{"title":"Perron’s Method in the Dirichlet Problem for the Soft Laplacian on a Stratified Set","authors":"N. S. Dairbekov, O. M. Penkin, D. V. Savasteev","doi":"10.1134/S1064562424602658","DOIUrl":"10.1134/S1064562424602658","url":null,"abstract":"<p>The solvability of the Dirichlet problem for the soft Laplacian on a stratified set is proved using a modification of the well-known Perron method.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"111 1","pages":"16 - 19"},"PeriodicalIF":0.6,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145316394","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 a construction of some homology d-manifolds","authors":"Biplab Basak, Sourav Sarkar","doi":"10.1016/j.disc.2025.114843","DOIUrl":"10.1016/j.disc.2025.114843","url":null,"abstract":"<div><div>The <em>g</em>-vector of a simplicial complex contains a lot of information about the combinatorial and topological structure of that complex. Several classification results regarding the structure of normal pseudomanifolds and homology manifolds have been established concerning the value of <span><math><msub><mrow><mi>g</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>. It is known that when <span><math><msub><mrow><mi>g</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mn>0</mn></math></span>, all normal pseudomanifolds of dimensions at least three are stacked spheres. In the cases of <span><math><msub><mrow><mi>g</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mn>1</mn></math></span> and 2, all homology manifolds are polytopal spheres and can be obtained through retriangulation or join operations from the previous ones. In this article, we provide a combinatorial characterization of the homology <em>d</em>-manifolds, where <span><math><mi>d</mi><mo>≥</mo><mn>3</mn></math></span> and <span><math><msub><mrow><mi>g</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mn>3</mn></math></span>. These are spheres and can be obtained through operations such as joins, some retriangulations, and connected sums from spheres with <span><math><msub><mrow><mi>g</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>≤</mo><mn>2</mn></math></span>. Furthermore, we have presented a structural result on prime normal <em>d</em>-pseudomanifolds with <span><math><msub><mrow><mi>g</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mn>3</mn></math></span>.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"349 2","pages":"Article 114843"},"PeriodicalIF":0.7,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145323850","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":"Representations of the Moore-Penrose inverse of a 2 × 2 block matrix based on Schur complements","authors":"Daochang Zhang , Leiming Ma , Dijana Mosić","doi":"10.1016/j.amc.2025.129776","DOIUrl":"10.1016/j.amc.2025.129776","url":null,"abstract":"<div><div>Utilizing two different Schur complements, our purpose is to derive new explicit representations of the Moore-Penrose inverse of a <span><math><mrow><mn>2</mn><mo>×</mo><mn>2</mn></mrow></math></span> complex block matrix under corresponding hypotheses. By this way, we generalized several known results in the literature. A numerical example is given to illustrate our results.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"512 ","pages":"Article 129776"},"PeriodicalIF":3.4,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145325545","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":"On the Zaremba Problem for Inhomogeneous p-Laplace Equation with Drift","authors":"Yu. A. Alkhutov, M. D. Surnachev, A. G. Chechkina","doi":"10.1134/S1064562424602749","DOIUrl":"10.1134/S1064562424602749","url":null,"abstract":"<p>A higher integrability of the gradient of a solution to the Zaremba problem in a bounded strictly Lipschitz domain is proved for an inhomogeneous <i>p</i>-Laplace equation with lower terms.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"111 1","pages":"1 - 5"},"PeriodicalIF":0.6,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145316134","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 Extraction of Random Bit Sequences in Quantum Random Number Generators with Several Independent Markov Sources","authors":"I. M. Arbekov, S. N. Molotkov","doi":"10.1134/S1064562424602701","DOIUrl":"10.1134/S1064562424602701","url":null,"abstract":"<p>The paper presents a method for extracting provably random bit sequences from several independent Markov chain trajectories, each having an arbitrary finite order. In implementing quantum random number generators, the combined use of several trajectories makes it possible to significantly increase the speed of generating output bit sequences.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"111 1","pages":"6 - 15"},"PeriodicalIF":0.6,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145316135","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 Some Number Theoretic Sum","authors":"V. V. Iudelevich","doi":"10.1134/S1064562424601586","DOIUrl":"10.1134/S1064562424601586","url":null,"abstract":"<p>We obtain an asymptotic formula for the sum \u0000 <span>(Q(x) = sumlimits_{substack{ n leqslant x r(n + 1) ne 0 } } frac{{r(n)}}{{r(n + 1)}};;(x to + infty ),)</span> \u0000where <span>(r(n))</span> denotes the number of representations of <i>n</i> as a sum of two squares.