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DYNAMICS FOR A CHEMOTAXIS MODEL WITH GENERAL LOGISTIC DAMPING AND SIGNAL DEPENDENT MOTILITY

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Acta Mathematica Scientia 2024年第3期44卷 1046-1063页

作者：涂馨予穆春来邱蜀燕张静 school of {1. and Statistics Southwest UniversityChongqing400715China Department of applied {1. The Hong Kong Polytechnic UniversityHung HomHong KongChina College of mathematics and Statistics Chongqing UniversityChongqing401331China school of Sciences Southwest Petroleum UniversityChengdu610500China

In this paper,we consider the fully parabolic Chemotaxis system with the general logistic source{ut=Δ(γ(v)u)+λu-μu^(k),x∈Ω,t>0,vt=△v+wz,x∈Ω,t>0,wt=-wz,x∈Ω,t>0,zt=△z-z+u,x∈Ω,t>0 whereΩ⊂ℝn(n≥1.is a smooth and bounded domain,λ≥0,μ≥0,κ>1.and the motility function satisfies thatγ(v)∈C3([0,∞)),γ(v)>0,γ′(v)≤0 for all v≥*** the Neumann boundary condition,we obtain the global boundedness of solutions if one of the following conditions holds:(i)λ=μ=0,1.nλ3;(ii)λ>0,μ>0,combined withκ>1.1.n≤3 or k>n+2/4,,n>***,we prove that the solution (u, v, w, z) exponentially converges to the constant steady state ((λ/μ)1.k-1.∫Ωv0dx+∫Ωw0dx/|Ω|,0,(λ/μ)1.k-1..

关键词： chemotaxis signal-dependent motility logistic source boundedness asymptotic behavior

EPR-Net: constructing a non-equilibrium potential landscape via a variational force projection formulation

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National Science Review 2024年第7期11卷 135-147页

作者： Yue Zhao Wei Zhang Tiejun Li Center for Data Science Peking University Zuse Institute Berlin Department of mathematics and Computer Science Freie Universit?t Berlin Laboratory of mathematics and {1. mathematics(LMAM)and school of Mathematical Sciences Peking University Center for Machine Learning Research Peking University

We present EPR-Net, a novel and effective deep learning approach that tackles a crucial challenge in biophysics: constructing potential landscapes for high-dimensional non-equilibrium steady-state ***-Net leverages a nice mathematical fact that the desired negative potential gradient is simply the orthogonal projection of the driving force of the underlying dynamics in a weighted inner-product ***, our loss function has an intimate connection with the steady entropy production rate(EPR),enabling simultaneous landscape construction and EPR estimation. We introduce an enhanced learning strategy for systems with small noise, and extend our framework to include dimensionality reduction and the state-dependent diffusion coefficient case in a unified fashion. Comparative evaluations on benchmark problems demonstrate the superior accuracy, effectiveness and robustness of EPR-Net compared to existing methods. We apply our approach to challenging biophysical problems, such as an eight-dimensional(8D)limit cycle and a 52D multi-stability problem, which provide accurate solutions and interesting insights on constructed landscapes. With its versatility and power, EPR-Net offers a promising solution for diverse landscape construction problems in biophysics.

关键词： high-dimensional potential landscape non-equilibrium system entropy production rate dimensionality reduction deep learning

Moderate Deviations for the Parameter Estimation in the Fractional Ornstein-Uhlenbeck Process with H∈(0,1.2)

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Acta Mathematicae Applicatae Sinica 2024年

作者： Hui JIANG Qing-shan YANG school of {1. Nanjing University of Aeronautics and Astronautics MOE Key Laboratory of applied Statistics School of Mathematics and StatisticsNortheast Normal University

Abstract In this paper,we study the asymptotic properties for estimators of two parameters in the drift function in the ergodic fractional Ornstein-Uhlenbeck process with Hurst index H∈(0,1.2).The Cramér-type moderate deviations,as well as the moderation deviations with explicit rate function can be *** main methods consist of the deviation inequalities and Cramér-type moderate deviations for multiple WienerIt?integrals,as well as the asymptotic analysis techniques.

关键词：

The Orthogonal Bases of Exponential Functions Based on Moran-Sierpinski Measures

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Acta Mathematica Sinica,English Series 2024年第7期40卷 1804-1824页

作者： Qi Rong DENG Xing Gang HE Ming Tian LI Yuan Ling YE school of {1. and Statistics Center for Applied Mathematics of Fujian Province&Key Laboratory of Analytical Mathematics and Applications(Ministry of Education)Fujian Normal UniversityFuzhou350117P.R.China school of {1. and Statistics Key Lab NAA-MOE and Hubei Key Lab-Math.Sci.Central China Normal UniversityWuhan430079P.R.China school of Mathematical Sciences&South China Research Center for {1. mathematics and Interdisciplinary Studies South China Normal UniversityGuangzhou510631P.R.China

Let An∈M2(ℤ)be integral matrices such that the infinite convolution of Dirac measures with equal weightsμ{A_(n),n≥1.δA_(1.^(-1.D*δA_(1.^(-1.A_(2)^(-2)D*…is a probability measure with compact support,where D={(0,0)^(t),(1.0)^(t),(0,1.^(t)}is the Sierpinski *** prove that there exists a setΛ⊂ℝ2 such that the family{e2πi〈λ,x〉:λ∈Λ} is an orthonormal basis of L^(2)(μ{A_(n),n≥1.)if and only if 1.3(1.-1.A_(n)∈Z^(2)for n≥2 under some metric conditions on A_(n).

