Science Publishing Group: Pure and Applied Mathematics Journal: Table of Contents
<i>Pure and Applied Mathematics Journal </i> is a mathematical journal for publishing early, high-impact results in the areas of mathematics and computer science/informatics. The journal also emphasizes mathematical articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, engineering and all applied sciences. For a paper to be considered for publication it is a precondition that it is not submitted for publication elsewhere and contains results that are new, significant and of interest to wide sections of the mathematical community. Editors may invite papers on special topics of current interest.All papers, whether contributed or invited, will be refereed.
http://www.sciencepublishinggroup.com/j/pamj Science Publishing Group: Pure and Applied Mathematics Journal: Table of Contents
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Pure and Applied Mathematics Journal
Pure and Applied Mathematics Journal
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Galois Groups of Polynomials and the Construction of Finite Fields
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In this note an attempt was made in constructing finite fields with the aid of Galois groups of polynomials of small degree. The properties of these polynomials, their base fields and their splitting fields werediscussed. From these properties corollaries were developed upon which the constructions were done. The aim was to provide concrete and physical explanations on some aspects of finite fields and Galois theory.
In this note an attempt was made in constructing finite fields with the aid of Galois groups of polynomials of small degree. The properties of these polynomials, their base fields and their splitting fields werediscussed. From these properties corollaries were developed upon which the constructions were done. The aim was to provide concrete and physical explanations on some aspects of finite fields and Galois theory.
Galois Groups of Polynomials and the Construction of Finite Fields
doi:10.11648/j.pamj.20120101.12
Pure and Applied Mathematics Journal
2014-01-01
© Science Publishing Group
S. M. Tudunkaya
A. I. Kiri
Galois Groups of Polynomials and the Construction of Finite Fields
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Construction of Polynomial Solutions to the Dirichlet Boundary Value Problem for the 3-Harmonic Equation in the Unit Ball
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Polynomial solution to the Dirichlet boundary value problem for the nonhomogeneous 3-harmonic equation in the unit ball with polynomial right-hand side and polynomial boundary data is constructed. Representation of the Green’s function of the Dirichlet boundary value problem in the unit ball in the case of polynomial data is found.
Polynomial solution to the Dirichlet boundary value problem for the nonhomogeneous 3-harmonic equation in the unit ball with polynomial right-hand side and polynomial boundary data is constructed. Representation of the Green’s function of the Dirichlet boundary value problem in the unit ball in the case of polynomial data is found.
Construction of Polynomial Solutions to the Dirichlet Boundary Value Problem for the 3-Harmonic Equation in the Unit Ball
doi:10.11648/j.pamj.20120101.11
Pure and Applied Mathematics Journal
2014-01-01
© Science Publishing Group
Valery V. Karachik
Sanjar Abdoulaev
Construction of Polynomial Solutions to the Dirichlet Boundary Value Problem for the 3-Harmonic Equation in the Unit Ball
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Definitions of Real Order Integrals and Derivatives Using Operator Approach
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The set E of functions f fulfilling some conditions is taken to be the definition domain of s-order integral operator J^s (iterative integral), first for any positive integer s and after for any positive s (fractional, transcendental π and e). The definition of k-order derivative operator D^k for any positive k (fractional, transcendental π and e) is derived from the definition of J^s. Some properties of J^sand D^k are given and demonstrated. The method is based on the properties of Euler’s gamma and beta functions.
The set E of functions f fulfilling some conditions is taken to be the definition domain of s-order integral operator J^s (iterative integral), first for any positive integer s and after for any positive s (fractional, transcendental π and e). The definition of k-order derivative operator D^k for any positive k (fractional, transcendental π and e) is derived from the definition of J^s. Some properties of J^sand D^k are given and demonstrated. The method is based on the properties of Euler’s gamma and beta functions.
Definitions of Real Order Integrals and Derivatives Using Operator Approach
doi:10.11648/j.pamj.20130201.11
Pure and Applied Mathematics Journal
2014-01-01
© Science Publishing Group
Raoelina Andriambololona
Definitions of Real Order Integrals and Derivatives Using Operator Approach
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Two Definitions of Fractional Derivative of Powers Functions
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We consider the set of powers functions defined on R_+ and their linear combinations. After recalling some properties of the gamma function, we give two general definitions of derivatives of positive and negative integers, positive and negative fractional orders. Properties of linearity and commutativity are studied and the notions of semi-equality, semi-linearity and semi-commutativity are introduced. Our approach gives a unified definition of the common derivatives and integrals and their generalization.
We consider the set of powers functions defined on R_+ and their linear combinations. After recalling some properties of the gamma function, we give two general definitions of derivatives of positive and negative integers, positive and negative fractional orders. Properties of linearity and commutativity are studied and the notions of semi-equality, semi-linearity and semi-commutativity are introduced. Our approach gives a unified definition of the common derivatives and integrals and their generalization.
Two Definitions of Fractional Derivative of Powers Functions
doi:10.11648/j.pamj.20130201.12
Pure and Applied Mathematics Journal
2014-01-01
© Science Publishing Group
Raoelina Andriambololona
Rakotoson Hanitriarivo
Tokiniaina Ranaivoson
Roland Raboanary
Two Definitions of Fractional Derivative of Powers Functions
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Existence Results for A Nonlocal Problem Involving the p(x)-Laplacian
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In the present paper, we deal with two different existence results of solutions for a nonlocal elliptic Dirichlet boundary value problem involving p(x)-Laplacian. The first one is based on the Brouwer fixed point theorem and the Galerkin method which gives a priori estimate of a nontrivial weak soltion. The second one is based on the variational methods. By using Mountain-Pass theorem, we obtain at least one nontrivial weak soltion.
In the present paper, we deal with two different existence results of solutions for a nonlocal elliptic Dirichlet boundary value problem involving p(x)-Laplacian. The first one is based on the Brouwer fixed point theorem and the Galerkin method which gives a priori estimate of a nontrivial weak soltion. The second one is based on the variational methods. By using Mountain-Pass theorem, we obtain at least one nontrivial weak soltion.
Existence Results for A Nonlocal Problem Involving the p(x)-Laplacian
doi:10.11648/j.pamj.20130201.13
Pure and Applied Mathematics Journal
2014-01-01
© Science Publishing Group
Mustafa Avci
Existence Results for A Nonlocal Problem Involving the p(x)-Laplacian
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About Solutions of Nonlinear Algebraic System with Two Variables
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For nonlinear algebraic system with two variables sufficient conditions of existence of solutions are given. The proof of these statements is received as a corollary of more common reviewing considered in this paper. In particular, in this work the existence of multiple base on eigen and associated vectors of a two parameter system of operators in fi-nite-dimensional spaces is proved. Definitions of the associated vectors, multiple completeness of eigen and associated vectors of two-parameter not selfadjoint systems, nonlinearly depending on spectral parameters are introduced. At the proof of these results we essentially used the notion of the analog of an resultant of two polynomial bundles.
For nonlinear algebraic system with two variables sufficient conditions of existence of solutions are given. The proof of these statements is received as a corollary of more common reviewing considered in this paper. In particular, in this work the existence of multiple base on eigen and associated vectors of a two parameter system of operators in fi-nite-dimensional spaces is proved. Definitions of the associated vectors, multiple completeness of eigen and associated vectors of two-parameter not selfadjoint systems, nonlinearly depending on spectral parameters are introduced. At the proof of these results we essentially used the notion of the analog of an resultant of two polynomial bundles.
About Solutions of Nonlinear Algebraic System with Two Variables
doi:10.11648/j.pamj.20130201.15
Pure and Applied Mathematics Journal
2014-01-01
© Science Publishing Group
Rakhshanda Dzhabarzadeh
About Solutions of Nonlinear Algebraic System with Two Variables
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Non Oscillatory Nonlinear Differential Systems with Slowly Varying Coefficients in Presence on Certain Damping Forces
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Krylov-Bogoliubov-Mitropolskii method is modified and applied to certain damped nonlinear systems with slowly varying coefficients. The results obtained by this method show excellent coincidence with those obtained by numerical method. The method is illustrated by an example.
Krylov-Bogoliubov-Mitropolskii method is modified and applied to certain damped nonlinear systems with slowly varying coefficients. The results obtained by this method show excellent coincidence with those obtained by numerical method. The method is illustrated by an example.
Non Oscillatory Nonlinear Differential Systems with Slowly Varying Coefficients in Presence on Certain Damping Forces
doi:10.11648/j.pamj.20130201.14
Pure and Applied Mathematics Journal
2014-01-01
© Science Publishing Group
Pinakee Dey
Non Oscillatory Nonlinear Differential Systems with Slowly Varying Coefficients in Presence on Certain Damping Forces
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Rhotrix Polynomials and Polynomial Rhotrices
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In this piece of note, polynomials defined over the ring R of rhotrices of n-dimension and rhotrices defined over polynomials in were explored, the aim is to study their nature and present their properties. The hope is that these polynomials (or these rhotrices) will have wider applications than those polynomials defined over the non-commutative ring of n-square matrices (or those matrices defined over polynomials) since R is a commutative ring. The shortcomings of these polynomials and rhotrices were also confirmed as it was proved that the rings R[x] and R[f] are not integral domains.
In this piece of note, polynomials defined over the ring R of rhotrices of n-dimension and rhotrices defined over polynomials in were explored, the aim is to study their nature and present their properties. The hope is that these polynomials (or these rhotrices) will have wider applications than those polynomials defined over the non-commutative ring of n-square matrices (or those matrices defined over polynomials) since R is a commutative ring. The shortcomings of these polynomials and rhotrices were also confirmed as it was proved that the rings R[x] and R[f] are not integral domains.
Rhotrix Polynomials and Polynomial Rhotrices
doi:10.11648/j.pamj.20130201.16
Pure and Applied Mathematics Journal
2014-01-01
© Science Publishing Group
S. M. Tudunkaya
Rhotrix Polynomials and Polynomial Rhotrices
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Modeling the Epidemiology of Malaria and Control with Estimate of the Basic Repro-duction Number
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Strategies for controlling the epidemiology of many infectious diseases such as malaria include a rapid reduc-tion in both the infected and susceptible population via treatment and vaccination. In this paper, we have modified the Tumwiine et al. (2007) mathematical model for the transmission of malaria by including a vaccination parameter. We have shown that the model has a unique disease-free equilibrium state which is locally and globally asymptotically stable, if 1, and that the endemic equilibrium exist provided > 1, where is a parameter which depends on the given model parameters. Numerical simulations of the modified model clearly show that, with a proper combination of treatment and vaccination, offered at about 65% each on the susceptible and infected population, malaria can be eradicated from the community.
Strategies for controlling the epidemiology of many infectious diseases such as malaria include a rapid reduc-tion in both the infected and susceptible population via treatment and vaccination. In this paper, we have modified the Tumwiine et al. (2007) mathematical model for the transmission of malaria by including a vaccination parameter. We have shown that the model has a unique disease-free equilibrium state which is locally and globally asymptotically stable, if 1, and that the endemic equilibrium exist provided > 1, where is a parameter which depends on the given model parameters. Numerical simulations of the modified model clearly show that, with a proper combination of treatment and vaccination, offered at about 65% each on the susceptible and infected population, malaria can be eradicated from the community.
Modeling the Epidemiology of Malaria and Control with Estimate of the Basic Repro-duction Number
doi:10.11648/j.pamj.20130201.17
Pure and Applied Mathematics Journal
2014-01-01
© Science Publishing Group
Adamu Abdul Kareem
Anande Richard Kimbir
Modeling the Epidemiology of Malaria and Control with Estimate of the Basic Repro-duction Number
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Time-Frequency Analysis and Harmonic Gaussian Functions
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A method for time-frequency analysis is given. The approach utilizes properties of Gaussian distribution, properties of Hermite polynomials and Fourier analysis. We begin by the definitions of a set of functions called Harmonic Gaussian Functions. Then these functions are used to define a set of transformations, noted T_n, which associate to a function ψ, of the time variable t, a set of functions Ψ_n which depend on time, frequency and frequency (or time) standard deviation. Some properties of the transformations T_n and the functions Ψ_n are given. It is proved in particular that the square of the modulus of each function Ψ_n can be interpreted as a representation of the energy distribution of the signal, represented by the function ψ, in the time-frequency plane for a given value of the frequency (or time) standard deviation. It is also shown that the function ψ can be recovered from the functions Ψ_n.
A method for time-frequency analysis is given. The approach utilizes properties of Gaussian distribution, properties of Hermite polynomials and Fourier analysis. We begin by the definitions of a set of functions called Harmonic Gaussian Functions. Then these functions are used to define a set of transformations, noted T_n, which associate to a function ψ, of the time variable t, a set of functions Ψ_n which depend on time, frequency and frequency (or time) standard deviation. Some properties of the transformations T_n and the functions Ψ_n are given. It is proved in particular that the square of the modulus of each function Ψ_n can be interpreted as a representation of the energy distribution of the signal, represented by the function ψ, in the time-frequency plane for a given value of the frequency (or time) standard deviation. It is also shown that the function ψ can be recovered from the functions Ψ_n.
Time-Frequency Analysis and Harmonic Gaussian Functions
doi:10.11648/j.pamj.20130202.14
Pure and Applied Mathematics Journal
2014-01-01
© Science Publishing Group
Tokiniaina Ranaivoson
Raoelina Andriambololona
Rakotoson Hanitriarivo
Time-Frequency Analysis and Harmonic Gaussian Functions
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Geometric Series of Numbers Approximating Positive Integers
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The predictability of cycles in the series of Pythagorean triples led to an investigation that yielded numbers (x) that are associated with irrational square roots (√n). The cycles recur with geometric factors (cycle factors y) that are comprised of a positive integer x where y = x + √(x^2±1). On raising the cycle factors to the positive integer powers (ym), a series is generated where each consecutive member comes closer and closer to positive integers as the series progresses. A formula associates the square root (√n) with these series. Prime factorising the positive integers in the power series (xm) produces predictable patterns among the prime factors in the series. In general, power series that have each consecutive member in the series come closer to positive integers are limited to (x + √(x^2±r))m where x and r are positive integers and r < (x + 1)2 – x2 for the + r condition and r < x2 – (x – 1)2 for the – r condition.
The predictability of cycles in the series of Pythagorean triples led to an investigation that yielded numbers (x) that are associated with irrational square roots (√n). The cycles recur with geometric factors (cycle factors y) that are comprised of a positive integer x where y = x + √(x^2±1). On raising the cycle factors to the positive integer powers (ym), a series is generated where each consecutive member comes closer and closer to positive integers as the series progresses. A formula associates the square root (√n) with these series. Prime factorising the positive integers in the power series (xm) produces predictable patterns among the prime factors in the series. In general, power series that have each consecutive member in the series come closer to positive integers are limited to (x + √(x^2±r))m where x and r are positive integers and r < (x + 1)2 – x2 for the + r condition and r < x2 – (x – 1)2 for the – r condition.
Geometric Series of Numbers Approximating Positive Integers
doi:10.11648/j.pamj.20130202.15
Pure and Applied Mathematics Journal
2014-01-01
© Science Publishing Group
Martin W. Bredenkamp
Geometric Series of Numbers Approximating Positive Integers
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Analysis of M/G/1 Queue Model with Priority
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Due to the queue phenomenon different customers needing different service quality, a model is established as follows: there are two types of customers in the system and their arrival rates are different; first-class customers have no preemptive priority, the different service time for the different customers and all the service time obeys the general distribution. The following conclusions are drawn: the Laplace - Steele Kyrgyz transform of the low-priority customers’ waiting time stationary distribution; the average waiting time in the system of low priority customers; the Laplace - Steele Kyrgyz transform of the low-priority customers’ staying time stationary distribution; At last, this paper points out the problems to be solved.
Due to the queue phenomenon different customers needing different service quality, a model is established as follows: there are two types of customers in the system and their arrival rates are different; first-class customers have no preemptive priority, the different service time for the different customers and all the service time obeys the general distribution. The following conclusions are drawn: the Laplace - Steele Kyrgyz transform of the low-priority customers’ waiting time stationary distribution; the average waiting time in the system of low priority customers; the Laplace - Steele Kyrgyz transform of the low-priority customers’ staying time stationary distribution; At last, this paper points out the problems to be solved.
Analysis of M/G/1 Queue Model with Priority
doi:10.11648/j.pamj.20130202.16
Pure and Applied Mathematics Journal
2014-01-01
© Science Publishing Group
Pan Quanru
Analysis of M/G/1 Queue Model with Priority
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Partial Derivatives of Some Types of Two-Variables Functions
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This paper mainly studies the evaluation of partial derivatives of four types of two-variables functions. We can obtain the infinite series forms of any order partial derivatives of these four types of functions by using differentiation term by term theorem, and hence reducing the difficulty of calculating their higher order partial derivative values greatly. On the other hand, we propose four functions of two-variables to evaluate their any order partial derivatives, and some of their higher order partial derivative values practically. At the same time, we employ Maple to calculate the approximations of these higher order partial derivative values and their infinite series forms for verifying our answers.
This paper mainly studies the evaluation of partial derivatives of four types of two-variables functions. We can obtain the infinite series forms of any order partial derivatives of these four types of functions by using differentiation term by term theorem, and hence reducing the difficulty of calculating their higher order partial derivative values greatly. On the other hand, we propose four functions of two-variables to evaluate their any order partial derivatives, and some of their higher order partial derivative values practically. At the same time, we employ Maple to calculate the approximations of these higher order partial derivative values and their infinite series forms for verifying our answers.
Partial Derivatives of Some Types of Two-Variables Functions
doi:10.11648/j.pamj.20130202.12
Pure and Applied Mathematics Journal
2014-01-01
© Science Publishing Group
Chii-Huei Yu
Partial Derivatives of Some Types of Two-Variables Functions
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Some Properties of the Line Graphs Associated to the Total Graph of a Commutative Ring
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Let be a commutative ring with identity and its total graph. The subject of this article is the investigation of the properties of the corresponding line graph In particular, we determine the girth and clique number of In addition to that, we find the condition for to be Eulerian.
Let be a commutative ring with identity and its total graph. The subject of this article is the investigation of the properties of the corresponding line graph In particular, we determine the girth and clique number of In addition to that, we find the condition for to be Eulerian.
Some Properties of the Line Graphs Associated to the Total Graph of a Commutative Ring
doi:10.11648/j.pamj.20130202.11
Pure and Applied Mathematics Journal
2014-01-01
© Science Publishing Group
Aleksandra Lj. Erić
Zoran S. Pucanović
Some Properties of the Line Graphs Associated to the Total Graph of a Commutative Ring
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Generating Functions for Generalized Mock Theta Functions
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We consider generalized mock theta functions and give generating functions for the partial generalized mock theta functions.
We consider generalized mock theta functions and give generating functions for the partial generalized mock theta functions.
Generating Functions for Generalized Mock Theta Functions
doi:10.11648/j.pamj.20130202.13
Pure and Applied Mathematics Journal
2014-01-01
© Science Publishing Group
Sameena Saba
Generating Functions for Generalized Mock Theta Functions
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Asymptotic Method for Certain over-Damped Nonlinear Vibrating Systems
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Krylov-Bogoliubov-Mitropolskii (KBM) method has been extended and applied to certain over-damped nonlinear system in which the linear equation has two almost equal roots. The method is illustrated by an example.
Krylov-Bogoliubov-Mitropolskii (KBM) method has been extended and applied to certain over-damped nonlinear system in which the linear equation has two almost equal roots. The method is illustrated by an example.
Asymptotic Method for Certain over-Damped Nonlinear Vibrating Systems
doi:10.11648/j.pamj.20130202.18
Pure and Applied Mathematics Journal
2014-01-01
© Science Publishing Group
Pinakee Dey
Asymptotic Method for Certain over-Damped Nonlinear Vibrating Systems
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Sub Hilbert Spaces in a Bi-Disk
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Recently, Sahni and Singh [7] have solved an open problem posed by Youseﬁ and Hesameddini [12] regarding Hilbert spaces contained algebraically in the Hardy space H2(T). In fact the result obtained by Sahni and Singh is much more general than the open problem. In the present note we examine the validity of the main results of [7] and [12] in two variables.
Recently, Sahni and Singh [7] have solved an open problem posed by Youseﬁ and Hesameddini [12] regarding Hilbert spaces contained algebraically in the Hardy space H2(T). In fact the result obtained by Sahni and Singh is much more general than the open problem. In the present note we examine the validity of the main results of [7] and [12] in two variables.
Sub Hilbert Spaces in a Bi-Disk
doi:10.11648/j.pamj.20130202.17
Pure and Applied Mathematics Journal
2014-01-01
© Science Publishing Group
Niteesh Sahni
Niteesh Sahni
Sub Hilbert Spaces in a Bi-Disk
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Condition for Existence of Positive Periodic Solution of Hepatitis B Virus Infection Model with Immune Response
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In this paper, we consider a periodic Hepatitis B Virus infection model with immune response. By using continuation theorem of coincidence degree theory, a condition for the existence of positive periodic solution is obtained
In this paper, we consider a periodic Hepatitis B Virus infection model with immune response. By using continuation theorem of coincidence degree theory, a condition for the existence of positive periodic solution is obtained
Condition for Existence of Positive Periodic Solution of Hepatitis B Virus Infection Model with Immune Response
doi:10.11648/j.pamj.20130202.19
Pure and Applied Mathematics Journal
2014-01-01
© Science Publishing Group
Min Long
Tiejun Zhou
Condition for Existence of Positive Periodic Solution of Hepatitis B Virus Infection Model with Immune Response
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10.11648/j.pamj.20130202.19
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20130202.19
© Science Publishing Group
On the Dynamic Response of an Ocean to Wind Stress in an Equatorial Region-II: Further Exact Solutions of the Rossby Equation
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20130203.11
In a beforehand paper they found some exact and explicit solutions for the standard Rossby form of the equation for the stream function for some specified and realistic wind stress. This equation, which is a third order linear partial differential equation for the stream function, relates the rate of change of vertical vortices to the curl of the applied wind stress. The equation involves the gradient of the Coriolis parameter and has particular relevance to the equatorial region, such as the North Indian Ocean. Some interesting physical properties of the solutions are considered. In this paper we find some more complicated but similar exact and explicit solutions. Some properties for these solutions are derived which are in some sense complementary to the kind of properties of the simpler solutions considered in advance.
In a beforehand paper they found some exact and explicit solutions for the standard Rossby form of the equation for the stream function for some specified and realistic wind stress. This equation, which is a third order linear partial differential equation for the stream function, relates the rate of change of vertical vortices to the curl of the applied wind stress. The equation involves the gradient of the Coriolis parameter and has particular relevance to the equatorial region, such as the North Indian Ocean. Some interesting physical properties of the solutions are considered. In this paper we find some more complicated but similar exact and explicit solutions. Some properties for these solutions are derived which are in some sense complementary to the kind of properties of the simpler solutions considered in advance.
On the Dynamic Response of an Ocean to Wind Stress in an Equatorial Region-II: Further Exact Solutions of the Rossby Equation
doi:10.11648/j.pamj.20130203.11
Pure and Applied Mathematics Journal
2014-01-01
© Science Publishing Group
M. Z. Rahman
A.B.M. Shamim. Ul Hasan
On the Dynamic Response of an Ocean to Wind Stress in an Equatorial Region-II: Further Exact Solutions of the Rossby Equation
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2014-01-01
10.11648/j.pamj.20130203.11
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20130203.11
© Science Publishing Group
Refutation Of Hard-Determinable Formulas In The System “Resolution Over Linear Equations” And Its Generalization
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20130203.13
We research the power of the propositional proof system R(lin) (Resolution over Linear Equations) described by Ran Raz and Iddo Tzameret. R (lin) is the generalization of R (Resolution System) and it is known that many tautologies, which require the exponential lower bounds of proof complexities in R, have polynomially bounded proofs in R (lin). We show that there are the sequences of unsatisfiable collections of disjuncts of linear equations, which require exponential lower bounds in R (lin). After adding the renaming rule, mentioned collections have polynomially bounded refutations.