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"111 1","pages":"25 - 28"},"PeriodicalIF":0.6,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145316396","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":"Equitable coloring of graphs beyond planarity","authors":"Weichan Liu","doi":"10.1016/j.dam.2025.10.020","DOIUrl":"10.1016/j.dam.2025.10.020","url":null,"abstract":"<div><div>An equitable coloring of a graph is a proper coloring where the sizes of any two different color classes do not differ by more than one. A graph is IC-planar if it can be drawn in the plane so that no two crossed edges have a common endpoint, and is NIC-planar graph if it can be embedded in the plane in such a way that no two pairs of crossed edges share two endpoints. Zhang, Wang, and Xu proved that every IC-planar graph with maximum degree <span><math><mrow><mi>Δ</mi><mo>≥</mo><mn>12</mn></mrow></math></span> and every NIC-planar graph with maximum degree <span><math><mrow><mi>Δ</mi><mo>≥</mo><mn>13</mn></mrow></math></span> have equitable <span><math><mi>Δ</mi></math></span>-colorings. In this paper, we reduce the threshold from 12 to 10 for IC-planar graphs and from 13 to 11 for NIC-planar graphs.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"379 ","pages":"Pages 685-693"},"PeriodicalIF":1.0,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145320100","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":"High-order asymptotic expansion for the nonlinear Klein-Gordon equation in the non-relativistic limit regime","authors":"Jia Shen , Yanni Wang , Haohao Zheng","doi":"10.1016/j.jde.2025.113832","DOIUrl":"10.1016/j.jde.2025.113832","url":null,"abstract":"<div><div>This paper presents an investigation into the high-order asymptotic expansion for 2D and 3D cubic nonlinear Klein-Gordon equations in the non-relativistic limit regime. There are extensive numerical and analytical results concerning that the solution of NLKG can be approximated by first-order modulated Schrödinger profiles in terms of <span><math><msup><mrow><mi>e</mi></mrow><mrow><mi>i</mi><mfrac><mrow><mi>t</mi></mrow><mrow><msup><mrow><mi>ε</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></mrow></msup><mi>v</mi><mo>+</mo><mi>c</mi><mo>.</mo><mi>c</mi><mo>.</mo></math></span>, where <em>v</em> is the solution of related NLS and “<span><math><mi>c</mi><mo>.</mo><mi>c</mi><mo>.</mo></math></span>” denotes the complex conjugate. Particularly, the best analytical result up to now is given in <span><span>[20]</span></span>, which proves that the <span><math><msubsup><mrow><mi>L</mi></mrow><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msubsup></math></span> norm of the error can be controlled by <span><math><msup><mrow><mi>ε</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mo>(</mo><msup><mrow><mi>ε</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>t</mi><mo>)</mo></mrow><mrow><mfrac><mrow><mi>α</mi></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></msup></math></span> for <span><math><msubsup><mrow><mi>H</mi></mrow><mrow><mi>x</mi></mrow><mrow><mi>α</mi></mrow></msubsup></math></span>-data, <span><math><mi>α</mi><mo>∈</mo><mo>[</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>]</mo></math></span>. As for the high-order expansion, to our best knowledge, there are only numerical results, while the theoretical one is lacking.</div><div>In this paper, we extend this study further and give the first high-order analytical result. We introduce the high-order expansion inspired by the numerical experiments in <span><span>[24]</span></span>, <span><span>[15]</span></span>:<span><span><span><math><msup><mrow><mi>e</mi></mrow><mrow><mi>i</mi><mfrac><mrow><mi>t</mi></mrow><mrow><msup><mrow><mi>ε</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></mrow></msup><mi>v</mi><mo>+</mo><msup><mrow><mi>ε</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>8</mn></mrow></mfrac><msup><mrow><mi>e</mi></mrow><mrow><mn>3</mn><mi>i</mi><mfrac><mrow><mi>t</mi></mrow><mrow><msup><mrow><mi>ε</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></mrow></msup><msup><mrow><mi>v</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>+</mo><msup><mrow><mi>e</mi></mrow><mrow><mi>i</mi><mfrac><mrow><mi>t</mi></mrow><mrow><msup><mrow><mi>ε</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></mrow></msup><mi>w</mi><mo>)</mo><mo>+</mo><mi>c</mi><mo>.</mo><mi>c</mi><mo>.</mo><mo>,</mo></math></span></span></span> where <em>w</em> is the solution to some specific Schrödinger-type equation. We show that the <span><math><msubsup><mrow><mi>L</mi></mrow><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msubsup></math></span> estimate of th","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"453 ","pages":"Article 113832"},"PeriodicalIF":2.3,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145325331","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":"Free interface problem of Navier-Stokes-Darcy equations without surface tension","authors":"Ningning Gao , Jinjing Liu , Lei Yao","doi":"10.1016/j.jde.2025.113850","DOIUrl":"10.1016/j.jde.2025.113850","url":null,"abstract":"<div><div>This paper investigates the free interface problem of incompressible Navier-Stokes-Darcy equations without surface tension in a finite-depth domain. We establish the global-in-time solution for the free interface problem of Navier-Stokes-Darcy equations in a horizontally infinite domain, without any low frequency assumptions of the initial data, in both two and three dimensions. Moreover, we present the decay of the solution. The key point lies in estimating <span><math><mn>4</mn><mi>N</mi><mo>−</mo><mn>1</mn></math></span> order horizontal spatial derivatives of the “Eulerian horizontal spatial derivative” <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>A</mi></mrow></msub></math></span> of the solution. This allows us to handle the 4<em>N</em> order horizontal spatial derivatives of the solution and facilitates the nonlinear cancellation of the highest order spatial regularity of the free boundary.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"453 ","pages":"Article 113850"},"PeriodicalIF":2.3,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145325339","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}
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