关键词： Moran-Sierpinski measures orthonormal basis of exponential functions self-affine measures spectral measures

TWO-GRID FINITE ELEMENT METHOD FOR TIME-FRACTIONAL NONLINEAR SCHRODINGER EQUATION

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Journal of Computational mathematics 2024年第4期42卷 1124-1144页

作者： Hanzhang Hu Yanping Chen Jianwei Zhou school of {1. Jiaying UniversityMeizhou 514015China school of Mathematical Science South China Normal UniversityGuangzhou 510631China school of {1. and Statistics Linyi UniversityLinyi 276005China

A two-grid finite element method with L1.scheme is presented for solving two-dimen-sional time-fractional nonlinear Schrodinger *** finite element solution in the L-norm are proved bounded without any time-step size conditions(dependent on spatial-step size).The classical L1.scheme is considered in the time direction,and the two-grid finite element method is applied in spatial *** optimal order error estimations of the two-grid solution in the LP-norm is proved without any time-step size *** is shown,both theoretically and numerically,that the coarse space can be extremely coarse,with no loss in the order of accuracy.

关键词： Time-fractional nonlinear Schrodinger equation Two-grid finite element me-thod The L1.scheme

Non-Convex Optimization of Resource Allocation in Fog Computing Using Successive Approximation

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Journal of Systems Science & Complexity 2024年第2期37卷 805-840页

作者： LI Shiyong LIU Huan LI Wenzhe SUN Wei school of Economics and {1. Yanshan UniversityQinhuangdao 066000China

Fog computing can deliver low delay and advanced IT services to end users with substantially reduced energy ***,with soaring demands for resource service and the limited capability of fog nodes,how to allocate and manage fog computing resources properly and stably has become the ***,the paper investigates the utility optimization-based resource allocation problem between fog nodes and end users in fog *** authors first introduce four types of utility functions due to the diverse tasks executed by end users and build the resource allocation model aiming at utility ***,for only the elastic tasks,the convex optimization method is applied to obtain the optimal results;for the elastic and inelastic tasks,with the assistance of Jensen’s inequality,the primal non-convex model is approximated to a sequence of equivalent convex optimization problems using successive approximation ***,a two-layer algorithm is proposed that globally converges to an optimal solution of the original ***,numerical simulation results demonstrate its superior performance and *** with other works,the authors emphasize the analysis for non-convex optimization problems and the diversity of tasks in fog computing resource allocation.

关键词： Fog computing non-convex optimization optimal resource allocation successive approximation method utility function

GLOBAL BOUND ON THE GRADIENT OF SOLUTIONS TO p-LAPLACE TYPE EQUATIONS WITH MIXED DATA

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Acta Mathematica Scientia 2024年第4期44卷 1394-1414页

作者： Minh-Phuong TRAN The-Quang TRAN Thanh-Nhan NGUYEN applied Analysis Research Group Faculty of Mathematics and StatisticsTon Duc Thang UniversityHo Chi Minh CityVietnam Nguyen Huu Huan High school Thu Duc CityVietnam Group of Analysis and applied {1. Department of MathematicsHo Chi Minh City University of EducationVietnam

In this paper,the study of gradient regularity for solutions of a class of elliptic problems of p-Laplace type is *** particular,we prove a global result concerning Lorentz-Morrey regularity of the non-homogeneous boundary data problem:-div((s^(2)+|▽u|^(2)p-2/2)▽u)=-div(|f|^(p-2)f)+g inΩ,u=h in■Ω,with the(sub-elliptic)degeneracy condition s∈[0,1.and with mixed data f∈L^(p)(Q;R^(n)),g∈Lp/(p-1.(Ω;R^(n))for p∈(1.n).This problem naturally arises in various applications such as dynamics of non-Newtonian fluid theory,electro-rheology,radiation of heat,plastic moulding and many *** on the idea of level-set inequality on fractional maximal distribution functions,it enables us to carry out a global regularity result of the solution via fractional maximal *** to the significance of M_(α)and its relation with Riesz potential,estimates via fractional maximal functions allow us to bound oscillations not only for solution but also its fractional derivatives of orderα.Our approach therefore has its own interest.

关键词： gradient estimates p-Laplace quasilinear elliptic equation fractional maximal operators Lorentz-Morrey spaces

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

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Communications on applied {1. 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 {1. 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

Burning Numbers of Barbells

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 526-538页

作者： Hui-qing LIU Rui-ting ZHANG Xiao-lan HU Hubei Key Laboratory of applied {1.&Faculty of {1. and Statistic Hubei UniversityWuhan 430062China Hubei Key Laboratory of Mathematical Sciences&school of {1. and Statistics Central China Normal UniversityWuhan 430079China

Motivated by a discrete-time process intended to measure the speed of the spread of contagion in a graph,the burning number b(G)of a graph G,is defined as the smallest integer k for which there are vertices x1.…xk su... 详细信息

关键词： burning number short/long barbell isometric subtree cycle