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Strong Edge Geodetic Problem on Complete Multipartite Graphs and Some Extremal Graphs for the Problem 完整多方图上的强边大地测量问题和该问题的一些极值图
IF 0.7 4区 数学
Bulletin of The Iranian Mathematical Society Pub Date : 2024-01-31 DOI: 10.1007/s41980-023-00849-6
{"title":"Strong Edge Geodetic Problem on Complete Multipartite Graphs and Some Extremal Graphs for the Problem","authors":"","doi":"10.1007/s41980-023-00849-6","DOIUrl":"https://doi.org/10.1007/s41980-023-00849-6","url":null,"abstract":"<h3>Abstract</h3> <p>A set of vertices <em>X</em> of a graph <em>G</em> is a strong edge geodetic set if, to any pair of vertices from <em>X</em>, we can assign one (or zero) shortest path between them, such that every edge of <em>G</em> is contained in at least one on these paths. The cardinality of a smallest strong edge geodetic set of <em>G</em> is the strong edge geodetic number <span> <span>(mathrm{sg_e}(G))</span> </span> of <em>G</em>. In this paper, the strong edge geodetic number of complete multipartite graphs is determined. Graphs <em>G</em> with <span> <span>(mathrm{sg_e}(G) = n(G))</span> </span> are characterized and <span> <span>(mathrm{sg_e})</span> </span> is determined for Cartesian products <span> <span>(P_n,square , K_m)</span> </span>. The latter result in particular corrects an error from the literature.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":"289 2 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139647842","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 Hilbert Function of General Unions of Curves in Projective Spaces 论投影空间中一般曲线联合的希尔伯特函数
IF 0.7 4区 数学
Bulletin of The Iranian Mathematical Society Pub Date : 2024-01-31 DOI: 10.1007/s41980-023-00847-8
Edoardo Ballico
{"title":"On the Hilbert Function of General Unions of Curves in Projective Spaces","authors":"Edoardo Ballico","doi":"10.1007/s41980-023-00847-8","DOIUrl":"https://doi.org/10.1007/s41980-023-00847-8","url":null,"abstract":"<p>Let <span>(X=X_1cup cdots cup X_ssubset mathbb {P}^n)</span>, <span>(nge 4)</span>, be a general union of smooth non-special curves with <span>(X_i)</span> of degree <span>(d_i)</span> and genus <span>(g_i)</span> and <span>(d_ige max {2g_i-1,g_i+n})</span> if <span>(g_i&gt;0)</span>. We prove that <i>X</i> has maximal rank, i.e., for any <span>(tin mathbb {N})</span> either <span>(h^0(mathcal {I}_X(t))=0)</span> or <span>(h^1(mathcal {I}_X(t))=0)</span> if it is so in a few explicit cases in <span>(mathbb {P}^4)</span>. We also prove an unconditional weaker result, maximal rank up to a positive integer <span>(delta _n)</span>.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":"11 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139648407","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
Classification of Initial Energy in a Pseudo-parabolic Equation with Variable Exponents and Singular Potential 具有可变指数和奇异势能的伪抛物方程中的初能量分类
IF 0.7 4区 数学
Bulletin of The Iranian Mathematical Society Pub Date : 2024-01-29 DOI: 10.1007/s41980-023-00844-x
Xizheng Sun, Zhiqing Han, Bingchen Liu
{"title":"Classification of Initial Energy in a Pseudo-parabolic Equation with Variable Exponents and Singular Potential","authors":"Xizheng Sun, Zhiqing Han, Bingchen Liu","doi":"10.1007/s41980-023-00844-x","DOIUrl":"https://doi.org/10.1007/s41980-023-00844-x","url":null,"abstract":"<p>This paper deals with a pseudo-parabolic equation with singular potential and variable exponents. First, we determine the existence and uniqueness of weak solutions in Sobolev spaces with variable exponents. Second, in the frame of variational methods, we classify the blow-up and the global existence of solutions completely using the initial energy. Third, we obtain lower and upper bounds of blow-up time for all possible initial energy. The results in this paper are compatible with the corresponding problems with constant exponents. Part results of the paper extend the recent ones in Lian et al. (J Differ Equ 269:4914–4959, 2020), Xu and Su (J Funct Anal 264:2732–2763, 2013), and Liu and Yu (J Funct Anal 274:1276–1283, 2018).</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":"30 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139579263","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
Certain Observations on a $${{,mathrm{U_{fin}},}}$$ -Type Selection Principle 关于$${{,mathrm{U_{fin}},}}$类型选择原则的若干观察结果
IF 0.7 4区 数学
Bulletin of The Iranian Mathematical Society Pub Date : 2024-01-27 DOI: 10.1007/s41980-023-00851-y
Debraj Chandra, Nur Alam
