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Positive bases, cones, Helly-type theorems 正基、锥体、赫利型定理
IF 1.6 3区 数学
Mathematica Slovaca Pub Date : 2024-07-01 DOI: 10.1515/ms-2024-0054
Imre Bárány
{"title":"Positive bases, cones, Helly-type theorems","authors":"Imre Bárány","doi":"10.1515/ms-2024-0054","DOIUrl":"https://doi.org/10.1515/ms-2024-0054","url":null,"abstract":"Assume that <jats:italic>k</jats:italic> ≤ <jats:italic>d</jats:italic> is a positive integer and 𝓒 is a finite collection of convex bodies in ℝ<jats:sup> <jats:italic>d</jats:italic> </jats:sup>. We prove a Helly-type theorem: If for every subfamily 𝓒<jats:sup>*</jats:sup> ⊂ 𝓒 of size at most max{<jats:italic>d</jats:italic> + 1, 2(<jats:italic>d</jats:italic> – <jats:italic>k</jats:italic> + 1)} the set ⋂ 𝓒<jats:sup>*</jats:sup> contains a <jats:italic>k</jats:italic>-dimensional cone, then so does ⋂ 𝓒. One ingredient in the proof is another Helly-type theorem about the dimension of lineality spaces of convex cones.","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":"141511864","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 nonlinear Filbert-like matrix with three free parameters: From linearity to nonlinearity 具有三个自由参数的非线性菲尔伯特类矩阵：从线性到非线性
IF 1.6 3区 数学
Mathematica Slovaca Pub Date : 2024-07-01 DOI: 10.1515/ms-2024-0044
Emrah Kiliç, Didem Ersanli
{"title":"A nonlinear Filbert-like matrix with three free parameters: From linearity to nonlinearity","authors":"Emrah Kiliç, Didem Ersanli","doi":"10.1515/ms-2024-0044","DOIUrl":"https://doi.org/10.1515/ms-2024-0044","url":null,"abstract":"Filbert and Lilbert matrices are defined by terms of <jats:italic>linear</jats:italic> Fibonacci-like sequences. By considering terms of such linear recurrences and additional free parameters, we define a nonlinear variant of these matrices via ratios of <jats:italic>q</jats:italic>-forms of terms of Fibonacci-like sequences whose indices are in nonlinear forms. We derive explicit formulae for the matrices <jats:italic>L</jats:italic> and <jats:italic>U</jats:italic> come from <jats:italic>LU</jats:italic>-decomposition, their inverses, inverse of the main matrices and their determinants.","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":"141511875","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
Influence of ideals in compactifications 理想在压缩中的影响
IF 1.6 3区 数学
Mathematica Slovaca Pub Date : 2024-07-01 DOI: 10.1515/ms-2024-0056
Manoranjan Singha, Sima Roy
{"title":"Influence of ideals in compactifications","authors":"Manoranjan Singha, Sima Roy","doi":"10.1515/ms-2024-0056","DOIUrl":"https://doi.org/10.1515/ms-2024-0056","url":null,"abstract":"One point compactification is studied in the light of ideal of subsets of ℕ. 𝓘-proper map is introduced and showed that a continuous map can be extended continuously to the one point 𝓘-compactification if and only if the map is 𝓘-proper. Nowhere tallness, introduced by P. Matet and J. Pawlikowski in [J. Symb. Log. 63(3) (1998), 1040–1054], plays an important role in this article to study various properties of 𝓘-proper maps. It is seen that one point 𝓘-compactification of a topological space may fail to be Hausdorff even if the underlying topological space is Hausdorff but a class {𝓘} of ideals has been identified for which one point 𝓘-compactification coincides with the one point compactification if the underlying topological space is metrizable. Let’s speak our minds that the results in this article will look elegant if one looks at it from a topological angle.","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":"141511873","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 universality in short intervals for zeta-functions of certain cusp forms 论某些顶点形式的zeta函数在短区间内的普遍性
IF 1.6 3区 数学
Mathematica Slovaca Pub Date : 2024-07-01 DOI: 10.1515/ms-2024-0045
Antanas Laurinčikas, Darius Šiaučiūnas
{"title":"On universality in short intervals for zeta-functions of certain cusp forms","authors":"Antanas Laurinčikas, Darius Šiaučiūnas","doi":"10.1515/ms-2024-0045","DOIUrl":"https://doi.org/10.1515/ms-2024-0045","url":null,"abstract":"In this paper, we consider universality in short intervals for the zeta-function attached to a normalized Hecke-eigen cusp form with respect to the modular group. For this, we apply a conjecture for the mean square in short interval on the critical strip for that zeta-function. The proof of the obtained universality theorem is based on a probabilistic limit theorem in the space of analytic functions.","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":"141511863","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 a solvable difference equations system of second order its solutions are related to a generalized Mersenne sequence 关于可解二阶差分方程系统，其解与广义梅森序列有关
