Journal of Mathematical Analysis and Applications最新文献

{"title":"A Radon-Nikodym type property for von Neumann algebras","authors":"Yuzhang Chen , Chi-Keung Ng","doi":"10.1016/j.jmaa.2025.130032","DOIUrl":"10.1016/j.jmaa.2025.130032","url":null,"abstract":"<div><div>Let <em>M</em> be a von Neumann algebra and <em>ϕ</em> be a normal semi-finite weight. Let <span><math><msub><mrow><mi>M</mi></mrow><mrow><mi>ϕ</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>s</mi></mrow><mrow><mi>ϕ</mi></mrow></msub></math></span> be the centralizer and the support of <em>ϕ</em>, respectively. Write <span><math><mi>Z</mi><mo>(</mo><msub><mrow><mi>M</mi></mrow><mrow><mi>ϕ</mi></mrow></msub><mo>)</mo></math></span> for the center of <span><math><msub><mrow><mi>M</mi></mrow><mrow><mi>ϕ</mi></mrow></msub></math></span>.</div><div>If <em>ϕ</em> satisfies the condition:</div><div>(1) <span><math><msubsup><mrow><mi>M</mi></mrow><mrow><mi>ϕ</mi></mrow><mrow><mo>′</mo></mrow></msubsup><mo>∩</mo><mi>M</mi><mo>⊆</mo><msub><mrow><mi>M</mi></mrow><mrow><mi>ϕ</mi></mrow></msub></math></span>,</div><div>then the following “Radon-Nikodym type property” holds:</div><div>(2) for each normal semi-finite weight <em>ψ</em>, if <span><math><msub><mrow><mi>s</mi></mrow><mrow><mi>ψ</mi></mrow></msub><mo>≤</mo><msub><mrow><mi>s</mi></mrow><mrow><mi>ϕ</mi></mrow></msub></math></span>, <span><math><msub><mrow><mi>s</mi></mrow><mrow><mi>ψ</mi></mrow></msub><mo>∈</mo><msub><mrow><mi>M</mi></mrow><mrow><mi>ϕ</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>M</mi></mrow><mrow><mi>ϕ</mi></mrow></msub><mo>⊆</mo><msub><mrow><mi>M</mi></mrow><mrow><mi>ψ</mi></mrow></msub></math></span>, then there is a self-adjoint positive operator <em>h</em> affiliated with <span><math><mi>Z</mi><mo>(</mo><msub><mrow><mi>M</mi></mrow><mrow><mi>ϕ</mi></mrow></msub><mo>)</mo></math></span> such that <span><math><mi>ψ</mi><mo>=</mo><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>h</mi></mrow></msub></math></span>.</div><div>It is shown that if <em>ϕ</em> is strictly semi-finite, then <span><math><mo>(</mo><mn>2</mn><mo>)</mo><mo>⇒</mo><mo>(</mo><mn>1</mn><mo>)</mo></math></span>, and they are equivalent to:</div><div>(2) for every <sup>⁎</sup>-automorphism <em>θ</em> on <em>M</em> with <span><math><mi>θ</mi><msub><mrow><mo>|</mo></mrow><mrow><msub><mrow><mi>M</mi></mrow><mrow><mi>ϕ</mi></mrow></msub></mrow></msub><mo>=</mo><msub><mrow><mi>id</mi></mrow><mrow><msub><mrow><mi>M</mi></mrow><mrow><mi>ϕ</mi></mrow></msub></mrow></msub></math></span>, one has <span><math><mi>ϕ</mi><mo>∘</mo><mi>θ</mi><mo>=</mo><mi>ϕ</mi></math></span>;</div><div>(4) there exists a unique normal conditional expectation from <em>M</em> onto <span><math><msub><mrow><mi>M</mi></mrow><mrow><mi>ϕ</mi></mrow></msub></math></span>.</div><div>When <em>M</em> has separable predual and <em>ϕ</em> is both strictly semi-finite and faithful, Condition (1) is also equivalent to</div><div>(5) <span><math><msub><mrow><mi>M</mi></mrow><mrow><mi>ϕ</mi></mrow></msub></math></span> contains a maximal abelian <sup>⁎</sup>-subalgebra of <em>M</em>.</div><div>Furthermore, if <em>M</em> has separable predual but has no type <span><math><msub><mrow><mi>III</mi></mrow><mrow><mn>1</mn></mrow></ms","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"554 2","pages":"Article 130032"},"PeriodicalIF":1.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145010003","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}

