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Time-dependent inverse source problems for a pseudoparabolic equation with memory 具有记忆的伪抛物方程的时变逆源问题
IF 2.5 2区 数学
Computers & Mathematics with Applications Pub Date : 2025-09-04 DOI: 10.1016/j.camwa.2025.08.029
Kh. Khompysh , M.J. Huntul , M. Mukhambetkaliyev
{"title":"Time-dependent inverse source problems for a pseudoparabolic equation with memory","authors":"Kh. Khompysh ,&nbsp;M.J. Huntul ,&nbsp;M. Mukhambetkaliyev","doi":"10.1016/j.camwa.2025.08.029","DOIUrl":"10.1016/j.camwa.2025.08.029","url":null,"abstract":"<div><div>In this paper, we deal with two inverse source problems for a pseudoparabolic equation with memory term, which in general, have important applications in various fields of science and technology such as non-Newtonian fluids, filtration, population dynamics, plasma physic, et al. However, the presence of certain additional terms in a system usually causes specific complications in mathematical point of view, both in analytical and numerical analysis, although they characterize important physical properties of media. The studied inverse problems consist of recovering a time-dependent source parameter under two types of integral overdetermination conditions. We establish the existence, uniqueness, and stability of strong solutions under suitable conditions on the data and explore numerical solutions by creating numerical algorithms and testing examples.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"198 ","pages":"Pages 239-254"},"PeriodicalIF":2.5,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144988429","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}
引用次数: 0
On an Erdős-type conjecture on Fq[x] 关于Fq[x]的一个Erdős-type猜想
IF 1.2 3区 数学
Finite Fields and Their Applications Pub Date : 2025-09-04 DOI: 10.1016/j.ffa.2025.102720
Rongyin Wang
{"title":"On an Erdős-type conjecture on Fq[x]","authors":"Rongyin Wang","doi":"10.1016/j.ffa.2025.102720","DOIUrl":"10.1016/j.ffa.2025.102720","url":null,"abstract":"<div><div>P. Erdős conjectured in 1962 that on the ring <span><math><mi>Z</mi></math></span>, every set of <em>n</em> congruence classes in <span><math><mi>Z</mi></math></span> that covers the first <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msup></math></span> positive integers also covers the ring <span><math><mi>Z</mi></math></span>. This conjecture was first confirmed in 1970 by R. B. Crittenden and C. L. Vanden Eynden. Later, in 2019, P. Balister, B. Bollobás, R. Morris, J. Sahasrabudhe, and M. Tiba provided a more transparent proof. In this paper, we follow the approach used by R. B. Crittenden and C. L. Vanden Eynden to prove the generalized Erdős' conjecture in the setting of polynomial rings over finite fields. We prove that every set of <em>n</em> cosets of ideals in <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>[</mo><mi>x</mi><mo>]</mo></math></span> that covers all polynomials whose degree is less than <em>n</em> covers the ring <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>[</mo><mi>x</mi><mo>]</mo></math></span>.</div></div>","PeriodicalId":50446,"journal":{"name":"Finite Fields and Their Applications","volume":"109 ","pages":"Article 102720"},"PeriodicalIF":1.2,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144988706","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
Constructive approximate transport maps with normalizing flows 具有规格化流的构造近似运输图
IF 1.7 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-09-04 DOI: 10.1007/s00245-025-10299-7
Antonio Álvarez-López, Borjan Geshkovski, Domènec Ruiz-Balet
{"title":"Constructive approximate transport maps with normalizing flows","authors":"Antonio Álvarez-López,&nbsp;Borjan Geshkovski,&nbsp;Domènec Ruiz-Balet","doi":"10.1007/s00245-025-10299-7","DOIUrl":"10.1007/s00245-025-10299-7","url":null,"abstract":"<div><p>We study an approximate controllability problem for the continuity equation and its application to constructing transport maps with normalizing flows. Specifically, we construct time-dependent controls <span>(theta =(w, a, b))</span> in the vector field <span>(xmapsto w(a^top x + b)_+)</span> to approximately transport a known base density <span>(rho _{textrm{B}})</span> to a target density <span>(rho _*)</span>. The approximation error is measured in relative entropy, and <span>(theta )</span> are constructed piecewise constant, with bounds on the number of switches being provided. Our main result relies on an assumption on the relative tail decay of <span>(rho _*)</span> and <span>(rho _{textrm{B}})</span>, and provides hints on characterizing the reachable space of the continuity equation in relative entropy.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"92 2","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-025-10299-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144990594","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}
引用次数: 0
A lower bound on volumes of end-periodic mapping tori 周期末映射环面的一个下界
IF 1.1 2区 数学
Journal of Topology Pub Date : 2025-09-04 DOI: 10.1112/topo.70037
Elizabeth Field, Autumn Kent, Christopher Leininger, Marissa Loving
