-averaged approach known as Reynolds-averaged Navier–Stokes equations (or RANS equations) and tackled by employing an efficient Runge-Kutta Fehlberg integration technique coupled with shooting scheme. Graphical results showing the effects of various thermophysical parameters on the velocity, temperature, local skin friction and local Nusselt number are presented and discussed quantitatively. In this paper, the combined effects of magnetic fields, buoyancy force, thermal radiation, viscous and Ohmic heating on turbulent hydromagnetic flow of an incompressible electrically conducting fluid over a moving vertical plate in a rotating system is investigated numerically. The governing equations are reduced to non-linear ordinary differential equations using the time-averaged approach known as Reynolds-averaged Navier–Stokes equations (or RANS equations) and tackled by employing an efficient Runge-Kutta Fehlberg integration technique coupled with shooting scheme. Graphical results showing the effects of various thermophysical parameters on the velocity, temperature, local skin friction and local Nusselt number are presented and discussed quantitatively. Analysis of Turbulent Hydromagnetic Flow with Radiative Heat over a Moving Vertical Plate in a Rotating System doi:10.11648/j.acm.20140303.15 Applied and Computational Mathematics 2014-07-03 © Science Publishing Group Dawit H. Gebre O. D. Makinde M. Kinyanjui Analysis of Turbulent Hydromagnetic Flow with Radiative Heat over a Moving Vertical Plate in a Rotating System 3 3 109 109 2014-07-03 2014-07-03 10.11648/j.acm.20140303.15 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140303.15 © Science Publishing Group Conversion of Energy Equation for Turbulent Motion and its Applications http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140303.16 Turbulent energy has developed revolutionary technology in the form of a portfolio of devices for the mixing, separation and the homogenization of liquids with liquids, liquids with gasses and gasses with gasses. The mixing technology may be applied to a wide variety including chemicals, pharmaceuticals, cosmetics, foods, agricultural, water treatment with purification and hybrid fuels. The paper reports the transformation of energy equation for turbulent flow in terms of correlation tensors of second order, where the correlation tensors are the functions of space coordinates, distance between two points and time. To reveal the relation of turbulent energy between two points, one point has been taken as the origin of the coordinate system. Correlation between pressure fluctuations and velocity fluctuations at the two points of flow field is applied to the turbulent energy equation. The applications of turbulent energy are discussed for the source of oceanic turbulence by means of Richardson number. A multiplication factor in terms of kinetic energy and potential energy is considered for finding the correlation between the multiplication factor and critical flux Richardson number and to signify the relative efficiency of mixing by Kelvin-Helmholtz billows and the critical flux Richardson number. Turbulent energy has developed revolutionary technology in the form of a portfolio of devices for the mixing, separation and the homogenization of liquids with liquids, liquids with gasses and gasses with gasses. The mixing technology may be applied to a wide variety including chemicals, pharmaceuticals, cosmetics, foods, agricultural, water treatment with purification and hybrid fuels. The paper reports the transformation of energy equation for turbulent flow in terms of correlation tensors of second order, where the correlation tensors are the functions of space coordinates, distance between two points and time. To reveal the relation of turbulent energy between two points, one point has been taken as the origin of the coordinate system. Correlation between pressure fluctuations and velocity fluctuations at the two points of flow field is applied to the turbulent energy equation. The applications of turbulent energy are discussed for the source of oceanic turbulence by means of Richardson number. A multiplication factor in terms of kinetic energy and potential energy is considered for finding the correlation between the multiplication factor and critical flux Richardson number and to signify the relative efficiency of mixing by Kelvin-Helmholtz billows and the critical flux Richardson number. Conversion of Energy Equation for Turbulent Motion and its Applications doi:10.11648/j.acm.20140303.16 Applied and Computational Mathematics 2014-07-14 © Science Publishing Group Shams Forruque Ahmed Conversion of Energy Equation for Turbulent Motion and its Applications 3 3 116 116 2014-07-14 2014-07-14 10.11648/j.acm.20140303.16 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140303.16 © Science Publishing Group A Variational Method in the Sturm-Liouville Problem with the Neumann and Dirichlet Boundary Values http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140304.11 A variational method for calculation of the eigenfunctions and eigenvalues in the Sturm-Liouville problem with the Neumann boundary values is offered. The method is based on a functional, which is introduced in this work. An appropriate numerical algorithm is developed. Calculations for the three potentials are produced: sin((x-π)2/π), cos(4x) and the high not isosceles triangle. The method is applied to the Sturm-Liouville problem with the Dirichlet boundary values. Some suppositions about the inverse Sturm-Liouville problem are made. A variational method for calculation of the eigenfunctions and eigenvalues in the Sturm-Liouville problem with the Neumann boundary values is offered. The method is based on a functional, which is introduced in this work. An appropriate numerical algorithm is developed. Calculations for the three potentials are produced: sin((x-π)2/π), cos(4x) and the high not isosceles triangle. The method is applied to the Sturm-Liouville problem with the Dirichlet boundary values. Some suppositions about the inverse Sturm-Liouville problem are made. A Variational Method in the Sturm-Liouville Problem with the Neumann and Dirichlet Boundary Values doi:10.11648/j.acm.20140304.11 Applied and Computational Mathematics 2014-07-16 © Science Publishing Group Khapaeva Tatiana Mikhailovna A Variational Method in the Sturm-Liouville Problem with the Neumann and Dirichlet Boundary Values 3 4 120 120 2014-07-16 2014-07-16 10.11648/j.acm.20140304.11 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140304.11 © Science Publishing Group The Relationship between the Condition Number, RGA and Interaction in Multivariable Systems http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140304.12 One of the most widely used input and output controllability measure is relative gain array (RGA). RGA measures input-output interaction in multi input multi output (MIMO) systems. The other significant measure in use is the smallest singular value of frequency subordinate. The condition number is defined as the ratio between the largest and smallest singular values of a system. In this paper, the relationship of relative gain array (RGA) with condition number and interaction as well as condition number in relation to interaction will be investigated respectively. The results indicate that the parameters under investigation are not always correlated, that is, the two-way relationship is not established between them all the time. One of the most widely used input and output controllability measure is relative gain array (RGA). RGA measures input-output interaction in multi input multi output (MIMO) systems. The other significant measure in use is the smallest singular value of frequency subordinate. The condition number is defined as the ratio between the largest and smallest singular values of a system. In this paper, the relationship of relative gain array (RGA) with condition number and interaction as well as condition number in relation to interaction will be investigated respectively. The results indicate that the parameters under investigation are not always correlated, that is, the two-way relationship is not established between them all the time. The Relationship between the Condition Number, RGA and Interaction in Multivariable Systems doi:10.11648/j.acm.20140304.12 Applied and Computational Mathematics 2014-07-18 © Science Publishing Group Aref Shahmansoorian Sahar Jamebozorg The Relationship between the Condition Number, RGA and Interaction in Multivariable Systems 3 4 124 124 2014-07-18 2014-07-18 10.11648/j.acm.20140304.12 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140304.12 © Science Publishing Group Modelling the Migratory Population Dynamics of the Serengeti Ecosystem http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140304.13 Many ecological studies have tried to explain the animal migrations, but none has embarked on modeling the Great Migration and its impact on the migratory animals’ population dynamics, in combination with food and the impact of predation. In this paper, we present a mathematical model of the four dynamic Ordinary Differential Equations of Grass, Herbivores, Lions and Crocodiles. Using secondary data covering ten years 1996-2006 we estimated the parameters in the model. The grass forage grew periodically, the herbivores population grew, the predation rate of lions grew and so did its population. But the crocodiles’ population grew less. The study has shown that there was no extinction and migration continued. Herbivores population grew provided that there was enough food. Many ecological studies have tried to explain the animal migrations, but none has embarked on modeling the Great Migration and its impact on the migratory animals’ population dynamics, in combination with food and the impact of predation. In this paper, we present a mathematical model of the four dynamic Ordinary Differential Equations of Grass, Herbivores, Lions and Crocodiles. Using secondary data covering ten years 1996-2006 we estimated the parameters in the model. The grass forage grew periodically, the herbivores population grew, the predation rate of lions grew and so did its population. But the crocodiles’ population grew less. The study has shown that there was no extinction and migration continued. Herbivores population grew provided that there was enough food. Modelling the Migratory Population Dynamics of the Serengeti Ecosystem doi:10.11648/j.acm.20140304.13 Applied and Computational Mathematics 2014-07-22 © Science Publishing Group Janeth James Ngana Livingstone Serwadda Luboobi Dmitry Kuznetsov Modelling the Migratory Population Dynamics of the Serengeti Ecosystem 3 4 129 129 2014-07-22 2014-07-22 10.11648/j.acm.20140304.13 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140304.13 © Science Publishing Group Generalized Difference Formula for a Nonlinear Equation http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140304.14 In this paper, a new iteration scheme is proposed to solve the roots of a nonlinear equation. It is the purpose of this paper to show that, although the new iteration method seems to be of high convergence, the results are promising in that it requires more computation work and even be divergent. In here, we use iteration method that applied derivatives of the first order and the second order; we substitute difference formulas in iteration formulas. This method cause that our iteration method have not any derivative formulas. In this paper, a new iteration scheme is proposed to solve the roots of a nonlinear equation. It is the purpose of this paper to show that, although the new iteration method seems to be of high convergence, the results are promising in that it requires more computation work and even be divergent. In here, we use iteration method that applied derivatives of the first order and the second order; we substitute difference formulas in iteration formulas. This method cause that our iteration method have not any derivative formulas. Generalized Difference Formula for a Nonlinear Equation doi:10.11648/j.acm.20140304.14 Applied and Computational Mathematics 2014-07-26 © Science Publishing Group Hamideh Eskandari Generalized Difference Formula for a Nonlinear Equation 3 4 136 136 2014-07-26 2014-07-26 10.11648/j.acm.20140304.14 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140304.14 © Science Publishing Group Theory and Application of the Generalized Integral Representation Method (GIRM) in Advection Diffusion Problem http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140304.15 The integral representation is developed for linear initial and boundary value problems. The fundamental solution is defined by the linear differential equation with constant coefficients and plays a key role in obtaining the integral representation. This becomes a very strong constraint in developing the theory to nonlinear problems. In the present paper, an innovative generalization of the integral representation or generalized integral representation is proposed. The numerical examples are given to verify the theory. The integral representation is developed for linear initial and boundary value problems. The fundamental solution is defined by the linear differential equation with constant coefficients and plays a key role in obtaining the integral representation. This becomes a very strong constraint in developing the theory to nonlinear problems. In the present paper, an innovative generalization of the integral representation or generalized integral representation is proposed. The numerical examples are given to verify the theory. Theory and Application of the Generalized Integral Representation Method (GIRM) in Advection Diffusion Problem doi:10.11648/j.acm.20140304.15 Applied and Computational Mathematics 2014-08-05 © Science Publishing Group H. Isshiki Theory and Application of the Generalized Integral Representation Method (GIRM) in Advection Diffusion Problem 3 4 149 149 2014-08-05 2014-08-05 10.11648/j.acm.20140304.15 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140304.15 © Science Publishing Group Modeling and Stability Analysis for a Varicella Zoster Virus Model with Vaccination http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140304.16 In this paper, a deterministic mathematical model for transmission dynamics of Varicella Zoster Virus (VZV) with vaccination is formulated. The effective reproduction number is computed in order to measure the relative impact for individual or combined intervention for effective disease control. The effective reproductive number, R_e is defined as the number of secondary cases that one infected individual will cause through the duration of the infectious period. The disease-free equilibrium is computed and proved to be locally asymptotically stable when R_e&lt;1 and unstable when R_e&gt;1 .It is proved that there exists at least one endemic equilibrium point for all R_e&gt;1. In the absence of disease-induced death, it is proved that the transcritical bifurcation at R_0=1 is supercritical (forward). Sensitivity analysis is performed on the basic reproduction number and it is noted that the most sensitive parameters are the probability of transmission of the disease from an infectious individual to a susceptible individual per contact, β, per capita contact rate ,c, per capita birth rate, π and the progression rate from latent to infectious stage, δ. Numerical simulations of the model show that, the combination of vaccination and treatment is the most effective way to combat the epidemiology of VZV in the community. In this paper, a deterministic mathematical model for transmission dynamics of Varicella Zoster Virus (VZV) with vaccination is formulated. The effective reproduction number is computed in order to measure the relative impact for individual or combined intervention for effective disease control. The effective reproductive number, R_e is defined as the number of secondary cases that one infected individual will cause through the duration of the infectious period. The disease-free equilibrium is computed and proved to be locally asymptotically stable when R_e&lt;1 and unstable when R_e&gt;1 .It is proved that there exists at least one endemic equilibrium point for all R_e&gt;1. In the absence of disease-induced death, it is proved that the transcritical bifurcation at R_0=1 is supercritical (forward). Sensitivity analysis is performed on the basic reproduction number and it is noted that the most sensitive parameters are the probability of transmission of the disease from an infectious individual to a susceptible individual per contact, β, per capita contact rate ,c, per capita birth rate, π and the progression rate from latent to infectious stage, δ. Numerical simulations of the model show that, the combination of vaccination and treatment is the most effective way to combat the epidemiology of VZV in the community. Modeling and Stability Analysis for a Varicella Zoster Virus Model with Vaccination doi:10.11648/j.acm.20140304.16 Applied and Computational Mathematics 2014-08-13 © Science Publishing Group Stephen Edward Dmitry Kuznetsov Silas Mirau Modeling and Stability Analysis for a Varicella Zoster Virus Model with Vaccination 3 4 162 162 2014-08-13 2014-08-13 10.11648/j.acm.20140304.16 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140304.16 © Science Publishing Group Regularized Minimum Length Method in Scattered Data Interpolation http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140304.17 In an attempt of accumulating more experiences of interpolating scattered data using the minimum length method, this study chooses new kernel functions from the machine learning technique to implementing this minimum length method. But, consulting with the regularization theory, a regularized minimum length method is created by solving coefficient of it in a penalized least squares approximation problem. The purpose of creating this regularized minimum length method is responding to a pilot observation finding the instability of original minimum length method under dense interpolation points. Testing the regularized minimum length method finds that applying it is time-saving but its performance is comparable to the radial point interpolation with polynomial reproduction. Inverse multiquadric and rational quadric kernel functions are two preferred kernel function to perform the regularized minimum length method. In conclusion, the proposed regularized minimum length method can be a useful scattered data interpolation method. In an attempt of accumulating more experiences of interpolating scattered data using the minimum length method, this study chooses new kernel functions from the machine learning technique to implementing this minimum length method. But, consulting with the regularization theory, a regularized minimum length method is created by solving coefficient of it in a penalized least squares approximation problem. The purpose of creating this regularized minimum length method is responding to a pilot observation finding the instability of original minimum length method under dense interpolation points. Testing the regularized minimum length method finds that applying it is time-saving but its performance is comparable to the radial point interpolation with polynomial reproduction. Inverse multiquadric and rational quadric kernel functions are two preferred kernel function to perform the regularized minimum length method. In conclusion, the proposed regularized minimum length method can be a useful scattered data interpolation method. Regularized Minimum Length Method in Scattered Data Interpolation doi:10.11648/j.acm.20140304.17 Applied and Computational Mathematics 2014-08-19 © Science Publishing Group Guang Y. Sheu Regularized Minimum Length Method in Scattered Data Interpolation 3 4 170 170 2014-08-19 2014-08-19 10.11648/j.acm.20140304.17 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140304.17 © Science Publishing Group Analysis of the Irrigation Water Price in Rice Production Tanzania http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140304.19 Over the past 50 years, cross-sectoral water utilization in Tanzania has grown considerably due to the increase of human populations which increasing food demands and growing of economic activities that require water in production. The agriculture sector is one of the major users of water resource for irrigation activities. The purpose of this paper was to analyse the irrigation water price in rice production in Tanzania. The secondary data were collected from the Ministry of Agriculture, Food Security and Cooperatives in Statistics Unit and zonal irrigation units. Elasticities were estimated using ordinary least squares technique with the help of STATA 11. Factor analysis technique was also applied. The estimated water price coefficient was found to be -0.03 and the average water price was estimated to be 5.50 Tshs/m3. However the water productivity was 0.3kg/m3, whereas the production was estimated to be 2.5ton/ha. Over the past 50 years, cross-sectoral water utilization in Tanzania has grown considerably due to the increase of human populations which increasing food demands and growing of economic activities that require water in production. The agriculture sector is one of the major users of water resource for irrigation activities. The purpose of this paper was to analyse the irrigation water price in rice production in Tanzania. The secondary data were collected from the Ministry of Agriculture, Food Security and Cooperatives in Statistics Unit and zonal irrigation units. Elasticities were estimated using ordinary least squares technique with the help of STATA 11. Factor analysis technique was also applied. The estimated water price coefficient was found to be -0.03 and the average water price was estimated to be 5.50 Tshs/m3. However the water productivity was 0.3kg/m3, whereas the production was estimated to be 2.5ton/ha. Analysis of the Irrigation Water Price in Rice Production Tanzania doi:10.11648/j.acm.20140304.19 Applied and Computational Mathematics 2014-08-29 © Science Publishing Group Amos Michael Dmitry Kuznetsov Silas Mirau Analysis of the Irrigation Water Price in Rice Production Tanzania 3 4 185 185 2014-08-29 2014-08-29 10.11648/j.acm.20140304.19 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140304.19 © Science Publishing Group Mathematical Model for the Population Dynamics of the Serengeti Ecosystem http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140304.18 Several ecological studies have tried to model the population dynamics of the ungulate migratory animals individually without including the food and predation factors in the models. In this paper, we analyze the population dynamics for herbivores, carnivores and the grass volume using the secondary data from the years 1996-2006. The lions’ data didn’t correlate with the model. Due to that, the sensitivity analysis was carried out for the parameters. The herbivores predation on grass reduces the volume of grass. The crocodile predation on herbivores decreases the population of herbivores. Then the crocodile population increases, when its’ natural death rate in the absence of prey decreases. The herbivores population increases as its’ intrinsic logistic rate increases. There is a trend of Grass periodic increase and decrease as the rainfall constant value changes periodically. The herbivores population decreases as the lion predation on them increases. And lastly, the lions’ population decreases as the natural death rate of lion in the absence of prey increased. Several ecological studies have tried to model the population dynamics of the ungulate migratory animals individually without including the food and predation factors in the models. In this paper, we analyze the population dynamics for herbivores, carnivores and the grass volume using the secondary data from the years 1996-2006. The lions’ data didn’t correlate with the model. Due to that, the sensitivity analysis was carried out for the parameters. The herbivores predation on grass reduces the volume of grass. The crocodile predation on herbivores decreases the population of herbivores. Then the crocodile population increases, when its’ natural death rate in the absence of prey decreases. The herbivores population increases as its’ intrinsic logistic rate increases. There is a trend of Grass periodic increase and decrease as the rainfall constant value changes periodically. The herbivores population decreases as the lion predation on them increases. And lastly, the lions’ population decreases as the natural death rate of lion in the absence of prey increased. Mathematical Model for the Population Dynamics of the Serengeti Ecosystem doi:10.11648/j.acm.20140304.18 Applied and Computational Mathematics 2014-08-29 © Science Publishing Group Janeth James Ngana Livingstone Serwadda Luboobi Dmitry Kuznetsov Mathematical Model for the Population Dynamics of the Serengeti Ecosystem 3 4 176 176 2014-08-29 2014-08-29 10.11648/j.acm.20140304.18 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140304.18 © Science Publishing Group Construction of Generalized Coordinates’ Basis Functions in Lagrangian Dynamics of Flat Manipulators http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140304.20 Second order Lagrange equations are used for describing dynamics of planar mechanism with rotation joints. For calculating kinetic energy of the links local coordinates of velocity vectors are used as well as recursive matrix transformations. Kinetic energy quadratic form coefficients are represented by linear combinations of seven independent trigonometric functions of generalized coordinates, i.e. basis functions. A number of these functions are connected to number of links by quadratic dependence. Constant coefficients in expansions in basic functions are determined from linear equation systems, representing kinetic energy of the mechanism in its several nonrecurring configurations with non-zero values for one or two generalized velocities. The resulting system of dynamics differential equations is integrated numerically with Runge-Kutta method in software environment Mathcad. Efficiency of the proposed method of creating and solving dynamic equations is demonstrated by example of numerical solution the direct dynamic problem of three-link mechanism. Second order Lagrange equations are used for describing dynamics of planar mechanism with rotation joints. For calculating kinetic energy of the links local coordinates of velocity vectors are used as well as recursive matrix transformations. Kinetic energy quadratic form coefficients are represented by linear combinations of seven independent trigonometric functions of generalized coordinates, i.e. basis functions. A number of these functions are connected to number of links by quadratic dependence. Constant coefficients in expansions in basic functions are determined from linear equation systems, representing kinetic energy of the mechanism in its several nonrecurring configurations with non-zero values for one or two generalized velocities. The resulting system of dynamics differential equations is integrated numerically with Runge-Kutta method in software environment Mathcad. Efficiency of the proposed method of creating and solving dynamic equations is demonstrated by example of numerical solution the direct dynamic problem of three-link mechanism. Construction of Generalized Coordinates’ Basis Functions in Lagrangian Dynamics of Flat Manipulators doi:10.11648/j.acm.20140304.20 Applied and Computational Mathematics 2014-09-10 © Science Publishing Group Bagautdinov Ildar Nyrgaiazovich Pavlov Alexander Ivanovich Zhuravlev Evgeny Alekseevich Bogdanov Evgeny Nikolaevich Construction of Generalized Coordinates’ Basis Functions in Lagrangian Dynamics of Flat Manipulators 3 4 190 190 2014-09-10 2014-09-10 10.11648/j.acm.20140304.20 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140304.20 © Science Publishing Group Hydromagnetic Stagnation Point Flow over a Porous Stretching Surface in the Presence of Radiation and Viscous Dissipation http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140305.11 This paper investigates the hydromagnetic stagnation point flow of an incompressible viscous electrically conducting fluid towards a stretching sheet in the presence of radiation and viscous dissipation. The Newton-Raphson shooting method along with the fourth-order Runge-Kutta integration algorithm has been employed to tackle the third order, nonlinear boundary layer problem governing the flow. Numerical results for dimensionless