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GLOBAL WEAK SOLUTIONS FOR AN ATTRACTION-REPULSION CHEMOTAXIS SYSTEM WITH p-LAPLACIAN DIFFUSION AND LOGISTIC SOURCE

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Acta Mathematica Scientia 2024年第3期44卷 909-924页

作者：王晓闪王忠谦贾哲 department of mathematics Luoyang Normal UniversityLuoyang471934China School of mathematics Science Jiangsu Second Normal UniversityNanjing210013China School of mathematics and statistics Linyi UniversityLinyi276005China

This paper is concerned with the following attraction-repulsion chemotaxis system with p-Laplacian diffusion and logistic source:■The system here is under a homogenous Neumann boundary condition in a bounded domainΩ ■ R^(n)(n≥2),with χ,ξ,α,β,γ,δ,k_(1),k_(2)> 0,p> *** addition,the function f is smooth and satisfies that f(s)≤κ-μs~l for all s≥0,with κ ∈ R,μ> 0,l> *** is shown that(ⅰ)if l> max{2k_(1),(2k_(1)n)/(2+n)+1/(p-1)},then system possesses a global bounded weak solution and(ⅱ)if k_(2)> max{2k_(1)-1,(2k_(1)n)/(2+n)+(2-p)/(p-1)} with l> 2,then system possesses a global bounded weak solution.

关键词： global weak solutions attraction-repulsion p-Laplacian logistic source

Iterative Subregion Correction Preconditioners with Adaptive Tolerance for Problems with Geometrically Localized Stiffness

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Communications on Applied mathematics and Computation 2024年第2期6卷 811-836页

作者： Michael Franco Per-Olof Persson Will Pazner department of mathematics University of CaliforniaBerkeleyBerkeleyCA 94720-3840USA Fariborz Maseeh department of mathematics and statistics Portland State UniversityPortlandOR 97201USA

We present a class of preconditioners for the linear systems resulting from a finite element or discontinuous Galerkin discretizations of advection-dominated *** preconditioners are designed to treat the case of geometrically localized stiffness,where the convergence rates of iterative methods are degraded in a localized subregion of the *** convergence may be caused by a number of factors,including the mesh size,anisotropy,highly variable coefficients,and more challenging *** approach taken in this work is to correct well-known preconditioners such as the block Jacobi and the block incomplete LU(ILU)with an adaptive inner subregion *** goal of these preconditioners is to reduce the number of costly global iterations by accelerating the convergence in the stiff region by iterating on the less expensive reduced *** tolerance for the inner iteration is adaptively chosen to minimize subregion-local work while guaranteeing global convergence *** present analysis showing that the convergence of these preconditioners,even when combined with an adaptively selected tolerance,is independent of discretization parameters(e.g.,the mesh size and diffusion coefficient)in the *** demonstrate significant performance improvements over black-box preconditioners when applied to several model convection-diffusion ***,we present performance results of several variations of iterative subregion correction preconditioners applied to the Reynolds number 2.25×10^(6)fluid flow over the NACA 0012 airfoil,as well as massively separated flow at 30°angle of attack.

关键词： Subregion correction Nested Krylov Geometrically localized stiffness

A Fluctuation Test for Structural Change Detection in Heterogeneous Panel Data Models

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Journal of Systems Science & Complexity 2024年第3期37卷 1184-1208页

作者： LI Fuxiao XIAO Yanting CHEN Zhanshou department of Applied mathematics Xi'an University of TechnologyXi'an 710048China School of mathematics and statistics Qinghai Normal UniversityXining 810008China Academy of Plateau Science and Sustainability Xining 810008China

Structural change in panel data is a widespread phenomena. This paper proposes a fluctuation test to detect a structural change at an unknown date in heterogeneous panel data models with or without common correlated effects. The asymptotic properties of the fluctuation statistics in two cases are developed under the null and local alternative hypothesis. Furthermore, the consistency of the change point estimator is proven. Monte Carlo simulation shows that the fluctuation test can control the probability of type I error in most cases, and the empirical power is high in case of small and moderate sample sizes. An application of the procedure to a real data is presented.

关键词： Common correlated effects fuctuation test heterogeneous panel data models structural change detection

Finite Groups with Some Bounded Codegrees

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Acta Mathematica Sinica,English Series 2024年第7期40卷 1778-1784页

作者： Dong Fang YANG Yu ZENG Heng LV School of mathematics and statistics Southwest UniversityChongqing400715P.R.China department of mathematics Changshu Institute of TechnologyChangshu215500P.R.China

For a characterχof a finite group G,the number cod(χ) := ∣G:ker(χ)∣/χ(1)is called the codegree ofχ.In this paper,we give a solvability criterion for a finite group G depending on the minimum of the ratioχ(1)^(... 详细信息

关键词： Finite group codegree degree simple group

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Global Solutions to Nonconvex Problems by Evolution of Hamilton-Jacobi PDEs

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Communications on Applied mathematics and Computation 2024年第2期6卷 790-810页

