Pub Date : 2023-03-20DOI: 10.11648/j.ijamtp.20230901.11
Pedro L. Contreras E., Dianela Osorio, A. Devi
This work is aimed at numerically investigating the behavior of the Fermi energy in Strontium-doped Lanthanum Cuprate, using a numerical zero temperature elastic scattering cross-section procedure in the unitary collision regime. The main task is to vary the zero temperature superconducting energy gap from its zero value in the normal state, to the highest value of 60 meV. We find that there are two different reduced phase space regimes for the first harmonic line node's order parameter. The first scenario considers that when the Fermi energy and the nearest hopping terms have the same order of magnitude, the physics can be described by a picture given by nonequilibrium statistical mechanics. A second scenario indicates, that when the Fermi energy parameter and the hopping term have different order of magnitude; the physical picture tends to be related to the nonrelativistic quantum mechanical degrees of freedom coming from quasi-stationary quantum energy levels, with a damping term seen in the probability density distribution function, that is described in the configuration space. Henceforth, it is concluded that the use of the zero temperature elastic scattering cross-section links the phase and configuration spaces through the inverse scattering lifetime, and helps to clarify the role of the degrees of freedom in Strontium-doped Lanthanum Cuprate. Finally, we think that the self-consistent numerical procedure with the reduced phase space, induces nonlocality in the inverse scattering lifetime.
{"title":"Self-Consistent Study of the Superconducting Gap in the Strontium-doped Lanthanum Cuprate","authors":"Pedro L. Contreras E., Dianela Osorio, A. Devi","doi":"10.11648/j.ijamtp.20230901.11","DOIUrl":"https://doi.org/10.11648/j.ijamtp.20230901.11","url":null,"abstract":"This work is aimed at numerically investigating the behavior of the Fermi energy in Strontium-doped Lanthanum Cuprate, using a numerical zero temperature elastic scattering cross-section procedure in the unitary collision regime. The main task is to vary the zero temperature superconducting energy gap from its zero value in the normal state, to the highest value of 60 meV. We find that there are two different reduced phase space regimes for the first harmonic line node's order parameter. The first scenario considers that when the Fermi energy and the nearest hopping terms have the same order of magnitude, the physics can be described by a picture given by nonequilibrium statistical mechanics. A second scenario indicates, that when the Fermi energy parameter and the hopping term have different order of magnitude; the physical picture tends to be related to the nonrelativistic quantum mechanical degrees of freedom coming from quasi-stationary quantum energy levels, with a damping term seen in the probability density distribution function, that is described in the configuration space. Henceforth, it is concluded that the use of the zero temperature elastic scattering cross-section links the phase and configuration spaces through the inverse scattering lifetime, and helps to clarify the role of the degrees of freedom in Strontium-doped Lanthanum Cuprate. Finally, we think that the self-consistent numerical procedure with the reduced phase space, induces nonlocality in the inverse scattering lifetime.","PeriodicalId":367229,"journal":{"name":"International Journal of Applied Mathematics and Theoretical Physics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122899284","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 : 2021-09-11DOI: 10.11648/J.IJAMTP.20210703.13
Muhammad Azam, N. Ullah
Abdullah Alotaibi defined a starlike function connected with a cosine hyperbolic function in the year 2020. We establish some appropriate conditions for several features of multivalent analytic starlike function subordinated with cosine hyperbolic function in this article. We determine conditions on α are subordinated by Janowski function. We acquire some suitable conditions by selecting specific values for functions we get some adequate conditions for multivalent starlik function related with cosine hyperbolic. Over the last decade, starlike functions have grown in popularity in both literature and application. Our goal in this work is look at some practical challenges with q-starlike functions. Moreover, we will show that the class described in this research, as well as the results gained, generalizes numerous previously published papers. We need to add some fundamental Geometric function theory literature here to comprehend the notions employed in our work in a straightforward way. To do so, we'll start with the notation, which signifies the class of holomorphic or analytic functions in the holomorphic or analytic functions. Then the relationships must be stable. In addition, all univalent functions will belong to the subfamily. Furthermore, the possibility of subjections between analytic functions and, as shown by, as; the functions, are related by the connection of subjection, if there exists an analytic function with restrictions and such that in addition, if the function is in, we get The aim of this paper is to define a family of multivalent q-starlike functions associated with circular domains and to study some of its useful properties of multivalent analytic functions subordinated cosine hyperbolic function.
