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On asymptotics for lacunary partition functions 关于裂隙分割函数的渐近论
IF 1.6 3区 数学
Mathematica Slovaca Pub Date : 2024-07-01 DOI: 10.1515/ms-2024-0046
Alexander E. Patkowski
{"title":"On asymptotics for lacunary partition functions","authors":"Alexander E. Patkowski","doi":"10.1515/ms-2024-0046","DOIUrl":"https://doi.org/10.1515/ms-2024-0046","url":null,"abstract":"We give asymptotic analysis of power series associated with lacunary partition functions. New partition theoretic interpretations of some basic hypergeometric series are offered as examples.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141511876","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
A topological duality for tense modal pseudocomplemented De Morgan algebras 时态模态伪补德摩根代数的拓扑对偶性
IF 1.6 3区 数学
Mathematica Slovaca Pub Date : 2024-07-01 DOI: 10.1515/ms-2024-0041
Gustavo Pelaitay, Maia Starobinsky
{"title":"A topological duality for tense modal pseudocomplemented De Morgan algebras","authors":"Gustavo Pelaitay, Maia Starobinsky","doi":"10.1515/ms-2024-0041","DOIUrl":"https://doi.org/10.1515/ms-2024-0041","url":null,"abstract":"In this paper, we define and study the variety of tense modal pseudocomplemented De Morgan algebras. This variety is a proper subvariety of the variety of tense tetravalent modal algebras. A tense modal pseudocomplemented De Morgan algebra is a modal pseudocomplemented De Morgan algebra endowed with two tense operators <jats:italic>G</jats:italic> and <jats:italic>H</jats:italic> satisfying additional conditions. Also, the variety of tense modal pseudocomplemented De Morgan algebras is intimately connected with some well-known varieties of De Morgan algebras with tense operators.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141511874","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Global existence and multiplicity of positive solutions for anisotropic eigenvalue problems 各向异性特征值问题正解的全局存在性和多重性
IF 1.6 3区 数学
Mathematica Slovaca Pub Date : 2024-07-01 DOI: 10.1515/ms-2024-0051
Zhenhai Liu, Nikolaos S. Papageorgiou
{"title":"Global existence and multiplicity of positive solutions for anisotropic eigenvalue problems","authors":"Zhenhai Liu, Nikolaos S. Papageorgiou","doi":"10.1515/ms-2024-0051","DOIUrl":"https://doi.org/10.1515/ms-2024-0051","url":null,"abstract":"We consider an eigenvalue problem driven by the anisotropic (<jats:italic>p</jats:italic>, <jats:italic>q</jats:italic>)-Laplacian and with a Carathéodory reaction which is (<jats:italic>p</jats:italic>(<jats:italic>z</jats:italic>) − 1)-sublinear as <jats:italic>x</jats:italic> → + ∞. We look for positive solutions. We prove an existence, nonexistence and multiplicity theorem which is global in the parameter λ &gt; 0, that is, we prove a bifurcation-type theorem which describes in an exact way the changes in the set of positive solutions as the parameter λ varies on ℝ̊<jats:sub>+</jats:sub> = (0, + ∞).","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141511868","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 𝓐-generators of the polynomial algebra as a module over the Steenrod algebra, I 关于多项式代数的𝓐生成器作为斯泰恩罗德代数上的模块，I
IF 1.6 3区 数学
Mathematica Slovaca Pub Date : 2024-07-01 DOI: 10.1515/ms-2024-0058
Nguyen Khac Tin, Phan Phuong Dung, Hoang Nguyen Ly
{"title":"On the 𝓐-generators of the polynomial algebra as a module over the Steenrod algebra, I","authors":"Nguyen Khac Tin, Phan Phuong Dung, Hoang Nguyen Ly","doi":"10.1515/ms-2024-0058","DOIUrl":"https://doi.org/10.1515/ms-2024-0058","url":null,"abstract":"Let 𝓟<jats:sub> <jats:italic>n</jats:italic> </jats:sub> := <jats:italic>H</jats:italic> <jats:sup>*</jats:sup>((ℝ<jats:italic>P</jats:italic> <jats:sup>∞</jats:sup>)<jats:sup> <jats:italic>n</jats:italic> </jats:sup>) ≅ ℤ<jats:sub>2</jats:sub>[<jats:italic>x</jats:italic> <jats:sub>1</jats:sub>, <jats:italic>x</jats:italic> <jats:sub>2</jats:sub>, …, <jats:italic>x</jats:italic> <jats:sub> <jats:italic>n</jats:italic> </jats:sub>] be the graded polynomial algebra over ℤ<jats:sub>2</jats:sub>, where ℤ<jats:sub>2</jats:sub> denotes the prime field of two elements. We investigate the Peterson hit problem for the polynomial algebra 𝓟<jats:sub> <jats:italic>n</jats:italic> </jats:sub>, viewed as a graded left module over the mod-2 Steenrod algebra, 𝓐. For <jats:italic>n</jats:italic> &gt; 4, this problem is still unsolved, even in the case of <jats:italic>n</jats:italic> = 5 with the help of computers. In this article, we study the hit problem for the case <jats:italic>n</jats:italic> = 6 in the generic degree <jats:italic>d<jats:sub>r</jats:sub> </jats:italic> = 6(2<jats:sup> <jats:italic>r</jats:italic> </jats:sup> − 1) + 4.2<jats:sup> <jats:italic>r</jats:italic> </jats:sup> with <jats:italic>r</jats:italic> an arbitrary non-negative integer. By considering ℤ<jats:sub>2</jats:sub> as a trivial 𝓐-module, then the hit problem is equivalent to the problem of finding a basis of ℤ<jats:sub>2</jats:sub>-vector space ℤ<jats:sub>2</jats:sub> ⊗<jats:sub>𝓐</jats:sub>𝓟<jats:sub> <jats:italic>n</jats:italic> </jats:sub>. The main goal of the current article is to explicitly determine an admissible monomial basis of the ℤ<jats:sub>2</jats:sub> vector space ℤ<jats:sub>2</jats:sub> ⊗<jats:sub>𝓐</jats:sub>𝓟<jats:sub>6</jats:sub> in some degrees. As an application, the behavior of the sixth Singer algebraic transfer in the degree 6(2<jats:sup> <jats:italic>r</jats:italic> </jats:sup> − 1) + 4.2<jats:sup> <jats:italic>r</jats:italic> </jats:sup> is also discussed at the end of this paper.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141511869","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Gröbner bases in the mod 2 cohomology of oriented Grassmann manifolds G͠ 2 t,3 面向格拉斯曼流形 G͠ 2 t,3 的模 2 同调中的格氏基
IF 1.6 3区 数学
Mathematica Slovaca Pub Date : 2024-05-28 DOI: 10.1515/ms-2024-0015
Uroš A. Colović, Branislav I. Prvulović
{"title":"Gröbner bases in the mod 2 cohomology of oriented Grassmann manifolds G͠ 2 t,3","authors":"Uroš A. Colović, Branislav I. Prvulović","doi":"10.1515/ms-2024-0015","DOIUrl":"https://doi.org/10.1515/ms-2024-0015","url":null,"abstract":"For <jats:italic>n</jats:italic> a power of two, we give a complete description of the cohomology algebra <jats:italic>H</jats:italic> <jats:sup>*</jats:sup>(<jats:italic>G͠</jats:italic> <jats:sub> <jats:italic>n</jats:italic>,3</jats:sub>; ℤ<jats:sub>2</jats:sub>) of the Grassmann manifold <jats:italic>G͠</jats:italic> <jats:sub> <jats:italic>n</jats:italic>,3</jats:sub> of oriented 3-planes in ℝ<jats:sup> <jats:italic>n</jats:italic> </jats:sup>. We do this by finding a reduced Gröbner basis for an ideal closely related to this cohomology algebra. Using this Gröbner basis we also present an additive basis for <jats:italic>H</jats:italic> <jats:sup>*</jats:sup>(<jats:italic>G͠</jats:italic> <jats:sub> <jats:italic>n</jats:italic>,3</jats:sub>; ℤ<jats:sub>2</jats:sub>).","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141168455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Class of bounds of the generalized Volterra functions 广义 Volterra 函数的边界类别
IF 1.6 3区 数学
Mathematica Slovaca Pub Date : 2024-05-28 DOI: 10.1515/ms-2024-0028
Khaled Mehrez, Kamel Brahim, Sergei M. Sitnik
{"title":"Class of bounds of the generalized Volterra functions","authors":"Khaled Mehrez, Kamel Brahim, Sergei M. Sitnik","doi":"10.1515/ms-2024-0028","DOIUrl":"https://doi.org/10.1515/ms-2024-0028","url":null,"abstract":"In the present paper, we prove the monotonicity property of the ratios of the generalized Volterra function. As consequences, new and interesting monotonicity concerning ratios of the exponential integral function, as well as it yields some new functional inequalities including Turán-type inequalities. Moreover, two-side bounding inequalities are then obtained for the generalized Volterra function. The main mathematical tools are some integral inequalities. As applications, a few of upper and lower bound inequalities for the exponential integral function are derived. The various results, which are established in this paper, are presumably new, and their importance is illustrated by several interesting consequences and examples accompanied by graphical representations to substantiate the accuracy of the obtained results. Some potential directions for analogous further research on the subject of the present investigation are indicated in the concluding section.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141168525","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Non-commutative effect algebras, L-algebras, and local duality 非交换效应代数、L代数和局部对偶性
IF 1.6 3区 数学
Mathematica Slovaca Pub Date : 2024-05-28 DOI: 10.1515/ms-2024-0034
Wolfgang Rump
