"In the paper, we study the oscillation of the half-linear second-order differential equations with deviating argument of the form begin{equation*} left(r(t)(y'(t))^{alpha}right)'=p(t)y^{alpha}(tau(t)). tag{$E$} end{equation*} We introduce new monotonic properties of nonoscillatory solutions and use them to offer new criteria for elimination of certain types of solutions. The presented results essentially improve existing ones even for linear differential equations."
{"title":"\"New asymptotic results for half-linear differential equations with deviating argument\"","authors":"B. Baculíková, J. Džurina","doi":"10.37193/cjm.2022.02.05","DOIUrl":"https://doi.org/10.37193/cjm.2022.02.05","url":null,"abstract":"\"In the paper, we study the oscillation of the half-linear second-order differential equations with deviating argument of the form begin{equation*} left(r(t)(y'(t))^{alpha}right)'=p(t)y^{alpha}(tau(t)). tag{$E$} end{equation*} We introduce new monotonic properties of nonoscillatory solutions and use them to offer new criteria for elimination of certain types of solutions. The presented results essentially improve existing ones even for linear differential equations.\"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47843155","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}
Metallic Riemannian manifolds with null trace and metallic Norden manifolds are generalizations of almost product Riemannian and almost golden Riemannian manifolds with null trace and almost Norden and almost Norden golden manifolds respectively. All these pure metrics geometries can be unified under the notion of α-metallic metric manifold. We classify this kind of manifolds in a consistent way with the well-known classifications of almost product Riemannian manifolds with null trace and almost Norden manifolds. We also characterize all classes of α-metallic metric manifolds by means of the first canonical connection which is a distinguished adapted connection.
{"title":"Classification of pure metallic metric geometries","authors":"F. Etayo, Araceli deFrancisco, Rafael Santamaría","doi":"10.37193/cjm.2022.02.12","DOIUrl":"https://doi.org/10.37193/cjm.2022.02.12","url":null,"abstract":"Metallic Riemannian manifolds with null trace and metallic Norden manifolds are generalizations of almost product Riemannian and almost golden Riemannian manifolds with null trace and almost Norden and almost Norden golden manifolds respectively. All these pure metrics geometries can be unified under the notion of α-metallic metric manifold. We classify this kind of manifolds in a consistent way with the well-known classifications of almost product Riemannian manifolds with null trace and almost Norden manifolds. We also characterize all classes of α-metallic metric manifolds by means of the first canonical connection which is a distinguished adapted connection.","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45337339","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}
"Let $C$ be a nonempty closed and convex subset of a uniformly smooth and uniformly convex real Banach space $E$ with dual space $E^*$. We present a novel hybrid method for finding a common solution of a family of equilibrium problems, a common solution of a family of variational inequality problems and a common element of fixed points of a family of a general class of nonlinear nonexpansive maps. The sequence of this new method is proved to converge strongly to a common element of the families. Our theorem and its applications complement, generalize, and extend various results in literature."
{"title":"A hybrid scheme for fixed points of a countable family of generalized nonexpansive-type maps and finite families of variational inequality and equilibrium problems, with applications","authors":"M. Uba, M. Onyido, C. I. Udeani, P. U. Nwokoro","doi":"10.37193/cjm.2023.01.19","DOIUrl":"https://doi.org/10.37193/cjm.2023.01.19","url":null,"abstract":"\"Let $C$ be a nonempty closed and convex subset of a uniformly smooth and uniformly convex real Banach space $E$ with dual space $E^*$. We present a novel hybrid method for finding a common solution of a family of equilibrium problems, a common solution of a family of variational inequality problems and a common element of fixed points of a family of a general class of nonlinear nonexpansive maps. The sequence of this new method is proved to converge strongly to a common element of the families. Our theorem and its applications complement, generalize, and extend various results in literature.\"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2021-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44319702","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}
In 1963, Peter Hagis, Jr. provided a Hardy-Ramanujan-Rademacher-type convergent series that can be used to compute an isolated value of the partition function $Q(n)$ which counts partitions of $n$ into distinct parts. Computing $Q(n)$ by this method requires arithmetic with very high-precision approximate real numbers and it is complicated. In this paper, we investigate new connections between partitions into distinct parts and overpartitions and obtain a surprising recurrence relation for the number of partitions of $n$ into distinct parts. By particularization of this relation, we derive two different linear recurrence relations for the partition function $Q(n)$. One of them involves the thrice square numbers and the other involves the generalized octagonal numbers. The recurrence relation involving the thrice square numbers provide a simple and fast computation of the value of $Q(n)$. This method uses only (large) integer arithmetic and it is simpler to program. Infinite families of linear inequalities involving partitions into distinct parts and overpartitions are introduced in this context.
