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Lyapunov Exponents for Generalized Szegő Cocycles 广义 Szegő Cocycles 的 Lyapunov 指数
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-04-29 DOI: 10.1007/s00025-024-02168-6
Licheng Fang, Fengpeng Wang
{"title":"Lyapunov Exponents for Generalized Szegő Cocycles","authors":"Licheng Fang, Fengpeng Wang","doi":"10.1007/s00025-024-02168-6","DOIUrl":"https://doi.org/10.1007/s00025-024-02168-6","url":null,"abstract":"<p>In this paper, we investigate the Lyapunov exponents of the generalized dynamically defined Szegő cocycle, corresponding to orthogonal polynomials on the circle with radius <span>(lambda )</span>. We give the upper and lower bounds of the top Lyapunov exponent in our setting by realification.\u0000</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":"16 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140811507","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
Sombor Index and Sombor Spectrum of Cozero-Divisor Graph of $$mathbb Z_n$$ $$mathbb Z_n$$ Cozero-Divisor Graph 的松博指数和松博谱
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-04-29 DOI: 10.1007/s00025-024-02174-8
M. Anwar, M. R. Mozumder, M. Rashid, M. A. Raza
{"title":"Sombor Index and Sombor Spectrum of Cozero-Divisor Graph of $$mathbb Z_n$$","authors":"M. Anwar, M. R. Mozumder, M. Rashid, M. A. Raza","doi":"10.1007/s00025-024-02174-8","DOIUrl":"https://doi.org/10.1007/s00025-024-02174-8","url":null,"abstract":"<p>Let <span>(mathscr {Z}(mathscr {R})')</span> be the set of all non-unit and non-zero elements of ring <span>(mathscr {R})</span>, a commutative ring with identity <span>(1ne 0)</span>. The cozero-divisor graph of <span>(mathscr {R})</span>, denoted by the notation <span>({Gamma '(mathscr {R})})</span>, is an undirected graph with vertex set <span>(mathscr {Z}(mathscr {R})')</span>. Any two distinct vertices <i>w</i> and <i>z</i> are adjacent if and only if <span>(wnotin zmathscr {R})</span> and <span>(znotin wmathscr {R})</span>, where <span>(qmathscr {R})</span> is the ideal generated by the element <i>q</i> in <span>(mathscr {R})</span>. In this article, we evaluate the Sombor index of the graphs <span>({Gamma '(mathbb Z_n)})</span> for different values of <i>n</i>. Additionally, we compute <span>({Gamma '(mathbb Z_{n})})</span>, the cozero-divisor graph Sombor spectrum.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":"22 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140811503","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
Further Generalizations of the (A.2) and (H.2) Supercongruences of Van Hamme 范哈姆（A.2）和（H.2）超共融的进一步概括
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-04-29 DOI: 10.1007/s00025-024-02175-7
Hanfei Song, Chun Wang
{"title":"Further Generalizations of the (A.2) and (H.2) Supercongruences of Van Hamme","authors":"Hanfei Song, Chun Wang","doi":"10.1007/s00025-024-02175-7","DOIUrl":"https://doi.org/10.1007/s00025-024-02175-7","url":null,"abstract":"<p>In this paper, in view of the transformation formulas for basic hypergeometric series and the creative microscoping method introduced by Guo and Zudilin, we establish new <i>q</i>-analogues of Van Hamme’s (A.2) and (H.2) supercongruences with two parameters</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":"73 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140811505","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
The Effect of Transport Noise on Interface Formulation 传输噪音对界面配方的影响
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-04-27 DOI: 10.1007/s00025-024-02172-w
Franco Flandoli, Satoshi Yokoyama
{"title":"The Effect of Transport Noise on Interface Formulation","authors":"Franco Flandoli, Satoshi Yokoyama","doi":"10.1007/s00025-024-02172-w","DOIUrl":"https://doi.org/10.1007/s00025-024-02172-w","url":null,"abstract":"<p>The paper discusses a mass conserving Allen–Cahn equation with a small parameter <span>(epsilon &gt;0)</span> perturbed by transport type noise involving the smeared noise <span>({dot{w}}^epsilon _i)</span> (formally converging to white noise <span>({dot{w}}_i)</span>), and investigate its sharp interface limit as <span>(epsilon rightarrow 0)</span>. We restrict our discussion over the two-dimensional domain to construct the hypersurface driven by the stochastic term appearing due to the contribution from the transport term when <span>(epsilon rightarrow 0)</span>. We make use of asymptotic expansion method to discuss the sharp interface limit.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":"103 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140799522","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
