Pub Date : 2024-08-19DOI: 10.1007/s00009-024-02716-y
Feng Zhang, HuiJuan Zhu, Fanglei Wang
Based on a generalization of the Krasnoselskii’s fixed point theorem and Avery–Peterson fixed point theorem, the object of this paper is to investigate the existence of positive solutions to a second-order Sturm–Liouville problem with derivative term and nonlocal boundary conditions. Also, some examples are given to illustrate our main results.
{"title":"Positive Solutions to a Second-Order Sturm–Liouville Problem with Nonlocal Boundary Conditions","authors":"Feng Zhang, HuiJuan Zhu, Fanglei Wang","doi":"10.1007/s00009-024-02716-y","DOIUrl":"https://doi.org/10.1007/s00009-024-02716-y","url":null,"abstract":"<p>Based on a generalization of the Krasnoselskii’s fixed point theorem and Avery–Peterson fixed point theorem, the object of this paper is to investigate the existence of positive solutions to a second-order Sturm–Liouville problem with derivative term and nonlocal boundary conditions. Also, some examples are given to illustrate our main results.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"88 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195268","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}
Pub Date : 2024-08-14DOI: 10.1007/s00009-024-02715-z
Yongqing Liu
In this paper, we completely characterize (L^{p,q})-boundedness of (maximal) Fock projections on (mathbb {C}) for (1le p,qle infty ). As applications, we identify the dual space of mixed norm space (F_alpha ^{p,q}) of entire functions and present an alternative proof of the Littlewood–Paley formula for (F_alpha ^{p,q}).
{"title":"Fock Projections on Mixed Norm Spaces","authors":"Yongqing Liu","doi":"10.1007/s00009-024-02715-z","DOIUrl":"https://doi.org/10.1007/s00009-024-02715-z","url":null,"abstract":"<p>In this paper, we completely characterize <span>(L^{p,q})</span>-boundedness of (maximal) Fock projections on <span>(mathbb {C})</span> for <span>(1le p,qle infty )</span>. As applications, we identify the dual space of mixed norm space <span>(F_alpha ^{p,q})</span> of entire functions and present an alternative proof of the Littlewood–Paley formula for <span>(F_alpha ^{p,q})</span>.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"169 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195236","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}
where A and B are bounded linear operators defined on a Banach space X, (f:{mathbb {N}}_0rightarrow X) is an X-valued sequence and (2<alpha <3). We introduce an operator theoretical method based on the notion of (alpha )-resolvent sequence of bounded linear operators, which gives an explicit representation of solution. Further, using Blunck’s operator-valued Fourier multipliers theorems on (ell ^p(mathbb {Z}; X)), we completely characterize the (ell ^p)-maximal regularity of solution when (1< p < infty ) and X is a UMD space.
本文研究了具有有限延迟的分数差分方程的最大正则性:$$begin{aligned}。 (begin{array}{ll})u(n)=Au(n)+B u(n-lambda )+f(n), nin {mathbb {N}}_0, lambda in {mathbb {N}}; u(i)=0, i=-lambda , -lambda +1,cdots , 1, 2, end{array}右边end{aligned}$$where A and B are bounded linear operators defined on a Banach space X, (f:{mathbb {N}}_0rightarrow X) is an X-valued sequence and (2<alpha <3).我们引入了一种基于有界线性算子的 (alpha )-残差序列概念的算子理论方法,它给出了解的显式表示。此外,利用布伦克关于(ell ^p(mathbb {Z}; X))的算子值傅里叶乘数定理,我们完全描述了当(1< p < infty )和X是UMD空间时解的(ell ^p)-最大正则性。
{"title":"Maximal Regularity for Fractional Difference Equations with Finite Delay on UMD Spaces","authors":"Jichao Zhang, Shangquan Bu","doi":"10.1007/s00009-024-02717-x","DOIUrl":"https://doi.org/10.1007/s00009-024-02717-x","url":null,"abstract":"<p>In this paper, we study the <span>(ell ^p)</span>-maximal regularity for the fractional difference equation with finite delay: </p><span>$$begin{aligned} left{ begin{array}{ll} Delta ^{alpha }u(n)=Au(n)+B u(n-lambda )+f(n), nin {mathbb {N}}_0, lambda in {mathbb {N}}; u(i)=0, i=-lambda , -lambda +1,cdots , 1, 2, end{array} right. end{aligned}$$</span><p>where <i>A</i> and <i>B</i> are bounded linear operators defined on a Banach space <i>X</i>, <span>(f:{mathbb {N}}_0rightarrow X)</span> is an <i>X</i>-valued sequence and <span>(2<alpha <3)</span>. We introduce an operator theoretical method based on the notion of <span>(alpha )</span>-resolvent sequence of bounded linear operators, which gives an explicit representation of solution. Further, using Blunck’s operator-valued Fourier multipliers theorems on <span>(ell ^p(mathbb {Z}; X))</span>, we completely characterize the <span>(ell ^p)</span>-maximal regularity of solution when <span>(1< p < infty )</span> and <i>X</i> is a UMD space.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195233","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}
Pub Date : 2024-08-07DOI: 10.1007/s00009-024-02706-0
Žiga Virk
This paper introduces a method to detect each geometrically significant loop that is a geodesic circle (an isometric embedding of (S^1)) and a bottleneck loop (meaning that each of its perturbations increases the length) in a geodesic space using persistent homology. Under fairly mild conditions, we show that such a loop either terminates a 1-dimensional homology class or gives rise to a 2-dimensional homology class in persistent homology. The main tool in this detection technique are selective Rips complexes, new custom made complexes that function as an appropriate combinatorial lens for persistent homology to detect the above mentioned loops. The main argument is based on a new concept of a local winding number, which turns out to be an invariant of certain homology classes.