local skin friction coefficient and the local Nusselt numbers are presented in tables while graphical results are presented for velocity and temperature profiles for various values of the controlling parameters. The results show that the heat transfer of a hydromagnetic fluid over a porous stretching surface subject to radiation and viscous dissipation can be controlled and a final product with desired characteristics can be achieved. This paper investigates the hydromagnetic stagnation point flow of an incompressible viscous electrically conducting fluid towards a stretching sheet in the presence of radiation and viscous dissipation. The Newton-Raphson shooting method along with the fourth-order Runge-Kutta integration algorithm has been employed to tackle the third order, nonlinear boundary layer problem governing the flow. Numerical results for dimensionless local skin friction coefficient and the local Nusselt numbers are presented in tables while graphical results are presented for velocity and temperature profiles for various values of the controlling parameters. The results show that the heat transfer of a hydromagnetic fluid over a porous stretching surface subject to radiation and viscous dissipation can be controlled and a final product with desired characteristics can be achieved. Hydromagnetic Stagnation Point Flow over a Porous Stretching Surface in the Presence of Radiation and Viscous Dissipation doi:10.11648/j.acm.20140305.11 Applied and Computational Mathematics 2014-09-16 © Science Publishing Group Emmanuel Maurice Arthur Ibrahim Yakubu Seini Hydromagnetic Stagnation Point Flow over a Porous Stretching Surface in the Presence of Radiation and Viscous Dissipation 3 5 196 196 2014-09-16 2014-09-16 10.11648/j.acm.20140305.11 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140305.11 © Science Publishing Group Small Gain Theorem for Distributed Feedback Control of Sturm-Liouville Dynamics http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140305.14 This paper constructs the small-gain theorem upon a general class of Sturm-Liouville systems. It appears that the feedback connection of two Sturm-Liouville sub-systems is guaranteed of well-posedness, Hurwitz, dissipativity and passivity in L2-spaces provided the loop gain is less than 1. To construct the theorem, spatiotemporal transfer-function and geometrical isomorphism between the space-time domain and the mode-frequency domain are developed, whereof the H∞-norm is extended to be 2D-H∞ norm in mode-frequency domain. On grounds of this small-gain theorem, robust performance of any Sturm-Liouville plant can be formulated as robust stability of a feedback connection, whereupon feedback syntheses can be performed via modal-spectral μ-loopshaping. This paper constructs the small-gain theorem upon a general class of Sturm-Liouville systems. It appears that the feedback connection of two Sturm-Liouville sub-systems is guaranteed of well-posedness, Hurwitz, dissipativity and passivity in L2-spaces provided the loop gain is less than 1. To construct the theorem, spatiotemporal transfer-function and geometrical isomorphism between the space-time domain and the mode-frequency domain are developed, whereof the H∞-norm is extended to be 2D-H∞ norm in mode-frequency domain. On grounds of this small-gain theorem, robust performance of any Sturm-Liouville plant can be formulated as robust stability of a feedback connection, whereupon feedback syntheses can be performed via modal-spectral μ-loopshaping. Small Gain Theorem for Distributed Feedback Control of Sturm-Liouville Dynamics doi:10.11648/j.acm.20140305.14 Applied and Computational Mathematics 2014-09-20 © Science Publishing Group Boe-Shong Hong Small Gain Theorem for Distributed Feedback Control of Sturm-Liouville Dynamics 3 5 224 224 2014-09-20 2014-09-20 10.11648/j.acm.20140305.14 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140305.14 © Science Publishing Group Analysis of the Effects of Diversification for Dar Es Salaam Stock Exchange Optimal Portfolio http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140305.13 Dar es Salaam stock exchange (DSE) market is among the stock markets dealing with financial securities transactions and it operates under the brokerage system. Different individuals have little knowledge on how these stock markets operate and many of them fear to invest in stock business because they don’t have the base line of their decision especially on the risk bearings. This paper is based solely on DSE stocks data for the period of past nine years and it tries to give out the nature of return of the stocks, the effects on restrictions at the DSE stock environment to the stock returns and also it explores the effect of diversification on return and on risk (standard deviation). The study uses the classical Markowitz Modern Portfolio Theory (MPT) model in its analysis with little modification so as to meet with the DSE environment. Data from DSE was analysed by using the excel solver and its macros like the solver add – in. After the analysis it is observed that restrictions have an effect on the stock risk and return, where it reduce risk and increases return because the unconstrained frontier is greater than the constrained frontier. Moreover it is found that for the diversification to have a significant effect the stocks have to be nearly or perfectly negatively correlated. Dar es Salaam stock exchange (DSE) market is among the stock markets dealing with financial securities transactions and it operates under the brokerage system. Different individuals have little knowledge on how these stock markets operate and many of them fear to invest in stock business because they don’t have the base line of their decision especially on the risk bearings. This paper is based solely on DSE stocks data for the period of past nine years and it tries to give out the nature of return of the stocks, the effects on restrictions at the DSE stock environment to the stock returns and also it explores the effect of diversification on return and on risk (standard deviation). The study uses the classical Markowitz Modern Portfolio Theory (MPT) model in its analysis with little modification so as to meet with the DSE environment. Data from DSE was analysed by using the excel solver and its macros like the solver add – in. After the analysis it is observed that restrictions have an effect on the stock risk and return, where it reduce risk and increases return because the unconstrained frontier is greater than the constrained frontier. Moreover it is found that for the diversification to have a significant effect the stocks have to be nearly or perfectly negatively correlated. Analysis of the Effects of Diversification for Dar Es Salaam Stock Exchange Optimal Portfolio doi:10.11648/j.acm.20140305.13 Applied and Computational Mathematics 2014-09-20 © Science Publishing Group Phares Kaboneka Wilson Mahera Charles Silas Mirau Analysis of the Effects of Diversification for Dar Es Salaam Stock Exchange Optimal Portfolio 3 5 216 216 2014-09-20 2014-09-20 10.11648/j.acm.20140305.13 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140305.13 © Science Publishing Group Realization of Inhomogeneous Boundary Conditions as Virtual Sources in Parabolic and Hyperbolic Dynamics http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140305.12 Scientists and engineers encounter many kinds of parabolic or hyperbolic distributed dynamics, which are often with inhomogeneous boundary conditions in practice. Boundary inhomogeneity makes the dynamics essentially nonlinear, which prevents the Hilbert space from being applied for modal decomposition and intelligent computation. Thus, this paper systematically deals with this situation via the conversion of the boundary inhomogeneity to a virtual source in conjunction with boundary homogeneity. For such a purpose, the 2D transfer-function is developed based on the Laplace-Galerkin integral transform as the main tool of this conversion. A section of numerical visualization is included to explore the topology of the virtual-source solution. Some interesting findings therein will be addressed. Scientists and engineers encounter many kinds of parabolic or hyperbolic distributed dynamics, which are often with inhomogeneous boundary conditions in practice. Boundary inhomogeneity makes the dynamics essentially nonlinear, which prevents the Hilbert space from being applied for modal decomposition and intelligent computation. Thus, this paper systematically deals with this situation via the conversion of the boundary inhomogeneity to a virtual source in conjunction with boundary homogeneity. For such a purpose, the 2D transfer-function is developed based on the Laplace-Galerkin integral transform as the main tool of this conversion. A section of numerical visualization is included to explore the topology of the virtual-source solution. Some interesting findings therein will be addressed. Realization of Inhomogeneous Boundary Conditions as Virtual Sources in Parabolic and Hyperbolic Dynamics doi:10.11648/j.acm.20140305.12 Applied and Computational Mathematics 2014-09-20 © Science Publishing Group Boe-Shong Hong Realization of Inhomogeneous Boundary Conditions as Virtual Sources in Parabolic and Hyperbolic Dynamics 3 5 204 204 2014-09-20 2014-09-20 10.11648/j.acm.20140305.12 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140305.12 © Science Publishing Group Mathematical Model and Regression Analysis of Acoustic Emission Signals Generated by Partial Discharges http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140305.15 An improved mathematical model describing acoustic emission (AE) signals generated by different types of partial discharges (PD) that occur in electric power transformer insulation system is presented in the paper. AE signals are analyzed within the AE method as applied for power transformer failure detection due to occurrence of PD. There are several types of basic defects, which are characterized by different types of PD. The mathematical model presented here is crucial for numerical analyses and simulations, where it acts as the function describing the acoustic source in an acoustic model of power transformer insulation system. The regression procedure was performed based on empirical AE signals, registered in a laboratory experiment. The AE signals are described by a mathematical model being a multi-parameter function, which involve both the time domain and the frequency domain. Goodness of the model was evaluated based on analysis of 480 data samples in the time, frequency and time-frequency domains. Also coherence between the registered and modeled signals was calculated. It was stated that the improved model fits very well to the real data, although, due to high level of noise embodied in signals registered in experiments, the coherence values remain low. Moreover, analyses of the estimated data were performed and some example results are presented in this paper. Based on the achieved outcomes a collection of parameter values was prepared for each of the eight considered PD basic types. One can simple use it now in a numerical model for simulation of AE signal source generated by specified type of PD, what corresponds to a particular power transformer insulation system failure. Furthermore, the regression procedure presented in this paper can be easily transferred to any other types of AE sources including processes of compression, tension and cracking. An improved mathematical model describing acoustic emission (AE) signals generated by different types of partial discharges (PD) that occur in electric power transformer insulation system is presented in the paper. AE signals are analyzed within the AE method as applied for power transformer failure detection due to occurrence of PD. There are several types of basic defects, which are characterized by different types of PD. The mathematical model presented here is crucial for numerical analyses and simulations, where it acts as the function describing the acoustic source in an acoustic model of power transformer insulation system. The regression procedure was performed based on empirical AE signals, registered in a laboratory experiment. The AE signals are described by a mathematical model being a multi-parameter function, which involve both the time domain and the frequency domain. Goodness of the model was evaluated based on analysis of 480 data samples in the time, frequency and time-frequency domains. Also coherence between the registered and modeled signals was calculated. It was stated that the improved model fits very well to the real data, although, due to high level of noise embodied in signals registered in experiments, the coherence values remain low. Moreover, analyses of the estimated data were performed and some example results are presented in this paper. Based on the achieved outcomes a collection of parameter values was prepared for each of the eight considered PD basic types. One can simple use it now in a numerical model for simulation of AE signal source generated by specified type of PD, what corresponds to a particular power transformer insulation system failure. Furthermore, the regression procedure presented in this paper can be easily transferred to any other types of AE sources including processes of compression, tension and cracking. Mathematical Model and Regression Analysis of Acoustic Emission Signals Generated by Partial Discharges doi:10.11648/j.acm.20140305.15 Applied and Computational Mathematics 2014-09-27 © Science Publishing Group Daria Wotzka Mathematical Model and Regression Analysis of Acoustic Emission Signals Generated by Partial Discharges 3 5 230 230 2014-09-27 2014-09-27 10.11648/j.acm.20140305.15 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140305.15 © Science Publishing Group A Third Runge Kutta Method Based on a Linear Combination of Arithmetic Mean, Harmonic Mean and Geometric Mean http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140305.16 We present a new third order Runge Kutta method based on linear combination of arithmetic mean, geometric mean and harmonic mean to solve a first order initial value problem. We also derive the local truncation error and show the stability region for the method. Moreover, we compare the new method with Runge Kutta method based on arithmetic mean, geometric mean and harmonic mean. The numerical results show that the performance of the new method is the same as known third order Runge-Kutta methods. We present a new third order Runge Kutta method based on linear combination of arithmetic mean, geometric mean and harmonic mean to solve a first order initial value problem. We also derive the local truncation error and show the stability region for the method. Moreover, we compare the new method with Runge Kutta method based on arithmetic mean, geometric mean and harmonic mean. The numerical results show that the performance of the new method is the same as known third order Runge-Kutta methods. A Third Runge Kutta Method Based on a Linear Combination of Arithmetic Mean, Harmonic Mean and Geometric Mean doi:10.11648/j.acm.20140305.16 Applied and Computational Mathematics 2014-09-27 © Science Publishing Group Rini Yanti M Imran Syamsudhuha A Third Runge Kutta Method Based on a Linear Combination of Arithmetic Mean, Harmonic Mean and Geometric Mean 3 5 234 234 2014-09-27 2014-09-27 10.11648/j.acm.20140305.16 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140305.16 © Science Publishing Group The Time-Dependent Similarity Solutions of Boundary Layer Equations of Power-Law Fluids with Non-Isothermal Surface http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140305.17 Unsteady, two dimensional boundary layer flows over a heated surface of power-law fluids are investigated. Surface temperature is assumed to have o power-law variation with the time and the distance. Similarity transformation is applied to the partial differential equation system with three independent variables is reduced into an ordinary differential equations systems. Numerical solutions of non-linear differential equations are found by using a finite difference scheme. Solutions are obtained for boundary layer flow velocity and thermal boundary layer profile. Effects of flow behavior index, Prandtl number, suction-injection parameter and surface temperature exponent with the time and the distance are outlined in the figures. Unsteady, two dimensional boundary layer flows over a heated surface of power-law fluids are investigated. Surface temperature is assumed to have o power-law variation with the time and the distance. Similarity transformation is applied to the partial differential equation system with three independent variables is reduced into an ordinary differential equations systems. Numerical solutions of non-linear differential equations are found by using a finite difference scheme. Solutions are obtained for boundary layer flow velocity and thermal boundary layer profile. Effects of flow behavior index, Prandtl number, suction-injection parameter and surface temperature exponent with the time and the distance are outlined in the figures. The Time-Dependent Similarity Solutions of Boundary Layer Equations of Power-Law Fluids with Non-Isothermal Surface doi:10.11648/j.acm.20140305.17 Applied and Computational Mathematics 2014-09-30 © Science Publishing Group Muhammet Yurusoy The Time-Dependent Similarity Solutions of Boundary Layer Equations of Power-Law Fluids with Non-Isothermal Surface 3 5 239 239 2014-09-30 2014-09-30 10.11648/j.acm.20140305.17 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140305.17 © Science Publishing Group Darboux Transformation of Lax Pair for an Integrable Coupling of the Integrable Differential-Difference Equation http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140305.18 An integrable coupling of the known integrable differential-difference equation and its Lax pair are presented. Based on the gauge transformation between the corresponding four-by- four matrix spectral problems, a Darboux transformation of Lax pair for the integrable coupling is established. As an application of the obtained Darboux transformation, an explicit solution is given. An integrable coupling of the known integrable differential-difference equation and its Lax pair are presented. Based on the gauge transformation between the corresponding four-by- four matrix spectral problems, a Darboux transformation of Lax pair for the integrable coupling is established. As an application of the obtained Darboux transformation, an explicit solution is given. Darboux Transformation of Lax Pair for an Integrable Coupling of the Integrable Differential-Difference Equation doi:10.11648/j.acm.20140305.18 Applied and Computational Mathematics 2014-10-09 © Science Publishing Group Xi-Xiang Xu Darboux Transformation of Lax Pair for an Integrable Coupling of the Integrable Differential-Difference Equation 3 5 246 246 2014-10-09 2014-10-09 10.11648/j.acm.20140305.18 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140305.18 © Science Publishing Group Transient MHD Boundary-Layer Slip-Flow of Heat and Mass Transfer Over a Stretching Surface Embedded in Porous Medium with Waste Discharge Concentration and Convective Boundary Conditions http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140305.19 The transient two-dimensional MHD boundary-layer stagnation point flow with heat and mass transfer in a saturated porous medium is presented here by taking into account the transient dispersion of a pollutant spewed by an external source in the presence of a uniform transverse magnetic field and stress (pressure) work. The laminar flow of viscous incompressible and electrically conducting fluid encompassing a convectively heated stationary permeable sheet is assumed to be described in terms of Darcian law. The nonlinear governing partial differential equations obtained are converted into ordinary differential equations by means of appropriate similarity transformations and consequently solved numerically using the forth order Runge-Kutta method with a shooting technique and depicted graphically for some pertinent values of the physical parameters embedded in the flow model. In addition, the skin-friction coefficient, the heat and pollution mass concentration rates are sorted out in tabular form, analyzed and discussed. We opine that findings of this present study will be found useful for environmental systems in pollution control and ventilation, and serve as complementary reference for researchers. The transient two-dimensional MHD boundary-layer stagnation point flow with heat and mass transfer in a saturated porous medium is presented here by taking into account the transient dispersion of a pollutant spewed by an external source in the presence of a uniform transverse magnetic field and stress (pressure) work. The laminar flow of viscous incompressible and electrically conducting fluid encompassing a convectively heated stationary permeable sheet is assumed to be described in terms of Darcian law. The nonlinear governing partial differential equations obtained are converted into ordinary differential equations by means of appropriate similarity transformations and consequently solved numerically using the forth order Runge-Kutta method with a shooting technique and depicted graphically for some pertinent values of the physical parameters embedded in the flow model. In addition, the skin-friction coefficient, the heat and pollution mass concentration rates are sorted out in tabular form, analyzed and discussed. We opine that findings of this present study will be found useful for environmental systems in pollution control and ventilation, and serve as complementary reference for researchers. Transient MHD Boundary-Layer Slip-Flow of Heat and Mass Transfer Over a Stretching Surface Embedded in Porous Medium with Waste Discharge Concentration and Convective Boundary Conditions doi:10.11648/j.acm.20140305.19 Applied and Computational Mathematics 2014-10-15 © Science Publishing Group Adetunji Adeniyan Joshua Aanuoluwapo Adigun Transient MHD Boundary-Layer Slip-Flow of Heat and Mass Transfer Over a Stretching Surface Embedded in Porous Medium with Waste Discharge Concentration and Convective Boundary Conditions 3 5 255 255 2014-10-15 2014-10-15 10.11648/j.acm.20140305.19 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140305.19 © Science Publishing Group Electricity Market and Its Risk Management in Nigeria http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140305.20 This paper is on the development of adequate mathematical model of electricity price via Fourier series. Fourier series is the representation of a function f(x) as an infinite series in sine and cosine terms. Our choice of Fourier series model for electricity price is as result of its volatility, fluctuation trends of hydro flow and poor market designs and we use actively-traded natural gas to hedge against electricity price in Nigeria. The natural gas prices are volatile but do not have a clear seasonal pattern, thus eliminating natural gas price volatility through hedging substantially reduce the electricity price, this development of logical mathematical frame work in the form of hedging tools assures an investor of his or her safety in the power sector. This paper is on the development of adequate mathematical model of electricity price via Fourier series. Fourier series is the representation of a function f(x) as an infinite series in sine and cosine terms. Our choice of Fourier series model for electricity price is as result of its volatility, fluctuation trends of hydro flow and poor market designs and we use actively-traded natural gas to hedge against electricity price in Nigeria. The natural gas prices are volatile but do not have a clear seasonal pattern, thus eliminating natural gas price volatility through hedging substantially reduce the electricity price, this development of logical mathematical frame work in the form of hedging tools assures an investor of his or her safety in the power sector. Electricity Market and Its Risk Management in Nigeria doi:10.11648/j.acm.20140305.20 Applied and Computational Mathematics 2014-10-27 © Science Publishing Group Achudume Celestine Chukwuma Raphael Nwozo Electricity Market and Its Risk Management in Nigeria 3 5 261 261 2014-10-27 2014-10-27 10.11648/j.acm.20140305.20 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140305.20 © Science Publishing Group Exact, Polynomial, Determination Solution Method of the Subset Sum Problem http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140305.21 In this paper we give original geometrical interpretation to the domain of definition of integer and combinatorial problems. The solution of the problems concerning NP class has been carried out on the hyperarches. The existence criterion of the solution on the hyperarches has been defined. The method for establishing the sequence of approximation to the solution on the hyperarches was constructed. Calculation experiments were conducted, and the obtained polynomial algorithm, practically and theoretically solved exactly the (SSP) problem. In this paper we give original geometrical interpretation to the domain of definition of integer and combinatorial problems. The solution of the problems concerning NP class has been carried out on the hyperarches. The existence criterion of the solution on the hyperarches has been defined. The method for establishing the sequence of approximation to the solution on the hyperarches was constructed. Calculation experiments were conducted, and the obtained polynomial algorithm, practically and theoretically solved exactly the (SSP) problem. Exact, Polynomial, Determination Solution Method of the Subset Sum Problem doi:10.11648/j.acm.20140305.21 Applied and Computational Mathematics 2014-11-03 © Science Publishing Group Mahammad Maharram Aliyev Exact, Polynomial, Determination Solution Method of the Subset Sum Problem 3 5 267 267 2014-11-03 2014-11-03 10.11648/j.acm.20140305.21 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140305.21 © Science Publishing Group The Equivalence of the Maximum Likelihood and a Modified Least Squares for a Case of Generalized Linear Model http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140305.22 During the analysis of statistical data, one of the most important steps is the estimation of the considered parameters model. The most common estimation methods are the maximum likelihood and the least squares. When the data are considered normal, there is equivalence between the two methods, so there is no privilege for one or the other method. However, if the data are not Gaussian, this equivalence is no longer valid. Also, if the normal equations are not linear, we make use of iterative methods (Newton-Raphson algorithm, Fisher, etc ...). In this work, we consider a particular case where the data are not normal and solving equations are not linear and that it leads to the equivalence of the maximum likelihood method at least squares but modified. At the end of the work, we concluded by referring to the application of this modified method for solving the equations of Liang and Zeger. During the analysis of statistical data, one of the most important steps is the estimation of the considered parameters model. The most common estimation methods are the maximum likelihood and the least squares. When the data are considered normal, there is equivalence between the two methods, so there is no privilege for one or the other method. However, if the data are not Gaussian, this equivalence is no longer valid. Also, if the normal equations are not linear, we make use of iterative methods (Newton-Raphson algorithm, Fisher, etc ...). In this work, we consider a particular case where the data are not normal and solving equations are not linear and that it leads to the equivalence of the maximum likelihood method at least squares but modified. At the end of the work, we concluded by referring to the application of this modified method for solving the equations of Liang and Zeger. The Equivalence of the Maximum Likelihood and a Modified Least Squares for a Case of Generalized Linear Model doi:10.11648/j.acm.20140305.22 Applied and Computational Mathematics 2014-11-10 © Science Publishing Group Ahsene Lanani The Equivalence of the Maximum Likelihood and a Modified Least Squares for a Case of Generalized Linear Model 3 5 272 272 2014-11-10 2014-11-10 10.11648/j.acm.20140305.22 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140305.22 © Science Publishing Group Finite Iterative Algorithm for