Pub Date : 2026-01-19DOI: 10.1016/j.jmaa.2026.130444
Razvan Gabriel Iagar , Diana-Rodica Munteanu
<div><div>We study the large time behavior of solutions to the Cauchy problem for the quasilinear absorption-diffusion equation<span><span><span><math><msub><mrow><mo>∂</mo></mrow><mrow><mi>t</mi></mrow></msub><mi>u</mi><mo>=</mo><mi>Δ</mi><msup><mrow><mi>u</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>−</mo><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>σ</mi></mrow></msup><msup><mrow><mi>u</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>,</mo><mspace></mspace><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>×</mo><mo>(</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo><mo>,</mo></math></span></span></span> with exponents <span><math><mi>p</mi><mo>></mo><mi>m</mi><mo>></mo><mn>1</mn></math></span> and <span><math><mi>σ</mi><mo>></mo><mn>0</mn></math></span> and with initial conditions either satisfying<span><span><span><math><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>)</mo><mo>∩</mo><mi>C</mi><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>)</mo><mo>,</mo><mspace></mspace><munder><mi>lim</mi><mrow><mo>|</mo><mi>x</mi><mo>|</mo><mo>→</mo><mo>∞</mo></mrow></munder><mo></mo><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>θ</mi></mrow></msup><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>A</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo></math></span></span></span> for some <span><math><mi>θ</mi><mo>≥</mo><mn>0</mn></math></span>. A number of different asymptotic profiles are identified, and uniform convergence on time-expanding sets towards them is established, according to the position of both <em>p</em> and <em>θ</em> with respect to the following critical exponents<span><span><span><math><msub><mrow><mi>p</mi></mrow><mrow><mi>F</mi></mrow></msub><mo>(</mo><mi>σ</mi><mo>)</mo><mo>=</mo><mi>m</mi><mo>+</mo><mfrac><mrow><mi>σ</mi><mo>+</mo><mn>2</mn></mrow><mrow><mi>N</mi></mrow></mfrac><mo>,</mo><mspace></mspace><msub><mrow><mi>θ</mi></mrow><mrow><mo>⁎</mo></mrow></msub><mo>=</mo><mfrac><mrow><mi>σ</mi><mo>+</mo><mn>2</mn></mrow><mrow><mi>p</mi><mo>−</mo><mi>m</mi></mrow></mfrac><mo>,</mo><mspace></mspace><msup><mrow><mi>θ</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>=</mo><mi>N</mi><mo>.</mo></math></span></span></span> More precisely, solutions in radially symmetric self-similar form decaying as <span><math><mo>|</mo><mi>x</mi><mo>|</mo><mo>→</mo><mo>∞</mo></math></span> with the rates<span><span><span><math><mi>u</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>∼</mo><mi>A</mi><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mo>−</mo><msub><mrow><mi>θ</mi></mrow><mrow><mo>⁎</mo></mrow></msub></mrow></msup><mo>,</mo><mspace></mspace><mrow><mi>or</mi></mrow><mspace></mspace><mi>u</mi><
{"title":"A porous medium equation with spatially inhomogeneous absorption. Part II: Large time behavior","authors":"Razvan Gabriel Iagar , Diana-Rodica Munteanu","doi":"10.1016/j.jmaa.2026.130444","DOIUrl":"10.1016/j.jmaa.2026.130444","url":null,"abstract":"<div><div>We study the large time behavior of solutions to the Cauchy problem for the quasilinear absorption-diffusion equation<span><span><span><math><msub><mrow><mo>∂</mo></mrow><mrow><mi>t</mi></mrow></msub><mi>u</mi><mo>=</mo><mi>Δ</mi><msup><mrow><mi>u</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>−</mo><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>σ</mi></mrow></msup><msup><mrow><mi>u</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>,</mo><mspace></mspace><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>×</mo><mo>(</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo><mo>,</mo></math></span></span></span> with exponents <span><math><mi>p</mi><mo>></mo><mi>m</mi><mo>></mo><mn>1</mn></math></span> and <span><math><mi>σ</mi><mo>></mo><mn>0</mn></math></span> and with initial conditions either satisfying<span><span><span><math><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>)</mo><mo>∩</mo><mi>C</mi><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>)</mo><mo>,</mo><mspace></mspace><munder><mi>lim</mi><mrow><mo>|</mo><mi>x</mi><mo>|</mo><mo>→</mo><mo>∞</mo></mrow></munder><mo></mo><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>θ</mi></mrow></msup><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>A</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo></math></span></span></span> for some <span><math><mi>θ</mi><mo>≥</mo><mn>0</mn></math></span>. A number of different asymptotic profiles are identified, and