{"title":"Persistent Homology with Selective Rips Complexes Detects Geodesic Circles","authors":"Žiga Virk","doi":"10.1007/s00009-024-02706-0","DOIUrl":"https://doi.org/10.1007/s00009-024-02706-0","url":null,"abstract":"<p>This paper introduces a method to detect each geometrically significant loop that is a geodesic circle (an isometric embedding of <span>(S^1)</span>) and a bottleneck loop (meaning that each of its perturbations increases the length) in a geodesic space using persistent homology. Under fairly mild conditions, we show that such a loop either terminates a 1-dimensional homology class or gives rise to a 2-dimensional homology class in persistent homology. The main tool in this detection technique are selective Rips complexes, new custom made complexes that function as an appropriate combinatorial lens for persistent homology to detect the above mentioned loops. The main argument is based on a new concept of a local winding number, which turns out to be an invariant of certain homology classes.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"58 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141947066","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}
Pub Date : 2024-08-06DOI: 10.1007/s00009-024-02712-2
Dulat S. Dzhumabaev, Anuar D. Dzhumabaev, Anar T. Assanova
The paper is concerned with a nonlocal problem for a partial Fredholm integro-differential equation (IDE) of hyperbolic type is investigated. This problem is reduced to a problem containing a family of boundary value problems for the ordinary Fredholm IDEs and some integral relationships. A novel concept of general solution to a family of the ordinary Fredholm IDEs is introduced, and its properties are discussed. A necessary and sufficient condition for the well-posedness of the nonlocal problem for the partial Fredholm integro-differential equation (IDE) of hyperbolic type is obtained, and an algorithm for finding its solution is offered.
本文研究的是一个双曲型偏弗雷德霍姆积分微分方程(IDE)的非局部问题。该问题被简化为一个包含普通弗雷德霍姆积分微分方程边界值问题族和一些积分关系的问题。引入了普通弗雷德霍姆 IDE 族一般解的新概念,并讨论了其性质。获得了双曲型偏弗雷德霍姆积分微分方程(IDE)非局部问题良好求解的必要条件和充分条件,并提供了求解算法。
{"title":"Properties of a Partial Fredholm Integro-differential Equations with Nonlocal Condition and Algorithms","authors":"Dulat S. Dzhumabaev, Anuar D. Dzhumabaev, Anar T. Assanova","doi":"10.1007/s00009-024-02712-2","DOIUrl":"https://doi.org/10.1007/s00009-024-02712-2","url":null,"abstract":"<p>The paper is concerned with a nonlocal problem for a partial Fredholm integro-differential equation (IDE) of hyperbolic type is investigated. This problem is reduced to a problem containing a family of boundary value problems for the ordinary Fredholm IDEs and some integral relationships. A novel concept of general solution to a family of the ordinary Fredholm IDEs is introduced, and its properties are discussed. A necessary and sufficient condition for the well-posedness of the nonlocal problem for the partial Fredholm integro-differential equation (IDE) of hyperbolic type is obtained, and an algorithm for finding its solution is offered.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"174 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141947069","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}
Pub Date : 2024-08-05DOI: 10.1007/s00009-024-02707-z
Ildefonso Castro-Infantes, Jorge Hidalgo
We prove that on every compact Riemann surface M, there is a Cantor set (C subset M) such that (M{ setminus }C) admits a proper conformal constant mean curvature one ((text {CMC-1})) immersion into hyperbolic 3-space (mathbb {H}^3). Moreover, we obtain that every bordered Riemann surface admits an almost proper (text {CMC-1}) face into de Sitter 3-space (mathbb {S}_1^3), and we show that on every compact Riemann surface M, there is a Cantor set (C subset M) such that (M {setminus } C) admits an almost proper (text {CMC-1}) face into (mathbb {S}_1^3). These results follow from different uniform approximation theorems for holomorphic null curves in (mathbb {C}^2 times mathbb {C}^*) that we also establish in this paper.
