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On Meromorphic Solutions of the Fermat Type Difference Equations 论费马型差分方程的同态解
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-05-14 DOI: 10.1007/s00009-024-02643-y
Xiaoguang Qi, Lianzhong Yang
{"title":"On Meromorphic Solutions of the Fermat Type Difference Equations","authors":"Xiaoguang Qi, Lianzhong Yang","doi":"10.1007/s00009-024-02643-y","DOIUrl":"https://doi.org/10.1007/s00009-024-02643-y","url":null,"abstract":"<p>In this paper, we discuss the form and related properties of meromorphic solutions of hyper-order strictly less than 1 to Fermat type difference equation, and extend the previous results.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140929661","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
Weighted $$W^{1,2}_{p(cdot )}$$ -Estimate for Fully Nonlinear Parabolic Equations with a Relaxed Convexity 具有松弛凸性的完全非线性抛物方程的加权 $$W^{1,2}_{p(cdot )}$$ - 估计值
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-05-13 DOI: 10.1007/s00009-024-02659-4
Hong Tian, Shenzhou Zheng
{"title":"Weighted $$W^{1,2}_{p(cdot )}$$ -Estimate for Fully Nonlinear Parabolic Equations with a Relaxed Convexity","authors":"Hong Tian, Shenzhou Zheng","doi":"10.1007/s00009-024-02659-4","DOIUrl":"https://doi.org/10.1007/s00009-024-02659-4","url":null,"abstract":"<p>We devote this paper to global estimate in weighted variable exponent Sobolev spaces for fully nonlinear parabolic equations under a relaxed convexity condition. It is assumed that the associated variable exponent is log-Hölder continuous, the weight belongs to certain Muckenhoupt class concerning the variable exponent, the leading part of nonlinearity satisfies a relaxed convexity in Hessian and is of VMO condition in space-time variables, and the boundary of underlying domain satisfies <span>(C^{1,1})</span>-smooth. Our key strategy is to utilize a unified approach based on the generalized versions of Fefferman–Stein theorem of the sharp functions and extrapolation to establish the estimates of <span>(D^{2}u)</span> and <span>(D_{t} u)</span> within the framework of weighted variable exponent Lebesgue spaces.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140929671","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
Clairaut Semi-invariant Riemannian Maps to Kähler Manifolds 到凯勒积分的克莱奥特半不变黎曼映射
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-05-13 DOI: 10.1007/s00009-024-02666-5
Murat Polat, Kiran Meena
{"title":"Clairaut Semi-invariant Riemannian Maps to Kähler Manifolds","authors":"Murat Polat, Kiran Meena","doi":"10.1007/s00009-024-02666-5","DOIUrl":"https://doi.org/10.1007/s00009-024-02666-5","url":null,"abstract":"<p>In this paper, first, we recall the notion of Clairaut Riemannian map (CRM) <i>F</i> using a geodesic curve on the base manifold and give the Ricci equation. We also show that if base manifold of CRM is space form then leaves of <span>((ker{F}_*)^perp )</span> become space forms and symmetric as well. Secondly, we define Clairaut semi-invariant Riemannian map (CSIRM) from a Riemannian manifold <span>((M, g_{M}))</span> to a Kähler manifold <span>((N, g_{N}, P))</span> with a non-trivial example. We find necessary and sufficient conditions for a curve on the base manifold of semi-invariant Riemannian map (SIRM) to be geodesic. Further, we obtain necessary and sufficient conditions for a SIRM to be CSIRM. Moreover, we find necessary and sufficient condition for CSIRM to be harmonic and totally geodesic. In addition, we find necessary and sufficient condition for the distributions <span>(bar{D_1})</span> and <span>(bar{D_2})</span> of <span>((ker{F}_*)^bot )</span> (which are arisen from the definition of CSIRM) to define totally geodesic foliations. Finally, we obtain necessary and sufficient conditions for <span>((ker{F}_*)^bot )</span> and base manifold to be locally product manifold <span>(bar{D_1} times bar{D_2})</span> and <span>({(range{F}_*)} times {(range{F}_*)^bot })</span>, respectively.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140929617","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
Minimal Weak Drazin Inverses in Semigroups and Rings 半群和环中的最小弱德拉辛倒数
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-05-13 DOI: 10.1007/s00009-024-02661-w
Shuxian Xu, Jianlong Chen, Cang Wu