We research the power of the propositional proof system R(lin) (Resolution over Linear Equations) described by Ran Raz and Iddo Tzameret. R (lin) is the generalization of R (Resolution System) and it is known that many tautologies, which require the exponential lower bounds of proof complexities in R, have polynomially bounded proofs in R (lin). We show that there are the sequences of unsatisfiable collections of disjuncts of linear equations, which require exponential lower bounds in R (lin). After adding the renaming rule, mentioned collections have polynomially bounded refutations.
Refutation Of Hard-Determinable Formulas In The System “Resolution Over Linear Equations” And Its Generalization
doi:10.11648/j.pamj.20130203.13
Pure and Applied Mathematics Journal
2014-01-01
© Science Publishing Group
Anahit Chubaryan
Armine Chubaryan
Arman Tshitoyan
Refutation Of Hard-Determinable Formulas In The System “Resolution Over Linear Equations” And Its Generalization
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http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20130203.13
© Science Publishing Group
Strong Reflection Principles and Large Cardinal Axioms
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20130203.12
In this article an possible generalization of the Löb’s theorem is considered. We proved so-called uniform strong reflection principle corresponding to formal theories which has ω-models.Main result is: let κ be an inaccessible cardinal and H_κ is a set of all sets having hereditary size less than κ,then:"¬Con" ("ZFC+" ("V=" "H" _"κ" ) )
In this article an possible generalization of the Löb’s theorem is considered. We proved so-called uniform strong reflection principle corresponding to formal theories which has ω-models.Main result is: let κ be an inaccessible cardinal and H_κ is a set of all sets having hereditary size less than κ,then:"¬Con" ("ZFC+" ("V=" "H" _"κ" ) )
Strong Reflection Principles and Large Cardinal Axioms
doi:10.11648/j.pamj.20130203.12
Pure and Applied Mathematics Journal
2014-01-01
© Science Publishing Group
J. Foukzon
E. R Men’kova
Strong Reflection Principles and Large Cardinal Axioms
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2014-01-01
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http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20130203.12
© Science Publishing Group
An Explicit Solution of Burgers’ Equation with Special Kinematic Viscosity Using Decomposition Technique
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20130203.14
In this article, Adomian’s Decomposition Method (ADM) is employed to approximate the solution of Burgers’ equationwhich is one-dimensional non-linear differential equations in fluid dynamics. The exact solution for Burger’s equation with low kinematic viscosity does not exist in the literatures.Thus, we obtained an explicit solution for this special case. We compared our solution using ADM with the exact solution and the existing numerical solution while .We found out that ADM converges very rapidly to the exact solution and performed better than the existing numerical method.
In this article, Adomian’s Decomposition Method (ADM) is employed to approximate the solution of Burgers’ equationwhich is one-dimensional non-linear differential equations in fluid dynamics. The exact solution for Burger’s equation with low kinematic viscosity does not exist in the literatures.Thus, we obtained an explicit solution for this special case. We compared our solution using ADM with the exact solution and the existing numerical solution while .We found out that ADM converges very rapidly to the exact solution and performed better than the existing numerical method.
An Explicit Solution of Burgers’ Equation with Special Kinematic Viscosity Using Decomposition Technique
doi:10.11648/j.pamj.20130203.14
Pure and Applied Mathematics Journal
2014-01-01
© Science Publishing Group
Bolujo Joseph Adegboyegun
An Explicit Solution of Burgers’ Equation with Special Kinematic Viscosity Using Decomposition Technique
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2014-01-01
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http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20130203.14
© Science Publishing Group
On the Strong Convergence Theorem of Noor Iterative Scheme in the Class of Zamfirescu Operators
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20130204.11
In this paper, we establish the strong convergence theorem of Noor iterative scheme for the class of Zamfirescu operators in arbitrary Banach spaces. Our results is extension and ralization of the recent results of B. L. Xu, M. A. Noor, Y. J. Cho, H. Zhou, G. Guo, S. Plubtieng, R. Wangkeeree, V. Berinde, P. Kumam, W. Kumethong, N. Jewwaiworn and many other authors in literature.
In this paper, we establish the strong convergence theorem of Noor iterative scheme for the class of Zamfirescu operators in arbitrary Banach spaces. Our results is extension and ralization of the recent results of B. L. Xu, M. A. Noor, Y. J. Cho, H. Zhou, G. Guo, S. Plubtieng, R. Wangkeeree, V. Berinde, P. Kumam, W. Kumethong, N. Jewwaiworn and many other authors in literature.
On the Strong Convergence Theorem of Noor Iterative Scheme in the Class of Zamfirescu Operators
doi:10.11648/j.pamj.20130204.11
Pure and Applied Mathematics Journal
2014-01-01
© Science Publishing Group
Mohammad Asaduzzaman
Mohammad Zulfikar Ali
On the Strong Convergence Theorem of Noor Iterative Scheme in the Class of Zamfirescu Operators
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2014-01-01
10.11648/j.pamj.20130204.11
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20130204.11
© Science Publishing Group
Derivation of Schrödinger Equation from a Variational Principle
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20130204.12
The aim of this research is to derive Schrödinger equation from calculus of variations (variational principle), so we use the methodology of calculus of variations. The variational principle one of great scientific significance as they provide a unified approach to various mathematical and physical problems and yield fundamental exploratory ideas.
The aim of this research is to derive Schrödinger equation from calculus of variations (variational principle), so we use the methodology of calculus of variations. The variational principle one of great scientific significance as they provide a unified approach to various mathematical and physical problems and yield fundamental exploratory ideas.
Derivation of Schrödinger Equation from a Variational Principle
doi:10.11648/j.pamj.20130204.12
Pure and Applied Mathematics Journal
2014-01-01
© Science Publishing Group
Sami. H. Altoum
Derivation of Schrödinger Equation from a Variational Principle
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10.11648/j.pamj.20130204.12
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20130204.12
© Science Publishing Group
A Decomposable Computer Oriented Method for Solving Interval LP Problems
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20130205.13
The purpose of this paper is to develop a computer oriented decomposition program for solving Interval Linear Programming (ILP) Problems. For this, we first analyze the existing methods for solving ILP problems. We also discuss the main stricter of Decomposable Interval programming (DIP) problems. Then a decomposable algorithm is analyzed for solving DIP problems. Using “Mathematica”, we develop a computer oriented program for solving such problems. We present step by step illustration of a numerical example to demonstrate our technique.
The purpose of this paper is to develop a computer oriented decomposition program for solving Interval Linear Programming (ILP) Problems. For this, we first analyze the existing methods for solving ILP problems. We also discuss the main stricter of Decomposable Interval programming (DIP) problems. Then a decomposable algorithm is analyzed for solving DIP problems. Using “Mathematica”, we develop a computer oriented program for solving such problems. We present step by step illustration of a numerical example to demonstrate our technique.
A Decomposable Computer Oriented Method for Solving Interval LP Problems
doi:10.11648/j.pamj.20130205.13
Pure and Applied Mathematics Journal
2014-01-01
© Science Publishing Group
Sharmin Afroz
M. Babul Hasan
A Decomposable Computer Oriented Method for Solving Interval LP Problems
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2014-01-01
10.11648/j.pamj.20130205.13
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20130205.13
© Science Publishing Group
The Case against Educated Mathematical Dogma (Precise Mathematical Pi Value by Finite Equation =3.14159292035) 3+(1/(7+1/16)) Precise Finite Value
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20130205.14
The relevance of this paper to current approximate mathematics and the sciences is a massive change, because this mathematics binds numbers in the rationality of a finite space of the primordial constriction from 4 to 3 coordinates, which leads to a specific calculable mathematical π, correct trigonometry, and the divergence of 1:3, and the placement of all prime numbers. We have also separately produced the continuous Prime number sieve at 1/3, 2/3, 5/ 6 and 1/6 (den- otter continuous sieve of Prime numbers). The method of the sieve is impossible for current mathematics to understand as the discoverer is uneducated and hard to comprehend except by chalk board. It is a continuous sieve accurate till billions. There has never been in the history of mathematics the mathematical derivation of the π value by precise mathematics of space constriction of value 4 to value 3. Current acceptable π value is by dogma and tradition and is not correct except by dogma, and does not have a pure mathematical derivation. Words like transcendental, are a dogma, and approximate mathematics.
The relevance of this paper to current approximate mathematics and the sciences is a massive change, because this mathematics binds numbers in the rationality of a finite space of the primordial constriction from 4 to 3 coordinates, which leads to a specific calculable mathematical π, correct trigonometry, and the divergence of 1:3, and the placement of all prime numbers. We have also separately produced the continuous Prime number sieve at 1/3, 2/3, 5/ 6 and 1/6 (den- otter continuous sieve of Prime numbers). The method of the sieve is impossible for current mathematics to understand as the discoverer is uneducated and hard to comprehend except by chalk board. It is a continuous sieve accurate till billions. There has never been in the history of mathematics the mathematical derivation of the π value by precise mathematics of space constriction of value 4 to value 3. Current acceptable π value is by dogma and tradition and is not correct except by dogma, and does not have a pure mathematical derivation. Words like transcendental, are a dogma, and approximate mathematics.
The Case against Educated Mathematical Dogma (Precise Mathematical Pi Value by Finite Equation =3.14159292035) 3+(1/(7+1/16)) Precise Finite Value
doi:10.11648/j.pamj.20130205.14
Pure and Applied Mathematics Journal
2014-01-01
© Science Publishing Group
Vinoo Cameron
The Case against Educated Mathematical Dogma (Precise Mathematical Pi Value by Finite Equation =3.14159292035) 3+(1/(7+1/16)) Precise Finite Value
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http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20130205.14
© Science Publishing Group
On Some Properties of Hollow and Hollow Dimension Modules
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20130205.12
No doubt, a notion of the hollow dimension modules can constitute a very important situation in the module theory. Therefore, our work presents a key role mainly in some properties and characterizations of hollow and hollow dimension module. We prove that if R be a V-ring and M is semisimple with indecomposable property, then M is hollow module. Also we study characterization the relation between lifting property and hollow-lifting module. We prove that if M is a nonzero indecomposable and lifting module over a commutative noetherian ring R then M is hollow module. Let M be an R-module and N be a submodule of M if hdim(M) = hdim(M/N) + hdim(N), then M is supplemented module.
No doubt, a notion of the hollow dimension modules can constitute a very important situation in the module theory. Therefore, our work presents a key role mainly in some properties and characterizations of hollow and hollow dimension module. We prove that if R be a V-ring and M is semisimple with indecomposable property, then M is hollow module. Also we study characterization the relation between lifting property and hollow-lifting module. We prove that if M is a nonzero indecomposable and lifting module over a commutative noetherian ring R then M is hollow module. Let M be an R-module and N be a submodule of M if hdim(M) = hdim(M/N) + hdim(N), then M is supplemented module.
On Some Properties of Hollow and Hollow Dimension Modules
doi:10.11648/j.pamj.20130205.12
Pure and Applied Mathematics Journal
2014-01-01
© Science Publishing Group
Majid Mohammed
Abd Ghafur Bin Ahmad
On Some Properties of Hollow and Hollow Dimension Modules
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2014-01-01
10.11648/j.pamj.20130205.12
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20130205.12
© Science Publishing Group
Proof for the Beal Conjecture and a New Proof for Fermat's Last Theorem
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20130205.11
The Beal Conjecture was formulated in 1997 and presented as a generalization of Fermat's Last Theorem, within the number theory´s field. It states that, for X, Y, Z, n_1, n_2 and n_3 positive integers with n_1, n_2, n_3> 2, if X^(n_1 )+Y^(n_2 )=Z^(n_3 ) then X, Y, Z must have a common prime factor. This article presents the proof for the Beal Conjecture, obtained from the correspondences between the real solutions of the equations in the forms A^2+B^2=C^2, δ^n+γ^n=α^n and X^(n_1 )+Y^(n_2 )=Z^(n_3 ). In addition, a proof for the Fermat's Last Theorem was performed using basic math.
The Beal Conjecture was formulated in 1997 and presented as a generalization of Fermat's Last Theorem, within the number theory´s field. It states that, for X, Y, Z, n_1, n_2 and n_3 positive integers with n_1, n_2, n_3> 2, if X^(n_1 )+Y^(n_2 )=Z^(n_3 ) then X, Y, Z must have a common prime factor. This article presents the proof for the Beal Conjecture, obtained from the correspondences between the real solutions of the equations in the forms A^2+B^2=C^2, δ^n+γ^n=α^n and X^(n_1 )+Y^(n_2 )=Z^(n_3 ). In addition, a proof for the Fermat's Last Theorem was performed using basic math.
Proof for the Beal Conjecture and a New Proof for Fermat's Last Theorem
doi:10.11648/j.pamj.20130205.11
Pure and Applied Mathematics Journal
2014-01-01
© Science Publishing Group
Leandro Torres Di Gregorio
Proof for the Beal Conjecture and a New Proof for Fermat's Last Theorem
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2014-01-01
10.11648/j.pamj.20130205.11
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20130205.11
© Science Publishing Group
Generalized Order–k Pell–Padovan–Like Numbers by Matrix Methods
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20130206.11
Weconsider the third – order recurrence relation Q_n=2Q_(n-2)+Q_(n-3) with initial conditionsQ_0=1,Q_1=0 "and" Q_2=2 and define these numbers as Pell – Padovan – like numbers.We extend this definition generalized order – k Pell – Padovan – like numbers and give some relations between thesenumbers and the Fibonacci numbers. Wealso obtain some relations of thesenumbers and matrices by using matrix methods.
Weconsider the third – order recurrence relation Q_n=2Q_(n-2)+Q_(n-3) with initial conditionsQ_0=1,Q_1=0 "and" Q_2=2 and define these numbers as Pell – Padovan – like numbers.We extend this definition generalized order – k Pell – Padovan – like numbers and give some relations between thesenumbers and the Fibonacci numbers. Wealso obtain some relations of thesenumbers and matrices by using matrix methods.
Generalized Order–k Pell–Padovan–Like Numbers by Matrix Methods
doi:10.11648/j.pamj.20130206.11
Pure and Applied Mathematics Journal
2014-01-01
© Science Publishing Group
Goksal Bilgici
Generalized Order–k Pell–Padovan–Like Numbers by Matrix Methods
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2014-01-01
10.11648/j.pamj.20130206.11
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20130206.11
© Science Publishing Group
Existence of Positive Solution for Fourth Order Superlinear Singular Semipositone Differential System
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20130206.12
By transforming the boundary value problem into the corresponding fixed-point problem of a completely continuous operator, the existence is obtained in the paper for two-point boundary value problem of fourth order superlinear singular semipositone differential system via the fixed point theorem concerning cone compression and expansion in norm type.
By transforming the boundary value problem into the corresponding fixed-point problem of a completely continuous operator, the existence is obtained in the paper for two-point boundary value problem of fourth order superlinear singular semipositone differential system via the fixed point theorem concerning cone compression and expansion in norm type.
Existence of Positive Solution for Fourth Order Superlinear Singular Semipositone Differential System
doi:10.11648/j.pamj.20130206.12
Pure and Applied Mathematics Journal
2014-01-01
© Science Publishing Group
Wang Feng
Junmin Zhang
Existence of Positive Solution for Fourth Order Superlinear Singular Semipositone Differential System
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2014-01-01
10.11648/j.pamj.20130206.12
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20130206.12
© Science Publishing Group
A Nonexistence of Solutions to a Supercritical Problem
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20130206.13
In this paper, we study the nonlinear elliptic problem involving nearly critical exponent (P_ϵ ) ∶ -∆u=K u^(□((n+2)/(n-2))+ϵ) in Ω ; u >0 in Ω and u=0 on ∂ Ω where is a smooth bounded domain in 〖IR〗^n n≥3, K is a C^3positive function and ϵ is a small positive real parameter. We prove that, for small, (Pε) has no positive solutions which blow up at one critical point of the function K.
In this paper, we study the nonlinear elliptic problem involving nearly critical exponent (P_ϵ ) ∶ -∆u=K u^(□((n+2)/(n-2))+ϵ) in Ω ; u >0 in Ω and u=0 on ∂ Ω where is a smooth bounded domain in 〖IR〗^n n≥3, K is a C^3positive function and ϵ is a small positive real parameter. We prove that, for small, (Pε) has no positive solutions which blow up at one critical point of the function K.
A Nonexistence of Solutions to a Supercritical Problem
doi:10.11648/j.pamj.20130206.13
Pure and Applied Mathematics Journal
2014-01-01
© Science Publishing Group
Kamal Ould Bouh
A Nonexistence of Solutions to a Supercritical Problem
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2014-01-01
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http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20130206.13
© Science Publishing Group
Derivation of Energy Equation for Turbulent Flow with Two-Point Correlation
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20130206.15
The energy equation for turbulent flow has been derived in terms of correlation tensors of second order, where the correlation tensors are the functions of space coordinates, distance between two points and time. An independent variable has been introduced in order to differentiate between the effects of distance and location. 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 energy equation for turbulent flow has been derived in terms of correlation tensors of second order, where the correlation tensors are the functions of space coordinates, distance between two points and time. An independent variable has been introduced in order to differentiate between the effects of distance and location. 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.
Derivation of Energy Equation for Turbulent Flow with Two-Point Correlation
doi:10.11648/j.pamj.20130206.15
Pure and Applied Mathematics Journal
2014-01-01
© Science Publishing Group
Shams Forruque Ahmed
Derivation of Energy Equation for Turbulent Flow with Two-Point Correlation
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http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20130206.15
© Science Publishing Group
Modular Cone Metric Spaces
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20130206.14
In this paper a generalization of a modular metric which is also a generalization of cone metric, is introduced and some of its topological properties are studied. Next, a fixed point theorem in this space is proved and finally by an example, it is proved that the fixed point result of the paper "Ch. Mongkolkeha, W. Sintunavarat, P. Kumam, Fixed point theorems for contraction mapping in modular metric spaces, Fixed Point Theory Appl. (2011)" is not true.
In this paper a generalization of a modular metric which is also a generalization of cone metric, is introduced and some of its topological properties are studied. Next, a fixed point theorem in this space is proved and finally by an example, it is proved that the fixed point result of the paper "Ch. Mongkolkeha, W. Sintunavarat, P. Kumam, Fixed point theorems for contraction mapping in modular metric spaces, Fixed Point Theory Appl. (2011)" is not true.
Modular Cone Metric Spaces
doi:10.11648/j.pamj.20130206.14
Pure and Applied Mathematics Journal
2014-01-01
© Science Publishing Group
Saeedeh Shamsi Gamchi
Asadollah Niknam
Modular Cone Metric Spaces
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2014-01-01
10.11648/j.pamj.20130206.14
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20130206.14
© Science Publishing Group
Precondition for Discretized Fractional Boundary Value Problem
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20140301.11
A precondition that uses the special structure of the algebraic system arising from the discretization of a fractional partial differential equation on the red black ordering grid is introduced. Comparison with the numerical solution of the classical Poisson’s equationis considered. A graphical representation for the precondition is illustrated. The performance of our treatment is calculated for different values of the fractional order. The results of the implementation of the SOR and the KSOR with the help of MATLAB are given in compact tables. The value of the relaxation parameter is chosen on the bases of the graphical representation of the behavior of the spectral radius of the iteration matrices. Also, the natural ordering grid is considered.
A precondition that uses the special structure of the algebraic system arising from the discretization of a fractional partial differential equation on the red black ordering grid is introduced. Comparison with the numerical solution of the classical Poisson’s equationis considered. A graphical representation for the precondition is illustrated. The performance of our treatment is calculated for different values of the fractional order. The results of the implementation of the SOR and the KSOR with the help of MATLAB are given in compact tables. The value of the relaxation parameter is chosen on the bases of the graphical representation of the behavior of the spectral radius of the iteration matrices. Also, the natural ordering grid is considered.
Precondition for Discretized Fractional Boundary Value Problem
doi:10.11648/j.pamj.20140301.11
Pure and Applied Mathematics Journal
2014-01-01
© Science Publishing Group
I. K. Youssef
A. M. Shukur
Precondition for Discretized Fractional Boundary Value Problem
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2014-01-01
2014-01-01
10.11648/j.pamj.20140301.11
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20140301.11
© Science Publishing Group
On the Symmetry Classes of Tensors Associated with Certain Frobenius Groups
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20140301.12
In this paper, we study the symmetry classes of tensors associated with some Frobenius groups of order pq, where q|p-1as a subgroups of the full symmetric group on p letters. We calculate the dimension of the symmetry classes of tensor associated with some Frobenius groups and some irreducible complex characters and we obtain two useful corollary with an example.
In this paper, we study the symmetry classes of tensors associated with some Frobenius groups of order pq, where q|p-1as a subgroups of the full symmetric group on p letters. We calculate the dimension of the symmetry classes of tensor associated with some Frobenius groups and some irreducible complex characters and we obtain two useful corollary with an example.
On the Symmetry Classes of Tensors Associated with Certain Frobenius Groups
doi:10.11648/j.pamj.20140301.12
Pure and Applied Mathematics Journal
2014-01-01
© Science Publishing Group
N. Shajareh Poursalavati
On the Symmetry Classes of Tensors Associated with Certain Frobenius Groups
3
1
10
10
2014-01-01
2014-01-01
10.11648/j.pamj.20140301.12
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20140301.12
© Science Publishing Group
Topological BCL+- Algebras
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20140301.13
BCL/BCL+-algebras [1, 2] are more extensive class than BCK/BCI/BCH-algebras [5-8], introduced by Yonghong Liu. In this paper, we aim to embed topological structure in BCL+-algebras, thus we should be introduced to the notion of “good taste”, which is both topological space and metric space. Thereupon, some fundamental properties of topological BCL+-algebras are obtained.
BCL/BCL+-algebras [1, 2] are more extensive class than BCK/BCI/BCH-algebras [5-8], introduced by Yonghong Liu. In this paper, we aim to embed topological structure in BCL+-algebras, thus we should be introduced to the notion of “good taste”, which is both topological space and metric space. Thereupon, some fundamental properties of topological BCL+-algebras are obtained.
Topological BCL+- Algebras
doi:10.11648/j.pamj.20140301.13
Pure and Applied Mathematics Journal
2014-01-01
© Science Publishing Group
Yonghong Liu
Topological BCL+- Algebras
3
1
13
13
2014-01-01
2014-01-01
10.11648/j.pamj.20140301.13
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20140301.13
© Science Publishing Group
Alternative Tools of Statistical Analysis: L-moments and TL-moments of Probability Distributions
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20140302.11
Moments and cumulants are commonly used to characterize the probability distribution or observed data set. The use of the moment method of parameter estimation is also common in the construction of an appropriate parametric distribution for a certain data set. The moment method does not always produce satisfactory results. It is difficult to determine exactly what information concerning the shape of the distribution is expressed by its moments of the third and higher order. In the case of small samples in particular, numerical values of sample moments can be very different from the corresponding values of theoretical moments of the relevant probability distribution from which the random sample comes. Parameter estimations of the probability distribution made by the moment method are often considerably less accurate than those obtained using other methods, particularly in the case of small samples. The present paper deals with an alternative approach to the construction of an appropriate parametric distribution for the considered data set using order statistics
Moments and cumulants are commonly used to characterize the probability distribution or observed data set. The use of the moment method of parameter estimation is also common in the construction of an appropriate parametric distribution for a certain data set. The moment method does not always produce satisfactory results. It is difficult to determine exactly what information concerning the shape of the distribution is expressed by its moments of the third and higher order. In the case of small samples in particular, numerical values of sample moments can be very different from the corresponding values of theoretical moments of the relevant probability distribution from which the random sample comes. Parameter estimations of the probability distribution made by the moment method are often considerably less accurate than those obtained using other methods, particularly in the case of small samples. The present paper deals with an alternative approach to the construction of an appropriate parametric distribution for the considered data set using order statistics
Alternative Tools of Statistical Analysis: L-moments and TL-moments of Probability Distributions
doi:10.11648/j.pamj.20140302.11
Pure and Applied Mathematics Journal
2014-04-18
© Science Publishing Group
Diana Bílková
Alternative Tools of Statistical Analysis: L-moments and TL-moments of Probability Distributions
3
2
25
25
2014-04-18
2014-04-18
10.11648/j.pamj.20140302.11
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20140302.11
© Science Publishing Group
On the System Analysis of the Foundations of Trigonometry
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20140302.12
Analysis of the foundations of standard trigonometry is proposed. The unity of formal logic and of rational dialectics is methodological basis of the analysis. It is shown that the foundations of trigonometry contradict to the principles of system approach and contain formal-logical errors. The principal logical error is that the definitions of trigonometric functions represent quantitative relationships between the different qualities: between qualitative determinacy of angle and qualitative determinacy of rectilinear segments (legs) in rectangular triangle. These relationships do not satisfy the standard definition of mathematical function because there are no mathematical operations that should be carry out on qualitative determinacy of angle to obtain qualitative determinacy of legs. Therefore, the left-hand and right-hand sides of the standard mathematical definitions have no the identical sense. The logical errors determine the essence of trigonometry: standard trigonometry is a false theory.
