Mathematica Slovaca最新文献

{"title":"Properties of the symmetric difference in lattices with complementation.","authors":"Václav Cenker, Ivan Chajda, Helmut Länger","doi":"10.1515/ms-2026-0136","DOIUrl":"https://doi.org/10.1515/ms-2026-0136","url":null,"abstract":"<p><p>The symmetric difference in Boolean lattices can be defined in two different but equivalent forms. However, it can be introduced also in every bounded lattice with complementation where these two forms need not coincide. We study lattices with complementation and the variety of such lattices where these two expressions coincide and point out explicitly some interesting subvarieties. Using a result of J. Berman we estimate the size of free algebras in these subvarieties. It is well-known that the symmetric difference is associative in every Boolean lattice. We prove that it is just the property of Boolean lattices, namely the symmetric difference in a lattice with complementation is associative if and only if this lattice is Boolean. Similarly, we prove that a lattice with complementation is Boolean if and only if the symmetric difference satisfies a certain simple identity in two variables. We also characterize lattices with a unary operation satisfying De Morgan's laws.</p>","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"76 3","pages":"591-604"},"PeriodicalIF":0.9,"publicationDate":"2026-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13308693/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148345829","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Equable parallelograms on the Eisenstein lattice","authors":"Christian Aebi, Grant Cairns","doi":"10.1515/ms-2024-0071","DOIUrl":"https://doi.org/10.1515/ms-2024-0071","url":null,"abstract":"This paper studies equable parallelograms whose vertices lie on the Eisenstein lattice. Using Rosenberger’s Theorem on generalised Markov equations, we show that the set of these parallelograms forms naturally an infinite tree, all of whose vertices have degree 4, bar the root which has degree 3. This study naturally complements the authors’ previous study of equable parallelograms whose vertices lie on the integer lattice.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"112 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221514","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}

{"title":"The Maxwell-Boltzmann-Exponential distribution with regression model","authors":"Emrah Altun, Gökçen Altun","doi":"10.1515/ms-2024-0074","DOIUrl":"https://doi.org/10.1515/ms-2024-0074","url":null,"abstract":"This paper proposes a new probability model called as <jats:italic>Maxwell</jats:italic>-<jats:italic>Boltzmann</jats:italic>-<jats:italic>Exponential</jats:italic> (MBE) distribution. The MBE distribution arises as a mixture distribution of the Maxwell-Boltzmann and exponential distributions. The statistical properties of the distributions are studied and obtained in closed-form expressions. Three methodologies are assessed and compared for the estimation of parameters in the MBE distribution. The MBE regression model is defined, with the proposed regression model being an alternative to the gamma regression model for response variables that are extremely right-skewed and bimodal. Two real data sets are used to demonstrate the applicability of the proposed models against the existing models.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"96 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221516","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}

{"title":"Rees short exact sequences and preenvelopes","authors":"XiaoQin Zhang, HuSheng Qiao, TingTing Zhao","doi":"10.1515/ms-2024-0064","DOIUrl":"https://doi.org/10.1515/ms-2024-0064","url":null,"abstract":"In this paper, we consider some properties of commutative diagrams of Rees short exact sequences, and we also investigate the sufficient and necessary condition under which the induced sequences by functors − ⊗ <jats:italic>M</jats:italic> for the left <jats:italic>S</jats:italic>-act <jats:italic>M</jats:italic>. The main conclusions extend some known results. Further, we investigate preenvelopes and precovers in the category 𝓔<jats:sub> <jats:italic>S</jats:italic> </jats:sub> of Rees short exact sequences of right <jats:italic>S</jats:italic>-acts.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"21 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221519","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}

