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GLOBAL SOLVABILITY IN A TWO-SPECIES CHEMOTAXIS SYSTEM WITH SIGNAL PRODUCTION

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arXiv 2021年

作者： Ren, Guoqiang Xiang, Tian School of Mathematics and Statistics Huazhong University of Science and Technology Hubei Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Hubei Wuhan430074 China Institute for Mathematical Sciences Renmin University of China Bejing100872 China

In this paper, we study the following prototypical two-species chemotaxis system with Lotka-Volterra competition and signal production: (Equation presented). We show that if (Equation presented). the associated Neumann initial-boundary value problem for (∗) admits a global generalized solutions in a bounded and smooth domain Ω ⊂ N (N ≥ 2) under merely integrable initial *** Codes 35A01, 35K57, 35Q92, 92C17 © 2021, CC BY.

关键词： Initial value problems

GLOBAL SOLVABILITY AND ASYMPTOTICAL BEHAVIOR IN A TWO-SPECIES CHEMOTAXIS MODEL WITH SIGNAL ABSORPTION

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arXiv 2021年

In this work, we study global existence, eventual smoothness and asymptotical behavior of positive solutions for the following two-species chemotaxis consumption model: ut = ∆u - χ1∇ · (u∇w), x ∈ Ω, t > 0, {{{{{{{ vt = ∆v - χ2∇ · (u∇w), x ∈ Ω, t > 0, wt = ∆w - (αu + βv)w, x ∈ Ω, t > 0, in a bounded smooth but not necessarily convex domain Ω ⊂ Rn(n = 2, 3, 4, 5) with nonnegative initial data u0, v0, w0 and homogeneous Neumann boundary data. Here, the parameters χ1, χ2 are positive and α, β are nonnegative. Under a smallness condition max{χ1, χ2}kw0kL∞ MSC Codes 35K59, 35K57 © 2021, CC BY.

关键词： Biochemistry

Pseudoinverse-free randomized block iterative algorithms for consistent and inconsistent linear systems

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arXiv 2020年

作者： Du, Kui Sun, Xiao-Hui School of Mathematical Sciences Fujian Provincial Key Laboratory of Mathematical Modeling and High Performance Scientific Computing Xiamen University Xiamen361005 China School of Mathematical Sciences Xiamen University Xiamen361005 China

Randomized iterative algorithms have attracted much attention in recent years because they can approximately solve large-scale linear systems of equations without accessing the entire coefficient matrix. In this paper, we propose two novel pseudoinverse-free randomized block iterative algorithms for solving consistent and inconsistent linear systems. The proposed algorithms require two user-defined random matrices: one for row sampling and the other for column sampling. We can recover the well-known doubly stochastic Gauss-Seidel, randomized Kaczmarz, randomized coordinate descent, and randomized extended Kaczmarz algorithms by choosing appropriate random matrices used in our algorithms. Because our algorithms allow for a much wider selection of these two random matrices, a number of new specific algorithms can be obtained. We prove the linear convergence in the mean square sense of our algorithms. Numerical experiments for linear systems with synthetic and real-world coefficient matrices demonstrate the efficiency of some special cases of our *** Codes 65F10, 65F20, 15A06 Copyright © 2020, The Authors. All rights reserved.

关键词： Linear systems

Single-pass randomized QLP decomposition for low-rank approximation

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arXiv 2020年

作者： Ren, Huan Bai, Zheng-Jian School of Mathematical Sciences Xiamen University Xiamen360015 China School of Mathematical Sciences Fujian Provincial Key Laboratory on Mathematical Modeling & High Performance Scientific Computing Xiamen University Xiamen361005 China

The QLP decomposition is one of the effective algorithms to approximate singular value decomposition (SVD) in numerical linear algebra. In this paper, we propose some single-pass randomized QLP decomposition algorithms for computing the low-rank matrix approximation. Compared with the deterministic QLP decomposition, the complexity of the proposed algorithms does not increase significantly and the system matrix needs to be accessed only once. Therefore, our algorithms are very suitable for a large matrix stored outside of memory or generated by stream data. In the error analysis, we give the bounds of matrix approximation error and singular value approximation error. Numerical experiments also reported to verify our results. key words: QLP decomposition, randomized algorithm, single-pass, singular value, low-rank approximation Copyright © 2020, The Authors. All rights reserved.

关键词： Singular value decomposition

On pole-zero assignment of vibratory systems by multi-input feedback control

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arXiv 2020年

作者： Bai, Zheng-Jian Wang, Yang School of Mathematical Sciences Fujian Provincial Key Laboratory on Mathematical Modeling & High Performance Scientific Computing Xiamen University Xiamen361005 China School of Mathematical Sciences Xiamen University Xiamen361005 China

In this paper, we consider the pole-zero assignment problem for vibratory systems via multi-input feedback control. We propose a multi-step two-stage approach for solving the multi-input pole-zero assignment problem. We first reformulate the assignment problem as a multi-step single-input pole-zero assignment problem. Then, in each step, we propose a two-stage approach for solving the single-input pole-zero assignment problem. In the first stage, based on the measured receptances, we replace the selected zeros of the prescribed open-loop point receptance to the desired locations, where we need to solve a small underdetermined linear equation for finding the corresponding columns of the feedback matrices. In the second stage, by using linear matrix inequalities, the complete closed-loop poles are assigned to the prescribed subregion of the complex left-hand plane. Finally, we give some numerical examples to demonstrate the effectiveness of our *** Codes 65F18 Copyright © 2020, The Authors. All rights reserved.

