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Upper bounds on distance vertex irregularity strength of some families of graphs 若干图族距离顶点不规则性强度的上界
IF 1
Opuscula Mathematica Pub Date : 2022-01-01 DOI: 10.7494/opmath.2022.42.4.561
S. Cichacz, Agnieszka G�rlich, Andrea Semani�ov�-Fe�ov��kov�
{"title":"Upper bounds on distance vertex irregularity strength of some families of graphs","authors":"S. Cichacz, Agnieszka G�rlich, Andrea Semani�ov�-Fe�ov��kov�","doi":"10.7494/opmath.2022.42.4.561","DOIUrl":"https://doi.org/10.7494/opmath.2022.42.4.561","url":null,"abstract":"For a graph (G) its distance vertex irregularity strength is the smallest integer (k) for which one can find a labeling (f: V(G)to {1, 2, dots, k}) such that [ sum_{xin N(v)}f(x)neq sum_{xin N(u)}f(x)] for all vertices (u,v) of (G), where (N(v)) is the open neighborhood of (v). In this paper we present some upper bounds on distance vertex irregularity strength of general graphs. Moreover, we give upper bounds on distance vertex irregularity strength of hypercubes and trees.","PeriodicalId":45563,"journal":{"name":"Opuscula Mathematica","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71342154","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}
引用次数: 0
Forced oscillation and asymptotic behavior of solutions of linear differential equations of second order 二阶线性微分方程解的强迫振荡和渐近性质
IF 1
Opuscula Mathematica Pub Date : 2022-01-01 DOI: 10.7494/opmath.2022.42.6.867
Y. Shoukaku
{"title":"Forced oscillation and asymptotic behavior of solutions of linear differential equations of second order","authors":"Y. Shoukaku","doi":"10.7494/opmath.2022.42.6.867","DOIUrl":"https://doi.org/10.7494/opmath.2022.42.6.867","url":null,"abstract":"","PeriodicalId":45563,"journal":{"name":"Opuscula Mathematica","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71342513","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}
引用次数: 0
Existence of positive continuous weak solutions for some semilinear elliptic eigenvalue problems 一类半线性椭圆型特征值问题正连续弱解的存在性
IF 1
Opuscula Mathematica Pub Date : 2022-01-01 DOI: 10.7494/opmath.2022.42.3.489
N. Zeddini, Rehab Saeed Sari
{"title":"Existence of positive continuous weak solutions for some semilinear elliptic eigenvalue problems","authors":"N. Zeddini, Rehab Saeed Sari","doi":"10.7494/opmath.2022.42.3.489","DOIUrl":"https://doi.org/10.7494/opmath.2022.42.3.489","url":null,"abstract":"","PeriodicalId":45563,"journal":{"name":"Opuscula Mathematica","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71342093","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}
引用次数: 0
All metric bases and fault-tolerant metric dimension for square of grid 网格正方形的所有度量基和容错度量尺寸
IF 1
Opuscula Mathematica Pub Date : 2022-01-01 DOI: 10.7494/opmath.2022.42.1.93
L. Saha, Mithun Basak, Kalishankar Tiwary
{"title":"All metric bases and fault-tolerant metric dimension for square of grid","authors":"L. Saha, Mithun Basak, Kalishankar Tiwary","doi":"10.7494/opmath.2022.42.1.93","DOIUrl":"https://doi.org/10.7494/opmath.2022.42.1.93","url":null,"abstract":"Summary: For a simple connected graph G = ( V, E ) and an ordered subset W = { w 1 , w 2 , . . . , w k } of V , the code of a vertex v ∈ V , denoted by code( v ) , with respect to W is a k -tuple ( d ( v, w 1 ) , . . . , d ( v, w k )) , where d ( v, w t ) represents the distance between v and w t . The set W is called a resolving set of G if code( u ) ̸ = code( v ) for every pair of distinct vertices u and v . A metric basis of G is a resolving set with the minimum cardinality. The metric dimension of G is the cardinality of a metric basis and is denoted by β ( G ) . A set F ⊂ V is called fault-tolerant resolving set of G if F { v } is a resolving set of G for every v ∈ F . The fault-tolerant metric dimension of G is the cardinality of a minimal fault-tolerant resolving set. In this article, a complete characterization of metric bases for G 2 mn has been given. In addition, we prove that the fault-tolerant metric dimension of G 2 mn is 4 if m + n is even. We also show that the fault-tolerant metric dimension of G 2 mn is at least 5 and at most 6 when m + n is","PeriodicalId":45563,"journal":{"name":"Opuscula Mathematica","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71342120","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}
引用次数: 2
The d-bar formalism for the modified Veselov-Novikov equation on the half-plane 半平面上修正Veselov-Novikov方程的d-bar形式
IF 1
Opuscula Mathematica Pub Date : 2022-01-01 DOI: 10.7494/opmath.2022.42.2.179
Guenbo Hwang, Byungsoo Moon
{"title":"The d-bar formalism for the modified Veselov-Novikov equation on the half-plane","authors":"Guenbo Hwang, Byungsoo Moon","doi":"10.7494/opmath.2022.42.2.179","DOIUrl":"https://doi.org/10.7494/opmath.2022.42.2.179","url":null,"abstract":"We study the modified Veselov-Novikov equation (mVN) posed on the half-plane via the Fokas method, considered as an extension of the inverse scattering transform for boundary value problems. The mVN equation is one of the most natural ((2+1))-dimensional generalization of the ((1+1))-dimensional modified Korteweg-de Vries equation in the sense as to how the Novikov-Veselov equation is related to the Korteweg-de Vries equation. In this paper, by means of the Fokas method, we present the so-called global relation for the mVN equation, which is an algebraic equation coupled with the spectral functions, and the (d)-bar formalism, also known as Pompieu's formula. In addition, we characterize the (d)-bar derivatives and the relevant jumps across certain domains of the complex plane in terms of the spectral functions.","PeriodicalId":45563,"journal":{"name":"Opuscula Mathematica","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71342208","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}
