Pub Date : 2022-01-02DOI: 10.1080/1726037X.2022.2079264
A. Mabrouk, Z. Douzi, B. Selmi
Abstract In this paper, a generalized fractal dimension is introduced based on a combination of the topological dimension, conformal dimension, and the ϕ-conformal dimension. Lower and upper bound estimates of the new variant of dimension are provided for the case of the Sierpinski carpet fractal set. Moreover, the equality of such bounds is proved for a large class of the basic measure ϕ.
{"title":"The ϕ-Topological Conformal Dimension for the Sierpinski Carpet","authors":"A. Mabrouk, Z. Douzi, B. Selmi","doi":"10.1080/1726037X.2022.2079264","DOIUrl":"https://doi.org/10.1080/1726037X.2022.2079264","url":null,"abstract":"Abstract In this paper, a generalized fractal dimension is introduced based on a combination of the topological dimension, conformal dimension, and the ϕ-conformal dimension. Lower and upper bound estimates of the new variant of dimension are provided for the case of the Sierpinski carpet fractal set. Moreover, the equality of such bounds is proved for a large class of the basic measure ϕ.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"20 1","pages":"33 - 53"},"PeriodicalIF":0.9,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47420978","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.2022.2079267
Praveen Kumar, G. S. Khadekar, V. Dagwal
Abstract Two fluids cosmological models with matter and radiating source in (2 + 1)−dimensional Saez-Ballester scalar-tensor theory of gravitation are investigated. In the two-fluid model, one fluid represent the CMB radiation and another fluid represent the matter content of the universe. To get determinate solution of the field equations we have consider the relation between pressure and energy density of the matter field through the gamma law equation of state pm = (γ − 1)ρm . Some physical and geometric behaviour of the models are also discussed with the uses of mathematical software.
{"title":"Two Fluids Cosmological Model in (2+1)-Dimensional Saez-Ballester Scalar-Tensor Theory of Gravitation","authors":"Praveen Kumar, G. S. Khadekar, V. Dagwal","doi":"10.1080/1726037X.2022.2079267","DOIUrl":"https://doi.org/10.1080/1726037X.2022.2079267","url":null,"abstract":"Abstract Two fluids cosmological models with matter and radiating source in (2 + 1)−dimensional Saez-Ballester scalar-tensor theory of gravitation are investigated. In the two-fluid model, one fluid represent the CMB radiation and another fluid represent the matter content of the universe. To get determinate solution of the field equations we have consider the relation between pressure and energy density of the matter field through the gamma law equation of state pm = (γ − 1)ρm . Some physical and geometric behaviour of the models are also discussed with the uses of mathematical software.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"20 1","pages":"91 - 114"},"PeriodicalIF":0.9,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42172958","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.2022.2063407
B. Senoussi
Abstract In this paper, we study triharmonic curves in Heisenberg group . We give necessary and sufficient conditions for helices to be triharmonic. We characterize the triharmonic curves in terms of their curvature and torsion.
{"title":"Triharmonic Curves in Heisenberg Group","authors":"B. Senoussi","doi":"10.1080/1726037X.2022.2063407","DOIUrl":"https://doi.org/10.1080/1726037X.2022.2063407","url":null,"abstract":"Abstract In this paper, we study triharmonic curves in Heisenberg group . We give necessary and sufficient conditions for helices to be triharmonic. We characterize the triharmonic curves in terms of their curvature and torsion.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"20 1","pages":"55 - 65"},"PeriodicalIF":0.9,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44182936","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 : 2021-07-03DOI: 10.1080/1726037X.2021.2011113
Ç. Camcı, A. Uçum, K. Ilarslan
Abstract In this paper, the curves associated with the Combescure transform are discussed. With the help of the fact that these curves have a common Frenet frame, an equivalence relation is defined. The equivalence classes obtained by this equivalence relation have been examined for some special curves and it has been obtained that all curves in the equivalence class of a helix curve are also helix curves. This is also true for k-slant helix curves. The important part of this paper consists of the useful construction method to obtain a curve from the given curve α with the help of Combescure transformation. With this method, some special curves such as Bertrand, Mannheim, Salkowski, anti-Salkowski or spherical curve can be obtained from any curve related by a Combescure transform. For example, we obtain an example of Mannheim curves explicitly obtained from an anti-Salkowski curve. It is not easy to find an example of Mannheim curves except circular helix in the literature. In general, the condition for being Bertrand anti-Salkowski or spherical curve of the curve β obtained from the given curve α with the help of Combescure transformation were obtained.