Existence, Multiplicity and $$C^1$$ -Regularity for Singular Parametric Problems Driven by the Sum of Three Distinct Anisotropic Operators 由三个不同各向异性算子之和驱动的奇异参数问题的存在性、多重性和 $$C^1$$ - 规则性
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-04-27 DOI: 10.1007/s00025-024-02162-y
Francesca Vetro
{"title":"Existence, Multiplicity and $$C^1$$ -Regularity for Singular Parametric Problems Driven by the Sum of Three Distinct Anisotropic Operators","authors":"Francesca Vetro","doi":"10.1007/s00025-024-02162-y","DOIUrl":"https://doi.org/10.1007/s00025-024-02162-y","url":null,"abstract":"<p>In this paper, we focus on a problem with parameter dependence both in the leading term and in the reaction term. Such problem is driven by the sum of three anisotropic operators with distinct variable exponents and has in the reaction the combined effects of a singular term and of concave and convex nonlinearities. Under very general assumptions, we produce positive solutions for this problem as well as we establish the precise dependence of the set of such solutions on the parameter <span>(lambda &gt;0)</span> (which appears in the reaction) as the latter varies. Our approach is based on the use of variational tools together with truncation and comparison techniques. We stress that here we also describe the asymptotic behavior of specific positive solutions as both parameters in the leading term and in the reaction term vary in an appropriate range.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":"30 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140799543","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 Finite Groups Factorised by Submodular Subgroups 论由次模子群因子化的有限群
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-04-26 DOI: 10.1007/s00025-024-02173-9
Victor S. Monakhov, Irina L. Sokhor
{"title":"On Finite Groups Factorised by Submodular Subgroups","authors":"Victor S. Monakhov, Irina L. Sokhor","doi":"10.1007/s00025-024-02173-9","DOIUrl":"https://doi.org/10.1007/s00025-024-02173-9","url":null,"abstract":"<p>A subgroup <i>H</i> of a finite group <i>G</i> is submodular in <i>G</i> if there is a subgroup chain <span>(H=H_0le ldots le H_ile H_{i+1}le ldots le H_n=G)</span> such that <span>(H_i)</span> is a modular subgroup of <span>(H_{i+1})</span> for every <i>i</i>. We investigate finite factorised groups with submodular primary (cyclic primary) subgroups in factors. We indicate a general approach to the description of finite groups factorised by supersolvable submodular subgroups.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":"22 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140799590","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 Magnetic Curves in Contact Metric Geometry 接触公元几何中的磁性曲线泛化
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-04-26 DOI: 10.1007/s00025-024-02169-5
Pablo Alegre, Joaquín Barrera, Alfonso Carriazo, Daniel García-Cano
{"title":"A Generalization of Magnetic Curves in Contact Metric Geometry","authors":"Pablo Alegre, Joaquín Barrera, Alfonso Carriazo, Daniel García-Cano","doi":"10.1007/s00025-024-02169-5","DOIUrl":"https://doi.org/10.1007/s00025-024-02169-5","url":null,"abstract":"<p>In this paper we study some curves of a trans-Sasakian manifold that generalize magnetic curves.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":"24 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140799469","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
Codazzi Tensor Fields in Reductive Homogeneous Spaces 还原均质空间中的科达齐张量场
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-04-19 DOI: 10.1007/s00025-024-02151-1
James Marshall Reber, Ivo Terek
