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The Ground State Solutions of Discrete Nonlinear Schrödinger Equations with Hardy Weights 具有哈代权重的离散非线性薛定谔方程的基态解
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-03-23 DOI: 10.1007/s00009-024-02618-z
Lidan Wang
{"title":"The Ground State Solutions of Discrete Nonlinear Schrödinger Equations with Hardy Weights","authors":"Lidan Wang","doi":"10.1007/s00009-024-02618-z","DOIUrl":"https://doi.org/10.1007/s00009-024-02618-z","url":null,"abstract":"<p>In this paper, we study the discrete nonlinear Schrödinger equation </p><span>$$begin{aligned} -Delta u+left( V(x)- frac{rho }{(|x|^2+1)}right) u=f(x,u),quad uin ell ^2({mathbb {Z}}^N), end{aligned}$$</span><p>where <span>(Nge 3)</span>, <i>V</i> is a bounded periodic potential and 0 lies in a spectral gap of the Schrödinger operator <span>(-Delta +V)</span>. The resulting problem engages two major difficulties: one is that the associated functional is strongly indefinite and the other is the lack of compactness of the Cerami sequence. We overcome these two major difficulties by the generalized linking theorem and Lions lemma. This enables us to establish the existence and asymptotic behavior of ground state solutions for small <span>(rho ge 0)</span>.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"15 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140201324","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
Product of Resolvents on Hadamard Manifolds 哈达玛德流形上的溶剂积
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-03-23 DOI: 10.1007/s00009-024-02622-3
Fatemeh Ahmadi, Parviz Ahmadi, Hadi Khatibzadeh
{"title":"Product of Resolvents on Hadamard Manifolds","authors":"Fatemeh Ahmadi, Parviz Ahmadi, Hadi Khatibzadeh","doi":"10.1007/s00009-024-02622-3","DOIUrl":"https://doi.org/10.1007/s00009-024-02622-3","url":null,"abstract":"<p>The aim of this paper is to study the product of resolvents of a finite number of monotone vector fields on a Hadamard manifold to approximate both the singular points of their sum and a common singular point among them. For the sum of any finitely many maximal monotone vector fields, with some suitable assumptions, it is proved that the obtained sequence of the iterative method is convergent. The paper ends with some examples and applications.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"30 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140201349","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
Mathematical Analysis and a Second-Order Compact Scheme for Nonlinear Caputo–Hadamard Fractional Sub-diffusion Equations 非线性卡普托-哈达玛德分数次扩散方程的数学分析和二阶紧凑方案
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-03-22 DOI: 10.1007/s00009-024-02617-0
{"title":"Mathematical Analysis and a Second-Order Compact Scheme for Nonlinear Caputo–Hadamard Fractional Sub-diffusion Equations","authors":"","doi":"10.1007/s00009-024-02617-0","DOIUrl":"https://doi.org/10.1007/s00009-024-02617-0","url":null,"abstract":"<h3>Abstract</h3> <p>In this paper, a compact finite difference scheme with <span> <span>(O(tau ^{min {ralpha ,2}}+h^4))</span> </span> convergence order for nonlinear Caputo–Hadamard fractional sub-differential equations is proposed, where <span> <span>(tau )</span> </span> represents the maximum step size in temporal direction, <em>h</em> represents the step size in spatial direction, and <span> <span>(alpha )</span> </span> is the order and <em>r</em> (<span> <span>(rge 1)</span> </span>) is an optional constant. First, we derive the implicit solution of the original equation using the modified Laplace transform and the finite Fourier sine transform. To obtain the regularity, an auxiliary function <span> <span>(t^{-kappa })</span> </span> is applied to handle the nonlinear term, which is crucial to the analysis. Second, we approximate the Caputo–Hadamard fractional derivative with the <span> <span>(L_{log ,2-1_sigma })</span> </span> formula on non-uniform grids. Furthermore, we adopt the Newton linearized method to handle the nonlinear term carefully. Based on the discrete fractional Gr<span> <span>(ddot{textrm{o}})</span> </span>nwall inequality, the stability and convergence of the derived scheme are obtained by the energy method. Ultimately, three examples are presented to show the effectiveness of our method.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"7 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140201713","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
Observability of Time-Varying Fractional Dynamical Systems with Caputo Fractional Derivative 具有卡普托分式衍生物的时变分式动态系统的可观测性