uniform convergence on time-expanding sets towards them is established, according to the position of both <em>p</em> and <em>θ</em> with respect to the following critical exponents<span><span><span><math><msub><mrow><mi>p</mi></mrow><mrow><mi>F</mi></mrow></msub><mo>(</mo><mi>σ</mi><mo>)</mo><mo>=</mo><mi>m</mi><mo>+</mo><mfrac><mrow><mi>σ</mi><mo>+</mo><mn>2</mn></mrow><mrow><mi>N</mi></mrow></mfrac><mo>,</mo><mspace></mspace><msub><mrow><mi>θ</mi></mrow><mrow><mo>⁎</mo></mrow></msub><mo>=</mo><mfrac><mrow><mi>σ</mi><mo>+</mo><mn>2</mn></mrow><mrow><mi>p</mi><mo>−</mo><mi>m</mi></mrow></mfrac><mo>,</mo><mspace></mspace><msup><mrow><mi>θ</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>=</mo><mi>N</mi><mo>.</mo></math></span></span></span> More precisely, solutions in radially symmetric self-similar form decaying as <span><math><mo>|</mo><mi>x</mi><mo>|</mo><mo>→</mo><mo>∞</mo></math></span> with the rates<span><span><span><math><mi>u</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>∼</mo><mi>A</mi><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mo>−</mo><msub><mrow><mi>θ</mi></mrow><mrow><mo>⁎</mo></mrow></msub></mrow></msup><mo>,</mo><mspace></mspace><mrow><mi>or</mi></mrow><mspace></mspace><mi>u</mi><","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"558 2","pages":"Article 130444"},"PeriodicalIF":1.2,"publicationDate":"2026-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146023452","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}
Pub Date : 2026-01-16DOI: 10.1016/j.jmaa.2026.130442
Zhengchao Ji
In this paper, we establish some inequalities for the higher eigenvalues of the clamped plate problem on Riemannian manifolds with bounded sectional curvature. Our proofs are based on a Laplacian comparison and the Fourier transform. As an application of the Laplacian comparison, we obtain a generalized inequality of Cheng-Wei in . We also prove an improved lower bound for .
{"title":"Upper and lower bounds for the eigenvalues of the clamped plate problem on Riemannian manifolds","authors":"Zhengchao Ji","doi":"10.1016/j.jmaa.2026.130442","DOIUrl":"10.1016/j.jmaa.2026.130442","url":null,"abstract":"<div><div>In this paper, we establish some inequalities for the higher eigenvalues <span><math><msub><mrow><mi>Λ</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> of the clamped plate problem on Riemannian manifolds with bounded sectional curvature. Our proofs are based on a Laplacian comparison and the Fourier transform. As an application of the Laplacian comparison, we obtain a generalized inequality of Cheng-Wei in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. We also prove an improved lower bound for <span><math><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>i</mi></mrow><mrow><mi>k</mi></mrow></msubsup><msub><mrow><mi>Λ</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"558 1","pages":"Article 130442"},"PeriodicalIF":1.2,"publicationDate":"2026-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146078040","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}
Pub Date : 2026-01-15DOI: 10.1016/j.jmaa.2026.130434
L. Paoli , M. Shillor
This work is motivated by recent developments in MEMS devices, such as actuators and grippers. It analyzes the dynamics of a thermo-mechanical system, which can be found in most MEMS, consisting of a vertical rod joined at one end to a horizontal beam. The thermal expansion or vibration of the rod may cause the other end to come into contact with another device, the obstacle. This contact closes an electrical circuit, which is the actuating or switching function of such MEMS. The interaction between the rod's contacting end and the obstacle is described by Signorini's non-penetration contact condition for the displacements and by an inclusion-type Barber's heat exchange condition for the temperature. The heat-exchange coefficient is assumed to be a multi-function taking into account the air resistance in the gap. Moreover, the beam and the rod are assumed to be purely elastic. The model consists of a non-linear variational inclusion for the temperature coupled with a non-linear variational inequality for the displacements. To show the existence of a weak solution to the problem, we introduce a sequence of approximate problems, by considering a regularization of both Signorini's and Barber's conditions. We establish the existence of solutions to the approximate problems and then prove the convergence of these approximate solutions, as the regularization parameters vanish, to a solution of the original problem.
