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The exact dimension of Liouville numbers: The Fourier side 刘维尔数的精确维数，傅里叶边
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-07-07 DOI: 10.1016/j.jmaa.2025.129872
Iván Polasek , Ezequiel Rela
{"title":"The exact dimension of Liouville numbers: The Fourier side","authors":"Iván Polasek ,&nbsp;Ezequiel Rela","doi":"10.1016/j.jmaa.2025.129872","DOIUrl":"10.1016/j.jmaa.2025.129872","url":null,"abstract":"<div><div>In this article we study the generalized Fourier dimension of the set of Liouville numbers <span><math><mi>L</mi></math></span>. Being a set of zero Hausdorff dimension, the analysis has to be done at the level of functions with a slow decay at infinity acting as control for the Fourier transform of (Rajchman) measures supported on <span><math><mi>L</mi></math></span>. We give an almost complete characterization of admissible decays for this set in terms of comparison to power-like functions. This work can be seen as the “Fourier side” of the analysis made by Olsen and Renfro regarding the generalized Hausdorff dimension using gauge functions. We also provide an approach to deal with the problem of classifying oscillating candidates for a Fourier decay for <span><math><mi>L</mi></math></span> relying on its translation invariance property.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"553 2","pages":"Article 129872"},"PeriodicalIF":1.2,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144596734","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 general quasilinear elliptic problem with variable exponents and Neumann boundary conditions for image processing 图像处理的一般变指数拟线性椭圆问题和Neumann边界条件
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-07-07 DOI: 10.1016/j.jmaa.2025.129874
Bogdan Maxim
{"title":"A general quasilinear elliptic problem with variable exponents and Neumann boundary conditions for image processing","authors":"Bogdan Maxim","doi":"10.1016/j.jmaa.2025.129874","DOIUrl":"10.1016/j.jmaa.2025.129874","url":null,"abstract":"<div><div>The aim of this paper is to state and prove existence and uniqueness results for a general elliptic problem with homogeneous Neumann boundary conditions, often associated with image processing tasks like denoising. The novelty is that we surpass the lack of coercivity of the Euler-Lagrange functional with an innovative technique that has at its core the idea of showing that the minimum of the energy functional over a subset of the space <span><math><msup><mrow><mi>W</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>p</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></msup><mo>(</mo><mi>Ω</mi><mo>)</mo></math></span> coincides with the global minimum. The obtained existence result applies to multiple-phase elliptic problems under remarkably weak assumptions.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"553 2","pages":"Article 129874"},"PeriodicalIF":1.2,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144614858","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
Sampling projections in the uniform norm 均匀范数的抽样投影
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-07-07 DOI: 10.1016/j.jmaa.2025.129873
David Krieg , Kateryna Pozharska , Mario Ullrich , Tino Ullrich
{"title":"Sampling projections in the uniform norm","authors":"David Krieg ,&nbsp;Kateryna Pozharska ,&nbsp;Mario Ullrich ,&nbsp;Tino Ullrich","doi":"10.1016/j.jmaa.2025.129873","DOIUrl":"10.1016/j.jmaa.2025.129873","url":null,"abstract":"<div><div>We show that there are sampling projections onto arbitrary <em>n</em>-dimensional subspaces of <span><math><mi>B</mi><mo>(</mo><mi>D</mi><mo>)</mo></math></span> with at most 2<em>n</em> samples and norm of order <span><math><msqrt><mrow><mi>n</mi></mrow></msqrt></math></span>, where <span><math><mi>B</mi><mo>(</mo><mi>D</mi><mo>)</mo></math></span> is the space of bounded functions on a set <em>D</em>. This gives a more explicit form of the Kadets-Snobar theorem for the uniform norm. We discuss consequences for optimal recovery in <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"553 2","pages":"Article 129873"},"PeriodicalIF":1.2,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144632892","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
Bifurcation analysis of a diffusive predator-prey system with stage structure 具有阶段结构的扩散捕食-食饵系统的分岔分析
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-07-05 DOI: 10.1016/j.jmaa.2025.129850
Qianqian Sun , Chunjin Wei , Junjie Wei
