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A Conjecture Generalizing Thomassen’s Chord Conjecture in Graph Theory 图论中托马森弦猜想的一般化猜想
IF 0.7 4区 数学
Bulletin of The Iranian Mathematical Society Pub Date : 2024-08-19 DOI: 10.1007/s41980-024-00909-5
Xingzhi Zhan
{"title":"A Conjecture Generalizing Thomassen’s Chord Conjecture in Graph Theory","authors":"Xingzhi Zhan","doi":"10.1007/s41980-024-00909-5","DOIUrl":"https://doi.org/10.1007/s41980-024-00909-5","url":null,"abstract":"<p>Thomassen’s chord conjecture from 1976 states that every longest cycle in a 3-connected graph has a chord. This is one of the most important unsolved problems in graph theory. We pose a new conjecture which implies Thomassen’s conjecture. It involves bound vertices in a longest path between two vertices in a <i>k</i>-connected graph. We also give supporting evidence and analyze a special case. The purpose of making this new conjecture is to explore the surroundings of Thomassen’s conjecture.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212589","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
Obstruction Theory for the $$mathbb {Z}_2$$ -Index of 4-Manifolds 4 扇形的 $$mathbb {Z}_2$$ -索引的阻塞理论
IF 0.7 4区 数学
Bulletin of The Iranian Mathematical Society Pub Date : 2024-08-15 DOI: 10.1007/s41980-024-00907-7
Chahrazade Matmat, Christian Blanchet
{"title":"Obstruction Theory for the $$mathbb {Z}_2$$ -Index of 4-Manifolds","authors":"Chahrazade Matmat, Christian Blanchet","doi":"10.1007/s41980-024-00907-7","DOIUrl":"https://doi.org/10.1007/s41980-024-00907-7","url":null,"abstract":"<p>We develop a complete obstruction theory for the <span>(mathbb {Z}_2)</span>-index of a compact connected 4-dimensional manifold with free involution. This <span>(mathbb {Z}_2)</span>-index, equal to the minimum integer <i>n</i> for which there exists an equivariant map with target the <i>n</i>-sphere with antipodal involution, is computed in two steps using cohomology with twisted coefficients. The key ingredient is a spectral sequence computing twisted cohomology of the orbit space of a free involution on odd complex projective spaces. We illustrate the main results with various examples including computation of the secondary obstruction.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212514","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
Cohomology of Hom-Associative Algebras in Loday–Pirashvili Category with Applications Loday-Pirashvili 类别中 Hom-Associative 算法的同调及其应用
IF 0.7 4区 数学
Bulletin of The Iranian Mathematical Society Pub Date : 2024-08-14 DOI: 10.1007/s41980-024-00905-9
Tao Zhang
{"title":"Cohomology of Hom-Associative Algebras in Loday–Pirashvili Category with Applications","authors":"Tao Zhang","doi":"10.1007/s41980-024-00905-9","DOIUrl":"https://doi.org/10.1007/s41980-024-00905-9","url":null,"abstract":"<p>We introduce the concept of Hom-associative algebra structures in Loday–Pirashvili category. The cohomology theory of Hom-associative algebras in this category is studied. Some applications on deformation and abelian extension theory are given. We also introduce the notion of Nijenhuis operators to describe trivial deformations. It is proved that equivalent classes of abelian extensions are one-to-one correspondence to the elements of the second cohomology groups.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212590","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
Higher-Order Efficiency Conditions for Vector Nonsmooth Optimization Problems Using the Higher-Order Gâteaux Derivatives 矢量非光滑优化问题的高阶效率条件--使用高阶伽托导数
IF 0.7 4区 数学
Bulletin of The Iranian Mathematical Society Pub Date : 2024-08-13 DOI: 10.1007/s41980-024-00904-w
Tran Van Su, Dinh Dieu Hang
{"title":"Higher-Order Efficiency Conditions for Vector Nonsmooth Optimization Problems Using the Higher-Order Gâteaux Derivatives","authors":"Tran Van Su, Dinh Dieu Hang","doi":"10.1007/s41980-024-00904-w","DOIUrl":"https://doi.org/10.1007/s41980-024-00904-w","url":null,"abstract":"<p>In this article, we investigate the higher-order nonsmooth optimality conditions for vector optimization problems with inequality, equality and set constraints in terms of the higher-order Gâteaux derivatives. First, we propose various higher-order Mangasarian–Fromovitz nonsmooth constraint qualifications for such problems. Second, we formulate higher-order KKT-type necessary optimality conditions for the local weak efficient solutions of the nonsmooth vector equilibrium problem with constraints (CVEP) and its special cases. An application of the result to the resources assignment problem with set, inequality, equality constraints is derived. Under some suitable assumptions involving a set constraint, the higher-order nonsmooth necessary optimality conditions become the higher-order sufficient optimality conditions via the higher-order directional/Gâteaux derivatives.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212513","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