{"title":"Minimal Weak Drazin Inverses in Semigroups and Rings","authors":"Shuxian Xu, Jianlong Chen, Cang Wu","doi":"10.1007/s00009-024-02661-w","DOIUrl":"https://doi.org/10.1007/s00009-024-02661-w","url":null,"abstract":"<p>In 1978, Campbell and Meyer proposed the notion of minimal rank weak Drazin inverses of complex matrices. In this paper, we define minimal weak Drazin inverses of elements in semigroups using Green’s preorder <span>(leqslant _{{mathcal {R}}},)</span> which generalize minimal rank weak Drazin inverses of complex matrices. For two elements <i>a</i>, <i>y</i> of a semigroup, it is proved that <i>y</i> is a minimal weak Drazin inverse of <i>a</i> if and only if <span>(ya^{k+1}=a^{k})</span> for some nonnegative integer <i>k</i> and <span>(ay^{2}=y.)</span></p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140929615","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
Brill–Noether Theory of Stable Vector Bundles on Ruled Surfaces 规则曲面上稳定向量束的布里尔-诺特理论
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-05-11 DOI: 10.1007/s00009-024-02657-6
L. Costa, Irene Macías Tarrío
{"title":"Brill–Noether Theory of Stable Vector Bundles on Ruled Surfaces","authors":"L. Costa, Irene Macías Tarrío","doi":"10.1007/s00009-024-02657-6","DOIUrl":"https://doi.org/10.1007/s00009-024-02657-6","url":null,"abstract":"<p>Let <i>X</i> be a ruled surface over a nonsingular curve <i>C</i> of genus <span>(gge 0.)</span> Let <span>(M_H:=M_{X,H}(2;c_1,c_2))</span> be the moduli space of <i>H</i>-stable rank 2 vector bundles <i>E</i> on <i>X</i> with fixed Chern classes <span>(c_i:=c_i(E))</span> for <span>(i=1,2.)</span> The main goal of this paper is to contribute to a better understanding of the geometry of the moduli space <span>(M_H)</span> in terms of its Brill–Noether locus <span>(W_H^k(2;c_1,c_2),)</span> whose points correspond to stable vector bundles in <span>(M_H)</span> having at least <i>k</i> independent sections. We deal with the non-emptiness of this Brill–Noether locus, getting in most of the cases sharp bounds for the values of <i>k</i> such that <span>(W_H^k(2;c_1,c_2))</span> is non-empty.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140929609","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 Sub-supersolution Method for Integro-differential Semilinear Elliptic Equations and Some Applications 积分微分半线性椭圆方程的子超解法及其若干应用
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-05-10 DOI: 10.1007/s00009-024-02662-9
Romildo N. de Lima, Alânnio B. Nóbrega, Leandro S. Tavares
{"title":"A Sub-supersolution Method for Integro-differential Semilinear Elliptic Equations and Some Applications","authors":"Romildo N. de Lima, Alânnio B. Nóbrega, Leandro S. Tavares","doi":"10.1007/s00009-024-02662-9","DOIUrl":"https://doi.org/10.1007/s00009-024-02662-9","url":null,"abstract":"<p>In this manuscript, we introduce a new sub-supersolution result for a problem involving an integro-differential operator with local and nonlocal terms, which arise in several applications such as thermal process, plasma reaction, and populational growth. The result obtained allows to consider a wide class of equations. Several applications of the result are provided which complements recent studies in the field.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140929660","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 Second-Order Derivatives of Boolean Functions and Cubic APN Permutations in Even Dimension 论偶数维布尔函数的二阶导数和立方 APN 排列
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-05-08 DOI: 10.1007/s00009-024-02660-x
Augustine Musukwa, Massimiliano Sala, Irene Villa, Marco Zaninelli
{"title":"On Second-Order Derivatives of Boolean Functions and Cubic APN Permutations in Even Dimension","authors":"Augustine Musukwa, Massimiliano Sala, Irene Villa, Marco Zaninelli","doi":"10.1007/s00009-024-02660-x","DOIUrl":"https://doi.org/10.1007/s00009-024-02660-x","url":null,"abstract":"<p>The big APN problem is one of the most important challenges in the theory of Boolean functions, i.e. finding a new APN permutation in even dimension. Among this class of functions, those with the lowest possible degree are cubic. Yet, none has been found so far. In this paper, we introduce new parameters for Boolean functions and for vectorial Boolean functions, mostly derived from the behavior of their second-order derivatives. These parameters are invariant under extended affine equivalence, and they are particularly relevant for small-degree functions. They allow studying bent, semi-bent and APN functions of degrees two and three. In particular, they allow tackling the big APN problem for cubic permutations. Notably, we focus on the case of dimension 8, providing some computational results.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140929928","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
