Abstract In this study an interesting symmetric linear system is considered. As a first step we obtain the Lagrangian of the system. Secondly, we derive the classical Euler- Lagrange equations of the system. Finally, numerical and analytic solution for these equations have been presented for some chosen initial conditions.
{"title":"Numerical aspects of two coupled harmonic oscillators","authors":"J. Asad, O. Florea","doi":"10.2478/auom-2020-0001","DOIUrl":"https://doi.org/10.2478/auom-2020-0001","url":null,"abstract":"Abstract In this study an interesting symmetric linear system is considered. As a first step we obtain the Lagrangian of the system. Secondly, we derive the classical Euler- Lagrange equations of the system. Finally, numerical and analytic solution for these equations have been presented for some chosen initial conditions.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89121914","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
F. Arabpur, M. Jafarpour, M. Aminizadeh, Š. Hošková-Mayerová
Abstract In this paper, we introduce a geodesic metric space called generalized Cayley graph (gCay(P,S)) on a finitely generated polygroup. We define a hyperaction of polygroup on gCayley graph and give some properties of this hyperaction. We show that gCayley graphs of a polygroup by two different generators are quasi-isometric. Finally, we express a connection between finitely generated polygroups and geodesic metric spaces.
{"title":"On geometric polygroups","authors":"F. Arabpur, M. Jafarpour, M. Aminizadeh, Š. Hošková-Mayerová","doi":"10.2478/auom-2020-0002","DOIUrl":"https://doi.org/10.2478/auom-2020-0002","url":null,"abstract":"Abstract In this paper, we introduce a geodesic metric space called generalized Cayley graph (gCay(P,S)) on a finitely generated polygroup. We define a hyperaction of polygroup on gCayley graph and give some properties of this hyperaction. We show that gCayley graphs of a polygroup by two different generators are quasi-isometric. Finally, we express a connection between finitely generated polygroups and geodesic metric spaces.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74607079","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We consider some lacunary power series with rational coefficients in p. We show that under certain conditions these series take transcendental values at non-zero rational number arguments, and we determine the classes of these transcendental values with respect to Mahler’s classification of p-adic numbers.
{"title":"On Mahler’s p-adic S-, T -, and U-numbers","authors":"Y. Bugeaud, Gülcan Kekeç","doi":"10.2478/auom-2020-0005","DOIUrl":"https://doi.org/10.2478/auom-2020-0005","url":null,"abstract":"Abstract We consider some lacunary power series with rational coefficients in p. We show that under certain conditions these series take transcendental values at non-zero rational number arguments, and we determine the classes of these transcendental values with respect to Mahler’s classification of p-adic numbers.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86699005","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We introduce the warped product of two holomorphic Finsler algebroids and we define a complex Finsler function on it. We study the Chern-Finsler connections of the bundles and of their product and we investigate their curvatures. We use the geometrical setting of the prolongations of the two bundles to obtain some similar and some different properties from the ones of the warped product of Finsler manifolds.
{"title":"The warped product of holomorphic Lie algebroids","authors":"A. Ionescu, G. Munteanu","doi":"10.2478/auom-2020-0009","DOIUrl":"https://doi.org/10.2478/auom-2020-0009","url":null,"abstract":"Abstract We introduce the warped product of two holomorphic Finsler algebroids and we define a complex Finsler function on it. We study the Chern-Finsler connections of the bundles and of their product and we investigate their curvatures. We use the geometrical setting of the prolongations of the two bundles to obtain some similar and some different properties from the ones of the warped product of Finsler manifolds.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84734860","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The resolution of the acceleration vector of a particle moving along a space curve is well known thanks to Siacci [1]. This resolution comprises two special oblique components which lie in the osculating plane of the curve. The jerk is the time derivative of acceleration vector. For the jerk vector of the aforementioned particle, a similar resolution is presented as a new contribution to field [2]. It comprises three special oblique components which lie in the osculating and rectifying planes. In this paper, we have studied the Siacci’s resolution of the acceleration vector and aforementioned resolution of the jerk vector for the space curves which are equipped with the modified orthogonal frame. Moreover, we have given some illustrative examples to show how the our theorems work.
