数学最新文献

{"title":"Application of the first exit time stochastic model with self-repair mechanism to human mortality rates.","authors":"Noriyuki Shimoyama, Masayasu Hosonuma","doi":"10.1007/s00285-024-02150-4","DOIUrl":"10.1007/s00285-024-02150-4","url":null,"abstract":"<p><p>The purpose of this study is to construct a mortality model that reasonably explains survival curves and mortality rates in terms of the decline in biological function, which is the phenomenon of ageing. In this model, an individual organism is regarded as a collection of subsystems, and for each subsystem, the model defines human mortality by introducing positive self-repair mechanisms and stochastically generated negative external shocks. The probability density function of the time of death is derived explicitly, and the model parameters are estimated using life tables from Japan and the UK, which demonstrate the existence of multiple parameter sets that fit well with the observed data.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11541399/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142584654","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global Weak Solutions to a Fluid-particle System of an Incompressible Non-Newtonian Fluid and the Vlasov Equation","authors":"Pei-yu Zhang,&nbsp;Li Fang,&nbsp;Zhen-hua Guo","doi":"10.1007/s10255-024-1080-0","DOIUrl":"10.1007/s10255-024-1080-0","url":null,"abstract":"<div><p>The purpose of this work is to investigate the existence and uniqueness of weak solutions to the initial-boundary value problem for a coupled system of an incompressible non-Newtonian fluid and the Vlasov equation. The coupling arises from the acceleration in the Vlasov equation and the drag force in the incompressible viscous non-Newtonian fluid with the stress tensor of a power-law structure for <span>(pgeqslant {11over 5})</span>. The main idea of the existence analysis is to reformulate the coupled system by means of a so-called truncation function. The advantage of the new formulation is to control the external force term <span>(G=-int_mathbb{{R}^{d}}(mathbf{u}-mathbf{v})fdmathbf{v} (d=2,3))</span>. The global existence of weak solutions to the reformulated system is shown by using the Faedo-Galerkin method and weak compactness techniques. We further prove the uniqueness of weak solutions to the considered system.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the Initial Layer and the Limit Behavior for Chemotaxis System with the Effect of Fluid in Fourier Space","authors":"Jian-xiang Wan,&nbsp;Hai-ping Zhong","doi":"10.1007/s10255-024-1134-3","DOIUrl":"10.1007/s10255-024-1134-3","url":null,"abstract":"<div><p>The paper deals with a Cauchy problem for the chemotaxis system with the effect of fluid </p><div><div><span>$$left{ {matrix{ {u_t^varepsilon + {u^varepsilon } cdot nabla {u^varepsilon } - Delta {u^varepsilon } + nabla {{rm{P}}^varepsilon } = {n^varepsilon }nabla {c^varepsilon },} hfill &amp; {{rm{in}}} hfill &amp; {{mathbb{R}^d} times left( {0,infty } right),} hfill cr {nabla cdot {u^varepsilon } = 0,} hfill &amp; {{rm{in}}} hfill &amp; {{mathbb{R}^d} times left( {0,infty } right),} hfill cr {n_t^varepsilon + {u^varepsilon } cdot nabla {n^varepsilon } - Delta {n^varepsilon } = - nabla cdot left( {{n^varepsilon }nabla {c^varepsilon }} right),} hfill &amp; {{rm{in}}} hfill &amp; {{mathbb{R}^d} times left( {0,infty } right),} hfill cr {{1 over varepsilon }c_t^varepsilon - Delta {c^varepsilon } = {n^varepsilon },} hfill &amp; {{rm{in}}} hfill &amp; {{mathbb{R}^d} times left( {0,infty } right),} hfill cr {left( {{u^varepsilon },{n^varepsilon },{c^varepsilon }} right){|_{t = 0}} = left( {{u_0},{n_0},{c_0}} right),} hfill &amp; {{rm{in}}} hfill &amp; {{mathbb{R}^d},} hfill cr } } right.$$</span></div></div><p> where <i>d</i> ≥ 2. It is known that for each <i>ϵ</i> &gt; 0 and all sufficiently small initial data (<i>u</i>₀, <i>n</i>₀, <i>c</i>₀) belongs to certain Fourier space, the problem possesses a unique global solution (<i>u</i>^<i>ϵ</i>, <i>n</i>^<i>ϵ</i>, <i>c</i>^<i>ϵ</i>) in Fourier space. The present work asserts that these solutions stabilize to (<i>u</i>^∞, <i>n</i>^∞, <i>c</i>^∞) as <i>ϵ</i>⁻¹ → 0. Moreover, we show that <i>c</i>^<i>ϵ</i>(<i>t</i>) has the initial layer as <i>ϵ</i>⁻¹ → 0. As one expects its limit behavior maybe give a new viewlook to understand the system.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10255-024-1134-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587905","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On β-extinction and Stability of a Stochastic Lotka-Volterra System with Infinite Delay","authors":"Shu-fen Zhao","doi":"10.1007/s10255-024-1078-7","DOIUrl":"10.1007/s10255-024-1078-7","url":null,"abstract":"<div><p>In this paper, a stochastic Lotka-Volterra system with infinite delay is considered. A new concept of extinction, namely, the almost sure <i>β</i>-extinction is proposed and sufficient conditions for the solution to be almost sure <i>β</i>-extinction are obtained. When the positive equilibrium exists and the intensities of the noises are small enough, any solution of the system is attracted by the positive equilibrium. Finally, numerical simulations are carried out to support the results.