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-03-20 DOI: 10.1007/s00009-024-02615-2
{"title":"Observability of Time-Varying Fractional Dynamical Systems with Caputo Fractional Derivative","authors":"","doi":"10.1007/s00009-024-02615-2","DOIUrl":"https://doi.org/10.1007/s00009-024-02615-2","url":null,"abstract":"<h3>Abstract</h3> <p>Modeling dynamical systems with real-life data having time-dependent disturbances is better captured with time-varying systems. The qualitative properties of such a system in a fractional sense are hardly examined. Observability is one property where the system’s initial states are determined based on the output of some observation system. In this paper, we investigate the observability of time-varying fractional dynamical systems. A state-transition matrix represents the solution of the time-varying fractional dynamical systems. The observability results of linear and nonlinear systems are obtained using the Gramian matrix technique and the Banach contraction mapping theorem respectively. The obtained theoretical results for the observability of the time-varying fractional dynamical systems are compared with those of the time-invariant fractional dynamical system (FDS). Several numerical examples are provided to validate the theoretical results. Also, a numerical example to study the observability of a fractional spring–mass system is provided to verify the applicability of this study.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"24 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140172977","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
Total Torsion and Spherical Curves Bending 总扭力和球形曲线弯曲
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-03-20 DOI: 10.1007/s00009-024-02595-3
Marija S. Najdanović, Svetozar R. Rančić, Ljubica S. Velimirović
{"title":"Total Torsion and Spherical Curves Bending","authors":"Marija S. Najdanović, Svetozar R. Rančić, Ljubica S. Velimirović","doi":"10.1007/s00009-024-02595-3","DOIUrl":"https://doi.org/10.1007/s00009-024-02595-3","url":null,"abstract":"<p>It is well known that the total torsion of a closed spherical curve is zero. Furthermore, if the total torsion of any closed curve on the surface is zero, then it is part of a plane or a sphere. In this paper, we examine the total torsion of a spherical curve during infinitesimal bending. We find the appropriate bending fields and show that the variation of the total torsion of a closed spherical curve is equal to zero. Some examples are considered both analytically and using our own software tool. For figures, we use colors to represent the value of torsion at different points of the curve, together with a colour-value scale.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"41 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140166161","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 Norms of p-Nilpotent Residuals of Subgroups in a Finite Group 论有限群中子群的 p 弱残差规范
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-03-20 DOI: 10.1007/s00009-024-02613-4
Baoyu Zhang, Quanfu Yan, Zhencai Shen
{"title":"On the Norms of p-Nilpotent Residuals of Subgroups in a Finite Group","authors":"Baoyu Zhang, Quanfu Yan, Zhencai Shen","doi":"10.1007/s00009-024-02613-4","DOIUrl":"https://doi.org/10.1007/s00009-024-02613-4","url":null,"abstract":"<p>Let <i>G</i> be a finite group and <i>p</i> be a prime. We define <span>(N^{mathcal {N}_p*}(G))</span> to be the intersection of the normalizers of the <i>p</i>-nilpotent residuals of all two-generator subgroups of <i>G</i> whose <i>p</i>-nilpotent residuals are nilpotent. We show that <span>(N^{mathcal {N}_p}(G)=N^{mathcal {N}_p*}(G))</span>. Using the method in the present paper, we will be able to give an affirmative answer to an open problem in Shen et al. (Mediterr J Math 19:191, 2022), which also indicates that similar conclusions hold for many formations. It is also proved that <span>(G=N^{mathcal {N}_p}(G))</span> if and only if every three-generator subgroup <i>H</i> of <i>G</i> satisfies <span>(H=N^{mathcal {N}_p}(H))</span>. To this end, we introduce and investigate the <i>IO</i>-<span>(N^{mathcal {N}_p})</span>-groups, i.e., the groups <i>G</i> such that <span>(Gne N^{mathcal {N}_p}(G),)</span> but each proper subgroup and each proper quotient of <i>G</i> equals its <i>p</i>-nilpotent norm. Moreover, new results in terms of the <i>p</i>-nilpotent norm and the <i>p</i>-nilpotent hypernorm <span>(N^{mathcal {N}_p}_infty (G))</span> are given.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"41 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140166163","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