{"title":"Distinct partitions and overpartitions","authors":"M. Merca","doi":"10.37193/cjm.2022.01.12","DOIUrl":"https://doi.org/10.37193/cjm.2022.01.12","url":null,"abstract":"In 1963, Peter Hagis, Jr. provided a Hardy-Ramanujan-Rademacher-type convergent series that can be used to compute an isolated value of the partition function $Q(n)$ which counts partitions of $n$ into distinct parts. Computing $Q(n)$ by this method requires arithmetic with very high-precision approximate real numbers and it is complicated. In this paper, we investigate new connections between partitions into distinct parts and overpartitions and obtain a surprising recurrence relation for the number of partitions of $n$ into distinct parts. By particularization of this relation, we derive two different linear recurrence relations for the partition function $Q(n)$. One of them involves the thrice square numbers and the other involves the generalized octagonal numbers. The recurrence relation involving the thrice square numbers provide a simple and fast computation of the value of $Q(n)$. This method uses only (large) integer arithmetic and it is simpler to program. Infinite families of linear inequalities involving partitions into distinct parts and overpartitions are introduced in this context.","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2021-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43576694","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}
Tools that focus on static code analysis for early error detection are of utmost importance in software development, especially since the propagation of errors is strongly related to higher costs in the development process. Formal Concept Analysis is a prominent field of applied mathematics that uses conceptual landscapes to discover and represent maximal clusters of data. Its expressive visualization method makes it suitable for exploratory analyses in different fields. In this paper we present a Formal Concept Analysis framework for static code analysis that can serve as a model for quantitative and qualitative exploration and interpretation of such results.
{"title":"Formal concept analysis model for static code analysis","authors":"S. Motogna, Diana Cristea, Diana Șotropa Molnar","doi":"10.37193/cjm.2022.01.13","DOIUrl":"https://doi.org/10.37193/cjm.2022.01.13","url":null,"abstract":"Tools that focus on static code analysis for early error detection are of utmost importance in software development, especially since the propagation of errors is strongly related to higher costs in the development process. Formal Concept Analysis is a prominent field of applied mathematics that uses conceptual landscapes to discover and represent maximal clusters of data. Its expressive visualization method makes it suitable for exploratory analyses in different fields. In this paper we present a Formal Concept Analysis framework for static code analysis that can serve as a model for quantitative and qualitative exploration and interpretation of such results.","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2021-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48552237","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}
In this paper we prove the Darboux integrability of a cubic differential system with a singular point of a center typer having at least two parallel invariant straight lines.
本文证明了具有至少两条平行不变直线的中心型奇异点的三次微分系统的Darboux可积性。
{"title":"Darboux integrability of a cubic differential system with two parallel invariant straight lines","authors":"D. Cozma","doi":"10.37193/cjm.2022.01.10","DOIUrl":"https://doi.org/10.37193/cjm.2022.01.10","url":null,"abstract":"In this paper we prove the Darboux integrability of a cubic differential system with a singular point of a center typer having at least two parallel invariant straight lines.","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2021-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43155524","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}
Andrei Horvat-Marc, Mariana Cufoian, Adriana Mitre
This paper aims to analyze the existence of fixed points for mappings defined on complete metric spaces satisfying almost contractive conditions and a general contractive inequality of integral type. The existence of a fixed point is ensured by hypotheses formulated in terms of equivalent metric spaces.
