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Annales Mathematicae Silesianae最新文献

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The Realizability of Theta Graphs as Reconfiguration Graphs of Minimum Independent Dominating Sets. θ图作为最小独立支配集重构图的可实现性。
IF 0.3
Annales Mathematicae Silesianae Pub Date : 2024-02-21 eCollection Date: 2025-03-01 DOI: 10.2478/amsil-2024-0002
R C Brewster, C M Mynhardt, L E Teshima
{"title":"The Realizability of Theta Graphs as Reconfiguration Graphs of Minimum Independent Dominating Sets.","authors":"R C Brewster, C M Mynhardt, L E Teshima","doi":"10.2478/amsil-2024-0002","DOIUrl":"https://doi.org/10.2478/amsil-2024-0002","url":null,"abstract":"<p><p>The independent domination number <i>i</i>(<i>G</i>) of a graph <i>G</i> is the minimum cardinality of a maximal independent set of <i>G</i>, also called an <i>i</i>(<i>G</i>)-set. The <i>i</i>-graph of <i>G</i>, denoted <i>ℐ</i> (<i>G</i>), is the graph whose vertices correspond to the <i>i</i>(<i>G</i>)-sets, and where two <i>i</i>(<i>G</i>)-sets are adjacent if and only if they differ by two adjacent vertices. Not all graphs are <i>i</i>-graph realizable, that is, given a target graph <i>H</i>, there does not necessarily exist a source graph <i>G</i> such that <i>H</i> ≅ <i>ℐ</i> (<i>G</i>). We consider a class of graphs called \"theta graphs\": a theta graph is the union of three internally disjoint nontrivial paths with the same two distinct end vertices. We characterize theta graphs that are <i>i</i>-graph realizable, showing that there are only finitely many that are not. We also characterize those line graphs and claw-free graphs that are <i>i</i>-graphs, and show that all 3-connected cubic bipartite planar graphs are <i>i</i>-graphs.</p>","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":"39 1","pages":"94-129"},"PeriodicalIF":0.3,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12024038/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144049557","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Determinants of Toeplitz–Hessenberg Matrices with Generalized Leonardo Number Entries 带有广义莱昂纳多数项的托普利兹-海森堡矩阵的确定性
IF 0.4
Annales Mathematicae Silesianae Pub Date : 2024-01-10 DOI: 10.2478/amsil-2023-0027
T. Goy, M. Shattuck
{"title":"Determinants of Toeplitz–Hessenberg Matrices with Generalized Leonardo Number Entries","authors":"T. Goy, M. Shattuck","doi":"10.2478/amsil-2023-0027","DOIUrl":"https://doi.org/10.2478/amsil-2023-0027","url":null,"abstract":"Abstract Let un = un(k) denote the generalized Leonardo number defined recursively by un = un−1 + un−2 + k for n ≥ 2, where u0 = u1 = 1. Terms of the sequence un(1) are referred to simply as Leonardo numbers. In this paper, we find expressions for the determinants of several Toeplitz–Hessenberg matrices having generalized Leonardo number entries. These results are obtained as special cases of more general formulas for the generating function of the corresponding sequence of determinants. Special attention is paid to the cases 1 ≤ k ≤ 7, where several connections are made to entries in the On-Line Encyclopedia of Integer Sequences. By Trudi’s formula, one obtains equivalent multi-sum identities involving sums of products of generalized Leonardo numbers. Finally, in the case k = 1, we also provide combinatorial proofs of the determinant formulas, where we make extensive use of sign-changing involutions on the related structures.","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":"5 4","pages":""},"PeriodicalIF":0.4,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139439412","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
Note on an Iterative Functional Equation 关于迭代函数式的说明
IF 0.4
Annales Mathematicae Silesianae Pub Date : 2024-01-10 DOI: 10.2478/amsil-2023-0031
Karol Baron, Janusz Morawiec
{"title":"Note on an Iterative Functional Equation","authors":"Karol Baron, Janusz Morawiec","doi":"10.2478/amsil-2023-0031","DOIUrl":"https://doi.org/10.2478/amsil-2023-0031","url":null,"abstract":"Abstract We study the problem of solvability of the equation ϕ(x)=∫Ωg(w)ϕ(f(x,ω))P(dω)+F(x), varphi left( x right) = int_Omega {gleft( w right)} varphi left( {fleft( {x,omega } right)} right)Pleft( {domega } right) + Fleft( x right), where P is a probability measure on a σ-algebra of subsets of Ω, assuming Hölder continuity of F on the range of f.","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":"55 9","pages":""},"PeriodicalIF":0.4,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139441125","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
Adaptive Integration of Convex Functions of One Real Variable 单实变数凸函数的自适应积分
IF 0.4
Annales Mathematicae Silesianae Pub Date : 2024-01-10 DOI: 10.2478/amsil-2023-0028
S. Wa̧sowicz
{"title":"Adaptive Integration of Convex Functions of One Real Variable","authors":"S. Wa̧sowicz","doi":"10.2478/amsil-2023-0028","DOIUrl":"https://doi.org/10.2478/amsil-2023-0028","url":null,"abstract":"Abstract We present an adaptive method of approximate integration of convex (as well as concave) functions based on a certain refinement of the celebrated Hermite–Hadamard inequality. Numerical experiments are performed and the role of harmonic numbers is shown.","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":"33 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139441527","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
The Subset-Strong Product of Graphs 图的子集-强积
IF 0.4
Annales Mathematicae Silesianae Pub Date : 2024-01-10 DOI: 10.2478/amsil-2023-0029
Mehdi Eliasi