{"title":"A dynamic thermo-mechanical system with Signorini's complementarity condition and Barber's boundary heat-exchange condition","authors":"L. Paoli , M. Shillor","doi":"10.1016/j.jmaa.2026.130434","DOIUrl":"10.1016/j.jmaa.2026.130434","url":null,"abstract":"<div><div>This work is motivated by recent developments in MEMS devices, such as actuators and grippers. It analyzes the dynamics of a thermo-mechanical system, which can be found in most MEMS, consisting of a vertical rod joined at one end to a horizontal beam. The thermal expansion or vibration of the rod may cause the other end to come into contact with another device, the <em>obstacle</em>. This contact closes an electrical circuit, which is the actuating or switching function of such MEMS. The interaction between the rod's contacting end and the obstacle is described by Signorini's non-penetration contact condition for the displacements and by an inclusion-type Barber's heat exchange condition for the temperature. The heat-exchange coefficient is assumed to be a multi-function taking into account the air resistance in the gap. Moreover, the beam and the rod are assumed to be purely elastic. The model consists of a non-linear variational inclusion for the temperature coupled with a non-linear variational inequality for the displacements. To show the existence of a weak solution to the problem, we introduce a sequence of approximate problems, by considering a regularization of both Signorini's and Barber's conditions. We establish the existence of solutions to the approximate problems and then prove the convergence of these approximate solutions, as the regularization parameters vanish, to a solution of the original problem.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 1","pages":"Article 130434"},"PeriodicalIF":1.2,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146024441","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}
Pub Date : 2026-01-15DOI: 10.1016/j.jmaa.2026.130410
Francisco Alegría , Rodrigo Ponce , Juan C. Pozo
In this paper, we study the moments of semi-Markovian versions of classical birth-death processes, focusing on the so-called Quadratic Asymptotically Symmetric (QAS) birth-death processes. By means of Tauberian theorems, we provide a complete description of their asymptotic behavior. Our results show a dichotomous pattern: when the birth rate dominates the death rate, the moments grow exponentially, while if the death rate exceeds the birth rate, the moments decay slowly. This contrasts with classical birth-death processes, where moment growth and decay are always exponential.
{"title":"Asymptotics of the moments of Quadratic Asymptotically Symmetric time non-local birth-death processes","authors":"Francisco Alegría , Rodrigo Ponce , Juan C. Pozo","doi":"10.1016/j.jmaa.2026.130410","DOIUrl":"10.1016/j.jmaa.2026.130410","url":null,"abstract":"<div><div>In this paper, we study the moments of semi-Markovian versions of classical birth-death processes, focusing on the so-called <em>Quadratic Asymptotically Symmetric (QAS) birth-death processes</em>. By means of Tauberian theorems, we provide a complete description of their asymptotic behavior. Our results show a dichotomous pattern: when the birth rate dominates the death rate, the moments grow exponentially, while if the death rate exceeds the birth rate, the moments decay slowly. This contrasts with classical birth-death processes, where moment growth and decay are always exponential.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"558 1","pages":"Article 130410"},"PeriodicalIF":1.2,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038147","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}
Pub Date : 2026-01-15DOI: 10.1016/j.jmaa.2026.130430
Xin-Yi Chi, Qi-Qing Song
In a socially structured game with characteristic function forms, a certain coalition can organize its members as some kinds of internal organizations, and different internal organizations determine different social strengths and attainable payoffs of their members. This study introduces socially structured games with organization utilities, and proposes -core, -core, and -core of such games. The sufficient conditions for the existence of -core and -core are given for discontinuous games, and the Hadamard well-posedness of the -core of such games is proven. By introducing a collectively feasible condition and a coalitionally C-secure condition for discontinuous socially structured games, the existence of -core is also established.
