Pub Date : 2021-01-02DOI: 10.1080/1726037X.2021.1909216
Kiattiyot Juagwon, W. Sripanya
Abstract In this work, we study the depth of a buried current electrode that constitutes an effect on the electric potential in a transition multilayer earth. A three-layered earth model is applied to simulate the data of electric potential. The model assumes that an overburden with the thickness has a constant conductivity over the layers of material having the feather of specific conductivity. The model is composed of a set of partial differential equations defined on the spatial domain. The Hankel transform is applied to derive equations defined on the wave number domain from the original problem. On the wave number domain, the analytic solution is determined by solving a boundary value problem. The achieved equations are then transformed back to get the equations defined on the spatial domain. The results of electric potential generated by the three-layered earth model are plotted and compared to indicate the behavior in response to different positions of current source while the parameters in the model are approximately assigned.
{"title":"Mathematical Modelling of Buried Electrode Resistivity Response from a Three-Layered Conductive Medium Containing Transitional Layers","authors":"Kiattiyot Juagwon, W. Sripanya","doi":"10.1080/1726037X.2021.1909216","DOIUrl":"https://doi.org/10.1080/1726037X.2021.1909216","url":null,"abstract":"Abstract In this work, we study the depth of a buried current electrode that constitutes an effect on the electric potential in a transition multilayer earth. A three-layered earth model is applied to simulate the data of electric potential. The model assumes that an overburden with the thickness has a constant conductivity over the layers of material having the feather of specific conductivity. The model is composed of a set of partial differential equations defined on the spatial domain. The Hankel transform is applied to derive equations defined on the wave number domain from the original problem. On the wave number domain, the analytic solution is determined by solving a boundary value problem. The achieved equations are then transformed back to get the equations defined on the spatial domain. The results of electric potential generated by the three-layered earth model are plotted and compared to indicate the behavior in response to different positions of current source while the parameters in the model are approximately assigned.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"19 1","pages":"1 - 12"},"PeriodicalIF":0.9,"publicationDate":"2021-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42075528","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 : 2021-01-02DOI: 10.1080/1726037X.2021.1909217
G. R. Avchar, D.R. Golechha, S. D. Tade
Abstract In this paper, axially symmetric space-time in presence of perfect fluid with viscosity has been considered and studied within the framework of F(R, T) theory of gravity proposed by (Harko et al. [14]). The solutions of the field equations axe evaluated by assuming the proportionality of expansion (θ) to the shear scalar (σ). The physical and kinematical aspects of the model have also been discussed.
{"title":"Axially Symmetric Bulk Viscous Cosmological Model in F(R, T) Theory of Gravity","authors":"G. R. Avchar, D.R. Golechha, S. D. Tade","doi":"10.1080/1726037X.2021.1909217","DOIUrl":"https://doi.org/10.1080/1726037X.2021.1909217","url":null,"abstract":"Abstract In this paper, axially symmetric space-time in presence of perfect fluid with viscosity has been considered and studied within the framework of F(R, T) theory of gravity proposed by (Harko et al. [14]). The solutions of the field equations axe evaluated by assuming the proportionality of expansion (θ) to the shear scalar (σ). The physical and kinematical aspects of the model have also been discussed.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"19 1","pages":"35 - 49"},"PeriodicalIF":0.9,"publicationDate":"2021-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49545130","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 : 2021-01-02DOI: 10.1080/1726037X.2020.1860457
K. Boukerrioua, Amira Ayari
Abstract The main objective in this paper is to investigate some Pachpatte- Gamidov-type inequalities in two independent variables. The obtained inequalities can be used as handy tools to study the properties of certain differential and integral equations.
{"title":"Further Refinements of Certain Pachpatte-Gamidov-Type Inequalities in Two Independent Variables and their Applications","authors":"K. Boukerrioua, Amira Ayari","doi":"10.1080/1726037X.2020.1860457","DOIUrl":"https://doi.org/10.1080/1726037X.2020.1860457","url":null,"abstract":"Abstract The main objective in this paper is to investigate some Pachpatte- Gamidov-type inequalities in two independent variables. The obtained inequalities can be used as handy tools to study the properties of certain differential and integral equations.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"19 1","pages":"13 - 24"},"PeriodicalIF":0.9,"publicationDate":"2021-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47204959","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 : 2021-01-02DOI: 10.1080/1726037X.2021.1909218
Sanjay M. Deshpande, R. Agrawal
Abstract In Vedic mathematics, digital root of a number is known as Beejank. Before the development of computer devices, the idea was used to check the results of mathematical operations. In this paper, we highlight the properties of digital root of a number and some results of digital roots. There are many interesting properties of digital root of a number. Perfect square number and a perfect cube number have specific digital roots. In modern mathematics, digital roots make partition of the set of natural numbers. Nowadays digital root of a number has many applications in generation of random sequence of numbers.