Skew-Adjoint Maps and Quadratic Lie Algebras 斜交映射与二次型李代数
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-05-07 DOI: 10.1007/s00009-024-02656-7
Pilar Benito, Javier Rández-Ibáñez, Jorge Roldán-López
{"title":"Skew-Adjoint Maps and Quadratic Lie Algebras","authors":"Pilar Benito, Javier Rández-Ibáñez, Jorge Roldán-López","doi":"10.1007/s00009-024-02656-7","DOIUrl":"https://doi.org/10.1007/s00009-024-02656-7","url":null,"abstract":"<p>The procedure of double extension of vector spaces endowed with non-degenerate bilinear forms allows us to introduce the class of generalized <span>(mathbb {K})</span>-oscillator algebras over an arbitrary field <span>(mathbb {K})</span>. Starting from basic structural properties and the canonical forms of skew-adjoint endomorphisms, we will proceed to classify the subclass of quadratic nilpotent algebras and characterize those algebras with quadratic dimension 2. This will enable us to recover the classification of real oscillator algebras, a.k.a Lorentzian algebras, given by Medina et al. (Ann Sci École Norm Sup 18:553–561, 1985).</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140886105","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
Brück’s Conjecture for Solutions of Second-Order Complex ODE 二阶复 ODE 解的布吕克猜想
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-05-05 DOI: 10.1007/s00009-024-02642-z
Riad Dida, Abdallah El Farissi
{"title":"Brück’s Conjecture for Solutions of Second-Order Complex ODE","authors":"Riad Dida, Abdallah El Farissi","doi":"10.1007/s00009-024-02642-z","DOIUrl":"https://doi.org/10.1007/s00009-024-02642-z","url":null,"abstract":"<p>Brück’s conjecture asserts that if a non-constant entire function <i>f</i>(<i>z</i>) with hyper-order <span>(rho _{2}(f) not in mathbb {N}cup {infty })</span> shares one finite value <i>a</i> CM (counting multiplicities) with its derivative, then <span>(f'-a=c(f-a))</span>, for some non-zero constant <i>c</i>. This conjecture has been affirmed for entire functions with finite order and hyper-order less than one. In this paper, we show that Brück’s conjecture is true for entire functions that satisfy second order differential equations with meromorphic coefficients of finite order.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140885971","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 Generalization of the Isosceles Constant in Banach Spaces 巴拿赫空间中等腰常数的一般化
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-05-04 DOI: 10.1007/s00009-024-02654-9
Marco Baronti, Valentina Bertella
{"title":"A Generalization of the Isosceles Constant in Banach Spaces","authors":"Marco Baronti, Valentina Bertella","doi":"10.1007/s00009-024-02654-9","DOIUrl":"https://doi.org/10.1007/s00009-024-02654-9","url":null,"abstract":"<p>N. Gastinel and J.L. Joly defined the rectangular constant <span>(mu )</span> in Banach spaces using the notion of orthogonality according to Birkhoff and its generalization <span>(mu _p)</span>, with <span>(pge 1)</span>. Recently, M. Baronti, E. Casini, and P.L. Papini defined a new constant, the isosceles constant <i>H</i>, in Banach spaces in a very similar way to the rectangular constant, but in this case using the isosceles orthogonality defined by James. In this paper, first of all, we generalize such constant, by defining a new constant <span>(H_p)</span> that generalizes the isosceles constant <i>H</i> as well <span>(mu _p)</span> generalizes <span>(mu )</span>. After that, we explain its properties, and we give a characterization of Hilbert spaces in terms of it. Moreover a partial characterization of uniformly non-square spaces is given. We conclude by a conjecture about the characterization of uniformly non-square spaces.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140886406","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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