Abdullah Alotaibi在2020年定义了一个与余弦双曲函数相连的星形函数。本文建立了余弦双曲函数从属的多价解析星形函数的几个特征的适当条件。我们确定α上的条件隶属于Janowski函数。通过选取函数的特定值，得到了关于余弦双曲的多价星形函数的适当条件。在过去的十年中，星形函数在文献和应用中都越来越受欢迎。我们在这项工作中的目标是研究q-星形函数的一些实际挑战。此外，我们将表明，在这项研究中描述的类，以及所获得的结果，概括了许多以前发表的论文。我们需要在这里添加一些基本的几何函数理论文献，以便以一种直接的方式理解我们工作中使用的概念。为此，我们将从符号开始，它表示全纯或解析函数中的全纯或解析函数类。那么关系必须是稳定的。此外，所有的一元函数都属于这个亚族。更进一步，分析函数之间的主词的可能性，如所示:本文的目的是定义与圆域有关的一类多价q-星形函数族，并研究其隶属于余弦双曲函数的多价解析函数的一些有用性质。
{"title":"Some Properties of Multivalent Analytic Starlike Function Subordinated with Cosine Hyperbolic Function","authors":"Muhammad Azam, N. Ullah","doi":"10.11648/J.IJAMTP.20210703.13","DOIUrl":"https://doi.org/10.11648/J.IJAMTP.20210703.13","url":null,"abstract":"Abdullah Alotaibi defined a starlike function connected with a cosine hyperbolic function in the year 2020. We establish some appropriate conditions for several features of multivalent analytic starlike function subordinated with cosine hyperbolic function in this article. We determine conditions on α are subordinated by Janowski function. We acquire some suitable conditions by selecting specific values for functions we get some adequate conditions for multivalent starlik function related with cosine hyperbolic. Over the last decade, starlike functions have grown in popularity in both literature and application. Our goal in this work is look at some practical challenges with q-starlike functions. Moreover, we will show that the class described in this research, as well as the results gained, generalizes numerous previously published papers. We need to add some fundamental Geometric function theory literature here to comprehend the notions employed in our work in a straightforward way. To do so, we'll start with the notation, which signifies the class of holomorphic or analytic functions in the holomorphic or analytic functions. Then the relationships must be stable. In addition, all univalent functions will belong to the subfamily. Furthermore, the possibility of subjections between analytic functions and, as shown by, as; the functions, are related by the connection of subjection, if there exists an analytic function with restrictions and such that in addition, if the function is in, we get The aim of this paper is to define a family of multivalent q-starlike functions associated with circular domains and to study some of its useful properties of multivalent analytic functions subordinated cosine hyperbolic function.","PeriodicalId":367229,"journal":{"name":"International Journal of Applied Mathematics and Theoretical Physics","volume":"83 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125876839","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 : 2021-07-02DOI: 10.11648/J.IJAMTP.20210702.12
Geleta Kinkino Meyu, Kedir Aliyi Koriche
The paper presented the basic treatment of the solution of heat equation in one dimension. Heat is a form of energy in transaction and it flows from one system to another if there is a temperature difference between the systems. Heat flow is the main concern of sciences which seeks to predict the energy transfer which may take place between material bodies as result of temperature difference. Thus, there are three modes of heat transfer, i.e., conduction, radiation and convection. Conduction can be steady state heat conduction, or unsteady state heat conduction. If the system is in steady state, temperature doesn’t vary with time, but if the system in unsteady state temperature may varies with time. However, if the temperature of material is changing with time or if there are heat sources or sinks within the material the situation is more complex. So, rather than to escape all problem, we are targeted to solve one problem of heat equation in one dimension. The treatment was from both the analytical and the numerical view point, so that the reader is afforded the insight that is gained from analytical solution as well as the numerical solution that must often be used in practice. Analytical we used the techniques of separation of variables. It is worthwhile to mention here that, analytical solution is not always possible to obtain; indeed, in many instants they are very cumber some and difficult to use. In that case a numerical technique is more appropriate. Among numerical techniques finite difference schema is used. In both approach we found a solution which agrees up to one decimal place.
