Bulletin of The Iranian Mathematical Society最新文献

{"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":null,"pages":null},"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}

{"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":null,"pages":null},"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}

{"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":null,"pages":null},"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}

{"title":"Inclusion Matrices for Rainbow Subsets","authors":"Chengyang Qian, Yaokun Wu, Yanzhen Xiong","doi":"10.1007/s41980-023-00829-w","DOIUrl":"https://doi.org/10.1007/s41980-023-00829-w","url":null,"abstract":"<p>Let <span>(text {S})</span> be a finite set, each element of which receives a color. A rainbow <i>t</i>-set of <span>(text {S})</span> is a <i>t</i>-subset of <span>(text {S})</span> in which different elements receive different colors. Let <span>(left( {begin{array}{c}text {S} tend{array}}right) )</span> denote the set of all rainbow <i>t</i>-sets of <span>(text {S})</span>, let <span>(left( {begin{array}{c}text {S} le tend{array}}right) )</span> represent the union of <span>(left( {begin{array}{c}text {S} iend{array}}right) )</span> for <span>(i=0,ldots , t)</span>, and let <span>(2^text {S})</span> stand for the set of all rainbow subsets of <span>(text {S})</span>. The rainbow inclusion matrix <span>(mathcal {W}^{text {S}})</span> is the <span>(2^text {S}times 2^{text {S}})</span> (0, 1) matrix whose (<i>T</i>, <i>K</i>)-entry is one if and only if <span>(Tsubseteq K)</span>. We write <span>(mathcal {W}_{t,k}^{text {S}})</span> and <span>(mathcal {W}_{le t,k}^{text {S}})</span> for the <span>(left( {begin{array}{c}text {S} tend{array}}right) times left( {begin{array}{c}text {S} kend{array}}right) )</span> submatrix and the <span>(left( {begin{array}{c}text {S} le tend{array}}right) times left( {begin{array}{c}text {S} kend{array}}right) )</span> submatrix of <span>(mathcal {W}^{text {S}})</span>, respectively, and so on. We determine the diagonal forms and the ranks of <span>(mathcal {W}_{t,k}^{text {S}})</span> and <span>(mathcal {W}_{le t,k}^{text {S}})</span>. We further calculate the singular values of <span>(mathcal {W}_{t,k}^{text {S}})</span> and construct accordingly a complete system of <span>((0,pm 1))</span> eigenvectors for them when the numbers of elements receiving any two given colors are the same. Let <span>(mathcal {D}^{text {S}}_{t,k})</span> denote the integral lattice orthogonal to the rows of <span>(mathcal {W}_{le t,k}^{text {S}})</span> and let <span>(overline{mathcal {D}}^{text {S}}_{t,k})</span> denote the orthogonal lattice of <span>(mathcal {D}^{text {S}}_{t,k})</span>. We make use of Frankl rank to present a <span>((0,pm 1))</span> basis of <span>(mathcal {D}^{text {S}}_{t,k})</span> and a (0, 1) basis of <span>(overline{mathcal {D}}^{text {S}}_{t,k})</span>. For any commutative ring <i>R</i>, those nonzero functions <span>(fin R^{2^{text {S}}})</span> satisfying <span>(mathcal {W}_{t,ge 0}^{text {S}}f=0)</span> are called null <i>t</i>-designs over <i>R</i>, while those satisfying <span>(mathcal {W}_{le t,ge 0}^{text {S}}f=0)</span> are called null <span>((le t))</span>-designs over <i>R</i>. We report some observations on the distributions of the support sizes of null designs as well as the structure of null designs with extremal support sizes.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138631479","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}

{"title":"Existence and Stability of Ulam–Hyers for Neutral Stochastic Functional Differential Equations","authors":"Arunachalam Selvam, Sriramulu Sabarinathan, Sandra Pinelas, Vaidhiyanathan Suvitha","doi":"10.1007/s41980-023-00827-y","DOIUrl":"https://doi.org/10.1007/s41980-023-00827-y","url":null,"abstract":"<p>The primary aim of this paper is to focus on the stability analysis of an advanced neural stochastic functional differential equation with finite delay driven by a fractional Brownian motion in a Hilbert space. We examine the existence and uniqueness of mild solution of <span>( {textrm{d}}left[ {x}_{a}(s) + {mathfrak {g}}(s, {x}_{a}(s - omega (s)))right] =left[ {mathfrak {I}}{x}_a(s) + {mathfrak {f}}(s, {x}_a(s -varrho (s)))right] {textrm{d}}s + varsigma (s){textrm{d}}varpi ^{{mathbb {H}}}(s),)</span> <span>(0le sle {mathcal {T}})</span>, <span>({x}_a(s) = zeta (s), -rho le sle 0. )</span> The main goal of this paper is to investigate the Ulam–Hyers stability of the considered equation. We have also provided numerical examples to illustrate the obtained results. This article also discusses the Euler–Maruyama numerical method through two examples.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138581728","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}