{"title":"A Note on the Acceleration and Jerk in Motion Along a Space Curve","authors":"Kahraman Esen Özen, M. Güner, M. Tosun","doi":"10.2478/auom-2020-0011","DOIUrl":"https://doi.org/10.2478/auom-2020-0011","url":null,"abstract":"Abstract The resolution of the acceleration vector of a particle moving along a space curve is well known thanks to Siacci [1]. This resolution comprises two special oblique components which lie in the osculating plane of the curve. The jerk is the time derivative of acceleration vector. For the jerk vector of the aforementioned particle, a similar resolution is presented as a new contribution to field [2]. It comprises three special oblique components which lie in the osculating and rectifying planes. In this paper, we have studied the Siacci’s resolution of the acceleration vector and aforementioned resolution of the jerk vector for the space curves which are equipped with the modified orthogonal frame. Moreover, we have given some illustrative examples to show how the our theorems work.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76264180","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The α* -relation is a fundamental relation on hyperrings, being the smallest strongly regular relation on hyperrings such that the quotient structure R/α* is a commutative ring. In this paper we introduce on hyperrings the relation ζm, which is smaller than α*, and show that, on a particular class of m-idempotent hyperrings R, it is the smallest strongly regular relation such that the quotient ring R/ζ*m is commutative. Some properties of this new relation and its differences from the α* -relation are illustrated and discussed. Finally, we show that ζm is a new representation for α* on this particular class of m-idempotent hyperrings.
{"title":"The commutative quotient structure of m-idempotent hyperrings","authors":"A. Zadeh, M. Norouzi, I. Cristea","doi":"10.2478/auom-2020-0015","DOIUrl":"https://doi.org/10.2478/auom-2020-0015","url":null,"abstract":"Abstract The α* -relation is a fundamental relation on hyperrings, being the smallest strongly regular relation on hyperrings such that the quotient structure R/α* is a commutative ring. In this paper we introduce on hyperrings the relation ζm, which is smaller than α*, and show that, on a particular class of m-idempotent hyperrings R, it is the smallest strongly regular relation such that the quotient ring R/ζ*m is commutative. Some properties of this new relation and its differences from the α* -relation are illustrated and discussed. Finally, we show that ζm is a new representation for α* on this particular class of m-idempotent hyperrings.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84037725","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract A set S ⊆ V is a dominating set in G if for every u ∈ V S, there exists v ∈ S such that (u, v) ∈ E, i.e., N[S] = V . A dominating set S is an isolate dominating set (IDS) if the induced subgraph G[S] has at least one isolated vertex. It is known that Isolate Domination Decision problem (IDOM) is NP-complete for bipartite graphs. In this paper, we extend this by showing that the IDOM is NP-complete for split graphs and perfect elimination bipartite graphs, a subclass of bipartite graphs. A set S ⊆ V is an independent set if G[S] has no edge. A set S ⊆ V is a secure dominating set of G if, for each vertex u ∈ V S, there exists a vertex v ∈ S such that (u, v) ∈ E and (S {v}) ∪ {u} is a dominating set of G. In addition, we initiate the study of a new domination parameter called, independent secure domination. A set S ⊆ V is an independent secure dominating set (InSDS) if S is an independent set and a secure dominating set of G. The minimum size of an InSDS in G is called the independent secure domination number of G and is denoted by γis(G). Given a graph G and a positive integer k, the InSDM problem is to check whether G has an independent secure dominating set of size at most k. We prove that InSDM is NP-complete for bipartite graphs and linear time solvable for bounded tree-width graphs and threshold graphs, a subclass of split graphs. The MInSDS problem is to find an independent secure dominating set of minimum size, in the input graph. Finally, we show that the MInSDS problem is APX-hard for graphs with maximum degree 5.
