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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 mathematics&Faculty of mathematics and Statistic Hubei UniversityWuhan 430062China hubei key laboratory of Mathematical sciences&school of mathematics 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

CONVERGENCE ANALYSIS OF SOME FINITE ELEMENT PARALLEL ALGORITHMS FOR THE STATIONARY INCOMPRESSIBLE MHD EQUATIONS

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Journal of computational mathematics 2024年第1期42卷 49-70页

作者： Xiaojing Dong Yinnian He Hunan key laboratory for Computation and Simulation in science and Engineering Key Laboratory of Intelligent Computing&Information Processing of Ministry of EducationSchool of Mathematics and Computational ScienceXiangtan UniversityXiangtan 411105China Institute of Applied Physics and computational mathematics Beijing 100088China school of mathematics and statistics Xi'an Jiaotong UniversityXi'an 710049China

By combination of iteration methods with the partition of unity method(PUM),some finite element parallel algorithms for the stationary incompressible magnetohydrodynamics(MHD)with different physical parameters are presented and *** algorithms are highly *** first,a global solution is obtained on a coarse grid for all approaches by one of the iteration *** parallelized residual schemes,local corrected solutions are calculated on finer meshes with overlapping *** subdomains can be achieved flexibly by a class of *** proposed algorithm is proved to be uniformly stable and ***,one numerical example is presented to confirm the theoretical findings.

关键词： Partition of unity method Local and parallel algorithm Finite element method Iteration methods Magnetohydrodynamics

SHARP POINTWISE-IN-TIME ERROR ESTIMATE OF L1 SCHEME FOR NONLINEAR SUBDIFFUSION EQUATIONS

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Journal of computational mathematics 2024年第3期42卷 662-678页

作者： Dongfang Li Hongyu Qin Jiwei Zhang school of mathematics and statistics Huazhong University of Science and TechnologyWuhan 430074China hubei key laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan 430074China school of mathematics and statistics Wuhan UniversityWuhan 430072China

An essential feature of the subdiffusion equations with theα-order time fractional derivative is the weak singularity at the initial *** weak regularity of the solution is usually characterized by a regularity parameterσ∈(0,1)∪(1,2).Under this general regularity assumption,we present a rigorous analysis for the truncation errors and develop a new tool to obtain the stability results,i.e.,a refined discrete fractional-type Grönwall inequality(DFGI).After that,we obtain the pointwise-in-time error estimate of the widely used L1 scheme for nonlinear subdiffusion *** present results fill the gap on some interesting convergence results of L1 scheme onσ∈(0,α)∪(α,1)∪(1,2].Numerical experiments are provided to demonstrate the effectiveness of our theoretical analysis.

关键词： Sharp pointwise-in-time error estimate Ll scheme Nonlinear subdiffusion equations Non-smooth solutions

Asymptotic Inference in the Random Coefficient Autoregressive Model with Time-functional Variance Noises

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 320-346页

作者： En-wen ZHU Zi-wei DENG Han-jun ZHANG Jun CAO Xiao-hui LIU Department of mathematics and statistics Changsha University of Science and TechnologyChangsha 410114China school of mathematics and computational science Xiangtan UniversityXiangtan 411105China school of statistics and Data science and Key Laboratory of Data Science in Finance and EconomicsJiangxi University of Finance and EconomicsNanchang 330013China

This paper considers the random coefficient autoregressive model with time-functional variance noises,hereafter the RCA-TFV *** first establish the consistency and asymptotic normality of the conditional least squares estimator for the constant *** semiparametric least squares estimator for the variance of the random coefficient and the nonparametric estimator for the variance function are constructed,and their asymptotic results are reported.A simulation study is presented along with an analysis of real data to assess the performance of our method in finite samples.

关键词： random coefficient autoregressive model time-functional variance conditional least squares semiparametric least squares

Spontaneous Infection and Periodic Evolving of Domain in a Diffusive SIS Epidemic Model

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Acta Mathematicae Applicatae Sinica 2024年第1期40卷 164-191页

作者： Qiang Wen Guo-qiang Ren Bin Liu school of mathematics and statistics Huazhong University of Science and TechnologyWuhan430074China hubei key laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan430074China

In this paper, we consider a susceptible-infective-susceptible(SIS) reaction-diffusion epidemic model with spontaneous infection and logistic source in a periodically evolving domain. Using the iterative technique,the uniform boundedness of solution is established. In addition, the spatial-temporal risk index R0(ρ) depending on the domain evolution rate ρ(t) as well as its analytical properties are discussed. The monotonicity of R0(ρ)with respect to the diffusion coefficients of the infected dI, the spontaneous infection rate η(ρ(t)y) and interval length L is investigated under appropriate conditions. Further, the existence and asymptotic behavior of periodic endemic equilibria are explored by upper and lower solution method. Finally, some numerical simulations are presented to illustrate our analytical results. Our results provide valuable information for disease control and prevention.