{"title":"Non-commutative effect algebras, L-algebras, and local duality","authors":"Wolfgang Rump","doi":"10.1515/ms-2024-0034","DOIUrl":"https://doi.org/10.1515/ms-2024-0034","url":null,"abstract":"GPE-algebras were introduced by Dvurečenskij and Vetterlein as unbounded pseudo-effect algebras. Recently, they have been characterized as partial <jats:italic>L</jats:italic>-algebras with local duality. In the present paper, GPE-algebras with an everywhere defined <jats:italic>L</jats:italic>-algebra operation are investigated. For example, linearly ordered GPE-algebra are of that type. They are characterized by their self-similar closures which are represented as negative cones of totally ordered groups. More generally, GPE-algebras with an everywhere defined multiplication are identified as negative cones of directed groups. If their partial <jats:italic>L</jats:italic>-algebra structure is globally defined, the enveloping group is lattice-ordered. For any self-similar <jats:italic>L</jats:italic>-algebra <jats:italic>A</jats:italic>, exponent maps are introduced, generalizing conjugation in the structure group. It is proved that the exponent maps are <jats:italic>L</jats:italic>-algebra automorphisms of <jats:italic>A</jats:italic> if and only if <jats:italic>A</jats:italic> is a GPE-algebra. As an application, a new characterization of cone algebras is obtained. Lattice GPE-algebras are shown to be equivalent to ∧-closed <jats:italic>L</jats:italic>-algebras with local duality.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141168538","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Decomposition in direct sum of seminormed vector spaces and Mazur–Ulam theorem 半规范向量空间直接和中的分解与马祖尔-乌兰定理
IF 1.6 3区 数学
Mathematica Slovaca Pub Date : 2024-05-28 DOI: 10.1515/ms-2024-0010
Oleksiy Dovgoshey, Jürgen Prestin, Igor Shevchuk
{"title":"Decomposition in direct sum of seminormed vector spaces and Mazur–Ulam theorem","authors":"Oleksiy Dovgoshey, Jürgen Prestin, Igor Shevchuk","doi":"10.1515/ms-2024-0010","DOIUrl":"https://doi.org/10.1515/ms-2024-0010","url":null,"abstract":"It was proved by S. Mazur and S. Ulam in 1932 that every isometric surjection between normed real vector spaces is affine. We generalize the Mazur–Ulam theorem and find necessary and sufficient conditions under which distance-preserving mappings between seminormed real vector spaces are linear.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141168635","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Solving Fredholm integro-differential equations involving integral condition: A new numerical method 求解涉及积分条件的弗雷德霍尔积分微分方程：一种新的数值方法
IF 1.6 3区 数学
Mathematica Slovaca Pub Date : 2024-05-28 DOI: 10.1515/ms-2024-0031
Zhazira Kadirbayeva, Elmira Bakirova, Agila Tleulessova
{"title":"Solving Fredholm integro-differential equations involving integral condition: A new numerical method","authors":"Zhazira Kadirbayeva, Elmira Bakirova, Agila Tleulessova","doi":"10.1515/ms-2024-0031","DOIUrl":"https://doi.org/10.1515/ms-2024-0031","url":null,"abstract":"In this work we investigate a nonlocal problem for the Fredholm integro-differential equation involving integral condition. The main tool used in our considerations is Dzhumabaev parametrization method. We make use of the numerical implementation of the Dzhumabaev parametrization method to obtain the desired result, which is well-supported with numerical examples.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141168524","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 von Bahr–Esseen inequality for pairwise independent random vectors in Hilbert spaces with applications to mean convergence 论希尔伯特空间中成对独立随机向量的 von Bahr-Esseen 不等式及其在均值收敛中的应用
IF 1.6 3区 数学
Mathematica Slovaca Pub Date : 2024-05-28 DOI: 10.1515/ms-2024-0016
Nguyen Chi Dzung, Nguyen Thi Thanh Hien
{"title":"On the von Bahr–Esseen inequality for pairwise independent random vectors in Hilbert spaces with applications to mean convergence","authors":"Nguyen Chi Dzung, Nguyen Thi Thanh Hien","doi":"10.1515/ms-2024-0016","DOIUrl":"https://doi.org/10.1515/ms-2024-0016","url":null,"abstract":"In this correspondence, we prove the von Bahr–Esseen moment inequality for pairwise independent random vectors in Hilbert spaces. Our constant in the von Bahr–Esseen moment inequality is better than that obtained for the real-valued random variables by Chen et al. [<jats:italic>The von Bahr–Esseen moment inequality for pairwise independent random variables and applications</jats:italic>, J. Math. Anal. Appl. 419 (2014), 1290–1302], and Chen and Sung [<jats:italic>Generalized Marcinkiewicz–Zygmund type inequalities for random variables and applications</jats:italic>, J. Math. Inequal. 10(3) (2016), 837–848]. The result is then applied to obtain mean convergence theorems for triangular arrays of rowwise and pairwise independent random vectors in Hilbert spaces. Some results in the literature are extended.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141170124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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