Pub Date : 2026-02-06DOI: 10.1016/j.amc.2026.130009
Ruijie Yin, Zhaojing Wu, Likang Feng
{"title":"Nested saturation control of Mecanum-wheeled mobile robot under stochastic disturbances and input constraints","authors":"Ruijie Yin, Zhaojing Wu, Likang Feng","doi":"10.1016/j.amc.2026.130009","DOIUrl":"https://doi.org/10.1016/j.amc.2026.130009","url":null,"abstract":"","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"162 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134762","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}
Pub Date : 2026-02-06DOI: 10.1016/j.jnt.2026.01.008
Sebastián Herrero , Tobías Martínez , Pedro Montero
Inspired by Bourqui's work on anticanonical height zeta functions on Hirzebruch surfaces, we study height zeta functions of complete smooth split toric varieties with Picard rank 2 over global function fields, with respect to height functions associated with big metrized line bundles. We show that these varieties can be naturally decomposed into a finite disjoint union of subvarieties, where precise analytic properties of the corresponding height zeta functions can be given. As application, we obtain asymptotic formulas for the number of rational points of large height on each subvariety, with explicit leading constants and controlled error terms.
{"title":"Counting rational points on Hirzebruch–Kleinschmidt varieties over global function fields","authors":"Sebastián Herrero , Tobías Martínez , Pedro Montero","doi":"10.1016/j.jnt.2026.01.008","DOIUrl":"10.1016/j.jnt.2026.01.008","url":null,"abstract":"<div><div>Inspired by Bourqui's work on anticanonical height zeta functions on Hirzebruch surfaces, we study height zeta functions of complete smooth split toric varieties with Picard rank 2 over global function fields, with respect to height functions associated with big metrized line bundles. We show that these varieties can be naturally decomposed into a finite disjoint union of subvarieties, where precise analytic properties of the corresponding height zeta functions can be given. As application, we obtain asymptotic formulas for the number of rational points of large height on each subvariety, with explicit leading constants and controlled error terms.</div></div>","PeriodicalId":50110,"journal":{"name":"Journal of Number Theory","volume":"285 ","pages":"Pages 1-53"},"PeriodicalIF":0.7,"publicationDate":"2026-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146147485","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}
We extend the classical Burgess estimates to character sums over proper generalized arithmetic progressions (GAPs) of rank 2 in prime fields . The core of our proof is a sharp upper bound for the multiplicative energy of these sets, established by adapting an argument of Konyagin and leveraging tools from the geometry of numbers. A key step in our argument involves establishing new upper bounds for the sizes of Bohr sets, which may be of independent interest.
{"title":"Burgess-type character sum estimates over generalized arithmetic progressions of rank 2","authors":"Ali Alsetri, Xuancheng Shao","doi":"10.1112/blms.70293","DOIUrl":"https://doi.org/10.1112/blms.70293","url":null,"abstract":"<p>We extend the classical Burgess estimates to character sums over proper generalized arithmetic progressions (GAPs) of rank 2 in prime fields <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>F</mi>\u0000 <mi>p</mi>\u0000 </msub>\u0000 <annotation>$mathbb {F}_p$</annotation>\u0000 </semantics></math>. The core of our proof is a sharp upper bound for the multiplicative energy of these sets, established by adapting an argument of Konyagin and leveraging tools from the geometry of numbers. A key step in our argument involves establishing new upper bounds for the sizes of Bohr sets, which may be of independent interest.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 2","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146129959","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 : 2026-02-06DOI: 10.1016/j.cnsns.2026.109817
R. Vanitha, T. Satheesh, V.T. Elayabharath, Y. Ren, R. Sakthivel
{"title":"Disturbance estimator-based tracking control for fractional-order Takagi-Sugeno fuzzy switched control systems","authors":"R. Vanitha, T. Satheesh, V.T. Elayabharath, Y. Ren, R. Sakthivel","doi":"10.1016/j.cnsns.2026.109817","DOIUrl":"https://doi.org/10.1016/j.cnsns.2026.109817","url":null,"abstract":"","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"71 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2026-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134760","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}
Pub Date : 2026-02-06DOI: 10.1016/j.amc.2026.129996
Souad Mohaoui, Andrii Dmytryshyn
{"title":"Tucker decomposition with a temporal regularization for gap recovery in 3D motion capture data","authors":"Souad Mohaoui, Andrii Dmytryshyn","doi":"10.1016/j.amc.2026.129996","DOIUrl":"https://doi.org/10.1016/j.amc.2026.129996","url":null,"abstract":"","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"37 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134763","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}
Nikolay Filonov, Michael Levitin, Iosif Polterovich, David A. Sher
We prove Pólya's conjecture for the eigenvalues of the Dirichlet Laplacian on annular domains. Our approach builds upon and extends the methods we previously developed for disks and balls. It combines variational bounds, estimates of Bessel phase functions, refined lattice point counting techniques and a rigorous computer-assisted analysis. As a by-product, we also derive a two-term upper bound for the Dirichlet eigenvalue counting function of the disk, improving upon Pólya's original estimate.