Analysis of the foundations of standard trigonometry is proposed. The unity of formal logic and of rational dialectics is methodological basis of the analysis. It is shown that the foundations of trigonometry contradict to the principles of system approach and contain formal-logical errors. The principal logical error is that the definitions of trigonometric functions represent quantitative relationships between the different qualities: between qualitative determinacy of angle and qualitative determinacy of rectilinear segments (legs) in rectangular triangle. These relationships do not satisfy the standard definition of mathematical function because there are no mathematical operations that should be carry out on qualitative determinacy of angle to obtain qualitative determinacy of legs. Therefore, the left-hand and right-hand sides of the standard mathematical definitions have no the identical sense. The logical errors determine the essence of trigonometry: standard trigonometry is a false theory.
On the System Analysis of the Foundations of Trigonometry
doi:10.11648/j.pamj.20140302.12
Pure and Applied Mathematics Journal
2014-04-27
© Science Publishing Group
Temur Z. Kalanov
On the System Analysis of the Foundations of Trigonometry
3
2
39
39
2014-04-27
2014-04-27
10.11648/j.pamj.20140302.12
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20140302.12
© Science Publishing Group
A Convex Hull’ Characterization
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20140302.13
Conditions so that a vector belongs to a convex hull are obtained. Multilinear convex functions are considered. If these maps are defined on a convex set, it is obtained the algebraic expression. As an application, infinite games, with linear convex payoff, are studied.
Conditions so that a vector belongs to a convex hull are obtained. Multilinear convex functions are considered. If these maps are defined on a convex set, it is obtained the algebraic expression. As an application, infinite games, with linear convex payoff, are studied.
A Convex Hull’ Characterization
doi:10.11648/j.pamj.20140302.13
Pure and Applied Mathematics Journal
2014-05-19
© Science Publishing Group
Franco Fineschi
Giovanni Quaranta
A Convex Hull’ Characterization
3
2
48
48
2014-05-19
2014-05-19
10.11648/j.pamj.20140302.13
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20140302.13
© Science Publishing Group
Stairs of Natural Set Theories
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All contemporary set theories have intersected classes. We have built the stairs of set theories with disjoint classes. We call such theories natural. We numerate these theories by ordinals. The first set theory is T_0. We build the theory from the set N of natural numbers by using the operations of direct products and of power set by finite times. The theory contains all results of Cantor’s theory. We argue that the theory can satisfy all needs of applied mathematics. We build theory T_1 by using the universe set of all sets of T_0 and by using the operations of direct products and of power set by finite times. We build theory T_α+1 from the set of previous by using the operations of direct products and of power set by finite times, too. We build theory T_ω from the set of all sets of T_α with α < ω again by using the operations of direct products and of power set by finite times. And so on for every theory T_α, if theory T_α-1 does not exists. We use the join of all these sets to build theory T_On without operation of power set. We call members of T_On families, members of families sets, families, which are not members of families, up-sets. Families are an analog of classes of the MK set theory and up-sets are an analog of proper classes of MK theory. The theory T_On is more strong than MK theory because we use more strong axiom of comprehension. The last theory T_On+1 is external to T_On. We use T_On+1 to prove those theorems of T_On that are unproved in T_On.
All contemporary set theories have intersected classes. We have built the stairs of set theories with disjoint classes. We call such theories natural. We numerate these theories by ordinals. The first set theory is T_0. We build the theory from the set N of natural numbers by using the operations of direct products and of power set by finite times. The theory contains all results of Cantor’s theory. We argue that the theory can satisfy all needs of applied mathematics. We build theory T_1 by using the universe set of all sets of T_0 and by using the operations of direct products and of power set by finite times. We build theory T_α+1 from the set of previous by using the operations of direct products and of power set by finite times, too. We build theory T_ω from the set of all sets of T_α with α < ω again by using the operations of direct products and of power set by finite times. And so on for every theory T_α, if theory T_α-1 does not exists. We use the join of all these sets to build theory T_On without operation of power set. We call members of T_On families, members of families sets, families, which are not members of families, up-sets. Families are an analog of classes of the MK set theory and up-sets are an analog of proper classes of MK theory. The theory T_On is more strong than MK theory because we use more strong axiom of comprehension. The last theory T_On+1 is external to T_On. We use T_On+1 to prove those theorems of T_On that are unproved in T_On.
Stairs of Natural Set Theories
doi:10.11648/j.pamj.20140303.11
Pure and Applied Mathematics Journal
2014-06-10
© Science Publishing Group
Maydim A. Malkov
Stairs of Natural Set Theories
3
3
65
65
2014-06-10
2014-06-10
10.11648/j.pamj.20140303.11
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20140303.11
© Science Publishing Group
A Note on Localization of Supplemented Modules
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20140303.12
In this paper we study on commutative rings with identity and all modules are unital left R-modules unless otherwise stated. We define the concept of small submodules for localization modules and additionally, we present the relation between an R-module M and an R_p-localization module M_p for all maximal ideals of R in view of being supplemented.
In this paper we study on commutative rings with identity and all modules are unital left R-modules unless otherwise stated. We define the concept of small submodules for localization modules and additionally, we present the relation between an R-module M and an R_p-localization module M_p for all maximal ideals of R in view of being supplemented.
A Note on Localization of Supplemented Modules
doi:10.11648/j.pamj.20140303.12
Pure and Applied Mathematics Journal
2014-07-10
© Science Publishing Group
Esra Öztürk
Şenol Eren
A Note on Localization of Supplemented Modules
3
3
69
69
2014-07-10
2014-07-10
10.11648/j.pamj.20140303.12
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20140303.12
© Science Publishing Group
On Expressive Construction of Solitons from Physiological Wave Phenomena
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Physiological waves, much like the waves of some other physical phenomena, consist of non-linear and dispersive terms. In studies involving patho-physiology, models on arterial pulse waves indicate that the waveforms behave like solitons. The Korteweg-deVrie (KdV) equation, which is known to admit soliton solutions, is seen to hold well for arterial pulse waves. The foregoing underpins the need for detailed knowledge of the construction of solitons. In the light of this, plane wave solution would fail to yield the desired goal, let alone where arterial pulse waves are physiological waves that decompose into a travelling wave representing fast transmission phenomena during systolic phase and a windkessel term representing slow transmission phenomena during diastolic phase. This paper elucidates the construction of the solitons that arise from the so called KdV equation. The goal is to enhance an authentic analysis of soliton-based clinical details.
Physiological waves, much like the waves of some other physical phenomena, consist of non-linear and dispersive terms. In studies involving patho-physiology, models on arterial pulse waves indicate that the waveforms behave like solitons. The Korteweg-deVrie (KdV) equation, which is known to admit soliton solutions, is seen to hold well for arterial pulse waves. The foregoing underpins the need for detailed knowledge of the construction of solitons. In the light of this, plane wave solution would fail to yield the desired goal, let alone where arterial pulse waves are physiological waves that decompose into a travelling wave representing fast transmission phenomena during systolic phase and a windkessel term representing slow transmission phenomena during diastolic phase. This paper elucidates the construction of the solitons that arise from the so called KdV equation. The goal is to enhance an authentic analysis of soliton-based clinical details.
On Expressive Construction of Solitons from Physiological Wave Phenomena
doi:10.11648/j.pamj.20140303.13
Pure and Applied Mathematics Journal
2014-07-18
© Science Publishing Group
Nzerem Francis Egenti
On Expressive Construction of Solitons from Physiological Wave Phenomena
3
3
77
77
2014-07-18
2014-07-18
10.11648/j.pamj.20140303.13
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20140303.13
© Science Publishing Group
First-Order Reactant of Homogeneous Dusty Fluid Turbulence Prior to the Final Period of Decay in a Rotating System for the Case of Multi-Point and Multi-Time at Four-Point Correlation
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20140304.11
In this paper following Deissler’s approach and taking Fourier transform, the decay for the concentration of a dilute contaminant undergoing a first-order chemical reaction in dusty fluid homogeneous turbulence at times prior to the ultimate phase in a rotating system for the case of multi-point and multi-time at four point correlation is studied. Here two and three point correlations between fluctuating quantities have been considered and the quadruple correlations are ignored in comparison to the second and third order correlations. Taking Fourier transform the correlation equations are converted to spectral form. Finally, integrating the energy spectrum over all wave numbers we obtained the decay law for the concentration fluctuations of first order reactant in homogeneous dusty fluid turbulence prior to the final period of decay in a rotating system for the case of multi-point and multi-time at four-point correlation.
In this paper following Deissler’s approach and taking Fourier transform, the decay for the concentration of a dilute contaminant undergoing a first-order chemical reaction in dusty fluid homogeneous turbulence at times prior to the ultimate phase in a rotating system for the case of multi-point and multi-time at four point correlation is studied. Here two and three point correlations between fluctuating quantities have been considered and the quadruple correlations are ignored in comparison to the second and third order correlations. Taking Fourier transform the correlation equations are converted to spectral form. Finally, integrating the energy spectrum over all wave numbers we obtained the decay law for the concentration fluctuations of first order reactant in homogeneous dusty fluid turbulence prior to the final period of decay in a rotating system for the case of multi-point and multi-time at four-point correlation.
First-Order Reactant of Homogeneous Dusty Fluid Turbulence Prior to the Final Period of Decay in a Rotating System for the Case of Multi-Point and Multi-Time at Four-Point Correlation
doi:10.11648/j.pamj.20140304.11
Pure and Applied Mathematics Journal
2014-08-07
© Science Publishing Group
M. Abu Bkar Pk
M. Monuar Hossain
M. Abul Kalam Azad
First-Order Reactant of Homogeneous Dusty Fluid Turbulence Prior to the Final Period of Decay in a Rotating System for the Case of Multi-Point and Multi-Time at Four-Point Correlation
3
4
86
86
2014-08-07
2014-08-07
10.11648/j.pamj.20140304.11
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20140304.11
© Science Publishing Group
On the Construction of Regions of Stability
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20140304.12
In this paper we built a stability region around the origin for the Liénard equation (4) to ensure stability and boundedness of solutions of this equation, without making use of the classical Second Method of Lyapunov. We compare our result with some others proposed by different authors.
In this paper we built a stability region around the origin for the Liénard equation (4) to ensure stability and boundedness of solutions of this equation, without making use of the classical Second Method of Lyapunov. We compare our result with some others proposed by different authors.
On the Construction of Regions of Stability
doi:10.11648/j.pamj.20140304.12
Pure and Applied Mathematics Journal
2014-08-26
© Science Publishing Group
Luciano Miguel Lugo
Juan Eduardo Nápoles Valdés
Samuel Iván Noya
On the Construction of Regions of Stability
3
4
91
91
2014-08-26
2014-08-26
10.11648/j.pamj.20140304.12
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20140304.12
© Science Publishing Group
Stability of a Jensen's Functional Equation in Banach Spaces
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20140304.13
Our aim in this note is to study the Hyers -Ulam stability and we investigate the Hyers-Ulam stability of generalized Jensen's Functional Equation in Banach Spaces: f ((x + y)/2) = (f(x) + f(y))/2
Our aim in this note is to study the Hyers -Ulam stability and we investigate the Hyers-Ulam stability of generalized Jensen's Functional Equation in Banach Spaces: f ((x + y)/2) = (f(x) + f(y))/2
Stability of a Jensen's Functional Equation in Banach Spaces
doi:10.11648/j.pamj.20140304.13
Pure and Applied Mathematics Journal
2014-09-20
© Science Publishing Group
Seyed Habib Shakoory
Stability of a Jensen's Functional Equation in Banach Spaces
3
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94
94
2014-09-20
2014-09-20
10.11648/j.pamj.20140304.13
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20140304.13
© Science Publishing Group
Oscillation Criteria for a Class of Second Order Neutral Delay Differential Equations
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20140305.11
Oscillation criteria for a class of second order neutral delay differential equations of the form [c(t)((x(t)+p(t)x(t-τ))^' )^α ]^'+q(t)f(x(t-σ) )=0,t≥t_0 is studied. By using first and second mean value theorem of integrals, the new sufficient condition is obtained and the corresponding result what was already obtained is generalized by the result in this paper.
Oscillation criteria for a class of second order neutral delay differential equations of the form [c(t)((x(t)+p(t)x(t-τ))^' )^α ]^'+q(t)f(x(t-σ) )=0,t≥t_0 is studied. By using first and second mean value theorem of integrals, the new sufficient condition is obtained and the corresponding result what was already obtained is generalized by the result in this paper.
Oscillation Criteria for a Class of Second Order Neutral Delay Differential Equations
doi:10.11648/j.pamj.20140305.11
Pure and Applied Mathematics Journal
2014-09-20
© Science Publishing Group
Yanxiang Shi
Di Liu
Oscillation Criteria for a Class of Second Order Neutral Delay Differential Equations
3
5
98
98
2014-09-20
2014-09-20
10.11648/j.pamj.20140305.11
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20140305.11
© Science Publishing Group
On Differential Growth Equation to Stochastic Growth Model Using Hyperbolic Sine Function in Height/Diameter Modeling of Pines
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20140305.12
Richrads growth equation being a generalized logistic growth equation was improved upon by introducing an allometric parameter using the hyperbolic sine function. The integral solution to this was called hyperbolic Richards growth model having transformed the solution from deterministic to a stochastic growth model. Its ability in model prediction was compared with the classical Richards growth model an approach which mimicked the natural variability of heights/diameter increment with respect to age and therefore provides a more realistic height/diameter predictions using the coefficient of determination (R2), Mean Absolute Error (MAE) and Mean Square Error (MSE) results. The Kolmogorov Smirnov test and Shapiro-Wilk test was also used to test the behavior of the error term for possible violations. The mean function of top height/Dbh over age using the two models under study predicted closely the observed values of top height/Dbh in the hyperbolic Richards nonlinear growth models better than the classical Richards growth model.
Richrads growth equation being a generalized logistic growth equation was improved upon by introducing an allometric parameter using the hyperbolic sine function. The integral solution to this was called hyperbolic Richards growth model having transformed the solution from deterministic to a stochastic growth model. Its ability in model prediction was compared with the classical Richards growth model an approach which mimicked the natural variability of heights/diameter increment with respect to age and therefore provides a more realistic height/diameter predictions using the coefficient of determination (R2), Mean Absolute Error (MAE) and Mean Square Error (MSE) results. The Kolmogorov Smirnov test and Shapiro-Wilk test was also used to test the behavior of the error term for possible violations. The mean function of top height/Dbh over age using the two models under study predicted closely the observed values of top height/Dbh in the hyperbolic Richards nonlinear growth models better than the classical Richards growth model.
On Differential Growth Equation to Stochastic Growth Model Using Hyperbolic Sine Function in Height/Diameter Modeling of Pines
doi:10.11648/j.pamj.20140305.12
Pure and Applied Mathematics Journal
2014-10-09
© Science Publishing Group
Oyamakin Samuel Oluwafemi
Chukwu Angela Unna
On Differential Growth Equation to Stochastic Growth Model Using Hyperbolic Sine Function in Height/Diameter Modeling of Pines
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5
104
104
2014-10-09
2014-10-09
10.11648/j.pamj.20140305.12
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20140305.12
© Science Publishing Group
A Study on Compactness in Metric Spaces and Topological Spaces
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20140305.13
Topology may be considered as an abstract study of the limit point concept. As such, it stems in part from recognition of the fact that many important mathematical topics depend entirely upon the properties of limit points. This study shows that compactness implies limit point compactness but not conversely and every compact space is locally compact but not conversely. This study also shows that compactness, limit point compactness and sequentially compactness are equivalent in metrizable spaces and the product of finitely many compact spaces is a locally compact space. This study introduce it here as an interesting application of the Tychonoff theorem.
Topology may be considered as an abstract study of the limit point concept. As such, it stems in part from recognition of the fact that many important mathematical topics depend entirely upon the properties of limit points. This study shows that compactness implies limit point compactness but not conversely and every compact space is locally compact but not conversely. This study also shows that compactness, limit point compactness and sequentially compactness are equivalent in metrizable spaces and the product of finitely many compact spaces is a locally compact space. This study introduce it here as an interesting application of the Tychonoff theorem.
A Study on Compactness in Metric Spaces and Topological Spaces
doi:10.11648/j.pamj.20140305.13
Pure and Applied Mathematics Journal
2014-10-15
© Science Publishing Group
Rabeya Akter
Nour Mohammed Chowdhury
Mohammad Safi Ullah
A Study on Compactness in Metric Spaces and Topological Spaces
3
5
112
112
2014-10-15
2014-10-15
10.11648/j.pamj.20140305.13
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20140305.13
© Science Publishing Group
Approximation of Functions by Singular Integrals
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20140306.11
In this work questions on approximation of locally summable functions by singular integrals are investigated. Was estimated the rate of approximation in terms of various metric characteristics describing the structural properties of the given function.
In this work questions on approximation of locally summable functions by singular integrals are investigated. Was estimated the rate of approximation in terms of various metric characteristics describing the structural properties of the given function.
Approximation of Functions by Singular Integrals
doi:10.11648/j.pamj.20140306.11
Pure and Applied Mathematics Journal
2014-11-17
© Science Publishing Group
Rahim M. Rzaev
Gulnara Kh. Mammadova
Mansur Sh. Maharramov
Approximation of Functions by Singular Integrals
3
6
120
120
2014-11-17
2014-11-17
10.11648/j.pamj.20140306.11
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20140306.11
© Science Publishing Group
Derivations of Some Filiform Leibniz Algebras
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20140306.12
In this paper the two classes of filiform Leibniz algebras μ_(0 )^n and μ_(1 )^n in (n+1) dimensions of filiform Leibniz algebras such that n≥2 will be considered. The study includes derivations of naturally graded Leibniz algebras of first class L_n and second class W_n, be algebras whose multiplications rules are defined by the μ_(0 )^n and μ_(1 )^n, respectively. The algebras of derivations of naturally graded Leibniz algebras are described by linear transformations and dimensions derivations. Finally, we determine number of derivations of naturally graded Leibniz algebras.
In this paper the two classes of filiform Leibniz algebras μ_(0 )^n and μ_(1 )^n in (n+1) dimensions of filiform Leibniz algebras such that n≥2 will be considered. The study includes derivations of naturally graded Leibniz algebras of first class L_n and second class W_n, be algebras whose multiplications rules are defined by the μ_(0 )^n and μ_(1 )^n, respectively. The algebras of derivations of naturally graded Leibniz algebras are described by linear transformations and dimensions derivations. Finally, we determine number of derivations of naturally graded Leibniz algebras.
Derivations of Some Filiform Leibniz Algebras
doi:10.11648/j.pamj.20140306.12
Pure and Applied Mathematics Journal
2014-11-18
© Science Publishing Group
AL-hossain Ahmad
Khiyar AL-hossain
Derivations of Some Filiform Leibniz Algebras
3
6
125
125
2014-11-18
2014-11-18
10.11648/j.pamj.20140306.12
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20140306.12
© Science Publishing Group
New Fixed Point Theorems of Condensing Mappings Satisfying the Interior Condition in Banach Space
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20140306.13
In this paper, based on a basic result on condensing mappings satisfying the interior condition, some new fixed point theorems of the condensing mappings of this kind are obtained. As a result, the famous Petryshyn's theorem and some results of the Reference [8] are extended to the condensing mappings satisfying the interior condition.
In this paper, based on a basic result on condensing mappings satisfying the interior condition, some new fixed point theorems of the condensing mappings of this kind are obtained. As a result, the famous Petryshyn's theorem and some results of the Reference [8] are extended to the condensing mappings satisfying the interior condition.
New Fixed Point Theorems of Condensing Mappings Satisfying the Interior Condition in Banach Space
doi:10.11648/j.pamj.20140306.13
Pure and Applied Mathematics Journal
2014-11-19
© Science Publishing Group
Shujia Chen
Shaoyuan Xu
New Fixed Point Theorems of Condensing Mappings Satisfying the Interior Condition in Banach Space
3
6
131
131
2014-11-19
2014-11-19
10.11648/j.pamj.20140306.13
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20140306.13
© Science Publishing Group
Visualization of Minkowski Patch
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20140306.14
This study is an introduction to visualize Minkowskian (n, 1) geometry for all n ³1. The Minkowski geometry naturally encodes the ideas of inertial frames, time and space dilation. Moreover, it also includes studying Minkowski patch which is the natural structure of Minkowski space.
This study is an introduction to visualize Minkowskian (n, 1) geometry for all n ³1. The Minkowski geometry naturally encodes the ideas of inertial frames, time and space dilation. Moreover, it also includes studying Minkowski patch which is the natural structure of Minkowski space.
Visualization of Minkowski Patch
doi:10.11648/j.pamj.20140306.14
Pure and Applied Mathematics Journal
2014-12-10
© Science Publishing Group
Rania Bahgat Mohamed Amer
Visualization of Minkowski Patch
3
6
136
136
2014-12-10
2014-12-10
10.11648/j.pamj.20140306.14
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20140306.14
© Science Publishing Group
Fractional Domination for Two Classes of Graphs
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20140306.15
Let be a graph, a real-valued function is said to be a dominating of G if holds for every vertex, the fractional domination function number is defined as, and the fractional total domination function number of G is analogous. In this paper we research the fractional domination problem for two classes of special graphs, obtained the fractional domination numbers of the generalized star graphs and the fractional total domination function numbers of the generalized wheel graphs.
Let be a graph, a real-valued function is said to be a dominating of G if holds for every vertex, the fractional domination function number is defined as, and the fractional total domination function number of G is analogous. In this paper we research the fractional domination problem for two classes of special graphs, obtained the fractional domination numbers of the generalized star graphs and the fractional total domination function numbers of the generalized wheel graphs.
Fractional Domination for Two Classes of Graphs
doi:10.11648/j.pamj.20140306.15
Pure and Applied Mathematics Journal
2015-01-04
© Science Publishing Group
Baogen Xu
Yan Zou
Lixin Zhao
Fractional Domination for Two Classes of Graphs
3
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139
139
2015-01-04
2015-01-04
10.11648/j.pamj.20140306.15
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20140306.15
© Science Publishing Group
New Types of Chaotic Maps
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2014030601.14
In this paper, we will study a new class of chaotic maps on locally compact Hausdorff spaces called Lambda -type chaotic maps and θ-type chaotic maps. The Lambda -type chaotic map implies chaotic map which implies θ-type chaotic map. Further, the definition of topological Lambda -type chaos implies John Tylar definition which implies topological θ-type chaos definition. Relationships with some other types of chaotic maps defined on topological spaces are given.