{"title":"Certain Observations on a $${{,mathrm{U_{fin}},}}$$ -Type Selection Principle","authors":"Debraj Chandra, Nur Alam","doi":"10.1007/s41980-023-00851-y","DOIUrl":"https://doi.org/10.1007/s41980-023-00851-y","url":null,"abstract":"<p>A weaker variant of the selection principle <span>({{,mathrm{U_{fin}},}}({mathcal {O}},Omega ),)</span> namely <span>({{,mathrm{U_{fin}},}}({mathcal {O}},overline{Omega }),)</span> is investigated in this article. We present situations where <span>({{,mathrm{U_{fin}},}}({mathcal {O}},Omega ))</span> behaves differently from <span>({{,mathrm{U_{fin}},}}({mathcal {O}},overline{Omega }).)</span> Few characterization results are obtained by considering mappings into the Baire space. Several results are presented concerning critical cardinalities. In particular, we perform investigations assuming near coherence of filters (NCF) and semifilter trichotomy. Besides, <span>({{,mathrm{U_{fin}},}}({mathcal {O}},overline{Omega }))</span> is characterized using weakly groupable and related covers. We also exhibit certain game theoretic observations.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":"4 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139590347","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
Fiedler Linearizations of Rectangular Rational Matrix Functions 矩形有理矩阵函数的费德勒线性化
IF 0.7 4区 数学
Bulletin of The Iranian Mathematical Society Pub Date : 2024-01-12 DOI: 10.1007/s41980-023-00843-y
Namita Behera, Avisek Bist, Volker Mehrmann
{"title":"Fiedler Linearizations of Rectangular Rational Matrix Functions","authors":"Namita Behera, Avisek Bist, Volker Mehrmann","doi":"10.1007/s41980-023-00843-y","DOIUrl":"https://doi.org/10.1007/s41980-023-00843-y","url":null,"abstract":"<p>Linearization is a standard approach in the computation of eigenvalues, eigenvectors and invariant subspaces of matrix polynomials and rational matrix valued functions. An important source of linearizations are the so called <i>Fiedler linearizations</i>, which are generalizations of the classical companion forms. In this paper the concept of Fiedler linearization is extended from square regular to rectangular rational matrix valued functions. The approach is applied to Rosenbrock functions arising in mathematical system theory.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":"3 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139465199","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
Finite Group Modular Field Extensions, Green Theory and Absolutely Indecomposable and Simple Modules 有限群模块场扩展、格林理论和绝对不可分解简单模块
IF 0.7 4区 数学
Bulletin of The Iranian Mathematical Society Pub Date : 2024-01-05 DOI: 10.1007/s41980-023-00838-9
Morton E. Harris
{"title":"Finite Group Modular Field Extensions, Green Theory and Absolutely Indecomposable and Simple Modules","authors":"Morton E. Harris","doi":"10.1007/s41980-023-00838-9","DOIUrl":"https://doi.org/10.1007/s41980-023-00838-9","url":null,"abstract":"<p>Let <span>(Phi )</span> be a field of prime characteristic <i>p</i> and let <i>G</i> be a finite group. We develop an equivalence relation between the set of isomorphism types of indecomposable (simple) <i>KG</i>-modules, where <i>K</i> is any finite subfield of <span>(Phi )</span>, and relate the equivalence classes to the set of isomorphism types of indecomposable (resp. simple) <span>(Phi G)</span>-modules. When <span>(Phi )</span> is the algebraic closure of a field <i>F</i> of order <i>p</i>, we study indecomposable (resp. simple) <span>(Phi G-)</span>modules and obtain a classification of the isomorphism types of simple <span>(Phi G)</span>-modules and a new formula for the number of such types in each equivalence class.\u0000</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":"208 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139373719","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
Embedding Dimensions of Matrices Whose Entries are Indefinite Distances in the Pseudo-Euclidean Space 伪欧几里得空间中条目为不定距离的矩阵的嵌入维数
IF 0.7 4区 数学
Bulletin of The Iranian Mathematical Society Pub Date : 2024-01-04 DOI: 10.1007/s41980-023-00842-z