{"title":"Pólya's conjecture for Dirichlet eigenvalues of annuli","authors":"Nikolay Filonov, Michael Levitin, Iosif Polterovich, David A. Sher","doi":"10.1112/jlms.70425","DOIUrl":"https://doi.org/10.1112/jlms.70425","url":null,"abstract":"<p>We prove Pólya's conjecture for the eigenvalues of the Dirichlet Laplacian on annular domains. Our approach builds upon and extends the methods we previously developed for disks and balls. It combines variational bounds, estimates of Bessel phase functions, refined lattice point counting techniques and a rigorous computer-assisted analysis. As a by-product, we also derive a two-term upper bound for the Dirichlet eigenvalue counting function of the disk, improving upon Pólya's original estimate.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"113 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70425","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146129956","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}
SIAM Journal on Numerical Analysis, Volume 64, Issue 1, Page 251-276, February 2026. Abstract. We address the convergence analysis of lattice Boltzmann methods for scalar nonlinear conservation laws, focusing on two-relaxation-times (TRT) schemes. Unlike Finite Difference/Finite Volume methods, lattice Boltzmann schemes offer exceptional computational efficiency and parallelization capabilities. However, their monotonicity and [math]-stability remain underexplored. Extending existing results on simpler BGK schemes, we derive conditions ensuring that TRT schemes are monotone and stable by leveraging their unique relaxation structure. Our analysis culminates in proving convergence of the numerical solution to the weak entropy solution of the conservation law. Compared to BGK schemes, TRT schemes achieve reduced numerical diffusion while retaining provable convergence. Numerical experiments validate and illustrate the theoretical findings.
{"title":"Monotonicity and Convergence of Two-Relaxation-Times Lattice Boltzmann Schemes for a Nonlinear Conservation Law","authors":"Denise Aregba-Driollet, Thomas Bellotti","doi":"10.1137/25m1725218","DOIUrl":"https://doi.org/10.1137/25m1725218","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 64, Issue 1, Page 251-276, February 2026. <br/> Abstract. We address the convergence analysis of lattice Boltzmann methods for scalar nonlinear conservation laws, focusing on two-relaxation-times (TRT) schemes. Unlike Finite Difference/Finite Volume methods, lattice Boltzmann schemes offer exceptional computational efficiency and parallelization capabilities. However, their monotonicity and [math]-stability remain underexplored. Extending existing results on simpler BGK schemes, we derive conditions ensuring that TRT schemes are monotone and stable by leveraging their unique relaxation structure. Our analysis culminates in proving convergence of the numerical solution to the weak entropy solution of the conservation law. Compared to BGK schemes, TRT schemes achieve reduced numerical diffusion while retaining provable convergence. Numerical experiments validate and illustrate the theoretical findings.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"15 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134778","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}
The main goal of this paper is to establish the higher dimensional Nevanlinna theory in tropical geometry. We first develop a theory of tropical meromorphic functions (tropical holomorphic maps) in several real variables, such as the proximity function, counting function and characteristic function, the first main theorem, higher dimensional tropical versions of the logarithmic derivative lemmas. Based on this, for algebraically non-degenerate tropical holomorphic maps with subnormal growth from into tropical projective space intersecting tropical hypersurfaces with degree , we then obtain the second main theorem
本文的主要目的是建立热带几何中的高维奈凡林纳理论。我们首先发展了几个实变量的热带亚纯函数（热带全纯映射）的理论，如邻近函数，计数函数和特征函数，第一个主要定理，高维热带版本的对数导数引理。基于此，从R n$ mathbb {R}^n$到热带投影空间TP m $mathbb {TP}^{m}$相交热带超曲面的代数非简并热带全纯映射f$ f${V P j} j=1 q $ rbrace V_{P_j}rbrace _{j=1}^{q}$J $d_{J}$，得到第二个主要定理
{"title":"Tropical Nevanlinna theory in several variables","authors":"Tingbin Cao, Jiahu Peng","doi":"10.1112/jlms.70449","DOIUrl":"https://doi.org/10.1112/jlms.70449","url":null,"abstract":"<p>The main goal of this paper is to establish the higher dimensional Nevanlinna theory in tropical geometry. We first develop a theory of tropical meromorphic functions (tropical holomorphic maps) in several real variables, such as the proximity function, counting function and characteristic function, the first main theorem, higher dimensional tropical versions of the logarithmic derivative lemmas. Based on this, for algebraically non-degenerate tropical holomorphic maps <span></span><math>\u0000 <semantics>\u0000 <mi>f</mi>\u0000 <annotation>$f$</annotation>\u0000 </semantics></math> with subnormal growth from <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <annotation>$mathbb {R}^n$</annotation>\u0000 </semantics></math> into tropical projective space <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>TP</mi>\u0000 <mi>m</mi>\u0000 </msup>\u0000 <annotation>$mathbb {TP}^{m}$</annotation>\u0000 </semantics></math> intersecting tropical hypersurfaces <span></span><math>\u0000 <semantics>\u0000 <msubsup>\u0000 <mrow>\u0000 <mo>{</mo>\u0000 <msub>\u0000 <mi>V</mi>\u0000 <msub>\u0000 <mi>P</mi>\u0000 <mi>j</mi>\u0000 </msub>\u0000 </msub>\u0000 <mo>}</mo>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>j</mi>\u0000 <mo>=</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <mi>q</mi>\u0000 </msubsup>\u0000 <annotation>$lbrace V_{P_j}rbrace _{j=1}^{q}$</annotation>\u0000 </semantics></math> with degree <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>d</mi>\u0000 <mi>j</mi>\u0000 </msub>\u0000 <annotation>$d_{j}$</annotation>\u0000 </semantics></math>, we then obtain the second main theorem\u0000\u0000 </p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"113 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146136161","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}
Pub Date : 2026-02-06DOI: 10.1016/j.amc.2026.130008
Yinxin Chang, Xiaojuan Cheng, Yalun Wu, Peng Wu, Gang Li
{"title":"Coevolution modeling for network public opinion with bidirectional feedback mechanism","authors":"Yinxin Chang, Xiaojuan Cheng, Yalun Wu, Peng Wu, Gang Li","doi":"10.1016/j.amc.2026.130008","DOIUrl":"https://doi.org/10.1016/j.amc.2026.130008","url":null,"abstract":"","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"307 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134766","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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