In this paper, we will study a new class of chaotic maps on locally compact Hausdorff spaces called Lambda -type chaotic maps and θ-type chaotic maps. The Lambda -type chaotic map implies chaotic map which implies θ-type chaotic map. Further, the definition of topological Lambda -type chaos implies John Tylar definition which implies topological θ-type chaos definition. Relationships with some other types of chaotic maps defined on topological spaces are given.
New Types of Chaotic Maps
doi:10.11648/j.pamj.s.2014030601.14
Pure and Applied Mathematics Journal
2014-10-24
© Science Publishing Group
Mohammed Nokhas Murad
New Types of Chaotic Maps
3
6
23
23
2014-10-24
2014-10-24
10.11648/j.pamj.s.2014030601.14
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2014030601.14
© Science Publishing Group
Two New Types of Chaotic Maps and Minimal Systems
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In this paper, we introduce and study the relationship between two different notions of chaotic maps, namely topological α–chaotic maps, topological θ-chaotic maps and investigate some of their properties in two topological spaces (X, τα) and (X, τθ), τα denotes the α–topology(resp. τθ denotes the θ–topology) of a given topological space (X, τ). The two notions are defined by using the concepts of α-transitive map and θ-transitive map respectively Also, we define and study the relationship between two types of minimal mappings, namely, α - minimal mapping and θ-minimal mapping, The main results are the following propositions: 1). Every topologically α-chaotic map is a chaotic map which implies topologically θ- chaotic map, but the converse not necessarily true. 2). Every α-minimal map is a minimal map which implies θ- minimal map in topological spaces, but the converse not necessarily true.
In this paper, we introduce and study the relationship between two different notions of chaotic maps, namely topological α–chaotic maps, topological θ-chaotic maps and investigate some of their properties in two topological spaces (X, τα) and (X, τθ), τα denotes the α–topology(resp. τθ denotes the θ–topology) of a given topological space (X, τ). The two notions are defined by using the concepts of α-transitive map and θ-transitive map respectively Also, we define and study the relationship between two types of minimal mappings, namely, α - minimal mapping and θ-minimal mapping, The main results are the following propositions: 1). Every topologically α-chaotic map is a chaotic map which implies topologically θ- chaotic map, but the converse not necessarily true. 2). Every α-minimal map is a minimal map which implies θ- minimal map in topological spaces, but the converse not necessarily true.
Two New Types of Chaotic Maps and Minimal Systems
doi:10.11648/j.pamj.s.2014030601.12
Pure and Applied Mathematics Journal
2014-09-17
© Science Publishing Group
Mohammed Nokhas Murad Kaki
Sherko Hassan Abdurrahman
Two New Types of Chaotic Maps and Minimal Systems
3
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12
12
2014-09-17
2014-09-17
10.11648/j.pamj.s.2014030601.12
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2014030601.12
© Science Publishing Group
Uncertain Relations on a Finite Set and their Properties
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2014030601.13
There exists some relationships which are difficult to be simply measured by “yes” or “no" in practice, and there must be a certain amount to indicate the extent of this relationship between the two elements. In this paper, the property of the uncertain relations is examined by the uncertainty theory. Firstly it offers the definition of uncertain relation and the concept of property index of the uncertain relation based on uncertain theory; secondly it gives the calculation method of the property index of the uncertain relation; finally, a simple example is presented to illustrate the method.
There exists some relationships which are difficult to be simply measured by “yes” or “no" in practice, and there must be a certain amount to indicate the extent of this relationship between the two elements. In this paper, the property of the uncertain relations is examined by the uncertainty theory. Firstly it offers the definition of uncertain relation and the concept of property index of the uncertain relation based on uncertain theory; secondly it gives the calculation method of the property index of the uncertain relation; finally, a simple example is presented to illustrate the method.
Uncertain Relations on a Finite Set and their Properties
doi:10.11648/j.pamj.s.2014030601.13
Pure and Applied Mathematics Journal
2014-10-20
© Science Publishing Group
Xiulian Gao
Uncertain Relations on a Finite Set and their Properties
3
6
19
19
2014-10-20
2014-10-20
10.11648/j.pamj.s.2014030601.13
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2014030601.13
© Science Publishing Group
New Types of Chaos and Non-Wandering Points in Topological Spaces
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2014030601.11
In this paper, we will define a new class of chaotic maps on locally compact Hausdorff spaces called α-type chaotic maps defined by α-type transitive maps. This new definition coincides with Devaney's definition for chaos when the topological space happens to be a metric space. Furthermore, we will study new types of non-wandering points called α-type nonwandering points. We have shown that the α-type nonwandering points imply nonwandering points but not conversely. Finally, we have defined new concepts of chaotic on topological space. Relationships with some other type of chaotic maps are given.
In this paper, we will define a new class of chaotic maps on locally compact Hausdorff spaces called α-type chaotic maps defined by α-type transitive maps. This new definition coincides with Devaney's definition for chaos when the topological space happens to be a metric space. Furthermore, we will study new types of non-wandering points called α-type nonwandering points. We have shown that the α-type nonwandering points imply nonwandering points but not conversely. Finally, we have defined new concepts of chaotic on topological space. Relationships with some other type of chaotic maps are given.
New Types of Chaos and Non-Wandering Points in Topological Spaces
doi:10.11648/j.pamj.s.2014030601.11
Pure and Applied Mathematics Journal
2014-09-02
© Science Publishing Group
Mohammed N. Murad Kaki
New Types of Chaos and Non-Wandering Points in Topological Spaces
3
6
6
6
2014-09-02
2014-09-02
10.11648/j.pamj.s.2014030601.11
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2014030601.11
© Science Publishing Group
Catastrophic Types Depending on Degree of Non-Linearity
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2014030601.15
In this paper, we present results on the projection of the folding part of the elementary catastrophe models on the control space to find stability and catastrophic phenomenon of the periodic solutions of some nonlinear differential equations (NLDE) by using methods of catastrophe theory. We have shown here, that the cusp and Butterfly types depend on the degree of nonlinear differential equations, and that the bifurcation can be classified as cusp or butterfly types catastrophe. Moreover, our aim, in this work, is to obtain periodic solutions of some nonlinear differential equation (NLDE) and to study the stability of these periodic solutions and the main result is the following proposition: The catastrophic Types depending on the degree of non-linear differential equation.
In this paper, we present results on the projection of the folding part of the elementary catastrophe models on the control space to find stability and catastrophic phenomenon of the periodic solutions of some nonlinear differential equations (NLDE) by using methods of catastrophe theory. We have shown here, that the cusp and Butterfly types depend on the degree of nonlinear differential equations, and that the bifurcation can be classified as cusp or butterfly types catastrophe. Moreover, our aim, in this work, is to obtain periodic solutions of some nonlinear differential equation (NLDE) and to study the stability of these periodic solutions and the main result is the following proposition: The catastrophic Types depending on the degree of non-linear differential equation.
Catastrophic Types Depending on Degree of Non-Linearity
doi:10.11648/j.pamj.s.2014030601.15
Pure and Applied Mathematics Journal
2014-12-27
© Science Publishing Group
Mohammed Nokhas Murad Kaki
Catastrophic Types Depending on Degree of Non-Linearity
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27
27
2014-12-27
2014-12-27
10.11648/j.pamj.s.2014030601.15
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2014030601.15
© Science Publishing Group
The Recillas’s Conjecture on Szegö Kernels Associated to Harish-Chandra Modules
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2014030602.15
The solution of the field equations that involves non-flat differential operators (curved case) can be obtained as the extensions Φ+Szegö operators in G/K with G, a non-compact Lie group with K, compact. This could be equivalent in the context of the Harish-Chandra modules category to the obtaining of extensions in certain sense (Cousin complexes of sheaves of differential operators to their classification) of Verma modules as classifying spaces of these differential operators and their corresponding integrals through of geometrical integral transforms.
The solution of the field equations that involves non-flat differential operators (curved case) can be obtained as the extensions Φ+Szegö operators in G/K with G, a non-compact Lie group with K, compact. This could be equivalent in the context of the Harish-Chandra modules category to the obtaining of extensions in certain sense (Cousin complexes of sheaves of differential operators to their classification) of Verma modules as classifying spaces of these differential operators and their corresponding integrals through of geometrical integral transforms.
The Recillas’s Conjecture on Szegö Kernels Associated to Harish-Chandra Modules
doi:10.11648/j.pamj.s.2014030602.15
Pure and Applied Mathematics Journal
2014-11-29
© Science Publishing Group
Francisco Bulnes
Kubo Watanabe
Ronin Goborov
The Recillas’s Conjecture on Szegö Kernels Associated to Harish-Chandra Modules
3
6
29
29
2014-11-29
2014-11-29
10.11648/j.pamj.s.2014030602.15
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2014030602.15
© Science Publishing Group
Functors on ∞- Categories and the Yoneda Embedding
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2014030602.14
Through the application of the Yoneda embedding in the context of the ∞- categories is obtained a classification of functors with their corresponding extended functors in the geometrical Langlands program. Also is obtained a functor formula that can be considered in the extending of functors to obtaining of generalized Verma modules. In this isomorphism formula are considered the Verma modules as classifying spaces of these functors.
Through the application of the Yoneda embedding in the context of the ∞- categories is obtained a classification of functors with their corresponding extended functors in the geometrical Langlands program. Also is obtained a functor formula that can be considered in the extending of functors to obtaining of generalized Verma modules. In this isomorphism formula are considered the Verma modules as classifying spaces of these functors.
Functors on ∞- Categories and the Yoneda Embedding
doi:10.11648/j.pamj.s.2014030602.14
Pure and Applied Mathematics Journal
2014-11-24
© Science Publishing Group
Yuri Stropovsvky
Functors on ∞- Categories and the Yoneda Embedding
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25
25
2014-11-24
2014-11-24
10.11648/j.pamj.s.2014030602.14
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2014030602.14
© Science Publishing Group
Moduli Spaces, Non-Commutative Geometry and Deformed Differential Categories
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2014030602.13
The following research plays a central role in deformation theory. If x, is a moduli space over a field k, of characteristic zero, then a formal neighborhood of any point xϵx, is controlled by a differential graded Lie algebra. Then using the derived categories language we give an analogous of the before sentence in the setting of non-commutative geometry, considering some aspects E∞— rings and derived moduli problems related with these rings. After is obtained a scheme to spectrum; by functor Spec and their ∞— category functor inside of the space Fun_(hoat_∞ )to these E∞— rings and their derived moduli in field theory.
The following research plays a central role in deformation theory. If x, is a moduli space over a field k, of characteristic zero, then a formal neighborhood of any point xϵx, is controlled by a differential graded Lie algebra. Then using the derived categories language we give an analogous of the before sentence in the setting of non-commutative geometry, considering some aspects E∞— rings and derived moduli problems related with these rings. After is obtained a scheme to spectrum; by functor Spec and their ∞— category functor inside of the space Fun_(hoat_∞ )to these E∞— rings and their derived moduli in field theory.
Moduli Spaces, Non-Commutative Geometry and Deformed Differential Categories
doi:10.11648/j.pamj.s.2014030602.13
Pure and Applied Mathematics Journal
2014-11-05
© Science Publishing Group
Ivan Verkelov
Moduli Spaces, Non-Commutative Geometry and Deformed Differential Categories
3
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19
19
2014-11-05
2014-11-05
10.11648/j.pamj.s.2014030602.13
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2014030602.13
© Science Publishing Group
Integral Geometry Methods on Deformed Categories in Field Theory II
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The integral geometry methods are applied on deformed categories to obtain correspondences in the geometrical Langlands program and construct the due equivalences between geometrical objects of the moduli stacks and algebraic objects of the corresponding categories and their L_(G-opers) characterizing the solution classes to field theory equations in the belonging cohomological context such as H^0 (g[[z] ],V_critical )=C[Op_LG (D^X)] which is natural in the framework of the integral transforms to the generalizing of the Zuckerman functors that will be useful to the obtaining of the different factors of the universal functor of derived sheaves of Harish-Chandra to the Langlands geometrical program in mirror symmetry. The cosmological problem that exists is to reduce the number of field equations that are resoluble under the same gauge field (Verma modules) and to extend the gauge solutions to other fields using the topological groups symmetries that define their interactions. This extension can be given by a global Langlands correspondence between the Hecke sheaves category H_(G^^ ) ∞ on an adequate moduli stack and the holomorphic L_(G-) bundles category with a special connection (Deligne connection). The corresponding 〖D 〗_-modules may be viewed as sheaves of conformal blocks (or co-invariants) (images under a generalized version of the Penrose transform) naturally arising in the framework of conformal field theory.
The integral geometry methods are applied on deformed categories to obtain correspondences in the geometrical Langlands program and construct the due equivalences between geometrical objects of the moduli stacks and algebraic objects of the corresponding categories and their L_(G-opers) characterizing the solution classes to field theory equations in the belonging cohomological context such as H^0 (g[[z] ],V_critical )=C[Op_LG (D^X)] which is natural in the framework of the integral transforms to the generalizing of the Zuckerman functors that will be useful to the obtaining of the different factors of the universal functor of derived sheaves of Harish-Chandra to the Langlands geometrical program in mirror symmetry. The cosmological problem that exists is to reduce the number of field equations that are resoluble under the same gauge field (Verma modules) and to extend the gauge solutions to other fields using the topological groups symmetries that define their interactions. This extension can be given by a global Langlands correspondence between the Hecke sheaves category H_(G^^ ) ∞ on an adequate moduli stack and the holomorphic L_(G-) bundles category with a special connection (Deligne connection). The corresponding 〖D 〗_-modules may be viewed as sheaves of conformal blocks (or co-invariants) (images under a generalized version of the Penrose transform) naturally arising in the framework of conformal field theory.
Integral Geometry Methods on Deformed Categories in Field Theory II
doi:10.11648/j.pamj.s.2014030602.11
Pure and Applied Mathematics Journal
2014-10-24
© Science Publishing Group
Francisco Bulnes
Integral Geometry Methods on Deformed Categories in Field Theory II
3
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5
5
2014-10-24
2014-10-24
10.11648/j.pamj.s.2014030602.11
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2014030602.11
© Science Publishing Group
Coverings and Axions: Topological Characterizing of the Energy Coverings in Space-Time
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2014030602.12
Inside the QFT and TFT frame is developed a geometrical and topological model of one wrapping energy particle or “axion” to establish the diffeomorphic relation between space and time through of universal coverings. Then is established a scheme that relates both aspects, time and space through of the different objects that these include and their spectrum that is characterized by their wrapping energy.
Inside the QFT and TFT frame is developed a geometrical and topological model of one wrapping energy particle or “axion” to establish the diffeomorphic relation between space and time through of universal coverings. Then is established a scheme that relates both aspects, time and space through of the different objects that these include and their spectrum that is characterized by their wrapping energy.
Coverings and Axions: Topological Characterizing of the Energy Coverings in Space-Time
doi:10.11648/j.pamj.s.2014030602.12
Pure and Applied Mathematics Journal
2014-10-24
© Science Publishing Group
Mario Ramírez
Luis Ramírez
Oscar Ramírez
Francisco Bulnes
Coverings and Axions: Topological Characterizing of the Energy Coverings in Space-Time
3
6
11
11
2014-10-24
2014-10-24
10.11648/j.pamj.s.2014030602.12
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2014030602.12
© Science Publishing Group
Integral Geometry and Complex Space-Time Cohomology in Field Theory
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2014030602.16
Through of a cohomological theory based in the relations between integrating invariants and their different differential operators classes in the field equations as well as of functions inside of the integral geometry are established equivalences among cycles and co-cycles of the closed sub-manifolds, line bundles and contours of the space-time modeled as complex Riemannian manifold obtaining a cohomology of general integrals useful in the evaluation and measurement of fields, particles and physical interactions of diverse nature in field theory. Also are used embeddings of cycles in the complex Riemannian manifold through of the dualities: line bundles with cohomological contours and closed sub-manifolds with cohomological functional to build cohomological spaces of integrals as solution classes of the corresponding field equations.
Through of a cohomological theory based in the relations between integrating invariants and their different differential operators classes in the field equations as well as of functions inside of the integral geometry are established equivalences among cycles and co-cycles of the closed sub-manifolds, line bundles and contours of the space-time modeled as complex Riemannian manifold obtaining a cohomology of general integrals useful in the evaluation and measurement of fields, particles and physical interactions of diverse nature in field theory. Also are used embeddings of cycles in the complex Riemannian manifold through of the dualities: line bundles with cohomological contours and closed sub-manifolds with cohomological functional to build cohomological spaces of integrals as solution classes of the corresponding field equations.
Integral Geometry and Complex Space-Time Cohomology in Field Theory
doi:10.11648/j.pamj.s.2014030602.16
Pure and Applied Mathematics Journal
2014-12-27
© Science Publishing Group
Francisco Bulnes
Ronin Goborov
Integral Geometry and Complex Space-Time Cohomology in Field Theory
3
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37
37
2014-12-27
2014-12-27
10.11648/j.pamj.s.2014030602.16
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2014030602.16
© Science Publishing Group
Approaching by DX- Schemes and Jets to Conformal Blocks in Commutative Moduli Schemes
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2014030602.17
The DX-schemes (and their particular tools example jets) are related to determine conformal blocks of space-time pieces that are invariant under conformal transformations. All algebras will be commutative and Sym will always denote SymOX However, all Hom, and , will be understood over the base ﬁeld k. This will permit the construction of one formal moduli problem on the base of CAlgk whose objects are obtained as limits of the corresponding jets in an AffSpec. An algebra B, belonging to the DX-schemes to the required formal moduli problem is the image under a corresponding generalized Penrose transform, in the conformal context, of many pieces of the space-time, having a structure as objects in commutative rings of CAlgk each one.
The DX-schemes (and their particular tools example jets) are related to determine conformal blocks of space-time pieces that are invariant under conformal transformations. All algebras will be commutative and Sym will always denote SymOX However, all Hom, and , will be understood over the base ﬁeld k. This will permit the construction of one formal moduli problem on the base of CAlgk whose objects are obtained as limits of the corresponding jets in an AffSpec. An algebra B, belonging to the DX-schemes to the required formal moduli problem is the image under a corresponding generalized Penrose transform, in the conformal context, of many pieces of the space-time, having a structure as objects in commutative rings of CAlgk each one.
Approaching by DX- Schemes and Jets to Conformal Blocks in Commutative Moduli Schemes
doi:10.11648/j.pamj.s.2014030602.17
Pure and Applied Mathematics Journal
2015-01-10
© Science Publishing Group
Sergei Fominko
Approaching by DX- Schemes and Jets to Conformal Blocks in Commutative Moduli Schemes
3
6
43
43
2015-01-10
2015-01-10
10.11648/j.pamj.s.2014030602.17
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2014030602.17
© Science Publishing Group
Orbital Euclidean Stability of the Solutions of Impulsive Equations on the Impulsive Moments
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150401.11
Curves given in a parametric form are studied in this paper. Curves are continuous on the left in the general case. Their corresponding parameters belong to the definitional intervals which is possible to not coincide for the different curves. Moreover, the points of discontinuity (if they exist) are first kind (jump discontinuity) and they are specific for each curve. Upper estimates of the Euclidean distance between two such curves are found. The results obtained are used in studies of the solutions of impulsive differential equations. Sufficient conditions for the orbital Euclidean stability of the solutions of such equations in respect to the impulsive effects on the initial condition and impulive moments are found. This type of stability is introduced and studied here for the first time.
Curves given in a parametric form are studied in this paper. Curves are continuous on the left in the general case. Their corresponding parameters belong to the definitional intervals which is possible to not coincide for the different curves. Moreover, the points of discontinuity (if they exist) are first kind (jump discontinuity) and they are specific for each curve. Upper estimates of the Euclidean distance between two such curves are found. The results obtained are used in studies of the solutions of impulsive differential equations. Sufficient conditions for the orbital Euclidean stability of the solutions of such equations in respect to the impulsive effects on the initial condition and impulive moments are found. This type of stability is introduced and studied here for the first time.
Orbital Euclidean Stability of the Solutions of Impulsive Equations on the Impulsive Moments
doi:10.11648/j.pamj.20150401.11
Pure and Applied Mathematics Journal
2015-01-27
© Science Publishing Group
Katya Georgieva Dishlieva
Orbital Euclidean Stability of the Solutions of Impulsive Equations on the Impulsive Moments
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1
8
8
2015-01-27
2015-01-27
10.11648/j.pamj.20150401.11
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150401.11
© Science Publishing Group
Applying Minimum Travel Cost Approach on 43–Nodes Travelling Salesman Problem
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150401.12
The minimum travel cost is a new approach to solve the Travelling Salesman Problem (TSP). The TSP library website (TSPLIB) provides several TSP problems with their best knownsolutions as a means to test any proposed algorithm. The present paper successfully applies the minimum travel cost algorithmto the 43 nodes P43problem which has the value of 5620 for its best knownsolution.This paper provides the details of the solution for value of 5621.
The minimum travel cost is a new approach to solve the Travelling Salesman Problem (TSP). The TSP library website (TSPLIB) provides several TSP problems with their best knownsolutions as a means to test any proposed algorithm. The present paper successfully applies the minimum travel cost algorithmto the 43 nodes P43problem which has the value of 5620 for its best knownsolution.This paper provides the details of the solution for value of 5621.
Applying Minimum Travel Cost Approach on 43–Nodes Travelling Salesman Problem
doi:10.11648/j.pamj.20150401.12
Pure and Applied Mathematics Journal
2015-01-30
© Science Publishing Group
Mohamed Eleiche
Applying Minimum Travel Cost Approach on 43–Nodes Travelling Salesman Problem
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23
23
2015-01-30
2015-01-30
10.11648/j.pamj.20150401.12
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150401.12
© Science Publishing Group
Certain Ranks of the Quotient Semigroup S/ρ and Prime Subsets of a Semigroup
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150401.13
In this paper we find a relationship between r2(S) and r2(S⁄ρ) where S is a finite semigroup, ρis a congruence on S and S /ρis the quotient semigroup (/S/ ≥ 2and/ S⁄ρ/ ≥ 2). We also determine r5(S⁄ρ) under certain conditions. Moreover we find prime subsets of S/ρ.
In this paper we find a relationship between r2(S) and r2(S⁄ρ) where S is a finite semigroup, ρis a congruence on S and S /ρis the quotient semigroup (/S/ ≥ 2and/ S⁄ρ/ ≥ 2). We also determine r5(S⁄ρ) under certain conditions. Moreover we find prime subsets of S/ρ.
Certain Ranks of the Quotient Semigroup S/ρ and Prime Subsets of a Semigroup
doi:10.11648/j.pamj.20150401.13
Pure and Applied Mathematics Journal
2015-02-01
© Science Publishing Group
Melis Minisker
Certain Ranks of the Quotient Semigroup S/ρ and Prime Subsets of a Semigroup
4
1
25
25
2015-02-01
2015-02-01
10.11648/j.pamj.20150401.13
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150401.13
© Science Publishing Group
Controllability of Co-Operative Neumann Parabolic Systems
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150401.15
In this communication, we introduce and study the various controllability problems for Neumann co-operative parabolic linear system involving Laplace operator with distributed or boundary controls and with observations belong to different spaces.
In this communication, we introduce and study the various controllability problems for Neumann co-operative parabolic linear system involving Laplace operator with distributed or boundary controls and with observations belong to different spaces.