Product of Factorials Equal Another Product of Factorials 阶乘的乘积等于另一个阶乘的乘积
IF 0.7 4区 数学
Bulletin of The Iranian Mathematical Society Pub Date : 2024-08-13 DOI: 10.1007/s41980-024-00906-8
Wataru Takeda
{"title":"Product of Factorials Equal Another Product of Factorials","authors":"Wataru Takeda","doi":"10.1007/s41980-024-00906-8","DOIUrl":"https://doi.org/10.1007/s41980-024-00906-8","url":null,"abstract":"<p>The Surányi–Hickerson conjecture is a long-standing unsolved problem of Diophantine equations. This conjecture states that all the solutions to <span>(ell _1!cdots ell _m!=k!)</span> with <span>(k-ell _mge 2)</span> are <span>((ell _1,ldots ,ell _m;k)=(6,7;10),(3,5,7;10),(2,5,14;16))</span> and (2, 3, 3, 7; 9). In this paper, we generalize the Surányi–Hickerson conjecture to <span>(ell _1!cdots ell _m!=k_1!cdots k_n!)</span>. We say that a solution <span>((ell _1,ldots ,ell _m;k_1,ldots ,k_n))</span> is trivial if there exists a pair (<i>i</i>, <i>j</i>) such that <span>(|ell _i-k_j|=1)</span>. As in the Surányi–Hickerson conjecture, we give theoretical and computational results. In particular, we suggest that all non-trivial solutions to the equation <span>(ell _1!ell _2=k_1!k_2!)</span> are <span>((ell _1,ell _2;k_1,k_2)=(7,13;4,15))</span>, (14, 62; 7, 66) and (22, 54; 18, 57).</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212517","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
Improved Lower Bound for the Radius of Analyticity of Solutions to the Fifth Order, KdV-BBM Type Equation 改进的五阶 KdV-BBM 型方程解的解析半径下限
IF 0.7 4区 数学
Bulletin of The Iranian Mathematical Society Pub Date : 2024-08-02 DOI: 10.1007/s41980-024-00882-z
Sileshi Mebrate, Tamirat Dufera, Achenef Tesfahun
{"title":"Improved Lower Bound for the Radius of Analyticity of Solutions to the Fifth Order, KdV-BBM Type Equation","authors":"Sileshi Mebrate, Tamirat Dufera, Achenef Tesfahun","doi":"10.1007/s41980-024-00882-z","DOIUrl":"https://doi.org/10.1007/s41980-024-00882-z","url":null,"abstract":"<p>We show that the uniform radius of spatial analyticity <span>(sigma (t))</span> of solutions at time <i>t</i> to the fifth order, KdV-BBM type equation cannot decay faster than <span>(1/ sqrt{t})</span> for large <i>t</i>, given initial data that is analytic with fixed radius <span>(sigma _0)</span>. This improves a recent result by Belayneh, Tegegn and the third author [2], where they obtained a 1/<i>t</i> decay of <span>(sigma (t))</span> for large time <i>t</i>.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141882043","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
2-Products of Idempotent by Nilpotent Matrices 2-无效矩阵的等价积
IF 0.7 4区 数学
Bulletin of The Iranian Mathematical Society Pub Date : 2024-07-31 DOI: 10.1007/s41980-024-00883-y
Grigore Călugăreanu, Horia F. Pop
{"title":"2-Products of Idempotent by Nilpotent Matrices","authors":"Grigore Călugăreanu, Horia F. Pop","doi":"10.1007/s41980-024-00883-y","DOIUrl":"https://doi.org/10.1007/s41980-024-00883-y","url":null,"abstract":"<p>Over Prüfer domains, we characterize idempotent by nilpotent 2-products of <span>(2times 2)</span> matrices. Nilpotents are always such products. We also provide large classes of rings over which every <span>(2times 2)</span> idempotent matrix is such a product. Finally, for <span>(2times 2)</span> matrices over GCD domains, idempotent–nilpotent products which are also nilpotent–idempotent products are characterized.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141873180","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
Commutator Formulas for Gradient Ricci Shrinkers and Their Application to Linear Stability of Gradient Ricci Shrinkers 梯度利玛窦收缩器的换元公式及其在梯度利玛窦收缩器线性稳定性中的应用
IF 0.7 4区 数学
Bulletin of The Iranian Mathematical Society Pub Date : 2024-07-13 DOI: 10.1007/s41980-024-00890-z
Mansour Mehrmohamadi, Asadollah Razavi