{"title":"Intervals of posets of a zero-divisor graph","authors":"John D. LaGrange","doi":"10.1515/ms-2024-0061","DOIUrl":"https://doi.org/10.1515/ms-2024-0061","url":null,"abstract":"This article is concerned with bounded partially ordered sets <jats:italic>P</jats:italic> such that for every <jats:italic>p</jats:italic> ∈ <jats:italic>P</jats:italic> ∖ {1} there exists <jats:italic>q</jats:italic> ∈ <jats:italic>P</jats:italic> ∖ {0} such that 0 is the only lower bound of {<jats:italic>p</jats:italic>, <jats:italic>q</jats:italic>}. The posets <jats:italic>P</jats:italic> such that <jats:italic>P</jats:italic> ≅ <jats:italic>Q</jats:italic> if and only if <jats:italic>P</jats:italic> and <jats:italic>Q</jats:italic> have isomorphic zero-divisor graphs are completely characterized. In the case of finite posets, this result is generalized by proving that posets with isomorphic zero-divisor graphs form an interval under the partial order given by <jats:italic>P</jats:italic> ≲ <jats:italic>Q</jats:italic> if and only if there exists a bijective poset-homomorphism <jats:italic>P</jats:italic> → <jats:italic>Q</jats:italic>. In particular, the singleton intervals correspond to the posets that are completely determined by their zero-divisor graphs. These results are obtained by exploring universal and couniversal orderings with respect to posets that have isomorphic zero-divisor graphs.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"12 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221522","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}

{"title":"Oscillatory and asymptotic behavior of even-order nonlinear differential equations with mixed neutral terms","authors":"Said R. Grace, Tongxing Li, Gokula Nanda Chhatria","doi":"10.1515/ms-2024-0068","DOIUrl":"https://doi.org/10.1515/ms-2024-0068","url":null,"abstract":"This paper deals with the oscillation and asymptotic behaviour of even order nonlinear differential equations with mixed nonlinear neutral terms. The findings are obtained via utilising an integral criterion as well as a comparison theorem with the oscillatory properties of a first order advanced and/or delay differential equation. We provide novel oscillation criteria that improve, extend, and simplify previously published ones. The results are illustrated by two examples.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"24 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221511","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}