{"title":"A lower bound on volumes of end-periodic mapping tori","authors":"Elizabeth Field,&nbsp;Autumn Kent,&nbsp;Christopher Leininger,&nbsp;Marissa Loving","doi":"10.1112/topo.70037","DOIUrl":"https://doi.org/10.1112/topo.70037","url":null,"abstract":"<p>We provide a lower bound on the volume of the compactified mapping torus of a strongly irreducible end-periodic homeomorphism <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>f</mi>\u0000 <mo>:</mo>\u0000 <mi>S</mi>\u0000 <mo>→</mo>\u0000 <mi>S</mi>\u0000 </mrow>\u0000 <annotation>$f: S rightarrow S$</annotation>\u0000 </semantics></math>. This result, together with work of Field, Kim, Leininger, and Loving [J. Topol. <b>16</b> (2023), no. 1, 57–105], shows that the volume of <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mover>\u0000 <mi>M</mi>\u0000 <mo>¯</mo>\u0000 </mover>\u0000 <mi>f</mi>\u0000 </msub>\u0000 <annotation>$overline{M}_f$</annotation>\u0000 </semantics></math> is comparable to the translation length of <span></span><math>\u0000 <semantics>\u0000 <mi>f</mi>\u0000 <annotation>$f$</annotation>\u0000 </semantics></math> on a connected component of the pants graph <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>P</mi>\u0000 <mo>(</mo>\u0000 <mi>S</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathcal {P}(S)$</annotation>\u0000 </semantics></math>, extending work of Brock [Comm. Anal. Geom. <b>11</b> (2003), no. 5, 987–999] in the finite-type setting on volumes of mapping tori of pseudo-Anosov homeomorphisms.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"18 3","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/topo.70037","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144990690","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}
引用次数: 0
Fractional moments of -functions and sums of two squares in short intervals 函数的分数阶矩和短间隔内两个平方和
IF 0.8 3区 数学
Mathematika Pub Date : 2025-09-04 DOI: 10.1112/mtk.70047
Siegfred Baluyot, Steven M. Gonek
{"title":"Fractional moments of -functions and sums of two squares in short intervals","authors":"Siegfred Baluyot,&nbsp;Steven M. Gonek","doi":"10.1112/mtk.70047","DOIUrl":"https://doi.org/10.1112/mtk.70047","url":null,"abstract":"<p>Let <span></span><math></math> if <span></span><math></math> is the sum of two perfect squares, and <span></span><math></math> otherwise. We study the variance of <span></span><math></math> in short intervals by relating the variance with the second moment of the generating function <span></span><math></math> along <span></span><math></math>. We develop a new method for estimating fractional moments of <span></span><math></math>-functions and apply it to the second moment of <span></span><math></math> to bound the variance of <span></span><math></math>. Our results are conditional on the Riemann hypothesis for the zeta-function and the Dirichlet <span></span><math></math>-function associated with the non-principal character modulo 4.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.70047","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144990783","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Conformalized Tensor Completion with Riemannian Optimization 黎曼优化的共形张量补全
IF 2.4 2区 数学
Journal of Computational and Graphical Statistics Pub Date : 2025-09-04 DOI: 10.1080/10618600.2025.2554671
Hu Sun, Yang Chen
{"title":"Conformalized Tensor Completion with Riemannian Optimization","authors":"Hu Sun, Yang Chen","doi":"10.1080/10618600.2025.2554671","DOIUrl":"https://doi.org/10.1080/10618600.2025.2554671","url":null,"abstract":"","PeriodicalId":15422,"journal":{"name":"Journal of Computational and Graphical Statistics","volume":"22 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144995562","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}
引用次数: 0
Gravitational least squares twin support vector machine based on optimal angle for class imbalance learning 基于最优角度的重力最小二乘双支持向量机类不平衡学习
IF 3.4 2区 数学
Applied Mathematics and Computation Pub Date : 2025-09-04 DOI: 10.1016/j.amc.2025.129705
Abdullah Mohammadi , Jalal A. Nasiri , Sohrab Effati
{"title":"Gravitational least squares twin support vector machine based on optimal angle for class imbalance learning","authors":"Abdullah Mohammadi ,&nbsp;Jalal A. Nasiri ,&nbsp;Sohrab Effati","doi":"10.1016/j.amc.2025.129705","DOIUrl":"10.1016/j.amc.2025.129705","url":null,"abstract":"<div><div>This paper introduces the Gravitational Least Squares Twin Support Vector Machine for Class Imbalance Learning (GLSTSVM-CIL), a novel binary classification method designed to address critical limitations in existing approaches for imbalanced large-scale datasets. Traditional methods like Fuzzy TSVM and KNN-based weighting fail to simultaneously capture both global positional relationships and local density characteristics of data points. Our proposed gravitational weighting function innovatively models data samples as masses influenced by their distance from class centroids and neighborhood density, effectively prioritizing representative points while suppressing outliers. The optimization framework uniquely incorporates angular constraints between hyperplanes to enhance structural risk control and generalization capability. For scalability, we reformulate the solution into a linear system solvable via conjugate gradient methods, avoiding computationally expensive matrix inversions. Comprehensive evaluations on 92 datasets (including synthetic, noisy, medical, text, and large-scale NDC benchmarks) demonstrate GLSTSVM-CIL’s superior performance, particularly in minority-class recognition where it achieves average F1-Score improvements over baseline methods. The model maintains robust Accuracy under high noise (20 %) and extreme class imbalance (ratio 20:1) while ables to process datasets up to 50,000 samples.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"510 ","pages":"Article 129705"},"PeriodicalIF":3.4,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144996174","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}