{"title":"Space Curves Related by a Transformation of Combescure","authors":"Ç. Camcı, A. Uçum, K. Ilarslan","doi":"10.1080/1726037X.2021.2011113","DOIUrl":"https://doi.org/10.1080/1726037X.2021.2011113","url":null,"abstract":"Abstract In this paper, the curves associated with the Combescure transform are discussed. With the help of the fact that these curves have a common Frenet frame, an equivalence relation is defined. The equivalence classes obtained by this equivalence relation have been examined for some special curves and it has been obtained that all curves in the equivalence class of a helix curve are also helix curves. This is also true for k-slant helix curves. The important part of this paper consists of the useful construction method to obtain a curve from the given curve α with the help of Combescure transformation. With this method, some special curves such as Bertrand, Mannheim, Salkowski, anti-Salkowski or spherical curve can be obtained from any curve related by a Combescure transform. For example, we obtain an example of Mannheim curves explicitly obtained from an anti-Salkowski curve. It is not easy to find an example of Mannheim curves except circular helix in the literature. In general, the condition for being Bertrand anti-Salkowski or spherical curve of the curve β obtained from the given curve α with the help of Combescure transformation were obtained.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"19 1","pages":"271 - 287"},"PeriodicalIF":0.9,"publicationDate":"2021-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48571850","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 : 2021-07-03DOI: 10.1080/1726037X.2021.2009200
M. Karami
Abstract In this paper, we study the order creators for integral and by putting new conditions on them we prove the observational form of monotone convergence theorem.
摘要本文研究了积分的阶创造者，并通过对它们提出新的条件，证明了单调收敛定理的观测形式。
{"title":"Observational form of Monotone Convergence Theorem","authors":"M. Karami","doi":"10.1080/1726037X.2021.2009200","DOIUrl":"https://doi.org/10.1080/1726037X.2021.2009200","url":null,"abstract":"Abstract In this paper, we study the order creators for integral and by putting new conditions on them we prove the observational form of monotone convergence theorem.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"19 1","pages":"203 - 215"},"PeriodicalIF":0.9,"publicationDate":"2021-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48094018","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 : 2021-07-03DOI: 10.1080/1726037X.2021.2009199
Fatemeh Rezaei, M. F. Nia
Abstract In this article, we consider an iterated functions system (IFS) whose functions are homeomorphisms on an annulus. We define rotational spanning and separating sets for the IFS and then provide two definitions for the rotational entropy of the IFS. We show that in the IFSs, the rotational entropy is a topological invariant. We prove that the rotational entropy of an annular IFS is equal to the rotational entropy on its non-wandering set for sequences of functions with a specific condition.
{"title":"Rotational Entropy of an Annular Iterated Functions System","authors":"Fatemeh Rezaei, M. F. Nia","doi":"10.1080/1726037X.2021.2009199","DOIUrl":"https://doi.org/10.1080/1726037X.2021.2009199","url":null,"abstract":"Abstract In this article, we consider an iterated functions system (IFS) whose functions are homeomorphisms on an annulus. We define rotational spanning and separating sets for the IFS and then provide two definitions for the rotational entropy of the IFS. We show that in the IFSs, the rotational entropy is a topological invariant. We prove that the rotational entropy of an annular IFS is equal to the rotational entropy on its non-wandering set for sequences of functions with a specific condition.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"19 1","pages":"189 - 202"},"PeriodicalIF":0.9,"publicationDate":"2021-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46171343","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 : 2021-07-03DOI: 10.1080/1726037X.2021.2020422
Mohabbat Ali, Mohd Vasiulla
Abstract The object of the present paper is to study almost pseudo Ricci symmetric manifold admitting Schouten tensor and investigated some geometric properties of this manifold.
摘要本文研究了含有Schouten张量的几乎伪Ricci对称流形，并研究了该流形的一些几何性质。
{"title":"Almost Pseudo Ricci Symmetric Manifold Admitting Schouten Tensor","authors":"Mohabbat Ali, Mohd Vasiulla","doi":"10.1080/1726037X.2021.2020422","DOIUrl":"https://doi.org/10.1080/1726037X.2021.2020422","url":null,"abstract":"Abstract The object of the present paper is to study almost pseudo Ricci symmetric manifold admitting Schouten tensor and investigated some geometric properties of this manifold.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"19 1","pages":"217 - 225"},"PeriodicalIF":0.9,"publicationDate":"2021-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45155586","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.2021.1978195
Shoma S. Sen, G. S. Khadekar, Shilpa W. Samdurkar
Abstract In the present study, the solutions are obtained for Bianchi type III cosmological models with modified Takabayasi string of the form ρ = (1 + ω) λ + Λ in the presence of bulk viscous fluid. To obtain the realistic model we assume the relation between metric potential i. e B = C n . We studied the role of Λ term in the evolution of universe. Here, we investigated two different cases for the cosmological model i. e case i) ω → ∞ and case ii) ω —> 0. In both the cases, we found the physical significance of the cosmological term Λ in quadratic form i. e Λ = Λ0 + Λ1 H + Λ2 H 2. All the physical and geometrical aspects of the model for both the cases are discussed for the corresponding solutions. It is observed that the resultant models follows the present day observations and literature favour the accelerating model of the universe. Also, we have plotted the graphs for detailed study of each case.