{"title":"The Subset-Strong Product of Graphs","authors":"Mehdi Eliasi","doi":"10.2478/amsil-2023-0029","DOIUrl":"https://doi.org/10.2478/amsil-2023-0029","url":null,"abstract":"Abstract In this paper, we introduce the subset-strong product of graphs and give a method for calculating the adjacency spectrum of this product. In addition, exact expressions for the first and second Zagreb indices of the subset-strong products of two graphs are reported. Examples are provided to illustrate the applications of this product in some growing graphs and complex networks.","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":"54 8","pages":""},"PeriodicalIF":0.4,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139441139","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
Generalized Polynomials on Semigroups 半群上的广义多项式
IF 0.4
Annales Mathematicae Silesianae Pub Date : 2024-01-10 DOI: 10.2478/amsil-2023-0026
B. Ebanks
{"title":"Generalized Polynomials on Semigroups","authors":"B. Ebanks","doi":"10.2478/amsil-2023-0026","DOIUrl":"https://doi.org/10.2478/amsil-2023-0026","url":null,"abstract":"Abstract This article has two main parts. In the first part we show that some of the basic theory of generalized polynomials on commutative semi-groups can be extended to all semigroups. In the second part we show that if a sub-semigroup S of a group G generates G in the sense that G = S · S−1, then a generalized polynomial on S with values in an Abelian group H can be extended to a generalized polynomial on G into H. Finally there is a short discussion of the extendability of exponential functions and generalized exponential polynomials.","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":"3 4","pages":""},"PeriodicalIF":0.4,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139439913","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
New Upper Bounds for the Weighted Chebyshev Functional 加权切比雪夫函数的新上限
IF 0.4
Annales Mathematicae Silesianae Pub Date : 2024-01-10 DOI: 10.2478/amsil-2023-0030
M. K. Bakula, J. Pečarić
{"title":"New Upper Bounds for the Weighted Chebyshev Functional","authors":"M. K. Bakula, J. Pečarić","doi":"10.2478/amsil-2023-0030","DOIUrl":"https://doi.org/10.2478/amsil-2023-0030","url":null,"abstract":"Abstract New upper bounds for the weighted Chebyshev functional under various conditions, including those of Steffensen type, are given. The obtained results are used to establish some new bounds for the Jensen functional.","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":"88 11","pages":""},"PeriodicalIF":0.4,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139440499","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
A Basic Set of Cancellation Violating Sequences for Finite Two-Dimensional Non-Additive Measurement 有限二维非加法测量的基本抵消违反序列集
IF 0.4
Annales Mathematicae Silesianae Pub Date : 2023-12-13 DOI: 10.2478/amsil-2023-0023
Che Tat Ng
{"title":"A Basic Set of Cancellation Violating Sequences for Finite Two-Dimensional Non-Additive Measurement","authors":"Che Tat Ng","doi":"10.2478/amsil-2023-0023","DOIUrl":"https://doi.org/10.2478/amsil-2023-0023","url":null,"abstract":"Abstract Cancellation conditions play a central role in the representation theory of measurement for a weak order on a finite two-dimensional Cartesian product set X. A weak order has an additive representation if and only if it violates no cancellation conditions. Given X, a longstanding open problem is to determine the simplest set of cancellation conditions that is violated by every linear order that is not additively representable. Here, we report that the simplest set of cancellation conditions on a 5 by 5 product X is obtained.","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":"253 6","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139005927","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
On Almost Everywhere K-Additive Set-Valued Maps 论几乎无处不在的 K 正集值映射
IF 0.4
Annales Mathematicae Silesianae Pub Date : 2023-12-13 DOI: 10.2478/amsil-2023-0025
Eliza Jabłońska
{"title":"On Almost Everywhere K-Additive Set-Valued Maps","authors":"Eliza Jabłońska","doi":"10.2478/amsil-2023-0025","DOIUrl":"https://doi.org/10.2478/amsil-2023-0025","url":null,"abstract":"Abstract Let X be an Abelian group, Y be a commutative monoid, K ⊂Y be a submonoid and F : X → 2Y {∅} be a set-valued map. Under some additional assumptions on ideals ℐ1 in X and ℐ2 in X2, we prove that if F is ℐ2-almost everywhere K-additive, then there exists a unique up to K K-additive set-valued map G : X → 2Y {∅} such that F = G ℐ1-almost everywhere in X. Our considerations refers to the well known de Bruijn’s result [1].","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":"81 3‐4","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138976886","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
Some General Theorems About a Class of Sets of Numbers 关于一类数集的一些通则
IF 0.4
Annales Mathematicae Silesianae Pub Date : 2023-12-13 DOI: 10.2478/amsil-2023-0024
R. Jakimczuk
{"title":"Some General Theorems About a Class of Sets of Numbers","authors":"R. Jakimczuk","doi":"10.2478/amsil-2023-0024","DOIUrl":"https://doi.org/10.2478/amsil-2023-0024","url":null,"abstract":"Abstract We prove a theorem which unifies some formulas, for example the counting function, of some sets of numbers including all positive integers, h-free numbers, h-full numbers, etc. We also establish a conjecture and give some examples where the conjecture holds.","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":"239 2","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139006015","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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