{"title":"Role of Digital Root in Number Theory","authors":"Sanjay M. Deshpande, R. Agrawal","doi":"10.1080/1726037X.2021.1909218","DOIUrl":"https://doi.org/10.1080/1726037X.2021.1909218","url":null,"abstract":"Abstract In Vedic mathematics, digital root of a number is known as Beejank. Before the development of computer devices, the idea was used to check the results of mathematical operations. In this paper, we highlight the properties of digital root of a number and some results of digital roots. There are many interesting properties of digital root of a number. Perfect square number and a perfect cube number have specific digital roots. In modern mathematics, digital roots make partition of the set of natural numbers. Nowadays digital root of a number has many applications in generation of random sequence of numbers.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"19 1","pages":"51 - 56"},"PeriodicalIF":0.9,"publicationDate":"2021-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45821604","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 : 2021-01-02DOI: 10.1080/1726037X.2021.1966946
Wagdi F. S. Ahmed, D. D. Pawar, Ahmad Y. A. Salamooni
Abstract In this article, we have investigate a solution of fractional Kinetic equation involving Katugampola type fractional integral by using H – function. We also present the solution of Kinetic equation involving Katugampola type fractional integral with the help of generalized I – function and Mellin transform.
{"title":"On the Solution of Kinetic Equation for Katugampola Type Fractional Differential Equations","authors":"Wagdi F. S. Ahmed, D. D. Pawar, Ahmad Y. A. Salamooni","doi":"10.1080/1726037X.2021.1966946","DOIUrl":"https://doi.org/10.1080/1726037X.2021.1966946","url":null,"abstract":"Abstract In this article, we have investigate a solution of fractional Kinetic equation involving Katugampola type fractional integral by using H – function. We also present the solution of Kinetic equation involving Katugampola type fractional integral with the help of generalized I – function and Mellin transform.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"19 1","pages":"125 - 134"},"PeriodicalIF":0.9,"publicationDate":"2021-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42118805","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 : 2021-01-02DOI: 10.1080/1726037X.2021.1911390
A. S. Nimkar, J. S. Wath, V. M. Wankhade
Abstract In this paper, we study macroscopic body cosmological model in the context of self-creation theory. We solve field equations by using relation between metric coefficients and equation of state for macroscopic body. Also, we discuss the features of the obtained solutions.
{"title":"Bianchi Type-IX Cosmological Model in Self-Creation Theory of Gravitation","authors":"A. S. Nimkar, J. S. Wath, V. M. Wankhade","doi":"10.1080/1726037X.2021.1911390","DOIUrl":"https://doi.org/10.1080/1726037X.2021.1911390","url":null,"abstract":"Abstract In this paper, we study macroscopic body cosmological model in the context of self-creation theory. We solve field equations by using relation between metric coefficients and equation of state for macroscopic body. Also, we discuss the features of the obtained solutions.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"19 1","pages":"25 - 34"},"PeriodicalIF":0.9,"publicationDate":"2021-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41994428","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 : 2021-01-02DOI: 10.1080/1726037X.2021.1945724
Seema Raut, S. Janardhan, G. Khekare
Abstract Epidemics of vector borne disease studied in this paper when disease incidence rate is non- monotone. Non monotonic behaviors of infected hosts as well as infected vectors are studied for influence of increase in disease on susceptible host population and effect of repellents and insecticides on vectors, respectively. Suitable Liapunov functions are constructed to discuss the global asymptotic stabilities at the equilibrium points. Results are verified by conducting numerical simulation. Mechanism of disease spread by vectors and hosts during the epidemic can be better understood with the help of this model.
{"title":"Dynamical Study of a Vector Host Epidemic Model With Non-Monotone Incidence","authors":"Seema Raut, S. Janardhan, G. Khekare","doi":"10.1080/1726037X.2021.1945724","DOIUrl":"https://doi.org/10.1080/1726037X.2021.1945724","url":null,"abstract":"Abstract Epidemics of vector borne disease studied in this paper when disease incidence rate is non- monotone. Non monotonic behaviors of infected hosts as well as infected vectors are studied for influence of increase in disease on susceptible host population and effect of repellents and insecticides on vectors, respectively. Suitable Liapunov functions are constructed to discuss the global asymptotic stabilities at the equilibrium points. Results are verified by conducting numerical simulation. Mechanism of disease spread by vectors and hosts during the epidemic can be better understood with the help of this model.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"19 1","pages":"77 - 94"},"PeriodicalIF":0.9,"publicationDate":"2021-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42035413","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 : 2021-01-02DOI: 10.1080/1726037X.2021.1966945
E. Siva Prasad, K. Phaneendra
Abstract We use non-polynomial spline with variable mesh to establish a numerical scheme for the solution of boundary value problem with singularity. The discrete equation of the problem is developed based on the condition of the class C 1 of non-polynomial spline at the inner nodes and it is not valid for singularity. At singularity t = 0, the problem is modified in order to have a three term relationship. The method’s tridiagonal scheme is analyzed using the well-known discrete imbedding invariant algorithm. We discuss the error analysis of the scheme and two examples with layer at one end of the boundary are consider to demonstrate the practical utility of the scheme. Maximum absolute errors are present in tabular form to show the efficiency of the proposed method.