引用次数: 0
Uniqueness of solution of a nonlinear evolution dam problem in a heterogeneous porous medium 非均质多孔介质中非线性演化坝问题解的唯一性
IF 1
Opuscula Mathematica Pub Date : 2022-01-01 DOI: 10.7494/opmath.2022.42.1.5
Messaouda Ben Attia, E. Zaouche, M. Bousselsal
{"title":"Uniqueness of solution of a nonlinear evolution dam problem in a heterogeneous porous medium","authors":"Messaouda Ben Attia, E. Zaouche, M. Bousselsal","doi":"10.7494/opmath.2022.42.1.5","DOIUrl":"https://doi.org/10.7494/opmath.2022.42.1.5","url":null,"abstract":"By choosing convenient test functions and using the method of doubling variables, we prove the uniqueness of the solution to a nonlinear evolution dam problem in an arbitrary heterogeneous porous medium of (mathbb{R}^n) ((nin {2,3})) with an impermeable horizontal bottom.","PeriodicalId":45563,"journal":{"name":"Opuscula Mathematica","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71342384","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}
引用次数: 0
Kneser-type oscillation criteria for second-order half-linear advanced difference equations 二阶半线性高级差分方程的kneser型振荡判据
IF 1
Opuscula Mathematica Pub Date : 2022-01-01 DOI: 10.7494/opmath.2022.42.1.55
N. Indrajith, J. Graef, E. Thandapani
{"title":"Kneser-type oscillation criteria for second-order half-linear advanced difference equations","authors":"N. Indrajith, J. Graef, E. Thandapani","doi":"10.7494/opmath.2022.42.1.55","DOIUrl":"https://doi.org/10.7494/opmath.2022.42.1.55","url":null,"abstract":"The authors present Kneser-type oscillation criteria for a class of advanced type second-order difference equations. The results obtained are new and they improve and complement known results in the literature. Two examples are provided to illustrate the importance of the main results.","PeriodicalId":45563,"journal":{"name":"Opuscula Mathematica","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71342394","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}
引用次数: 2
New aspects for the oscillation of first-order difference equations with deviating arguments 一阶带偏离参数差分方程振荡问题的新认识
IF 1
Opuscula Mathematica Pub Date : 2022-01-01 DOI: 10.7494/opmath.2022.42.3.393
E. Attia, B. El-Matary
{"title":"New aspects for the oscillation of first-order difference equations with deviating arguments","authors":"E. Attia, B. El-Matary","doi":"10.7494/opmath.2022.42.3.393","DOIUrl":"https://doi.org/10.7494/opmath.2022.42.3.393","url":null,"abstract":"We study the oscillation of first-order linear difference equations with non-monotone deviating arguments. Iterative oscillation criteria are obtained which essentially improve, extend, and simplify some known conditions. These results will be applied to some numerical examples.","PeriodicalId":45563,"journal":{"name":"Opuscula Mathematica","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71342421","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}
引用次数: 0
Growth of solutions of a class of linear fractional differential equations with polynomial coefficients 一类系数为多项式的线性分数阶微分方程解的增长
IF 1
Opuscula Mathematica Pub Date : 2022-01-01 DOI: 10.7494/opmath.2022.42.3.415
S. Hamouda, S. Mahmoudi
{"title":"Growth of solutions of a class of linear fractional differential equations with polynomial coefficients","authors":"S. Hamouda, S. Mahmoudi","doi":"10.7494/opmath.2022.42.3.415","DOIUrl":"https://doi.org/10.7494/opmath.2022.42.3.415","url":null,"abstract":"This paper is devoted to the study of the growth of solutions of certain class of linear fractional differential equations with polynomial coefficients involving the Caputo fractional derivatives by using the generalized Wiman-Valiron theorem in the fractional calculus.","PeriodicalId":45563,"journal":{"name":"Opuscula Mathematica","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71342432","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}
引用次数: 0
Nordhaus-Gaddum bounds for upper total domination 上总支配的诺德豪斯-加德姆界
IF 1
Opuscula Mathematica Pub Date : 2022-01-01 DOI: 10.7494/opmath.2022.42.4.573
T. Haynes, Michael A. Henning
{"title":"Nordhaus-Gaddum bounds for upper total domination","authors":"T. Haynes, Michael A. Henning","doi":"10.7494/opmath.2022.42.4.573","DOIUrl":"https://doi.org/10.7494/opmath.2022.42.4.573","url":null,"abstract":"A set (S) of vertices in an isolate-free graph (G) is a total dominating set if every vertex in (G) is adjacent to a vertex in (S). A total dominating set of (G) is minimal if it contains no total dominating set of (G) as a proper subset. The upper total domination number (Gamma_t(G)) of (G) is the maximum cardinality of a minimal total dominating set in (G). We establish Nordhaus-Gaddum bounds involving the upper total domination numbers of a graph (G) and its complement (overline{G}). We prove that if (G) is a graph of order (n) such that both (G) and (overline{G}) are isolate-free, then (Gamma_t(G) + Gamma_t(overline{G}) leq n + 2) and (Gamma_t(G)Gamma_t(overline{G}) leq frac{1}{4}(n+2)^2), and these bounds are tight.","PeriodicalId":45563,"journal":{"name":"Opuscula Mathematica","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71342586","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}
引用次数: 0
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