{"title":"Analytical Solution vs. Numerical Solution of Heat Equation Flow Through Rod of Length 8 Units in One Dimension","authors":"Geleta Kinkino Meyu, Kedir Aliyi Koriche","doi":"10.11648/J.IJAMTP.20210702.12","DOIUrl":"https://doi.org/10.11648/J.IJAMTP.20210702.12","url":null,"abstract":"The paper presented the basic treatment of the solution of heat equation in one dimension. Heat is a form of energy in transaction and it flows from one system to another if there is a temperature difference between the systems. Heat flow is the main concern of sciences which seeks to predict the energy transfer which may take place between material bodies as result of temperature difference. Thus, there are three modes of heat transfer, i.e., conduction, radiation and convection. Conduction can be steady state heat conduction, or unsteady state heat conduction. If the system is in steady state, temperature doesn’t vary with time, but if the system in unsteady state temperature may varies with time. However, if the temperature of material is changing with time or if there are heat sources or sinks within the material the situation is more complex. So, rather than to escape all problem, we are targeted to solve one problem of heat equation in one dimension. The treatment was from both the analytical and the numerical view point, so that the reader is afforded the insight that is gained from analytical solution as well as the numerical solution that must often be used in practice. Analytical we used the techniques of separation of variables. It is worthwhile to mention here that, analytical solution is not always possible to obtain; indeed, in many instants they are very cumber some and difficult to use. In that case a numerical technique is more appropriate. Among numerical techniques finite difference schema is used. In both approach we found a solution which agrees up to one decimal place.","PeriodicalId":367229,"journal":{"name":"International Journal of Applied Mathematics and Theoretical Physics","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125273919","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 : 2021-03-30DOI: 10.11648/J.IJAMTP.20210701.14
Justin Mouyedo Loufouilou, J. B. Yindoula, Gabriel Bissanga
Solving systems of partial differential equations (linear or nonlinear) with dirchelet boundary conditions has rarely made use of the Adomian decompositional method. The aim of this paper is to obtain the exact solution of some systems of linear and nonlinear partial differential equations using the adomian decomposition method.After having generated the basic principles of the general theory of this method, five systems of equations are solved, after calculation of the algorithm.Our results suggest that the use of the adomian method to solve systems of partial differential equations is efficient.However, further research should study other systems of linear or nonlinear partial differential equations to better understand the problem of uniqueness of solutions and boundary conditions.
{"title":"Application of the Adomian Decomposition Method (ADM) to Solving the Systems of Partial Differential Equations","authors":"Justin Mouyedo Loufouilou, J. B. Yindoula, Gabriel Bissanga","doi":"10.11648/J.IJAMTP.20210701.14","DOIUrl":"https://doi.org/10.11648/J.IJAMTP.20210701.14","url":null,"abstract":"Solving systems of partial differential equations (linear or nonlinear) with dirchelet boundary conditions has rarely made use of the Adomian decompositional method. The aim of this paper is to obtain the exact solution of some systems of linear and nonlinear partial differential equations using the adomian decomposition method.After having generated the basic principles of the general theory of this method, five systems of equations are solved, after calculation of the algorithm.Our results suggest that the use of the adomian method to solve systems of partial differential equations is efficient.However, further research should study other systems of linear or nonlinear partial differential equations to better understand the problem of uniqueness of solutions and boundary conditions.","PeriodicalId":367229,"journal":{"name":"International Journal of Applied Mathematics and Theoretical Physics","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117166504","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 : 2021-03-12DOI: 10.11648/J.IJAMTP.20200604.11
B. Borah
A particle which is positively charged with spherically symmetry and non-rotating in empty space is taken to find out a metric or line element. The particle is under the influence of both gravitational and electro-magnetic field and the time component of this metric is depend on the combine effect of these two fields. Therefore in this work especial attention is given in Einstein gravitational and Maxwell’s electro-magnetic field equations. Einstein field equations are individually considered for gravitational and electro-magnetic fields in empty space for an isolated charged particle and combined them like two classical waves. To solve this new metric initially Schwarzschild like solution is used. There after a simple elegant and systematic method is used to determine the value of space coefficient and time coefficient of the metric. Finally to solve the metric the e-m field tensor is used from Maxwell’s electro-magnetic field equations. Thus in the metric the values of space and time coefficient is found a new one. The space and time coefficient in the new metric is not same in the metric as devised by Reissner and Nordstrom, The new space and time coefficient gives such an information about the massive body that at particular mass of a body can stop electro-magnetic interaction. Thus the new metric able to gives us some new information and conclusions.