{"title":"Embedding Dimensions of Matrices Whose Entries are Indefinite Distances in the Pseudo-Euclidean Space","authors":"","doi":"10.1007/s41980-023-00842-z","DOIUrl":"https://doi.org/10.1007/s41980-023-00842-z","url":null,"abstract":"<h3>Abstract</h3> <p>A finite set of the Euclidean space is called an <em>s</em>-distance set provided that the number of Euclidean distances in the set is <em>s</em>. Determining the largest possible <em>s</em>-distance set for the Euclidean space of a given dimension is challenging. This problem was solved only when dealing with small values of <em>s</em> and dimensions. Lisoněk (J Combin Theory Ser A 77(2):318–338, 1997) achieved the classification of the largest 2-distance sets for dimensions up to 7, using computer assistance and graph representation theory. In this study, we consider a theory analogous to these results of Lisoněk for the pseudo-Euclidean space <span> <span>(mathbb {R}^{p,q})</span> </span>. We consider an <em>s</em>-indefinite-distance set in a pseudo-Euclidean space that uses the value <span> <span>$$begin{aligned} || varvec{x}-varvec{y}||&amp;=(x_1-y_1)^2 +cdots +(x_p -y_p)^2 &amp;quad -(x_{p+1}-y_{p+1})^2-cdots -(x_{p+q}-y_{p+q})^2 end{aligned}$$</span> </span>instead of the Euclidean distance. We develop a representation theory for symmetric matrices in the context of <em>s</em>-indefinite-distance sets, which includes or improves the results of Euclidean <em>s</em>-distance sets with large <em>s</em> values. Moreover, we classify the largest possible 2-indefinite-distance sets for small dimensions.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139103605","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
Metrical Stepanov Almost Automorphy and Applications 元斯捷潘诺夫几乎自动形态及其应用
IF 0.7 4区 数学
Bulletin of The Iranian Mathematical Society Pub Date : 2024-01-04 DOI: 10.1007/s41980-023-00840-1
Belkacem Chaouchi, Marko Kostić, Halis Can Koyuncuoğlu
{"title":"Metrical Stepanov Almost Automorphy and Applications","authors":"Belkacem Chaouchi, Marko Kostić, Halis Can Koyuncuoğlu","doi":"10.1007/s41980-023-00840-1","DOIUrl":"https://doi.org/10.1007/s41980-023-00840-1","url":null,"abstract":"<p>In this paper, we analyze various classes of multi-dimensional Stepanov almost automorphic type functions in general metric. We clarify the main structural properties for the introduced classes of metrically Stepanov almost automorphic type functions, providing also some applications to the abstract Volterra integro-differential equations.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":"2 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139372884","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 Non-degeneracy of the Robin Function for the Fractional Laplacian on Symmetric Domains 论对称域上分数拉普拉奇的罗宾函数的非退化性
IF 0.7 4区 数学
Bulletin of The Iranian Mathematical Society Pub Date : 2024-01-04 DOI: 10.1007/s41980-023-00841-0
Alejandro Ortega
{"title":"On the Non-degeneracy of the Robin Function for the Fractional Laplacian on Symmetric Domains","authors":"Alejandro Ortega","doi":"10.1007/s41980-023-00841-0","DOIUrl":"https://doi.org/10.1007/s41980-023-00841-0","url":null,"abstract":"<p>In this work we prove, under symmetry and convexity assumptions on the domain <span>(Omega )</span>, the non- degeneracy at zero of the Hessian matrix of the Robin function for the spectral fractional Laplacian. This work extends to the fractional setting the results of M. Grossi concerning the classical Laplace operator.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":"2 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139376616","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 Comparison of Two Meshless Finite Difference Methods for Solving Shallow Water Equations 关于两种求解浅水方程的无网格有限差分法的比较
IF 0.7 4区 数学
Bulletin of The Iranian Mathematical Society Pub Date : 2024-01-04 DOI: 10.1007/s41980-023-00839-8
Juan José Benito, Ángel García, Mihaela Negreanu, Francisco Ureña, Antonio Manuel Vargas
{"title":"On the Comparison of Two Meshless Finite Difference Methods for Solving Shallow Water Equations","authors":"Juan José Benito, Ángel García, Mihaela Negreanu, Francisco Ureña, Antonio Manuel Vargas","doi":"10.1007/s41980-023-00839-8","DOIUrl":"https://doi.org/10.1007/s41980-023-00839-8","url":null,"abstract":"<p>In this article, we present a numerical analysis of the Korteweg-de Vries (KdV) and Regularized Long Wave (RLW) equations using a finite difference space-time method. The KdV and RLW equations are partial differential equations that describe the behavior of long shallow water waves. We show that the finite difference space-time method is an effective way to solve these equations numerically, and we compare the results with those obtained using explicit method and generalized finite difference (GFD) formulae. Our results indicate that the finite difference space-time method provides accurate and stable solutions for both the KdV and RLW equations.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139103724","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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