我们证明,在每一个紧凑黎曼曲面 M 上,都有一个康托集(C 子集 M),使得(M{ setminus }C)允许一个适当的保角恒定平均曲率一((text {CMC-1}))浸入双曲 3 空间(mathbb {H}^3)。此外,我们还得到每个有边界的黎曼曲面都有一个几乎合适的(text {CMC-1})面进入德西特 3 空间(mathbb {S}_1^3)、并且我们证明了在每一个紧凑黎曼曲面M上,都有一个康托集(C子集M),使得(M{setminus } C )有一个几乎合适的(text {CMC-1})面进入(mathbb {S}_1^3)。这些结果来自于我们在本文中建立的针对 (mathbb {C}^2 times mathbb {C}^*) 中全形空曲线的不同均匀逼近定理。
{"title":"$$text {CMC-1}$$ Surfaces in Hyperbolic and de Sitter Spaces with Cantor Ends","authors":"Ildefonso Castro-Infantes, Jorge Hidalgo","doi":"10.1007/s00009-024-02707-z","DOIUrl":"https://doi.org/10.1007/s00009-024-02707-z","url":null,"abstract":"<p>We prove that on every compact Riemann surface <i>M</i>, there is a Cantor set <span>(C subset M)</span> such that <span>(M{ setminus }C)</span> admits a proper conformal constant mean curvature one (<span>(text {CMC-1})</span>) immersion into hyperbolic 3-space <span>(mathbb {H}^3)</span>. Moreover, we obtain that every bordered Riemann surface admits an almost proper <span>(text {CMC-1})</span> face into de Sitter 3-space <span>(mathbb {S}_1^3)</span>, and we show that on every compact Riemann surface <i>M</i>, there is a Cantor set <span>(C subset M)</span> such that <span>(M {setminus } C)</span> admits an almost proper <span>(text {CMC-1})</span> face into <span>(mathbb {S}_1^3)</span>. These results follow from different uniform approximation theorems for holomorphic null curves in <span>(mathbb {C}^2 times mathbb {C}^*)</span> that we also establish in this paper.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"4 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141969673","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}
Pub Date : 2024-08-05DOI: 10.1007/s00009-024-02709-x
Fuensanta Aroca, José M. Tornero
Quasiordinary power series were introduced by Jung at the beginning of the 20th century, and were not paid much attention until the work of Lipman and, later on, Gao. They have been thoroughly studied since, as they form a very interesting family of singular varieties, whose properties (or at least many of them) can be encoded in a discrete set of integers, much as what happens with curves. Hironaka proposed a generalization of this concept, the so-called (nu )-quasiordinary power series, which has not been examined in the literature in such detailed way. This paper explores the behavior of these series under the resolution process in the surface case.
准平凡幂级数是荣格在 20 世纪初提出的,直到利普曼和后来的高晓松的研究才引起人们的注意。此后,人们对它们进行了深入研究,因为它们构成了一个非常有趣的奇异品种族,其性质(或至少其中的许多性质)可以用离散的整数集来编码,就像曲线一样。Hironaka 提出了这一概念的广义化,即所谓的 (nu )-准平凡幂级数,但文献中还没有对它进行如此详细的研究。本文探讨了这些序列在曲面情况下的解析过程中的行为。
{"title":"On $$nu $$ -Quasiordinary Surface Singularities and Their Resolution","authors":"Fuensanta Aroca, José M. Tornero","doi":"10.1007/s00009-024-02709-x","DOIUrl":"https://doi.org/10.1007/s00009-024-02709-x","url":null,"abstract":"<p>Quasiordinary power series were introduced by Jung at the beginning of the 20th century, and were not paid much attention until the work of Lipman and, later on, Gao. They have been thoroughly studied since, as they form a very interesting family of singular varieties, whose properties (or at least many of them) can be encoded in a discrete set of integers, much as what happens with curves. Hironaka proposed a generalization of this concept, the so-called <span>(nu )</span>-quasiordinary power series, which has not been examined in the literature in such detailed way. This paper explores the behavior of these series under the resolution process in the surface case.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"61 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141947068","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}
Pub Date : 2024-08-05DOI: 10.1007/s00009-024-02704-2
Giorgia Bellomonte, Stefan Ivković, Camillo Trapani
The GNS construction for positive invariant sesquilinear forms on quasi *-algebra ((mathfrak A,{mathfrak A}_{scriptscriptstyle 0})) is generalized to a class of positive sesquilinear maps from (mathfrak Atimes mathfrak A) into a (C^*)-algebra ({mathfrak {C}}). The result is a *-representation taking values in a space of operators acting on a certain quasi-normed ({mathfrak {C}})-module.