{"title":"The existence and Hadamard well-posedness of cooperative equilibria for discontinuous socially structured games","authors":"Xin-Yi Chi, Qi-Qing Song","doi":"10.1016/j.jmaa.2026.130430","DOIUrl":"10.1016/j.jmaa.2026.130430","url":null,"abstract":"<div><div>In a socially structured game with characteristic function forms, a certain coalition can organize its members as some kinds of internal organizations, and different internal organizations determine different social strengths and attainable payoffs of their members. This study introduces socially structured games with organization utilities, and proposes <span><math><mi>E</mi><msub><mrow><mi>S</mi></mrow><mrow><mi>α</mi></mrow></msub></math></span>-core, <span><math><msup><mrow><mi>E</mi></mrow><mrow><mi>α</mi></mrow></msup></math></span>-core, and <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>α</mi></mrow></msub></math></span>-core of such games. The sufficient conditions for the existence of <span><math><mi>E</mi><msub><mrow><mi>S</mi></mrow><mrow><mi>α</mi></mrow></msub></math></span>-core and <span><math><msup><mrow><mi>E</mi></mrow><mrow><mi>α</mi></mrow></msup></math></span>-core are given for discontinuous games, and the Hadamard well-posedness of the <span><math><msup><mrow><mi>E</mi></mrow><mrow><mi>α</mi></mrow></msup></math></span>-core of such games is proven. By introducing a collectively feasible condition and a coalitionally <em>C</em>-secure condition for discontinuous socially structured games, the existence of <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>α</mi></mrow></msub></math></span>-core is also established.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"558 2","pages":"Article 130430"},"PeriodicalIF":1.2,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146023457","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}
Pub Date : 2026-01-15DOI: 10.1016/j.jmaa.2026.130435
Ilmari Kangasniemi
Given a bounded domain , a result by Bourgain, Brezis, and Mironescu characterizes when a function is in the Sobolev space based on the limiting behavior of its Besov seminorms. We prove a direct analogue of this result which characterizes when a differential k-form has a weak exterior derivative , where the analogue of the Besov seminorm that our result uses is based on integration over simplices.
{"title":"A Bourgain-Brezis-Mironescu -type characterization for Sobolev differential forms","authors":"Ilmari Kangasniemi","doi":"10.1016/j.jmaa.2026.130435","DOIUrl":"10.1016/j.jmaa.2026.130435","url":null,"abstract":"<div><div>Given a bounded domain <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>, a result by Bourgain, Brezis, and Mironescu characterizes when a function <span><math><mi>f</mi><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mi>Ω</mi><mo>)</mo></math></span> is in the Sobolev space <span><math><msup><mrow><mi>W</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>p</mi></mrow></msup><mo>(</mo><mi>Ω</mi><mo>)</mo></math></span> based on the limiting behavior of its Besov seminorms. We prove a direct analogue of this result which characterizes when a differential <em>k</em>-form <span><math><mi>ω</mi><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><msup><mrow><mo>∧</mo></mrow><mrow><mi>k</mi></mrow></msup><msup><mrow><mi>T</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mi>Ω</mi><mo>)</mo></math></span> has a weak exterior derivative <span><math><mi>d</mi><mi>ω</mi><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><msup><mrow><mo>∧</mo></mrow><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msup><msup><mrow><mi>T</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mi>Ω</mi><mo>)</mo></math></span>, where the analogue of the Besov seminorm that our result uses is based on integration over simplices.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 1","pages":"Article 130435"},"PeriodicalIF":1.2,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146024434","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}
Pub Date : 2026-01-15DOI: 10.1016/j.jmaa.2026.130441
Grigory Ivanov
John's inclusion states that a convex body in can be covered by the d-dilation of its maximal volume ellipsoid. We obtain a certain John-type inclusion for log-concave functions. As a byproduct of our approach, we establish the following asymptotically tight inequality: For any log-concave function f with finite, positive integral, there exist a positive definite matrix A, a point , and a positive constant α such that where is the indicator function of the unit ball .