{"title":"Commutator Formulas for Gradient Ricci Shrinkers and Their Application to Linear Stability of Gradient Ricci Shrinkers","authors":"Mansour Mehrmohamadi, Asadollah Razavi","doi":"10.1007/s41980-024-00890-z","DOIUrl":"https://doi.org/10.1007/s41980-024-00890-z","url":null,"abstract":"<p>In this paper we have found a number of commutator formulas between the weighted divergence, the weighted Laplacian, the weighted Lichnerowicz Laplacian and the Lie derivtive on closed orientable gradient Ricci shrinkers, then using them we have generalized a Theorem of Cao and Zhu about the necessary condition for linear stability of a gradient Ricci shrinker. Recentlly they have also extended our results.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141611544","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 m-Closure of Ideals in LBI-Subalgebras 论 LBI 子代数中的 m 闭合顶点
IF 0.7 4区 数学
Bulletin of The Iranian Mathematical Society Pub Date : 2024-07-11 DOI: 10.1007/s41980-024-00884-x
Masoumeh Etebar, Mehdi Parsinia, Alireza Salehi
{"title":"On m-Closure of Ideals in LBI-Subalgebras","authors":"Masoumeh Etebar, Mehdi Parsinia, Alireza Salehi","doi":"10.1007/s41980-024-00884-x","DOIUrl":"https://doi.org/10.1007/s41980-024-00884-x","url":null,"abstract":"<p>Let <i>C</i>(<i>X</i>) be the ring of all continuous real-valued functions on a completely regular Hausdorff space <i>X</i>. A subalgebra <i>A</i>(<i>X</i>) of <i>C</i>(<i>X</i>) is said to be closed under local bounded inversion, briefly an <i>LBI</i>-subalgebra, if for every function <i>f</i> in <i>A</i>(<i>X</i>) that is bounded away from zero on a cozero-set <i>E</i> of <i>X</i>, there exists <span>(gin A(X))</span> such that <span>(fg|_E=1)</span>. In this paper, for an <i>LBI</i>-subalgebra <i>A</i>(<i>X</i>) the compactification <span>(beta _AX)</span> of <i>X</i> which is homeomorphic with the structure space of <i>A</i>(<i>X</i>) is investigated. Some properties of <span>(beta _AX)</span> similar to the counterparts in <span>(beta X)</span> and some main differences between these compactifications are given. Using the compactification <span>(beta _AX)</span>, we establish an <i>m</i>-closure formula for ideals in a class of <i>LBI</i>-subalgebras which provides a generalization of <i>m</i>-closure of ideals in intermediate algebras of <i>C</i>(<i>X</i>) and <span>(C_c(X))</span>. We also investigate a characterization of <span>(beta )</span>-ideals for <i>LBI</i>-subalgebras from which it turns out that <i>m</i>-closed ideals coincide with <span>(beta )</span>-ideals in that class of <i>LBI</i>-subalgebras.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141584763","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
Derived Analytic Geometry for $$mathbb {Z}$$ -Valued Functions Part I: Topological Properties $$mathbb {Z}$$ 值函数的衍生解析几何 第一部分：拓扑特性
IF 0.7 4区 数学
Bulletin of The Iranian Mathematical Society Pub Date : 2024-07-09 DOI: 10.1007/s41980-024-00879-8
Federico Bambozzi, Tomoki Mihara
{"title":"Derived Analytic Geometry for $$mathbb {Z}$$ -Valued Functions Part I: Topological Properties","authors":"Federico Bambozzi, Tomoki Mihara","doi":"10.1007/s41980-024-00879-8","DOIUrl":"https://doi.org/10.1007/s41980-024-00879-8","url":null,"abstract":"<p>We study the Banach algebras <span>(textrm{C}(X, R))</span> of continuous functions from a compact Hausdorff topological space <i>X</i> to a Banach ring <i>R</i> whose topology is discrete. We prove that the Berkovich spectrum of <span>(textrm{C}(X, R))</span> is homeomorphic to <span>(zeta (X) times mathscr {M}(R))</span>, where <span>(zeta (X))</span> is the Banaschewski compactification of <i>X</i> and <span>(mathscr {M}(R))</span> is the Berkovich spectrum of <i>R</i>. We study how the topology of the spectrum of <span>(textrm{C}(X, R))</span> is related to the notion of homotopy Zariski open embedding used in derived geometry. We find that the topology of <span>(zeta (X))</span> can be easily reconstructed from the homotopy Zariski topology associated with <span>(textrm{C}(X, R))</span>. We also prove some results about the existence of Schauder bases on <span>(textrm{C}(X, R))</span> and a generalization of the Stone–Weierstrass Theorem, under suitable hypotheses on <i>X</i> and <i>R</i>.\u0000</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573065","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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