{"title":"Algorithmic Aspects of Some Variants of Domination in Graphs","authors":"J. P. Kumar, P. V. S. Reddy","doi":"10.2478/auom-2020-0039","DOIUrl":"https://doi.org/10.2478/auom-2020-0039","url":null,"abstract":"Abstract A set S ⊆ V is a dominating set in G if for every u ∈ V S, there exists v ∈ S such that (u, v) ∈ E, i.e., N[S] = V . A dominating set S is an isolate dominating set (IDS) if the induced subgraph G[S] has at least one isolated vertex. It is known that Isolate Domination Decision problem (IDOM) is NP-complete for bipartite graphs. In this paper, we extend this by showing that the IDOM is NP-complete for split graphs and perfect elimination bipartite graphs, a subclass of bipartite graphs. A set S ⊆ V is an independent set if G[S] has no edge. A set S ⊆ V is a secure dominating set of G if, for each vertex u ∈ V S, there exists a vertex v ∈ S such that (u, v) ∈ E and (S {v}) ∪ {u} is a dominating set of G. In addition, we initiate the study of a new domination parameter called, independent secure domination. A set S ⊆ V is an independent secure dominating set (InSDS) if S is an independent set and a secure dominating set of G. The minimum size of an InSDS in G is called the independent secure domination number of G and is denoted by γis(G). Given a graph G and a positive integer k, the InSDM problem is to check whether G has an independent secure dominating set of size at most k. We prove that InSDM is NP-complete for bipartite graphs and linear time solvable for bounded tree-width graphs and threshold graphs, a subclass of split graphs. The MInSDS problem is to find an independent secure dominating set of minimum size, in the input graph. Finally, we show that the MInSDS problem is APX-hard for graphs with maximum degree 5.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79658073","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Here we have studied f-biharmonic and bi-f-harmonic submanifolds of generalized (k, µ)-space-forms and obtained a necessary and sufficient condition on a submanifold of generalized (k, µ)-space-form to be f-biharmonic and bi-f-harmonic submanifold. We have also studied f-biharmonic hypersurfaces of said ambient space forms.
{"title":"f-biharmonic and bi-f-harmonic submanifolds of generalized (k, µ)-space-forms","authors":"S. Hui, D. Breaz, Pradip Mandal","doi":"10.2478/auom-2019-0036","DOIUrl":"https://doi.org/10.2478/auom-2019-0036","url":null,"abstract":"Abstract Here we have studied f-biharmonic and bi-f-harmonic submanifolds of generalized (k, µ)-space-forms and obtained a necessary and sufficient condition on a submanifold of generalized (k, µ)-space-form to be f-biharmonic and bi-f-harmonic submanifold. We have also studied f-biharmonic hypersurfaces of said ambient space forms.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74113655","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The aim of this work is to tackle the three–dimensional (3D) Heston– Cox–Ingersoll–Ross (HCIR) time–dependent partial differential equation (PDE) computationally by employing a non–uniform discretization and gathering the finite difference (FD) weighting coe cients into differentiation matrices. In fact, a non–uniform discretization of the 3D computational domain is employed to achieve the second–order of accuracy for all the spatial variables. It is contributed that under what conditions the proposed procedure is stable. This stability bound is novel in literature for solving this model. Several financial experiments are worked out along with computation of the hedging quantities Delta and Gamma.
{"title":"On an improved computational solution for the 3D HCIR PDE in finance","authors":"F. Soleymani, A. Akgül, E. Akgül","doi":"10.2478/auom-2019-0042","DOIUrl":"https://doi.org/10.2478/auom-2019-0042","url":null,"abstract":"Abstract The aim of this work is to tackle the three–dimensional (3D) Heston– Cox–Ingersoll–Ross (HCIR) time–dependent partial differential equation (PDE) computationally by employing a non–uniform discretization and gathering the finite difference (FD) weighting coe cients into differentiation matrices. In fact, a non–uniform discretization of the 3D computational domain is employed to achieve the second–order of accuracy for all the spatial variables. It is contributed that under what conditions the proposed procedure is stable. This stability bound is novel in literature for solving this model. Several financial experiments are worked out along with computation of the hedging quantities Delta and Gamma.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86964937","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this paper, we introduce the notion of interpolative Rus-Reich-Ćirić type 𝒵- contractions in the setting of complete metric space. We also consider some immediate consequences of our main results.
{"title":"Interpolative Rus-Reich-Ćirić Type Contractions via Simulation Functions","authors":"E. Karapınar, R. Agarwal","doi":"10.2478/auom-2019-0038","DOIUrl":"https://doi.org/10.2478/auom-2019-0038","url":null,"abstract":"Abstract In this paper, we introduce the notion of interpolative Rus-Reich-Ćirić type 𝒵- contractions in the setting of complete metric space. We also consider some immediate consequences of our main results.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78815798","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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