Controllability of Co-Operative Neumann Parabolic Systems
doi:10.11648/j.pamj.20150401.15
Pure and Applied Mathematics Journal
2015-02-02
© Science Publishing Group
Mohammed Shehata
Controllability of Co-Operative Neumann Parabolic Systems
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38
38
2015-02-02
2015-02-02
10.11648/j.pamj.20150401.15
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150401.15
© Science Publishing Group
On the Accelerated Overrelaxation Method
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150401.14
A new variant of the accelerated over relaxation (AOR) method for solving systems of linear algebraic equations, the KAOR method is established. The treatment depends on the use of the extrapolation techniques introduced by Hadjidimos (1978) and the KSOR introduced by Youssef (2012) and its modified version published in (2013). The KAOR is an extrapolation version of the KSOR. This approach has enables us in establishing eigenvalue functional relations concerning the eigenvalues of the iteration matrices and their spectral radii. Moreover, our eigenvalue functional relation depends directly on the eigenvalues of Jacobi iteration matrix. The proposed method considers the advantages of the AOR in addition to those of the KSOR. A graphical representation of the behavior of the spectral radius near the minimum value illustrates the smoothness in the choice of optimum parameters.
A new variant of the accelerated over relaxation (AOR) method for solving systems of linear algebraic equations, the KAOR method is established. The treatment depends on the use of the extrapolation techniques introduced by Hadjidimos (1978) and the KSOR introduced by Youssef (2012) and its modified version published in (2013). The KAOR is an extrapolation version of the KSOR. This approach has enables us in establishing eigenvalue functional relations concerning the eigenvalues of the iteration matrices and their spectral radii. Moreover, our eigenvalue functional relation depends directly on the eigenvalues of Jacobi iteration matrix. The proposed method considers the advantages of the AOR in addition to those of the KSOR. A graphical representation of the behavior of the spectral radius near the minimum value illustrates the smoothness in the choice of optimum parameters.
On the Accelerated Overrelaxation Method
doi:10.11648/j.pamj.20150401.14
Pure and Applied Mathematics Journal
2015-02-02
© Science Publishing Group
I. K. Youssef
M. M. Farid
On the Accelerated Overrelaxation Method
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31
31
2015-02-02
2015-02-02
10.11648/j.pamj.20150401.14
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150401.14
© Science Publishing Group
Consistency Results in Topology and Homotopy Theory
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040101.11
Main results is: (1) let κ be an inaccessible cardinal and Hk is a set of all sets having hereditary size less then κ, then Con(ZFC + (V = Hk )), (2) there is a Lindelöf T3 indestructible space of pseudocharacter ≤N1 and size N2 in L.
Main results is: (1) let κ be an inaccessible cardinal and Hk is a set of all sets having hereditary size less then κ, then Con(ZFC + (V = Hk )), (2) there is a Lindelöf T3 indestructible space of pseudocharacter ≤N1 and size N2 in L.
Consistency Results in Topology and Homotopy Theory
doi:10.11648/j.pamj.s.2015040101.11
Pure and Applied Mathematics Journal
2014-10-31
© Science Publishing Group
Jaykov Foukzon
Consistency Results in Topology and Homotopy Theory
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5
5
2014-10-31
2014-10-31
10.11648/j.pamj.s.2015040101.11
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040101.11
© Science Publishing Group
Relevant First-Order Logic LP# and Curry’s Paradox Resolution
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040101.12
In 1942 Haskell B. Curry presented what is now called Curry's paradox which can be found in a logic independently of its stand on negation. In recent years there has been a revitalised interest in non-classical solutions to the semantic paradoxes. In this article the non-classical resolution of Curry’s Paradox and Shaw-Kwei' sparadox without rejection any contraction postulate is proposed. In additional relevant paraconsistent logic C ̌_n^#,1≤n<ω, in fact,provide an effective way of circumventing triviality of da Costa’s paraconsistent Set Theories〖NF〗_n^C
In 1942 Haskell B. Curry presented what is now called Curry's paradox which can be found in a logic independently of its stand on negation. In recent years there has been a revitalised interest in non-classical solutions to the semantic paradoxes. In this article the non-classical resolution of Curry’s Paradox and Shaw-Kwei' sparadox without rejection any contraction postulate is proposed. In additional relevant paraconsistent logic C ̌_n^#,1≤n<ω, in fact,provide an effective way of circumventing triviality of da Costa’s paraconsistent Set Theories〖NF〗_n^C
Relevant First-Order Logic LP# and Curry’s Paradox Resolution
doi:10.11648/j.pamj.s.2015040101.12
Pure and Applied Mathematics Journal
2015-01-19
© Science Publishing Group
Jaykov Foukzon
Relevant First-Order Logic LP# and Curry’s Paradox Resolution
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12
12
2015-01-19
2015-01-19
10.11648/j.pamj.s.2015040101.12
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040101.12
© Science Publishing Group
Generalized Nörlund Summability of Fuzzy Real Numbers
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040102.17
Fuzzy set, mathematical modelling in order to some uncertainty in 1965 was described by L. A. Zadeh [7]. In studies on fuzzy sets, fuzzy numbers [5], fuzzy relations [5], fuzzy function [5], fuzzy sequence [4] is defined as concepts. After Nörlund fuzzy and blurry Riez summability have been identified [6]. In this study, fuzzy Generalized Nörlund summability have been defined and Generalized Nörlund summability necessary and sufficient conditions to ensure the regular was investigated.
Fuzzy set, mathematical modelling in order to some uncertainty in 1965 was described by L. A. Zadeh [7]. In studies on fuzzy sets, fuzzy numbers [5], fuzzy relations [5], fuzzy function [5], fuzzy sequence [4] is defined as concepts. After Nörlund fuzzy and blurry Riez summability have been identified [6]. In this study, fuzzy Generalized Nörlund summability have been defined and Generalized Nörlund summability necessary and sufficient conditions to ensure the regular was investigated.
Generalized Nörlund Summability of Fuzzy Real Numbers
doi:10.11648/j.pamj.s.2015040102.17
Pure and Applied Mathematics Journal
2015-01-12
© Science Publishing Group
Adem Eroglu
Saban Yilmaz
Generalized Nörlund Summability of Fuzzy Real Numbers
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30
30
2015-01-12
2015-01-12
10.11648/j.pamj.s.2015040102.17
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040102.17
© Science Publishing Group
On Semi-Invariant Submanifolds of a Generalized Kenmotsu Manifold Admitting a Semi-Symmetric Non-Metric Connection
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040102.14
In this paper, semi-invariant submanifolds of a generalized Kenmotsu manifold endowed with a semi-symmetric non-metric connection are studied. Necessary and sufficient conditions are given on a submanifold of a generalized Kenmotsu manifold to be semi-invarinat submanifold with semi-symmetric non-metric connection. Morever, we studied the integrability condition of the distribution on semi-invariant submanifolds of generalized Kenmotsu manifold with semi-symmetric non-metric connection.
In this paper, semi-invariant submanifolds of a generalized Kenmotsu manifold endowed with a semi-symmetric non-metric connection are studied. Necessary and sufficient conditions are given on a submanifold of a generalized Kenmotsu manifold to be semi-invarinat submanifold with semi-symmetric non-metric connection. Morever, we studied the integrability condition of the distribution on semi-invariant submanifolds of generalized Kenmotsu manifold with semi-symmetric non-metric connection.
On Semi-Invariant Submanifolds of a Generalized Kenmotsu Manifold Admitting a Semi-Symmetric Non-Metric Connection
doi:10.11648/j.pamj.s.2015040102.14
Pure and Applied Mathematics Journal
2015-01-12
© Science Publishing Group
Aysel Turgut Vanli
Ramazan Sari
On Semi-Invariant Submanifolds of a Generalized Kenmotsu Manifold Admitting a Semi-Symmetric Non-Metric Connection
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18
18
2015-01-12
2015-01-12
10.11648/j.pamj.s.2015040102.14
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040102.14
© Science Publishing Group
Connection Forms of an Orthonormal Frame Field in the Minkowski Space
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040102.13
In this work, connection formulas and forms of an orthonormal frame field in the Minkowski space were introduced and then the variation of connection forms was studied. In addition, the relation between the matrix of connection forms and the transition matrix of an orthonormal basis of tangent space were established, and an example was illustrated.
In this work, connection formulas and forms of an orthonormal frame field in the Minkowski space were introduced and then the variation of connection forms was studied. In addition, the relation between the matrix of connection forms and the transition matrix of an orthonormal basis of tangent space were established, and an example was illustrated.
Connection Forms of an Orthonormal Frame Field in the Minkowski Space
doi:10.11648/j.pamj.s.2015040102.13
Pure and Applied Mathematics Journal
2015-01-12
© Science Publishing Group
Keziban Orbay
Connection Forms of an Orthonormal Frame Field in the Minkowski Space
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13
13
2015-01-12
2015-01-12
10.11648/j.pamj.s.2015040102.13
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040102.13
© Science Publishing Group
Terquem Theorem with the Spherical Helix Strip
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040102.11
The spherical helix and the strip are respectively proved firstly by Scofield and Sabuncuoglu and Hacısalihoglu. In this paper helix strip on sphere is investigated by using characteristics of spherical helix and strip. Firstly using strip after helixand finally spherical helix. So spherical helix strips are obtained. Furhermore Joachimsthal Theorem and Terquem Theorem are investigated when the strip and helix strips which lie on the sphere and given a characterization about spherical helix strips.
The spherical helix and the strip are respectively proved firstly by Scofield and Sabuncuoglu and Hacısalihoglu. In this paper helix strip on sphere is investigated by using characteristics of spherical helix and strip. Firstly using strip after helixand finally spherical helix. So spherical helix strips are obtained. Furhermore Joachimsthal Theorem and Terquem Theorem are investigated when the strip and helix strips which lie on the sphere and given a characterization about spherical helix strips.
Terquem Theorem with the Spherical Helix Strip
doi:10.11648/j.pamj.s.2015040102.11
Pure and Applied Mathematics Journal
2015-01-11
© Science Publishing Group
Filiz Ertem Kaya
Terquem Theorem with the Spherical Helix Strip
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5
5
2015-01-11
2015-01-11
10.11648/j.pamj.s.2015040102.11
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040102.11
© Science Publishing Group
On Involute and Evolute of the Curve and Curve-Surface Pair in Euclidean 3-Space
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040102.12
In this paper, the involute and evolute of the curve is studied in type of the curve-surface pair at first time. In additional whenβ is considered evolute and involute of the curveα, involute and evolute curve-surface pairs (called as strip) and strip of the curveαis shown as(α,M) are given with depending on the constant angleφthat is between in and in Euclidean 3-Space E^3.
In this paper, the involute and evolute of the curve is studied in type of the curve-surface pair at first time. In additional whenβ is considered evolute and involute of the curveα, involute and evolute curve-surface pairs (called as strip) and strip of the curveαis shown as(α,M) are given with depending on the constant angleφthat is between in and in Euclidean 3-Space E^3.
On Involute and Evolute of the Curve and Curve-Surface Pair in Euclidean 3-Space
doi:10.11648/j.pamj.s.2015040102.12
Pure and Applied Mathematics Journal
2015-01-12
© Science Publishing Group
Filiz Ertem Kaya
On Involute and Evolute of the Curve and Curve-Surface Pair in Euclidean 3-Space
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9
9
2015-01-12
2015-01-12
10.11648/j.pamj.s.2015040102.12
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040102.12
© Science Publishing Group
Constant Curvatures of Parallel Hypersurfaces in E1n+1Lorentz Space
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040102.16
In this paper generalized Gaussian and mean curvatures of a parallel hypersurface in E^(n+1) Euclidean space will be denoted respectively by K ̅ and H ̅, and Generalized Gaussian and mean curvatures of a parallel hypersurface in E₁ⁿ⁺¹ Lorentz space will be denoted respectively by K ̿ and H ̿.Generalized Gaussian curvature and mean curvatures, K ̅and H ̅ofaparallel hypersurface in E^(n+1)Euclidean space are givenin[2].Before nowwe studied relations between curvatures of a hypersurface in Lorentzian space and we introduced higher order Gaussian curvatures of hypersurfaces in Lorentzian space. In this paper, by considering our last studieson higher order Gaussian and mean curvatures, we calculate the generalized K ̿and H ̿ofaparallel hypersurface in E₁ⁿ⁺¹ Lorentz space and we prove theorems about generalized K ̿and H ̿ ofa parallel hypersurface in E₁ⁿ⁺¹ Lorentz space.
In this paper generalized Gaussian and mean curvatures of a parallel hypersurface in E^(n+1) Euclidean space will be denoted respectively by K ̅ and H ̅, and Generalized Gaussian and mean curvatures of a parallel hypersurface in E₁ⁿ⁺¹ Lorentz space will be denoted respectively by K ̿ and H ̿.Generalized Gaussian curvature and mean curvatures, K ̅and H ̅ofaparallel hypersurface in E^(n+1)Euclidean space are givenin[2].Before nowwe studied relations between curvatures of a hypersurface in Lorentzian space and we introduced higher order Gaussian curvatures of hypersurfaces in Lorentzian space. In this paper, by considering our last studieson higher order Gaussian and mean curvatures, we calculate the generalized K ̿and H ̿ofaparallel hypersurface in E₁ⁿ⁺¹ Lorentz space and we prove theorems about generalized K ̿and H ̿ ofa parallel hypersurface in E₁ⁿ⁺¹ Lorentz space.
Constant Curvatures of Parallel Hypersurfaces in E1n+1Lorentz Space
doi:10.11648/j.pamj.s.2015040102.16
Pure and Applied Mathematics Journal
2015-01-12
© Science Publishing Group
Ayşe Yavuz
F. Nejat Ekmekci
Constant Curvatures of Parallel Hypersurfaces in E1n+1Lorentz Space
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27
27
2015-01-12
2015-01-12
10.11648/j.pamj.s.2015040102.16
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040102.16
© Science Publishing Group
On the Explicit Parametric Equation of a General Helix with First and Second Curvature in Nil 3-Space
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040102.15
Nil geometry is one of the eight geometries of Thurston's conjecture. In this paper we study in Nil 3-space and the Nil metric with respect to the standard coordinates (x,y,z) is gNil₃=(dx)²+(dy)²+(dz-xdy)² in IR³. In this paper, we find out the explicit parametric equation of a general helix. Further, we write the explicit equations Frenet vector fields, the first and the second curvatures of general helix in Nil 3-Space. The parametric equation the Normal and Binormal ruled surface of general helix in Nil 3-space in terms of their curvature and torsion has been already examined in [12], in Nil 3-Space.
Nil geometry is one of the eight geometries of Thurston's conjecture. In this paper we study in Nil 3-space and the Nil metric with respect to the standard coordinates (x,y,z) is gNil₃=(dx)²+(dy)²+(dz-xdy)² in IR³. In this paper, we find out the explicit parametric equation of a general helix. Further, we write the explicit equations Frenet vector fields, the first and the second curvatures of general helix in Nil 3-Space. The parametric equation the Normal and Binormal ruled surface of general helix in Nil 3-space in terms of their curvature and torsion has been already examined in [12], in Nil 3-Space.
On the Explicit Parametric Equation of a General Helix with First and Second Curvature in Nil 3-Space
doi:10.11648/j.pamj.s.2015040102.15
Pure and Applied Mathematics Journal
2015-01-12
© Science Publishing Group
Şeyda Kılıçoğlu
On the Explicit Parametric Equation of a General Helix with First and Second Curvature in Nil 3-Space
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23
23
2015-01-12
2015-01-12
10.11648/j.pamj.s.2015040102.15
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040102.15
© Science Publishing Group
On an Almost C(α)-Manifold Satisfying Certain Conditions on the Concircular Curvature Tensor
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040102.18
We classify almost C(α)-manifolds, which satisfy the curvature conditions (Z ) ̃(ξ,X)R=0, (Z ) ̃(ξ,X) (Z ) ̃=0, (Z ) ̃(ξ,X)S=0 and (Z ) ̃(ξ,X)P=0, where (Z ) ̃ is the concircular curvature tensor, P is the Weyl projective curvature tensor, S is the Ricci tensor and R is Riemannian curvature tensor of manifold.
We classify almost C(α)-manifolds, which satisfy the curvature conditions (Z ) ̃(ξ,X)R=0, (Z ) ̃(ξ,X) (Z ) ̃=0, (Z ) ̃(ξ,X)S=0 and (Z ) ̃(ξ,X)P=0, where (Z ) ̃ is the concircular curvature tensor, P is the Weyl projective curvature tensor, S is the Ricci tensor and R is Riemannian curvature tensor of manifold.
On an Almost C(α)-Manifold Satisfying Certain Conditions on the Concircular Curvature Tensor
doi:10.11648/j.pamj.s.2015040102.18
Pure and Applied Mathematics Journal
2015-04-12
© Science Publishing Group
Mehmet Atçeken
Umit Yildirim
On an Almost C(α)-Manifold Satisfying Certain Conditions on the Concircular Curvature Tensor
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34
34
2015-04-12
2015-04-12
10.11648/j.pamj.s.2015040102.18
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040102.18
© Science Publishing Group
Graded Essential Extensions and Graded Injective Modules
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150402.13
In this paper we establish the relation between graded essential extensions of graded modules and injectivity of such modules. We relate the graded injective hull Egr (M) of a graded module M with the graded essential extensions of M. We round off by establishing necessary and sufficient conditions for indecomposability of graded injective modules in terms of their graded injective hulls.
In this paper we establish the relation between graded essential extensions of graded modules and injectivity of such modules. We relate the graded injective hull Egr (M) of a graded module M with the graded essential extensions of M. We round off by establishing necessary and sufficient conditions for indecomposability of graded injective modules in terms of their graded injective hulls.
Graded Essential Extensions and Graded Injective Modules
doi:10.11648/j.pamj.20150402.13
Pure and Applied Mathematics Journal
2015-02-11
© Science Publishing Group
Salah El Din S. Hussein
Essam El Seidy
H. S. Diab
Graded Essential Extensions and Graded Injective Modules
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51
51
2015-02-11
2015-02-11
10.11648/j.pamj.20150402.13
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150402.13
© Science Publishing Group
The Automatic Continuity of Linear Operators on Some Semi-Prime Banach Algebra
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150402.12
Conditions are given for Banach algebras A and Banach algebras B which insure that every homomorphism T from A into B is automatic continuous. Similar results are obtained for derivations which either map the algebra A into itself.
Conditions are given for Banach algebras A and Banach algebras B which insure that every homomorphism T from A into B is automatic continuous. Similar results are obtained for derivations which either map the algebra A into itself.
The Automatic Continuity of Linear Operators on Some Semi-Prime Banach Algebra
doi:10.11648/j.pamj.20150402.12
Pure and Applied Mathematics Journal
2015-02-11
© Science Publishing Group
Youssef Tidli
The Automatic Continuity of Linear Operators on Some Semi-Prime Banach Algebra
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46
2015-02-11
2015-02-11
10.11648/j.pamj.20150402.12
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150402.12
© Science Publishing Group
Chaos: Exact, Mixing and Weakly Mixing Maps
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150402.11
In this work, I studied a new class of topological λ-type chaos maps, λ-exact chaos and weakly λ-mixing chaos. Relationships with some other type of chaotic maps are given. I will list some relevant properties of λ-type chaotic map. The existence of chaotic behavior in deterministic systems has attracted researchers for many years. In engineering applications such as biological engineering, and chaos control, chaoticity of a topological system is an important subject for investigation. The definitions of λ-type chaos, λ-type exact chaos, λ-type mixing chaos, and weak λ-type mixing chaos are extended to topological spaces. This paper proves that these chaotic properties are all preserved under λr-conjugation. We have the following relationships: λ-type exact chaos⇒ λ-type mixing chaos ⇒ weak λ-type mixing chaos ⇒λ-type chaos.
In this work, I studied a new class of topological λ-type chaos maps, λ-exact chaos and weakly λ-mixing chaos. Relationships with some other type of chaotic maps are given. I will list some relevant properties of λ-type chaotic map. The existence of chaotic behavior in deterministic systems has attracted researchers for many years. In engineering applications such as biological engineering, and chaos control, chaoticity of a topological system is an important subject for investigation. The definitions of λ-type chaos, λ-type exact chaos, λ-type mixing chaos, and weak λ-type mixing chaos are extended to topological spaces. This paper proves that these chaotic properties are all preserved under λr-conjugation. We have the following relationships: λ-type exact chaos⇒ λ-type mixing chaos ⇒ weak λ-type mixing chaos ⇒λ-type chaos.
Chaos: Exact, Mixing and Weakly Mixing Maps
doi:10.11648/j.pamj.20150402.11
Pure and Applied Mathematics Journal
2015-02-11
© Science Publishing Group
Mohammed Nokhas Murad Kaki
Chaos: Exact, Mixing and Weakly Mixing Maps
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2015-02-11
2015-02-11
10.11648/j.pamj.20150402.11
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150402.11
© Science Publishing Group
On Application of a New Quasi-Newton Algorithm for Solving Optimal Control Problems
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150402.14
In this work, we review the construction of the linear operator associated with a class of linear regulator problems subject to the state differential equation. The associated linear operator is then utilized in the derivation of a New Quasi-Newton Method (QNM) for solving this class of optimal control problems. Our results show an improvement over the Classical Quasi-Newton Method.
In this work, we review the construction of the linear operator associated with a class of linear regulator problems subject to the state differential equation. The associated linear operator is then utilized in the derivation of a New Quasi-Newton Method (QNM) for solving this class of optimal control problems. Our results show an improvement over the Classical Quasi-Newton Method.
On Application of a New Quasi-Newton Algorithm for Solving Optimal Control Problems
doi:10.11648/j.pamj.20150402.14
Pure and Applied Mathematics Journal
2015-03-04
© Science Publishing Group
Felix Makanjuola Aderibigbe
Adejoke O. Dele-Rotimi
Kayode James Adebayo
On Application of a New Quasi-Newton Algorithm for Solving Optimal Control Problems
4
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56
56
2015-03-04
2015-03-04
10.11648/j.pamj.20150402.14
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150402.14
© Science Publishing Group
Lakshmi - Manoj Generalized Yang-Fourier Transforms to Heat-Conduction in a Semi-Infinite Fractal Bar
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150402.15
In the present era, fractional calculus plays an important role in various fields. Fractional Calculus is a field of mathematic study that grows out of the traditional definitions of the calculus integral and derivative operators in much the same way fractional exponents is an outgrowth of exponents with integer value. Based on the wide applications in engineering and sciences such as physics, mechanics, chemistry, and biology, research on fractional ordinary or partial differential equations and other relative topics is active and extensive around the world. In the past few years, the increase of the subject is witnessed by hundreds of research papers, several monographs, and many international conferences.The purpose of present paper to solve 1-D fractal heat-conduction problem in a fractal semi-infinite bar has been developed by local fractional calculus employing the analytical Manoj Generalized Yang-Fourier transforms method.
In the present era, fractional calculus plays an important role in various fields. Fractional Calculus is a field of mathematic study that grows out of the traditional definitions of the calculus integral and derivative operators in much the same way fractional exponents is an outgrowth of exponents with integer value. Based on the wide applications in engineering and sciences such as physics, mechanics, chemistry, and biology, research on fractional ordinary or partial differential equations and other relative topics is active and extensive around the world. In the past few years, the increase of the subject is witnessed by hundreds of research papers, several monographs, and many international conferences.The purpose of present paper to solve 1-D fractal heat-conduction problem in a fractal semi-infinite bar has been developed by local fractional calculus employing the analytical Manoj Generalized Yang-Fourier transforms method.
Lakshmi - Manoj Generalized Yang-Fourier Transforms to Heat-Conduction in a Semi-Infinite Fractal Bar
doi:10.11648/j.pamj.20150402.15
Pure and Applied Mathematics Journal
2015-03-24
© Science Publishing Group
Lakshmi Narayan Mishra
Manoj Sharma
Vishnu Narayan Mishra
Lakshmi - Manoj Generalized Yang-Fourier Transforms to Heat-Conduction in a Semi-Infinite Fractal Bar
4
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61
61
2015-03-24
2015-03-24
10.11648/j.pamj.20150402.15
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150402.15
© Science Publishing Group
Oscillation of Second Order Nonlinear Neutral Differential Equations
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150402.16
The oscillation criteria are investigated for all solutions of second order nonlinear neutral delay differential equations. Our results extend and improve some results well known in the literature see ( [14] theorem 3.2.1 and theorem 3.2.2 pp.385-388). Some examples are given to illustrate our main results.