{"title":"Gravitational and Electromagnetic Field of an Isolated Positively Charged Particle","authors":"B. Borah","doi":"10.11648/J.IJAMTP.20200604.11","DOIUrl":"https://doi.org/10.11648/J.IJAMTP.20200604.11","url":null,"abstract":"A particle which is positively charged with spherically symmetry and non-rotating in empty space is taken to find out a metric or line element. The particle is under the influence of both gravitational and electro-magnetic field and the time component of this metric is depend on the combine effect of these two fields. Therefore in this work especial attention is given in Einstein gravitational and Maxwell’s electro-magnetic field equations. Einstein field equations are individually considered for gravitational and electro-magnetic fields in empty space for an isolated charged particle and combined them like two classical waves. To solve this new metric initially Schwarzschild like solution is used. There after a simple elegant and systematic method is used to determine the value of space coefficient and time coefficient of the metric. Finally to solve the metric the e-m field tensor is used from Maxwell’s electro-magnetic field equations. Thus in the metric the values of space and time coefficient is found a new one. The space and time coefficient in the new metric is not same in the metric as devised by Reissner and Nordstrom, The new space and time coefficient gives such an information about the massive body that at particular mass of a body can stop electro-magnetic interaction. Thus the new metric able to gives us some new information and conclusions.","PeriodicalId":367229,"journal":{"name":"International Journal of Applied Mathematics and Theoretical Physics","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126844104","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 : 2021-03-04DOI: 10.11648/J.IJAMTP.20210704.13
Christopher Mayero, Joseph Omolo, S. Okeyo
Quantum gates are fundamental in Quantum computing for their role in manipulating elementary information carriers referred to as quantum bits. In this paper, a theoretical scheme for realizing a quantum Hadamard and a quantum controlled-NOT logic gates operations in the anti-Jaynes-Cummings interaction process is provided. Standard Hadamard operation for a specified initial atomic state is achieved by setting a specific sum frequency and photon number in the normalized anti-Jaynes-Cummings qubit state transition operation with the interaction component of the anti-Jaynes-Cummings Hamiltonian generating the state transitions. The quantum controlled-NOT logic gate is realized when a single atomic qubit defined in a two-dimensional Hilbert space is the control qubit and two non-degenerate and orthogonal polarized cavities defined in a two-dimensional Hilbert space make the target qubit. With precise choice of interaction time in the anti-Jaynes-Cummings qubit state transition operations defined in the anti-Jaynes-Cummings sub-space spanned by normalized but non-orthogonal basic qubit state vectors, ideal unit probabilities of success in the quantum controlled-NOT operations is determined.
{"title":"Theoretical Realization of a Two Qubit Quantum Controlled-NOT Logic Gate and a Single Qubit Quantum Hadamard Logic Gate in the Anti-Jaynes-Cummings Model","authors":"Christopher Mayero, Joseph Omolo, S. Okeyo","doi":"10.11648/J.IJAMTP.20210704.13","DOIUrl":"https://doi.org/10.11648/J.IJAMTP.20210704.13","url":null,"abstract":"Quantum gates are fundamental in Quantum computing for their role in manipulating elementary information carriers referred to as quantum bits. In this paper, a theoretical scheme for realizing a quantum Hadamard and a quantum controlled-NOT logic gates operations in the anti-Jaynes-Cummings interaction process is provided. Standard Hadamard operation for a specified initial atomic state is achieved by setting a specific sum frequency and photon number in the normalized anti-Jaynes-Cummings qubit state transition operation with the interaction component of the anti-Jaynes-Cummings Hamiltonian generating the state transitions. The quantum controlled-NOT logic gate is realized when a single atomic qubit defined in a two-dimensional Hilbert space is the control qubit and two non-degenerate and orthogonal polarized cavities defined in a two-dimensional Hilbert space make the target qubit. With precise choice of interaction time in the anti-Jaynes-Cummings qubit state transition operations defined in the anti-Jaynes-Cummings sub-space spanned by normalized but non-orthogonal basic qubit state vectors, ideal unit probabilities of success in the quantum controlled-NOT operations is determined.","PeriodicalId":367229,"journal":{"name":"International Journal of Applied Mathematics and Theoretical Physics","volume":"116 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124059392","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 : 2019-12-25DOI: 10.11648/J.IJAMTP.20190504.14
S. Massou, A. Adomou, J. Edou
In this research work, we opt for the static spherical symmetric metric. Thus, taking into account the own gravitational field of elementary particles, we have obtained exact static spheric symmetric solutions of the nonlinear spinor and gravitational fields equations. The nonlinear terms in the spinor lagrangian density characterize the self-interaction of a spinor field. We have investigated in detail equations with power and polynomial nonlinearities. In this case, we have obtained exact regular solutions which have a localized energy density and limited total energy (soliton-like solutions) only if the mass parameter in the spinor field equations is equal to zero. In additional to this, the total charge and the total spin are bounded. We have also shown that in the linear case, soliton-like solutions are absent. But in the flat space-time, the obtained solutions are soliton-like configurations. Therefore, the proper gravitational field of elementary particles, the geometrical properties of the metric and the nonlinear terms in the lagrangian density play a crucial role in the purpose to get the regular solutions with localized energy density and limited total energy.