{"title":"The John inclusion for log-concave functions","authors":"Grigory Ivanov","doi":"10.1016/j.jmaa.2026.130441","DOIUrl":"10.1016/j.jmaa.2026.130441","url":null,"abstract":"<div><div>John's inclusion states that a convex body in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> can be covered by the <em>d</em>-dilation of its maximal volume ellipsoid. We obtain a certain John-type inclusion for log-concave functions. As a byproduct of our approach, we establish the following asymptotically tight inequality: For any log-concave function <em>f</em> with finite, positive integral, there exist a positive definite matrix <em>A</em>, a point <span><math><mi>a</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>, and a positive constant <em>α</em> such that<span><span><span><math><msub><mrow><mi>χ</mi></mrow><mrow><msup><mrow><mi>B</mi></mrow><mrow><mi>d</mi></mrow></msup></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>≤</mo><mi>α</mi><mi>f</mi><mrow><mo>(</mo><mi>A</mi><mo>(</mo><mi>x</mi><mo>−</mo><mi>a</mi><mo>)</mo><mo>)</mo></mrow><mo>≤</mo><msqrt><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msqrt><mo>⋅</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><mfrac><mrow><mo>|</mo><mi>x</mi><mo>|</mo></mrow><mrow><mi>d</mi><mo>+</mo><mn>2</mn></mrow></mfrac><mo>+</mo><mo>(</mo><mi>d</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></msup><mo>,</mo></math></span></span></span> where <span><math><msub><mrow><mi>χ</mi></mrow><mrow><msup><mrow><mi>B</mi></mrow><mrow><mi>d</mi></mrow></msup></mrow></msub></math></span> is the indicator function of the unit ball <span><math><msup><mrow><mi>B</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 1","pages":"Article 130441"},"PeriodicalIF":1.2,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146024442","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}
Pub Date : 2026-01-15DOI: 10.1016/j.jmaa.2026.130439
Yurii Kolomoitsev
Traditional measures of smoothness often fail to provide accurate -error estimates for approximation by sampling or interpolation operators, especially for functions with low smoothness. To address this issue, we introduce a modified measure of smoothness that incorporates the local behavior of a function at the sampling points through the use of averaged operators. With this new tool, we obtain matching direct and inverse error estimates for a wide class of sampling operators and functions in spaces. Additionally, we derive a criterion for the convergence of sampling operators in , identify conditions that ensure the exact rate of approximation, construct realizations of K-functionals based on these operators, and study the smoothness properties of sampling operators. We also demonstrate how our results apply to several well-known operators, including the classical Whittaker-Shannon sampling operator, sampling operators generated by B-splines, and those based on the Gaussian.
{"title":"Special measures of smoothness for approximation by sampling operators in Lp(Rd)","authors":"Yurii Kolomoitsev","doi":"10.1016/j.jmaa.2026.130439","DOIUrl":"10.1016/j.jmaa.2026.130439","url":null,"abstract":"<div><div>Traditional measures of smoothness often fail to provide accurate <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-error estimates for approximation by sampling or interpolation operators, especially for functions with low smoothness. To address this issue, we introduce a modified measure of smoothness that incorporates the local behavior of a function at the sampling points through the use of averaged operators. With this new tool, we obtain matching direct and inverse error estimates for a wide class of sampling operators and functions in <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> spaces. Additionally, we derive a criterion for the convergence of sampling operators in <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>, identify conditions that ensure the exact rate of approximation, construct realizations of <em>K</em>-functionals based on these operators, and study the smoothness properties of sampling operators. We also demonstrate how our results apply to several well-known operators, including the classical Whittaker-Shannon sampling operator, sampling operators generated by <em>B</em>-splines, and those based on the Gaussian.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 1","pages":"Article 130439"},"PeriodicalIF":1.2,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146024440","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}
Pub Date : 2026-01-15DOI: 10.1016/j.jmaa.2026.130436
Ravindra Singh , Kiran Meena , Kapish Chand Meena
This paper presents general forms of Casorati inequalities for Riemannian maps and Riemannian submersions between Riemannian manifolds. Using these general forms, we obtain Casorati inequalities for Riemannian maps (resp. submersions) whose target (resp. source) spaces are generalized complex and generalized Sasakian space forms. As a consequence, we give Casorati inequalities for Riemannian maps (resp. submersions) when the target (resp. source) spaces are real, complex, real Kähler, Sasakian, Kenmotsu, cosymplectic, and almost space forms. To support these general forms, in the particular cases when the target or source spaces are real, complex, Sasakian, and Kenmotsu space forms, we verify known Casorati inequalities for Riemannian maps and Riemannian submersions. Further, we give Casorati inequalities for invariant and anti-invariant Riemannian maps (resp. submersions) whose target (resp. source) spaces are generalized complex and generalized Sasakian space forms. Toward information on geometric characteristics, we discuss the equality cases. We also exemplify the general forms.
