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ON N-VERTEX CHEMICAL GRAPHS WITH A FIXED CYCLOMATIC NUMBER AND MINIMUM GENERAL RANDI´C INDEX 具有固定圈数和最小一般随机指数的n顶点化学图
IF 0.1 4区 数学
Mathematical Reports Pub Date : 2022-01-01 DOI: 10.59277/mrar.2023.25.75.1.113
Akbar Ali, S. Balachandran, S. Elumalai
{"title":"ON N-VERTEX CHEMICAL GRAPHS WITH A FIXED CYCLOMATIC NUMBER AND MINIMUM GENERAL RANDI´C INDEX","authors":"Akbar Ali, S. Balachandran, S. Elumalai","doi":"10.59277/mrar.2023.25.75.1.113","DOIUrl":"https://doi.org/10.59277/mrar.2023.25.75.1.113","url":null,"abstract":"\"The general Randi´c index of a graph G is defined as Rα(G) = P uv∈E(G)(dudv)α, where du and dv denote the degrees of the vertices u and v, respectively, α is a real number, and E(G) is the edge set of G. The minimum number of edges of a graph G whose removal makes G as acyclic is known as the cyclomatic number and it is usually denoted by ν. A graph with the maximum degree at most 4 is known as a chemical graph. For ν = 0, 1, 2 and α > 1, the problem of finding graph(s) with the minimum general Randi´c index Rα among all n-vertex chemical graphs with the cyclomatic number ν has already been solved. In this paper, this problem is solved for the case when ν ≥ 3, n ≥ 5(ν − 1), and 1 < α < α0, where α0 ≈ 11.4496 is the unique positive root of the equation 4(8α − 6α) + 4α − 9α = 0.\"","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"44 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84704854","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}
引用次数: 2
Singular limiting radial solutions for 4-dimensional elliptic problem involving exponentially dominated nonlinearity 含指数主导非线性的四维椭圆问题的奇异极限径向解
IF 0.1 4区 数学
Mathematical Reports Pub Date : 2022-01-01 DOI: 10.59277/mrar.2023.25.75.1.23
S. Baraket, Rima Chetouane, F. Mtiri
{"title":"Singular limiting radial solutions for 4-dimensional elliptic problem involving exponentially dominated nonlinearity","authors":"S. Baraket, Rima Chetouane, F. Mtiri","doi":"10.59277/mrar.2023.25.75.1.23","DOIUrl":"https://doi.org/10.59277/mrar.2023.25.75.1.23","url":null,"abstract":"We study the existence of solutions having singular limits for some four-di-men-sion-al semilinear elliptic problems involving exponential nonlinearity with nonlinear terms with Navier boundary condition. In particular, we extend the result of cite{BBT}.","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"96 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73417601","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}
引用次数: 1
GENERALIZATIONS OF C3 MODULES AND C4 MODULES c3模块和c4模块的推广
IF 0.1 4区 数学
Mathematical Reports Pub Date : 2022-01-01 DOI: 10.59277/mrar.2023.25.75.1.187
Zhanmin Zhu
{"title":"GENERALIZATIONS OF C3 MODULES AND C4 MODULES","authors":"Zhanmin Zhu","doi":"10.59277/mrar.2023.25.75.1.187","DOIUrl":"https://doi.org/10.59277/mrar.2023.25.75.1.187","url":null,"abstract":"\"Let A be a class of right R-modules that is closed under isomorphisms, and let M be a right R-module. Then M is called A -C3 if, whenever N and K are direct summands of M with N ∩K = 0 and K ∈ A , then N ⊕K is also a direct summand of M; M is called an A -C4 module, if whenever M = A⊕B where A and B are submodules of M and A ∈ A , then every monomorphism f : A → B splits. Some characterizations and properties of these classes of modules are investigated. As applications, some new characterizations of semisimple artinian rings, right V-rings, quasi-Frobenius rings and von Neumann regular rings are given.\"","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"130 ","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72494971","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}
引用次数: 2
HYPERSURFACES WITH CONSTANT QUASI-GAUSS-KRONECKER CURVATURE IN Mn+1(c) Mn+1(c)中具有常准gauss - kronecker曲率的超曲面