Automorphisms in Certain Nilpotent-by-Abelian Varieties of Groups 群的某些无幂次阿贝尔变项中的自动形
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-03-20 DOI: 10.1007/s00009-024-02614-3
C. E. Kofinas
{"title":"Automorphisms in Certain Nilpotent-by-Abelian Varieties of Groups","authors":"C. E. Kofinas","doi":"10.1007/s00009-024-02614-3","DOIUrl":"https://doi.org/10.1007/s00009-024-02614-3","url":null,"abstract":"<p>For positive integers <i>n</i> and <i>k</i>, with <span>(n ge 4)</span>, let <span>(F_{n})</span> be the free group of rank <i>n</i> and let <span>(G_{n,k} = F_{n}/gamma _{3}(F^{prime }_{n})[F^{prime prime }_{n},~_{k}F_{n}])</span>. We show that for sufficiently large <i>n</i>, the automorphism group <span>({textrm{Aut}}(G_{n,k}))</span> of <span>(G_{n,k})</span> is generated by the tame automorphisms and one more non-tame automorphism.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"142 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140166031","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
Fractal Dimension of $$alpha $$ -Fractal Functions Without Endpoint Conditions $$alpha $$ 的分形维度 - 无端点条件的分形函数
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-03-18 DOI: 10.1007/s00009-024-02610-7
{"title":"Fractal Dimension of $$alpha $$ -Fractal Functions Without Endpoint Conditions","authors":"","doi":"10.1007/s00009-024-02610-7","DOIUrl":"https://doi.org/10.1007/s00009-024-02610-7","url":null,"abstract":"<h3>Abstract</h3> <p>In this article, we manifest the existence of a new class of <span> <span>(alpha )</span> </span>-fractal functions without endpoint conditions in the space of continuous functions. Furthermore, we add the existence of the same class in numerous spaces such as the Hölder space, the convex Lipschitz space, and the oscillation space. We also estimate the fractal dimensions of the graphs of the newly constructed <span> <span>(alpha )</span> </span>-fractal functions adopting some function spaces and covering methods.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"84 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140149704","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
Multiple Lines of Maximum Genus in $${mathbb {P}}^3$$ $${/mathbb{P}}^3$$中的多行最大属种
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-03-18 DOI: 10.1007/s00009-024-02608-1
Enrico Schlesinger
{"title":"Multiple Lines of Maximum Genus in $${mathbb {P}}^3$$","authors":"Enrico Schlesinger","doi":"10.1007/s00009-024-02608-1","DOIUrl":"https://doi.org/10.1007/s00009-024-02608-1","url":null,"abstract":"<p>We introduce a notion of good cohomology for multiple lines in <span>({mathbb {P}}^3)</span> and we classify multiple lines with good cohomology up to multiplicity 4. In particular, we show that the family of space curves of degree <i>d</i>, not lying on a surface of degree <span>(&lt;d)</span>, and of maximal arithmetic genus is not irreducible already for <span>(d=4)</span> and <span>(d=5)</span>.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"142 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140166268","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 Spatial Mechanisms in Lorentzian 3-Space 论洛伦兹 3 空间中的空间机制
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-03-15 DOI: 10.1007/s00009-024-02606-3
{"title":"On Spatial Mechanisms in Lorentzian 3-Space","authors":"","doi":"10.1007/s00009-024-02606-3","DOIUrl":"https://doi.org/10.1007/s00009-024-02606-3","url":null,"abstract":"<h3>Abstract</h3> <p>Let <span> <span>(L^{4})</span> </span> be a 4-dimensional Lorentzian space with the sign (−,+,+,+). The aim of this study is to investigate the other missing algebraic forms of the constraint manifolds of 2C and 3C spatial open chains in <span> <span>(L^{4})</span> </span>. For this purpose, firstly, we obtain the structure equations of a spatial open chain using the equations of open chains of the Lorentz plane and Lorentz sphere. After then, using these structure equations, we search the algebraic forms of the constraint manifolds of 2C and 3C spatial open chains in Lorentzian 3-space with respect to the causal characters of the first link and the axis of rotation of the joint.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":"39 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140149726","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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