{"title":"Bifurcation analysis of a diffusive predator-prey system with stage structure","authors":"Qianqian Sun ,&nbsp;Chunjin Wei ,&nbsp;Junjie Wei","doi":"10.1016/j.jmaa.2025.129850","DOIUrl":"10.1016/j.jmaa.2025.129850","url":null,"abstract":"<div><div>In this paper, we consider the dynamics of a diffusive predator-prey system with stage structure. The upper-lower solution method and the comparison principle are used in proving the nonnegativity of the solutions. Then the stability of the positive constant steady state solutions is determined by analyzing the distribution of the eigenvalues. Based on the analysis, a bifurcation set in a parameters plane is given, which shows how the dynamics change as the parameters vary. Furthermore, the potential Hopf bifurcations are explored. Finally, numerical simulations validate theoretical predictions and illustrate model dynamics.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"553 2","pages":"Article 129850"},"PeriodicalIF":1.2,"publicationDate":"2025-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144572747","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
Finite-rank approximation of affine processes on positive Hilbert-Schmidt operators 正Hilbert-Schmidt算子上仿射过程的有限秩逼近
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-07-05 DOI: 10.1016/j.jmaa.2025.129852
Sven Karbach
{"title":"Finite-rank approximation of affine processes on positive Hilbert-Schmidt operators","authors":"Sven Karbach","doi":"10.1016/j.jmaa.2025.129852","DOIUrl":"10.1016/j.jmaa.2025.129852","url":null,"abstract":"<div><div>In this paper, we introduce a method for approximating affine processes on the cone of positive Hilbert-Schmidt operators using positive semi-definite matrix-valued affine processes. First, we identify a set of admissible parameters and a pair of associated operator-valued generalized Riccati equations that characterize the class of affine processes. We then show that certain finite-dimensional projections of these admissible parameters align with the parameters of a Galerkin approximation of the generalized Riccati equations. Leveraging the theory of matrix-valued affine processes, we show that these approximations are identifiable with a sequence of finite-rank operator-valued affine processes. By establishing convergence rates for the Galerkin approximation, we prove the weak convergence of this sequence of finite-rank operator-valued affine processes and provide convergence rates for their Laplace transforms. The introduced method not only offers a practical and efficient approximation scheme for operator-valued affine processes, but also introduces a novel proof for the existence of Hilbert-valued affine processes, in particular of càdlàg versions of these. An example of an affine operator-valued process with infinite variation and state-dependent jump intensity is highlighted. Beyond its theoretical implications, this paper offers valuable tools for the analysis and approximation of infinite-dimensional affine stochastic volatility models.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"553 2","pages":"Article 129852"},"PeriodicalIF":1.2,"publicationDate":"2025-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144589324","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
Asymptotic behavior of an age-structured SIS model with nonlinear force of infection 具有非线性感染力的年龄结构SIS模型的渐近行为
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-07-04 DOI: 10.1016/j.jmaa.2025.129858
Soumak Nag, Suman Kumar Tumuluri
{"title":"Asymptotic behavior of an age-structured SIS model with nonlinear force of infection","authors":"Soumak Nag,&nbsp;Suman Kumar Tumuluri","doi":"10.1016/j.jmaa.2025.129858","DOIUrl":"10.1016/j.jmaa.2025.129858","url":null,"abstract":"<div><div>A nonlocal nonlinear SIS epidemic model with diffusion in space having restriction of movement of individual across the boundary of the region is considered. Existence and uniqueness of the steady state has been studied using spectral analysis and monotonicity of nonlinear operator, respectively. Sufficient conditions are given for local stability of the zero steady state. Moreover, global stability of the nonzero steady state is also discussed.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"553 2","pages":"Article 129858"},"PeriodicalIF":1.2,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144631152","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 law of large numbers and convergence rates for the discrete Fourier transform of random fields 随机场离散傅里叶变换的大数定律和收敛速率
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-07-04 DOI: 10.1016/j.jmaa.2025.129851
Vishakha