{"title":"General Casorati inequalities and implications for Riemannian maps and Riemannian submersions","authors":"Ravindra Singh , Kiran Meena , Kapish Chand Meena","doi":"10.1016/j.jmaa.2026.130436","DOIUrl":"10.1016/j.jmaa.2026.130436","url":null,"abstract":"<div><div>This paper presents general forms of Casorati inequalities for Riemannian maps and Riemannian submersions between Riemannian manifolds. Using these general forms, we obtain Casorati inequalities for Riemannian maps (resp. submersions) whose target (resp. source) spaces are generalized complex and generalized Sasakian space forms. As a consequence, we give Casorati inequalities for Riemannian maps (resp. submersions) when the target (resp. source) spaces are real, complex, real Kähler, Sasakian, Kenmotsu, cosymplectic, and almost <span><math><mi>C</mi><mo>(</mo><mi>α</mi><mo>)</mo></math></span> space forms. To support these general forms, in the particular cases when the target or source spaces are real, complex, Sasakian, and Kenmotsu space forms, we verify known Casorati inequalities for Riemannian maps and Riemannian submersions. Further, we give Casorati inequalities for invariant and anti-invariant Riemannian maps (resp. submersions) whose target (resp. source) spaces are generalized complex and generalized Sasakian space forms. Toward information on geometric characteristics, we discuss the equality cases. We also exemplify the general forms.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"558 1","pages":"Article 130436"},"PeriodicalIF":1.2,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038210","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}
Pub Date : 2026-01-15DOI: 10.1016/j.jmaa.2026.130437
Dan Li
We analyze the asymptotic stability in distribution of an SIRS epidemic model described by stochastic differential equations with degenerate diffusion and Markov switching. A deterministic threshold parameter Λ for disease extinction and persistence is obtained. When , the disease will eventually disappear, and the distributions of the solutions of the model converge weakly to a singular measure. If , the disease will be persistent, and by constructing a stochastically equivalent process, we establish a Markov semigroup representation of the distribution densities and demonstrate the asymptotic stability of the semigroup.
{"title":"Asymptotic stability in distribution for a stochastic SIRS epidemic model with Markov switching","authors":"Dan Li","doi":"10.1016/j.jmaa.2026.130437","DOIUrl":"10.1016/j.jmaa.2026.130437","url":null,"abstract":"<div><div>We analyze the asymptotic stability in distribution of an SIRS epidemic model described by stochastic differential equations with degenerate diffusion and Markov switching. A deterministic threshold parameter <strong>Λ</strong> for disease extinction and persistence is obtained. When <span><math><mi>Λ</mi><mo><</mo><mn>0</mn></math></span>, the disease will eventually disappear, and the distributions of the solutions of the model converge weakly to a singular measure. If <span><math><mi>Λ</mi><mo>></mo><mn>0</mn></math></span>, the disease will be persistent, and by constructing a stochastically equivalent process, we establish a Markov semigroup representation of the distribution densities and demonstrate the asymptotic stability of the semigroup.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"557 2","pages":"Article 130437"},"PeriodicalIF":1.2,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146037697","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}
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