Pub Date : 2022-07-03DOI: 10.1080/1726037X.2022.2120272
S. Yadav, Mukesh Kumar, Virendra Kumar
Abstract In this paper, the resonance due to equatorial ellipticity of Earth, spin rate of Earth and angular velocity of bary-center are investigated. Using spherical coordinate system, we have determined equations of motion of the moon. By using perturbations relative to moon, equations of motion are simplified to second order ordinary differential equation containing the equatorial ellipticity parameter of the Earth. Two types of resonant curves due to the frequencies (a) , and (b) are analyzed. It is observed that the amplitudes of the oscillation are different at different resonant points due to different size of the bandwidth. Finally, the phase portrait of the orbits of the moon and the phase spaces are analyzed by using Poincare section with periodicity in time t for the unpertubed system.
{"title":"Analysis of Resonant Curve and Phase Portrait Due to Earth’s Equatorial Ellipticity In the Earth-Moon System Using Perturbation Technique","authors":"S. Yadav, Mukesh Kumar, Virendra Kumar","doi":"10.1080/1726037X.2022.2120272","DOIUrl":"https://doi.org/10.1080/1726037X.2022.2120272","url":null,"abstract":"Abstract In this paper, the resonance due to equatorial ellipticity of Earth, spin rate of Earth and angular velocity of bary-center are investigated. Using spherical coordinate system, we have determined equations of motion of the moon. By using perturbations relative to moon, equations of motion are simplified to second order ordinary differential equation containing the equatorial ellipticity parameter of the Earth. Two types of resonant curves due to the frequencies (a) , and (b) are analyzed. It is observed that the amplitudes of the oscillation are different at different resonant points due to different size of the bandwidth. Finally, the phase portrait of the orbits of the moon and the phase spaces are analyzed by using Poincare section with periodicity in time t for the unpertubed system.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"20 1","pages":"275 - 298"},"PeriodicalIF":0.9,"publicationDate":"2022-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47087112","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 : 2022-07-03DOI: 10.1080/1726037X.2022.2079269
M. R. Farhangdoost, R. B. Ziabari, A. Armakan
Abstract Some classes of almost contact structures on 5-dimensional nilpotent Lie algebras were investigated in the literature. On the other hand, there are several generalizations of Lie algebras and their characterizations. In particular, an effective characterization of all Hom-Lie algebras of sl(2) type and construction of all the 3-dimensional Hom-Lie algebras for a class of twisting homomorphisms has been presented. A list of twenty 3-dimensional Hom-Lie algebras has been given. In this paper, we consider some classes of almost contact metric structure on all those twenty 3-dimensional Hom-Lie algebras separately. We study semi-cosymplectic, almost cosymplectic and cosymlectic structures. Moreover, we study K-contact and Sasakian structures on 3-dimensional Hom-Lie algebras.
{"title":"Geometric Structures On 3-Dimensional Hom-Lie Algebras","authors":"M. R. Farhangdoost, R. B. Ziabari, A. Armakan","doi":"10.1080/1726037X.2022.2079269","DOIUrl":"https://doi.org/10.1080/1726037X.2022.2079269","url":null,"abstract":"Abstract Some classes of almost contact structures on 5-dimensional nilpotent Lie algebras were investigated in the literature. On the other hand, there are several generalizations of Lie algebras and their characterizations. In particular, an effective characterization of all Hom-Lie algebras of sl(2) type and construction of all the 3-dimensional Hom-Lie algebras for a class of twisting homomorphisms has been presented. A list of twenty 3-dimensional Hom-Lie algebras has been given. In this paper, we consider some classes of almost contact metric structure on all those twenty 3-dimensional Hom-Lie algebras separately. We study semi-cosymplectic, almost cosymplectic and cosymlectic structures. Moreover, we study K-contact and Sasakian structures on 3-dimensional Hom-Lie algebras.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"20 1","pages":"137 - 175"},"PeriodicalIF":0.9,"publicationDate":"2022-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41520465","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 : 2022-07-03DOI: 10.1080/1726037X.2022.2142353
C. Valls
Abstract In this paper we deal with the equations a(x)dy/dx = A(x)y 2 + B(x)y 3, where a(x), A(x) and B(x) are complex polynomials with a(x)B(x) ≢ 0 and a(x) non-constant. First we show that the unique rational limit cycles that these equations can have are of the form y = 1/p(x) being p(x) some polynomial. Second we provide an upper bound on the number of these rational limit cycles. Moreover, we prove that if deg(B(x)) − deg(a(x)) + 1 is odd, or deg(A) > (deg(B(x)) + deg(a(x)) − 1)/2, then these Abel equations have at most two rational limit cycles and we provide examples of these Abel equations with three nontrivial rational periodic solutions.