The oscillation criteria are investigated for all solutions of second order nonlinear neutral delay differential equations. Our results extend and improve some results well known in the literature see ( [14] theorem 3.2.1 and theorem 3.2.2 pp.385-388). Some examples are given to illustrate our main results.
Oscillation of Second Order Nonlinear Neutral Differential Equations
doi:10.11648/j.pamj.20150402.16
Pure and Applied Mathematics Journal
2015-03-31
© Science Publishing Group
Hussain Ali Mohamad
Intidhar Zamil Mushtt
Oscillation of Second Order Nonlinear Neutral Differential Equations
4
2
65
65
2015-03-31
2015-03-31
10.11648/j.pamj.20150402.16
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150402.16
© Science Publishing Group
Class Number Formula for Certain Imaginary Quadratic Fields
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040201.11
In this note we shall show how Carlitz in 1954 could have reached an analogue of the Voronoi congruence in the more difficult case of p≡1(mod4): h(-4p) ≡B(p+1)/2(x4)(mod p), where B(p+1)/2(x4) is the generalized Bernoulli number with x4 being the Kronecker symbol associated to the Gaussian field Q(√-4).
In this note we shall show how Carlitz in 1954 could have reached an analogue of the Voronoi congruence in the more difficult case of p≡1(mod4): h(-4p) ≡B(p+1)/2(x4)(mod p), where B(p+1)/2(x4) is the generalized Bernoulli number with x4 being the Kronecker symbol associated to the Gaussian field Q(√-4).
Class Number Formula for Certain Imaginary Quadratic Fields
doi:10.11648/j.pamj.s.2015040201.11
Pure and Applied Mathematics Journal
2014-11-29
© Science Publishing Group
N. L. Wang
T. Arai
Class Number Formula for Certain Imaginary Quadratic Fields
4
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6
6
2014-11-29
2014-11-29
10.11648/j.pamj.s.2015040201.11
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040201.11
© Science Publishing Group
Dielectric Properties of Au/C60 (OH) 24-26/Au Structure
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040201.14
Dielectric properties of the Au/C60 (OH)24-26/Au structure were studied by measuring a.c. impedance and d.c. current in a wide temperature range. Three dielectric response characteristics were identified from Cole-Cole plots of a.c. impedance and dielectric dissipation factor of the structure. First, the bulk resistance and capacitance of the structure were observed at frequencies below 10 Hz, regardless of preparation condition of the Au electrode. Secondly, an interfacial characteristic of the Au foil/C60 (OH)24-26 contact was observed as a peak of dielectric dissipation factor at frequency of 200 Hz. Thirdly, an interfacial characteristic of the Au paste/C60 (OH)24-26 contact was also observed as a peak of dielectric dissipation factor at frequency of 1.7×〖10〗^5 Hz.
Dielectric properties of the Au/C60 (OH)24-26/Au structure were studied by measuring a.c. impedance and d.c. current in a wide temperature range. Three dielectric response characteristics were identified from Cole-Cole plots of a.c. impedance and dielectric dissipation factor of the structure. First, the bulk resistance and capacitance of the structure were observed at frequencies below 10 Hz, regardless of preparation condition of the Au electrode. Secondly, an interfacial characteristic of the Au foil/C60 (OH)24-26 contact was observed as a peak of dielectric dissipation factor at frequency of 200 Hz. Thirdly, an interfacial characteristic of the Au paste/C60 (OH)24-26 contact was also observed as a peak of dielectric dissipation factor at frequency of 1.7×〖10〗^5 Hz.
Dielectric Properties of Au/C60 (OH) 24-26/Au Structure
doi:10.11648/j.pamj.s.2015040201.14
Pure and Applied Mathematics Journal
2014-12-27
© Science Publishing Group
Y. Sun
S. Kanemitsu
K. Kirimoto
Dielectric Properties of Au/C60 (OH) 24-26/Au Structure
4
2
24
24
2014-12-27
2014-12-27
10.11648/j.pamj.s.2015040201.14
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040201.14
© Science Publishing Group
Tychonoff’s Theorem as a Direct Application of Zorn’s Lemma
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040201.13
A simple proof of Tychonoff’s theorem (the compactness of the product of compact spaces) as a direct application of Zorn’s lemma is given. In contrast to the classical Cartan-Bourbaki proof which uses Zorn’s lemma twice, our proof uses it only once.
A simple proof of Tychonoff’s theorem (the compactness of the product of compact spaces) as a direct application of Zorn’s lemma is given. In contrast to the classical Cartan-Bourbaki proof which uses Zorn’s lemma twice, our proof uses it only once.
Tychonoff’s Theorem as a Direct Application of Zorn’s Lemma
doi:10.11648/j.pamj.s.2015040201.13
Pure and Applied Mathematics Journal
2014-12-27
© Science Publishing Group
Haruo Tsukada
Tychonoff’s Theorem as a Direct Application of Zorn’s Lemma
4
2
17
17
2014-12-27
2014-12-27
10.11648/j.pamj.s.2015040201.13
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040201.13
© Science Publishing Group
Descartes’ Dream: Cartesian Products
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040201.12
In the last century, especially in the last half of the century, there was the paradigm of sectionalism prevailing and sciences and engineering were divided into very small parts which are mutually independent. It was like in Babel where there was no common language to communicate. The purpose of this paper is to present one of the possible glues—the notion of Cartesian product—to stick some remotely separated parts of science and engineering together. This concept appears in various places and it will turn out that it can unify the scattered notions quite well. Our two main objectives are the interpretation of cyclic codes as polynomials and nested PSO. We make clear the meaning of polynomials through Cartesian product or rather as terminating formal power series. The latter, formal power series, is not touched in engineering disciplines but is quite useful in unifying and interpreting various notions. In particular, it will make clear the meaning of addition of polynomials. This reminds us of topologization of adéles. PSO (Particle Swarm Optimization), a developed form of genetic algorithm, has come to our attention through the papers [4], [23] and [24]. In [4], the PSO is used to find optimal choice of parameters in the FOPID. In other two papers, PSO algorithm is used in cell balancing in the Lithium-ion battery pack for EV’s. Motivated by the passage on [3] that the stability is preserved by the Cartesian product of many copies of the attractor, we may conceive of the nested PSO.
In the last century, especially in the last half of the century, there was the paradigm of sectionalism prevailing and sciences and engineering were divided into very small parts which are mutually independent. It was like in Babel where there was no common language to communicate. The purpose of this paper is to present one of the possible glues—the notion of Cartesian product—to stick some remotely separated parts of science and engineering together. This concept appears in various places and it will turn out that it can unify the scattered notions quite well. Our two main objectives are the interpretation of cyclic codes as polynomials and nested PSO. We make clear the meaning of polynomials through Cartesian product or rather as terminating formal power series. The latter, formal power series, is not touched in engineering disciplines but is quite useful in unifying and interpreting various notions. In particular, it will make clear the meaning of addition of polynomials. This reminds us of topologization of adéles. PSO (Particle Swarm Optimization), a developed form of genetic algorithm, has come to our attention through the papers [4], [23] and [24]. In [4], the PSO is used to find optimal choice of parameters in the FOPID. In other two papers, PSO algorithm is used in cell balancing in the Lithium-ion battery pack for EV’s. Motivated by the passage on [3] that the stability is preserved by the Cartesian product of many copies of the attractor, we may conceive of the nested PSO.
Descartes’ Dream: Cartesian Products
doi:10.11648/j.pamj.s.2015040201.12
Pure and Applied Mathematics Journal
2014-12-27
© Science Publishing Group
Keiichi Takahashi
Takayasu Kaida
Descartes’ Dream: Cartesian Products
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13
13
2014-12-27
2014-12-27
10.11648/j.pamj.s.2015040201.12
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040201.12
© Science Publishing Group
Applications of the Hurwitz-Lerch Zeta-Function
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040201.16
In this paper, we shall exhibit the use of two principles, “principle of decomposition into residue classes” and “binomial principle of analytic continuation” due to Ram Murty and Sinha and indicate a certain distribution property and the functional equation for the Lipschitz-Lerch transcendent at integral arguments ofs. By considering the limiting cases ,we can also deduce new striking identities for Lipschizt-Lerch transcendent, among which is the Gauss second formula for the digamma function, Lipschitz-Lerch transcendent
In this paper, we shall exhibit the use of two principles, “principle of decomposition into residue classes” and “binomial principle of analytic continuation” due to Ram Murty and Sinha and indicate a certain distribution property and the functional equation for the Lipschitz-Lerch transcendent at integral arguments ofs. By considering the limiting cases ,we can also deduce new striking identities for Lipschizt-Lerch transcendent, among which is the Gauss second formula for the digamma function, Lipschitz-Lerch transcendent
Applications of the Hurwitz-Lerch Zeta-Function
doi:10.11648/j.pamj.s.2015040201.16
Pure and Applied Mathematics Journal
2014-12-27
© Science Publishing Group
Tomihiro Arai
Kalyan Chakraborty
Jing Ma
Applications of the Hurwitz-Lerch Zeta-Function
4
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35
35
2014-12-27
2014-12-27
10.11648/j.pamj.s.2015040201.16
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040201.16
© Science Publishing Group
Codons and Codes
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040201.15
In this paper we assemble a few ingredients that are remotely connected to each other, but governed by the rule of coding theory ([1], [12]) and formal language theory, i.e. cyclic codes and DNA codes. Our interest arose from the remark that there exist both linear and circular DNAs in higher living organisms. We state the theory of codes in a wide sense due to [1] in order to understand the circular DNAs while we state rudiments of formal language theory as a means to interpret genes. We hope this will be a starter for unifying two approaches depending on the theory of codes and that of formal language.
In this paper we assemble a few ingredients that are remotely connected to each other, but governed by the rule of coding theory ([1], [12]) and formal language theory, i.e. cyclic codes and DNA codes. Our interest arose from the remark that there exist both linear and circular DNAs in higher living organisms. We state the theory of codes in a wide sense due to [1] in order to understand the circular DNAs while we state rudiments of formal language theory as a means to interpret genes. We hope this will be a starter for unifying two approaches depending on the theory of codes and that of formal language.
Codons and Codes
doi:10.11648/j.pamj.s.2015040201.15
Pure and Applied Mathematics Journal
2014-12-27
© Science Publishing Group
Kalyan Chakraborty
Shigeru Kanemitsu
Y. Sun
Codons and Codes
4
2
29
29
2014-12-27
2014-12-27
10.11648/j.pamj.s.2015040201.15
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040201.15
© Science Publishing Group
A Note on the Rank Bounded Distance and Its Algorithms for Cyclic Codes
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040201.17
The minimum distance for linear codes is one of the important parameters. The shift bound is a good lower bound of the minimum distance for cyclic codes, Reed-Muller codes and geometric Goppa codes. It is necessary to construct the maximum value of the independent set for the calculation of the shift bound. However, its computational complexity is very large, because the construction of the independent set is not unique. The authors proposed an algorithm for calculation of the independent set using the discrete Fourier transform in 2010. In this paper we give simple modification and new recurrent algorithms to improve the original algorithm.
The minimum distance for linear codes is one of the important parameters. The shift bound is a good lower bound of the minimum distance for cyclic codes, Reed-Muller codes and geometric Goppa codes. It is necessary to construct the maximum value of the independent set for the calculation of the shift bound. However, its computational complexity is very large, because the construction of the independent set is not unique. The authors proposed an algorithm for calculation of the independent set using the discrete Fourier transform in 2010. In this paper we give simple modification and new recurrent algorithms to improve the original algorithm.
A Note on the Rank Bounded Distance and Its Algorithms for Cyclic Codes
doi:10.11648/j.pamj.s.2015040201.17
Pure and Applied Mathematics Journal
2015-02-11
© Science Publishing Group
Takayasu Kaida
Junru Zheng
A Note on the Rank Bounded Distance and Its Algorithms for Cyclic Codes
4
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41
41
2015-02-11
2015-02-11
10.11648/j.pamj.s.2015040201.17
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040201.17
© Science Publishing Group
On Some Point Groups
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040201.18
In this note, we indicate the coincidence as abstract groups of some point groups which belong to different molecular orbitals. This elucidates somewhat vague presentation in many existing textbooks on molecular orbitals, thus abridging between group theory and quantum chemistry.
In this note, we indicate the coincidence as abstract groups of some point groups which belong to different molecular orbitals. This elucidates somewhat vague presentation in many existing textbooks on molecular orbitals, thus abridging between group theory and quantum chemistry.
On Some Point Groups
doi:10.11648/j.pamj.s.2015040201.18
Pure and Applied Mathematics Journal
2015-02-12
© Science Publishing Group
Y. Sun
S. Kanemitsu
H. Kitajima
On Some Point Groups
4
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46
46
2015-02-12
2015-02-12
10.11648/j.pamj.s.2015040201.18
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040201.18
© Science Publishing Group
An Adaptation Method for Removing Arsenate Species from Water Solution
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040201.19
This paper is based on the idea of adaptation under which we mean the replacement of one element in a system with another with similar aspects. The first adaptation comes from the replacement of orthophospheric acid H3PO4 by arsenious acid H3AsO4. There is a close relation between calcium-sulfate and calcium carbonate-arsenate species. The main objective of this note is to give an explicit formula for the ratio of each arsenal species to the total and to make an adaptation of the former by the latter to develop a new adsorption material of arsenic acid which spends almost no energy. Some recently proposed methods of using calcium sulphate or other material has ambivalent aspects regarding energy spending as well as the treatment after adsorption.
This paper is based on the idea of adaptation under which we mean the replacement of one element in a system with another with similar aspects. The first adaptation comes from the replacement of orthophospheric acid H3PO4 by arsenious acid H3AsO4. There is a close relation between calcium-sulfate and calcium carbonate-arsenate species. The main objective of this note is to give an explicit formula for the ratio of each arsenal species to the total and to make an adaptation of the former by the latter to develop a new adsorption material of arsenic acid which spends almost no energy. Some recently proposed methods of using calcium sulphate or other material has ambivalent aspects regarding energy spending as well as the treatment after adsorption.
An Adaptation Method for Removing Arsenate Species from Water Solution
doi:10.11648/j.pamj.s.2015040201.19
Pure and Applied Mathematics Journal
2015-03-06
© Science Publishing Group
Sainyam Galhotra
Shigeru Kanemitsu
Hiroyuki Kondo
An Adaptation Method for Removing Arsenate Species from Water Solution
4
2
54
54
2015-03-06
2015-03-06
10.11648/j.pamj.s.2015040201.19
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040201.19
© Science Publishing Group
Difficulties and Errors of 1st Grade Computer Teaching and Technology Department Students on Discontinuity Types of Partial Functions and Some Certain Functions
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150403.11
The aim of this study is to investigate difficulties and errors of 1st grade Computer Teaching and Technology Department students on discontinuity kinds of partial functions and some certain functions. The data is gathered by the questionnaire containing 10 open ended questions. The answers of students are categorized according to 0-3 points’ schema. Based on the results and detailed analysis of students’ responses it is observed that students have many difficulties on finding the right and left hand side limit of partial functions on specific points. So it leads errors on determining the discontinuity types of these functions. Moreover, the results of analysis show that students have some difficulties on determining the discontinuity of some specific functions.
The aim of this study is to investigate difficulties and errors of 1st grade Computer Teaching and Technology Department students on discontinuity kinds of partial functions and some certain functions. The data is gathered by the questionnaire containing 10 open ended questions. The answers of students are categorized according to 0-3 points’ schema. Based on the results and detailed analysis of students’ responses it is observed that students have many difficulties on finding the right and left hand side limit of partial functions on specific points. So it leads errors on determining the discontinuity types of these functions. Moreover, the results of analysis show that students have some difficulties on determining the discontinuity of some specific functions.
Difficulties and Errors of 1st Grade Computer Teaching and Technology Department Students on Discontinuity Types of Partial Functions and Some Certain Functions
doi:10.11648/j.pamj.20150403.11
Pure and Applied Mathematics Journal
2015-04-20
© Science Publishing Group
Melis Minisker
Difficulties and Errors of 1st Grade Computer Teaching and Technology Department Students on Discontinuity Types of Partial Functions and Some Certain Functions
4
3
69
69
2015-04-20
2015-04-20
10.11648/j.pamj.20150403.11
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150403.11
© Science Publishing Group
An Extension of a Fixed Point Result in Cone Banach Space
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150403.12
In this paper we study a class of mappings in a ConeBanach Space which have at least one fixed point. More precisely for a closed and convex subset C of a cone Banach space with a generalized norm that satisfy a special condition. We are proposing some extensions of the results of Karapinar.
In this paper we study a class of mappings in a ConeBanach Space which have at least one fixed point. More precisely for a closed and convex subset C of a cone Banach space with a generalized norm that satisfy a special condition. We are proposing some extensions of the results of Karapinar.
An Extension of a Fixed Point Result in Cone Banach Space
doi:10.11648/j.pamj.20150403.12
Pure and Applied Mathematics Journal
2015-04-24
© Science Publishing Group
Elvin Rada
Agron Tato
An Extension of a Fixed Point Result in Cone Banach Space
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74
74
2015-04-24
2015-04-24
10.11648/j.pamj.20150403.12
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150403.12
© Science Publishing Group
Refined Definitions in Real Numbers and Vectors and Proof of Field Theories
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150403.13
A set of new and refined principles and definitions in Real Numbers and Vectors are presented. What is a Vector? What is the meaning of the Addition of two Vectors? What is a Real Number? What is the meaning of their signs? What is the meaning of the Addition of two Real Numbers? What is the Summation Principle in Addition Operation? What is the Cancellation Principle in Addition Operation? What is the Meaning of the Multiplication of two Real Numbers? Is Field Theory a law? Can it be proved? All these issues are addressed in this paper. With better pictures and graphical presentations, proof of Field Theories in Real Numbers and Vectors including Commutativity, Associativity and Distributivity are also proposed.
A set of new and refined principles and definitions in Real Numbers and Vectors are presented. What is a Vector? What is the meaning of the Addition of two Vectors? What is a Real Number? What is the meaning of their signs? What is the meaning of the Addition of two Real Numbers? What is the Summation Principle in Addition Operation? What is the Cancellation Principle in Addition Operation? What is the Meaning of the Multiplication of two Real Numbers? Is Field Theory a law? Can it be proved? All these issues are addressed in this paper. With better pictures and graphical presentations, proof of Field Theories in Real Numbers and Vectors including Commutativity, Associativity and Distributivity are also proposed.
Refined Definitions in Real Numbers and Vectors and Proof of Field Theories
doi:10.11648/j.pamj.20150403.13
Pure and Applied Mathematics Journal
2015-04-24
© Science Publishing Group
Edward T. H. Wu
Refined Definitions in Real Numbers and Vectors and Proof of Field Theories
4
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79
79
2015-04-24
2015-04-24
10.11648/j.pamj.20150403.13
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150403.13
© Science Publishing Group
Generalized Riesz Sequence Space of Non-Absolute Type and Some Matrix Mapping
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150403.15
Recently several authors defined and studied Riesz sequence space r^q(u, p) of non-absolute type. In this paper for some weight s ≥ 0, we define the generalized Risez sequence space r^q(u, p, s) of non-absolute type and determine its Kothe-Toeplitz dual. We also consider the matrix mapping r^q(u, p, s) to l_∞ and r^q(u, p, s) to c, where l_∞ is the space of all bounded sequences and c is the space of all convergent sequences.
Recently several authors defined and studied Riesz sequence space r^q(u, p) of non-absolute type. In this paper for some weight s ≥ 0, we define the generalized Risez sequence space r^q(u, p, s) of non-absolute type and determine its Kothe-Toeplitz dual. We also consider the matrix mapping r^q(u, p, s) to l_∞ and r^q(u, p, s) to c, where l_∞ is the space of all bounded sequences and c is the space of all convergent sequences.
Generalized Riesz Sequence Space of Non-Absolute Type and Some Matrix Mapping
doi:10.11648/j.pamj.20150403.15
Pure and Applied Mathematics Journal
2015-05-15
© Science Publishing Group
Md. Fazlur Rahman
A. B. M. Rezaul Karim
Generalized Riesz Sequence Space of Non-Absolute Type and Some Matrix Mapping
4
3
95
95
2015-05-15
2015-05-15
10.11648/j.pamj.20150403.15
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150403.15
© Science Publishing Group
Numerical Study on the Boundary Value Problem by Using a Shooting Method
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150403.16
In the present paper, a shooting method for the numerical solution of nonlinear two-point boundary value problems is analyzed. Dirichlet, Neumann, and Sturm- Liouville boundary conditions are considered and numerical results are obtained. Numerical examples to illustrate the method are presented to verify the effectiveness of the proposed derivations. The solutions are obtained by the proposed method have been compared with the analytical solution available in the literature and the numerical simulation is guarantee the desired accuracy. Finally the results have been shown in graphically.
In the present paper, a shooting method for the numerical solution of nonlinear two-point boundary value problems is analyzed. Dirichlet, Neumann, and Sturm- Liouville boundary conditions are considered and numerical results are obtained. Numerical examples to illustrate the method are presented to verify the effectiveness of the proposed derivations. The solutions are obtained by the proposed method have been compared with the analytical solution available in the literature and the numerical simulation is guarantee the desired accuracy. Finally the results have been shown in graphically.
Numerical Study on the Boundary Value Problem by Using a Shooting Method
doi:10.11648/j.pamj.20150403.16
Pure and Applied Mathematics Journal
2015-05-26
© Science Publishing Group
Md. Mizanur Rahman
Mst. Jesmin Ara
Md. Nurul Islam
Md. Shajib Ali
Numerical Study on the Boundary Value Problem by Using a Shooting Method
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100
100
2015-05-26
2015-05-26
10.11648/j.pamj.20150403.16
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150403.16
© Science Publishing Group
MHD Micropolar Fluid Near a Vertical Plate with Newtonian Heating and Thermal Radiation in the Presence of Mass Diffusion
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150403.14
The effects of chemical reaction and thermal radiation on unsteady free convection flow of a micropolar fluid past a semi-infinite vertical plate embedded in a porous medium in the presence of heat absorption with Newtonian heating have been investigated. Both physically important boundary conditions of uniform wall concentration (UWC) and uniform mass flux (UMF) are considered. Rosseland diffusion approximation is used to describe the radiative heat flux in the energy equation. Numerical results of velocity profiles of micropolar fluids are compared with the corresponding flow problems for a Newtonian fluid in UWC and UMF cases. Graphical results for velocity, temperature and concentration profiles of both phases based on the analytical solutions are presented and discussed. Finally the effects of the pertinent parameters on the skin friction, couple stress and the rate of heat transfer coefficient at the plate are discussed.
The effects of chemical reaction and thermal radiation on unsteady free convection flow of a micropolar fluid past a semi-infinite vertical plate embedded in a porous medium in the presence of heat absorption with Newtonian heating have been investigated. Both physically important boundary conditions of uniform wall concentration (UWC) and uniform mass flux (UMF) are considered. Rosseland diffusion approximation is used to describe the radiative heat flux in the energy equation. Numerical results of velocity profiles of micropolar fluids are compared with the corresponding flow problems for a Newtonian fluid in UWC and UMF cases. Graphical results for velocity, temperature and concentration profiles of both phases based on the analytical solutions are presented and discussed. Finally the effects of the pertinent parameters on the skin friction, couple stress and the rate of heat transfer coefficient at the plate are discussed.