{"title":"On the law of large numbers and convergence rates for the discrete Fourier transform of random fields","authors":"Vishakha","doi":"10.1016/j.jmaa.2025.129851","DOIUrl":"10.1016/j.jmaa.2025.129851","url":null,"abstract":"<div><div>We study the Marcinkiewicz-Zygmund strong law of large numbers for the cubic partial sums of the discrete Fourier transform of random fields. We establish Marcinkiewicz-Zygmund types rate of convergence for the discrete Fourier transform of random fields under weaker conditions than identical distribution.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"553 1","pages":"Article 129851"},"PeriodicalIF":1.2,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144571125","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
Classification of separable hypersurfaces with constant sectional curvature 常截面曲率可分离超曲面的分类
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-07-04 DOI: 10.1016/j.jmaa.2025.129859
Muhittin Evren Aydin , Rafael López , Gabriel-Eduard Vîlcu
{"title":"Classification of separable hypersurfaces with constant sectional curvature","authors":"Muhittin Evren Aydin ,&nbsp;Rafael López ,&nbsp;Gabriel-Eduard Vîlcu","doi":"10.1016/j.jmaa.2025.129859","DOIUrl":"10.1016/j.jmaa.2025.129859","url":null,"abstract":"<div><div>In this paper, we give a full classification of the separable hypersurfaces of constant sectional curvature in the Euclidean <em>n</em>-space <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. In dimension <span><math><mi>n</mi><mo>=</mo><mn>3</mn></math></span>, this classification was solved by Hasanis and López (2021) <span><span>[18]</span></span>. When <span><math><mi>n</mi><mo>&gt;</mo><mn>3</mn></math></span>, we prove that the separable hypersurfaces of null sectional curvature are three particular families of such hypersurfaces. Finally, we prove that hyperspheres are the only separable hypersurfaces with nonzero constant sectional curvature.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"553 1","pages":"Article 129859"},"PeriodicalIF":1.2,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144581212","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
Non-uniform dependence for the two-component Camassa-Holm shallow water system 双组分Camassa-Holm浅水系统的非均匀依赖性
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-07-04 DOI: 10.1016/j.jmaa.2025.129853
Jinlu Li , Yanghai Yu , Weipeng Zhu
{"title":"Non-uniform dependence for the two-component Camassa-Holm shallow water system","authors":"Jinlu Li ,&nbsp;Yanghai Yu ,&nbsp;Weipeng Zhu","doi":"10.1016/j.jmaa.2025.129853","DOIUrl":"10.1016/j.jmaa.2025.129853","url":null,"abstract":"<div><div>In this paper, we consider the initial value problem to the two-component Camassa-Holm equation on the line. We give a new approach to studying non-uniform dependence on initial data. We prove that the solution map of this problem is not uniformly continuous in Sobolev spaces <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>s</mi></mrow></msup><mo>(</mo><mi>R</mi><mo>)</mo><mo>×</mo><msup><mrow><mi>H</mi></mrow><mrow><mi>s</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>(</mo><mi>R</mi><mo>)</mo></math></span> with <span><math><mi>s</mi><mo>&gt;</mo><mn>3</mn><mo>/</mo><mn>2</mn></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"553 2","pages":"Article 129853"},"PeriodicalIF":1.2,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144589325","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 novel approach to induce chaos for vibratory PDE systems 一种振动PDE系统诱导混沌的新方法
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-07-04 DOI: 10.1016/j.jmaa.2025.129856
Zi-Qing Tian , Hongyinping Feng
{"title":"A novel approach to induce chaos for vibratory PDE systems","authors":"Zi-Qing Tian ,&nbsp;Hongyinping Feng","doi":"10.1016/j.jmaa.2025.129856","DOIUrl":"10.1016/j.jmaa.2025.129856","url":null,"abstract":"<div><div>In this paper, we propose a novel method for inducing chaos in infinite-dimensional systems. The new approach, referred to as the kernel function method, regulates a carefully chosen performance output to exhibit chaotic dynamics governed by a pre-specified ODE system. Unlike the method of characteristics, the proposed technique is applicable not only to wave equations but also to the Euler-Bernoulli beam equation. Moreover, by appropriately selecting the pre-specified chaotic ODE system, a wide variety of chaotic oscillations can be generated. Specifically, by choosing the well-known Van der Pol equation, we derive a new nonlinear boundary condition for an Euler-Bernoulli beam that demonstrates chaotic oscillations. Numerical simulations are provided to help visualize the theoretical results.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"553 1","pages":"Article 129856"},"PeriodicalIF":1.2,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144581171","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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