{"title":"On a solvable four-dimensional system of difference equations","authors":"İbrahim Erdem, Yasin Yazlik","doi":"10.1515/ms-2024-0069","DOIUrl":"https://doi.org/10.1515/ms-2024-0069","url":null,"abstract":"In this paper we show that the following four-dimensional system of difference equations &lt;jats:disp-formula&gt; &lt;jats:alternatives&gt; &lt;jats:graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_ms-2024-0069_eq_001.png\"/&gt; &lt;m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"&gt; &lt;m:mtable columnalign=\"center\" rowspacing=\"4pt\" columnspacing=\"1em\"&gt; &lt;m:mtr&gt; &lt;m:mtd&gt; &lt;m:mstyle displaystyle=\"true\"&gt; &lt;m:msub&gt; &lt;m:mi&gt;x&lt;/m:mi&gt; &lt;m:mrow&gt; &lt;m:mi&gt;n&lt;/m:mi&gt; &lt;m:mo&gt;+&lt;/m:mo&gt; &lt;m:mn&gt;1&lt;/m:mn&gt; &lt;/m:mrow&gt; &lt;/m:msub&gt; &lt;m:mo&gt;=&lt;/m:mo&gt; &lt;m:msubsup&gt; &lt;m:mi&gt;y&lt;/m:mi&gt; &lt;m:mrow&gt; &lt;m:mi&gt;n&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mrow&gt; &lt;m:mi&gt;α&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;/m:msubsup&gt; &lt;m:msubsup&gt; &lt;m:mi&gt;z&lt;/m:mi&gt; &lt;m:mrow&gt; &lt;m:mi&gt;n&lt;/m:mi&gt; &lt;m:mo&gt;−&lt;/m:mo&gt; &lt;m:mn&gt;1&lt;/m:mn&gt; &lt;/m:mrow&gt; &lt;m:mrow&gt; &lt;m:mi&gt;β&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;/m:msubsup&gt; &lt;m:mo&gt;,&lt;/m:mo&gt; &lt;m:mspace width=\"1em\"/&gt; &lt;m:msub&gt; &lt;m:mi&gt;y&lt;/m:mi&gt; &lt;m:mrow&gt; &lt;m:mi&gt;n&lt;/m:mi&gt; &lt;m:mo&gt;+&lt;/m:mo&gt; &lt;m:mn&gt;1&lt;/m:mn&gt; &lt;/m:mrow&gt; &lt;/m:msub&gt; &lt;m:mo&gt;=&lt;/m:mo&gt; &lt;m:msubsup&gt; &lt;m:mi&gt;z&lt;/m:mi&gt; &lt;m:mrow&gt; &lt;m:mi&gt;n&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mrow&gt; &lt;m:mi&gt;γ&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;/m:msubsup&gt; &lt;m:msubsup&gt; &lt;m:mi&gt;t&lt;/m:mi&gt; &lt;m:mrow&gt; &lt;m:mi&gt;n&lt;/m:mi&gt; &lt;m:mo&gt;−&lt;/m:mo&gt; &lt;m:mn&gt;1&lt;/m:mn&gt; &lt;/m:mrow&gt; &lt;m:mrow&gt; &lt;m:mi&gt;δ&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;/m:msubsup&gt; &lt;m:mo&gt;,&lt;/m:mo&gt; &lt;m:mspace width=\"1em\"/&gt; &lt;m:msub&gt; &lt;m:mi&gt;z&lt;/m:mi&gt; &lt;m:mrow&gt; &lt;m:mi&gt;n&lt;/m:mi&gt; &lt;m:mo&gt;+&lt;/m:mo&gt; &lt;m:mn&gt;1&lt;/m:mn&gt; &lt;/m:mrow&gt; &lt;/m:msub&gt; &lt;m:mo&gt;=&lt;/m:mo&gt; &lt;m:msubsup&gt; &lt;m:mi&gt;t&lt;/m:mi&gt; &lt;m:mrow&gt; &lt;m:mi&gt;n&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mrow&gt; &lt;m:mi&gt;ϵ&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;/m:msubsup&gt; &lt;m:msubsup&gt; &lt;m:mi&gt;x&lt;/m:mi&gt; &lt;m:mrow&gt; &lt;m:mi&gt;n&lt;/m:mi&gt; &lt;m:mo&gt;−&lt;/m:mo&gt; &lt;m:mn&gt;1&lt;/m:mn&gt; &lt;/m:mrow&gt; &lt;m:mrow&gt; &lt;m:mi&gt;μ&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;/m:msubsup&gt; &lt;m:mo&gt;,&lt;/m:mo&gt; &lt;m:mspace width=\"1em\"/&gt; &lt;m:msub&gt; &lt;m:mi&gt;t&lt;/m:mi&gt; &lt;m:mrow&gt; &lt;m:mi&gt;n&lt;/m:mi&gt; &lt;m:mo&gt;+&lt;/m:mo&gt; &lt;m:mn&gt;1&lt;/m:mn&gt; &lt;/m:mrow&gt; &lt;/m:msub&gt; &lt;m:mo&gt;=&lt;/m:mo&gt; &lt;m:msubsup&gt; &lt;m:mi&gt;x&lt;/m:mi&gt; &lt;m:mrow&gt; &lt;m:mi&gt;n&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mrow&gt; &lt;m:mi&gt;ξ&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;/m:msubsup&gt; &lt;m:msubsup&gt; &lt;m:mi&gt;y&lt;/m:mi&gt; &lt;m:mrow&gt; &lt;m:mi&gt;n&lt;/m:mi&gt; &lt;m:mo&gt;−&lt;/m:mo&gt; &lt;m:mn&gt;1&lt;/m:mn&gt; &lt;/m:mrow&gt; &lt;m:mrow&gt; &lt;m:mi&gt;ρ&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;/m:msubsup&gt; &lt;m:mo&gt;,&lt;/m:mo&gt; &lt;m:mspace width=\"2em\"/&gt; &lt;m:mi&gt;n&lt;/m:mi&gt; &lt;m:mo&gt;∈&lt;/m:mo&gt; &lt;m:msub&gt; &lt;m:mrow&gt; &lt;m:mi mathvariant=\"double-struck\"&gt;N&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mrow&gt; &lt;m:mn&gt;0&lt;/m:mn&gt; &lt;/m:mrow&gt; &lt;/m:msub&gt; &lt;m:mo&gt;,&lt;/m:mo&gt; &lt;/m:mstyle&gt; &lt;/m:mtd&gt; &lt;/m:mtr&gt; &lt;/m:mtable&gt; &lt;/m:math&gt; &lt;jats:tex-math&gt;$$begin{array}{} displaystyle x_{n+1}=y_{n}^{alpha}z_{n-1}^{beta}, quad y_{n+1}=z_{n}^{gamma}t_{n-1}^{delta}, quad z_{n+1}=t_{n}^{epsilon}x_{n-1}^{mu}, quad t_{n+1}=x_{n}^{xi}y_{n-1}^{rho}, qquad nin mathbb{N}_{0}, end{array}$$&lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:disp-formula&gt; where the parameters &lt;jats:italic&gt;α&lt;/jats:italic&gt;, &lt;jats:italic&gt;β&lt;/jats:italic&gt;, &lt;jats:italic&gt;γ&lt;/jats:italic&gt;, &lt;jats:italic&gt;δ&lt;/jats:italic&gt;, &lt;jats:italic&gt;ϵ&lt;/jats:italic&gt;, &lt;jats:italic&gt;μ&lt;/jats:italic&gt;, &lt;jats:italic&gt;ξ&lt;/jats:italic&gt;, &lt;jats:italic&gt;ρ&lt;/jats:italic&gt; ∈ ℤ and the initial values &lt;jats:italic&gt;x&lt;/jats:italic&gt; &lt;jats:sub&gt;–&lt;jats:italic&gt;i&lt;/jats:italic&gt; &lt;/jats:sub&gt;, &lt;jats:italic&gt;y&lt;/jats:italic&gt; &lt;jats:sub&gt;–&lt;jats:italic&gt;i&lt;/jats:italic&gt; &lt;/jats:sub&gt;, &lt;jats:italic&gt;z&lt;/jats:it","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"58 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221513","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}