MHD Micropolar Fluid Near a Vertical Plate with Newtonian Heating and Thermal Radiation in the Presence of Mass Diffusion
doi:10.11648/j.pamj.20150403.14
Pure and Applied Mathematics Journal
2015-05-13
© Science Publishing Group
Ahmed A. Bakr
Z. A. S. Raizah
Ahmed M. Elaiw
MHD Micropolar Fluid Near a Vertical Plate with Newtonian Heating and Thermal Radiation in the Presence of Mass Diffusion
4
3
89
89
2015-05-13
2015-05-13
10.11648/j.pamj.20150403.14
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150403.14
© Science Publishing Group
Maximum Principle and the Applications of Mean-Field Backward Doubly Stochastic System
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Since Pardoux and Peng firstly studied the following nonlinear backward stochastic differential equations in 1990. The theory of BSDE has been widely studied and applied, especially in the stochastic control, stochastic differential games, financial mathematics and partial differential equations. In 1994, Pardoux and Peng came up with backward doubly stochastic differential equations to give the probabilistic interpretation for stochastic partial differential equations. Backward doubly stochastic differential equations theory has been widely studied because of its importance in stochastic partial differential equations and stochastic control problems. In this article, we will study the theory of doubly stochastic systems and related topics further.
Since Pardoux and Peng firstly studied the following nonlinear backward stochastic differential equations in 1990. The theory of BSDE has been widely studied and applied, especially in the stochastic control, stochastic differential games, financial mathematics and partial differential equations. In 1994, Pardoux and Peng came up with backward doubly stochastic differential equations to give the probabilistic interpretation for stochastic partial differential equations. Backward doubly stochastic differential equations theory has been widely studied because of its importance in stochastic partial differential equations and stochastic control problems. In this article, we will study the theory of doubly stochastic systems and related topics further.
Maximum Principle and the Applications of Mean-Field Backward Doubly Stochastic System
doi:10.11648/j.pamj.20150403.17
Pure and Applied Mathematics Journal
2015-06-02
© Science Publishing Group
Hong Zhang
Jingyi Wang
Tengyu Zhao
Li Zhou
Maximum Principle and the Applications of Mean-Field Backward Doubly Stochastic System
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108
108
2015-06-02
2015-06-02
10.11648/j.pamj.20150403.17
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150403.17
© Science Publishing Group
The Maximum Principle of Forward Backward Transformation Stochastic Control System
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150403.18
In the paper, we discuss the maximum principle for the forward backward stochastic system. Assume the system follows a coupled forward backward stochastic differential equation modulated by a Marlcov chain and the control domain is convex. By convex variable method, we give the necessary and sufficient conditions for the existence of optimal control.
In the paper, we discuss the maximum principle for the forward backward stochastic system. Assume the system follows a coupled forward backward stochastic differential equation modulated by a Marlcov chain and the control domain is convex. By convex variable method, we give the necessary and sufficient conditions for the existence of optimal control.
The Maximum Principle of Forward Backward Transformation Stochastic Control System
doi:10.11648/j.pamj.20150403.18
Pure and Applied Mathematics Journal
2015-06-02
© Science Publishing Group
Li Zhou
Hong Zhang
Jie Zhu
Shucong Ming
The Maximum Principle of Forward Backward Transformation Stochastic Control System
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114
114
2015-06-02
2015-06-02
10.11648/j.pamj.20150403.18
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150403.18
© Science Publishing Group
The Mean Field Forward Backward Stochastic Differential Equations and Stochastic Partial Differential Equations
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150403.20
Since 1990 Pardoux and Peng, proposed the theory of backward stochastic differential equation Backward stochastic differential equation and is backward stochastic differential equations (short for FBSDE) theory has been widely research (see El Karoui, Peng and Cauenez, Ma and Yong, etc.) Generally, a backward stochastic differential equation is a type Ito stochastic differential equation and a coupling Pardoux - Peng and backward stochastic differential equation. Antonelli, Ma, Protter and Yong is backward stochastic differential equation for a series of research, and apply to the financial. One of the research direction is put forward by Hu and Peng first. Peng and Wu Peng and Shi made a further research, and Yong to a more detailed discussion of this method, by introducing the concept of the bridge, systematically studied the FBSDE continuity method. Because such a system can be applied to random Feynman - Kac of partial differential equations of research, And a double optimal control problem of stochastic control systems, we will be working in Peng and Shi further in-depth study on the basis of this category are backward stochastic differential equation. In this paper, we are considering various constraint conditions with backward stochastic differential equation.
Since 1990 Pardoux and Peng, proposed the theory of backward stochastic differential equation Backward stochastic differential equation and is backward stochastic differential equations (short for FBSDE) theory has been widely research (see El Karoui, Peng and Cauenez, Ma and Yong, etc.) Generally, a backward stochastic differential equation is a type Ito stochastic differential equation and a coupling Pardoux - Peng and backward stochastic differential equation. Antonelli, Ma, Protter and Yong is backward stochastic differential equation for a series of research, and apply to the financial. One of the research direction is put forward by Hu and Peng first. Peng and Wu Peng and Shi made a further research, and Yong to a more detailed discussion of this method, by introducing the concept of the bridge, systematically studied the FBSDE continuity method. Because such a system can be applied to random Feynman - Kac of partial differential equations of research, And a double optimal control problem of stochastic control systems, we will be working in Peng and Shi further in-depth study on the basis of this category are backward stochastic differential equation. In this paper, we are considering various constraint conditions with backward stochastic differential equation.
The Mean Field Forward Backward Stochastic Differential Equations and Stochastic Partial Differential Equations
doi:10.11648/j.pamj.20150403.20
Pure and Applied Mathematics Journal
2015-06-06
© Science Publishing Group
Jie Zhu
Hong Zhang
Li Zhou
Yuhang Feng
The Mean Field Forward Backward Stochastic Differential Equations and Stochastic Partial Differential Equations
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127
127
2015-06-06
2015-06-06
10.11648/j.pamj.20150403.20
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150403.20
© Science Publishing Group
Enumeration of Triangles in Cayley Graphs
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150403.21
Significant contributions can be found on the study of the cycle structure in graphs, particularly in Cayley graphs. Determination of Hamilton cycles and triangles, the longest and shortest cycles attracts special attention. In this paper an enumeration process for the determination of number of triangles in the Cayley graph associated with a group not necessarily abelian and a symmetric subset of the group.
Significant contributions can be found on the study of the cycle structure in graphs, particularly in Cayley graphs. Determination of Hamilton cycles and triangles, the longest and shortest cycles attracts special attention. In this paper an enumeration process for the determination of number of triangles in the Cayley graph associated with a group not necessarily abelian and a symmetric subset of the group.
Enumeration of Triangles in Cayley Graphs
doi:10.11648/j.pamj.20150403.21
Pure and Applied Mathematics Journal
2015-06-12
© Science Publishing Group
Levaku Madhavi
Tekuri Chalapathi
Enumeration of Triangles in Cayley Graphs
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132
132
2015-06-12
2015-06-12
10.11648/j.pamj.20150403.21
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150403.21
© Science Publishing Group
Stochastic differential equation driven by the Wiener process in a Banach space, existence and uniqueness of the generalized solution
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150403.22
In this paper the stochastic differential equation in a Banach space is considered for the case when the Wiener process in the equation is Banach space valued and the integrand non-anticipating function is operator-valued. At first the stochastic differential equation for the generalized random process is introduced and developed existence and uniqueness of solutions as the generalized random process. The corresponding results for the stochastic differential equation in a Banach space is given. In [5] we consider the stochastic differential equation in a Banach space in the case, when the Wiener process is one dimensional and the integrand non-anticipating function is Banach space valued.
In this paper the stochastic differential equation in a Banach space is considered for the case when the Wiener process in the equation is Banach space valued and the integrand non-anticipating function is operator-valued. At first the stochastic differential equation for the generalized random process is introduced and developed existence and uniqueness of solutions as the generalized random process. The corresponding results for the stochastic differential equation in a Banach space is given. In [5] we consider the stochastic differential equation in a Banach space in the case, when the Wiener process is one dimensional and the integrand non-anticipating function is Banach space valued.
Stochastic differential equation driven by the Wiener process in a Banach space, existence and uniqueness of the generalized solution
doi:10.11648/j.pamj.20150403.22
Pure and Applied Mathematics Journal
2015-06-12
© Science Publishing Group
Badri Mamporia
Stochastic differential equation driven by the Wiener process in a Banach space, existence and uniqueness of the generalized solution
4
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138
138
2015-06-12
2015-06-12
10.11648/j.pamj.20150403.22
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150403.22
© Science Publishing Group
A Novel Way to Construct the Fibonacci Sequence and the Uni-Phi-cation of Mathematics and Physics
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150404.11
When the Fibonacci number sequence is based on the number seven and its multiples, the Fibonacci sequence self-reflexively reappears when differences are calculated between it and this new number-seven-based Fibonacci sequence. The same thing happens with Lucas numbers. Can this same procedure be applied to any two numbers at the beginning of a Fibonacci/Lucas-like sequence? The answer is in the negative. This special quality of the golden proportion casts light on the fine structure constant of hydrogen, which is the unique, lightest, and most pervasive element in nature, plus other constants in nature, all of which have a dimensionless number close to the golden proportion (Phi) of the Fibonacci sequence, and provides the basis for the binary computer code as well as a uni-Phi-ed theory of mathematics and physics.
When the Fibonacci number sequence is based on the number seven and its multiples, the Fibonacci sequence self-reflexively reappears when differences are calculated between it and this new number-seven-based Fibonacci sequence. The same thing happens with Lucas numbers. Can this same procedure be applied to any two numbers at the beginning of a Fibonacci/Lucas-like sequence? The answer is in the negative. This special quality of the golden proportion casts light on the fine structure constant of hydrogen, which is the unique, lightest, and most pervasive element in nature, plus other constants in nature, all of which have a dimensionless number close to the golden proportion (Phi) of the Fibonacci sequence, and provides the basis for the binary computer code as well as a uni-Phi-ed theory of mathematics and physics.
A Novel Way to Construct the Fibonacci Sequence and the Uni-Phi-cation of Mathematics and Physics
doi:10.11648/j.pamj.20150404.11
Pure and Applied Mathematics Journal
2015-06-16
© Science Publishing Group
David F. Haight
A Novel Way to Construct the Fibonacci Sequence and the Uni-Phi-cation of Mathematics and Physics
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146
146
2015-06-16
2015-06-16
10.11648/j.pamj.20150404.11
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150404.11
© Science Publishing Group
Mathematical Methodologies in Physics and Their Applications in Derivation of Velocity and Acceleration Theories
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The principles to use variables and mathematical methodologies in physics are addressed. A set of refined definitions with designated variables are used to derive the Velocity and Acceleration Theories in Distance Field and Vector Space. Mathematical methodologies such as Linear Algebra and Vector Calculus are used systematically in a step by step derivation process. The proof of the theories can be easily achieved by substitution of the designated variables with a set of parameters that matches the same assumptions and conditions in every step of the derivation process.
The principles to use variables and mathematical methodologies in physics are addressed. A set of refined definitions with designated variables are used to derive the Velocity and Acceleration Theories in Distance Field and Vector Space. Mathematical methodologies such as Linear Algebra and Vector Calculus are used systematically in a step by step derivation process. The proof of the theories can be easily achieved by substitution of the designated variables with a set of parameters that matches the same assumptions and conditions in every step of the derivation process.
Mathematical Methodologies in Physics and Their Applications in Derivation of Velocity and Acceleration Theories
doi:10.11648/j.pamj.20150404.12
Pure and Applied Mathematics Journal
2015-06-19
© Science Publishing Group
Edward T. H. Wu
Mathematical Methodologies in Physics and Their Applications in Derivation of Velocity and Acceleration Theories
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154
154
2015-06-19
2015-06-19
10.11648/j.pamj.20150404.12
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150404.12
© Science Publishing Group
Fixed Point Theorems for Occasionally Weakly Compatible Maps in Intuitionistic Fuzzy Semi- Metric Space
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150404.13
In this paper, using the concept of occasionally weakly compatible maps, we prove common fixed point theorems for two maps and pairs of maps in intuitionistic fuzzy semi-metric space. Example is also given to prove the validity of proved results. Our results extends and generalizes various known fixed point theorems in the setting of metric, fuzzy, intuitionistic fuzzy and modified fuzzy metric spaces.
In this paper, using the concept of occasionally weakly compatible maps, we prove common fixed point theorems for two maps and pairs of maps in intuitionistic fuzzy semi-metric space. Example is also given to prove the validity of proved results. Our results extends and generalizes various known fixed point theorems in the setting of metric, fuzzy, intuitionistic fuzzy and modified fuzzy metric spaces.
Fixed Point Theorems for Occasionally Weakly Compatible Maps in Intuitionistic Fuzzy Semi- Metric Space
doi:10.11648/j.pamj.20150404.13
Pure and Applied Mathematics Journal
2015-07-28
© Science Publishing Group
Harpreet Kaur
Saurabh Manro
Fixed Point Theorems for Occasionally Weakly Compatible Maps in Intuitionistic Fuzzy Semi- Metric Space
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4
158
158
2015-07-28
2015-07-28
10.11648/j.pamj.20150404.13
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150404.13
© Science Publishing Group
Fixed-point Theorems in G-complete Fuzzy Metric Spaces
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150404.14
In the present paper we introduce generalized contraction mapping in fuzzy metric space and some fixed-point theorems for G-complete fuzzy metric space are proved. Our results generalize and extend many known results in metric spaces to a (non-Archimedean) fuzzy metric space in the in the sense of George and Veeramani [George A, Veeramani P, On some results in fuzzy metric spaces, Fuzzy Sets and Systems 1994;64:395-9].
In the present paper we introduce generalized contraction mapping in fuzzy metric space and some fixed-point theorems for G-complete fuzzy metric space are proved. Our results generalize and extend many known results in metric spaces to a (non-Archimedean) fuzzy metric space in the in the sense of George and Veeramani [George A, Veeramani P, On some results in fuzzy metric spaces, Fuzzy Sets and Systems 1994;64:395-9].
Fixed-point Theorems in G-complete Fuzzy Metric Spaces
doi:10.11648/j.pamj.20150404.14
Pure and Applied Mathematics Journal
2015-07-31
© Science Publishing Group
Naser Abbasi
Hamid Mottaghi Golshan
Mahmood Shakori
Fixed-point Theorems in G-complete Fuzzy Metric Spaces
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163
163
2015-07-31
2015-07-31
10.11648/j.pamj.20150404.14
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150404.14
© Science Publishing Group
The Ito Formula for the Ito Processes Driven by the Wiener Processes in a Banach Space
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150404.15
Using traditional methods it is possible to prove the Ito formula in a Hilbert space and some Banach spaces with special geometrical properties. The class of such Banach spaces is very narrow-they are subclass of reflexive Banach spaces. Using the definition of a generalized stochastic integral, early we proved the Ito formula in an arbitrary Banach space for the case, when as initial Ito process was the Wiener process. For an arbitrary Banach space and an arbitrary Ito process it is impossible to find the sequence of corresponding step functions with the desired convergence. We consider the space of generalized random processes, introduce general Ito process there and prove in it the Ito formula. Afterward, from the main Ito process in a Banach space we receive the generalized Ito process in the space of generalized random processes and we get the Ito formula in this space. Then we check decompasibilility of the members of the received equality and as they turn out Banach space valued, we get the Ito formula in an arbitrary Banach space. We implemented this approach when the stochastic integral in the Ito process was taken from a Banach space valued non-anticipating random process by the one dimensional Wiener process. In this paper we consider the case, when the stochastic integral is taken from an operator- valued non-anticipating random process by the Wiener process with values in a Banach space.
Using traditional methods it is possible to prove the Ito formula in a Hilbert space and some Banach spaces with special geometrical properties. The class of such Banach spaces is very narrow-they are subclass of reflexive Banach spaces. Using the definition of a generalized stochastic integral, early we proved the Ito formula in an arbitrary Banach space for the case, when as initial Ito process was the Wiener process. For an arbitrary Banach space and an arbitrary Ito process it is impossible to find the sequence of corresponding step functions with the desired convergence. We consider the space of generalized random processes, introduce general Ito process there and prove in it the Ito formula. Afterward, from the main Ito process in a Banach space we receive the generalized Ito process in the space of generalized random processes and we get the Ito formula in this space. Then we check decompasibilility of the members of the received equality and as they turn out Banach space valued, we get the Ito formula in an arbitrary Banach space. We implemented this approach when the stochastic integral in the Ito process was taken from a Banach space valued non-anticipating random process by the one dimensional Wiener process. In this paper we consider the case, when the stochastic integral is taken from an operator- valued non-anticipating random process by the Wiener process with values in a Banach space.
The Ito Formula for the Ito Processes Driven by the Wiener Processes in a Banach Space
doi:10.11648/j.pamj.20150404.15
Pure and Applied Mathematics Journal
2015-08-11
© Science Publishing Group
Badri Mamporia
The Ito Formula for the Ito Processes Driven by the Wiener Processes in a Banach Space
4
4
171
171
2015-08-11
2015-08-11
10.11648/j.pamj.20150404.15
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150404.15
© Science Publishing Group
Fourier Coefficients of a Class of Eta Quotients of Weight 18 with Level 12
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150404.17
Williams [16] and later Yao, Xia and Jin[15] discovered explicit formulas for the coefficients of the Fourier series expansions of a class of eta quotients. Williams expressed all coefficients of 126 eta quotients in terms of σ(n),σ(n/2),σ(n/3) and σ(n/6) and Yao, Xia and Jin, following the method of proof of Williams, expressed only even coefficients of 104 eta quotients in terms of σ_3 (n),σ_3 (n/2),σ_3 (n/3) and σ_3 (n/6). Here, we will express the even Fourier coefficients of 324 eta quotients in terms of σ_17 (n),σ_17 (n/2),σ_17 (n/3),σ_17 (n/4),σ_17 (n/6) and σ_17 (n/12).
Williams [16] and later Yao, Xia and Jin[15] discovered explicit formulas for the coefficients of the Fourier series expansions of a class of eta quotients. Williams expressed all coefficients of 126 eta quotients in terms of σ(n),σ(n/2),σ(n/3) and σ(n/6) and Yao, Xia and Jin, following the method of proof of Williams, expressed only even coefficients of 104 eta quotients in terms of σ_3 (n),σ_3 (n/2),σ_3 (n/3) and σ_3 (n/6). Here, we will express the even Fourier coefficients of 324 eta quotients in terms of σ_17 (n),σ_17 (n/2),σ_17 (n/3),σ_17 (n/4),σ_17 (n/6) and σ_17 (n/12).
Fourier Coefficients of a Class of Eta Quotients of Weight 18 with Level 12
doi:10.11648/j.pamj.20150404.17
Pure and Applied Mathematics Journal
2015-08-13
© Science Publishing Group
Baris Kendirli
Fourier Coefficients of a Class of Eta Quotients of Weight 18 with Level 12
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188
2015-08-13
2015-08-13
10.11648/j.pamj.20150404.17
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150404.17
© Science Publishing Group
Post's thesis and wrong Janov-Mucnik's statement in multi-valued logic
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150404.16
Post stated that multi-valued logic has no principle difference with respect to two-valued logic. But Janov and Mucnik stated that multi-valued logic has essentially difference with respect to two-valued logic. We show that Post’s thesis is well but Janov-Mucnik’s statement is wrong
Post stated that multi-valued logic has no principle difference with respect to two-valued logic. But Janov and Mucnik stated that multi-valued logic has essentially difference with respect to two-valued logic. We show that Post’s thesis is well but Janov-Mucnik’s statement is wrong
Post's thesis and wrong Janov-Mucnik's statement in multi-valued logic
doi:10.11648/j.pamj.20150404.16
Pure and Applied Mathematics Journal
2015-08-13
© Science Publishing Group
Maydim A. Malkov
Post's thesis and wrong Janov-Mucnik's statement in multi-valued logic
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177
2015-08-13
2015-08-13
10.11648/j.pamj.20150404.16
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150404.16
© Science Publishing Group
Multiparameter System of Operators with Two Parameters in Finite Dimensional Spaces
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040401.11
The authors have proved the existence of the multiple basis on the eigen and associated elements of the two parameter system of operators in finite dimensional spaces. The proof uses the notion of the abstract analog of resultant of two operator pencils, acting, generally speaking, in different Hilbert spaces. In this paper necessary and sufficient conditions of the existence of multiple completeness of the eigen and associated vectors of two parameter system of operators in finite dimensional Hilbert space is given.
The authors have proved the existence of the multiple basis on the eigen and associated elements of the two parameter system of operators in finite dimensional spaces. The proof uses the notion of the abstract analog of resultant of two operator pencils, acting, generally speaking, in different Hilbert spaces. In this paper necessary and sufficient conditions of the existence of multiple completeness of the eigen and associated vectors of two parameter system of operators in finite dimensional Hilbert space is given.
Multiparameter System of Operators with Two Parameters in Finite Dimensional Spaces
doi:10.11648/j.pamj.s.2015040401.11
Pure and Applied Mathematics Journal
2015-05-12
© Science Publishing Group
Rakhshanda Dzhabarzadeh
Afet Jabrailova
Multiparameter System of Operators with Two Parameters in Finite Dimensional Spaces
4
4
4
4
2015-05-12
2015-05-12
10.11648/j.pamj.s.2015040401.11
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040401.11
© Science Publishing Group
Multiparameter Operator Systems with Three Parameters
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040401.12
For the multiparameter system of operators in three parameters the conditions of the existence of multiple basis of eigen and associated vectors in finite dimensional space is proved. The proof of this fact uses essentially the notion of the Resultant of two operator pencils, acting in, generally speaking, in different Hilbert spaces and the criterion of existence of common eigenvalues of several operator pencils, acting in Hilbert spaces.
For the multiparameter system of operators in three parameters the conditions of the existence of multiple basis of eigen and associated vectors in finite dimensional space is proved. The proof of this fact uses essentially the notion of the Resultant of two operator pencils, acting in, generally speaking, in different Hilbert spaces and the criterion of existence of common eigenvalues of several operator pencils, acting in Hilbert spaces.
Multiparameter Operator Systems with Three Parameters
doi:10.11648/j.pamj.s.2015040401.12
Pure and Applied Mathematics Journal
2015-05-12
© Science Publishing Group
Rakhshanda Dzhabarzadeh
Kamilla Alimardanova
Multiparameter Operator Systems with Three Parameters
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10
10
2015-05-12
2015-05-12
10.11648/j.pamj.s.2015040401.12
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040401.12
© Science Publishing Group
Criterion of Existence of Eigen Values of Linear Multiparameter Systems
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040401.13
It is considered the linear multiparameter system of operators when the number of equations may be more than the number of parameters. For such multiparameter systems the authors have proved the criterion of existence of eigen values. Under certain conditions, the authors a have proved that all components of the eigen values of the considered multiparameter systems are real numbers.
It is considered the linear multiparameter system of operators when the number of equations may be more than the number of parameters. For such multiparameter systems the authors have proved the criterion of existence of eigen values. Under certain conditions, the authors a have proved that all components of the eigen values of the considered multiparameter systems are real numbers.