Solving a Class of Complex Matrix Equation with Two Unknowns of General Form http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140305.23 This paper is concerned with an efficient iterative algorithm to solve general the Sylvester-conjugate matrix equation of the form ∑_(i= 1)^s▒〖A_i V B_i 〗+ ∑_(j=1)^t▒〖C_j W D_j 〗=∑_(l=1)^m▒〖E_1 V ̅ 〗 F_1+C The proposed algorithm is an extension to our proposed general Sylvester-conjugate equation of the form ∑_(i= 1)^s▒〖A_i V 〗+ ∑_(j=1)^t▒〖B_j W 〗=∑_(l=1)^m▒〖E_1 V ̅ 〗 F_1+C When a solution exists for this matrix equation, for any initial matrices, the solutions can be obtained within finite iterative steps in the absence of round off errors. Some lemmas and theorems are stated and proved where the iterative solutions are obtained. Finally, a numerical example is given to verify the effectiveness of the proposed algorithm. This paper is concerned with an efficient iterative algorithm to solve general the Sylvester-conjugate matrix equation of the form ∑_(i= 1)^s▒〖A_i V B_i 〗+ ∑_(j=1)^t▒〖C_j W D_j 〗=∑_(l=1)^m▒〖E_1 V ̅ 〗 F_1+C The proposed algorithm is an extension to our proposed general Sylvester-conjugate equation of the form ∑_(i= 1)^s▒〖A_i V 〗+ ∑_(j=1)^t▒〖B_j W 〗=∑_(l=1)^m▒〖E_1 V ̅ 〗 F_1+C When a solution exists for this matrix equation, for any initial matrices, the solutions can be obtained within finite iterative steps in the absence of round off errors. Some lemmas and theorems are stated and proved where the iterative solutions are obtained. Finally, a numerical example is given to verify the effectiveness of the proposed algorithm. Finite Iterative Algorithm for Solving a Class of Complex Matrix Equation with Two Unknowns of General Form doi:10.11648/j.acm.20140305.23 Applied and Computational Mathematics 2014-11-14 © Science Publishing Group Mohamed A. Ramadan Mokhtar A. Abdel Naby Talaat S. El-Danaf Ahmed M. E. Bayoumi Finite Iterative Algorithm for Solving a Class of Complex Matrix Equation with Two Unknowns of General Form 3 5 284 284 2014-11-14 2014-11-14 10.11648/j.acm.20140305.23 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140305.23 © Science Publishing Group Effect of Gravitational Acceleration on Unsteady Biomagnetic Fluid Flow http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140306.11 This paper investigates the effect of gravitational acceleration on unsteady biomagnetic fluid flow in a channel under the influence of a spatially varying magnetic field. The study on biomagnetic fluid under the action of an applied magnetic field is important in the development of Biomagnetic Fluid Dynamics (BFD). Most existing studies analyze flows in steady state conditions and the effect of gravitational acceleration has not been addressed. For the mathematical model, the Navier-Stokes equations, energy equation and an additional term that describes the magnetic force and gravitational effect which is consistent with the principles of ferrohydrodynamics (FHD) are employed. The nonlinear governing differential equations are non-dimensionalized and then discretized based on a finite difference technique on a staggered grid system. The solution of these problems is obtained numerically using pressure correction method with SIMPLE algorithm. For a range of governing parameters such as the magnetic number MnF and Richardson number Ri, the numerical results show that the gravitational acceleration has a profound effect on both velocity and temperature profiles. The streamlines plotted also show that vortices appear near the lower plate where the magnetic source is located. This paper investigates the effect of gravitational acceleration on unsteady biomagnetic fluid flow in a channel under the influence of a spatially varying magnetic field. The study on biomagnetic fluid under the action of an applied magnetic field is important in the development of Biomagnetic Fluid Dynamics (BFD). Most existing studies analyze flows in steady state conditions and the effect of gravitational acceleration has not been addressed. For the mathematical model, the Navier-Stokes equations, energy equation and an additional term that describes the magnetic force and gravitational effect which is consistent with the principles of ferrohydrodynamics (FHD) are employed. The nonlinear governing differential equations are non-dimensionalized and then discretized based on a finite difference technique on a staggered grid system. The solution of these problems is obtained numerically using pressure correction method with SIMPLE algorithm. For a range of governing parameters such as the magnetic number MnF and Richardson number Ri, the numerical results show that the gravitational acceleration has a profound effect on both velocity and temperature profiles. The streamlines plotted also show that vortices appear near the lower plate where the magnetic source is located. Effect of Gravitational Acceleration on Unsteady Biomagnetic Fluid Flow doi:10.11648/j.acm.20140306.11 Applied and Computational Mathematics 2014-11-25 © Science Publishing Group Nor Amirah Idris Norsarahaida Amin Hamisan Rahmat Effect of Gravitational Acceleration on Unsteady Biomagnetic Fluid Flow 3 6 294 294 2014-11-25 2014-11-25 10.11648/j.acm.20140306.11 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140306.11 © Science Publishing Group Multisorted Tree Algebra http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140306.12 This paper introduces basic concepts describing a hierarchical algebraic structure called multisorted tree algebra. This structure is constructed by placing multisorted algebra at the bottom of a hierarchy and placing at other intermediate nodes the aggregation of algebras placed at their immediate subordinate nodes. These constructions are different from the one of subalgebras, homomorphic images and product algebras used to characterize varieties in universal algebra theory. The resulting hierarchical algebraic structures cannot be easily classified in common universal algebra varieties. The aggregation method and the fundamental properties of the aggregated algebras have been presented with an illustrative example. Multisorted tree algebras spans multisorted algebra concepts and can be used as modelling framework for building hierarchical abstract data types for information processing in organizations. This paper introduces basic concepts describing a hierarchical algebraic structure called multisorted tree algebra. This structure is constructed by placing multisorted algebra at the bottom of a hierarchy and placing at other intermediate nodes the aggregation of algebras placed at their immediate subordinate nodes. These constructions are different from the one of subalgebras, homomorphic images and product algebras used to characterize varieties in universal algebra theory. The resulting hierarchical algebraic structures cannot be easily classified in common universal algebra varieties. The aggregation method and the fundamental properties of the aggregated algebras have been presented with an illustrative example. Multisorted tree algebras spans multisorted algebra concepts and can be used as modelling framework for building hierarchical abstract data types for information processing in organizations. Multisorted Tree Algebra doi:10.11648/j.acm.20140306.12 Applied and Computational Mathematics 2014-12-17 © Science Publishing Group Erick Patrick Zobo Marcel Fouda Ndjodo Multisorted Tree Algebra 3 6 302 302 2014-12-17 2014-12-17 10.11648/j.acm.20140306.12 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140306.12 © Science Publishing Group (α, β)- Infimum and Supremum of Q- Fuzzy Subgroups over Implication Operator of M* ([0,1]) http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140306.13 In this paper, the concept of (α,β)- inf-sup Q-fuzzy set is generalized and there after we defined (α,β)- inf-sup Q-fuzzy group and a few of its properties are discussed. On the other hand we give the definition of the upper normal Q- fuzzy subgroups, and study the main theorem for this. We also give new results on this subject. Characterization of inf-sup normal Q-fuzzy subgroups also investigated. In this paper, the concept of (α,β)- inf-sup Q-fuzzy set is generalized and there after we defined (α,β)- inf-sup Q-fuzzy group and a few of its properties are discussed. On the other hand we give the definition of the upper normal Q- fuzzy subgroups, and study the main theorem for this. We also give new results on this subject. Characterization of inf-sup normal Q-fuzzy subgroups also investigated. (α, β)- Infimum and Supremum of Q- Fuzzy Subgroups over Implication Operator of M* ([0,1]) doi:10.11648/j.acm.20140306.13 Applied and Computational Mathematics 2014-12-26 © Science Publishing Group R. Nagarajan K. Balamurugan (α, β)- Infimum and Supremum of Q- Fuzzy Subgroups over Implication Operator of M* ([0,1]) 3 6 306 306 2014-12-26 2014-12-26 10.11648/j.acm.20140306.13 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140306.13 © Science Publishing Group An Approximate Analytical Solution of Higher-Order Linear Differential Equations with Variable Coefficients Using Improved Rational Chebyshev Collocation Method http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140306.15 The purpose of this paper is to investigate the use of rational Chebyshev (RC) collocation method for solving high-order linear ordinary differential equations with variable coefficients. Using the rational Chebyshev collocation points, this method transforms the high-order linear ordinary differential equations and the given conditions to matrix equations with unknown rational Chebyshev coefficients. These matrices together with the collocation method are utilized to reduce the solution of higher-order ordinary differential equations to the solution of a system of algebraic equations. The solution is obtained in terms of RC functions. Numerical examples are given to demonstrate the validity and applicability of the method. The obtained numerical results are compared with others existing methods and the exact solution where it shown to be very attractive and maintains better accuracy. The purpose of this paper is to investigate the use of rational Chebyshev (RC) collocation method for solving high-order linear ordinary differential equations with variable coefficients. Using the rational Chebyshev collocation points, this method transforms the high-order linear ordinary differential equations and the given conditions to matrix equations with unknown rational Chebyshev coefficients. These matrices together with the collocation method are utilized to reduce the solution of higher-order ordinary differential equations to the solution of a system of algebraic equations. The solution is obtained in terms of RC functions. Numerical examples are given to demonstrate the validity and applicability of the method. The obtained numerical results are compared with others existing methods and the exact solution where it shown to be very attractive and maintains better accuracy. An Approximate Analytical Solution of Higher-Order Linear Differential Equations with Variable Coefficients Using Improved Rational Chebyshev Collocation Method doi:10.11648/j.acm.20140306.15 Applied and Computational Mathematics 2014-12-29 © Science Publishing Group Mohamed A. Ramadan Kamal R. Raslan Mahmoud A. Nassar An Approximate Analytical Solution of Higher-Order Linear Differential Equations with Variable Coefficients Using Improved Rational Chebyshev Collocation Method 3 6 322 322 2014-12-29 2014-12-29 10.11648/j.acm.20140306.15 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140306.15 © Science Publishing Group Evaluation of Holomorphic Ackermanns http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140306.14 Holomorphic extension of the Ackermann function is suggested. Algorithms of evaluation of tetration and pentation are discussed and illustrated with explicit plots and complex maps. Holomorphic extension of the Ackermann function is suggested. Algorithms of evaluation of tetration and pentation are discussed and illustrated with explicit plots and complex maps. Evaluation of Holomorphic Ackermanns doi:10.11648/j.acm.20140306.14 Applied and Computational Mathematics 2014-12-29 © Science Publishing Group Dmitrii Kouznetsov Evaluation of Holomorphic Ackermanns 3 6 314 314 2014-12-29 2014-12-29 10.11648/j.acm.20140306.14 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140306.14 © Science Publishing Group An Analytical Treatment to Fractional Gas Dynamics Equation http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140306.16 In this paper, the new iterative method (NIM) is applied to solve nonlinear fractional gas dynamics equation. Further, a coupling of the Sumudu transform and Adomian decomposion (STADM) is used to get an approximate solution of the same problem. The results obtained by the two methods are found to be in agreement. Therefore, the NIM may be considered efficient method for finding approximate solutions of both linear and nonlinear fractional differential equations. In this paper, the new iterative method (NIM) is applied to solve nonlinear fractional gas dynamics equation. Further, a coupling of the Sumudu transform and Adomian decomposion (STADM) is used to get an approximate solution of the same problem. The results obtained by the two methods are found to be in agreement. Therefore, the NIM may be considered efficient method for finding approximate solutions of both linear and nonlinear fractional differential equations. An Analytical Treatment to Fractional Gas Dynamics Equation doi:10.11648/j.acm.20140306.16 Applied and Computational Mathematics 2014-12-30 © Science Publishing Group Mohamed S. Al-luhaibi Nahed A. Saker An Analytical Treatment to Fractional Gas Dynamics Equation 3 6 329 329 2014-12-30 2014-12-30 10.11648/j.acm.20140306.16 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140306.16 © Science Publishing Group The Line Method Combined with Spectral Chebyshev for Space-Time Fractional Diffusion Equation http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140306.17 The Method of Lines Combined with Chebyshev Spectral Method respect to weighted residual (Collocation Points) for Space-Time fractional diffusion equation is considered, the direct way will be used for approximating Time fractional and the expiation of shifted first kind of Chebyshev polynomial will be used to approximate unknown functions, the structure of the systems and the matrices will be fund, the algorithm steps is illustrated, The tables and figures of the results of the implementation by using this method at different values of fractional order will be shown, with the helping of programs of matlab. The Method of Lines Combined with Chebyshev Spectral Method respect to weighted residual (Collocation Points) for Space-Time fractional diffusion equation is considered, the direct way will be used for approximating Time fractional and the expiation of shifted first kind of Chebyshev polynomial will be used to approximate unknown functions, the structure of the systems and the matrices will be fund, the algorithm steps is illustrated, The tables and figures of the results of the implementation by using this method at different values of fractional order will be shown, with the helping of programs of matlab. The Line Method Combined with Spectral Chebyshev for Space-Time Fractional Diffusion Equation doi:10.11648/j.acm.20140306.17 Applied and Computational Mathematics 2014-12-31 © Science Publishing Group I. K. Youssef A. M. Shukur The Line Method Combined with Spectral Chebyshev for Space-Time Fractional Diffusion Equation 3 6 336 336 2014-12-31 2014-12-31 10.11648/j.acm.20140306.17 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140306.17 © Science Publishing Group The Taylor Vortex and the Driven Cavity Problems in the Stream Function-Vorticity Formulation http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140306.18 In this work, two problems will be presented: The Taylor Vortex problem and the Driven Cavity problem. Both problems are solved using the Stream function-Vorticity formulation of the Navier-Stokes equations in 2D. Results are obtained using two methods: A fixed point iterative method and another one working with matrixes A and B resulting from the discretization of the Laplacian and the advective term, respectively. This second method resulted faster than the fixed point iterative one. In this work, two problems will be presented: The Taylor Vortex problem and the Driven Cavity problem. Both problems are solved using the Stream function-Vorticity formulation of the Navier-Stokes equations in 2D. Results are obtained using two methods: A fixed point iterative method and another one working with matrixes A and B resulting from the discretization of the Laplacian and the advective term, respectively. This second method resulted faster than the fixed point iterative one. The Taylor Vortex and the Driven Cavity Problems in the Stream Function-Vorticity Formulation doi:10.11648/j.acm.20140306.18 Applied and Computational Mathematics 2015-01-04 © Science Publishing Group Blanca Bermúdez Juárez René Posadas Hernández Wuiyevaldo Fermín Guerrero Sánchez The Taylor Vortex and the Driven Cavity Problems in the Stream Function-Vorticity Formulation 3 6 342 342 2015-01-04 2015-01-04 10.11648/j.acm.20140306.18 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140306.18 © Science Publishing Group A Cubic Bézier Model with Shape Parameters http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140306.19 A novel extension of the cubic Bézier curve with two shape parameters is presented in this work. The proposed curve is still a cubic polynomial model, which has simpler structure than other similar models. The proposed curve has the same properties with the usual cubic Bézier curve and its shape can be adjusted by altering values of the two shape parameters while the control points are fixed. With the two shape parameters, the proposed curve can approach to its control polygon farther or closer. The corresponding surface with four shape parameters has the similar properties with the proposed curve and enjoys the shape adjustable property. A novel extension of the cubic Bézier curve with two shape parameters is presented in this work. The proposed curve is still a cubic polynomial model, which has simpler structure than other similar models. The proposed curve has the same properties with the usual cubic Bézier curve and its shape can be adjusted by altering values of the two shape parameters while the control points are fixed. With the two shape parameters, the proposed curve can approach to its control polygon farther or closer. The corresponding surface with four shape parameters has the similar properties with the proposed curve and enjoys the shape adjustable property. A Cubic Bézier Model with Shape Parameters doi:10.11648/j.acm.20140306.19 Applied and Computational Mathematics 2015-01-08 © Science Publishing Group Juncheng Li A Cubic Bézier Model with Shape Parameters 3 6 348 348 2015-01-08 2015-01-08 10.11648/j.acm.20140306.19 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20140306.19 © Science Publishing Group Performance Measure of Binomial Model for Pricing American and European Options http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2014030601.14 Binomial model is a powerful technique that can be used to solve many complex option-pricing problems. In contrast to the Black-Scholes model and other option pricing models that require solutions to stochastic differential equations, the binomial option pricing model is mathematically simple. It is based on the assumption of no arbitrage. The assumption of no arbitrage implies that all risk-free investments earn the risk-free rate of return and no investment opportunities exists that requires zero amount of investment but yield positive returns. It is the activity of many individuals operating within the context of financial market that, in fact, upholds these conditions. The activities of the arbitrageurs or speculators are often maligned in the media, but their activities insure that financial markets work. They insure that financial assets such as options are priced within a narrow tolerance of their theoretical values. In this paper we use binomial model to derive the Black-Scholes equation using the risk-neutral expectation formula. We also use binomial model for the valuation of European and American options. Lastly, the primary reason why the binomial model is used is its flexibility compared to the Black-Scholes model and it is also used to price a wide variety of options. Binomial model is a powerful technique that can be used to solve many complex option-pricing problems. In contrast to the Black-Scholes model and other option pricing models that require solutions to stochastic differential equations, the binomial option pricing model is mathematically simple. It is based on the assumption of no arbitrage. The assumption of no arbitrage implies that all risk-free investments earn the risk-free rate of return and no investment opportunities exists that requires zero amount of investment but yield positive returns. It is the activity of many individuals operating within the context of financial market that, in fact, upholds these conditions. The activities of the arbitrageurs or speculators are often maligned in the media, but their activities insure that financial markets work. They insure that financial assets such as options are priced within a narrow tolerance of their theoretical values. In this paper we use binomial model to derive the Black-Scholes equation using the risk-neutral expectation formula. We also use binomial model for the valuation of European and American options. Lastly, the primary reason why the binomial model is used is its flexibility compared to the Black-Scholes model and it is also used to price a wide variety of options. Performance Measure of Binomial Model for Pricing American and European Options doi:10.11648/j.acm.s.2014030601.14 Applied and Computational Mathematics 2014-10-20 © Science Publishing Group Fadugba Sunday Emmanuel Ajayi Olayinka Adedoyin Okedele Olanrewaju Hammed Performance Measure of Binomial Model for Pricing American and European Options 3 6 30 30 2014-10-20 2014-10-20 10.11648/j.acm.s.2014030601.14 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2014030601.14 © Science Publishing Group On Martingales and the Use of Optional Stopping Theorem to Determine the Mean and Variance of a Stopping Time http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2014030601.13 This paper examines the roles martingale property played in the use of optional stopping theorem (OST). It also examines the implication of this property in the use of optional stopping theorem for the determination of mean and variance of a stopping time. A simple example relating to betting system of a gambler with limited amount of money has been provided. The analysis of the betting system showed that the gambler leaves with the same amount of money as when he started and therefore satisfied martingale property. Linearity of expectation property was used as a reliable tool in the use of the martingale property. This paper examines the roles martingale property played in the use of optional stopping theorem (OST). It also examines the implication of this property in the use of optional stopping theorem for the determination of mean and variance of a stopping time. A simple example relating to betting system of a gambler with limited amount of money has been provided. The analysis of the betting system showed that the gambler leaves with the same amount of money as when he started and therefore satisfied martingale property. Linearity of expectation property was used as a reliable tool in the use of the martingale property. On Martingales and the Use of Optional Stopping Theorem to Determine the Mean and Variance of a Stopping Time doi:10.11648/j.acm.s.2014030601.13 Applied and Computational Mathematics 2014-09-05 © Science Publishing Group Ganiyu, A. A. Fakunle, I. On Martingales and the Use of Optional Stopping Theorem to Determine the Mean and Variance of a Stopping Time 3 6 17 17 2014-09-05 2014-09-05 10.11648/j.acm.s.2014030601.13 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2014030601.13 © Science Publishing Group On Hybrid Model for the Valuation of Credit Risk http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2014030601.12 This paper presents hybrid model for the valuation of credit risk. Credit risk arises whenever a borrower is expecting to use future cash flows to pay a current debt. It is closely tied to the potential return of investment, the most notable being that the yields on bonds correlate strongly to their perceived credit risk. Hybrid model combines the structural and intensity-based approaches. While avoiding their difficulties, it picks the best features of both approaches; the economic and intuitive appeal of the structural approach and the tractability and empirical fit of the intensity-based approach. In credit derivatives market there are quite a few securities that depend on more than one source of risk, like corporate bonds and convertible bonds, most attractive credit models should involve all these three sources of risk, and interest-rate risk. Our framework brings together these standard block. This paper presents hybrid model for the valuation of credit risk. Credit risk arises whenever a borrower is expecting to use future cash flows to pay a current debt. It is closely tied to the potential return of investment, the most notable being that the yields on bonds correlate strongly to their perceived credit risk. Hybrid model combines the structural and intensity-based approaches. While avoiding their difficulties, it picks the best features of both approaches; the economic and intuitive appeal of the structural approach and the tractability and empirical fit of the intensity-based approach. In credit derivatives market there are quite a few securities that depend on more than one source of risk, like corporate bonds and convertible bonds, most attractive credit models should involve all these three sources of risk, and interest-rate risk. Our framework brings together these standard block. On Hybrid Model for the Valuation of Credit Risk doi:10.11648/j.acm.s.2014030601.12 Applied and Computational Mathematics 2014-08-13 © Science Publishing Group Fadugba Sunday Emmanuel Edogbanya Olaronke Helen On Hybrid Model for the Valuation of Credit Risk 3 6 11 11 2014-08-13 2014-08-13 10.11648/j.acm.s.2014030601.12 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2014030601.12 © Science Publishing Group The Mellin Transform Method as an Alternative Analytic Solution for the Valuation of Geometric Asian Option http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2014030601.11 This paper presents the Mellin transform method as an alternative analytic solution for the valuation of geometric Asian option. Asian options are options in which the variable is the average price over a period of time. The analytical solution of the Black-Scholes partial differential equation for Asian option is known as an explicit formula, this is due to the fact that the geometric average of a set of lognormal random variables is lognormally distributed. We derive a closed form solution for a continuous geometric Asian option by means of the partial differential equations. We also provide an alternative method for solving geometric Asian options partial differential equations using the Mellin transform method. This paper presents the Mellin transform method as an alternative analytic solution for the valuation of geometric Asian option. Asian options are options in which the variable is the average price over a period of time. The analytical solution of the Black-Scholes partial differential equation for Asian option is known as an explicit formula, this is due to the fact that the geometric average of a set of lognormal random variables is lognormally distributed. We derive a closed form solution for a continuous geometric Asian option by means of the partial differential equations. We also provide an alternative method for solving geometric Asian options partial differential equations using the Mellin transform method. The Mellin Transform Method as an Alternative Analytic Solution for the Valuation of Geometric Asian Option doi:10.11648/j.acm.s.2014030601.11 Applied and Computational Mathematics 2014-08-05 © Science Publishing Group Fadugba Sunday Emmanuel The Mellin Transform Method as an Alternative Analytic Solution for the Valuation