{"title":"Soliton-Like Spherical Symmetric Solutions of the Nonlinear Spinor Field equations in General Relativity","authors":"S. Massou, A. Adomou, J. Edou","doi":"10.11648/J.IJAMTP.20190504.14","DOIUrl":"https://doi.org/10.11648/J.IJAMTP.20190504.14","url":null,"abstract":"In this research work, we opt for the static spherical symmetric metric. Thus, taking into account the own gravitational field of elementary particles, we have obtained exact static spheric symmetric solutions of the nonlinear spinor and gravitational fields equations. The nonlinear terms in the spinor lagrangian density characterize the self-interaction of a spinor field. We have investigated in detail equations with power and polynomial nonlinearities. In this case, we have obtained exact regular solutions which have a localized energy density and limited total energy (soliton-like solutions) only if the mass parameter in the spinor field equations is equal to zero. In additional to this, the total charge and the total spin are bounded. We have also shown that in the linear case, soliton-like solutions are absent. But in the flat space-time, the obtained solutions are soliton-like configurations. Therefore, the proper gravitational field of elementary particles, the geometrical properties of the metric and the nonlinear terms in the lagrangian density play a crucial role in the purpose to get the regular solutions with localized energy density and limited total energy.","PeriodicalId":367229,"journal":{"name":"International Journal of Applied Mathematics and Theoretical Physics","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133803248","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 : 2019-12-07DOI: 10.11648/J.IJAMTP.20190504.12
L. Moukala
In Quantum Mechanics, one knows that the wave function interpretation is probabilistic. We previously established that any particle scalar field is the cause of its existence. Here, one examined the plane solution regarding a moving particle in vacuum, through the relativistic formalism. It appeared the following. (i) The solution presents four alternatives, like in Dirac unified formalism; when searching stationary solutions of the system vacuum-particle or the system vacuum-antiparticle. (ii) Considering the former, each spinner component shows the interaction of one particle charge with three vacuum fermions of spin-½; each oriented along one space direction. Furthermore, this allows deducting the triple nature of any gauge fermion. (iii) Each solution case is definable with a same wave front width. This determination became possible from the vector companion of that wave function one introduced before. Here, this points out the existence of transverse time. (iv) Both functions let emphasizing the existence of a third fundamental field of long range, which is identifiable to the fundamental spin field. (v) This unites the particle spin and orbital momenta and bears in addition a magnetic-like field, which is yet unknown. (vi) According to the charge, a particle field is observable in wave phenomena, from the manifestations of its gauge fermions or gauge bosons; when ejected from their stationary states by a perturbation… At last, the results highlight the quantum composition of wave functions, the spin-field patency, and the wave nature manifestation from five differentiable fields.
{"title":"Microscopic Manifestations of the Wave Nature and the Fifth Fundamental Field","authors":"L. Moukala","doi":"10.11648/J.IJAMTP.20190504.12","DOIUrl":"https://doi.org/10.11648/J.IJAMTP.20190504.12","url":null,"abstract":"In Quantum Mechanics, one knows that the wave function interpretation is probabilistic. We previously established that any particle scalar field is the cause of its existence. Here, one examined the plane solution regarding a moving particle in vacuum, through the relativistic formalism. It appeared the following. (i) The solution presents four alternatives, like in Dirac unified formalism; when searching stationary solutions of the system vacuum-particle or the system vacuum-antiparticle. (ii) Considering the former, each spinner component shows the interaction of one particle charge with three vacuum fermions of spin-½; each oriented along one space direction. Furthermore, this allows deducting the triple nature of any gauge fermion. (iii) Each solution case is definable with a same wave front width. This determination became possible from the vector companion of that wave function one introduced before. Here, this points out the existence of transverse time. (iv) Both functions let emphasizing the existence of a third fundamental field of long range, which is identifiable to the fundamental spin field. (v) This unites the particle spin and orbital momenta and bears in addition a magnetic-like field, which is yet unknown. (vi) According to the charge, a particle field is observable in wave phenomena, from the manifestations of its gauge fermions or gauge bosons; when ejected from their stationary states by a perturbation… At last, the results highlight the quantum composition of wave functions, the spin-field patency, and the wave nature manifestation from five differentiable fields.","PeriodicalId":367229,"journal":{"name":"International Journal of Applied Mathematics and Theoretical Physics","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115111914","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 : 2019-09-23DOI: 10.11648/J.IJAMTP.20190503.16
M. Soliman, H. Selim, I. A. Hassan
Where Earth is not strictly rigid body but can responds to any effects that tend to its rotation and shape, we will explain, in the present paper, the goal which is to define the forced nutation for a rigid Earth model using two different theories. We will formulate a first order Hamiltonian of a deformable Earth for its rotational motion around the Sun through the contribution of triaxial symmetry of the Earth. The formulation of the theory will be formed twice times. Firstly, deduce the tidal affect’s forces by Luni - Solar attraction coupling with the Earth’s geopotential force. Secondly, through the formulation, we will neglect the coupling between the different effects (the geopotential Earth force effect and the Luni - Solar attraction force), so, we will find the transform of the Hamiltonian for each force separately. The analytical solution for the formulated Hamiltonian will be derived for the two cases by using perturbation technique of Lie - Hori series. Once can get the analytical solution by getting the generation function, we will derive the nutation series analytically and numerically for each case and conclude over the results.