{"title":"On the weak Sard property","authors":"Roman V. Dribas,&nbsp;Andrew S. Golovnev,&nbsp;Nikolay A. Gusev","doi":"10.1016/j.jmaa.2025.130022","DOIUrl":"10.1016/j.jmaa.2025.130022","url":null,"abstract":"<div><div>If <span><math><mi>f</mi><mo>:</mo><msup><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>→</mo><mi>R</mi></math></span> is of class <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> then Sard's theorem implies that <em>f</em> has the following <em>relaxed Sard property</em>: the image under <em>f</em> of the Lebesgue measure restricted to the critical set of <em>f</em> is a singular measure. We show that for <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>α</mi></mrow></msup></math></span> functions with <span><math><mi>α</mi><mo>&lt;</mo><mn>1</mn></math></span> this property is strictly stronger than the <em>weak Sard property</em> introduced by Alberti, Bianchini and Crippa, while for any monotone continuous function these two properties are equivalent.</div><div>We also show that even in the one-dimensional setting Hölder regularity is not sufficient for the relaxed Sard property.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"555 1","pages":"Article 130022"},"PeriodicalIF":1.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145020223","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}

{"title":"A two-stage sheep brucellosis transmission dynamic model in a patchy environment: Stability analysis and optimization of transportation scheme","authors":"Shuangjie Bai ,&nbsp;Boqiang Cao ,&nbsp;Ting Kang ,&nbsp;Qingyun Wang","doi":"10.1016/j.jmaa.2025.130026","DOIUrl":"10.1016/j.jmaa.2025.130026","url":null,"abstract":"<div><div>The cross-regional transport of sheep breaks geographical restrictions and expands the range of sheep, leading to the spread of brucellosis, one of the most widely spread zoonotic diseases transmitted by animals, and exposing more sheep and people to the threat of infection. To this end, a two-stage sheep brucellosis transmission dynamic model in a patchy environment is formulated based on the transmission characteristics of brucellosis. Firstly, the basic reproduction number is determined, and the global stabilities of disease-free, nontrivial boundary, and endemic equilibria are established, respectively. Subsequently, numerical simulations are applied to verify the correctness of the theoretical results. Finally, based on the recruitment rates of lambs and the basic reproduction number of two patches, the optimal transportation scheme for lambs and adult sheep is provided to reduce the risk of transmission of brucellosis.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"555 1","pages":"Article 130026"},"PeriodicalIF":1.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145049971","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}

{"title":"Stochastic very weak solutions to parabolic equations with singular coefficients","authors":"Snežana Gordić ,&nbsp;Tijana Levajković ,&nbsp;Ljubica Oparnica","doi":"10.1016/j.jmaa.2025.130023","DOIUrl":"10.1016/j.jmaa.2025.130023","url":null,"abstract":"<div><div>A class of stochastic parabolic equations with singular potentials is analyzed within the chaos expansion framework, utilizing the Wick product to handle the multiplication of generalized stochastic processes. The analysis combines the chaos expansion method from white noise analysis with the concept of very weak solutions from partial differential equation theory. The stochastic very weak solution to the parabolic evolution problem is defined, and its existence and uniqueness are established. For sufficiently regular potentials and data, we demonstrate the consistency of the stochastic very weak solution with a stochastic weak solution. An illustrative example is provided, potential applications are reviewed, and future challenges are outlined.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"555 1","pages":"Article 130023"},"PeriodicalIF":1.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145010782","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}

{"title":"Multiple zeta values and coefficients of Laurent series expansion of Beta function","authors":"Dilip K. Sahoo","doi":"10.1016/j.jmaa.2025.130031","DOIUrl":"10.1016/j.jmaa.2025.130031","url":null,"abstract":"<div><div>In <span><span>[12]</span></span>, we proved a translation formula for multiple zeta functions, which is analogous to that of Riemann zeta function proved by V. Ramaswami <span><span>[11]</span></span>. In this article we present a nice application of this formula. Particularly we express the coefficients of Laurent series expansion of one variable Beta function <span><math><mi>B</mi><mrow><mo>(</mo><mi>s</mi><mo>,</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></mrow></math></span> in terms of certain series involving multiple zeta values. As a consequence, we are able to calculate the values of these series recursively.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"555 1","pages":"Article 130031"},"PeriodicalIF":1.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144997599","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}

{"title":"Stability and averaging principle for distribution dependent SDEs driven by G-Brownian motion","authors":"Wensheng Yin ,&nbsp;Yong Ren ,&nbsp;Kaile Cao","doi":"10.1016/j.jmaa.2025.130024","DOIUrl":"10.1016/j.jmaa.2025.130024","url":null,"abstract":"<div><div>This paper concerns the asymptotic behavior for distribution dependent stochastic differential equations driven by <em>G</em>-Brownian motion (<em>G</em>-SDEs). Under Lipschitz condition, we study exponentially second-moment ultimate boundedness, stability and averaging principle. Under non-Lipschitz condition, we first prove the existence and uniqueness for distribution dependent <em>G</em>-SDEs by adopting Carathéodory approximation approach. In particular, the fast time oscillating distribution dependent <em>G</em>-SDEs is treated and its solution can be approximated by the averaged distribution dependent <em>G</em>-SDEs under averaging condition. Additionally, two illustrative examples are provided to validate the averaged-distribution-dependent <em>G</em>-SDEs.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"555 1","pages":"Article 130024"},"PeriodicalIF":1.2,"publicationDate":"2025-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144926738","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}