of Geometric Asian Option 3 6 7 7 2014-08-05 2014-08-05 10.11648/j.acm.s.2014030601.11 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2014030601.11 © Science Publishing Group Stability Analysis for Finite Difference Scheme Used for Seismic Imaging Using Amplitude and Phase Portrait http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150401.11 A finite difference scheme is produced when partial derivatives in the partial differential equation(s) governing a physical phenomenon like the propagation of seismic waves through real media are replaced by a finite difference approximation. The result is a single algebraic equation which, when solved, provide an approximation to the solution of the original partial differential equation at selected points of a solution grid. Stability of a numerical scheme like that of finite difference scheme in the solution of partial differential equations is crucial for correctness and validity and it means that the error caused by small perturbation in the numerical solution remains bound. This paper considers important concepts like the amplitude and phase portrait used to analyze the stability of finite difference scheme. Applying these concepts produces an amplification factor and celerity for the components of the numerical solution. A finite difference scheme is produced when partial derivatives in the partial differential equation(s) governing a physical phenomenon like the propagation of seismic waves through real media are replaced by a finite difference approximation. The result is a single algebraic equation which, when solved, provide an approximation to the solution of the original partial differential equation at selected points of a solution grid. Stability of a numerical scheme like that of finite difference scheme in the solution of partial differential equations is crucial for correctness and validity and it means that the error caused by small perturbation in the numerical solution remains bound. This paper considers important concepts like the amplitude and phase portrait used to analyze the stability of finite difference scheme. Applying these concepts produces an amplification factor and celerity for the components of the numerical solution. Stability Analysis for Finite Difference Scheme Used for Seismic Imaging Using Amplitude and Phase Portrait doi:10.11648/j.acm.20150401.11 Applied and Computational Mathematics 2015-01-14 © Science Publishing Group Olowofela Joseph A. Akinyemi Olukayode D. Ajani Olumide Oyewale Stability Analysis for Finite Difference Scheme Used for Seismic Imaging Using Amplitude and Phase Portrait 4 1 4 4 2015-01-14 2015-01-14 10.11648/j.acm.20150401.11 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150401.11 © Science Publishing Group Texture Classification Using Spline, Wavelet Decomposition and Fractal Dimension http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150401.12 Feature extraction is an important process for texture classification. This paper suggests two sets of features for texture analysis. In the first set of features, a set of fractal features is obtained from the eight wavelet sub-bands that are generated by applying Haar wavelet transform twice times according to dyadic architecture. The fractal features are determined using the differential box counting method. While for determining the second set of features, the cubic spline representation is applied to decompose the image signal into rough and smooth components; then applying the wavelet transform and finally compute the fractal dimension for all the sub-bands of both images. Each type of these two extracted feature sets is studied individually, and they are used together. Their overall performance is investigated. The proposed features set has been applied on two texture datasets, one consists of textures with directional properties, and the second set consists of textures samples that have directional attributes. The test results showed that the proposed methods give a high level of classification with images that have or do not have directional properties. Feature extraction is an important process for texture classification. This paper suggests two sets of features for texture analysis. In the first set of features, a set of fractal features is obtained from the eight wavelet sub-bands that are generated by applying Haar wavelet transform twice times according to dyadic architecture. The fractal features are determined using the differential box counting method. While for determining the second set of features, the cubic spline representation is applied to decompose the image signal into rough and smooth components; then applying the wavelet transform and finally compute the fractal dimension for all the sub-bands of both images. Each type of these two extracted feature sets is studied individually, and they are used together. Their overall performance is investigated. The proposed features set has been applied on two texture datasets, one consists of textures with directional properties, and the second set consists of textures samples that have directional attributes. The test results showed that the proposed methods give a high level of classification with images that have or do not have directional properties. Texture Classification Using Spline, Wavelet Decomposition and Fractal Dimension doi:10.11648/j.acm.20150401.12 Applied and Computational Mathematics 2015-01-27 © Science Publishing Group Saad Al-Momen Loay E. George Raid K. Naji Texture Classification Using Spline, Wavelet Decomposition and Fractal Dimension 4 1 10 10 2015-01-27 2015-01-27 10.11648/j.acm.20150401.12 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150401.12 © Science Publishing Group Effects of First-Order Reactant on MHD Turbulence at Four-Point Correlation http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150401.13 The purpose of this study is to determine the effect of first order reactant of MHD fluid turbulence for four-point correlations earlier than the ending phase. Three and four point correlation equations are obtained. The correlation equations are changed to spectral type by their Fourier-transform. By neglecting the quintuple correlations in comparison to the fourth order correlation terms. As a final point integrating the energy spectrum over all wave numbers and we obtained the energy decompose rule of MHD turbulence for magnetic field fluctuations due to the effect of first order reactant and the result has been shown graphically. The purpose of this study is to determine the effect of first order reactant of MHD fluid turbulence for four-point correlations earlier than the ending phase. Three and four point correlation equations are obtained. The correlation equations are changed to spectral type by their Fourier-transform. By neglecting the quintuple correlations in comparison to the fourth order correlation terms. As a final point integrating the energy spectrum over all wave numbers and we obtained the energy decompose rule of MHD turbulence for magnetic field fluctuations due to the effect of first order reactant and the result has been shown graphically. Effects of First-Order Reactant on MHD Turbulence at Four-Point Correlation doi:10.11648/j.acm.20150401.13 Applied and Computational Mathematics 2015-01-30 © Science Publishing Group M. Abu Bkar Pk Abdul Malek M. Abul Kalam Azad Effects of First-Order Reactant on MHD Turbulence at Four-Point Correlation 4 1 19 19 2015-01-30 2015-01-30 10.11648/j.acm.20150401.13 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150401.13 © Science Publishing Group Optimal Harvesting Policy of Discrete-Time Predator-Prey Dynamic System with Holling Type-IV Functional Response and Its Simulation http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150401.14 This paper deals with a discrete-time prey-predator system with Holling type-IV function response in the presence of some alternative food to predator and harvesting of prey species. By theoretical analysis and numerical simulation, comparing with the system without harvesting, ecological equilibrium point of the system is removed if harvesting effort is changed, and the appropriate harvesting effort can increase the stability of the system. Moreover, optimal harvesting policy is obtained using Pontryagin’s maximum principle. Meanwhile, some numerical simulations verify our analytical results. This study also gains the maximum economic profit which is based on the ecological equilibrium. The suitable price of resources can control the excessive harvest to promote the sustainable development of species. This paper deals with a discrete-time prey-predator system with Holling type-IV function response in the presence of some alternative food to predator and harvesting of prey species. By theoretical analysis and numerical simulation, comparing with the system without harvesting, ecological equilibrium point of the system is removed if harvesting effort is changed, and the appropriate harvesting effort can increase the stability of the system. Moreover, optimal harvesting policy is obtained using Pontryagin’s maximum principle. Meanwhile, some numerical simulations verify our analytical results. This study also gains the maximum economic profit which is based on the ecological equilibrium. The suitable price of resources can control the excessive harvest to promote the sustainable development of species. Optimal Harvesting Policy of Discrete-Time Predator-Prey Dynamic System with Holling Type-IV Functional Response and Its Simulation doi:10.11648/j.acm.20150401.14 Applied and Computational Mathematics 2015-02-02 © Science Publishing Group Rui-Ling Zhang Wan-Xiong Wang Li-Juan Qin Optimal Harvesting Policy of Discrete-Time Predator-Prey Dynamic System with Holling Type-IV Functional Response and Its Simulation 4 1 29 29 2015-02-02 2015-02-02 10.11648/j.acm.20150401.14 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150401.14 © Science Publishing Group 3D Goursat Problem in the Non-Classical Treatment for Manjeron Generalized Equation with Non-Smooth Coefficients http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2015040101.11 In this paper substantiated for a Manjeron generalized equation with non-smooth coefficients a three dimensional Goursat problem -3D Goursat problem with non-classical boundary conditions is considered, which requires no matching conditions. Equivalence of these conditions three dimensional boundary condition is substantiated classical, in the case if the solution of the problem in the isotropic S. L. Sobolev&apos;s space is found. The considered equation as a hyperbolic equation generalizes not only classic equations of mathematical physics (heat-conductivity equations, string vibration equation) and also many models differential equations (telegraph equation, Aller&apos;s equation, moisture transfer generalized equation, Manjeron equation, Boussinesq - Love equation and etc.). It is grounded that the 3D Goursat boundary conditions in the classic and non-classic treatment are equivalent to each other. Thus, namely in this paper, the non-classic problem with 3D Goursat conditions is grounded for a hyperbolic equation of sixth order. For simplicity, this was demonstrated for one model case in one of S.L. Sobolev isotropic space.W_p^((2,2,2) ) (G) In this paper substantiated for a Manjeron generalized equation with non-smooth coefficients a three dimensional Goursat problem -3D Goursat problem with non-classical boundary conditions is considered, which requires no matching conditions. Equivalence of these conditions three dimensional boundary condition is substantiated classical, in the case if the solution of the problem in the isotropic S. L. Sobolev&apos;s space is found. The considered equation as a hyperbolic equation generalizes not only classic equations of mathematical physics (heat-conductivity equations, string vibration equation) and also many models differential equations (telegraph equation, Aller&apos;s equation, moisture transfer generalized equation, Manjeron equation, Boussinesq - Love equation and etc.). It is grounded that the 3D Goursat boundary conditions in the classic and non-classic treatment are equivalent to each other. Thus, namely in this paper, the non-classic problem with 3D Goursat conditions is grounded for a hyperbolic equation of sixth order. For simplicity, this was demonstrated for one model case in one of S.L. Sobolev isotropic space.W_p^((2,2,2) ) (G) 3D Goursat Problem in the Non-Classical Treatment for Manjeron Generalized Equation with Non-Smooth Coefficients doi:10.11648/j.acm.s.2015040101.11 Applied and Computational Mathematics 2014-06-30 © Science Publishing Group Ilgar Gurbat oglu Mamedov 3D Goursat Problem in the Non-Classical Treatment for Manjeron Generalized Equation with Non-Smooth Coefficients 4 1 5 5 2014-06-30 2014-06-30 10.11648/j.acm.s.2015040101.11 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2015040101.11 © Science Publishing Group Implicit Runge-Kutta Method for Van Der Pol Problem http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2015040101.12 In this manuscript the implicit Runge-Kutta (IRK) method, with three slopes of order five has been explained, and is applied to Van der pol stiff differential equation. Truncation error, of order five, has been estimated. Stability of the procedure for the Van der pol equation, is analyzed by the Lyapunov method. To illustrate the structure of the method, an Algorithm is presented to solve this stiff problem. Results confirm the validity and the ability of this approach. In this manuscript the implicit Runge-Kutta (IRK) method, with three slopes of order five has been explained, and is applied to Van der pol stiff differential equation. Truncation error, of order five, has been estimated. Stability of the procedure for the Van der pol equation, is analyzed by the Lyapunov method. To illustrate the structure of the method, an Algorithm is presented to solve this stiff problem. Results confirm the validity and the ability of this approach. Implicit Runge-Kutta Method for Van Der Pol Problem doi:10.11648/j.acm.s.2015040101.12 Applied and Computational Mathematics 2014-07-13 © Science Publishing Group Jafar Biazar Meysam Navidyan Implicit Runge-Kutta Method for Van Der Pol Problem 4 1 11 11 2014-07-13 2014-07-13 10.11648/j.acm.s.2015040101.12 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2015040101.12 © Science Publishing Group Comparison between Finite Volume Method (FVM) Based on Inviscid and Viscous Flow with Experimental and Fluent Results http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2015040101.13 The Finite Volume Method (FVM) is currently the most popular method in CFD. The main reason is that it can resolve some of the difficulties that the other methods have. Finite volume methods are a class of discretization schemes that have proven highly successful in approximating the solution of a wide variety of conservation law systems . Finite volume method can be classified into three groups: (1) Cell-centered scheme, (2) Cell-vertex scheme with overlapping control volumes and (3), Cell-vertex scheme with dual control volumes . The present work used Finite volume based Cell Cell-centered. This approach used the grid cell identical to its control volume. While in view of a manner the grid cells in this work can be defined numerically, it can follow as a structured grid based on Elliptic grid generation PDEs . Computer code had been developed by using a cell centered Finite volume scheme combined with structured grid approach. The computer codes applied for the case of compressible flow past through an airfoil NACA 0012, in which the flow problem can be treated as purely inviscid flow or as the flow with viscous effect but considered to be as a laminar flow. The comparison result presented in term of pressure coefficient Cp for different angle of attack using available experimental result and the result provided by Fluent software. In term for the case of flow problem treated as an inviscid flow, both the developed computer code and Fluent software produce the result closed to the experimental result. However if the developed computer code as well as fluent software treated the flow problem to include the viscous effect by considering them as a laminar flow both are slightly deviate with the experimental results. Strictly speaking the present developed computer code give a similar result as the experimental result, which both showing that this type of airfoil having a sensitive effect to the angle of attack. A small change of angle of attack will produce a significant change to the location of shock will occurred. The Finite Volume Method (FVM) is currently the most popular method in CFD. The main reason is that it can resolve some of the difficulties that the other methods have. Finite volume methods are a class of discretization schemes that have proven highly successful in approximating the solution of a wide variety of conservation law systems . Finite volume method can be classified into three groups: (1) Cell-centered scheme, (2) Cell-vertex scheme with overlapping control volumes and (3), Cell-vertex scheme with dual control volumes . The present work used Finite volume based Cell Cell-centered. This approach used the grid cell identical to its control volume. While in view of a manner the grid cells in this work can be defined numerically, it can follow as a structured grid based on Elliptic grid generation PDEs . Computer code had been developed by using a cell centered Finite volume scheme combined with structured grid approach. The computer codes applied for the case of compressible flow past through an airfoil NACA 0012, in which the flow problem can be treated as purely inviscid flow or as the flow with viscous effect but considered to be as a laminar flow. The comparison result presented in term of pressure coefficient Cp for different angle of attack using available experimental result and the result provided by Fluent software. In term for the case of flow problem treated as an inviscid flow, both the developed computer code and Fluent software produce the result closed to the experimental result. However if the developed computer code as well as fluent software treated the flow problem to include the viscous effect by considering them as a laminar flow both are slightly deviate with the experimental results. Strictly speaking the present developed computer code give a similar result as the experimental result, which both showing that this type of airfoil having a sensitive effect to the angle of attack. A small change of angle of attack will produce a significant change to the location of shock will occurred. Comparison between Finite Volume Method (FVM) Based on Inviscid and Viscous Flow with Experimental and Fluent Results doi:10.11648/j.acm.s.2015040101.13 Applied and Computational Mathematics 2015-02-09 © Science Publishing Group Abobaker Mohammed Alakashi Bambang Basuno Hasan Taher. M. Elkamel Comparison between Finite Volume Method (FVM) Based on Inviscid and Viscous Flow with Experimental and Fluent Results 4 1 17 17 2015-02-09 2015-02-09 10.11648/j.acm.s.2015040101.13 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2015040101.13 © Science Publishing Group A New Method for Solving Fully Fuzzy Linear Programming Problems by Using the Lexicography Method http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2015040102.11 In this paper by using the lexicography method, we proposed a new model to solve fully fuzzy linear programming problem with L-R fuzzy number and find the fuzzy optimal solution of it. Our method has graceful structure and is easy to implement compared with some existing methods. To illustrate our method, a numerical example is solved. In this paper by using the lexicography method, we proposed a new model to solve fully fuzzy linear programming problem with L-R fuzzy number and find the fuzzy optimal solution of it. Our method has graceful structure and is easy to implement compared with some existing methods. To illustrate our method, a numerical example is solved. A New Method for Solving Fully Fuzzy Linear Programming Problems by Using the Lexicography Method doi:10.11648/j.acm.s.2015040102.11 Applied and Computational Mathematics 2014-10-24 © Science Publishing Group Mohammad Mehdi Shamooshaki Ali Hosseinzadeh Seyyed Ahmad Edalatpanah A New Method for Solving Fully Fuzzy Linear Programming Problems by Using the Lexicography Method 4 1 3 3 2014-10-24 2014-10-24 10.11648/j.acm.s.2015040102.11 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2015040102.11 © Science Publishing Group ON (m, n) –Upper Q-Fuzzy Soft Subgroups http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2015040102.12 In this paper we shall study some properties for upper Q- fuzzy subgroups, some lemma and theorem for this subject. We shall study the upper Q- fuzzy index with the upper fuzzy sub groups; also we shall give some new definitions for this subject. On the other hand we shall give the definition of the upper normal fuzzy subgroups, and study the main theorem for this. We shall also give new results on this subject. In this paper we shall study some properties for upper Q- fuzzy subgroups, some lemma and theorem for this subject. We shall study the upper Q- fuzzy index with the upper fuzzy sub groups; also we shall give some new definitions for this subject. On the other hand we shall give the definition of the upper normal fuzzy subgroups, and study the main theorem for this. We shall also give new results on this subject. ON (m, n) –Upper Q-Fuzzy Soft Subgroups doi:10.11648/j.acm.s.2015040102.12 Applied and Computational Mathematics 2014-11-03 © Science Publishing Group Rathinam Nagarajan K. Venugopal ON (m, n) –Upper Q-Fuzzy Soft Subgroups 4 1 9 9 2014-11-03 2014-11-03 10.11648/j.acm.s.2015040102.12 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2015040102.12 © Science Publishing Group A Note on Zadeh&apos;s Extension Principle http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2015040102.13 For a mapping, fuzzy sets obtained by Zadeh&apos;s extension principle are images of other fuzzy sets on the domain of the mapping under the mapping. Some relationships between images of level sets of one or two fuzzy sets under a mapping and another fuzzy set obtained from the one or two fuzzy sets by Zadeh&apos;s extension principle are known. In the present paper, the known results are extended to more general ones, and some useful results for applications are derived by the extended ones. For a mapping, fuzzy sets obtained by Zadeh&apos;s extension principle are images of other fuzzy sets on the domain of the mapping under the mapping. Some relationships between images of level sets of one or two fuzzy sets under a mapping and another fuzzy set obtained from the one or two fuzzy sets by Zadeh&apos;s extension principle are known. In the present paper, the known results are extended to more general ones, and some useful results for applications are derived by the extended ones. A Note on Zadeh&apos;s Extension Principle doi:10.11648/j.acm.s.2015040102.13 Applied and Computational Mathematics 2014-12-27 © Science Publishing Group Masamichi Kon A Note on Zadeh&apos;s Extension Principle 4 1 14 14 2014-12-27 2014-12-27 10.11648/j.acm.s.2015040102.13 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2015040102.13 © Science Publishing Group Pseudo Similar Intuitionistic Fuzzy Matrices http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2015040102.14 In this paper, we shall define Pseudo Similarity and Semi Similarity for Intuitionistic Fuzzy Matrix (IFM) and prove that the Pseudo similarity relation on a pair of IFMs is inherited by all its powers and their transposes are similar. Also we exibit that the Pseudo similarity relation preserve regularity and impotency of their matrices. In this paper, we shall define Pseudo Similarity and Semi Similarity for Intuitionistic Fuzzy Matrix (IFM) and prove that the Pseudo similarity relation on a pair of IFMs is inherited by all its powers and their transposes are similar. Also we exibit that the Pseudo similarity relation preserve regularity and impotency of their matrices. Pseudo Similar Intuitionistic Fuzzy Matrices doi:10.11648/j.acm.s.2015040102.14 Applied and Computational Mathematics 2014-12-31 © Science Publishing Group T. Gandhimathi A. R. Meenakshi Pseudo Similar Intuitionistic Fuzzy Matrices 4 1 19 19 2014-12-31 2014-12-31 10.11648/j.acm.s.2015040102.14 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2015040102.14 © Science Publishing Group Linear Fractional Multi-Objective Optimization Problems Subject to Fuzzy Relational Equations with the Max-Average Composition http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2015040102.15 ‎In this paper‎, ‎linear fractional multi-objective optimization problems subject to a system of fuzzy relational equations (FRE) using the max-average composition are considered‎. ‎First‎, ‎some theorems and results are presented to thoroughly identify and reduce the feasible set of the fuzzy relation equations‎. ‎Next‎, ‎the linear fractional multi-objective optimization problem is converted to a linear one using Nykowski and Zolkiewski&apos;s approach‎. ‎Then‎, ‎the efficient solutions are obtained by applying the improved ε-constraint method‎. ‎‎Finally‎, ‎the proposed method is effectively tested by solving a consistent test problem‎. ‎In this paper‎, ‎linear fractional multi-objective optimization problems subject to a system of fuzzy relational equations (FRE) using the max-average composition are considered‎. ‎First‎, ‎some theorems and results are presented to thoroughly identify and reduce the feasible set of the fuzzy relation equations‎. ‎Next‎, ‎the linear fractional multi-objective optimization problem is converted to a linear one using Nykowski and Zolkiewski&apos;s approach‎. ‎Then‎, ‎the efficient solutions are obtained by applying the improved ε-constraint method‎. ‎‎Finally‎, ‎the proposed method is effectively tested by solving a consistent test problem‎. Linear Fractional Multi-Objective Optimization Problems Subject to Fuzzy Relational Equations with the Max-Average Composition doi:10.11648/j.acm.s.2015040102.15 Applied and Computational Mathematics 2015-02-08 © Science Publishing Group Z‎. ‎ Valizadeh-Gh E‎. ‎Khorram Linear Fractional Multi-Objective Optimization Problems Subject to Fuzzy Relational Equations with the Max-Average Composition 4 1 30 30 2015-02-08 2015-02-08 10.11648/j.acm.s.2015040102.15 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2015040102.15 © Science Publishing Group Numerical Solution of an Optimal Control Problem Governed by Two Dimensional Schrodinger Equation http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150402.11 In this study, the finite difference method is applied to an optimal control problem controlled by two functions which are in the coefficients of two-dimensional Schrodinger equation. Convergence of the finite difference approximation according to the functional is proved. We have used the implicit method for solving the two-dimensional Schrodinger equation. Although the implicit scheme obtained from solution of the system of the linear equations is generally numerically stable and convergent without time-step condition, the solution of considered equation is numerically stable with time-step condition, due to the gradient term. In this study, the finite difference method is applied to an optimal control problem controlled by two functions which are in the coefficients of two-dimensional Schrodinger equation. Convergence of the finite difference approximation according to the functional is proved. We have used the implicit method for solving the two-dimensional Schrodinger equation. Although the implicit scheme obtained from solution of the system of the linear equations is generally numerically stable and convergent without time-step condition, the solution of considered equation is numerically stable with time-step condition, due to the gradient term. Numerical Solution of an Optimal Control Problem Governed by Two Dimensional Schrodinger Equation doi:10.11648/j.acm.20150402.11 Applied and Computational Mathematics 2015-03-04 © Science Publishing Group Fatma Toyoglu Gabil Yagubov Numerical Solution of an Optimal Control Problem Governed by Two Dimensional Schrodinger Equation 4 2 38 38 2015-03-04 2015-03-04 10.11648/j.acm.20150402.11 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150402.11 © Science Publishing Group The Continuous Finite Element Methods for a Simple Case of Separable Hamiltonian Systems