准*代数((mathfrak A,{mathfrak A}_{scriptscriptstyle 0}))上的正不变倍线性形式的GNS构造被推广到从(mathfrak Atimes mathfrak A) 到(C^*)-代数({mathfrak {C}})的一类正倍线性映射。结果是在作用于某个准规范的({mathfrak {C}})模块的算子空间中取值的*表示。
{"title":"GNS Construction for $$C^*$$ -Valued Positive Sesquilinear Maps on a quasi *-algebra","authors":"Giorgia Bellomonte, Stefan Ivković, Camillo Trapani","doi":"10.1007/s00009-024-02704-2","DOIUrl":"https://doi.org/10.1007/s00009-024-02704-2","url":null,"abstract":"<p>The GNS construction for positive invariant sesquilinear forms on quasi *-algebra <span>((mathfrak A,{mathfrak A}_{scriptscriptstyle 0}))</span> is generalized to a class of positive sesquilinear maps from <span>(mathfrak Atimes mathfrak A)</span> into a <span>(C^*)</span>-algebra <span>({mathfrak {C}})</span>. The result is a *-representation taking values in a space of operators acting on a certain quasi-normed <span>({mathfrak {C}})</span>-module.\u0000</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"11 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141947067","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}
Pub Date : 2024-08-05DOI: 10.1007/s00009-024-02710-4
Othman Tyr
In this paper, we consider (mathcal {E}) the set of all infinitely differentiable functions with compact support included on the interval (I=[-1,1]). We use the distributions in (mathcal {E}), as a tool to prove the continuity of the Dunkl operator and the Dunkl translation. Some properties of the modulus of smoothness related to the Dunkl operator are verified. By means of generalized Dunkl–Lipschitz conditions on Dunkl–Sobolev spaces, a result of Younis on the torus, which is an analog of Titchmarsh’s theorem, is deduced as a special case. In addition, certain conditions and a characterization of the Dini–Lipschitz classes on I in terms of the behavior of their Fourier–Dunkl coefficients are derived.
{"title":"On the Fourier–Dunkl Coefficients of Generalized Lipschitz Classes on the Interval $$[-1,1]$$","authors":"Othman Tyr","doi":"10.1007/s00009-024-02710-4","DOIUrl":"https://doi.org/10.1007/s00009-024-02710-4","url":null,"abstract":"<p>In this paper, we consider <span>(mathcal {E})</span> the set of all infinitely differentiable functions with compact support included on the interval <span>(I=[-1,1])</span>. We use the distributions in <span>(mathcal {E})</span>, as a tool to prove the continuity of the Dunkl operator and the Dunkl translation. Some properties of the modulus of smoothness related to the Dunkl operator are verified. By means of generalized Dunkl–Lipschitz conditions on Dunkl–Sobolev spaces, a result of Younis on the torus, which is an analog of Titchmarsh’s theorem, is deduced as a special case. In addition, certain conditions and a characterization of the Dini–Lipschitz classes on <i>I</i> in terms of the behavior of their Fourier–Dunkl coefficients are derived.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"118 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141947070","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}
Pub Date : 2024-08-03DOI: 10.1007/s00009-024-02708-y
Pratulananda Das, Ayan Ghosh
A subgroup H of the circle group ({mathbb {T}}) is called characterized by a sequence of integers ((u_n)) if (H={xin {mathbb {T}}: lim _{nrightarrow infty } u_nx=0}). In this note, we primarily consider a non-arithmetic sequence arising out of an arithmetic sequence in line of Bíró et al. (Stud Sci Math Hung 38: 97–113, 2001) and investigate the corresponding characterized subgroup thoroughly which includes its cardinality aspects. The whole investigation reiterates that these characterized subgroups are infinitely generated unbounded torsion countable subgroups of the circle group ({mathbb {T}}). Finally, we delve into certain structure theoretic observations.
{"title":"Characterized Subgroups Related to some Non-arithmetic Sequence of Integers","authors":"Pratulananda Das, Ayan Ghosh","doi":"10.1007/s00009-024-02708-y","DOIUrl":"https://doi.org/10.1007/s00009-024-02708-y","url":null,"abstract":"<p>A subgroup <i>H</i> of the circle group <span>({mathbb {T}})</span> is called characterized by a sequence of integers <span>((u_n))</span> if <span>(H={xin {mathbb {T}}: lim _{nrightarrow infty } u_nx=0})</span>. In this note, we primarily consider a non-arithmetic sequence arising out of an arithmetic sequence in line of Bíró et al. (Stud Sci Math Hung 38: 97–113, 2001) and investigate the corresponding characterized subgroup thoroughly which includes its cardinality aspects. The whole investigation reiterates that these characterized subgroups are infinitely generated unbounded torsion countable subgroups of the circle group <span>({mathbb {T}})</span>. Finally, we delve into certain structure theoretic observations.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"30 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141885702","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}