{"title":"Inclusion Properties of the Triangular Ratio Metric Balls","authors":"Oona Rainio","doi":"10.1007/s41980-023-00837-w","DOIUrl":"https://doi.org/10.1007/s41980-023-00837-w","url":null,"abstract":"<p>Inclusion properties are studied for balls of the triangular ratio metric, the hyperbolic metric, the <span>(j^*)</span>-metric, and the distance ratio metric defined in the unit ball domain. Several sharp results are proven and a conjecture about the relation between triangular ratio metric balls and hyperbolic balls is given. An algorithm is also built for drawing triangular ratio circles or three-dimensional spheres.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138504530","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}

{"title":"Super-Simple (v, 5, 2) Directed Designs and Their Smallest Defining Sets with Application in LDPC Codes","authors":"Maryam Mohammadnezhad, Somayye Golalizadeh, Mahsa Boostan, Nasrin Soltankhah","doi":"10.1007/s41980-023-00835-y","DOIUrl":"https://doi.org/10.1007/s41980-023-00835-y","url":null,"abstract":"<p>In this paper, we show that for all <span>(vequiv 0,1)</span> (mod 5) and <span>(vge 15)</span>, there exists a super-simple (<i>v</i>, 5, 2) directed design. Moreover, for these parameters, there exists a super-simple (<i>v</i>, 5, 2) directed design such that its smallest defining sets contain at least half of its blocks. Also, we show that these designs are useful in constructing parity-check matrices of LDPC codes.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138504529","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}

{"title":"A Relativistic Abelian Chern–Simons Model on Graph","authors":"Juan Zhao","doi":"10.1007/s41980-023-00830-3","DOIUrl":"https://doi.org/10.1007/s41980-023-00830-3","url":null,"abstract":"<p>In this paper, we consider a relativistic Abelian Chern–Simons equation </p><span>$$begin{aligned} left{ begin{array}{l} Delta u=lambda left( a(b-a)e^{u}-b(b-a)e^{v}+a^{2}e^{2u}-abe^{2v}+b(b-a)e^{u+v}right) +4pi sum limits _{j=1}^{N_{1}} delta _{p_{j}}, Delta v=lambda left( -b(b-a)e^{u}+a(b-a)e^{v}-abe^{2u} +a^{2}e^{2v}+b(b-a)e^{u+v}right) +4pi sum limits _{j=1}^{N_{2}} delta _{q_{j}}, end{array} right. end{aligned}$$</span><p>on a connected finite graph <span>(G=(V, E))</span>, where <span>(lambda &gt;0)</span> is a constant; <span>(a&gt;b&gt;0)</span>; <span>(N_{1})</span> and <span>(N_{2})</span> are positive integers; <span>(p_{1}, p_{2}, ldots , p_{N_{1}})</span> and <span>(q_{1}, q_{2}, ldots , q_{N_{2}})</span> denote distinct vertices of <i>V</i>. Additionally, <span>(delta _{p_{j}})</span> and <span>(delta _{q_{j}})</span> represent the Dirac delta masses located at vertices <span>(p_{j})</span> and <span>(q_{j})</span>. By employing the method of constrained minimization, we prove that there exists a critical value <span>(lambda _{0})</span>, such that the above equation admits a solution when <span>(lambda ge lambda _{0})</span>. Furthermore, we employ the mountain pass theorem developed by Ambrosetti–Rabinowitz to establish that the equation has at least two solutions when <span>(lambda &gt;lambda _{0})</span>.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138504528","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}

{"title":"The Non-Toric $$U_{q}(sl_{2})$$ -Symmetries on Quantum Polynomial Algebra $$k_{q}[x^{pm 1},y]$$","authors":"Xuejun Xia, Xiaoming Li, Libin Li","doi":"10.1007/s41980-023-00832-1","DOIUrl":"https://doi.org/10.1007/s41980-023-00832-1","url":null,"abstract":"<p>In this paper, we present the complete list of <span>(U_{q}(sl_{2}))</span>-symmetries on quantum polynomial algebra <span>(k_q[x^{pm 1},y])</span> in the case that the action of the generator <i>K</i> of <span>(U_{q}(sl_{2}))</span> is a non-toric automorphism. The conditions for the isomorphism of such structures are explored as well.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138504505","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}

{"title":"Nilpotent Category of Monoidal Category and Tensor–Hom Adjunction","authors":"Yan’en Ni, Yunfei Tan, Yunfei Yi, Yuehui Zhang","doi":"10.1007/s41980-023-00831-2","DOIUrl":"https://doi.org/10.1007/s41980-023-00831-2","url":null,"abstract":"<p>Let <span>(mathcal {C})</span> be an abelian monoidal category. It is proved that the nilpotent category <span>({text {Nil}}(mathcal {C}))</span> of <span>(mathcal {C})</span> admits almost monoidal structure except the unit axiom. As an application, it is proved that Hom and Tensor functors exist over <span>({text {Nil}}(mathcal {C}))</span> and tensor–hom adjunction remains true over the nilpotent category of the category of finite-dimensional vector spaces, which develops some recent results on this topic.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138517420","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}