作者： Howard Heaton Samy Wu Fung Stanley Osher Typal Research Typal LLCLos AngelesUSA department of Applied mathematics and statistics Colorado School of MinesGoldenUSA department mathematics UCLALos AngelesUSA

Computing tasks may often be posed as optimization *** objective functions for real-world scenarios are often nonconvex and/or ***-of-the-art methods for solving these problems typically only guarantee convergence to local *** work presents Hamilton-Jacobi-based Moreau adaptive descent(HJ-MAD),a zero-order algorithm with guaranteed convergence to global minima,assuming continuity of the objective *** core idea is to compute gradients of the Moreau envelope of the objective(which is"piece-wise convex")with adaptive smoothing *** of the Moreau envelope(i.e.,proximal operators)are approximated via the Hopf-Lax formula for the viscous Hamilton-Jacobi *** numerical examples illustrate global convergence.

关键词： Global optimization Moreau envelope Hamilton-Jacobi Hopf-Lax-Cole-Hopf Proximals Zero-order optimization

The Path-Connectivity of Hierarchical Cubic Networks

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Acta Mathematicae Applicatae Sinica 2024年

作者： Ruo-xuan LI Rong-xia HAO Zhen HE Young Soo KWON School of mathematics and statistics Beijing Jiaotong University department of mathematics Yeungnam University

Let G be a simple connected graph with vertex set V （G）.For S?V （G）,letπG（S） denote the maximum cardinality of internally disjoint S-paths in *** an integer k with k≥2,the k-path-connectivityπk（G） is defined as the minimumπG（S） over all k-subsets S of V （G）.It is proved that deciding whetherπG（S）≥r is NP-complete problem[Graphs Combin.37 （2021） 2521–2533].The hypercube Qn is the famous Cayley graph,which is widely studied in the research of developing multiprocessor *** hierarchical cubic network HCNn is given in[IEEE TPDS 6 （1995） 427–435]which takes Qn as building clusters and emulates the desirable properties very *** this paper,we consider the 3-path-connectivity of HCN_n and prove that π3（HCN_n） = [（3n+2）/4] for n≥2 by constructing multiple internally disjoint *** result improves the 3-tree-connectivity[Discrete ***.322 （2022） 203–209]from trees to paths.

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THE GLOBAL EXISTENCE AND ANALYTICITY OF A MILD SOLUTION TO THE 3D REGULARIZED MHD EQUATIONS

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Acta Mathematica Scientia 2024年第3期44卷 973-983页

作者：肖存涛邱华姚正安 School of mathematics and statistics Guangdong University of TechnologyGuangzhou510090China department of mathematics South China Agricultural UniversityGuangzhou510642China School of mathematics Sun Yat-sen UniversityGuangzhou510275China

In this paper,we study the three-dimensional regularized MHD equations with fractional Laplacians in the dissipative and diffusive *** establish the global existence of mild solutions to this system with small initial... 详细信息

关键词： regularized MHD equations fractional Laplacian global well-posedness analyticity decay rate

The Ananthakrishna Model Under Non-synchronous Perturbation

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Acta Mathematicae Applicatae Sinica 2024年第4期 1078-1097页

作者： Yi-wen TAO Sue Ann CAMPBELL Jing-li REN School of mathematics and statistics Zhengzhou University department of Applied mathematics University of Waterloo

The Ananthakrishna model, seeking to explain the Portevin-Le Chatelier effect, is studied with or without non-synchronous perturbations. For the unperturbed model, Bogdanov-Takens bifurcation and zeroHopf bifurcation are detected. For the perturbed model, rich dynamical behaviors are given by researching the Poincaré map, including solutions of different periods, quasi-periodic solutions, chaotic solutions, and ***, an augmented temperature-dependent perturbation amplitude induces a transition from non-serrated to serrated flow on the stress-time curve. Notably, on the stress-strain curve, the phenomenon of repeated yielding diminishes with an increase in the value of a temperature-dependent parameter, while it persists with an increase in the value of a temperature-independent parameter. Sensitivity analysis sheds light on the factors exerting the most significant influence on dislocation density.

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Multicolored Bipartite Ramsey Numbers of Large Cycles

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 347-357页

作者： Shao-qiang LIU Yue-jian PENG College of mathematics and statistics Hanshan Normal UniversityChaozhou 521041China School of mathematics Hunan UniversityChangsha 410082China

For an integer r≥2 and bipartite graphs Hi,where 1≤i≤r,the bipartite Ramsey number br(H1,H2,…,Hr)is the minimum integer N such that any r-edge coloring of the complete bipartite graph KN;N contains a monochromatic subgraph isomorphic to Hi in color i for some 1≤i≤*** show that if r≥3;α1,α2>0,αj+2≥[(j+2)!-1]Σi=1^(j+1)α1 for j=1,2…r-2,then br(C2[α1n],C2[α2n],…,C2[αrn]=(Σ=j=1^(r)a j+o(1))n.

关键词： ramsey number bipartite ramsey number regularity lemma