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587784","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Measures in the dual of BV: perimeter bounds and relations with divergence-measure fields","authors":"Giovanni E. Comi ,&nbsp;Gian Paolo Leonardi","doi":"10.1016/j.na.2024.113686","DOIUrl":"10.1016/j.na.2024.113686","url":null,"abstract":"<div><div>We analyze some properties of the measures in the dual of the space <span><math><mrow><mi>B</mi><mi>V</mi></mrow></math></span>, by considering (signed) Radon measures satisfying a perimeter bound condition, which means that the absolute value of the measure of a set is controlled by the perimeter of the set itself, and whose total variations also belong to the dual of <span><math><mrow><mi>B</mi><mi>V</mi></mrow></math></span>. We exploit and refine the results of Cong Phuc and Torres (2017), in particular exploring the relation with divergence-measure fields and proving the stability of the perimeter bound from sets to <span><math><mrow><mi>B</mi><mi>V</mi></mrow></math></span> functions under a suitable approximation of the given measure. As an important tool, we obtain a refinement of Anzellotti-Giaquinta approximation for <span><math><mrow><mi>B</mi><mi>V</mi></mrow></math></span> functions, which is of separate interest in itself and, in the context of Anzellotti’s pairing theory for divergence-measure fields, implies a new way of approximating <span><math><mi>λ</mi></math></span>-pairings, as well as new bounds for their total variation. These results are also relevant due to their application in the study of weak solutions to the non-parametric prescribed mean curvature equation with measure data, which is explored in a subsequent work.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142592583","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Threshold value for a quasilinear Keller–Segel chemotaxis system with the intermediate exponent in a bounded domain","authors":"Hua Zhong","doi":"10.1016/j.nonrwa.2024.104253","DOIUrl":"10.1016/j.nonrwa.2024.104253","url":null,"abstract":"&lt;div&gt;&lt;div&gt;We consider a quasilinear chemotaxis model &lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;⋅&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;⋅&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;τ&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; with nonlinear diffusion function &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;∞&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and chemotactic sensitivity &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;∞&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; in a bounded domain &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;⊂&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. Here the rate &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; grows like &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; with &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; as &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;mi&gt;∞&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;τ&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;.&lt;/div&gt;&lt;div&gt;It is first shown that there exists a &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∗&lt;/mo&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; such that if free energy with initial data is suitably small and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∗&lt;/mo&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; with &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mrow&gt;","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142592774","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":"Positive definite functions on a regular domain","authors":"Martin Buhmann, Yuan Xu","doi":"10.1093/imanum/drae074","DOIUrl":"https://doi.org/10.1093/imanum/drae074","url":null,"abstract":"We define positive and strictly positive definite functions on a domain and study these functions on a list of regular domains. The list includes the unit ball, conic surface, hyperbolic surface, solid hyperboloid and the simplex. Each of these domains is embedded in a quadrant or a union of quadrants of the unit sphere by a distance-preserving map, from which characterizations of positive definite and strictly positive definite functions are derived for these regular domains.