IF 1.6 3区 数学
Mathematica Slovaca Pub Date : 2024-07-01 DOI: 10.1515/ms-2024-0053
Murad Khan Hassani, Nouressadat Touafek, Yasin Yazlik
{"title":"On a solvable difference equations system of second order its solutions are related to a generalized Mersenne sequence","authors":"Murad Khan Hassani, Nouressadat Touafek, Yasin Yazlik","doi":"10.1515/ms-2024-0053","DOIUrl":"https://doi.org/10.1515/ms-2024-0053","url":null,"abstract":"In this paper, we consider a class of two-dimensional nonlinear difference equations system of second order, which is a considerably extension of some recent results in the literature. Our main results show that class of system of difference equations is solvable in closed form theoretically. It is noteworthy that the solutions of aforementioned system are associated with generalized Mersenne numbers. The asymptotic behavior of solution to aforementioned system of difference equations when <jats:italic>a</jats:italic> = <jats:italic>b</jats:italic> and <jats:italic>p</jats:italic> = 0 are also given. Finally, numerical examples are given to support the theoretical results presented in 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":"141511867","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
New q-analogues of Van Hamme’s (F.2) supercongruence and of some related supercongruences 范哈姆（F.2）超共融和一些相关超共融的新 q-analogues
IF 1.6 3区 数学
Mathematica Slovaca Pub Date : 2024-07-01 DOI: 10.1515/ms-2024-0048
Qiuxia Hu
{"title":"New q-analogues of Van Hamme’s (F.2) supercongruence and of some related supercongruences","authors":"Qiuxia Hu","doi":"10.1515/ms-2024-0048","DOIUrl":"https://doi.org/10.1515/ms-2024-0048","url":null,"abstract":"In terms of a very-well-poised <jats:sub>6</jats:sub> <jats:italic>ϕ</jats:italic> <jats:sub>5</jats:sub> summation formula, the creative microscoping method recently introduced by Guo and Zudilin, and the Chinese remainder theorem for coprime polynomials, we establish four new <jats:italic>q</jats:italic>-supercongruences for truncated basic hypergeometric series. One of these results is a new <jats:italic>q</jats:italic>-analogue of the (F.2) supercongruence of Van Hamme.","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":"141511935","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
Fibonacci numbers as mixed concatenations of Fibonacci and Lucas numbers 斐波那契数是斐波那契数和卢卡斯数的混合并集
IF 1.6 3区 数学
Mathematica Slovaca Pub Date : 2024-07-01 DOI: 10.1515/ms-2024-0042
Alaa Altassan, Murat Alan
{"title":"Fibonacci numbers as mixed concatenations of Fibonacci and Lucas numbers","authors":"Alaa Altassan, Murat Alan","doi":"10.1515/ms-2024-0042","DOIUrl":"https://doi.org/10.1515/ms-2024-0042","url":null,"abstract":"Let (<jats:italic>F<jats:sub>n</jats:sub> </jats:italic>)<jats:sub> <jats:italic>n</jats:italic>≥0</jats:sub> and (<jats:italic>L<jats:sub>n</jats:sub> </jats:italic>)<jats:sub> <jats:italic>n</jats:italic>≥0</jats:sub> be the Fibonacci and Lucas sequences, respectively. In this paper we determine all Fibonacci numbers which are mixed concatenations of a Fibonacci and a Lucas numbers. By mixed concatenations of <jats:italic>a</jats:italic> and <jats:italic>b</jats:italic>, we mean the both concatenations <jats:overline> <jats:italic>ab</jats:italic> </jats:overline> and <jats:overline> <jats:italic>ba</jats:italic> </jats:overline> together, where <jats:italic>a</jats:italic> and <jats:italic>b</jats:italic> are any two nonnegative integers. So, the mathematical formulation of this problem leads us searching the solutions of two Diophantine equations <jats:italic>F<jats:sub>n</jats:sub> </jats:italic> = 10<jats:sup> <jats:italic>d</jats:italic> </jats:sup> <jats:italic>F<jats:sub>m</jats:sub> </jats:italic> + <jats:italic>L<jats:sub>k</jats:sub> </jats:italic> and <jats:italic>F<jats:sub>n</jats:sub> </jats:italic> = 10<jats:sup> <jats:italic>d</jats:italic> </jats:sup> <jats:italic>L<jats:sub>m</jats:sub> </jats:italic> + <jats:italic>F<jats:sub>k</jats:sub> </jats:italic> in nonnegative integers (<jats:italic>n</jats:italic>, <jats:italic>m</jats:italic>, <jats:italic>k</jats:italic>), where <jats:italic>d</jats:italic> denotes the number of digits of <jats:italic>L<jats:sub>k</jats:sub> </jats:italic> and <jats:italic>F<jats:sub>k</jats:sub> </jats:italic>, respectively. We use lower bounds for linear forms in logarithms and reduction method in Diophantine approximation to get the results.","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":"141511865","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
Kneser-type oscillation theorems for second-order functional differential equations with unbounded neutral coefficients 具有无约束中性系数的二阶函数微分方程的克奈瑟型振荡定理
