Table of Content

    26 October 2022, Volume 42 Issue 5 Previous Issue    Next Issue
    Similarity and Unitary Similarity of a Class of Upper Triangular Operator Matrices
    Liqiong Lin,Jiahua Que,Yunnan Zhang
    Acta mathematica scientia,Series A. 2022, 42 (5):  1281-1293. 
    Abstract ( 150 )   RICH HTML PDF (268KB) ( 218 )   Save

    This paper introduces a class of upper triangular operator matrices related to Cowen-Douglas operators, and studies its similarity on Banach spaces and its unitary similarity on Hilbert spaces.

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    The Maximal Operator of Vilenkin-like System on Hardy Spaces
    Chuanzhou Zhang,Chaoyue Wang,Xueying Zhang
    Acta mathematica scientia,Series A. 2022, 42 (5):  1294-1305. 
    Abstract ( 82 )   RICH HTML PDF (311KB) ( 92 )   Save

    In this paper, we discuss the boundedness of maximal operator with respect to bounded Vilenkin-like system (or $\psi\alpha$ system) which is generalization of bounded Vilenkin system. We prove that when $0 < p <1/2$ the maximal operator $\tilde{\sigma}_p^*f=\sup\limits_{n\in {\Bbb N}}\frac{|\sigma_nf|}{(n+1)^{1/p-2}}$ is bounded from the martingale Hardy space $H_p$ to the space $L_p$, where $\sigma_nf$ is $n$-th Fej\'er mean with respect to bounded Vilenkin-like system. By a counterexample, we also prove that the maximal operator $\sup\limits_{n\in {\Bbb N}}\frac{|\sigma_nf|}{\varphi(n)}$ is not bounded from the martingale Hardy space $H_{p}$ to the space $L_{p,\infty}$ when $0 < p <1/2$ and $\mathop{\overline{\lim}}\limits_{n\rightarrow \infty}\frac{(n+1)^{1/p-2}}{\varphi(n)}=+\infty$.

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    Composition Operators from Normal Weight General Function Spaces to Bloch Type Spaces
    Yuting Guo,Xuejun Zhang
    Acta mathematica scientia,Series A. 2022, 42 (5):  1306-1319. 
    Abstract ( 53 )   RICH HTML PDF (366KB) ( 95 )   Save

    In this paper, the boundedness and compactness of the composition operator from normal weight general function spaces to specific normal weight Bloch type spaces are investigated. The authors give the necessary and sufficient conditions for all cases.

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    Spectral Analysis of the Main Operator of Rotenberg Equation with Time Delay Under Nonsmooth Boundary Conditions
    Yage Tong,Kaisu Wu
    Acta mathematica scientia,Series A. 2022, 42 (5):  1320-1331. 
    Abstract ( 39 )   RICH HTML PDF (387KB) ( 59 )   Save

    After considering the time delay of cell division, the Rotenberg transport equation with time-delay is introduced in this paper. In $L_1$ space, under the condition of non-smooth boundary (the boundary operator is unbounded), it is proved that the transport operator can generate a $C_0$-semigroup. Furthermore, we study the spectrum of the transport operator and prove that the region $\Gamma=\sigma(A_H)\cap \{\lambda\in C | {\rm Re}\lambda>\gamma\}$ ($\gamma>{\rm max}\{\lambda_0, -\sigma_0\}$) is only consists of a finite number of discrete eigenvalues with finite algebraic multiplicity.

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    Boundedness of Differential Transforms for Heat Semigroups Generated by Fractional Laplacian
    Jingjing Cao,Xinyu Ren,Xuewen Bi,Chao Zhang
    Acta mathematica scientia,Series A. 2022, 42 (5):  1332-1347. 
    Abstract ( 37 )   RICH HTML PDF (393KB) ( 58 )   Save

    In this paper we analyze the convergence of the following type of series where $\{e^{-t(-\Delta)^\alpha} \}_{t>0}$ is the heat semigroup of the fractional Laplacian $(-\Delta)^\alpha, $ $N=(N_1, N_2)\in {\Bbb Z}^2$ with $N_1<N_2, $ $\{v_j\}_{j\in {\Bbb Z}}$ is a bounded real sequences and $\{a_j\}_{j\in {\Bbb Z}}$ is an increasing real sequence. Our analysis will consist in the boundedness, in $L^p(\mathbb{R} ^n)$ and in $BMO(\mathbb{R} ^n)$, of the operators $T_N$ and its maximal operator $\displaystyle T^*f(x)= \sup_N |T_N f(x)|.$ It is also shown that the local size of the maximal differential transform operators is the same with the order of a singular integral for functions $f$ having local support.