http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150402.12 Combined with the characteristics of separable Hamiltonian systems and the finite element methods of ordinary differential equations, we prove that the composition of linear, quadratic, cubic finite element methods are symplectic integrator to separable Hamiltonian systems, i.e. the symplectic condition is preserved exactly, but the energy is only approximately conservative after compound. These conclusions are confirmed by our numerical experiments. Combined with the characteristics of separable Hamiltonian systems and the finite element methods of ordinary differential equations, we prove that the composition of linear, quadratic, cubic finite element methods are symplectic integrator to separable Hamiltonian systems, i.e. the symplectic condition is preserved exactly, but the energy is only approximately conservative after compound. These conclusions are confirmed by our numerical experiments. The Continuous Finite Element Methods for a Simple Case of Separable Hamiltonian Systems doi:10.11648/j.acm.20150402.12 Applied and Computational Mathematics 2015-03-06 © Science Publishing Group Qiong Tang Luohua Liua Yujun Zheng The Continuous Finite Element Methods for a Simple Case of Separable Hamiltonian Systems 4 2 46 46 2015-03-06 2015-03-06 10.11648/j.acm.20150402.12 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150402.12 © Science Publishing Group A Particular Matrix, Its Inversion and Some Norms http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150402.13 In this note we study a new nn matrix of the form A=[a^(min⁡(i,j)-1) ]_(i,j=1)^n, where a1 is a real positive constant. We find determinant and inversion of this matrix and its Hadamard inverse. Then some bounds for the spectral norm of this matrix are presented. Finally we represent some properties of particular block diagonal matrices that their diagonal elements are these matrices. In this note we study a new nn matrix of the form A=[a^(min⁡(i,j)-1) ]_(i,j=1)^n, where a1 is a real positive constant. We find determinant and inversion of this matrix and its Hadamard inverse. Then some bounds for the spectral norm of this matrix are presented. Finally we represent some properties of particular block diagonal matrices that their diagonal elements are these matrices. A Particular Matrix, Its Inversion and Some Norms doi:10.11648/j.acm.20150402.13 Applied and Computational Mathematics 2015-03-19 © Science Publishing Group Seyyed Hossein Jafari-Petroudi Behzad Pirouz A Particular Matrix, Its Inversion and Some Norms 4 2 52 52 2015-03-19 2015-03-19 10.11648/j.acm.20150402.13 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150402.13 © Science Publishing Group A Mathematical Model for the Dynamics of Cholera with Control Measures http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150402.14 Cholera, an acute gastro-intestinal infection and a waterborne disease continues to emerge in developing countries and remains an important global health challenge. In this paper, we formulate a mathematical model that captures some essential dynamics of cholera transmission with public health educational campaigns, vaccination, sanitation and treatment as control strategies in limiting the disease. The reproduction numbers with single and combined controls are computed and compared with each other to assess the possible community benefits. Numerical simulation shows that in a unique control strategy, treatment yields the best results followed by education campaign, then sanitation and vaccination being the last. Furthermore, we noted that the control of cholera is very much better when we incorporated more than one strategy, in two controls the results were better than one strategy, and in three control strategies the results were far better than in two control strategies. Further simulations with all four interventions showed the best results among all combinations attained before. We performed sensitivity analysis on the key parameters that drive the disease dynamics in order to determine their relative importance to disease transmission and prevalence. Cholera, an acute gastro-intestinal infection and a waterborne disease continues to emerge in developing countries and remains an important global health challenge. In this paper, we formulate a mathematical model that captures some essential dynamics of cholera transmission with public health educational campaigns, vaccination, sanitation and treatment as control strategies in limiting the disease. The reproduction numbers with single and combined controls are computed and compared with each other to assess the possible community benefits. Numerical simulation shows that in a unique control strategy, treatment yields the best results followed by education campaign, then sanitation and vaccination being the last. Furthermore, we noted that the control of cholera is very much better when we incorporated more than one strategy, in two controls the results were better than one strategy, and in three control strategies the results were far better than in two control strategies. Further simulations with all four interventions showed the best results among all combinations attained before. We performed sensitivity analysis on the key parameters that drive the disease dynamics in order to determine their relative importance to disease transmission and prevalence. A Mathematical Model for the Dynamics of Cholera with Control Measures doi:10.11648/j.acm.20150402.14 Applied and Computational Mathematics 2015-03-21 © Science Publishing Group Stephen Edward Nkuba Nyerere A Mathematical Model for the Dynamics of Cholera with Control Measures 4 2 63 63 2015-03-21 2015-03-21 10.11648/j.acm.20150402.14 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150402.14 © Science Publishing Group A Galerkin Finite Element Method for Two-Point Boundary Value Problems of Ordinary Differential Equations http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150402.15 In this paper, we present a new method for solving two-point boundary value problem for certain ordinary differential equation. The two point boundary value problems have great importance in chemical engineering, deflection of beams etc. In this study, Galerkin finite element method is developed for inhomogeneous second-order ordinary differential equations. Several examples are solved to demonstrate the application of the finite element method. It is shown that the finite element method is simple, accurate and well behaved in the presence of singularities. In this paper, we present a new method for solving two-point boundary value problem for certain ordinary differential equation. The two point boundary value problems have great importance in chemical engineering, deflection of beams etc. In this study, Galerkin finite element method is developed for inhomogeneous second-order ordinary differential equations. Several examples are solved to demonstrate the application of the finite element method. It is shown that the finite element method is simple, accurate and well behaved in the presence of singularities. A Galerkin Finite Element Method for Two-Point Boundary Value Problems of Ordinary Differential Equations doi:10.11648/j.acm.20150402.15 Applied and Computational Mathematics 2015-03-21 © Science Publishing Group Gentian Zavalani A Galerkin Finite Element Method for Two-Point Boundary Value Problems of Ordinary Differential Equations 4 2 68 68 2015-03-21 2015-03-21 10.11648/j.acm.20150402.15 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150402.15 © Science Publishing Group Transformation of Nonlinear Mixture Chopped Stochastic Program Model http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150402.16 This paper describes a new approach to obtain the global optimization problem of nonlinear mixture chopped stochastic program model. The study focused on the issue of two-stage stochastic with the lack of nonlinearity, which is contained in the objective function and constraints. Variables in the first stage is worth a count, while the variable in the second stage is a mixture of chopped and continuous. Issues formulated by scenario-based representation. The approach used to complete the large scale nonlinear mix chopped program lifting unfounded variable value of the limit, forcing a variable-value basis chopped. Problems reduced is processed at the time of chopped variables held constant, and the changes made during discrete steps, in order to obtain a global optimal solution. This paper describes a new approach to obtain the global optimization problem of nonlinear mixture chopped stochastic program model. The study focused on the issue of two-stage stochastic with the lack of nonlinearity, which is contained in the objective function and constraints. Variables in the first stage is worth a count, while the variable in the second stage is a mixture of chopped and continuous. Issues formulated by scenario-based representation. The approach used to complete the large scale nonlinear mix chopped program lifting unfounded variable value of the limit, forcing a variable-value basis chopped. Problems reduced is processed at the time of chopped variables held constant, and the changes made during discrete steps, in order to obtain a global optimal solution. Transformation of Nonlinear Mixture Chopped Stochastic Program Model doi:10.11648/j.acm.20150402.16 Applied and Computational Mathematics 2015-03-30 © Science Publishing Group Togi Panjaitan Iryanto Iryanto Transformation of Nonlinear Mixture Chopped Stochastic Program Model 4 2 76 76 2015-03-30 2015-03-30 10.11648/j.acm.20150402.16 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150402.16 © Science Publishing Group On Fractional Order Influenza A Epidemic Model http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150402.17 This paper examines the fractional order of influenza using an epidemic model. The stability of disease-free and positive fixed points is explored and studied. The Adams-Bashforth-Moulton algorithm is employed to determine the solution and also simulate the system of differential equations. It is observed that Adams-Bashforth-Moulton method gives similar results as obtained in Runge-Kutta technique and ODE 45. This paper examines the fractional order of influenza using an epidemic model. The stability of disease-free and positive fixed points is explored and studied. The Adams-Bashforth-Moulton algorithm is employed to determine the solution and also simulate the system of differential equations. It is observed that Adams-Bashforth-Moulton method gives similar results as obtained in Runge-Kutta technique and ODE 45. On Fractional Order Influenza A Epidemic Model doi:10.11648/j.acm.20150402.17 Applied and Computational Mathematics 2015-03-30 © Science Publishing Group Bonyah Ebenezer On Fractional Order Influenza A Epidemic Model 4 2 82 82 2015-03-30 2015-03-30 10.11648/j.acm.20150402.17 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150402.17 © Science Publishing Group Power Assessment of the Human Ankle during the Stance Phase of Walking for Designing a Safe Active Prosthesis in Below-Knee Amputees http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2015040201.12 Many studies have been done on the biological human ankle and prosthesis replaced with this limb. Although some of these works targeted to design a prosthesis which mimics the behavior of biological ankle, additional system is required to support the elastic components; any of them have obviously introduced an active system in designing ankle prosthesis until now. In this study the power of the non-disabled human ankle joint was examined during the stance phase of walking in sagittal plane. The study aimed to better understand the ankle’s dynamic behavior for designing foot prosthesis with active mechanism. Kinematic and Kinetic data of the lower limb were collected from 18 healthy, young subjects (i.e. 6 females and 13 males) walking over a speed range of slow, normal and fast (i.e. 0.86 to 1.80 m/s). The ankle moment versus angle curves were plotted and total, mean and maximum values of powers were calculated for each trial. The results indicated that the total, mean and maximum values of the power could increase as the walking speed increased. The main findings of this study were the total, mean and maximum values of the power as a function of the linear velocity of walking. These results showed that the speed of 1.06 m/s was a critical velocity, below which the system was negative, showing energy consumer system, and above it the system was positive, suggesting generated energy. With the intent to design a prosthesis mimicking a biologic foot, an augmented system which is able to adjust the power to the speed is necessary. Many studies have been done on the biological human ankle and prosthesis replaced with this limb. Although some of these works targeted to design a prosthesis which mimics the behavior of biological ankle, additional system is required to support the elastic components; any of them have obviously introduced an active system in designing ankle prosthesis until now. In this study the power of the non-disabled human ankle joint was examined during the stance phase of walking in sagittal plane. The study aimed to better understand the ankle’s dynamic behavior for designing foot prosthesis with active mechanism. Kinematic and Kinetic data of the lower limb were collected from 18 healthy, young subjects (i.e. 6 females and 13 males) walking over a speed range of slow, normal and fast (i.e. 0.86 to 1.80 m/s). The ankle moment versus angle curves were plotted and total, mean and maximum values of powers were calculated for each trial. The results indicated that the total, mean and maximum values of the power could increase as the walking speed increased. The main findings of this study were the total, mean and maximum values of the power as a function of the linear velocity of walking. These results showed that the speed of 1.06 m/s was a critical velocity, below which the system was negative, showing energy consumer system, and above it the system was positive, suggesting generated energy. With the intent to design a prosthesis mimicking a biologic foot, an augmented system which is able to adjust the power to the speed is necessary. Power Assessment of the Human Ankle during the Stance Phase of Walking for Designing a Safe Active Prosthesis in Below-Knee Amputees doi:10.11648/j.acm.s.2015040201.12 Applied and Computational Mathematics 2015-03-02 © Science Publishing Group Sara Soltani Ch. Ali Esteki Power Assessment of the Human Ankle during the Stance Phase of Walking for Designing a Safe Active Prosthesis in Below-Knee Amputees 4 2 11 11 2015-03-02 2015-03-02 10.11648/j.acm.s.2015040201.12 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2015040201.12 © Science Publishing Group Comparing Two Meta-Heuristic Approaches for Solving Complex System Reliability Optimization http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2015040201.11 Using meta-heuristic approaches to solve reliability and redundancy allocation problems (RRAP) has become attractive for researchers in recent years. In this paper, an optimization model is presented to maximize system reliability and minimize system cost simultaneously for multi-state weighted k-out-of-n systems. The model tends to optimize system design and maintenance activities over functioning periods that provides a dynamic modeling. A recently developed meta-heuristic approach imperialist competitive algorithm (ICA) and genetic algorithm (GA) are used to solve the model. The computational results have been compared to find out which approach is more appropriate for solving complex system reliability optimization models. It is shown that GA can find the better solution while ICA is a faster approach. In addition, an investigation is done on different parameters of the ICA. Using meta-heuristic approaches to solve reliability and redundancy allocation problems (RRAP) has become attractive for researchers in recent years. In this paper, an optimization model is presented to maximize system reliability and minimize system cost simultaneously for multi-state weighted k-out-of-n systems. The model tends to optimize system design and maintenance activities over functioning periods that provides a dynamic modeling. A recently developed meta-heuristic approach imperialist competitive algorithm (ICA) and genetic algorithm (GA) are used to solve the model. The computational results have been compared to find out which approach is more appropriate for solving complex system reliability optimization models. It is shown that GA can find the better solution while ICA is a faster approach. In addition, an investigation is done on different parameters of the ICA. Comparing Two Meta-Heuristic Approaches for Solving Complex System Reliability Optimization doi:10.11648/j.acm.s.2015040201.11 Applied and Computational Mathematics 2015-03-02 © Science Publishing Group Hadi Akbarzade Khorshidi Sanaz Nikfalazar Comparing Two Meta-Heuristic Approaches for Solving Complex System Reliability Optimization 4 2 6 6 2015-03-02 2015-03-02 10.11648/j.acm.s.2015040201.11 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2015040201.11 © Science Publishing Group An Hermitian Boundary Integral Hybrid Formulation for Nonlinear Fisher-Type Equations http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150403.11 This paper explores the application of an Hermitian hybrid boundary integral formulation for handling Fisher-type equations. The Hermite system incorporates the problem unknowns with their space derivatives and as a consequence produces a relatively larger coefficient matrix than the corresponding linear approximation. However by adopting a finite element-like integral numerical procedure, the modified boundary integral formulation otherwise known as the Green element method (GEM) produces slender and sparse coefficient matrices which enhance an efficient solution algorithm. The resulting equations appear in the form of local elemental integral equations whose contributions add up to the coefficient matrix. This process is amply simplified in the Green element method due to the presence of the source point inside an element thereby encouraging integration to be carried out locally and accurately. This so called ‘divide and conquer’ approach is significantly much better than working with the entire matrix especially for nonlinear problems where an encounter with the problem domain can not be totally avoided. Numerical tests are carried out to illustrate the utility of this technique by comparing results obtained from both the Hermite and non-Hermite discretizations. It is observed that for each of the problems tested, not only do the results agree with those from literature, it took the Hermitian approximation fewer number of elements to achieve the same level of accuracy than its non-Hermitian version. However, application of same technique to multi-dimensional problems may not be as straightforward due to the construction and storing of the Hermite system matrix which will not only involve non-trivial operations in terms of a high computational cost but also a compromise in the quality of the numerical solution arising from significant round-off errors. This paper explores the application of an Hermitian hybrid boundary integral formulation for handling Fisher-type equations. The Hermite system incorporates the problem unknowns with their space derivatives and as a consequence produces a relatively larger coefficient matrix than the corresponding linear approximation. However by adopting a finite element-like integral numerical procedure, the modified boundary integral formulation otherwise known as the Green element method (GEM) produces slender and sparse coefficient matrices which enhance an efficient solution algorithm. The resulting equations appear in the form of local elemental integral equations whose contributions add up to the coefficient matrix. This process is amply simplified in the Green element method due to the presence of the source point inside an element thereby encouraging integration to be carried out locally and accurately. This so called ‘divide and conquer’ approach is significantly much better than working with the entire matrix especially for nonlinear problems where an encounter with the problem domain can not be totally avoided. Numerical tests are carried out to illustrate the utility of this technique by comparing results obtained from both the Hermite and non-Hermite discretizations. It is observed that for each of the problems tested, not only do the results agree with those from literature, it took the Hermitian approximation fewer number of elements to achieve the same level of accuracy than its non-Hermitian version. However, application of same technique to multi-dimensional problems may not be as straightforward due to the construction and storing of the Hermite system matrix which will not only involve non-trivial operations in terms of a high computational cost but also a compromise in the quality of the numerical solution arising from significant round-off errors. An Hermitian Boundary Integral Hybrid Formulation for Nonlinear Fisher-Type Equations doi:10.11648/j.acm.20150403.11 Applied and Computational Mathematics 2015-04-20 © Science Publishing Group Okey Oseloka Onyejekwe An Hermitian Boundary Integral Hybrid Formulation for Nonlinear Fisher-Type Equations 4 3 99 99 2015-04-20 2015-04-20 10.11648/j.acm.20150403.11 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150403.11 © Science Publishing Group Study on Dynamic Risk Measurement Based on ARMA-GJR-AL Model http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150403.13 This paper established the ARMA-GJR-AL model of dynamic risk VaR and CVaR measurement. Considering from aspects of the correlation and volatility and residual distribution characteristics, studying the dynamic risk measures of VaR and CVaR based on ARMA-GJR-AL model. Through empirical research, Risk prediction and accuracy of inspection are given of the Shanghai stock market and the New York stock market. And we study the effectiveness of the model. The results show that the dynamic risk measurement model based on AL distribution is more reasonable and applicability, so it can effectively measure risk. This paper established the ARMA-GJR-AL model of dynamic risk VaR and CVaR measurement. Considering from aspects of the correlation and volatility and residual distribution characteristics, studying the dynamic risk measures of VaR and CVaR based on ARMA-GJR-AL model. Through empirical research, Risk prediction and accuracy of inspection are given of the Shanghai stock market and the New York stock market. And we study the effectiveness of the model. The results show that the dynamic risk measurement model based on AL distribution is more reasonable and applicability, so it can effectively measure risk. Study on Dynamic Risk Measurement Based on ARMA-GJR-AL Model doi:10.11648/j.acm.20150403.13 Applied and Computational Mathematics 2015-04-28 © Science Publishing Group Hong Zhang Li Zhou Jian Guo Study on Dynamic Risk Measurement Based on ARMA-GJR-AL Model 4 3 121 121 2015-04-28 2015-04-28 10.11648/j.acm.20150403.13 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150403.13 © Science Publishing Group Exact and Solitary Wave Solutions to the Generalized Fifth-order KdV Equation by Using the Modified Simple Equation Method http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150403.14 Although the modified simple equation (MSE) method effectively provides exact traveling wave solutions to nonlinear evolution equations (NLEEs) in the field of engineering and mathematical physics, it has some limitations. When the balance number is greater than one, usually the method does not give any solution. In this article, we have exposed a process how to implement the MSE method to solve NLEEs for balance number two. In order to verify the process, the generalized fifth-order KdV equation has been solved. By means of this scheme, we found some fresh traveling wave solutions to the above mentioned equation. When the parameters receive special values, solitary wave solutions are derived from the exact solutions. We analyze the solitary wave properties by the graphs of the solutions. This shows the validity, usefulness, and necessity of the process. Although the modified simple equation (MSE) method effectively provides exact traveling wave solutions to nonlinear evolution equations (NLEEs) in the field of engineering and mathematical physics, it has some limitations. When the balance number is greater than one, usually the method does not give any solution. In this article, we have exposed a process how to implement the MSE method to solve NLEEs for balance number two. In order to verify the process, the generalized fifth-order KdV equation has been solved. By means of this scheme, we found some fresh traveling wave solutions to the above mentioned equation. When the parameters receive special values, solitary wave solutions are derived from the exact solutions. We analyze the solitary wave properties by the graphs of the solutions. This shows the validity, usefulness, and necessity of the process. Exact and Solitary Wave Solutions to the Generalized Fifth-order KdV Equation by Using the Modified Simple Equation Method doi:10.11648/j.acm.20150403.14 Applied and Computational Mathematics 2015-05-01 © Science Publishing Group M. Ashrafuzzaman Khan M. Ali Akbar Exact and Solitary Wave Solutions to the Generalized Fifth-order KdV Equation by Using the Modified Simple Equation Method 4 3 129 129 2015-05-01 2015-05-01 10.11648/j.acm.20150403.14 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150403.14 © Science Publishing Group Empirical Analysis of the Fractal Features Analysis on London Gold Futures Market http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150403.15 In this paper, we study the fractal characteristics of the futures market. We take the empirical study on London Gold Futures yield by Rescaled Range Analysis, analyzing the fractal characteristics of the futures market. We further determine fractal characteristics and the structure of the nonlinear time series through random disturb the original time series observation sequence. The result of R/S analysis shows that the movement of market prices of the financial markets has obvious nonperiodic circle, with Hurst index large than 0.5 and C (t) large than 0, which indicates clear fractal properties. And the result also shows that the influence of price limit on the fractal properties of London Gold Futures Market is very remarkable. In this paper, we study the fractal characteristics of the futures market. We take the empirical study on London Gold Futures yield by Rescaled Range Analysis, analyzing the fractal characteristics of the futures market. We further determine fractal characteristics and the structure of the nonlinear time series through random disturb the original time series observation sequence. The result of R/S analysis shows that the movement of market prices of the financial markets has obvious nonperiodic circle, with Hurst index large than 0.5 and C (t) large than 0, which indicates clear fractal properties. And the result also shows that the influence of price limit on the fractal properties of London Gold Futures Market is very remarkable. Empirical Analysis of the Fractal Features Analysis on London Gold Futures Market doi:10.11648/j.acm.20150403.15 Applied and Computational Mathematics 2015-05-05 © Science Publishing Group Hong Zhang Li Zhou Jian Guo Empirical Analysis of the Fractal Features Analysis on London Gold Futures Market 4 3 134 134 2015-05-05 2015-05-05 10.11648/j.acm.20150403.15 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150403.15 © Science Publishing Group Hydrogen-Natural Gas Mixture Leak Detection Using Reduced Order Modelling http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150403.16 Transient pressure wave detection analysis to detect the location of leakage on a pipeline containinghydrogen-natural gas mixture is presented. The transient pressure wave is generated either by rapid or sudden closure of the downstream shut-off valve. The governing equations of unsteady, compressible and isothermal one-dimensional flow are solved using the reduced order modelling technique. The solutions obtained when the transient condition is generated using the rapid closure valve show good agreement with published results. When the sudden closure valve is considered, the transient