{"title":"Some fixed point theorems on equivalent metric spaces","authors":"Andrei Horvat-Marc, Mariana Cufoian, Adriana Mitre","doi":"10.37193/cjm.2022.01.11","DOIUrl":"https://doi.org/10.37193/cjm.2022.01.11","url":null,"abstract":"This paper aims to analyze the existence of fixed points for mappings defined on complete metric spaces satisfying almost contractive conditions and a general contractive inequality of integral type. The existence of a fixed point is ensured by hypotheses formulated in terms of equivalent metric spaces.","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2021-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45928930","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}
This paper includes Voronovskaya type results and convergence in variation for the exponential Bernstein Kantorovich operators. The Voronovskaya type result is accompanied by a relation between the mentioned operators and suitable auxiliary discrete operators. Convergence of the operators with respect to the variation seminorm is obtained in the space of functions with bounded variation. We propose a general framework covering the results provided by previous literature.
{"title":"Generalized Bernstein Kantorovich operators: Voronovskaya type results, convergence in variation","authors":"A. Acu, A. Aral, I. Raşa","doi":"10.37193/cjm.2022.01.01","DOIUrl":"https://doi.org/10.37193/cjm.2022.01.01","url":null,"abstract":"This paper includes Voronovskaya type results and convergence in variation for the exponential Bernstein Kantorovich operators. The Voronovskaya type result is accompanied by a relation between the mentioned operators and suitable auxiliary discrete operators. Convergence of the operators with respect to the variation seminorm is obtained in the space of functions with bounded variation. We propose a general framework covering the results provided by previous literature.","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2021-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46715653","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}
In this paper we give a description of the structure of compact global attractor (Levinson center) for monotone Bohr/Levitan almost periodic dynamical system $x'=f(t,x)$ (*) with the strictly monotone first integral. It is shown that Levinson center of equation (*) consists of the Bohr/Levitan almost periodic (respectively, almost automorphic, recurrent or Poisson stable) solutions. We establish the main results in the framework of general non-autonomous (cocycle) dynamical systems. We also give some applications of theses results to different classes of differential/difference equations.
{"title":"On the structure of the Levinson center for monotone non-autonomous dynamical systems with a first integral","authors":"D. Cheban","doi":"10.37193/cjm.2022.01.07","DOIUrl":"https://doi.org/10.37193/cjm.2022.01.07","url":null,"abstract":"In this paper we give a description of the structure of compact global attractor (Levinson center) for monotone Bohr/Levitan almost periodic dynamical system $x'=f(t,x)$ (*) with the strictly monotone first integral. It is shown that Levinson center of equation (*) consists of the Bohr/Levitan almost periodic (respectively, almost automorphic, recurrent or Poisson stable) solutions. We establish the main results in the framework of general non-autonomous (cocycle) dynamical systems. We also give some applications of theses results to different classes of differential/difference equations.","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2021-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45610011","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}
In this paper we develop an iterative numerical method based on Bernstein splines for solving two-point boundary problems associated to differential equations of fractional order $alphainleft( 0,1right) $. The convergence of the method is proved by providing the error estimate and it is tested on a numerical example.
{"title":"Iterative numerical method for fractional order two-point boundary value problems","authors":"A. Bica","doi":"10.37193/cjm.2022.01.05","DOIUrl":"https://doi.org/10.37193/cjm.2022.01.05","url":null,"abstract":"In this paper we develop an iterative numerical method based on Bernstein splines for solving two-point boundary problems associated to differential equations of fractional order $alphainleft( 0,1right) $. The convergence of the method is proved by providing the error estimate and it is tested on a numerical example.","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2021-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43462355","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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