{"title":"Rational Periodic Solutions on Some Generalized Abel Equations","authors":"C. Valls","doi":"10.1080/1726037X.2022.2142353","DOIUrl":"https://doi.org/10.1080/1726037X.2022.2142353","url":null,"abstract":"Abstract In this paper we deal with the equations a(x)dy/dx = A(x)y 2 + B(x)y 3, where a(x), A(x) and B(x) are complex polynomials with a(x)B(x) ≢ 0 and a(x) non-constant. First we show that the unique rational limit cycles that these equations can have are of the form y = 1/p(x) being p(x) some polynomial. Second we provide an upper bound on the number of these rational limit cycles. Moreover, we prove that if deg(B(x)) − deg(a(x)) + 1 is odd, or deg(A) > (deg(B(x)) + deg(a(x)) − 1)/2, then these Abel equations have at most two rational limit cycles and we provide examples of these Abel equations with three nontrivial rational periodic solutions.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"20 1","pages":"177 - 189"},"PeriodicalIF":0.9,"publicationDate":"2022-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48970935","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 : 2022-07-03DOI: 10.1080/1726037X.2022.2142355
Zafar Iqbal
Abstract We inquire the motion of charged particles varying under the effect of Lorentz force produced by magnetic and Killing magnetic fields in anti-de Sitter 3-space . Primarily, we characterize magnetic trajectories in in terms of their Frenet apparatus. Thereafter, utilizing a geometrical model of split-quaternions for (where corresponds to a subspace of the Lie group H of split-quaternions) we find 6 independent unit Killing vector fields on which constitutes a basis for the corresponding 6D Lie algebra i(). We conclude with characterizations of Killing magnetic trajectories in with respect to quasi-slope, curvature and torsion or pseudo-torsion (depending on the situation).
{"title":"Geometrical Aspects of Motion of Charged Particles in Magnetic and Killing Magnetic Fields and Their Corresponding Trajectories in Anti-De Sitter 3-Space","authors":"Zafar Iqbal","doi":"10.1080/1726037X.2022.2142355","DOIUrl":"https://doi.org/10.1080/1726037X.2022.2142355","url":null,"abstract":"Abstract We inquire the motion of charged particles varying under the effect of Lorentz force produced by magnetic and Killing magnetic fields in anti-de Sitter 3-space . Primarily, we characterize magnetic trajectories in in terms of their Frenet apparatus. Thereafter, utilizing a geometrical model of split-quaternions for (where corresponds to a subspace of the Lie group H of split-quaternions) we find 6 independent unit Killing vector fields on which constitutes a basis for the corresponding 6D Lie algebra i(). We conclude with characterizations of Killing magnetic trajectories in with respect to quasi-slope, curvature and torsion or pseudo-torsion (depending on the situation).","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"20 1","pages":"191 - 226"},"PeriodicalIF":0.9,"publicationDate":"2022-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41349223","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 : 2022-07-03DOI: 10.1080/1726037X.2022.2142356
D. Dey
Abstract The object of this offering article is to introduce the notion of *- Miao-Tam critical equation on almost contact metric manifolds and it is studied on almost Kenmotsu manifolds with some nullity condition. It is proved that if the metric of a (2n + 1)-dimensional (k, µ) ! -almost Kenmotsu manifold (M, g) satisfies the *-Miao-Tam critical equation, then the manifold (M, g) is *-Ricci flat and locally isometric to a product space. Finally, the result is verified by an example.
{"title":"Almost Kenmotsu Manifolds Admitting Certain Critical Metric","authors":"D. Dey","doi":"10.1080/1726037X.2022.2142356","DOIUrl":"https://doi.org/10.1080/1726037X.2022.2142356","url":null,"abstract":"Abstract The object of this offering article is to introduce the notion of *- Miao-Tam critical equation on almost contact metric manifolds and it is studied on almost Kenmotsu manifolds with some nullity condition. It is proved that if the metric of a (2n + 1)-dimensional (k, µ) ! -almost Kenmotsu manifold (M, g) satisfies the *-Miao-Tam critical equation, then the manifold (M, g) is *-Ricci flat and locally isometric to a product space. Finally, the result is verified by an example.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"20 1","pages":"299 - 309"},"PeriodicalIF":0.9,"publicationDate":"2022-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45776941","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 : 2022-07-03DOI: 10.1080/1726037X.2022.2139928
V. Sreenivasa Rao, V. Ganesh, K. Dasunaidu, Y. Aditya, D. Reddy
Abstract This article examines the physical behaviour of the Kaluza-Klein FRW type space-time with f(R,T) gravity proposed by Harko et al. (Phys. Rev. D 84:024020, 2011) in the presence of a massive scalar meson field. Here, ”R” stands for the Ricci tensor, while ”T” stands for the energy-momentum tensor’s trace. We employed the (i ) hybrid expansion law (Akarsu et al. JCAP, 01:022, 2014), (ii ) the variable deceleration parameter (Mishra et al. Int. J. Theor. Phys. 52:2546, 2013), and (iii ) the linearly varying deceleration parameter (Akarsu and Dereli. Int. J. Theor. Phys. 51:612, 2012) to solve the field equations. Additionally, we looked at some of the model’s physical and kinematic characteristics. Our models have been found to show a smooth transition from the universe’s early slowdown to its current acceleration, and the current value of the deceleration parameter is found to be reasonably consistent with the observational data. The early stages of the universe’s evolution will be better understood through the study of domain wall cosmological models.