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142588647","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Traveling Fronts for a Time-periodic Population Model with Dispersal","authors":"Hai-qin Zhao","doi":"10.1007/s10255-024-1052-4","DOIUrl":"10.1007/s10255-024-1052-4","url":null,"abstract":"<div><p>In this paper, we study a class of time-periodic population model with dispersal. It is well known that the existence of the periodic traveling fronts has been established. However, the uniqueness and stability of such fronts remain unsolved. In this paper, we first prove the uniqueness of non-critical periodic traveling fronts. Then, we show that all non-critical periodic traveling fronts are exponentially asymptotically stable.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587787","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Packing directed cycles of specified odd length into digraphs and alternating cycles into bipartite graphs","authors":"Shuya Chiba ,&nbsp;Koshin Yoshida","doi":"10.1016/j.disc.2024.114306","DOIUrl":"10.1016/j.disc.2024.114306","url":null,"abstract":"<div><div>In this paper, we prove the following result. For given integers <span><math><mi>k</mi><mo>≥</mo><mn>1</mn><mo>,</mo><mspace></mspace><mi>t</mi><mo>≥</mo><mn>0</mn></math></span> with <span><math><mi>k</mi><mo>≥</mo><mi>t</mi></math></span> and an odd integer <span><math><mi>ℓ</mi><mo>≥</mo><mn>3</mn></math></span>, there exists an integer <span><math><msub><mrow><mi>n</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><msub><mrow><mi>n</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>k</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>ℓ</mi><mo>)</mo></math></span> satisfying the following: If <em>D</em> is a digraph of order <span><math><mi>n</mi><mo>≥</mo><msub><mrow><mi>n</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>, and if <span><math><msubsup><mrow><mi>d</mi></mrow><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>(</mo><mi>u</mi><mo>)</mo><mo>+</mo><msubsup><mrow><mi>d</mi></mrow><mrow><mi>D</mi></mrow><mrow><mo>−</mo></mrow></msubsup><mo>(</mo><mi>v</mi><mo>)</mo><mo>≥</mo><mi>n</mi><mo>+</mo><mi>t</mi></math></span> for every two distinct vertices <em>u</em> and <em>v</em> with <span><math><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo><mo>∉</mo><mi>A</mi><mo>(</mo><mi>D</mi><mo>)</mo></math></span>, then <em>D</em> contains <em>k</em> vertex-disjoint directed cycles of length <em>ℓ</em> or <span><math><mi>ℓ</mi><mo>+</mo><mn>1</mn></math></span> such that at least <em>t</em> of them are of length <em>ℓ</em>. This is a common extension of the results obtained by Brandt et al. (1997) and, Chiba and Yamashita (2018). We also discuss the relation between our result and problems on packing alternating cycles into bipartite graphs.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142593040","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":"The vector space generated by permutations of a trade or a design","authors":"E. Ghorbani ,&nbsp;S. Kamali ,&nbsp;G.B. Khosrovshahi","doi":"10.1016/j.jcta.2024.105969","DOIUrl":"10.1016/j.jcta.2024.105969","url":null,"abstract":"<div><div>Motivated by a classical result of Graver and Jurkat (1973) and Graham, Li, and Li (1980) in combinatorial design theory, which states that the permutations of <em>t</em>-<span><math><mo>(</mo><mi>v</mi><mo>,</mo><mi>k</mi><mo>)</mo></math></span> minimal trades generate the vector space of all <em>t</em>-<span><math><mo>(</mo><mi>v</mi><mo>,</mo><mi>k</mi><mo>)</mo></math></span> trades, we investigate the vector space spanned by permutations of an arbitrary trade. We prove that this vector space possesses a decomposition as a direct sum of subspaces formed in the same way by a specific family of so-called total trades. As an application, we demonstrate that for any <em>t</em>-<span><math><mo>(</mo><mi>v</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>λ</mi><mo>)</mo></math></span> design, its permutations can span the vector space generated by all <em>t</em>-<span><math><mo>(</mo><mi>v</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>λ</mi><mo>)</mo></math></span> designs for sufficiently large values of <em>v</em>. In other words, any <em>t</em>-<span><math><mo>(</mo><mi>v</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>λ</mi><mo>)</mo></math></span> design, or even any <em>t</em>-trade, can be expressed as a linear combination of permutations of a fixed <em>t</em>-design. This substantially extends a result by Ghodrati (2019), who proved the same result for Steiner designs.</div></div>","PeriodicalId":50230,"journal":{"name":"Journal of Combinatorial Theory Series A","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142593648","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}