pressure, celerity wave, mass flux and the amount of leak discharge are shown to increase when the hydrogen mass ratio is increased. The amount of leak discharge which is calculated based on the computed celerity and pressure waves is found to be dependent on the leak positions. Transient pressure wave detection analysis to detect the location of leakage on a pipeline containinghydrogen-natural gas mixture is presented. The transient pressure wave is generated either by rapid or sudden closure of the downstream shut-off valve. The governing equations of unsteady, compressible and isothermal one-dimensional flow are solved using the reduced order modelling technique. The solutions obtained when the transient condition is generated using the rapid closure valve show good agreement with published results. When the sudden closure valve is considered, the transient pressure, celerity wave, mass flux and the amount of leak discharge are shown to increase when the hydrogen mass ratio is increased. The amount of leak discharge which is calculated based on the computed celerity and pressure waves is found to be dependent on the leak positions. Hydrogen-Natural Gas Mixture Leak Detection Using Reduced Order Modelling doi:10.11648/j.acm.20150403.16 Applied and Computational Mathematics 2015-05-16 © Science Publishing Group Norazlina Subani Norsarahaida Amin Baba Galadima Agaie Hydrogen-Natural Gas Mixture Leak Detection Using Reduced Order Modelling 4 3 144 144 2015-05-16 2015-05-16 10.11648/j.acm.20150403.16 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150403.16 © Science Publishing Group Meshless Local Petrov-Galerkin Method for Scattering from 2-D Rectangular Cavities in a Ground Plane http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150403.17 In this paper, we develop the meshless local Petrov-Galerkin formulation of the scattering from rectangular cavities embedded in a ground plane. The electromagnetic scattering by the cavity is governed by the Helmholtz equation along with Sommerfeld&apos;s radiation conditions imposed at infinity. The MLPG method is a truly meshless method wherein no elements or background cells are needed, in either the interpolation or integration. Based on local weak form and the moving least square (MLS) approximation, this truly meshless method is applied to solve the scattering problem. The results of numerical experiments have shown the efficiency and accuracy of the proposed method. In this paper, we develop the meshless local Petrov-Galerkin formulation of the scattering from rectangular cavities embedded in a ground plane. The electromagnetic scattering by the cavity is governed by the Helmholtz equation along with Sommerfeld&apos;s radiation conditions imposed at infinity. The MLPG method is a truly meshless method wherein no elements or background cells are needed, in either the interpolation or integration. Based on local weak form and the moving least square (MLS) approximation, this truly meshless method is applied to solve the scattering problem. The results of numerical experiments have shown the efficiency and accuracy of the proposed method. Meshless Local Petrov-Galerkin Method for Scattering from 2-D Rectangular Cavities in a Ground Plane doi:10.11648/j.acm.20150403.17 Applied and Computational Mathematics 2015-05-23 © Science Publishing Group Meiling Zhao Li Li Meshless Local Petrov-Galerkin Method for Scattering from 2-D Rectangular Cavities in a Ground Plane 4 3 151 151 2015-05-23 2015-05-23 10.11648/j.acm.20150403.17 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150403.17 © Science Publishing Group Second Law Analysis of Buoyancy Driven Unsteady Channel Flow of Nanofluids with Convective Cooling http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150403.12 We investigate the combined effects of buoyancy force and convective cooling on entropy generation in unsteady channel flow of water based nanofluids containing Copper (Cu) and Alumina (Al2O3) as nanoparticles. Both first and second laws of thermodynamics are utilised to analyze the model problem. Using a semi discretization finite difference method together with Runge-Kutta Fehlberg integration scheme, the governing partial differential equations are solved numerically. Graphical results on the effects of parameter variation on velocity, temperature, skin friction, Nusselt number, entropy generation rate, irreversibility ratio and Bejan number are presented and discussed. We investigate the combined effects of buoyancy force and convective cooling on entropy generation in unsteady channel flow of water based nanofluids containing Copper (Cu) and Alumina (Al2O3) as nanoparticles. Both first and second laws of thermodynamics are utilised to analyze the model problem. Using a semi discretization finite difference method together with Runge-Kutta Fehlberg integration scheme, the governing partial differential equations are solved numerically. Graphical results on the effects of parameter variation on velocity, temperature, skin friction, Nusselt number, entropy generation rate, irreversibility ratio and Bejan number are presented and discussed. Second Law Analysis of Buoyancy Driven Unsteady Channel Flow of Nanofluids with Convective Cooling doi:10.11648/j.acm.20150403.12 Applied and Computational Mathematics 2015-04-22 © Science Publishing Group Michael Hamza Mkwizu Oluwole Daniel Makinde Yaw Nkansah-Gyekye Second Law Analysis of Buoyancy Driven Unsteady Channel Flow of Nanofluids with Convective Cooling 4 3 115 115 2015-04-22 2015-04-22 10.11648/j.acm.20150403.12 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150403.12 © Science Publishing Group Volterra Integral Equations with Vanishing Delay http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150403.18 In this article, we use a Chebyshev spectral-collocation method to solve the Volterra integral equations with vanishing delay. Then a rigorous error analysis provided by the proposed method shows that the numerical error decay exponentially in the infinity norm and in the Chebyshev weighted Hilbert space norm. Numerical results are presented, which confirm the theoretical predicition of the exponential rate of convergence. In this article, we use a Chebyshev spectral-collocation method to solve the Volterra integral equations with vanishing delay. Then a rigorous error analysis provided by the proposed method shows that the numerical error decay exponentially in the infinity norm and in the Chebyshev weighted Hilbert space norm. Numerical results are presented, which confirm the theoretical predicition of the exponential rate of convergence. Volterra Integral Equations with Vanishing Delay doi:10.11648/j.acm.20150403.18 Applied and Computational Mathematics 2015-05-27 © Science Publishing Group Xiaoxuan Li Weishan Zheng Jiena Wu Volterra Integral Equations with Vanishing Delay 4 3 161 161 2015-05-27 2015-05-27 10.11648/j.acm.20150403.18 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150403.18 © Science Publishing Group Taylor-SPH Method for Viscoplastic Damage Material http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150403.19 In this paper, we apply the meshless method Taylor-SPH to solve the propagation of shock wave in viscoplastic material coupled to damage. The equations are written in terms of stress and velocity. Taylor-SPH method is based on the Taylor series expansion of stress and velocity and on the corrected SPH approximation. Numerical stability of the method as a function of the smoothing length and the Courant number is analysed in the elastic case. The Taylor-SPH method is used to simulate localization in a one dimensional viscoplastic damage problem. The numerical results show that the Taylor-SPH method is able to model localization phenomena in viscoplastic damage material without lose of hyperbolicity of partial differential equations. In this paper, we apply the meshless method Taylor-SPH to solve the propagation of shock wave in viscoplastic material coupled to damage. The equations are written in terms of stress and velocity. Taylor-SPH method is based on the Taylor series expansion of stress and velocity and on the corrected SPH approximation. Numerical stability of the method as a function of the smoothing length and the Courant number is analysed in the elastic case. The Taylor-SPH method is used to simulate localization in a one dimensional viscoplastic damage problem. The numerical results show that the Taylor-SPH method is able to model localization phenomena in viscoplastic damage material without lose of hyperbolicity of partial differential equations. Taylor-SPH Method for Viscoplastic Damage Material doi:10.11648/j.acm.20150403.19 Applied and Computational Mathematics 2015-05-29 © Science Publishing Group Hajar Idder Mokhtar Mabssout Taylor-SPH Method for Viscoplastic Damage Material 4 3 173 173 2015-05-29 2015-05-29 10.11648/j.acm.20150403.19 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150403.19 © Science Publishing Group Modelling Infectiology and Optimal Control of Dengue Epidemic http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150403.21 A mathematical model is presented to examine the interaction between human and vector populations. The model consists of five control strategies i.e. campaign aimed in educating careless individuals as a mean of minimizing or eliminating mosquito-human contact, control effort aimed at reducing mosquito-human contact, the control effort for removing vector breeding places, insecticide application and the control effort aimed at reducing the maturation rate from larvae to adult in order to reduce the number of infected individual. Optimal Control (OC) approach is used in order to find the best strategy to fight the disease and minimize the cost. A mathematical model is presented to examine the interaction between human and vector populations. The model consists of five control strategies i.e. campaign aimed in educating careless individuals as a mean of minimizing or eliminating mosquito-human contact, control effort aimed at reducing mosquito-human contact, the control effort for removing vector breeding places, insecticide application and the control effort aimed at reducing the maturation rate from larvae to adult in order to reduce the number of infected individual. Optimal Control (OC) approach is used in order to find the best strategy to fight the disease and minimize the cost. Modelling Infectiology and Optimal Control of Dengue Epidemic doi:10.11648/j.acm.20150403.21 Applied and Computational Mathematics 2015-06-05 © Science Publishing Group Laurencia Ndelamo Massawe Estomih S. Massawe Oluwole Daniel Makinde Modelling Infectiology and Optimal Control of Dengue Epidemic 4 3 191 191 2015-06-05 2015-06-05 10.11648/j.acm.20150403.21 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150403.21 © Science Publishing Group Modelling Infectiology of Dengue Epidemic http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150403.22 In this paper a mathematical model for the transmission dynamics of dengue fever disease is presented. We present a SITR (susceptible, infected, treated, recovery) and ASI (aquatic, susceptible, infected) epidemic model to describe the interaction between human and dengue fever mosquito populations. In order to assess the transmission of Dengue fever disease, the susceptible population is divided into two, namely, careful and careless human susceptible population. The model presents four possible equilibria: two disease-free and two endemic equilibrium.The results show that the disease-free equilibrium point is locally and globally asymptotically stable if the reproduction number is less than unity. Endemic equilibrium point is locally and globally asymptotically stable under certain conditions using additive compound matrix and Lyapunov method respectively. Sensitivity analysis of the model is implemented in order to investigate the sensitivity of certain key parameters of dengue fever disease with treatment, Careful and Careless Susceptibles on the transmission of Dengue fever Disease. In this paper a mathematical model for the transmission dynamics of dengue fever disease is presented. We present a SITR (susceptible, infected, treated, recovery) and ASI (aquatic, susceptible, infected) epidemic model to describe the interaction between human and dengue fever mosquito populations. In order to assess the transmission of Dengue fever disease, the susceptible population is divided into two, namely, careful and careless human susceptible population. The model presents four possible equilibria: two disease-free and two endemic equilibrium.The results show that the disease-free equilibrium point is locally and globally asymptotically stable if the reproduction number is less than unity. Endemic equilibrium point is locally and globally asymptotically stable under certain conditions using additive compound matrix and Lyapunov method respectively. Sensitivity analysis of the model is implemented in order to investigate the sensitivity of certain key parameters of dengue fever disease with treatment, Careful and Careless Susceptibles on the transmission of Dengue fever Disease. Modelling Infectiology of Dengue Epidemic doi:10.11648/j.acm.20150403.22 Applied and Computational Mathematics 2015-06-08 © Science Publishing Group Laurencia Ndelamo Massawe Estomih S. Massawe Oluwole Daniel Makinde Modelling Infectiology of Dengue Epidemic 4 3 206 206 2015-06-08 2015-06-08 10.11648/j.acm.20150403.22 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150403.22 © Science Publishing Group Option Pricing Variance Reduction Techniques Under the Levy Process http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150403.20 After the 2008 financial crisis, the global derivatives trading volume in options proportion is growing, more and more investors build portfolios using options to hedge or arbitrage, our futures and stock options will soon open. Theoretical research of options is also changing, option pricing models under Levy processes developed rapidly. In this context, a review of the China&apos;s warrants market and the introduction of option pricing models can not only help us to reflect Chinese financial derivatives market regulation, but also to explore the option pricing theory for China`s financial market environment. In the framework of Monte Carlo simulation pricing, we established mufti-Levy process option pricing models, the structural model for the given parameter estimation and risk-neutral adjustment method are discussed, the last part of this chapter is an empirical analysis of China warrants trading data in order to prove the validate of Levy models. Key word: Levy stochastic processes, option pricing models, Chinese warrants market, American option pricing, risk-neutral adjustment, variance reduction techniques. After the 2008 financial crisis, the global derivatives trading volume in options proportion is growing, more and more investors build portfolios using options to hedge or arbitrage, our futures and stock options will soon open. Theoretical research of options is also changing, option pricing models under Levy processes developed rapidly. In this context, a review of the China&apos;s warrants market and the introduction of option pricing models can not only help us to reflect Chinese financial derivatives market regulation, but also to explore the option pricing theory for China`s financial market environment. In the framework of Monte Carlo simulation pricing, we established mufti-Levy process option pricing models, the structural model for the given parameter estimation and risk-neutral adjustment method are discussed, the last part of this chapter is an empirical analysis of China warrants trading data in order to prove the validate of Levy models. Key word: Levy stochastic processes, option pricing models, Chinese warrants market, American option pricing, risk-neutral adjustment, variance reduction techniques. Option Pricing Variance Reduction Techniques Under the Levy Process doi:10.11648/j.acm.20150403.20 Applied and Computational Mathematics 2015-05-29 © Science Publishing Group Li Zhou Hong Zhang Jian Guo Shucong Ming Option Pricing Variance Reduction Techniques Under the Levy Process 4 3 180 180 2015-05-29 2015-05-29 10.11648/j.acm.20150403.20 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150403.20 © Science Publishing Group Hedging Stock Options Using Futures Contracts on the Stock http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150403.24 The aim of this paper is to present the price and replicating strategy for an European option on spot (or cash) underlier with continuous dividend yield, when the instrument used in the dynamic hedging of the option is a futures contract on the respective underlier. It formalizes the heuristic practice among option traders to replicate options on a stock index using futures on the respective stock index and investigates weather the obtained results differ significantly from what they would get using the actual stock index, as required by Black-Scholes pricing. Heuristically, the substitution is supported by index and futures prices being close, at least for small dividends and time to maturity. Our method is to express this practice in accounting terms, derive the self-financing portfolio dynamics and then the closed form option price and delta. Finally, run numerical simulations and compare results obtained by Black-Scholes versus our approach. Results show both the price and delta formulas differ from Black-Scholes, however numeric simulation doesn’t yield high enough differences to warrant obvious arbitrage, meaning that while not rigorously exact, the approximation is good enough for most practical use cases. The aim of this paper is to present the price and replicating strategy for an European option on spot (or cash) underlier with continuous dividend yield, when the instrument used in the dynamic hedging of the option is a futures contract on the respective underlier. It formalizes the heuristic practice among option traders to replicate options on a stock index using futures on the respective stock index and investigates weather the obtained results differ significantly from what they would get using the actual stock index, as required by Black-Scholes pricing. Heuristically, the substitution is supported by index and futures prices being close, at least for small dividends and time to maturity. Our method is to express this practice in accounting terms, derive the self-financing portfolio dynamics and then the closed form option price and delta. Finally, run numerical simulations and compare results obtained by Black-Scholes versus our approach. Results show both the price and delta formulas differ from Black-Scholes, however numeric simulation doesn’t yield high enough differences to warrant obvious arbitrage, meaning that while not rigorously exact, the approximation is good enough for most practical use cases. Hedging Stock Options Using Futures Contracts on the Stock doi:10.11648/j.acm.20150403.24 Applied and Computational Mathematics 2015-06-16 © Science Publishing Group Mihai Grigore Bunea Domsa Hedging Stock Options Using Futures Contracts on the Stock 4 3 219 219 2015-06-16 2015-06-16 10.11648/j.acm.20150403.24 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150403.24 © Science Publishing Group Some Convalescent Methods for the Solution of Systems of Linear Equations http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150403.23 In a variety of problems in the fields of physical sciences, engineering, economics, etc., we are led to systems of linear equations, Ax = b, comprising n linear equations in n unknowns x1, x2, …, xn, where A = [aij] is an nxn coefficient matrix, and x = [x1 x2 . . .xn]T, b = [b1 b2 . . .bn]T are the column vectors. There are many analytical as well as numerical methods[1}–  to solve such systems of equations, including Gauss elimination method, and its modifications namely Doolittle’s method, Crout’s method and Cholesky’s method, which employ LU-decomposition method, where L = [iij] and u = [uij] are the lower and upper triangular matrices respectively. The LU-decomposition method was first introduced by the mathematician Alan M. Turing- in 1948. Here, in this paper we have made an effort to modify the existing LU-decomposition methods to solve the above mentioned system Ax = b, with the least possible endeavour. It may be seen that the Gauss elimination method, , ,  needs about 2n3/3 operations, while Doolittle’s and Crout’s methods require n2 operations. Accordingly, in these methods we are required to evaluate n2 number of unknown elements of the L and U matrices. Moreover, Cholesky’s method requires 2n2/3 operations. Accordingly this method requires evaluation of 2n2/3 number of unknown elements of the L and U matrices But, in contrast, the improved Doolittle’s, Crout’s and Cholesky’s methods presented in this paper require evaluation of only (n–1)2 number of unknown elements of the L and U matrices. Moreover, an innovative method is also presented in this paper which requires evaluation of even less number of unknown elements of the L and U matrices. In this method we need to evaluate only (n–2)2 number of the said unknown elements. Thus, by employing these methods, the computational time and effort required for the purpose can substantially be reduced. In a variety of problems in the fields of physical sciences, engineering, economics, etc., we are led to systems of linear equations, Ax = b, comprising n linear equations in n unknowns x1, x2, …, xn, where A = [aij] is an nxn coefficient matrix, and x = [x1 x2 . . .xn]T, b = [b1 b2 . . .bn]T are the column vectors. There are many analytical as well as numerical methods[1}–  to solve such systems of equations, including Gauss elimination method, and its modifications namely Doolittle’s method, Crout’s method and Cholesky’s method, which employ LU-decomposition method, where L = [iij] and u = [uij] are the lower and upper triangular matrices respectively. The LU-decomposition method was first introduced by the mathematician Alan M. Turing- in 1948. Here, in this paper we have made an effort to modify the existing LU-decomposition methods to solve the above mentioned system Ax = b, with the least possible endeavour. It may be seen that the Gauss elimination method, , ,  needs about 2n3/3 operations, while Doolittle’s and Crout’s methods require n2 operations. Accordingly, in these methods we are required to evaluate n2 number of unknown elements of the L and U matrices. Moreover, Cholesky’s method requires 2n2/3 operations. Accordingly this method requires evaluation of 2n2/3 number of unknown elements of the L and U matrices But, in contrast, the improved Doolittle’s, Crout’s and Cholesky’s methods presented in this paper require evaluation of only (n–1)2 number of unknown elements of the L and U matrices. Moreover, an innovative method is also presented in this paper which requires evaluation of even less number of unknown elements of the L and U matrices. In this method we need to evaluate only (n–2)2 number of the said unknown elements. Thus, by employing these methods, the computational time and effort required for the purpose can substantially be reduced. Some Convalescent Methods for the Solution of Systems of Linear Equations doi:10.11648/j.acm.20150403.23 Applied and Computational Mathematics 2015-06-10 © Science Publishing Group M. Rafique Sidra Ayub Some Convalescent Methods for the Solution of Systems of Linear Equations 4 3 213 213 2015-06-10 2015-06-10 10.11648/j.acm.20150403.23 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150403.23 © Science Publishing Group Ill-Posed Algebraic Systems with Noise Data http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150403.25 Finding a numerical solution of linear algebraic equations is known to present an ill-posed in the sense that small perturbation in the right hand side may lead to large errors in the solution. It is important to verify the accuracy of an approximate solution by taking into account all possible errors in the elements of the matrix, and of the vector at the right hand side as well as roundoff errors. There may be computational difficulties with ill-posed systems as well. If to apply standard methods such as the method of Gauss elimination to such systems it may be not possible to obtain the correct solution though discrepancy can be less accuracy of data errors. Besides, a small discrepancy will not always guarantee proximity to a correct solution. Actually there is no need for preliminary assessment whether a given system of linear algebraic equations is inherently ill-conditioned or well-conditioned. In this paper we consider a new approach to the solution of algebraic systems, which is based on statistical effect in matrices of big order. It will be shown that the conditionality of the systems of equation may change with a high probability, if the matrix distorted by random noise. After applying some standard methods, we may introduce the received &quot;chaotic&quot; solution is used as a source of a priori information a more general variational problem. Finding a numerical solution of linear algebraic equations is known to present an ill-posed in the sense that small perturbation in the right hand side may lead to large errors in the solution. It is important to verify the accuracy of an approximate solution by taking into account all possible errors in the elements of the matrix, and of the vector at the right hand side as well as roundoff errors. There may be computational difficulties with ill-posed systems as well. If to apply standard methods such as the method of Gauss elimination to such systems it may be not possible to obtain the correct solution though discrepancy can be less accuracy of data errors. Besides, a small discrepancy will not always guarantee proximity to a correct solution. Actually there is no need for preliminary assessment whether a given system of linear algebraic equations is inherently ill-conditioned or well-conditioned. In this paper we consider a new approach to the solution of algebraic systems, which is based on statistical effect in matrices of big order. It will be shown that the conditionality of the systems of equation may change with a high probability, if the matrix distorted by random noise. After applying some standard methods, we may introduce the received &quot;chaotic&quot; solution is used as a source of a priori information a more general variational problem. Ill-Posed Algebraic Systems with Noise Data doi:10.11648/j.acm.20150403.25 Applied and Computational Mathematics 2015-06-19 © Science Publishing Group Vladimir V. Ternovski Mikhail M. Khapaev Alexander S. Grushicin Ill-Posed Algebraic Systems with Noise Data 4 3 224 224 2015-06-19 2015-06-19 10.11648/j.acm.20150403.25 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150403.25 © Science Publishing Group From Integral Representation Method (IRM) to Generalized Integral Representation Method (GIRM) http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2015040301.11 Integral Representation Method (IRM) is one of convenient methods to solve Initial and Boundary Value Problems (IBVP). It can be applied to irregular mesh, and the solution is stable and accurate. However, it was originally developed for linear equations with known fundamental solutions. In order to apply to general nonlinear equations, we must generalize the method. In the present paper, a generalization of IRM (GIRM) is discussed and applied to specific problems and the numerical solutions obtained. The numerical results are stable and accurate. The generalized method is called Generalized Integral Representation Method (GIRM). Brief explanations on the relationships with other numerical methods are also given. Integral Representation Method (IRM) is one of convenient methods to solve Initial and Boundary Value Problems (IBVP). It can be applied to irregular mesh, and the solution is stable and accurate. However, it was originally developed for linear equations with known fundamental solutions. In order to apply to general nonlinear equations, we must generalize the method. In the present paper, a generalization of IRM (GIRM) is discussed and applied to specific problems and the numerical solutions obtained. The numerical results are stable and accurate. The generalized method is called Generalized Integral Representation Method (GIRM). Brief explanations on the relationships with other numerical methods are also given. From Integral Representation Method (IRM) to Generalized Integral Representation Method (GIRM) doi:10.11648/j.acm.s.2015040301.11 Applied and Computational Mathematics 2015-02-12 © Science Publishing Group Hiroshi Isshiki From Integral Representation Method (IRM) to Generalized Integral Representation Method (GIRM) 4 3 14 14 2015-02-12 2015-02-12 10.11648/j.acm.s.2015040301.11 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2015040301.11 © Science Publishing Group Application of Generalized Integral Representation (GIRM) Method to Fluid Dynamic Motion of Gas or Particles in Cosmic Space Driven by Gravitational Force http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2015040301.12 Some aspect of the motion of gas or vast-number-of-particles distributed in cosmic space under action of the gravitational force may be treated as a fluid dynamic motion without pressure. Generalized Integral representation Method (GIRM) is applied to fluid dynamic motion of gas or particles to obtain the accurate numerical solutions. In the present theory, the relativistic effects are neglected. The numerical results by GIRM are compared with the solutions by Finite Difference Method (FDM). Spreading and merging of gas or particles and effects of initial velocity distribution are studied numerically. GIRM solutions give reasonable and accurate solutions. Some aspect of the motion of gas or vast-number-of-particles distributed in cosmic space under action of the gravitational force may be treated as a fluid dynamic motion without pressure. Generalized Integral representation Method (GIRM) is applied to fluid dynamic motion of gas or particles to obtain the accurate numerical solutions. In the present theory, the relativistic effects are neglected. The numerical results by GIRM are compared with the solutions by Finite Difference Method (FDM). Spreading and merging of gas or particles and effects of initial velocity distribution are studied numerically. GIRM solutions give reasonable and accurate solutions. Application of Generalized Integral Representation (GIRM) Method to Fluid Dynamic Motion of Gas or Particles in Cosmic Space Driven by Gravitational Force doi:10.11648/j.acm.s.2015040301.12 Applied and Computational Mathematics 2015-02-12 © Science Publishing Group Hiroshi Isshiki Toshio Takiya Hideyuki Niizato Application of Generalized Integral Representation (GIRM) Method to Fluid Dynamic Motion of Gas or Particles in Cosmic Space Driven by Gravitational Force 4 3 39 39 2015-02-12 2015-02-12 10.11648/j.acm.s.2015040301.12 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2015040301.12 © Science Publishing Group Effects of Generalized Fundamental Solution (GFS) on Generalized Integral Representation Method (GIRM) http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2015040301.13 Integral Representation Method (IRM) is one of convenient methods to solve Initial and Boundary Value Problems (IBVP). It can be applied to irregular mesh, and the solution is stable and accurate. IRM is developed to Generalized Integral Representation Method (GIRM) to treat any kinds of problems including nonlinear problems. In GIRM, Generalized Fundamental Solution (GFS) is used instead of Fundamental Solution (FS) in IRM. Since GFS is not limited to one, the effects of individual GFSs must be clarified. The continuity of GFS is related to the characteristics of individual GFSs. Integral Representation Method (IRM) is one of convenient methods to solve Initial and Boundary Value Problems (IBVP). It can be applied to irregular mesh, and the solution is stable and accurate. IRM is developed to Generalized Integral Representation Method (GIRM) to treat any kinds of problems including nonlinear problems. In GIRM, Generalized Fundamental Solution (GFS) is used instead of Fundamental Solution (FS) in IRM. Since GFS is not limited to one, the effects of individual GFSs must be clarified. The continuity of GFS is related to the characteristics of individual GFSs. Effects of Generalized Fundamental Solution (GFS) on Generalized Integral Representation Method (GIRM) doi:10.11648/j.acm.s.2015040301.13 Applied and Computational Mathematics 2015-03-13 © Science Publishing Group Hiroshi Isshiki Effects of Generalized Fundamental Solution (GFS) on Generalized Integral Representation Method (GIRM) 4 3 51 51 2015-03-13 2015-03-13 10.11648/j.acm.s.2015040301.13 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2015040301.13 © Science Publishing Group Application of the Generalized Integral Representation Method (GIRM) to Tidal Wave Propagation http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2015040301.14 Integral Representation Method (IRM) is one of convenient methods to solve Initial and Boundary Value Problems (IBVP). It can be applied to irregular mesh, and the solution is stable and accurate. IRM is developed to Generalized Integral Representation Method (GIRM) to treat any kinds of problems including nonlinear problems. In GIRM, Generalized Fundamental Solution (GFS) is used instead of Fundamental Solution (FS) in IRM. We can use a variety of GFSs in GIRM. The effects of typical GFSs are investigated. In the present paper, an application of GIRM to tidal wave propagation is discussed, and the time evolution involves the second order time derivatives. An explicit time evolution is used successfully in the present paper. Integral Representation Method (IRM) is one of convenient methods to solve Initial and Boundary Value Problems (IBVP). It can be applied to irregular mesh, and the solution is stable and accurate. IRM is developed to Generalized Integral Representation Method (GIRM) to treat any kinds of problems including nonlinear problems. In GIRM, Generalized Fundamental Solution (GFS) is used instead of Fundamental Solution (FS) in IRM. We can use a variety of GFSs in GIRM. The effects of typical GFSs are investigated. In the present paper, an application of GIRM to tidal wave propagation is discussed, and the time evolution involves the second order time derivatives. An explicit time evolution is used successfully in the present paper. Application of the Generalized Integral Representation Method (GIRM) to Tidal Wave Propagation doi:10.11648/j.acm.s.2015040301.14 Applied and Computational Mathematics 2015-03-27 © Science Publishing Group Hiroshi Isshiki Application of the Generalized Integral Representation Method (GIRM) to Tidal Wave Propagation 4 3 58 58 2015-03-27 2015-03-27 10.11648/j.acm.s.2015040301.14 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2015040301.14 © Science Publishing Group Implementation of One and Two-Step Generalized Integral Representation Methods (GIRMs) http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2015040301.15 In this study, we summarize and implement one- and two-step Generalized Integral Representation Methods (GIRMs). Although GIRM requires matrix inversion, the solution is stable and the accuracy is high. Moreover, it can be applied to an irregular mesh. In order to validate the theory, we apply one- and two-step GIRMs to the one-dimensional Initial and Boundary Value Problem for advective diffusion. The numerical experiments are conducted and the approximate solutions coincide with the exact ones in both cases. The corresponding computer codes implemented in most popular computational languages are also given. In this study, we summarize and implement one- and two-step Generalized Integral Representation Methods (GIRMs). Although GIRM requires matrix inversion, the solution is stable and the accuracy is high. Moreover, it can be applied to an irregular mesh. In order to validate the theory, we apply one- and two-step GIRMs to the one-dimensional Initial and Boundary Value Problem for advective diffusion. The numerical experiments are conducted and the approximate solutions coincide with the exact ones in both cases. The corresponding computer codes implemented in most popular computational languages are also given. Implementation of One and Two-Step Generalized Integral Representation Methods (GIRMs) doi:10.11648/j.acm.s.2015040301.15 Applied and Computational Mathematics 2015-04-08 © Science Publishing Group Hideyuki Niizato Gantulga Tsedendorj Hiroshi Isshiki Implementation of One and Two-Step Generalized Integral Representation Methods (GIRMs) 4 3 77 77 2015-04-08 2015-04-08 10.11648/j.acm.s.2015040301.15 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2015040301.15 © Science Publishing Group Application of Generalized Integral Method (GIRM) to Numerical Evaluations of Soliton-to-Soliton and Soliton-to-Bottom Interactions http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2015040301.16 Numerical evaluations of soliton-soliton and soliton-to-bottom interaction have many applications in various fields. On the other hand, Generalized Integral Representation Method (GIRM) is known as a convenient numerical method for solving Initial and Boundary Value Problem of differential equations such as advective diffusion. In this work, we apply one-step GIRM to numerical evaluations of propagation of a single soliton, soliton-to-soliton interaction and soliton-to-bottom interaction. Firstly, in case of a single soliton, the bottom is considered to be constant in order to understand the behavior of the soliton propagation as it travels in the middle of the sea. Next, in case of soliton-to-bottom, we study behavior of a single soliton propagation when the bottom has different geometries. Finally, we evaluate interaction of two different i.e., big and small solitons. To carry out with the studies, we derive and implement GIRM to numerically solve the Korteweg-de Vries (KdV) equation. In order to verify the theory, numerical experiments are conducted and accurate approximate solutions are obtained in each case of the soliton interactions. Numerical evaluations of soliton-soliton and soliton-to-bottom interaction have many applications in various fields. On the other hand, Generalized Integral Representation Method (GIRM) is known as a convenient numerical method for solving Initial and Boundary Value Problem of differential equations such as advective diffusion. In this work, we apply one-step GIRM to numerical evaluations of propagation of a single soliton, soliton-to-soliton interaction and soliton-to-bottom interaction. Firstly, in case of a single soliton, the bottom is considered to be constant in order to understand the behavior of the soliton propagation as it travels in the middle of the sea. Next, in case of soliton-to-bottom, we study behavior of a single soliton propagation when the bottom has different geometries. Finally, we evaluate interaction of two different i.e., big and small solitons. To carry out with the studies, we derive and implement GIRM to numerically solve the Korteweg-de Vries (KdV) equation. In order to verify the theory, numerical experiments are conducted and accurate approximate solutions are obtained in each case of the soliton interactions. Application of Generalized Integral Method (GIRM) to Numerical Evaluations of Soliton-to-Soliton and Soliton-to-Bottom Interactions doi:10.11648/j.acm.s.2015040301.16 Applied and Computational Mathematics 2015-05-12 © Science Publishing Group Gantulga Tsedendorj Hiroshi Isshiki Rinchinbazar Ravsal Application of Generalized Integral Method (GIRM) to Numerical Evaluations of Soliton-to-Soliton and Soliton-to-Bottom Interactions 4 3 86 86 2015-05-12 2015-05-12 10.11648/j.acm.s.2015040301.16 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2015040301.16 © Science Publishing Group Optimal Control of a Threatened Wildebeest-lion Prey-predator System Incorporating a Constant Prey Refuge in the Serengeti Ecosystem http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150404.18 In this paper a two species prey-predator model is developed in which prey is wildebeest and predator is lion and both are threatened by poaching, drought and diseases.The system is found in the Serengeti ecosystem.The model is constructed based on Holling type II functional response incorporating a constant prey refuge. We apply optimal control theory to investigate optimal strategies for controlling the threats in the system where anti-poaching patrols are used for controlling poaching, construction of dams for mitigating drought and vaccination for diseases control. The possible impact of using combinations of three controls either one at a time or two at a time on the threatened system plus a refuge factor is examined. All control strategies have shown significant increase in prey and predator populations . However, the best result is achieved by controlling all threats together. The effect of variation of prey refuge to the control of threats is studied and results indicate that increase of causes more prey individuals to be saved and reduces the number of predator individuals saved. This behaviour agrees with theoretical results obtained in co-existence equilibrium point. In this paper a two species prey-predator model is developed in which prey is wildebeest and predator is lion and both are threatened by poaching, drought and diseases.The system is found in the Serengeti ecosystem.The model is constructed based on Holling type II functional response incorporating a constant prey refuge. We apply optimal control theory to investigate optimal strategies for controlling the threats in the system where anti-poaching patrols are used for controlling poaching, construction of dams for mitigating drought and vaccination for diseases control. The possible impact of using combinations of three controls either one at a time or two at a time on the threatened system plus a refuge factor is examined. All control strategies have shown significant increase in prey and predator populations . However, the best result is achieved by controlling all threats together. The effect of variation of prey refuge to the control of threats is studied and results indicate that increase of causes more prey individuals to be saved and reduces the number of predator individuals saved. This behaviour agrees with theoretical results obtained in co-existence equilibrium point. Optimal Control of a Threatened Wildebeest-lion Prey-predator System Incorporating a Constant Prey Refuge in the Serengeti Ecosystem doi:10.11648/j.acm.20150404.18 Applied and Computational Mathematics 2015-07-17 © Science Publishing Group Thadei Damas Sagamiko Nyimvua Shaban Cuthbert Leonard Nahonyo Oluwole Daniel Makinde Optimal Control of a Threatened Wildebeest-lion Prey-predator System Incorporating a Constant Prey Refuge in the Serengeti Ecosystem 4 4 312 312 2015-07-17 2015-07-17 10.11648/j.acm.20150404.18 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150404.18 © Science Publishing Group Mathematical Modelling of the Transmission Dynamics of Ebola Virus http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150404.19 The study simulated the transmission dynamics of Ebola Zaire virus using two models: a modified SIR model with the understanding that the recovered can become infected again and the infected die at a certain rate and a quarantine model, which ascertained the effects of quarantining the infected. Furthermore, an appropriate system of Ordinary Differential Equations (ODE) was formulated for the transmission and the method of linearized stability approach was used to solve the equations. Stability analysis of both models indicated that, the Disease Free Equilibrium (DFE) states of the models were unstable if they exist. These equilibria states showed that the disease can easily be triggered off, so there is need to be constantly alert and effective preventive measures put in place against its spread. In addition, numerical experiments were carried out with the models&apos; parameters assigned specific hypothetical values and graphs were plotted to investigate the effect of these parameters on the transmission of the disease. The results showed that, with the nature of Ebola Zaire virus, uncontrolled transmittable contacts between the infected and the susceptible can lead to a very serious outbreak with high mortality rate, since no immunity and drugs at moment. However, with effective quarantining structures put in place such situation can be better managed and outbreak controlled. The study simulated the transmission dynamics of Ebola Zaire virus using two models: a modified SIR model with the understanding that the recovered can become infected again and the infected die at a certain rate and a quarantine model, which ascertained the effects of quarantining the infected. Furthermore, an appropriate system of Ordinary Differential Equations (ODE) was formulated for the transmission and the method of linearized stability approach was used to solve the equations. Stability analysis of both models indicated that, the Disease Free Equilibrium (DFE) states of the models were unstable if they exist. These equilibria states showed that the disease can easily be triggered off, so there is need to be constantly alert and effective preventive measures put in place against its spread. In addition, numerical experiments were carried out with the models&apos; parameters assigned specific hypothetical values and graphs were plotted to investigate the effect of these parameters on the transmission of the disease. The results showed that, with the nature of Ebola Zaire virus, uncontrolled transmittable contacts between the infected and the susceptible can lead to a very serious outbreak with high mortality rate, since no immunity and drugs at moment. However, with effective quarantining structures put in place such situation can be better managed and outbreak controlled. Mathematical Modelling of the Transmission Dynamics of Ebola Virus doi:10.11648/j.acm.20150404.19 Applied and Computational Mathematics 2015-07-18 © Science Publishing Group Amenaghawon C. Osemwinyen Aboubakary Diakhaby Mathematical Modelling of the Transmission Dynamics of Ebola Virus 4 4 320 320 2015-07-18 2015-07-18 10.11648/j.acm.20150404.19 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150404.19 © Science Publishing Group Dynamical Systems and Network Flows: Traffic Flow Problem on Multi-lane Intersections (Economic Analysis) http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150404.20 Nowadays due to rapid population growth and hence increasing demand for transportation, traffic congestion at road intersections become a serious problem for developed as well as developing countries. Traffic congestion causes considerable costs due to unproductive time losses, extra fuel consumption, accidents and also has a negative impact on the environment such as air pollution, noise and stress. Thus, economic analysis of multi-lane intersections and improvement alternatives take account of vehicles cost of fuel consumption and time costs incurred by users of the road junctions. The objective of this study was about determining average waiting time of vehicles and estimating cost incurred due to delay at unsignalized double lane roundabouts and signalized cross intersections. In this study MMAS Cellular Automata model and Poisson queuing model were used. The study tried to calculate the average waiting time (delay) of vehicles in the system (in queue plus in service) at both types of road intersections. The study was tried to quantify vehicles waiting time at both types of road intersections (cost incurred due to delay); that is cost of time lost for passengers and cost of extra fuel consumed by vehicles. Based on the findings of the study, that is based on time and fuel lost (though other factors are not included), signalized cross intersections are better than roundabouts to minimize traffic congestion problem at road junctions. Nowadays due to rapid population growth and hence increasing demand for transportation, traffic congestion at road intersections become a serious problem for developed as well as developing countries. Traffic congestion causes considerable costs due to unproductive time losses, extra fuel consumption, accidents and also has a negative impact on the environment such as air pollution, noise and stress. Thus, economic analysis of multi-lane intersections and improvement alternatives take account of vehicles cost of fuel consumption and time costs incurred by users of the road junctions. The objective of this study was about determining average waiting time of vehicles and estimating cost incurred due to delay at unsignalized double lane roundabouts and signalized cross intersections. In this study MMAS Cellular Automata model and Poisson queuing model were used. The study tried to calculate the average waiting time (delay) of vehicles in the system (in queue plus in service) at both types of road intersections. The study was tried to quantify vehicles waiting time at both types of road intersections (cost incurred due to delay); that is cost of time lost for passengers and cost of extra fuel consumed by vehicles. Based on the findings of the study, that is based on time and fuel lost (though other factors are not included), signalized cross intersections are better than roundabouts to minimize traffic congestion problem at road junctions. Dynamical Systems and Network Flows: Traffic Flow Problem on Multi-lane Intersections (Economic Analysis) doi:10.11648/j.acm.20150404.20 Applied and Computational Mathematics 2015-07-29 © Science Publishing Group Tarekegn Mitiku Agajie Dynamical Systems and Network Flows: Traffic Flow Problem on Multi-lane Intersections (Economic Analysis) 4 4 330 330 2015-07-29 2015-07-29 10.11648/j.acm.20150404.20 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150404.20 © Science Publishing Group The General Forms of the Multiple-Soliton Solutions for the Completely Integrable Equations by Using the Simplest Equation Method http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150404.21 The simplest equation method with the Burgers’ equation as the simplest equation is used to handle two completely integrable equations, the KdV equation and the potential KdV equation. The general forms of the multiple-soliton solutions are formally established. It is shown that the simplest equation method may provide us with a straightforward and effective mathematic tool for generating multiple-soliton solutions of nonlinear wave equations in fluid mechanics The simplest equation method with the Burgers’ equation as the simplest equation is used to handle two completely integrable equations, the KdV equation and the potential KdV equation. The general forms of the multiple-soliton solutions are formally established. It is shown that the simplest equation method may provide us with a straightforward and effective mathematic tool for generating multiple-soliton solutions of nonlinear wave equations in fluid mechanics The General Forms of the Multiple-Soliton Solutions for the Completely Integrable Equations by Using the Simplest Equation Method doi:10.11648/j.acm.20150404.21 Applied and Computational Mathematics 2015-08-14 © Science Publishing Group Sen-Yung Lee Chun-Ku Kuo The General Forms of the Multiple-Soliton Solutions for the Completely Integrable Equations by Using the Simplest Equation Method 4 4 334 334 2015-08-14 2015-08-14 10.11648/j.acm.20150404.21 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150404.21 © Science Publishing Group Epidemiological Modeling of Measles Infection with Optimal Control of Vaccination and Supportive Treatment http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150404.15 We consider an SEIR model with constant population size and formulate an optimal control problem subject to vaccination and supportive treatment as controls. Our aim is to find the optimal combination of vaccination and supportive treatment strategies that will minimize the cost of the two control measures as well as the number of infectives while efficiently balancing vaccination and management of measles applied to the models with various cost scenarios. We used Pontryagin’s maximum principle to characterize the optimal levels of the two controls. The resulting optimality system is solved numerically by forward-backward sweep method. The results show that the optimal combination of the strategies required to achieve the set objective will depend on the relative cost of each of the control measures and the resulting optimality system showed that, the use of vaccinating and supportive treating at the same time at the highest possible rate to the population as early as possible is essential for controlling measles epidemic. The results from our simulation are discussed. We consider an SEIR model with constant population size and formulate an optimal control problem subject to vaccination and supportive treatment as controls. Our aim is to find the optimal combination of vaccination and supportive treatment strategies that will minimize the cost of the two control measures as well as the number of infectives while efficiently balancing vaccination and management of measles applied to the models with various cost scenarios. We used Pontryagin’s maximum principle to characterize the optimal levels of the two controls. The resulting optimality system is solved numerically by forward-backward sweep method. The results show that the optimal combination of the strategies required to achieve the set objective will depend on the relative cost of each of the control measures and the resulting optimality system showed that, the use of vaccinating and supportive treating at the same time at the highest possible rate to the population as early as possible is essential for controlling measles epidemic. The results from our simulation are discussed. Epidemiological Modeling of Measles Infection with Optimal Control of Vaccination and Supportive Treatment doi:10.11648/j.acm.20150404.15 Applied and Computational Mathematics 2015-07-01 © Science Publishing Group Okey Oseloka Onyejekwe Esayas Zewdie Kebede Epidemiological Modeling of Measles Infection with Optimal Control of Vaccination and Supportive Treatment 4 4 274 274 2015-07-01 2015-07-01 10.11648/j.acm.20150404.15 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150404.15 © Science Publishing Group Homotopy Method for Solving Finite Level Fuzzy Nonlinear Integral Equation http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150404.13 In this paper, non – linear finite fuzzy Volterra integral equation of the second kind (NFVIEK2) is considered. The Homotopy analysis method will be used to solve it, and comparing with the exact solution and calculate the absolute error between them. Some numerical examples are prepared to show the efficiency and simplicity of the method. In this paper, non – linear finite fuzzy Volterra integral equation of the second kind (NFVIEK2) is considered. The Homotopy analysis method will be used to solve it, and comparing with the exact solution and calculate the absolute error between them. Some numerical examples are prepared to show the efficiency and simplicity of the method. Homotopy Method for Solving Finite Level Fuzzy Nonlinear Integral Equation doi:10.11648/j.acm.20150404.13 Applied and Computational Mathematics 2015-06-29 © Science Publishing Group Alan Jalal Abdulqader Homotopy Method for Solving Finite Level Fuzzy Nonlinear Integral Equation 4 4 257 257 2015-06-29 2015-06-29 10.11648/j.acm.20150404.13 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150404.13 © Science Publishing Group Population Dynamics Model for Coexistence of Three Interacting Species http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150404.14 Over the years applications of mathematics in the form of mathematical modeling in a whole range of different fields including physical, social, management, biological, and medical sciences have broken all bounds. In particular, the mathematical models to study population dynamics of various interacting species in an isolated environment have attracted the attention of mathematical biologists. In nature, there may be two, three, or more species interacting within themselves giving rise to the corresponding predator-prey models. In each case, both predator and prey evolve their own strategies to deal with the situation. The parameters which influence both the predator and the pry to evoke strategies for their survival include environmental conditions, predator’s appetite, aggressiveness, liking for some particular prey, its physical fitness versus that of the prey, prey’s agility, active prudence to run away or hide, etc. In the literature interactions between, two, three or more species, sharing the same habitat have been discussed in detail. In this paper we present a model pertaining to the interaction between three species. It is a realistic model in which three species, x, y and z, interact within themselves