{"title":"Orbit counting for sofic shift-flip systems","authors":"Azmeer Nordin ,&nbsp;Mohd Salmi Md Noorani ,&nbsp;Mohd Hafiz Mohd","doi":"10.1016/j.jmaa.2025.130021","DOIUrl":"10.1016/j.jmaa.2025.130021","url":null,"abstract":"<div><div>A sofic shift is a discrete dynamical system which consists of bi-infinite sequences of labels corresponding to paths in a labeled graph. If it is subjected to a certain automorphism called a flip, then it forms a sofic shift-flip system. The flip system is regarded as an action of infinite dihedral group on the sofic shift. The distribution of finite orbits under this action may indicate the complexity of the flip system. For this purpose, the prime orbit counting function is used to describe the growth of the finite orbits. In the literature, the asymptotic behavior of the counting function has been obtained for shift-flip systems of finite type (SFT-flip systems), which are a subclass of the sofic shift-flip systems. In this paper, we will prove a similar asymptotic result for a sofic shift-flip system. The proof relies on the construction of an underlying SFT-flip system to serve as a presentation of the sofic shift-flip system. The number of finite orbits in the said system is then estimated from the SFT-flip system via combinatorial calculations. Our finding here is complete since it is applicable to both irreducible and reducible sofic shifts.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"555 1","pages":"Article 130021"},"PeriodicalIF":1.2,"publicationDate":"2025-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144997596","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}

{"title":"Self-similar singularities for electron MHD","authors":"Mimi Dai,&nbsp;Hannah Guerra,&nbsp;Chao Wu","doi":"10.1016/j.jmaa.2025.130029","DOIUrl":"10.1016/j.jmaa.2025.130029","url":null,"abstract":"<div><div>We study several types of self-similar solutions for the electron magnetohydrodynamics (MHD) without resistivity, including locally self-similar solutions and pseudo-self-similar solutions. We show that under certain conditions, these types of self-similar blowup solutions can be excluded.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"555 1","pages":"Article 130029"},"PeriodicalIF":1.2,"publicationDate":"2025-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144997600","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}

{"title":"Limit theorems and fractal properties of digit gaps in Pierce expansions","authors":"Liuhui Lu ,&nbsp;Cai Long ,&nbsp;Lei Shang","doi":"10.1016/j.jmaa.2025.130019","DOIUrl":"10.1016/j.jmaa.2025.130019","url":null,"abstract":"<div><div>In this paper, we revisit Shallit's results on the law of large numbers, the central limit theorem, and the law of the iterated logarithm for the digits of Pierce expansions. We extend these limit theorems to the setting of digit gaps in Pierce expansions, showing that digit gaps exhibit the same limit behavior as the digits themselves. However, the fractal properties of digit gaps differ significantly from those of the digits. To capture this difference, we compute the Hausdorff dimension of the exceptional sets associated with the law of large numbers for digit gaps and obtain explicit formulas for these dimensions.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"555 1","pages":"Article 130019"},"PeriodicalIF":1.2,"publicationDate":"2025-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144988712","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}

{"title":"Traveling wave solutions in a discrete diffusive epidemic model with stage structure and nonlinear incidence rate","authors":"Peng Yang","doi":"10.1016/j.jmaa.2025.130027","DOIUrl":"10.1016/j.jmaa.2025.130027","url":null,"abstract":"<div><div>In order to understand the geographical spread of infectious diseases, classical epidemic models should consider spatial effects. Compared to the continuous diffusion version, the discrete diffusive version will be more realistic and meaningful. To our knowledge, there are not many studies on discrete diffusive epidemic models, therefore, this article investigates the existence, nonexistence, and asymptotic behavior of traveling wave solutions for a discrete diffusive epidemic model incorporating stage structure and a nonlinear incidence rate. Concretely, to begin with, we obtain the basic reproduction number. And then, we get that the critical wave speed determines the existence and nonexistence of traveling wave solutions. Meanwhile, by establishing an appropriate Lyapunov functional and applying Lebesgue dominated convergence theorem, we derive the boundary asymptotic behavior of traveling wave solutions. Ultimately, we employ these results to two examples (i.e. discrete diffusion stage epidemic models).</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"555 1","pages":"Article 130027"},"PeriodicalIF":1.2,"publicationDate":"2025-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144988713","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}