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    Two Types of Multi-Component Heisenberg Ferromagnet Models
    Fei Wang,Denghui Li,Yangjie Jia,Zhaowen Yan
    Acta mathematica scientia,Series A. 2022, 42 (5):  1348-1359. 
    Abstract ( 36 )   RICH HTML PDF (307KB) ( 45 )   Save

    This paper is concerned with two kinds of multi-component Heisenberg ferromagnet models. They are the (1+1)-dimensional Myrzakulov series equations and the (2+1)-dimensional Myrzakulov Lakshmanan series equations. Moving the space curve in Euclidean space presents the corresponding geometrical equivalent equations. Meanwhile the Lax representations of two types of multi-component Heisenberg ferromagnet models are investigated.

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    Positive Doubly Periodic Solutions To Telegraph Equations: Existence, Uniqueness, Multiplicity and Asymptotic Behavior
    Nan Deng,Meiqiang Feng
    Acta mathematica scientia,Series A. 2022, 42 (5):  1360-1380. 
    Abstract ( 53 )   RICH HTML PDF (393KB) ( 87 )   Save

    By using topological degree theory and the theory of convex operator, this paper discusses the existence, uniqueness and multiplicity of positive doubly periodic solutions to a class of telegraph equations, as well as the asymptotic behavior of positive doubly periodic solutions for telegraph equations.

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    The Critical Exponents for the Evolution p-Laplacian Equation with Nonlinear Gradient Terms
    Heqian Lu,Zhengce Zhang
    Acta mathematica scientia,Series A. 2022, 42 (5):  1381-1397. 
    Abstract ( 43 )   RICH HTML PDF (402KB) ( 59 )   Save

    This article studies the critical exponents for the homogeneous evolution $p$-Laplacian equation $u_{t}-\Delta_{p}u=u^{m}+|\nabla u|^{q}$ and its inhomogeneous version $u_{t}-\Delta_{p}u=u^{m}+|\nabla u|^{q}+h(x)$ in $\mathbb{R} ^{N}\times\mathbb{R} ^{+}$, $u(x, 0)=u_{0}(x)$ in $\mathbb{R} ^{N}$, where $N\geq1$, $p$, $m$, $q>1$. We obtain a discontinuous critical exponent result for the homogeneous evolution $p$-Laplacian equation, which demonstrates the gradient term brings about a significant phenomenon of the critical exponent, changing from $m=p-1+p/N$ to $m=\infty$ as $q$ goes to the value $p-N/(N+1)$ from above. Meanwhile, we also investigate the inhomogeneous evolution $p$-Laplacian equation and get a different discontinuous critical exponent result.

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    On a Double Phase Problem with Singular Weights
    Zhiyuan Chen,Bin Ge
    Acta mathematica scientia,Series A. 2022, 42 (5):  1398-1408. 
    Abstract ( 30 )   RICH HTML PDF (361KB) ( 47 )   Save

    In the present paper, in view of the variational approach, we consider the existence of positive weak solutions for a class of the double phase problem where $N\geq 2$ and $1<p<q<N$, $\alpha,\beta,\lambda,\mu$ are positive real numbers, $V_1$ and $V_2$ are weight functions in generalized Lebesgue spaces $L^{s_1}(\Omega)$ and $L^{s_2}(\Omega)$ respectively such that $V_1$ may change sign in $\Omega$ and $V_2\geq 0$ on $\Omega$.

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    Traveling Wave of a Nonlocal Dispersal SIR Model
    Yu Yang
    Acta mathematica scientia,Series A. 2022, 42 (5):  1409-1415. 
    Abstract ( 50 )   RICH HTML PDF (286KB) ( 55 )   Save

    This paper is concerned with a nonlocal dispersal SIR model. We first prove the existence of critical traveling wave for this model when $ {\cal R}_0>1 $, $ c=c^* $. Finally, the nonexistence of traveling wave solution for this model is established when $ {\cal R}_0<1 $. Our results improve some known results.

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    Long Time Existence of the Solutions for the Navier-Stokes-Coriolis Equations
    Xiaochun Sun,Gangjing He
    Acta mathematica scientia,Series A. 2022, 42 (5):  1416-1423. 
    Abstract ( 50 )   RICH HTML PDF (274KB) ( 55 )   Save

    In this paper, we proved the long time existence of classical solutions to the incompressible Navier-Stokes-Coriolis equation in the Sobolev space $ H^{s}(s>4) $. Here we obtained the classical solutions via Littlewood-Paley decomposition, Strichartz estimate and high and low frequency decomposition methods.