关键词： diffusive SIS model spontaneous infection periodically evolving domain periodic endemic equilibrium

Stabilization and Blow-up in an Infinite Memory Wave Equation with Logarithmic Nonlinearity and Acoustic Boundary Conditions

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Journal of Systems science & Complexity 2024年第4期37卷 1368-1391页

作者： PENG Qingqing ZHANG Zhifei school of mathematics and statistics Huazhong University of Science and TechnologyWuhan 430074China hubei key laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan 430074China

In this paper,the authors consider the stabilization and blow up of the wave equation with infinite memory,logarithmic nonlinearity and acoustic boundary *** authors discuss the existence of global solutions for the initial energy less than the depth of the potential well and investigate the energy decay estimates by introducing a Lyapunov ***,the authors establish the finite time blow up results of solutions and give the blow up time with upper bounded initial energy.

关键词： Acoustic boundary condition finite time blow-up general decay infinite memory logarithmic nonlinearity

MULTIFRACTAL ANALYSIS OF CONVERGENCE EXPONENTS FOR PRODUCTS OF CONSECUTIVE PARTIAL QUOTIENTS IN CONTINUED FRACTIONS

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Acta Mathematica Scientia 2024年第4期44卷 1594-1608页

作者： Lulu FANG Jihua MA Kunkun SONG Xin YANG school of mathematics and statistics Nanjing University of Science and TechnologyNanjing210094China school of mathematics and statistics Wuhan UniversityWuhan 430072China key laboratory of Computing and Stochastic mathematics(Ministry of Education) School of Mathematics and StatisticsHunan Normal UniversityChangsha 410081China

For each real number x∈(0,1),let[a_(1)(x),a_(2)(x),…,a_n(x),…]denote its continued fraction *** study the convergence exponent defined byτ(x)=inf{s≥0:∞∑n=1(a_(n)(x)a_(n+1)(x))^(-s)<∞},which reflects the growth rate of the product of two consecutive partial *** a main result,the Hausdorff dimensions of the level sets ofτ(x)are determined.

关键词： continued fractions product of partial quotients Hausdorff dimension

ONE-PARAMETER FINITE DIFFERENCE METHODS AND THEIR ACCELERATED SCHEMES FOR SPACE-FRACTIONAL SINE-GORDON EQUATIONS WITH DISTRIBUTED DELAY

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Journal of computational mathematics 2024年第3期42卷 705-734页

作者： Tao Sun Chengjian Zhang Haiwei Sun school of mathematics and statistics Huazhong University of Science and TechnologyWuhan 430074China hubei key laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan 430074China Department of mathematics University of MacaoMacaoChina

This paper deals with numerical methods for solving one-dimensional(1D)and twodimensional(2D)initial-boundary value problems(IBVPs)of space-fractional sine-Gordon equations(SGEs)with distributed *** 1D problems,we construct a kind of oneparameter finite difference(OPFD)*** is shown that,under a suitable condition,the proposed method is convergent with second order accuracy both in time and *** implementation,the preconditioned conjugate gradient(PCG)method with the Strang circulant preconditioner is carried out to improve the computational efficiency of the OPFD *** 2D problems,we develop another kind of OPFD *** such a method,two classes of accelerated schemes are suggested,one is alternative direction implicit(ADI)scheme and the other is ADI-PCG *** particular,we prove that ADI scheme can arrive at second-order accuracy in time and *** some numerical experiments,the computational effectiveness and accuracy of the methods are further ***,for the suggested methods,a numerical comparison in computational efficiency is presented.

关键词： Fractional sine-Gordon equation with distributed delay One-parameter finite difference methods Convergence analysis ADI scheme PCG method

THE WEIGHTED KATO SQUARE ROOT PROBLEMOF ELLIPTIC OPERATORS HAVING A BMOANTI-SYMMETRICPART

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Acta Mathematica Scientia 2024年第2期44卷 532-550页

作者：马文贤杨四辈 school of mathematics and statistics Gansu Key Laboratory of Applied Mathematics and Complex SystemsLanzhou UniversityLanzhou730000China

Let n≥2 and let L be a second-order elliptic operator of divergence form with coefficients consisting of both an elliptic symmetric part and a BMO anti-symmetric part in ℝ^(n).In this article,we consider the weighted Kato square root problem for *** precisely,we prove that the square root L^(1/2)satisfies the weighted L^(p)estimates||L^(1/2)(f)||L_(ω)^p(R^(n))≤C||■f||L_(ω)^p(R^(n);R^(n))for any p∈(1,∞)andω∈Ap(ℝ^(n))(the class of Muckenhoupt weights),and that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,2+ε)andω∈Ap(ℝ^(n))∩RH_(2+ε/p),(R^(n))(the class of reverse Hölder weights),whereε∈(0,∞)is a constant depending only on n and the operator L,and where(2+ε/p)'denotes the Hölder conjugate exponent of 2+ε/***,for any given q∈(2,∞),we give a sufficient condition to obtain that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,q)andω∈A_(p)(R^(n))∩pRH_(q/p),(R^(n)).As an application,we prove that when the coefficient matrix A that appears in L satisfies the small BMO condition,the Riesz transform∇L^(−1/2)is bounded on L_(ω)^(p)(ℝ^(n))for any given p∈(1,∞)andω∈Ap(ℝ^(n)).Furthermore,applications to the weighted L^(2)-regularity problem with the Dirichlet or the Neumann boundary condition are also given.

关键词： elliptic operator Kato square root problem Muckenhoupt weight Riesz transform reverse Hölder inequality