引用次数: 0
Non-convergence of the Navier–Stokes Equations Toward the Euler Equations in the Endpoint Besov Spaces 端点Besov空间中Navier-Stokes方程向Euler方程的非收敛性
IF 1.7 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-09-04 DOI: 10.1007/s00245-025-10313-y
Yanghai Yu, Jinlu Li
{"title":"Non-convergence of the Navier–Stokes Equations Toward the Euler Equations in the Endpoint Besov Spaces","authors":"Yanghai Yu,&nbsp;Jinlu Li","doi":"10.1007/s00245-025-10313-y","DOIUrl":"10.1007/s00245-025-10313-y","url":null,"abstract":"<div><p>In this paper, we consider the inviscid limit problem to the higher dimensional incompressible Navier–Stokes equations in the whole space. It was proved in [Guo et al. J. Funct. Anal. 276:2821–2830, 2019] that given initial data <span>(u_0in B^{s}_{p,r})</span> with <span>(1le r&lt;infty)</span>, the solution of the Navier–Stokes equations converges strongly in <span>(B^{s}_{p,r})</span> to the solution of the Euler equations as the viscosity parameter tends to zero. In the case when <span>(r=infty)</span>, we prove the failure of the <span>(B^{s}_{p,infty })</span>-convergence of the Navier-Stokes equations toward the Euler equations in the inviscid limit.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"92 2","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144934731","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}
引用次数: 0
Taking limits in topological recursion 在拓扑递归中求极限
IF 1.2 2区 数学
Journal of the London Mathematical Society-Second Series Pub Date : 2025-09-04 DOI: 10.1112/jlms.70286
Gaëtan Borot, Vincent Bouchard, Nitin Kumar Chidambaram, Reinier Kramer, Sergey Shadrin
{"title":"Taking limits in topological recursion","authors":"Gaëtan Borot,&nbsp;Vincent Bouchard,&nbsp;Nitin Kumar Chidambaram,&nbsp;Reinier Kramer,&nbsp;Sergey Shadrin","doi":"10.1112/jlms.70286","DOIUrl":"https://doi.org/10.1112/jlms.70286","url":null,"abstract":"<p>When does topological recursion applied to a family of spectral curves commute with taking limits? This problem is subtle, especially when the ramification structure of the spectral curve changes at the limit point. We provide sufficient (straightforward-to-use) conditions for checking when the commutation with limits holds, thereby closing a gap in the literature where this compatibility has been used several times without justification. This takes the form of a stronger result of analyticity of the topological recursion along suitable families. To tackle this question, we formalise the notion of global topological recursion and provide sufficient conditions for its equivalence with local topological recursion. The global version facilitates the study of analyticity and limits. For non-degenerate algebraic curves, we reformulate these conditions purely in terms of the structure of its underlying singularities. Finally, we apply this to study deformations of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>r</mi>\u0000 <mo>,</mo>\u0000 <mi>s</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$ (r,s)$</annotation>\u0000 </semantics></math>-spectral curves, spectral curves for weighted Hurwitz numbers and provide several other examples and non-examples (where the commutation with limits fails).</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70286","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144934887","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}
引用次数: 0
Equivariant cohomology of a complexity-one four-manifold is determined by combinatorial data 用组合数据确定了复一四流形的等变上同调
IF 1.5 1区 数学
Advances in Mathematics Pub Date : 2025-09-04 DOI: 10.1016/j.aim.2025.110497
Tara S. Holm , Liat Kessler
{"title":"Equivariant cohomology of a complexity-one four-manifold is determined by combinatorial data","authors":"Tara S. Holm ,&nbsp;Liat Kessler","doi":"10.1016/j.aim.2025.110497","DOIUrl":"10.1016/j.aim.2025.110497","url":null,"abstract":"<div><div>For Hamiltonian circle actions on compact, connected four-dimensional manifolds, we give a generators and relations description for the even part of the equivariant cohomology, as an algebra over the equivariant cohomology of a point. This description depends on combinatorial data encoded in the decorated graph of the manifold. We then give an explicit combinatorial description of all weak algebra isomorphisms. We use this description to prove that the even parts of the equivariant cohomology algebras are weakly isomorphic and the odd groups have the same ranks if and only if the labeled graphs obtained from the decorated graphs by forgetting the height and area labels are isomorphic.</div><div>As a consequence, we give an example of an isomorphism of equivariant cohomology algebras that cannot be induced by an equivariant diffeomorphism of manifolds preserving a compatible almost complex structure. We also provide a soft proof that there are finitely many maximal Hamiltonian circle actions on a fixed compact, connected, four-dimensional symplectic manifold.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"480 ","pages":"Article 110497"},"PeriodicalIF":1.5,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144988158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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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