{"title":"Solution of Singularly Perturbed Boundary Value Problems with Singularity Using Variable Mesh Finite Difference Method","authors":"E. Siva Prasad, K. Phaneendra","doi":"10.1080/1726037X.2021.1966945","DOIUrl":"https://doi.org/10.1080/1726037X.2021.1966945","url":null,"abstract":"Abstract We use non-polynomial spline with variable mesh to establish a numerical scheme for the solution of boundary value problem with singularity. The discrete equation of the problem is developed based on the condition of the class C 1 of non-polynomial spline at the inner nodes and it is not valid for singularity. At singularity t = 0, the problem is modified in order to have a three term relationship. The method’s tridiagonal scheme is analyzed using the well-known discrete imbedding invariant algorithm. We discuss the error analysis of the scheme and two examples with layer at one end of the boundary are consider to demonstrate the practical utility of the scheme. Maximum absolute errors are present in tabular form to show the efficiency of the proposed method.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"19 1","pages":"113 - 124"},"PeriodicalIF":0.9,"publicationDate":"2021-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49581336","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 : 2020-07-02DOI: 10.1080/1726037X.2020.1856339
S. Dey, Soumendu Roy
Abstract In this paper we study ∗-η-Ricci soliton on Sasakian manifolds. Here, we have discussed some curvature properties on Sasakian manifold admitting ∗-η-Ricci soliton. We have obtained some significant results on ∗-η-Ricci soliton in Sasakian manifolds satisfying R(ξ, X) · S = 0, S(ξ, X) · R = 0, P̄ (ξ, X) · S = 0, where P̄ is Pseudo-projective curvature tensor.The conditions for ∗-η-Ricci soliton on ϕ-conharmonically flat and ϕ-projectively flat Sasakian manifolds have been obtained in this article. Lastly, we have given an example of 5-dimensional Sasakian manifolds satisfying ∗-η-Ricci soliton.
{"title":"∗-η-Ricci Soliton within the Framework of Sasakian Manifold","authors":"S. Dey, Soumendu Roy","doi":"10.1080/1726037X.2020.1856339","DOIUrl":"https://doi.org/10.1080/1726037X.2020.1856339","url":null,"abstract":"Abstract In this paper we study ∗-η-Ricci soliton on Sasakian manifolds. Here, we have discussed some curvature properties on Sasakian manifold admitting ∗-η-Ricci soliton. We have obtained some significant results on ∗-η-Ricci soliton in Sasakian manifolds satisfying R(ξ, X) · S = 0, S(ξ, X) · R = 0, P̄ (ξ, X) · S = 0, where P̄ is Pseudo-projective curvature tensor.The conditions for ∗-η-Ricci soliton on ϕ-conharmonically flat and ϕ-projectively flat Sasakian manifolds have been obtained in this article. Lastly, we have given an example of 5-dimensional Sasakian manifolds satisfying ∗-η-Ricci soliton.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"18 1","pages":"163 - 181"},"PeriodicalIF":0.9,"publicationDate":"2020-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2020.1856339","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43975155","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 : 2020-07-02DOI: 10.1080/1726037X.2020.1847765
Samuel Everett
Abstract We study the dynamics of a geometric piecewise map defined on the set of three pairwise nonparallel, nonconcurrent lines in R2. The geometric map of study may be analogized to the billiard map with a different reflection rule so that each iteration is a contraction over the space, thereby providing asymptotic behavior of interest. Our study puts particular emphasis on the behavior of periodic orbits generated by the map, with description of their geometry and bifurcation behavior. We establish that for any initial point in the space, the orbit will converge to a fixed point or periodic orbit, and we demonstrate that there exists an infinite variety of periodic orbits the orbits may converge to, dependent on the parameters of the underlying space.
{"title":"A Piecewise Contractive Map on Triangles","authors":"Samuel Everett","doi":"10.1080/1726037X.2020.1847765","DOIUrl":"https://doi.org/10.1080/1726037X.2020.1847765","url":null,"abstract":"Abstract We study the dynamics of a geometric piecewise map defined on the set of three pairwise nonparallel, nonconcurrent lines in R2. The geometric map of study may be analogized to the billiard map with a different reflection rule so that each iteration is a contraction over the space, thereby providing asymptotic behavior of interest. Our study puts particular emphasis on the behavior of periodic orbits generated by the map, with description of their geometry and bifurcation behavior. We establish that for any initial point in the space, the orbit will converge to a fixed point or periodic orbit, and we demonstrate that there exists an infinite variety of periodic orbits the orbits may converge to, dependent on the parameters of the underlying space.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"18 1","pages":"183 - 192"},"PeriodicalIF":0.9,"publicationDate":"2020-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2020.1847765","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42134138","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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