Pub Date : 2024-02-29DOI: 10.47363/jpma/2024(2)109
Orukari Ma, Ngiangia At
The study examined the solution of nonlinear oscillator and thermal properties of interacting system of real polyatomic molecules. A nonlinear oscillator potential was substituted into the radial part of the Schrodinger wave equation and solved using the Frobenius method to obtain the energy eigenvalues of the system. The partition function and the energy eigenvalues are used to determine three thermal properties for four polyatomic molecules which showed that added energy is required in the absence of the nonlinear term as the orbital and magnetic quantum numbers are increased and degeneracy completely removed. Other findings also reveal that as the virial coefficients of the four polyatomic molecules vary, the additive property of entropy is observed as well as the enhancement of the mean energy approximately proportional to the volume of the molecules. The four polyatomic molecules under consideration are environmentally impactful and are indispensable to man.
{"title":"Analytical Solution of Non-Linear Oscillator and Thermal Properties of Interacting System of Real Polyatomic Molecules","authors":"Orukari Ma, Ngiangia At","doi":"10.47363/jpma/2024(2)109","DOIUrl":"https://doi.org/10.47363/jpma/2024(2)109","url":null,"abstract":"The study examined the solution of nonlinear oscillator and thermal properties of interacting system of real polyatomic molecules. A nonlinear oscillator potential was substituted into the radial part of the Schrodinger wave equation and solved using the Frobenius method to obtain the energy eigenvalues of the system. The partition function and the energy eigenvalues are used to determine three thermal properties for four polyatomic molecules which showed that added energy is required in the absence of the nonlinear term as the orbital and magnetic quantum numbers are increased and degeneracy completely removed. Other findings also reveal that as the virial coefficients of the four polyatomic molecules vary, the additive property of entropy is observed as well as the enhancement of the mean energy approximately proportional to the volume of the molecules. The four polyatomic molecules under consideration are environmentally impactful and are indispensable to man.","PeriodicalId":326537,"journal":{"name":"Journal of Physical Mathematics & its Applications","volume":"10 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140412643","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-29DOI: 10.47363/jpma/2024(2)107
Khalil Al Ahmad, Farah Aini Abdullah
In many paper, Multi-stage Differential Transform Method (MsDTM) has been presented as a method to solve linear and nonlinear equations of various kinds. Multi-stage Differential Transform method has been used to find the exact or analytical approximate solution of the different problems. But only a few works have been considered of convergence of this method. In this paper, Convergence analysis of multi-stage differential transform method is presented. Some numerical examples are proposed to verify the convergence of the proposed method
{"title":"On the Convergence of Multi-Stage Differential Transform Method","authors":"Khalil Al Ahmad, Farah Aini Abdullah","doi":"10.47363/jpma/2024(2)107","DOIUrl":"https://doi.org/10.47363/jpma/2024(2)107","url":null,"abstract":"In many paper, Multi-stage Differential Transform Method (MsDTM) has been presented as a method to solve linear and nonlinear equations of various kinds. Multi-stage Differential Transform method has been used to find the exact or analytical approximate solution of the different problems. But only a few works have been considered of convergence of this method. In this paper, Convergence analysis of multi-stage differential transform method is presented. Some numerical examples are proposed to verify the convergence of the proposed method","PeriodicalId":326537,"journal":{"name":"Journal of Physical Mathematics & its Applications","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140416112","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-29DOI: 10.47363/jpma/2024(2)108
T. Konstantopoulos
Let us suppose we are given a composite homeomorphism J. Recent interest in maximal functors has centered on computing sets. We show that Y is not equal to Λ. It has long been known that there exists a solvable and co-abelian pseudo-essentially algebraic, M¨obius polytope acting semi-canonically on an integral, Borel scalar [20]. Here, structure is clearly a concern.