本文研究了Harko等人提出的具有f(R,T)引力的Kaluza-Klein FRW型时空的物理行为。Rev. D 84: 024020,2011)在存在大量标量介子场的情况下。这里，“R”代表里奇张量，而“T”代表能量动量张量的轨迹。我们采用了(i)混合膨胀定律(Akarsu等)。JCAP, 01:22, 2014)， (ii)可变减速参数(Mishra et al.;Int。j理论的。(iii)线性变化的减速参数(Akarsu and Dereli。Int。j理论的。物理学报，51:612,2012)求解场方程。此外，我们还研究了模型的一些物理和运动学特征。我们的模型显示了宇宙从早期的减速到当前的加速的平滑过渡，并且发现当前的减速参数值与观测数据相当一致。通过域壁宇宙学模型的研究，宇宙演化的早期阶段将得到更好的理解。
{"title":"Study of Frw Type Kaluza-Klein Domain Wall Cosmological Models in the Presence of Massive Scalar Field in a Modified Gravity","authors":"V. Sreenivasa Rao, V. Ganesh, K. Dasunaidu, Y. Aditya, D. Reddy","doi":"10.1080/1726037X.2022.2139928","DOIUrl":"https://doi.org/10.1080/1726037X.2022.2139928","url":null,"abstract":"Abstract This article examines the physical behaviour of the Kaluza-Klein FRW type space-time with f(R,T) gravity proposed by Harko et al. (Phys. Rev. D 84:024020, 2011) in the presence of a massive scalar meson field. Here, ”R” stands for the Ricci tensor, while ”T” stands for the energy-momentum tensor’s trace. We employed the (i ) hybrid expansion law (Akarsu et al. JCAP, 01:022, 2014), (ii ) the variable deceleration parameter (Mishra et al. Int. J. Theor. Phys. 52:2546, 2013), and (iii ) the linearly varying deceleration parameter (Akarsu and Dereli. Int. J. Theor. Phys. 51:612, 2012) to solve the field equations. Additionally, we looked at some of the model’s physical and kinematic characteristics. Our models have been found to show a smooth transition from the universe’s early slowdown to its current acceleration, and the current value of the deceleration parameter is found to be reasonably consistent with the observational data. The early stages of the universe’s evolution will be better understood through the study of domain wall cosmological models.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"20 1","pages":"227 - 247"},"PeriodicalIF":0.9,"publicationDate":"2022-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46855062","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 : 2022-07-03DOI: 10.1080/1726037X.2022.2120271
Drs Ren, D. Khadjiev, Mer Peken, Gayrat Beshimov
Abstract In this paper, ”the concept of T-object” is defined in two dimensional Minkowski space. By this concept, the complete systems of invariants of m-point, paths and vector fields are investigated as a single theory. Using this approach, we obtain the complete systems of invariants of T-object and the equivalence conditions of two T-objects are given in terms of their global invariants.
{"title":"Global Invariants of Objects in two-Dimensional Minkowski Space","authors":"Drs Ren, D. Khadjiev, Mer Peken, Gayrat Beshimov","doi":"10.1080/1726037X.2022.2120271","DOIUrl":"https://doi.org/10.1080/1726037X.2022.2120271","url":null,"abstract":"Abstract In this paper, ”the concept of T-object” is defined in two dimensional Minkowski space. By this concept, the complete systems of invariants of m-point, paths and vector fields are investigated as a single theory. Using this approach, we obtain the complete systems of invariants of T-object and the equivalence conditions of two T-objects are given in terms of their global invariants.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"20 1","pages":"249 - 273"},"PeriodicalIF":0.9,"publicationDate":"2022-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48008678","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 : 2022-01-02DOI: 10.1080/1726037X.2022.2079265
S. Kumbhare, G. S. Khadekar
Abstract In present paper, we have studied magnetized quark and strange quark matter with conformal motions in higher dimensional spherically symmetric space-time. We found Einstein's eld equations in higher dimensional spherically symmetric space-time using conformal motions. In the framework of higher dimension, various physical quantities have discussed.