{"title":"Codazzi Tensor Fields in Reductive Homogeneous Spaces","authors":"James Marshall Reber, Ivo Terek","doi":"10.1007/s00025-024-02151-1","DOIUrl":"https://doi.org/10.1007/s00025-024-02151-1","url":null,"abstract":"<p>We extend the results about left-invariant Codazzi tensor fields on Lie groups equipped with left-invariant Riemannian metrics obtained by d’Atri in 1985 to the setting of reductive homogeneous spaces <i>G</i>/<i>H</i>, where the curvature of the canonical connection of second kind associated with the fixed reductive decomposition <span>(mathfrak {g} = mathfrak {h}oplus mathfrak {m})</span> enters the picture. In particular, we show that invariant Codazzi tensor fields on a naturally reductive homogeneous space are parallel.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":"8 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140628405","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
Distortion Estimations and Metric Dimensions of Some Hyperbolic-Type Metrics in the Unit Disk 单位盘中某些双曲型度量的失真估计和度量尺寸
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-04-19 DOI: 10.1007/s00025-024-02170-y
Siji Wei, Yingqing Xiao
{"title":"Distortion Estimations and Metric Dimensions of Some Hyperbolic-Type Metrics in the Unit Disk","authors":"Siji Wei, Yingqing Xiao","doi":"10.1007/s00025-024-02170-y","DOIUrl":"https://doi.org/10.1007/s00025-024-02170-y","url":null,"abstract":"<p>The article considers two properties of several metrics defined in the unit disk <span>(Delta )</span> in <span>({mathbb {C}})</span>. One is the Lipschitz constant of Möbius transformation preserving <span>(Delta )</span>, especially the <i>t</i>-metric case and the Hilbert metric case. In particular, we confirm a conjecture posed by Rainio and Vuorinen (Results Math 77:71–80, 2022) about <i>t</i>-metric, and disprove the conjecture posed by Rainio and Vuorinen (Stud Sci Math Hung 60:175–191, 2023) about Hilbert metric. Moreover, we show that the metric dimensions of metric spaces <span>((Delta , d))</span>, where <i>d</i> includes hyperbolic metric, <i>j</i>-metric, Hilbert metric and <i>t</i>-metric, are 3. Thus, we solve the open question posed by Bau and Beardon (Comput Methods Funct Theory 13:295–305, 2013) about these metrics in the unit disk case.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":"25 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140628497","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
Functional Analysis Approach to the Collatz Conjecture 科拉茨猜想的函数分析方法
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-04-19 DOI: 10.1007/s00025-024-02167-7
Mikhail Neklyudov
{"title":"Functional Analysis Approach to the Collatz Conjecture","authors":"Mikhail Neklyudov","doi":"10.1007/s00025-024-02167-7","DOIUrl":"https://doi.org/10.1007/s00025-024-02167-7","url":null,"abstract":"<p>We examine the problems associated with the Collatz map <i>T</i> from the point of view of functional analysis. We associate with <i>T</i> a certain linear operator <span>(mathcal {T})</span> and show that cycles and (hypothetical) divergent trajectories (generated by <i>T</i>) correspond to certain classes of fixed points of the operator <span>(mathcal {T})</span>. We also show the relationship between the dynamic properties of the operator <span>(mathcal {T})</span> and the map <i>T</i>. We prove that the absence of non-trivial cycles of <i>T</i> leads to hypercyclicity of the operator <span>(mathcal {T})</span>. In the second part, we show that the index of the operator <span>(Id-mathcal {T}in mathcal {L}(H^2(D)))</span> provides an upper estimate for the number of cycles of <i>T</i>. For the proof, we consider the adjoint operator <span>(mathcal {F}=mathcal {T}^*)</span></p><span>$$begin{aligned} mathcal {F}: grightarrow g(z^2)+frac{z^{-frac{1}{3}}}{3}left( g(z^{frac{2}{3}})+e^{frac{2pi i}{3}}g(z^{frac{2}{3}}e^{frac{2pi i}{3}})+e^{frac{4pi i}{3}}g(z^{frac{2}{3}}e^{frac{4pi i}{3}})right) , end{aligned}$$</span><p>which was first introduced by Berg, Meinardus in [3], and show that it has no non-trivial fixed points in <span>(H^2(D))</span>. Furthermore, we calculate the resolvent of the operator <span>(mathcal {F})</span> and derive the equation for the characteristic function of the total stopping time <span>(sigma _{infty })</span> as an application. In addition, we construct an invariant measure for <span>(mathcal {T})</span> in a slightly different setup, and investigate how the operator <span>(mathcal {T})</span> acts on generalized arithmetic progressions.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":"131 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140628944","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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