Three determinants for symmetric and skew-symmetric matrices are explicitly evaluated, in closed form, as circular products. One of them gives a solution to a problem proposed by Dzhumadil’daev [ Amer. Math. Monthly 129 (2022) 486].
{"title":"Three determinants evaluated in circular products","authors":"Shuling Gao, W. Chu","doi":"10.47443/cm.2022.029","DOIUrl":"https://doi.org/10.47443/cm.2022.029","url":null,"abstract":"Three determinants for symmetric and skew-symmetric matrices are explicitly evaluated, in closed form, as circular products. One of them gives a solution to a problem proposed by Dzhumadil’daev [ Amer. Math. Monthly 129 (2022) 486].","PeriodicalId":48938,"journal":{"name":"Contributions To Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79576173","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}
A set S of vertices in a connected graph G is an irregular dominating set if the vertices of S can be labeled with distinct positive integers in such a way that for every vertex u of G , there is a vertex v ∈ S such that the distance from u to v is the label assigned to v . If for every vertex v ∈ S , there is a vertex u of G such that v is the only vertex of S whose distance to u is the label of v , then S is a minimal irregular dominating set. A graph H is an irregular domination graph if there exists a graph G with a minimal irregular dominating set S such that H is isomorphic to the subgraph G [ S ] of G induced by S . We determine all paths and cycles that are irregular domination graphs as well as the familiar graphs of ladders and prisms, which are Cartesian products of K 2 with paths and cycles, respectively. Other results and problems are also presented on this topic.
{"title":"Irregular domination graphs","authors":"Caryn Mays, Ping Zhang","doi":"10.47443/cm.2022.033","DOIUrl":"https://doi.org/10.47443/cm.2022.033","url":null,"abstract":"A set S of vertices in a connected graph G is an irregular dominating set if the vertices of S can be labeled with distinct positive integers in such a way that for every vertex u of G , there is a vertex v ∈ S such that the distance from u to v is the label assigned to v . If for every vertex v ∈ S , there is a vertex u of G such that v is the only vertex of S whose distance to u is the label of v , then S is a minimal irregular dominating set. A graph H is an irregular domination graph if there exists a graph G with a minimal irregular dominating set S such that H is isomorphic to the subgraph G [ S ] of G induced by S . We determine all paths and cycles that are irregular domination graphs as well as the familiar graphs of ladders and prisms, which are Cartesian products of K 2 with paths and cycles, respectively. Other results and problems are also presented on this topic.","PeriodicalId":48938,"journal":{"name":"Contributions To Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81952655","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 X ⊂ P r be a projective embedded variety defined over a field K . Results relating maximum and generic X -rank of points of P r ( K ) and P r ( L ) are given, where L is a field containing K . Some of these results are algebraically closed for K and L . In other results (e.g. on the cactus rank), L is a finite extension of K .
设X∧P r是定义在域K上的一个射影内嵌变量。给出了P r (K)和P r (L)的点的极大值和一般X -秩的结果，其中L是包含K的域。其中一些结果对K和L在代数上是封闭的。在其他结果中(例如仙人掌的排名)，L是K的有限扩展。
{"title":"X-ranks for embedded varieties and extensions of fields","authors":"E. Ballico","doi":"10.47443/cm.2022.021","DOIUrl":"https://doi.org/10.47443/cm.2022.021","url":null,"abstract":"Let X ⊂ P r be a projective embedded variety defined over a field K . Results relating maximum and generic X -rank of points of P r ( K ) and P r ( L ) are given, where L is a field containing K . Some of these results are algebraically closed for K and L . In other results (e.g. on the cactus rank), L is a finite extension of K .","PeriodicalId":48938,"journal":{"name":"Contributions To Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73885832","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, using a generalized integral operator, new Hermite-Hadamard type inequalities are obtained for differentiable modified ( h, m ) -convex functions of the second type.
{"title":"On the Hermite-Hadamard type inequalities involving generalized integrals","authors":"J. E. Valdés","doi":"10.47443/cm.2022.020","DOIUrl":"https://doi.org/10.47443/cm.2022.020","url":null,"abstract":"In this paper, using a generalized integral operator, new Hermite-Hadamard type inequalities are obtained for differentiable modified ( h, m ) -convex functions of the second type.","PeriodicalId":48938,"journal":{"name":"Contributions To Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72471718","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}
The aim of this short note is to establish an elegant sum involving central binomial coefficients, due to L´aszl´o [ Amer. Math. Monthly 108 (2001) 851–855], via a hypergeometric series approach.
