This paper proposes a new probability model called as Maxwell-Boltzmann-Exponential (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.
{"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":null,"pages":null},"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}
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 − ⊗ M for the left S-act M. The main conclusions extend some known results. Further, we investigate preenvelopes and precovers in the category 𝓔S of Rees short exact sequences of right S-acts.
在本文中，我们考虑了里斯短精确序列交换图的一些性质，还研究了左S行为M的函数- ⊗ M诱导序列的充分必要条件。此外，我们还研究了右 S 行为的里斯短精确序列的𝓔 S 类别中的前包络和前覆盖。
{"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":null,"pages":null},"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}
This article is concerned with bounded partially ordered sets P such that for every p ∈ P ∖ {1} there exists q ∈ P ∖ {0} such that 0 is the only lower bound of {p, q}. The posets P such that P ≅ Q if and only if P and Q 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 P ≲ Q if and only if there exists a bijective poset-homomorphism P → Q. 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.
本文关注有界部分有序集合 P，对于每一个 p∈P ∖ {1} 存在 q∈P ∖ {0} ，使得 0 是 {p, q} 的唯一下界。当且仅当 P 和 Q 具有同构的零分维图形时，P ≅ Q 的正集 P 才具有完全的特征。在有限正集的情况下，通过证明具有同构零因子图的正集在 P ≲ Q 给定的偏序下形成一个区间，当且仅当存在一个双射正集同构 P → Q 时，这一结果得到了推广。这些结果是通过探索与具有同构零分因子图的正集有关的普遍排序和反普遍排序得到的。
{"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":null,"pages":null},"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}
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.
{"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":null,"pages":null},"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}
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.
{"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":null,"pages":null},"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}
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.
{"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":null,"pages":null},"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}
本文证明了以下四维差分方程组 x n + 1 = y n α z n - 1 β , y n + 1 = z n γ t n - 1 δ , z n + 1 = t n ϵ x n - 1 μ , t n + 1 = x n ξ y n - 1 ρ , n∈ N 0 , $$begin{array}{}displaystyle x_{n+1}=y_{n}^{alpha}z_{n-1}^{beta}, quad y_{n+1}=z_{n}^{gamma}t_{n-1}^{delta},quad z_{n+1}=t_{n}^{epsilon}x_{n-1}^{mu}, quad t_{n+1}=x_{n}^{xi}y_{n-1}^{rho}, qquad nin mathbb{N}_{0}、end{array}$$ 其中参数 α, β, γ, δ, ϵ, μ, ξ, ρ∈ ℤ 和初始值 x -i , y -i , z -i , t -i , i∈ {0, 1} 均为实数，可以用封闭形式求解，进一步扩展了文献中的一些结果。
In this paper, we show that there is no polynomial D(n)-quadruple in ℤ[X] for some polynomials n ∈ ℤ[X] that are not representable as a difference of squares of two polynomials in ℤ[X].
{"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":null,"pages":null},"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}
José G. Anaya, Martha Hernández-Castañeda, David Maya
The symbol TD(X) denotes the hyperspace of all nonempty totally disconnected compact subsets of a Hausdorff space X. This hyperspace is endowed with the Vietoris topology. For a mapping between Hausdorff spaces f : X → Y, define the induced mapping TD(f) : TD(X) → TD(Y) by TD(f)(A) = f(A) (the image of A under f). In the current paper, we study the relationships between the condition f belongs to a class of mappings between Hausdorff spaces 𝕄 and the condition TD(f) belongs to 𝕄.
符号 TD(X) 表示豪斯多夫空间 X 的所有非空完全断开紧凑子集的超空间。对于 Hausdorff 空间 f : X → Y 之间的映射，定义诱导映射 TD(f) ：TD(X)→TD(Y)定义为 TD(f)(A)=f(A)（f 下 A 的像）。在本文中，我们将研究 f 属于 Hausdorff 空间 𝕄 之间的一类映射的条件与 TD(f) 属于 𝕄 的条件之间的关系。
{"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":null,"pages":null},"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}
Priya G. Krishnan, Ravichandran Vaithiyanathan, Ponnaiah Saikrishnan
For normalized starlike functions f : 𝔻 → ℂ, we consider the analytic functions g : 𝔻 → ℂ defined by g(z) = (1 + z(f″(z))/f′(z))/(zf′(z)/f(z)) and g(z) = (1 − α)(zf′(z))/f(z) + α(1 + (zf″(z))/f′(z)), 0 ≤ α ≤ 1. We determine the largest radius ρ with 0 < ρ ≤ 1 such that g(ρ z) is subordinate to various functions with positive real part.
{"title":"Radius problem associated with certain ratios and linear combinations of analytic functions","authors":"Priya G. Krishnan, Ravichandran Vaithiyanathan, Ponnaiah Saikrishnan","doi":"10.1515/ms-2024-0066","DOIUrl":"https://doi.org/10.1515/ms-2024-0066","url":null,"abstract":"For normalized starlike functions <jats:italic>f</jats:italic> : 𝔻 → ℂ, we consider the analytic functions <jats:italic>g</jats:italic> : 𝔻 → ℂ defined by <jats:italic>g</jats:italic>(<jats:italic>z</jats:italic>) = (1 + <jats:italic>z</jats:italic>(<jats:italic>f</jats:italic>″(<jats:italic>z</jats:italic>))/<jats:italic>f</jats:italic>′(<jats:italic>z</jats:italic>))/(<jats:italic>zf</jats:italic>′(<jats:italic>z</jats:italic>)/<jats:italic>f</jats:italic>(<jats:italic>z</jats:italic>)) and <jats:italic>g</jats:italic>(<jats:italic>z</jats:italic>) = (1 − <jats:italic>α</jats:italic>)(<jats:italic>zf</jats:italic>′(<jats:italic>z</jats:italic>))/<jats:italic>f</jats:italic>(<jats:italic>z</jats:italic>) + <jats:italic>α</jats:italic>(1 + (<jats:italic>zf</jats:italic>″(<jats:italic>z</jats:italic>))/<jats:italic>f</jats:italic>′(<jats:italic>z</jats:italic>)), 0 ≤ <jats:italic>α</jats:italic> ≤ 1. We determine the largest radius <jats:italic>ρ</jats:italic> with 0 < <jats:italic>ρ</jats:italic> ≤ 1 such that <jats:italic>g</jats:italic>(<jats:italic>ρ z</jats:italic>) is subordinate to various functions with positive real part.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221520","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}
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