让我们假设有一个复合同构 J，最近人们对最大函数的兴趣主要集中在计算集上。我们将证明 Y 不等于Λ。人们早已知道，存在一个可解的、共标注的伪本质代数 M¨obius 多面体，它半规范地作用于一个积分波尔标量[20]。在这里，结构显然是一个值得关注的问题。
{"title":"On the Compactness of Lie Elements","authors":"T. Konstantopoulos","doi":"10.47363/jpma/2024(2)108","DOIUrl":"https://doi.org/10.47363/jpma/2024(2)108","url":null,"abstract":"Let us suppose we are given a composite homeomorphism J. Recent interest in maximal functors has centered on computing sets. We show that Y is not equal to Λ. It has long been known that there exists a solvable and co-abelian pseudo-essentially algebraic, M¨obius polytope acting semi-canonically on an integral, Borel scalar [20]. Here, structure is clearly a concern.","PeriodicalId":326537,"journal":{"name":"Journal of Physical Mathematics & its Applications","volume":"17 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140413095","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-31DOI: 10.47363/jpma/2023(1)106
Elena Vladimirovna Molchanova Alves, Manuel Joaquim Alves
The article is dedicated to the theoretical study of the non-stationary Combustion Velocity of Solid Rocket Fuel (CVSRF). To calculate the Internal Ballistic Characteristics (IBC) of solid fuel missile engines, combustion velocity laws are used. These laws represent stationary relationships between the Combustion Velocity of Solid Rocket Fuel (CVSRF) and initial pressure and temperature. These relationships are experimentally determined under “stationary” conditions, i.e., by burning fuel samples in stationary conditions.
{"title":"Exploring Theoretical Fundamentals of a Physical-Mathematical Model for Unsteady Combustion in Solid Rocket Fuel and Developing Methods for Unsteady Velocity Calculation","authors":"Elena Vladimirovna Molchanova Alves, Manuel Joaquim Alves","doi":"10.47363/jpma/2023(1)106","DOIUrl":"https://doi.org/10.47363/jpma/2023(1)106","url":null,"abstract":"The article is dedicated to the theoretical study of the non-stationary Combustion Velocity of Solid Rocket Fuel (CVSRF). To calculate the Internal Ballistic Characteristics (IBC) of solid fuel missile engines, combustion velocity laws are used. These laws represent stationary relationships between the Combustion Velocity of Solid Rocket Fuel (CVSRF) and initial pressure and temperature. These relationships are experimentally determined under “stationary” conditions, i.e., by burning fuel samples in stationary conditions.","PeriodicalId":326537,"journal":{"name":"Journal of Physical Mathematics & its Applications","volume":"109 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139133766","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-31DOI: 10.47363/jpma/2023(1)105
Elena Vladimirovna Molchanova Alves, Manuel Joaquim Alves
Investigating a functional differential equation of even order, we explore a class of self-adjoint boundary value problems with two-point conditions. We establish the basis property of the system of eigenfunctions and compare the eigenvalues.
{"title":"On Self-Adjoint Boundary Value Problems for a Functional Equation of Even Order","authors":"Elena Vladimirovna Molchanova Alves, Manuel Joaquim Alves","doi":"10.47363/jpma/2023(1)105","DOIUrl":"https://doi.org/10.47363/jpma/2023(1)105","url":null,"abstract":"Investigating a functional differential equation of even order, we explore a class of self-adjoint boundary value problems with two-point conditions. We establish the basis property of the system of eigenfunctions and compare the eigenvalues.","PeriodicalId":326537,"journal":{"name":"Journal of Physical Mathematics & its Applications","volume":"113 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139133143","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-30DOI: 10.47363/jpma/2023(1)103
C. Mora
In examining the area of a square within the area of a circle whose diagonal line bisects the square into two equal halves of the right triangles; is the diameter of that circle’s area in consideration. Clearly, transformation of a circle determines the ratio of expansion- in relation to its radius given that it is increasing by half. Thus, as the difference of the areas of the relative circles is half of pi; then subtracting the larger area of a circle from its larger relative square which is within its circumference: with that of the smaller area of a circle whose smaller square is also within its radius- results into half of pi minus half. Where then it is easier from such, to deduce the Archimedes constant.while the GDP is projected to increase from $603 billion in 2020 to $15 trillion in 2063. The military spending is projected to increase from $2.6 billion to $33.94 billion, and the trade balance is projected to increase from $15 billion in 2020 to $29.99 billion in 2063. The study concludes that the projected indicators align with the 2063 Africa Agenda and recommends policies that would foster sustainable economic growth and development in Nigeria. By understanding the trends and patterns of these socioeconomic indicators, policymakers can make informed decisions about how to allocate resources and promote sustainable development in Nigeria and beyond
