Science Publishing Group: International Journal of Applied Mathematics and Theoretical Physics: Table of Contents
The <i>International Journal of Applied Mathematics and Theoretical Physics (IJAMTP)</i> publishes papers in the fields of applied mathematics and theoretical physics; these two fields are vital for basic sciences and engineering. The journal presents original papers, reviews and letters. The primary goal of this journal is to advance the understanding of applications in mathematics and physics by introducing mathematical techniques and applications to mathematics in other areas of science and engineering. The journal is addressed to applied mathematicians and theoretical physics specialists.
http://www.sciencepublishinggroup.com/j/ijamtp Science Publishing Group: International Journal of Applied Mathematics and Theoretical Physics: Table of Contents
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International Journal of Applied Mathematics and Theoretical Physics
International Journal of Applied Mathematics and Theoretical Physics
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Study on Linear Canonical Transformation in a Framework of a Phase Space Representation of Quantum Mechanics
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=322&doi=10.11648/j.ijamtp.20150101.11
We present a study on linear canonical transformation in the framework of a phase space representation of quantum mechanics that we have introduced in our previous work [1]. We begin with a brief recall about the so called phase space representation. We give the definition of linear canonical transformation with the transformation law of coordinate and momentum operators. We establish successively the transformation laws of mean values, dispersions, basis state and wave functions. Then we introduce the concept of isodispersion linear canonical transformation.
We present a study on linear canonical transformation in the framework of a phase space representation of quantum mechanics that we have introduced in our previous work [1]. We begin with a brief recall about the so called phase space representation. We give the definition of linear canonical transformation with the transformation law of coordinate and momentum operators. We establish successively the transformation laws of mean values, dispersions, basis state and wave functions. Then we introduce the concept of isodispersion linear canonical transformation.
Study on Linear Canonical Transformation in a Framework of a Phase Space Representation of Quantum Mechanics
doi:10.11648/j.ijamtp.20150101.11
International Journal of Applied Mathematics and Theoretical Physics
2015-04-08
© Science Publishing Group
Raoelina Andriambololona
Ravo Tokiniaina Ranaivoson
Rakotoson Hanitriarivo
Wilfrid Chrysante Solofoarisina
Study on Linear Canonical Transformation in a Framework of a Phase Space Representation of Quantum Mechanics
1
1
8
8
2015-04-08
2015-04-08
10.11648/j.ijamtp.20150101.11
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=322&doi=10.11648/j.ijamtp.20150101.11
© Science Publishing Group
Calculating the Lowest Reportable Concentrations of Toxic Chemicals in the Environment
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=322&doi=10.11648/j.ijamtp.20150101.12
The equation promulgated by 40 Code of Federal Regulations (CFR) to calculate method detection limit (MDL) and used since 1981 in the United States and other countries to protect public health and the environment is incorrect. As a result, toxic chemicals in a large number of air, food, water, wastes, and other environmental samples may in fact be present at measurable concentrations even though they are currently being reported as “not detected”. That is, the air we breathe, the food we eat, and the water and other liquids we drink may have measurable concentrations of toxic chemicals, despite being reported as not detected and assumed to be absent. Furthermore, many chemicals, such as arsenic (As) in drinking water, are so toxic that they cannot be measured to safe levels and the allowable limits must be set at the lowest reportable concentrations. As a result, the allowable limits for some extremely toxic chemicals may be incorrectly set too high. Therefore, the consequences of this error pose a risk to public health and the environment. The sources of this error are explained and two improved ways of calculating method detection limit are presented.
The equation promulgated by 40 Code of Federal Regulations (CFR) to calculate method detection limit (MDL) and used since 1981 in the United States and other countries to protect public health and the environment is incorrect. As a result, toxic chemicals in a large number of air, food, water, wastes, and other environmental samples may in fact be present at measurable concentrations even though they are currently being reported as “not detected”. That is, the air we breathe, the food we eat, and the water and other liquids we drink may have measurable concentrations of toxic chemicals, despite being reported as not detected and assumed to be absent. Furthermore, many chemicals, such as arsenic (As) in drinking water, are so toxic that they cannot be measured to safe levels and the allowable limits must be set at the lowest reportable concentrations. As a result, the allowable limits for some extremely toxic chemicals may be incorrectly set too high. Therefore, the consequences of this error pose a risk to public health and the environment. The sources of this error are explained and two improved ways of calculating method detection limit are presented.
Calculating the Lowest Reportable Concentrations of Toxic Chemicals in the Environment
doi:10.11648/j.ijamtp.20150101.12
International Journal of Applied Mathematics and Theoretical Physics
2015-05-08
© Science Publishing Group
Seth H. Frisbie
Erika J. Mitchell
Marwan S. Abualrub
Yousef Abosalem
Calculating the Lowest Reportable Concentrations of Toxic Chemicals in the Environment
1
1
13
13
2015-05-08
2015-05-08
10.11648/j.ijamtp.20150101.12
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=322&doi=10.11648/j.ijamtp.20150101.12
© Science Publishing Group