关键词： Combinatorial optimization

Large deviations principle for stochastic delay differential equations with super-linearly growing coefficients

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arXiv 2022年

作者： Jin, Diancong Chen, Ziheng Zhou, Tau School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China School of Mathematics and Statistics Yunnan University Kunming650500 China Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

We utilize the weak convergence method to establish the Freidlin-Wentzell large deviations principle (LDP) for stochastic delay differential equations (SDDEs) with super-linearly growing coefficients, which covers a large class of cases with non-globally Lipschitz coefficients. The key ingredient in our proof is the uniform moment estimate of the controlled equation, where we handle the super-linear growth of the coefficients by an iterative argument. Our results allow both the drift and diffusion coefficients of the considered equations to super-linearly grow not only with respect to the delay variable but also to the state variable. This work extends the existing results which develop the LDPs for SDDEs with super-linearly growing coefficients only with respect to the delay *** Codes 60H10, 60F10, 60H30 Copyright © 2022, The Authors. All rights reserved.

关键词： Stochastic systems

A modified orthogonal matching pursuit for construction of sparse probabilistic Boolean networks

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arXiv 2020年

作者： Xiao, Guiyun Bai, Zheng-Jian Ching, Wai-Ki School of Mathematical Sciences Xiamen University Xiamen361005 China School of Mathematical Sciences Fujian Provincial Key Laboratory on Mathematical Modeling & High Performance Scientific Computing Xiamen University Xiamen361005 China Advanced Modeling and Applied Computing Laboratory Department of Mathematics The University of Hong Kong Pokfulam Road Hong Kong

Probabilistic Boolean Networks play a remarkable role in the modelling and control of gene regulatory networks. In this paper, we consider the inverse problem of constructing a sparse probabilistic Boolean network from the prescribed transition probability matrix. We propose a modified orthogonal matching pursuit for solving the inverse problem. We provide some conditions under which the proposed algorithm can recover a sparse probabilistic Boolean network. We also report some numerical results to illustrate the effectiveness of the proposed algorithm. Copyright © 2020, The Authors. All rights reserved.

关键词： Inverse problems

Upper capacity entropy and packing entropy of saturated sets for amenable group actions

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arXiv 2021年

作者： Ren, Xiankun Zhang, Wenda Zhang, Yiwei College of Mathematics and Statistics Chongqing University Chongqing 401331 China College of Mathematics and Statistics Chongqing Jiaotong University Chongqing 400074 China School of Mathematics and Statistics Center for Mathematical Sciences Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Sciences and Technology Wuhan430074 China

Let (X, G) be a G-action topological system, where G is a countable infinite discrete amenable group and X a compact metric space. In this paper we study the upper capacity entropy and packing entropy for systems with weaker version of specification. We prove that the upper capacity always carries full entropy while there is a variational principle for packing entropy of saturated sets. © 2021, CC BY-NC-ND.

关键词： Specifications

A Hermite WENO scheme with artificial linear weights for hyperbolic conservation laws

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arXiv 2020年

作者： Zhao, Zhuang Qiu, Jianxian School of Mathematical Sciences Xiamen University Xiamen Fujian361005 China School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing Xiamen University Xiamen Fujian361005 China

In this paper, a fifth-order Hermite weighted essentially non-oscillatory (HWENO) scheme with artificial linear weights is proposed for one and two dimensional hyperbolic conservation laws, where the zeroth-order and the first-order moments are used in the spatial reconstruction. We construct the HWENO methodology using a nonlinear convex combination of a high degree polynomial with several low degree polynomials, and the associated linear weights can be any artificial positive numbers with only requirement that their summation equals one. The one advantage of the HWENO scheme is its simplicity and easy extension to multidimension in engineering applications for we can use any artificial linear weights which are independent on geometry of mesh. The another advantage is its higher order numerical accuracy using less candidate stencils for two dimensional problems. In addition, the HWENO scheme still keeps the compactness as only immediate neighbor information is needed in the reconstruction and has high efficiency for directly using linear approximation in the smooth regions. In order to avoid nonphysical oscillations nearby strong shocks or contact discontinuities, we adopt the thought of limiter for discontinuous Galerkin method to control the spurious oscillations. Some benchmark numerical tests are performed to demonstrate the capability of the proposed *** Codes 65M60, 35L65 Copyright © 2020, The Authors. All rights reserved.

关键词： Galerkin methods