{"title":"Newton’s Calculus Revised","authors":"C. Mora","doi":"10.47363/jpma/2023(1)103","DOIUrl":"https://doi.org/10.47363/jpma/2023(1)103","url":null,"abstract":"In examining the area of a square within the area of a circle whose diagonal line bisects the square into two equal halves of the right triangles; is the diameter of that circle’s area in consideration. Clearly, transformation of a circle determines the ratio of expansion- in relation to its radius given that it is increasing by half. Thus, as the difference of the areas of the relative circles is half of pi; then subtracting the larger area of a circle from its larger relative square which is within its circumference: with that of the smaller area of a circle whose smaller square is also within its radius- results into half of pi minus half. Where then it is easier from such, to deduce the Archimedes constant.while the GDP is projected to increase from $603 billion in 2020 to $15 trillion in 2063. The military spending is projected to increase from $2.6 billion to $33.94 billion, and the trade balance is projected to increase from $15 billion in 2020 to $29.99 billion in 2063. The study concludes that the projected indicators align with the 2063 Africa Agenda and recommends policies that would foster sustainable economic growth and development in Nigeria. By understanding the trends and patterns of these socioeconomic indicators, policymakers can make informed decisions about how to allocate resources and promote sustainable development in Nigeria and beyond","PeriodicalId":326537,"journal":{"name":"Journal of Physical Mathematics & its Applications","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133803838","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.47363/jpma/2023(1)101
H. Deyssenroth
What happens to a laser beam that points from the bottom of a train (at rest) to a point in the ceiling when the train is moving very fast. Will the beam still hit this point, or will it hit the ceiling behind this point? In the years around 1900 scientists were convinced that photons get a lateral momentum in the direction of movement, because they are particles. But R. Feynman concluded that a mirror emits new photons and is therefore a light source and together with Einstein’s second STR-postulate the laser beam should hit the ceiling behind this point. This can be tested with the return rates of photons from a mirror on the Moon. The results show clearly with an error of probability < 10-80 that photons do not get a lateral momentum but arrive at that location where the Earth was 2.55 seconds before. Besides the detection of an additional velocity of Earth in the Universe this article proves that Einstein’s geometric spacetime idea is wrong because the physical basis for that is wrong
{"title":"The Data from the Lunar Laser Ranging Project Contradict Einstein’s Genius Spacetime Idea","authors":"H. Deyssenroth","doi":"10.47363/jpma/2023(1)101","DOIUrl":"https://doi.org/10.47363/jpma/2023(1)101","url":null,"abstract":"What happens to a laser beam that points from the bottom of a train (at rest) to a point in the ceiling when the train is moving very fast. Will the beam still hit this point, or will it hit the ceiling behind this point? In the years around 1900 scientists were convinced that photons get a lateral momentum in the direction of movement, because they are particles. But R. Feynman concluded that a mirror emits new photons and is therefore a light source and together with Einstein’s second STR-postulate the laser beam should hit the ceiling behind this point. This can be tested with the return rates of photons from a mirror on the Moon. The results show clearly with an error of probability < 10-80 that photons do not get a lateral momentum but arrive at that location where the Earth was 2.55 seconds before. Besides the detection of an additional velocity of Earth in the Universe this article proves that Einstein’s geometric spacetime idea is wrong because the physical basis for that is wrong","PeriodicalId":326537,"journal":{"name":"Journal of Physical Mathematics & its Applications","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128305614","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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