{"title":"Magnetized Quark and Strange Quark Matter in the Higher Dimensional Spherically Symmetric Space Time Admitting One Parameter Group of Conformal Motions","authors":"S. Kumbhare, G. S. Khadekar","doi":"10.1080/1726037X.2022.2079265","DOIUrl":"https://doi.org/10.1080/1726037X.2022.2079265","url":null,"abstract":"Abstract In present paper, we have studied magnetized quark and strange quark matter with conformal motions in higher dimensional spherically symmetric space-time. We found Einstein's eld equations in higher dimensional spherically symmetric space-time using conformal motions. In the framework of higher dimension, various physical quantities have discussed.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"20 1","pages":"67 - 79"},"PeriodicalIF":0.9,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46073330","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 : 2022-01-02DOI: 10.1080/1726037X.2022.2079266
Damodhar F Shastrakar, Sharad S Pokley, S. Anwar
Abstract A limited source Queuing model having single server is considering here to discuss its various parameters. The number of arriving customers in this model is fixed. Since the arriving customers are already fixed and system is busy in serving the customers one by one, the arrival rate of next coming customer gets reduced. This reduces the further congestion. The service discipline in the model is general discipline. As the arriving customers in the system are limited, binomial distribution is used to deal with the arrival rate of customers and service rate of server. Uniform distribution is applied to the inter-arrival time and service time. By using the binomial distribution, formula is derived to find the expected waiting time of a customer in the queue. The derived formula and littles formula are then used together to study the various parameters of the Queuing model. Finally comparing the results calculated by the newly derived formulae and existing formulae.
{"title":"Analysis of Various Parameters of Limited Source Queuing Model Having Single Server by Using Binomial and Uniform Distribution","authors":"Damodhar F Shastrakar, Sharad S Pokley, S. Anwar","doi":"10.1080/1726037X.2022.2079266","DOIUrl":"https://doi.org/10.1080/1726037X.2022.2079266","url":null,"abstract":"Abstract A limited source Queuing model having single server is considering here to discuss its various parameters. The number of arriving customers in this model is fixed. Since the arriving customers are already fixed and system is busy in serving the customers one by one, the arrival rate of next coming customer gets reduced. This reduces the further congestion. The service discipline in the model is general discipline. As the arriving customers in the system are limited, binomial distribution is used to deal with the arrival rate of customers and service rate of server. Uniform distribution is applied to the inter-arrival time and service time. By using the binomial distribution, formula is derived to find the expected waiting time of a customer in the queue. The derived formula and littles formula are then used together to study the various parameters of the Queuing model. Finally comparing the results calculated by the newly derived formulae and existing formulae.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"20 1","pages":"81 - 90"},"PeriodicalIF":0.9,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42973462","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 : 2022-01-02DOI: 10.1080/1726037X.2022.2079268
D. D. Pawar, R. Mapari
Abstract We have explored a plane symmetric cosmological model in f(R, T) gravity. We have used an interacting field as a source of energy, as well as dark energy. In this case, the interacting field is simply a linear coupling between an electromagnetic field, a massless scalar field, and a charged perfect fluid. Four cases have been described 1) Perfect fluid, 2) Disordered radiation, 3) Dust fluid, and 4) Dark energy. We used the relationship between metric potential to solve field equations. By using equation of state, we observed the pressure and density profiles in various models. We also went over some cosmological and dynamical parameters in depth. Also, we discovered both negative and positive deceleration parameters in different time intervals, indicating the Universe’s transition phase.
{"title":"Plane Symmetry Cosmology Model of Interacting Field in f(R, T) Theory","authors":"D. D. Pawar, R. Mapari","doi":"10.1080/1726037X.2022.2079268","DOIUrl":"https://doi.org/10.1080/1726037X.2022.2079268","url":null,"abstract":"Abstract We have explored a plane symmetric cosmological model in f(R, T) gravity. We have used an interacting field as a source of energy, as well as dark energy. In this case, the interacting field is simply a linear coupling between an electromagnetic field, a massless scalar field, and a charged perfect fluid. Four cases have been described 1) Perfect fluid, 2) Disordered radiation, 3) Dust fluid, and 4) Dark energy. We used the relationship between metric potential to solve field equations. By using equation of state, we observed the pressure and density profiles in various models. We also went over some cosmological and dynamical parameters in depth. Also, we discovered both negative and positive deceleration parameters in different time intervals, indicating the Universe’s transition phase.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"20 1","pages":"115 - 136"},"PeriodicalIF":0.9,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42548137","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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