{"title":"Existence results for a fourth order problem with functional perturbed clamped beam boundary conditions","authors":"Alberto Cabada, Rochdi Jebari, Lucía López-Somoza","doi":"10.1515/ms-2024-0067","DOIUrl":"https://doi.org/10.1515/ms-2024-0067","url":null,"abstract":"In this paper, we study the existence of positive solutions for a fourth order boundary value problem coupled to functional perturbed clamped beam boundary conditions. Our main ingredient is the classical fixed point index. The problem investigated is an extension of other problems studied in previous papers by covering very general nonlocal perturbed conditions on the boundary.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"190 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221523","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}

{"title":"On nonexistence of D(n)-quadruples","authors":"Zrinka Franušić, Ana Jurasić","doi":"10.1515/ms-2024-0063","DOIUrl":"https://doi.org/10.1515/ms-2024-0063","url":null,"abstract":"In this paper, we show that there is no polynomial <jats:italic>D</jats:italic>(<jats:italic>n</jats:italic>)-quadruple in ℤ[<jats:italic>X</jats:italic>] for some polynomials <jats:italic>n</jats:italic> ∈ ℤ[<jats:italic>X</jats:italic>] that are not representable as a difference of squares of two polynomials in ℤ[<jats:italic>X</jats:italic>].","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"7 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221509","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}

{"title":"Induced mappings on the hyperspace of totally disconnected sets","authors":"José G. Anaya, Martha Hernández-Castañeda, David Maya","doi":"10.1515/ms-2024-0077","DOIUrl":"https://doi.org/10.1515/ms-2024-0077","url":null,"abstract":"The symbol <jats:italic>TD</jats:italic>(<jats:italic>X</jats:italic>) denotes the hyperspace of all nonempty totally disconnected compact subsets of a Hausdorff space <jats:italic>X</jats:italic>. This hyperspace is endowed with the Vietoris topology. For a mapping between Hausdorff spaces <jats:italic>f</jats:italic> : <jats:italic>X</jats:italic> → <jats:italic>Y</jats:italic>, define the induced mapping <jats:italic>TD</jats:italic>(<jats:italic>f</jats:italic>) : <jats:italic>TD</jats:italic>(<jats:italic>X</jats:italic>) → <jats:italic>TD</jats:italic>(<jats:italic>Y</jats:italic>) by <jats:italic>TD</jats:italic>(<jats:italic>f</jats:italic>)(<jats:italic>A</jats:italic>) = <jats:italic>f</jats:italic>(<jats:italic>A</jats:italic>) (the image of <jats:italic>A</jats:italic> under <jats:italic>f</jats:italic>). In the current paper, we study the relationships between the condition <jats:italic>f</jats:italic> belongs to a class of mappings between Hausdorff spaces 𝕄 and the condition <jats:italic>TD</jats:italic>(<jats:italic>f</jats:italic>) belongs to 𝕄.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"60 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221524","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}