IF 0.1 4区 数学
Mathematical Reports Pub Date : 2022-01-01 DOI: 10.59277/mrar.2023.25.75.1.1
S. Shu
{"title":"HYPERSURFACES WITH CONSTANT QUASI-GAUSS-KRONECKER CURVATURE IN Mn+1(c)","authors":"S. Shu","doi":"10.59277/mrar.2023.25.75.1.1","DOIUrl":"https://doi.org/10.59277/mrar.2023.25.75.1.1","url":null,"abstract":"\"Let Mn be an n-dimensional (n ≥ 3) complete smooth connected and oriented hypersurface in a real space form Mn+1(c) (c = 0, 1, −1) with constant quasiGauss-Kronecker curvature and two distinct principal curvatures. Denoting by H the mean curvature, |A| 2 the squared norm of the second fundamental form and Kq the quasi-Gauss-Kronecker curvature of Mn , we obtain some characterizations of S k (a)×Rn−k or S k (a)×S n−k ( √ 1 − a 2) or S k (a)×Hn−k (− √ 1 + a 2) in terms of H, |A| 2 and Kq, where 1 ≤ k ≤ n−1 and S k (a) is the k-dimensional sphere with radius a\"","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"452 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75113780","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}
引用次数: 0
ON THE INDEPENDENT RAINBOW DOMINATION STABLE GRAPHS 关于独立彩虹支配稳定图
IF 0.1 4区 数学
Mathematical Reports Pub Date : 2022-01-01 DOI: 10.59277/mrar.2023.25.75.1.179
Elham Gholami, J. Rad, A. Tehranian
{"title":"ON THE INDEPENDENT RAINBOW DOMINATION STABLE GRAPHS","authors":"Elham Gholami, J. Rad, A. Tehranian","doi":"10.59277/mrar.2023.25.75.1.179","DOIUrl":"https://doi.org/10.59277/mrar.2023.25.75.1.179","url":null,"abstract":"\"For a graph G and an integer k ≥ 2, let f : V (G) → P({1, 2, ..., k}) be a function. If for each vertex v ∈ V (G) such that f(v) = ∅ we have ∪u∈N(v)f(u) = {1, 2, ..., k}, then f is called a k-rainbow dominating function (or simply kRDF) of G. The weight of a kRDF f is defined as w(f) = P v∈V (G) |f(v)|. The minimum weight of a kRDF of G is called the k-rainbow domination number of G, and is denoted by γrk(G). An independent k-rainbow dominating function (IkRDF) is a kRDF f with the property that {v : f(v) ̸= ∅} is an independent set. The minimum weight of an IkRDF of G is called the independent k-rainbow domination number of G, and is denoted by irk(G). A graph G is k-rainbow domination stable if the k-rainbow domination number of G remains unchanged under removal of any vertex. Likewise, a graph G is independent k-rainbow domination stable if the independent k-rainbow domination number of G remains unchanged under removal of any vertex. In this paper, we prove that determining whether a graph is k-rainbow domination stable or independent k-rainbow domination stable is NP-hard even when restricted to bipartite or planar graphs, thus answering a question posed in [11].\"","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"5 ","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72440278","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}
引用次数: 0
"ON p -CRITICAL MODULES AND THE GREEN CORRESPONDENCE" “论临界模块与绿色对应关系”
IF 0.1 4区 数学
Mathematical Reports Pub Date : 2022-01-01 DOI: 10.59277/mrar.2023.25.75.1.63
Wenlin Huang
{"title":"\"ON p -CRITICAL MODULES AND THE GREEN CORRESPONDENCE\"","authors":"Wenlin Huang","doi":"10.59277/mrar.2023.25.75.1.63","DOIUrl":"https://doi.org/10.59277/mrar.2023.25.75.1.63","url":null,"abstract":"\"We define p-critical kG-modules, and prove that the Green correspondence induces a bijection between the isomorphism classes of indecomposable p-critical kG-modules and those of indecomposable p-critical kH -modules.\"","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"29 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75756140","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}
引用次数: 0
"AN UNIFIED DIFFERENCE METHOD FOR THE NUMERICAL SOLUTION OF THE TROESCH’S BOUNDARY VALUE PROBLEM" 数值解troesch边值问题的统一差分法
IF 0.1 4区 数学
Mathematical Reports Pub Date : 2022-01-01 DOI: 10.59277/mrar.2023.25.75.1.123