IF 1.6 3区 数学
Mathematica Slovaca Pub Date : 2024-07-01 DOI: 10.1515/ms-2024-0049
Irena Jadlovská, George E. Chatzarakis, Ercan Tunç
{"title":"Kneser-type oscillation theorems for second-order functional differential equations with unbounded neutral coefficients","authors":"Irena Jadlovská, George E. Chatzarakis, Ercan Tunç","doi":"10.1515/ms-2024-0049","DOIUrl":"https://doi.org/10.1515/ms-2024-0049","url":null,"abstract":"In this paper, we initiate the study of asymptotic and oscillatory properties of solutions to second-order functional differential equations with noncanonical operators and unbounded neutral coefficients, using a recent method of iteratively improved monotonicity properties of nonoscillatory solutions. Our results rely on ideas that essentially improve standard techniques for the investigation of differential equations with unbounded neutral terms with delay or advanced argument. The core of the method is presented in a form that suggests further generalizations for higher-order differential equations with unbounded neutral coefficients.","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":"141511878","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 bivariate distribution with generalized exponential conditionals 具有广义指数条件的二元分布
IF 1.6 3区 数学
Mathematica Slovaca Pub Date : 2024-07-01 DOI: 10.1515/ms-2024-0059
Božidar V. Popović, Ali İ. Genç, Miroslav M. Ristić
{"title":"A bivariate distribution with generalized exponential conditionals","authors":"Božidar V. Popović, Ali İ. Genç, Miroslav M. Ristić","doi":"10.1515/ms-2024-0059","DOIUrl":"https://doi.org/10.1515/ms-2024-0059","url":null,"abstract":"In this work, we construct a new bivariate statistical distribution by the conditionally specified model approach. The conditional distributions follow the well-known generalized exponential distribution which includes the ordinary exponential distribution and is more flexible than gamma and Weibull in some ways. The newly defined distribution has four parameters that increase the flexibility of the model in data fitting. By equating the dependence parameter to zero, the marginal distributions become independent generalized exponential distributions. The new bivariate distribution depends on the classical exponential integral function which is not difficult to evaluate numerically. The basic properties of the distribution such as distribution functions, moments and stress-strength reliability are derived. The parameters are estimated by the method of maximum likelihood. Two real data fitting applications prove its usefulness in case of negatively correlated bivariate data modelling.","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":"141511872","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 Paley graph of a quadratic character 关于二次函数的帕利图形
IF 1.6 3区 数学
Mathematica Slovaca Pub Date : 2024-07-01 DOI: 10.1515/ms-2024-0040
Ján Mináč, Lyle Muller, Tung T. Nguyen, Nguyễn Duy Tân
{"title":"On the Paley graph of a quadratic character","authors":"Ján Mináč, Lyle Muller, Tung T. Nguyen, Nguyễn Duy Tân","doi":"10.1515/ms-2024-0040","DOIUrl":"https://doi.org/10.1515/ms-2024-0040","url":null,"abstract":"Paley graphs form a nice link between the distribution of quadratic residues and graph theory. These graphs possess remarkable properties which make them useful in several branches of mathematics. Classically, for each prime number <jats:italic>p</jats:italic> we can construct the corresponding Paley graph using quadratic and non-quadratic residues modulo <jats:italic>p</jats:italic>. Therefore, Paley graphs are naturally associated with the Legendre symbol at <jats:italic>p</jats:italic> which is a quadratic Dirichlet character of conductor <jats:italic>p</jats:italic>. In this article, we introduce the generalized Paley graphs. These are graphs that are associated with a general quadratic Dirichlet character. We will then provide some of their basic properties. In particular, we describe their spectrum explicitly. We then use those generalized Paley graphs to construct some new families of Ramanujan graphs. Finally, using special values of <jats:italic>L</jats:italic>-functions, we provide an effective upper bound for their Cheeger number. As a by-product of our approach, we settle a question raised in [Cramer et al.: <jats:italic>The isoperimetric and Kazhdan constants associated to a Paley graph</jats:italic>, Involve 9 (2016), 293–306] about the size of this upper bound.","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":"141511866","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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