{"title":"Bulk Viscous Bianchi Type-III Cosmological Model with Modified Takabayasi String in the Presence of Varying Λ","authors":"Shoma S. Sen, G. S. Khadekar, Shilpa W. Samdurkar","doi":"10.1080/1726037X.2021.1978195","DOIUrl":"https://doi.org/10.1080/1726037X.2021.1978195","url":null,"abstract":"Abstract In the present study, the solutions are obtained for Bianchi type III cosmological models with modified Takabayasi string of the form ρ = (1 + ω) λ + Λ in the presence of bulk viscous fluid. To obtain the realistic model we assume the relation between metric potential i. e B = C n . We studied the role of Λ term in the evolution of universe. Here, we investigated two different cases for the cosmological model i. e case i) ω → ∞ and case ii) ω —> 0. In both the cases, we found the physical significance of the cosmological term Λ in quadratic form i. e Λ = Λ0 + Λ1 H + Λ2 H 2. All the physical and geometrical aspects of the model for both the cases are discussed for the corresponding solutions. It is observed that the resultant models follows the present day observations and literature favour the accelerating model of the universe. Also, we have plotted the graphs for detailed study of each case.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"19 1","pages":"95 - 112"},"PeriodicalIF":0.9,"publicationDate":"2021-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45670228","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.2021.1909219
R. M. Patne, G. R. Avachar
Abstract Let G = (V (G), E(G)) be a finite graph with n vertices, where V (G) = {v i, … , v n} denote vertex set of G and E(G) denote an edge set G. In this paper, we have introduced the graph G p , q for G. The motivation for introducing the graph G p , q are as follows: Many mathematicians studied the properties of graph G by using boundary operator and co-boundary operator which consider only the relation between vertices and an edges of a graph G. There is no place for complete subgraph (whose vertices greater than 2) of a graph G in boundary operator and co-boundary operator of G. Hence to study the relation between complete subgraph of G and also to study the properties of G, we have introduced an edge-boundary operator and an edge-co-boundary operator on G p,q .
{"title":"On Numerical Invariant of Graph","authors":"R. M. Patne, G. R. Avachar","doi":"10.1080/1726037X.2021.1909219","DOIUrl":"https://doi.org/10.1080/1726037X.2021.1909219","url":null,"abstract":"Abstract Let G = (V (G), E(G)) be a finite graph with n vertices, where V (G) = {v i, … , v n} denote vertex set of G and E(G) denote an edge set G. In this paper, we have introduced the graph G p , q for G. The motivation for introducing the graph G p , q are as follows: Many mathematicians studied the properties of graph G by using boundary operator and co-boundary operator which consider only the relation between vertices and an edges of a graph G. There is no place for complete subgraph (whose vertices greater than 2) of a graph G in boundary operator and co-boundary operator of G. Hence to study the relation between complete subgraph of G and also to study the properties of G, we have introduced an edge-boundary operator and an edge-co-boundary operator on G p,q .","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"19 1","pages":"57 - 75"},"PeriodicalIF":0.9,"publicationDate":"2021-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41372253","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.2021.1965705
S. Islam, P. Kumar
Abstract We present the interior solutions of distributions of charged fluid inside a sphere in f (R, T) gravity and which admits the existence of conformal Killing vectors. The charged sphere is embedded in an exterior RN metric. We assume that all physical quantities axe in static equilibrium. The perfect fluid matter is studied under a particular form of the Lagrangian density f (R, T), and smooth matching conditions with the exterior RN metric are applied. The energy conditions as well as the stability of the solutions are also investigated. Emission from the surface of such a star is shown to blueshifted, rather than redshifted, and we calculate its value. Furthermore, the fluid body under f (R, T) gravity is shown to be non-geodesic in nature.
{"title":"Gravitational Model of Compact Spherical Reissner-Nordström-Type Star Under f(R, T) Gravity","authors":"S. Islam, P. Kumar","doi":"10.1080/1726037X.2021.1965705","DOIUrl":"https://doi.org/10.1080/1726037X.2021.1965705","url":null,"abstract":"Abstract We present the interior solutions of distributions of charged fluid inside a sphere in f (R, T) gravity and which admits the existence of conformal Killing vectors. The charged sphere is embedded in an exterior RN metric. We assume that all physical quantities axe in static equilibrium. The perfect fluid matter is studied under a particular form of the Lagrangian density f (R, T), and smooth matching conditions with the exterior RN metric are applied. The energy conditions as well as the stability of the solutions are also investigated. Emission from the surface of such a star is shown to blueshifted, rather than redshifted, and we calculate its value. Furthermore, the fluid body under f (R, T) gravity is shown to be non-geodesic in nature.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"19 1","pages":"135 - 154"},"PeriodicalIF":0.9,"publicationDate":"2021-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49314858","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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