{"title":"Forced Nutation for Rigid Earth Model with Different Theories","authors":"M. Soliman, H. Selim, I. A. Hassan","doi":"10.11648/J.IJAMTP.20190503.16","DOIUrl":"https://doi.org/10.11648/J.IJAMTP.20190503.16","url":null,"abstract":"Where Earth is not strictly rigid body but can responds to any effects that tend to its rotation and shape, we will explain, in the present paper, the goal which is to define the forced nutation for a rigid Earth model using two different theories. We will formulate a first order Hamiltonian of a deformable Earth for its rotational motion around the Sun through the contribution of triaxial symmetry of the Earth. The formulation of the theory will be formed twice times. Firstly, deduce the tidal affect’s forces by Luni - Solar attraction coupling with the Earth’s geopotential force. Secondly, through the formulation, we will neglect the coupling between the different effects (the geopotential Earth force effect and the Luni - Solar attraction force), so, we will find the transform of the Hamiltonian for each force separately. The analytical solution for the formulated Hamiltonian will be derived for the two cases by using perturbation technique of Lie - Hori series. Once can get the analytical solution by getting the generation function, we will derive the nutation series analytically and numerically for each case and conclude over the results.","PeriodicalId":367229,"journal":{"name":"International Journal of Applied Mathematics and Theoretical Physics","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116955341","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 : 2019-09-20DOI: 10.11648/J.IJAMTP.20190503.15
Zhang Yue
Although the mathematicians all over the world offered hard explorations of more than one hundred years, the proof of using pure mathematical theories on the conjecture of twin primes has not born in the world. This paper is trying to apply computer program to prove that corresponding to infinite primes p, there are infinite p+2 primes. As a mathematical proof, the paper uses the concept of mapping to connect the computer program and the pure mathematical theory. With the requirement of a mathematical proof, in accord with the restriction of the integer of which the computer allows to take, an assumption is suggested, and on the basis of it, using the program of C language the paper presents, or regarding the C program as the mapping from infinite p primes to infinite p+2 primes, the paper proves that corresponding to infinite primes p, there are infinite p+2 primes; namely, the conjecture of twin primes is true.
{"title":"A Proof on the Conjecture of Twin Primes","authors":"Zhang Yue","doi":"10.11648/J.IJAMTP.20190503.15","DOIUrl":"https://doi.org/10.11648/J.IJAMTP.20190503.15","url":null,"abstract":"Although the mathematicians all over the world offered hard explorations of more than one hundred years, the proof of using pure mathematical theories on the conjecture of twin primes has not born in the world. This paper is trying to apply computer program to prove that corresponding to infinite primes p, there are infinite p+2 primes. As a mathematical proof, the paper uses the concept of mapping to connect the computer program and the pure mathematical theory. With the requirement of a mathematical proof, in accord with the restriction of the integer of which the computer allows to take, an assumption is suggested, and on the basis of it, using the program of C language the paper presents, or regarding the C program as the mapping from infinite p primes to infinite p+2 primes, the paper proves that corresponding to infinite primes p, there are infinite p+2 primes; namely, the conjecture of twin primes is true.","PeriodicalId":367229,"journal":{"name":"International Journal of Applied Mathematics and Theoretical Physics","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126572900","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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