这篇短文的目的是建立一个涉及中心二项式系数的优雅和，由于L ' aszl ' o [Amer]。数学。月刊108(2001)851-855]，通过超几何级数方法。
{"title":"A short derivation of an elegant sum involving central binomial coefficients due to Laszlo via a hypergeometric series approach","authors":"D. Lim, A. Rathie","doi":"10.47443/cm.2022.025","DOIUrl":"https://doi.org/10.47443/cm.2022.025","url":null,"abstract":"The aim of this short note is to establish an elegant sum involving central binomial coefficients, due to L´aszl´o [ Amer. Math. Monthly 108 (2001) 851–855], via a hypergeometric series approach.","PeriodicalId":48938,"journal":{"name":"Contributions To Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84482879","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, several erroneous results appeared in the papers [T.-Y. Zhang, A.-P. Ji, F. Qi, Abstr. Appl. Anal. 2012 (2012) #560586] and [T.-Y. Zhang, M. Tunc¸, A.-P. Ji, B.-Y. Xi, Abstr. Appl. Anal. 2014 (2014) #294739] are corrected. † 2020 Mathematics
{"title":"Notes on several integral inequalities of Hermite–Hadamard type for s-geometrically\u0000convex functions","authors":"Chun-Ying He, Feng Qi (祁锋)","doi":"10.47443/cm.2022.015","DOIUrl":"https://doi.org/10.47443/cm.2022.015","url":null,"abstract":"In this paper, several erroneous results appeared in the papers [T.-Y. Zhang, A.-P. Ji, F. Qi, Abstr. Appl. Anal. 2012 (2012) #560586] and [T.-Y. Zhang, M. Tunc¸, A.-P. Ji, B.-Y. Xi, Abstr. Appl. Anal. 2014 (2014) #294739] are corrected. † 2020 Mathematics","PeriodicalId":48938,"journal":{"name":"Contributions To Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89255931","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 G be a longest cycle in the directed graph G = ( V, A ) . Let q be the total number of cycles in G . It is proved that if 1 ≤ q ≤ | V ( C G ) | then there exists an arc a ∈ A ( G ) whose reversal decreases the total number of cycles in G .
设C G是有向图G = (V, a)中的最长环。设q为G中循环的总数。证明了如果1≤q≤| V (C G) |则存在一个弧a∈a (G)，其反转使G中的总圈数减小。
{"title":"On Arc Reversal in Digraphs With a Restricted Number of Cycles","authors":"Z. R. Bogdanowicz","doi":"10.47443/cm.2022.014","DOIUrl":"https://doi.org/10.47443/cm.2022.014","url":null,"abstract":"Let C G be a longest cycle in the directed graph G = ( V, A ) . Let q be the total number of cycles in G . It is proved that if 1 ≤ q ≤ | V ( C G ) | then there exists an arc a ∈ A ( G ) whose reversal decreases the total number of cycles in G .","PeriodicalId":48938,"journal":{"name":"Contributions To Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84970282","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 study offers the averaging principle for fuzzy stochastic differential equations (FSDEs). The solutions to FSDEs can be approximated in the sense of mean square solutions of averaged fuzzy stochastic system under certain assumptions.
{"title":"Averaging Principle for Fuzzy Stochastic Differential Equations","authors":"Elhoussain Arhrrabi, M. Elomari, S. Melliani","doi":"10.47443/cm.2022.003","DOIUrl":"https://doi.org/10.47443/cm.2022.003","url":null,"abstract":"This study offers the averaging principle for fuzzy stochastic differential equations (FSDEs). The solutions to FSDEs can be approximated in the sense of mean square solutions of averaged fuzzy stochastic system under certain assumptions.","PeriodicalId":48938,"journal":{"name":"Contributions To Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88427412","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}
{"title":"On A_alpha–Eigenvalues of Graphs and Topological Indices","authors":"","doi":"10.47443/cm.2022.010","DOIUrl":"https://doi.org/10.47443/cm.2022.010","url":null,"abstract":"","PeriodicalId":48938,"journal":{"name":"Contributions To Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78145874","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}
The purpose of this paper is to investigate the existence and uniqueness of weak solutions for a class of nonlinear degenerate elliptic problems of the form: where ν 1 , ν 2 , and ν 3 are A p -weight functions and the operators a , b and g are Carat´eodory functions that satisfy some certain conditions, and φ ∈ L p (cid:48) (Ω , ν 1 − p (cid:48) 1 ) . The approach used for attaining the mentioned purpose is based on the Browder-Minty theorem and the theory of weighted Sobolev spaces.
{"title":"On the Existence and Uniqueness of Solutions for a Class of Nonlinear Degenerate Elliptic Problems via Browder-Minty Theorem","authors":"Mohamed El Ouaarabi, C. Allalou, S. Melliani","doi":"10.47443/cm.2022.001","DOIUrl":"https://doi.org/10.47443/cm.2022.001","url":null,"abstract":"The purpose of this paper is to investigate the existence and uniqueness of weak solutions for a class of nonlinear degenerate elliptic problems of the form: where ν 1 , ν 2 , and ν 3 are A p -weight functions and the operators a , b and g are Carat´eodory functions that satisfy some certain conditions, and φ ∈ L p (cid:48) (Ω , ν 1 − p (cid:48) 1 ) . The approach used for attaining the mentioned purpose is based on the Browder-Minty theorem and the theory of weighted Sobolev spaces.","PeriodicalId":48938,"journal":{"name":"Contributions To Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74765189","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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