in such a way that species y (predator) preys on species x (prey), while the species z preys on both the species x and y. Accordingly, the resulting situation has been analyzed. The objective of this paper is to analyze the possibility for three interacting species to live in an isolated environment harmoniously. The model presented here has three equilibrium points, however, only one of them has been ascertained to be locally stable. The existence of this equilibrium point signifies amicable coexistence of the three species, if no outside intervention accrues any destabilization to the existing environment. Over the years applications of mathematics in the form of mathematical modeling in a whole range of different fields including physical, social, management, biological, and medical sciences have broken all bounds. In particular, the mathematical models to study population dynamics of various interacting species in an isolated environment have attracted the attention of mathematical biologists. In nature, there may be two, three, or more species interacting within themselves giving rise to the corresponding predator-prey models. In each case, both predator and prey evolve their own strategies to deal with the situation. The parameters which influence both the predator and the pry to evoke strategies for their survival include environmental conditions, predator’s appetite, aggressiveness, liking for some particular prey, its physical fitness versus that of the prey, prey’s agility, active prudence to run away or hide, etc. In the literature interactions between, two, three or more species, sharing the same habitat have been discussed in detail. In this paper we present a model pertaining to the interaction between three species. It is a realistic model in which three species, x, y and z, interact within themselves in such a way that species y (predator) preys on species x (prey), while the species z preys on both the species x and y. Accordingly, the resulting situation has been analyzed. The objective of this paper is to analyze the possibility for three interacting species to live in an isolated environment harmoniously. The model presented here has three equilibrium points, however, only one of them has been ascertained to be locally stable. The existence of this equilibrium point signifies amicable coexistence of the three species, if no outside intervention accrues any destabilization to the existing environment. Population Dynamics Model for Coexistence of Three Interacting Species doi:10.11648/j.acm.20150404.14 Applied and Computational Mathematics 2015-06-29 © Science Publishing Group M. Rafique M. Abdul Qader Population Dynamics Model for Coexistence of Three Interacting Species 4 4 263 263 2015-06-29 2015-06-29 10.11648/j.acm.20150404.14 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150404.14 © Science Publishing Group Existence Theorem for Abstract Measure Delay Integro-Differential Equations http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150404.11 In this paper, we have proved the existence and uniqueness results for an abstract measure delay integro-differential equation by using Leray-Schauder nonlinear alternative under certain Caratheodory conditions. The various aspects of the solutions of the abstract measure integro-differential equations have been studied in the literature using the various fixed point techniques such as Schauder,s fixed point principle and Banach contraction mapping principal etc. In this paper we have proved existence and uniqueness condition for Abstract Measure delay integro-differential equations. In this paper, we have proved the existence and uniqueness results for an abstract measure delay integro-differential equation by using Leray-Schauder nonlinear alternative under certain Caratheodory conditions. The various aspects of the solutions of the abstract measure integro-differential equations have been studied in the literature using the various fixed point techniques such as Schauder,s fixed point principle and Banach contraction mapping principal etc. In this paper we have proved existence and uniqueness condition for Abstract Measure delay integro-differential equations. Existence Theorem for Abstract Measure Delay Integro-Differential Equations doi:10.11648/j.acm.20150404.11 Applied and Computational Mathematics 2015-06-25 © Science Publishing Group S. S. Bellale S. B. Birajdar D. S. Palimkar Existence Theorem for Abstract Measure Delay Integro-Differential Equations 4 4 231 231 2015-06-25 2015-06-25 10.11648/j.acm.20150404.11 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150404.11 © Science Publishing Group Effect of Hall Current on Unsteady MHD Couette Flow and Heat Transfer of Nanofluids in a Rotating System http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150404.12 The Hall effect on MHD Couette flow and heat transfer between two parallel plates in a rotating channel is investigated. A uniform magnetic field is applied normal to the plates and the flow is induced by the effects of Coriolis force, moving upper plate and the constant pressure gradients. Cu-water, Al2O3-water and TiO2-water nanofluids are compared for heat transfer performance. The Galerkin approximation and method of lines are employed to tackle the governing non-linear PDEs. The results show that Hall current significantly affects the flow system. The skin friction and Nusselt number profiles are presented graphically and discussed quantitatively. The Hall effect on MHD Couette flow and heat transfer between two parallel plates in a rotating channel is investigated. A uniform magnetic field is applied normal to the plates and the flow is induced by the effects of Coriolis force, moving upper plate and the constant pressure gradients. Cu-water, Al2O3-water and TiO2-water nanofluids are compared for heat transfer performance. The Galerkin approximation and method of lines are employed to tackle the governing non-linear PDEs. The results show that Hall current significantly affects the flow system. The skin friction and Nusselt number profiles are presented graphically and discussed quantitatively. Effect of Hall Current on Unsteady MHD Couette Flow and Heat Transfer of Nanofluids in a Rotating System doi:10.11648/j.acm.20150404.12 Applied and Computational Mathematics 2015-06-25 © Science Publishing Group Ahmada Omar Ali Oluwole Daniel Makinde Yaw Nkansah-Gyekye Effect of Hall Current on Unsteady MHD Couette Flow and Heat Transfer of Nanofluids in a Rotating System 4 4 244 244 2015-06-25 2015-06-25 10.11648/j.acm.20150404.12 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150404.12 © Science Publishing Group An Efficient Scheme of Differential Quadrature Based on Upwind Difference for Solving Two-dimensional Heat Transfer Problems http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150404.16 In this paper, a new technique of differential quadature method called the upwind difference - differential quadature method (UDDQM) for solving two-dimensional heat transfer (convection-diffusion) problems is proposed. Also, investigated the effects of physical quantities on behavior of flow problems, and combined effects of upwind difference mechanism together with differential quadrature method to modified the numerical solutions of heat transfer problems are presented. To validate our proposed UDDQM, two convection-diffusion problems ((i) Steady-state incompressible flow problem has exact solution and (ii) Natural convection motion of the incompressible fluid flow problem hasn&apos;t exact solution) are solving numerically. Graphical results on the effects of parameter variation on velocity, temperature, Peclet number, Grashof number, and Prandtl number are presented and discussed. Numerical experiments are conducted to test its accuracy and convergence and compare it with the standard DQM and other numerical methods that are available in literature. The numerical results show the efficiency of the proposed method to handle the problems, and it is more accurate and convergent than other methods. In this paper, a new technique of differential quadature method called the upwind difference - differential quadature method (UDDQM) for solving two-dimensional heat transfer (convection-diffusion) problems is proposed. Also, investigated the effects of physical quantities on behavior of flow problems, and combined effects of upwind difference mechanism together with differential quadrature method to modified the numerical solutions of heat transfer problems are presented. To validate our proposed UDDQM, two convection-diffusion problems ((i) Steady-state incompressible flow problem has exact solution and (ii) Natural convection motion of the incompressible fluid flow problem hasn&apos;t exact solution) are solving numerically. Graphical results on the effects of parameter variation on velocity, temperature, Peclet number, Grashof number, and Prandtl number are presented and discussed. Numerical experiments are conducted to test its accuracy and convergence and compare it with the standard DQM and other numerical methods that are available in literature. The numerical results show the efficiency of the proposed method to handle the problems, and it is more accurate and convergent than other methods. An Efficient Scheme of Differential Quadrature Based on Upwind Difference for Solving Two-dimensional Heat Transfer Problems doi:10.11648/j.acm.20150404.16 Applied and Computational Mathematics 2015-07-02 © Science Publishing Group Abdul-Sattar Jaber Ali Al-Saif An Efficient Scheme of Differential Quadrature Based on Upwind Difference for Solving Two-dimensional Heat Transfer Problems 4 4 285 285 2015-07-02 2015-07-02 10.11648/j.acm.20150404.16 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150404.16 © Science Publishing Group The Taylor-SPH Meshfree Method: Basis and Validation http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150404.17 This paper presents the basis and validation of the Taylor-SPH meshless method formulated in terms of stresses and velocities which can be applied to Solid Dynamic problems. The proposed method consists of applying first the time discretization by means of a Taylor series expansion in two steps and a corrected SPH method for the space discretization. In order to avoid numerical instabilities, two different sets of particles are used in the time discretization. To validate the Taylor-SPH method, it has been applied to solve the propagation of shock waves in elastic materials and the results have been compared with those obtained with a corrected SPH discretization combined with a 4th order Runge-Kutta time integration. The Taylor-SPH method is shown to be stable, robust and efficient and it provides more accurate results than those obtained with the standard SPH along with the Runge-Kutta time integration scheme. Numerical dispersion and diffusion are eliminated and only a reduced number of particles is required to obtain accurate results. This paper presents the basis and validation of the Taylor-SPH meshless method formulated in terms of stresses and velocities which can be applied to Solid Dynamic problems. The proposed method consists of applying first the time discretization by means of a Taylor series expansion in two steps and a corrected SPH method for the space discretization. In order to avoid numerical instabilities, two different sets of particles are used in the time discretization. To validate the Taylor-SPH method, it has been applied to solve the propagation of shock waves in elastic materials and the results have been compared with those obtained with a corrected SPH discretization combined with a 4th order Runge-Kutta time integration. The Taylor-SPH method is shown to be stable, robust and efficient and it provides more accurate results than those obtained with the standard SPH along with the Runge-Kutta time integration scheme. Numerical dispersion and diffusion are eliminated and only a reduced number of particles is required to obtain accurate results. The Taylor-SPH Meshfree Method: Basis and Validation doi:10.11648/j.acm.20150404.17 Applied and Computational Mathematics 2015-07-02 © Science Publishing Group H. Idder M. Mabssout M. I. Herreros The Taylor-SPH Meshfree Method: Basis and Validation 4 4 295 295 2015-07-02 2015-07-02 10.11648/j.acm.20150404.17 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150404.17 © Science Publishing Group On a Subclass of Close-to-Convex Functions Associated with Fixed Second Coefficient http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150405.12 We consider a subclass of univalent functions f (z) for which there corresponds a convex function g(z) of order α such that Re(zf&apos;(z) / g(z)) ≥ β. We investigate the influence of the second coefficient of g(z) on this class. We also prove distortion, covering, and radius of convexity theorems We consider a subclass of univalent functions f (z) for which there corresponds a convex function g(z) of order α such that Re(zf&apos;(z) / g(z)) ≥ β. We investigate the influence of the second coefficient of g(z) on this class. We also prove distortion, covering, and radius of convexity theorems On a Subclass of Close-to-Convex Functions Associated with Fixed Second Coefficient doi:10.11648/j.acm.20150405.12 Applied and Computational Mathematics 2015-08-19 © Science Publishing Group Selvaraj Chellian Stelin Simpson Logu Sivalingam On a Subclass of Close-to-Convex Functions Associated with Fixed Second Coefficient 4 5 345 345 2015-08-19 2015-08-19 10.11648/j.acm.20150405.12 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150405.12 © Science Publishing Group The General Form of Linearized Exact Solution for the KdV Equation by the Simplest Equation Method http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150405.11 The general form of linearized exact solution for the Korteweg and de Vries (KdV) equation, with an arbitrary nonlinear coefficient, is derived by the simplest equation method with the Bernoulli equation as the simplest equation. It is shown that the proposed exact solution overcomes the long existing problem of discontinuity and can be successfully reduced to linearity, while the nonlinear term coefficient approaches zero. Comparison of four different soliton solutions is presented. A new phenomenon, named soliton sliding, is observed. The general form of linearized exact solution for the Korteweg and de Vries (KdV) equation, with an arbitrary nonlinear coefficient, is derived by the simplest equation method with the Bernoulli equation as the simplest equation. It is shown that the proposed exact solution overcomes the long existing problem of discontinuity and can be successfully reduced to linearity, while the nonlinear term coefficient approaches zero. Comparison of four different soliton solutions is presented. A new phenomenon, named soliton sliding, is observed. The General Form of Linearized Exact Solution for the KdV Equation by the Simplest Equation Method doi:10.11648/j.acm.20150405.11 Applied and Computational Mathematics 2015-08-19 © Science Publishing Group Sen-Yung Lee Chun-Ku Kuo The General Form of Linearized Exact Solution for the KdV Equation by the Simplest Equation Method 4 5 314 314 2015-08-19 2015-08-19 10.11648/j.acm.20150405.11 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150405.11 © Science Publishing Group Numerical Study of Convective Heat Transfer on the Power Law Fluid over a Vertical Exponentially Stretching Cylinder http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150405.13 The present paper is the study of boundary layer flow and heat transfer of Power law fluid flowing over a vertical exponentially stretching cylinder along its axial direction. The governing partial differential equations and the associated boundary conditions are reduced to nonlinear ordinary differential equations after using the boundary layer approximation and similarity transformations. The obtained system of nonlinear ordinary differential equations subject to the boundary conditions is solved numerically with the help of Fehlberg method. The effects of Power law index , Reynolds number , Prandtl number , the natural convection parameter and local Reynolds number are presented through graphs. The skin friction coefficient and Nusselt number are presented through tables for different parameters.The present paper is the study of boundary layer flow and heat transfer of Power law fluid flowing over a vertical exponentially stretching cylinder along its axial direction. The governing partial differential equations and the associated boundary conditions are reduced to nonlinear ordinary differential equations after using the boundary layer approximation and similarity transformations. The obtained system of nonlinear ordinary differential equations subject to the boundary conditions is solved numerically with the help of Fehlberg method. The effects of Power law index , Reynolds number , Prandtl number , the natural convection parameter &lambda; and local Reynolds number Re&lt;sub&gt;a&lt;/sub&gt; are presented through graphs. The skin friction coefficient and Nusselt number are presented through tables for different parameters. The present paper is the study of boundary layer flow and heat transfer of Power law fluid flowing over a vertical exponentially stretching cylinder along its axial direction. The governing partial differential equations and the associated boundary conditions are reduced to nonlinear ordinary differential equations after using the boundary layer approximation and similarity transformations. The obtained system of nonlinear ordinary differential equations subject to the boundary conditions is solved numerically with the help of Fehlberg method. The effects of Power law index , Reynolds number , Prandtl number , the natural convection parameter and local Reynolds number are presented through graphs. The skin friction coefficient and Nusselt number are presented through tables for different parameters.The present paper is the study of boundary layer flow and heat transfer of Power law fluid flowing over a vertical exponentially stretching cylinder along its axial direction. The governing partial differential equations and the associated boundary conditions are reduced to nonlinear ordinary differential equations after using the boundary layer approximation and similarity transformations. The obtained system of nonlinear ordinary differential equations subject to the boundary conditions is solved numerically with the help of Fehlberg method. The effects of Power law index , Reynolds number , Prandtl number , the natural convection parameter &lambda; and local Reynolds number Re&lt;sub&gt;a&lt;/sub&gt; are presented through graphs. The skin friction coefficient and Nusselt number are presented through tables for different parameters. Numerical Study of Convective Heat Transfer on the Power Law Fluid over a Vertical Exponentially Stretching Cylinder doi:10.11648/j.acm.20150405.13 Applied and Computational Mathematics 2015-08-22 © Science Publishing Group M. Naseer M. Y. Malik Abdul Rehman Numerical Study of Convective Heat Transfer on the Power Law Fluid over a Vertical Exponentially Stretching Cylinder 4 5 350 350 2015-08-22 2015-08-22 10.11648/j.acm.20150405.13 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150405.13 © Science Publishing Group Effect of Varying StepSizes in Numerical Approximation of Stochastic Differential Equations Using One Step Milstein Method http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150405.14 This paper examines the effect of varying stepsizes in finding the approximate solution of stochastic differential equations (SDEs). One step Milstein method (MLSTM) for solution of general first order stochastic differential equations (SDEs) has been derived using Itô Lemma and Euler-Maruyama Method as supporting tools. Two problems in the form of first order SDEs have been considered. The method of solution used is one step Milstein method. The absolute errors were calculated using the exact solution and numerical solution. Comparison of varying the stepsizes was achieved using mean absolute error criterion. The results showed that the mean absolute error due to approximation decreases as the stepsizes decreases. The order of convergence is approximately 1, which indicates the accuracy of the method. Also, the effect of varying stepsizes can also be identified using graphical method constructed for various stepsizes. This paper examines the effect of varying stepsizes in finding the approximate solution of stochastic differential equations (SDEs). One step Milstein method (MLSTM) for solution of general first order stochastic differential equations (SDEs) has been derived using Itô Lemma and Euler-Maruyama Method as supporting tools. Two problems in the form of first order SDEs have been considered. The method of solution used is one step Milstein method. The absolute errors were calculated using the exact solution and numerical solution. Comparison of varying the stepsizes was achieved using mean absolute error criterion. The results showed that the mean absolute error due to approximation decreases as the stepsizes decreases. The order of convergence is approximately 1, which indicates the accuracy of the method. Also, the effect of varying stepsizes can also be identified using graphical method constructed for various stepsizes. Effect of Varying StepSizes in Numerical Approximation of Stochastic Differential Equations Using One Step Milstein Method doi:10.11648/j.acm.20150405.14 Applied and Computational Mathematics 2015-09-09 © Science Publishing Group Sunday Jacob Kayode Akeem Adebayo Ganiyu Effect of Varying StepSizes in Numerical Approximation of Stochastic Differential Equations Using One Step Milstein Method 4 5 362 362 2015-09-09 2015-09-09 10.11648/j.acm.20150405.14 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150405.14 © Science Publishing Group Identification of Company-Specific Stress Scenarios in Non-Life Insurance http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2016050101.11 This paper provides an effective approach, known as dynamic financial analysis, to the systematic development of stress scenarios for the risk profile of non-life insurers, which can be used in risk analysis for the regulatory and rating assessment. The determination of company-specific stress scenarios is demonstrated, the resulting critical scenarios are described. Non-linear dependencies have a significant impact on the scenarios, some of which have not previously been adequately considered are introduced. The recent global financial crisis illustrates that the analysis of extreme events, which can affect both sides of the balance sheet, is essential in an asset-liability management context. This paper provides an effective approach, known as dynamic financial analysis, to the systematic development of stress scenarios for the risk profile of non-life insurers, which can be used in risk analysis for the regulatory and rating assessment. The determination of company-specific stress scenarios is demonstrated, the resulting critical scenarios are described. Non-linear dependencies have a significant impact on the scenarios, some of which have not previously been adequately considered are introduced. The recent global financial crisis illustrates that the analysis of extreme events, which can affect both sides of the balance sheet, is essential in an asset-liability management context. Identification of Company-Specific Stress Scenarios in Non-Life Insurance doi:10.11648/j.acm.s.2016050101.11 Applied and Computational Mathematics 2015-06-10 © Science Publishing Group Wiltrud Weidner J.-Matthias Graf von der Schulenburg Identification of Company-Specific Stress Scenarios in Non-Life Insurance 5 1 13 13 2015-06-10 2015-06-10 10.11648/j.acm.s.2016050101.11 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2016050101.11 © Science Publishing Group Impact of Interest Rate Shocks on the Asset Structure of Private Households in Germany with Particular Reference to Insurance http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2016050101.12 This paper investigates the portfolio structure of private households in Germany from 1994 to 2014. We focus on the question of how sensitively private households react to a shock in the interest rate level. We use a vector autoregressive model and analyze the corresponding impulse-response functions. The data set is provided by Deutsche Bundesbank. Our hypothesis that the asset class Insurance reacts less sensitively to changes in the interest rate level than other asset classes cannot be confirmed. In general, the results show almost no reactions in the portfolio proportions after an interest rate shock. From our results, it appears that private households in Germany clearly do not integrate interest rate information into their portfolio allocation decisions. This paper investigates the portfolio structure of private households in Germany from 1994 to 2014. We focus on the question of how sensitively private households react to a shock in the interest rate level. We use a vector autoregressive model and analyze the corresponding impulse-response functions. The data set is provided by Deutsche Bundesbank. Our hypothesis that the asset class Insurance reacts less sensitively to changes in the interest rate level than other asset classes cannot be confirmed. In general, the results show almost no reactions in the portfolio proportions after an interest rate shock. From our results, it appears that private households in Germany clearly do not integrate interest rate information into their portfolio allocation decisions. Impact of Interest Rate Shocks on the Asset Structure of Private Households in Germany with Particular Reference to Insurance doi:10.11648/j.acm.s.2016050101.12 Applied and Computational Mathematics 2015-06-10 © Science Publishing Group Tim Linderkamp Impact of Interest Rate Shocks on the Asset Structure of Private Households in Germany with Particular Reference to Insurance 5 1 20 20 2015-06-10 2015-06-10 10.11648/j.acm.s.2016050101.12 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2016050101.12 © Science Publishing Group Pensions and Growth: A Cointegration Analysis http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2016050101.13 This article investigates the long-term relationship between economic growth and old-age provision using time series analysis, particularly the techniques of cointegration. The neoclassical growth model by Solow (1956) provides atheoretical basis for the empirical analysis. The results are based onquarterly data from 1970 to 2013 for the US-economy. In this work, the existence of a cointegrating relation between economic growth and pensions is verified by use of scientifically accepted statistical methods and proven for historical US-data. The empirical analysis confirms that improved technological capabilities constitute a very important determinant of growth in the context of neoclassical theory. The effects within the cointegrated relationship cannot be determined at this point and there is no information if the effect is reciprocal or not. For this purpose, further investigations are necessary and can build on the results presented here. This article investigates the long-term relationship between economic growth and old-age provision using time series analysis, particularly the techniques of cointegration. The neoclassical growth model by Solow (1956) provides atheoretical basis for the empirical analysis. The results are based onquarterly data from 1970 to 2013 for the US-economy. In this work, the existence of a cointegrating relation between economic growth and pensions is verified by use of scientifically accepted statistical methods and proven for historical US-data. The empirical analysis confirms that improved technological capabilities constitute a very important determinant of growth in the context of neoclassical theory. The effects within the cointegrated relationship cannot be determined at this point and there is no information if the effect is reciprocal or not. For this purpose, further investigations are necessary and can build on the results presented here. Pensions and Growth: A Cointegration Analysis doi:10.11648/j.acm.s.2016050101.13 Applied and Computational Mathematics 2015-07-03 © Science Publishing Group Miguel Rodriguez Gonzalez Christoph Schwarzbach Pensions and Growth: A Cointegration Analysis 5 1 35 35 2015-07-03 2015-07-03 10.11648/j.acm.s.2016050101.13 http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.s.2016050101.13 © Science Publishing Group