P. Pandey
{"title":"\"AN UNIFIED DIFFERENCE METHOD FOR THE NUMERICAL SOLUTION OF THE TROESCH’S BOUNDARY VALUE PROBLEM\"","authors":"P. Pandey","doi":"10.59277/mrar.2023.25.75.1.123","DOIUrl":"https://doi.org/10.59277/mrar.2023.25.75.1.123","url":null,"abstract":"\"In this article, the unified difference and quasi qudratization method are developed and discussed to obtain an approximate numerical solution for the Troesch’s problem, a nonlinear differential equation and corresponding boundary value problems. The degree of accuracy in numerical solution by the proposed method is good and comparable to other existing methods in literature for the range of values of parameter in Troesch’s problem.\"","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"44 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72533135","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}
引用次数: 0
"ADJOINT PREENVELOPES AND ADJOINT PRECOVERS IN THE FUNCTOR CATEGORY" 函子范畴中的伴随预包络和伴随预包络
IF 0.1 4区 数学
Mathematical Reports Pub Date : 2022-01-01 DOI: 10.59277/mrar.2023.25.75.1.85
Shoutao Guo, Xiaoyan Yang
{"title":"\"ADJOINT PREENVELOPES AND ADJOINT PRECOVERS IN THE FUNCTOR CATEGORY\"","authors":"Shoutao Guo, Xiaoyan Yang","doi":"10.59277/mrar.2023.25.75.1.85","DOIUrl":"https://doi.org/10.59277/mrar.2023.25.75.1.85","url":null,"abstract":"\"Adjoint preenvelopes and adjoint precovers are defined in the category of functors by replacing the functor Hom with ⊗. We investigate the existence and basic properties of adjoint preenvelopes and adjoint precovers. The F-projective (F-injective, F-flat) functors introduced by Mao are characterized in terms of adjoint preenvelopes and adjoint precovers. We obtain relationships among adjoint preenvelopes, adjoint precovers, preenvelopes and precovers.\"","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"35 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82249385","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}
引用次数: 0
WHEN PRIME SUBMODULES ARE PRIME IDEALS? 什么时候素子模是素理想?
IF 0.1 4区 数学
Mathematical Reports Pub Date : 2022-01-01 DOI: 10.59277/mrar.2023.25.75.1.167
Mohamed Khalifa
{"title":"WHEN PRIME SUBMODULES ARE PRIME IDEALS?","authors":"Mohamed Khalifa","doi":"10.59277/mrar.2023.25.75.1.167","DOIUrl":"https://doi.org/10.59277/mrar.2023.25.75.1.167","url":null,"abstract":"\"We study commutative ring extensions R ⊂ S in which every ideal of S that is a prime R-submodule of S is prime.\"","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"6 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82535970","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}
引用次数: 1
ON YAQUB NIL-CLEAN RINGS 在yaqub上，干净的戒指
IF 0.1 4区 数学
Mathematical Reports Pub Date : 2022-01-01 DOI: 10.59277/mrar.2023.25.75.1.153
Huanyin Chen, M. Sheibani
{"title":"ON YAQUB NIL-CLEAN RINGS","authors":"Huanyin Chen, M. Sheibani","doi":"10.59277/mrar.2023.25.75.1.153","DOIUrl":"https://doi.org/10.59277/mrar.2023.25.75.1.153","url":null,"abstract":"\"A ring R is Yaqub nil-clean if a+a3 or a−a3 is nilpotent for all a ∈ R. We prove that a ring R is a Yaqub nil-clean ring if and only if R ∼= R1,R2,R3,R1 ×R2 or R1×R3, where R1/J(R1) is Boolean, R2/J(R2) is a Yaqub ring, R3/J(R3) ∼= Z5 and each J(Ri) is nil, if and only if J(R) is nil and R/J(R) is isomorphic to a Boolean ring R1, a Yaqub ring R2, Z5, R1×R2, or R1×Z5, if and only if for any a ∈ R, there exists e3 = e such that a − e or a + 3e is nilpotent and ae = ea, if and only if R is an exchange Hirano ring. The structure of such rings is thereby completely determined.\"","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"58 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86568570","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}
引用次数: 0
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