Criterion of Existence of Eigen Values of Linear Multiparameter Systems
doi:10.11648/j.pamj.s.2015040401.13
Pure and Applied Mathematics Journal
2015-05-12
© Science Publishing Group
Rakhshanda Dzhabarzadeh
Elnara Sultanova
Criterion of Existence of Eigen Values of Linear Multiparameter Systems
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2015-05-12
2015-05-12
10.11648/j.pamj.s.2015040401.13
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040401.13
© Science Publishing Group
On Existence of Eigen Values of Several Operator Bundles with Two Parameters
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040401.14
For the several operator bundles with two parameters when the number of equation is greater than the number of parameters in the Hilbert spaces is given the criterion of existence of the common point of spectra. In the special case the common point of spectra is the common eigen value. In the proof of the theorem the authors use the results of the spectral theory of multiparameter systems
For the several operator bundles with two parameters when the number of equation is greater than the number of parameters in the Hilbert spaces is given the criterion of existence of the common point of spectra. In the special case the common point of spectra is the common eigen value. In the proof of the theorem the authors use the results of the spectral theory of multiparameter systems
On Existence of Eigen Values of Several Operator Bundles with Two Parameters
doi:10.11648/j.pamj.s.2015040401.14
Pure and Applied Mathematics Journal
2015-08-22
© Science Publishing Group
Makhmudova Malaka Gasan
Sultanova Elnara Bayram
On Existence of Eigen Values of Several Operator Bundles with Two Parameters
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21
21
2015-08-22
2015-08-22
10.11648/j.pamj.s.2015040401.14
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040401.14
© Science Publishing Group
Spectral Theory of Operator Pencils in the Hilbert Spaces
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040401.15
The theorem on possibility of multiple summation of the series on eigen and associated vectors of the operator pencil in the Hilbert space is proved. Research of multiple completeness and multiple expansions of eigen and associated vectors of such operator pencils are closely connected with the research of differential operator equation with the boundary conditions
The theorem on possibility of multiple summation of the series on eigen and associated vectors of the operator pencil in the Hilbert space is proved. Research of multiple completeness and multiple expansions of eigen and associated vectors of such operator pencils are closely connected with the research of differential operator equation with the boundary conditions
Spectral Theory of Operator Pencils in the Hilbert Spaces
doi:10.11648/j.pamj.s.2015040401.15
Pure and Applied Mathematics Journal
2015-08-22
© Science Publishing Group
Rakhshanda Dzhabarzadeh
Spectral Theory of Operator Pencils in the Hilbert Spaces
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4
26
26
2015-08-22
2015-08-22
10.11648/j.pamj.s.2015040401.15
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040401.15
© Science Publishing Group
On Multiple Bases of Eigen and Associated Vectors of Operator Pencils in the Hilbert Spaces
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040401.16
It is proved the theorem about of multiple basis of eigen and associated vectors of the operator pencil, non-linear depending on parameter in the Hilbert space. This work is the generalization of existing results on the multiple completeness of the eigen and associated vectors of polynomial pencils, rationally depending on parameters. At the proof the author uses the methods of spectral theory of operators
It is proved the theorem about of multiple basis of eigen and associated vectors of the operator pencil, non-linear depending on parameter in the Hilbert space. This work is the generalization of existing results on the multiple completeness of the eigen and associated vectors of polynomial pencils, rationally depending on parameters. At the proof the author uses the methods of spectral theory of operators
On Multiple Bases of Eigen and Associated Vectors of Operator Pencils in the Hilbert Spaces
doi:10.11648/j.pamj.s.2015040401.16
Pure and Applied Mathematics Journal
2015-08-22
© Science Publishing Group
Rakhshanda Dzhabarzadeh
On Multiple Bases of Eigen and Associated Vectors of Operator Pencils in the Hilbert Spaces
4
4
32
32
2015-08-22
2015-08-22
10.11648/j.pamj.s.2015040401.16
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040401.16
© Science Publishing Group
Spectral Problems of Two-Parameter System of Operators
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040401.17
The author has proved the existence of the multiple basis of the eigen and associated vectors of the two parameter system of operators in Hilbert spaces. The proof essentially uses the theorem of the existence of multiple basis of operator bundles and the notion of the abstract analog of resultant of two operator pencils, acting, generally speaking, in different Hilbert spaces. Considerable non-selfadjoint two parameter systems depend on both parameters in a complicated manner
The author has proved the existence of the multiple basis of the eigen and associated vectors of the two parameter system of operators in Hilbert spaces. The proof essentially uses the theorem of the existence of multiple basis of operator bundles and the notion of the abstract analog of resultant of two operator pencils, acting, generally speaking, in different Hilbert spaces. Considerable non-selfadjoint two parameter systems depend on both parameters in a complicated manner
Spectral Problems of Two-Parameter System of Operators
doi:10.11648/j.pamj.s.2015040401.17
Pure and Applied Mathematics Journal
2015-08-22
© Science Publishing Group
Rakhshanda Dzhabarzadeh
Spectral Problems of Two-Parameter System of Operators
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4
37
37
2015-08-22
2015-08-22
10.11648/j.pamj.s.2015040401.17
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040401.17
© Science Publishing Group
Research Methods of Multiparameter System in Hilbert Spaces
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040401.18
The work is devoted to the presentation of the methods, available in the literature, of the study of multiparameter spectral problems in Hilbert space. In particular, the method of Atkinson and his followers for a purely self-adjoint multiparameter systems and methods proposed by the author for the study, in general, non- selfadjoint multiparameter system in Hilbert space. These approaches solve questions of completeness, multiple completeness, the basis and a multiple basis property of eigen and associated vectors of multiparameter systems with a complex dependence on the parameters
The work is devoted to the presentation of the methods, available in the literature, of the study of multiparameter spectral problems in Hilbert space. In particular, the method of Atkinson and his followers for a purely self-adjoint multiparameter systems and methods proposed by the author for the study, in general, non- selfadjoint multiparameter system in Hilbert space. These approaches solve questions of completeness, multiple completeness, the basis and a multiple basis property of eigen and associated vectors of multiparameter systems with a complex dependence on the parameters
Research Methods of Multiparameter System in Hilbert Spaces
doi:10.11648/j.pamj.s.2015040401.18
Pure and Applied Mathematics Journal
2015-08-25
© Science Publishing Group
Rakhshanda Dzhabarzadeh
Research Methods of Multiparameter System in Hilbert Spaces
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2015-08-25
2015-08-25
10.11648/j.pamj.s.2015040401.18
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040401.18
© Science Publishing Group
Existence of Time Periodic Solutions of New Classes of Nonlinear Problems
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150405.11
We study the existence of one or more weak periodic solutions of nonlinear evolution PDEs in a cylinder of RN+1 with conditions on lateral surface by using the results connected to a general evolution variational equation depending on a parameter.
We study the existence of one or more weak periodic solutions of nonlinear evolution PDEs in a cylinder of RN+1 with conditions on lateral surface by using the results connected to a general evolution variational equation depending on a parameter.
Existence of Time Periodic Solutions of New Classes of Nonlinear Problems
doi:10.11648/j.pamj.20150405.11
Pure and Applied Mathematics Journal
2015-08-27
© Science Publishing Group
Luisa Toscano
Speranza Toscano
Existence of Time Periodic Solutions of New Classes of Nonlinear Problems
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2015-08-27
2015-08-27
10.11648/j.pamj.20150405.11
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150405.11
© Science Publishing Group
The Simulation of a Queueing System Consist of Two Parallel Heterogeneous Channels with no Waiting Line
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150405.12
A queueing system with two parallel heterogenous channels without waiting is considered. In this queueing system customer arrivals are Poisson distributed with λ rate. Each customer has exponentially distributed service time with μ_k (k=1,2) parameter at k-th channel. When a customer arrives this system if both the service channels are available, the customer has service with α or β=1-α probabilities at first and second service channels respectively. If one of the service channels is available, the customer has service at this service channel or leaves the system without being served if both of the service channels are busy. We have obtained mean waiting time and mean number of customers of the system and a simulation of this system is performed.
A queueing system with two parallel heterogenous channels without waiting is considered. In this queueing system customer arrivals are Poisson distributed with λ rate. Each customer has exponentially distributed service time with μ_k (k=1,2) parameter at k-th channel. When a customer arrives this system if both the service channels are available, the customer has service with α or β=1-α probabilities at first and second service channels respectively. If one of the service channels is available, the customer has service at this service channel or leaves the system without being served if both of the service channels are busy. We have obtained mean waiting time and mean number of customers of the system and a simulation of this system is performed.
The Simulation of a Queueing System Consist of Two Parallel Heterogeneous Channels with no Waiting Line
doi:10.11648/j.pamj.20150405.12
Pure and Applied Mathematics Journal
2015-09-08
© Science Publishing Group
Vedat Sağlam
Murat Sağır
Erdinç Yücesoy
Müjgan Zobu
The Simulation of a Queueing System Consist of Two Parallel Heterogeneous Channels with no Waiting Line
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2015-09-08
2015-09-08
10.11648/j.pamj.20150405.12
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150405.12
© Science Publishing Group
Solving Fourth Order Parabolic PDE with Variable Coefficients Using Aboodh Transform Homotopy Perturbation Method
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150405.13
Here, a new method called Aboodh transform homotopy perturbation method (ATHPM) is used to solve one dimensional fourth order parabolic linear partial differential equations with variable coefficients. The proposed method is a combination of the new integral transform “Aboodh transform” and the homotopy perturbation method. Some cases of one dimensional fourth order parabolic linear partial differential equations are solved to illustrate ability and reliability of mixture of Aboodh transform and homotopy perturbation method. We have compared the obtained analytical solution with the available Aboodh decomposition solution and homotopy perturbation method solution which is found to be exactly same. The results obtained reveal that the combination of Aboodh transform and homotopy perturbation method is quite capable, practically well appropriate for use in such problems.
Here, a new method called Aboodh transform homotopy perturbation method (ATHPM) is used to solve one dimensional fourth order parabolic linear partial differential equations with variable coefficients. The proposed method is a combination of the new integral transform “Aboodh transform” and the homotopy perturbation method. Some cases of one dimensional fourth order parabolic linear partial differential equations are solved to illustrate ability and reliability of mixture of Aboodh transform and homotopy perturbation method. We have compared the obtained analytical solution with the available Aboodh decomposition solution and homotopy perturbation method solution which is found to be exactly same. The results obtained reveal that the combination of Aboodh transform and homotopy perturbation method is quite capable, practically well appropriate for use in such problems.
Solving Fourth Order Parabolic PDE with Variable Coefficients Using Aboodh Transform Homotopy Perturbation Method
doi:10.11648/j.pamj.20150405.13
Pure and Applied Mathematics Journal
2015-09-08
© Science Publishing Group
Khalid Suliman Aboodh
Solving Fourth Order Parabolic PDE with Variable Coefficients Using Aboodh Transform Homotopy Perturbation Method
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2015-09-08
2015-09-08
10.11648/j.pamj.20150405.13
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.20150405.13
© Science Publishing Group
The Higher Derivation of the Hurwitz Zeta-function
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040501.12
In this paper, the Euler-Maclaurin Summation formula was researched, the purpose of research is to promote the application of the Hurwitz Zeta-function ; Combination method of number theory special a function and Euler-Maclaurin Summation Formula was been used ; By three derivatives of the the Euler-Maclaurin Summation formula , three formulas of Hurwitz Zeta-function were been given.
In this paper, the Euler-Maclaurin Summation formula was researched, the purpose of research is to promote the application of the Hurwitz Zeta-function ; Combination method of number theory special a function and Euler-Maclaurin Summation Formula was been used ; By three derivatives of the the Euler-Maclaurin Summation formula , three formulas of Hurwitz Zeta-function were been given.
The Higher Derivation of the Hurwitz Zeta-function
doi:10.11648/j.pamj.s.2015040501.12
Pure and Applied Mathematics Journal
2015-07-14
© Science Publishing Group
Qianli Yang
The Higher Derivation of the Hurwitz Zeta-function
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14
14
2015-07-14
2015-07-14
10.11648/j.pamj.s.2015040501.12
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040501.12
© Science Publishing Group
The Effects of Counterparts on the Wear Properties and Surface Microstructure of TC4 Alloy
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040501.11
The wear properties and wear surfaces microstructure of TC4 alloy were studied with GCr15 and SiC counterparts, respectively. The results show that the friction coefficients of TC4 alloy with GCr15 was higher and the mass loss was lower compared with those of SiC. The wear mechanisms of TC4 alloy with GCr15 and SiC could be concluded as grinding abrasion, adhesion abrasion and oxidation abrasion. However, adhesion abrasion and oxidation abrasion mechanisms were predominant with GCr15 counterpart.
The wear properties and wear surfaces microstructure of TC4 alloy were studied with GCr15 and SiC counterparts, respectively. The results show that the friction coefficients of TC4 alloy with GCr15 was higher and the mass loss was lower compared with those of SiC. The wear mechanisms of TC4 alloy with GCr15 and SiC could be concluded as grinding abrasion, adhesion abrasion and oxidation abrasion. However, adhesion abrasion and oxidation abrasion mechanisms were predominant with GCr15 counterpart.
The Effects of Counterparts on the Wear Properties and Surface Microstructure of TC4 Alloy
doi:10.11648/j.pamj.s.2015040501.11
Pure and Applied Mathematics Journal
2015-07-14
© Science Publishing Group
Guo Bao hui
The Effects of Counterparts on the Wear Properties and Surface Microstructure of TC4 Alloy
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5
5
2015-07-14
2015-07-14
10.11648/j.pamj.s.2015040501.11
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040501.11
© Science Publishing Group
On the Riesz Sums in Number Theory
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040501.13
The Riesz means, or sometimes typical means, were introduced by M. Riesz and have been studied in connection with summability of Fourier series and of Dirichlet series [8] and [11]. In number-theoretic context, it is the Riesz sum rather than the Riesz mean that has been extensively studied. The Riesz sums appear as long as there appears the G-function. Cf. Remark 1 and [14]. As is shown below, the Riesz sum corresponds to integration while Landau's differencing is an analogue of differentiation. This integration-differentiation aspect has been the driving force of many researches on number-theoretic asymptotic formulas. Ingham's decent treatment [13] of the prime number theorem is one typical example. We state some efficient theorems that give asymptotic formulas for the sums of coefficients of the generating Dirichlet series not necessarily satisfying the functional equation.
The Riesz means, or sometimes typical means, were introduced by M. Riesz and have been studied in connection with summability of Fourier series and of Dirichlet series [8] and [11]. In number-theoretic context, it is the Riesz sum rather than the Riesz mean that has been extensively studied. The Riesz sums appear as long as there appears the G-function. Cf. Remark 1 and [14]. As is shown below, the Riesz sum corresponds to integration while Landau's differencing is an analogue of differentiation. This integration-differentiation aspect has been the driving force of many researches on number-theoretic asymptotic formulas. Ingham's decent treatment [13] of the prime number theorem is one typical example. We state some efficient theorems that give asymptotic formulas for the sums of coefficients of the generating Dirichlet series not necessarily satisfying the functional equation.
On the Riesz Sums in Number Theory
doi:10.11648/j.pamj.s.2015040501.13
Pure and Applied Mathematics Journal
2015-07-17
© Science Publishing Group
Hailong Li
Qianli Yang
On the Riesz Sums in Number Theory
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19
19
2015-07-17
2015-07-17
10.11648/j.pamj.s.2015040501.13
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040501.13
© Science Publishing Group
On The Parameter Function Involving Gamma Function and Its Applications
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040501.14
In this paper, the complete monotonic parameter function involving the Gamma function is considered. The necessary and sufficient condition of the parameter f is presented. As an application, two meaningful inequalities of Gamma function are obtained
In this paper, the complete monotonic parameter function involving the Gamma function is considered. The necessary and sufficient condition of the parameter f is presented. As an application, two meaningful inequalities of Gamma function are obtained
On The Parameter Function Involving Gamma Function and Its Applications
doi:10.11648/j.pamj.s.2015040501.14
Pure and Applied Mathematics Journal
2015-07-25
© Science Publishing Group
Bin Chen
Rong Miao
On The Parameter Function Involving Gamma Function and Its Applications
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23
23
2015-07-25
2015-07-25
10.11648/j.pamj.s.2015040501.14
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040501.14
© Science Publishing Group
Study on Stable Scanning of Terminal Sensitivity Projectile and Hardware-in-the-Loop Simulation System
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040501.15
In order to study the attitude control and target detectivity of terminal sensitivity projectile during the process of attacking the target, theoretical modeling is firstly conducted for the steady scanning process of terminal sensitivity projectile; on this basis, the core part of terminal sensitivity projectile -- infrared detector is introduced as hardware to hardware-in-the-loop simulation loop with hardware-in-the-loop simulation technology and virtual reality technology, and an analysis is made from the aspects of attacking accuracy, false detection rate and miss rate of terminal sensitivity projectile to verify the performance of such detector and also provide reference for new weapon development in the future
In order to study the attitude control and target detectivity of terminal sensitivity projectile during the process of attacking the target, theoretical modeling is firstly conducted for the steady scanning process of terminal sensitivity projectile; on this basis, the core part of terminal sensitivity projectile -- infrared detector is introduced as hardware to hardware-in-the-loop simulation loop with hardware-in-the-loop simulation technology and virtual reality technology, and an analysis is made from the aspects of attacking accuracy, false detection rate and miss rate of terminal sensitivity projectile to verify the performance of such detector and also provide reference for new weapon development in the future
Study on Stable Scanning of Terminal Sensitivity Projectile and Hardware-in-the-Loop Simulation System
doi:10.11648/j.pamj.s.2015040501.15
Pure and Applied Mathematics Journal
2015-07-29
© Science Publishing Group
Yuan Wei
Zhang Jianqi
Feng Yang
Study on Stable Scanning of Terminal Sensitivity Projectile and Hardware-in-the-Loop Simulation System
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27
27
2015-07-29
2015-07-29
10.11648/j.pamj.s.2015040501.15
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040501.15
© Science Publishing Group
An Approach for Intrusion Detection of IPv6 Network Based on LS-SVM Algorithm
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040501.16
IPv6 has enough IP addresses to solve the problem of lack of IP address space. However, there are many security problems to be concerned. The detection ability of current intrusion detection system is poor when given less priori knowledge. In this paper, we analyze the Least Squares Support Vector Machine (LS-SVM) algorithm and the working process of snort intrusion detection system. And then we study the methods of intrusion detection in IPv6, and use LS-SVM to optimize snort intrusion detection system. Simulation results show that intrusion detection system with LS-SVM has a robust performance and has high detection efficiency
IPv6 has enough IP addresses to solve the problem of lack of IP address space. However, there are many security problems to be concerned. The detection ability of current intrusion detection system is poor when given less priori knowledge. In this paper, we analyze the Least Squares Support Vector Machine (LS-SVM) algorithm and the working process of snort intrusion detection system. And then we study the methods of intrusion detection in IPv6, and use LS-SVM to optimize snort intrusion detection system. Simulation results show that intrusion detection system with LS-SVM has a robust performance and has high detection efficiency
An Approach for Intrusion Detection of IPv6 Network Based on LS-SVM Algorithm
doi:10.11648/j.pamj.s.2015040501.16
Pure and Applied Mathematics Journal
2015-07-29
© Science Publishing Group
Liu Jing
An Approach for Intrusion Detection of IPv6 Network Based on LS-SVM Algorithm
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32
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2015-07-29
2015-07-29
10.11648/j.pamj.s.2015040501.16
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040501.16
© Science Publishing Group
Some identities on the Higher-order Daehee and Changhee Numbers
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040501.17
In this note, we shall give an explicit formula for the coefficients of the expansion of given generating function, when that function has an appropriate form, the coefficients can be represented by the higher-order Daehee and Changhee polynomials and numbers of the first kind. By the classical method of comparing the coefficients of the generating function, we show some interesting identities related to the Higher-order Daehee and Changhee numbers.
In this note, we shall give an explicit formula for the coefficients of the expansion of given generating function, when that function has an appropriate form, the coefficients can be represented by the higher-order Daehee and Changhee polynomials and numbers of the first kind. By the classical method of comparing the coefficients of the generating function, we show some interesting identities related to the Higher-order Daehee and Changhee numbers.
Some identities on the Higher-order Daehee and Changhee Numbers
doi:10.11648/j.pamj.s.2015040501.17
Pure and Applied Mathematics Journal
2015-08-05
© Science Publishing Group
Nian Liang Wang
Hailong Li
Some identities on the Higher-order Daehee and Changhee Numbers
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37
37
2015-08-05
2015-08-05
10.11648/j.pamj.s.2015040501.17
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040501.17
© Science Publishing Group
An Improved Algorithm of Precise Point Cloud Registration
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040501.19
Basing on the application of digital protection of cultural sites, this paper presented a precise algorithm for the multi-resolution point cloud based on sequence iterative. Firstly, based on the synchronous scanning image, a rough registration of the adjacent point cloud can be obtained in an interactive way. Secondly, based on a normal-based algorithm of registration sphere center, the points of sphere surface are filtered from all scanned point cloud data according to the normal data points and the characteristic of viewpoint, and then the center of registration sphere can be calculated accurately and the initial registration of the adjacent point cloud can be obtained by setting Matching Registration Labels mode as the constraint condition. Finally, based on the 3D edge points of the adjacent point cloud from mahalanobis distance calculations, some overlapping images can be eliminated by the way of constantly optimizing the transition matrix in the iteration process. The engineering practice of the Small Wild Goose Pagoda in Tang Dynasty and the Ancient Tomb in Han Dynasty proves that the method is reliable and easy to design and implement and can effectively restrain the accumulative errors of sequence registrations.
Basing on the application of digital protection of cultural sites, this paper presented a precise algorithm for the multi-resolution point cloud based on sequence iterative. Firstly, based on the synchronous scanning image, a rough registration of the adjacent point cloud can be obtained in an interactive way. Secondly, based on a normal-based algorithm of registration sphere center, the points of sphere surface are filtered from all scanned point cloud data according to the normal data points and the characteristic of viewpoint, and then the center of registration sphere can be calculated accurately and the initial registration of the adjacent point cloud can be obtained by setting Matching Registration Labels mode as the constraint condition. Finally, based on the 3D edge points of the adjacent point cloud from mahalanobis distance calculations, some overlapping images can be eliminated by the way of constantly optimizing the transition matrix in the iteration process. The engineering practice of the Small Wild Goose Pagoda in Tang Dynasty and the Ancient Tomb in Han Dynasty proves that the method is reliable and easy to design and implement and can effectively restrain the accumulative errors of sequence registrations.
An Improved Algorithm of Precise Point Cloud Registration
doi:10.11648/j.pamj.s.2015040501.19
Pure and Applied Mathematics Journal
2015-09-02
© Science Publishing Group
Jun Liu
An Improved Algorithm of Precise Point Cloud Registration
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50
50
2015-09-02
2015-09-02
10.11648/j.pamj.s.2015040501.19
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040501.19
© Science Publishing Group
Emerging Importance of EVs in the Green Grid Era
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040501.18
A very plausible picture of the near future–some decades from now–would be the Green Grid Era and the emerging importance of EVs in the spectrum, where by Green Grid we mean the advanced Smart Grid in which essential part of the whole electric power is supplied by distributed generation, i.e. it is generated by renewable energy including solar energy, biogas, geothermal energy, etc. The crucial ingredients in this grid system are enhanced batteries and the participation of EVs in the grid as a pool of electricity. Our primary concern in this paper is the control of EV participation in the Green Grid, and in particular the study of linear systems and elucidation of various state equations in [HHP] etc.
A very plausible picture of the near future–some decades from now–would be the Green Grid Era and the emerging importance of EVs in the spectrum, where by Green Grid we mean the advanced Smart Grid in which essential part of the whole electric power is supplied by distributed generation, i.e. it is generated by renewable energy including solar energy, biogas, geothermal energy, etc. The crucial ingredients in this grid system are enhanced batteries and the participation of EVs in the grid as a pool of electricity. Our primary concern in this paper is the control of EV participation in the Green Grid, and in particular the study of linear systems and elucidation of various state equations in [HHP] etc.
Emerging Importance of EVs in the Green Grid Era
doi:10.11648/j.pamj.s.2015040501.18
Pure and Applied Mathematics Journal
2015-09-02
© Science Publishing Group
Fuhuo Li
S. Galhotra
S. Kanemitsu
Emerging Importance of EVs in the Green Grid Era
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2015-09-02
2015-09-02
10.11648/j.pamj.s.2015040501.18
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=141&doi=10.11648/j.pamj.s.2015040501.18
© Science Publishing Group