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    Existence of Nontrivial Solutions for Non-autonomous Kirchhoff-type Equations with Critical Growth in $ {{\Bbb R}} ^{3} $
    Penghui Zhang,Zhiqing Han
    Acta mathematica scientia,Series A. 2022, 42 (5):  1424-1432. 
    Abstract ( 49 )   RICH HTML PDF (332KB) ( 50 )   Save

    We are concerned with the following non-autonomous Kirchhoff type equation in $ {{\Bbb R}} ^{3} $ with vanishing potentials $ V(x), K(x) $ at infinity and a Sobolev critical term $ u^{5} $, where $ \lambda\geq 0 $ is a parameter. We prove that there exists $ \lambda^*>0 $ such that the equation has a nontrivial solution $ u_{\lambda} $ for all $ \lambda\geq\lambda^* $.

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    Existence of Periodic Mild Solutions for Fractional Evolution Equations with Periodic Impulses
    Qiang Li,Lishan Liu
    Acta mathematica scientia,Series A. 2022, 42 (5):  1433-1450. 
    Abstract ( 39 )   RICH HTML PDF (401KB) ( 35 )   Save

    This paper discusses the fractional evolution equations with piecewise Caputo derivative and periodic impulses. The existence and uniqueness of periodic mild solutions for the associated linear evolution equation with periodic impulses is established. With the aid of the expression of the solution operator for the linear impulsive periodic problem, some new existence results of periodic mild solutions for semilinear impulsive periodic problems are showed by means of the operator semigroup theory and fixed point theorems.

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    Ground State Travelling Waves in Infinite Lattices with Superquadratic Potentials
    Chunhui Shao,Jijiang Sun,Shiwang Ma
    Acta mathematica scientia,Series A. 2022, 42 (5):  1451-1461. 
    Abstract ( 79 )   RICH HTML PDF (396KB) ( 37 )   Save

    In this paper, we consider one dimensional FPU type lattices with particles of unit mass. The dynamics of the system is described by the followingwhere U is the potential of interaction between two adjacent particles and qn denotes the displacement. By directly using the usual variational method, we study the existence of ground state travelling waves, i.e., non-trivial travelling waves with least possible energy, for the above system with more general superquadratic potentials than the previous work of Pankov[10] and Zhang and Ma [20]. Moreover, we also concern the monotonicity of the solitary ground state travelling waves.

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    Large Multiple Periodic Solutions for the 1-Dimensional Sub-Linear p-Laplacian Equation
    Xuelei Wang
    Acta mathematica scientia,Series A. 2022, 42 (5):  1462-1472. 
    Abstract ( 41 )   RICH HTML PDF (401KB) ( 44 )   Save

    In this paper, we obtain existence and multiplicity of periodic solutions for 1-dimensional p-Laplacian equation $(|x'|^{p-2}x')'+f(t, x)=0$, where $f\in C(\mathbb{R} \times\mathbb{R} , \mathbb{R} )$ is \pi$-periodic in the first variable and satisfies the assumption $\frac{f(t, x)}{\mid x\mid^{p-2}x}\rightarrow 0$, as $\mid x\mid \rightarrow 0$. The new existence results can be applied to situations in which the more classical equation $x''+f(t, x)=0$. Proofs are based on Poincaré-Birkhoff twist theorem.

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    Regularity Criterion for 3D Incompressible Navier-Stokes Equations via the Pressure in Triebel-Lizorkin Spaces
    Yaqi Wan,Xiaoli Chen
    Acta mathematica scientia,Series A. 2022, 42 (5):  1473-1481. 
    Abstract ( 23 )   RICH HTML PDF (301KB) ( 38 )   Save

    In this paper, we consider the regularity criterion of weak solution to Navier-Stokes equations in $\mathbb{R}^3$. It is proved that a Leray-Hopf weak solution $u$ becomes a regular solution if the pressure $\pi\in L^p(0, T; \dot{F}_{q, \frac{10q}{5q+6}}^0(\mathbb{R}^3)) $ with $ \frac{2}{p}+\frac{3}{q}<\frac{7}{4}, \frac{12}{5}<q \leq \infty$. Meanwhile the authors also prove that if the gradient of the pressure $\nabla\pi\in L^p(0, T;\dot{F}_{q, \frac{8q}{12-3q}}^0(\mathbb{R}^3))$ with $\frac{2}{p}+\frac{3}{q}=\frac{11}{4}, \frac{12}{11}<q<4 $, then the weak solution u can be smoothly extended beyond t=T

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    On Testing Pseudo Random Generators Via Statistical Tests Based on the Poissonian Pair Correlations
    Xiao Ye,Yiming Ding
    Acta mathematica scientia,Series A. 2022, 42 (5):  1482-1495. 
    Abstract ( 38 )   RICH HTML PDF (1066KB) ( 65 )   Save

    Testing the quality of pseudo random number generators is an important issue. In general, PRNGs' randomness is measured by whether it passes the statistical test of testing uniformity and independence. In 1998, Rudnick and Sarnak proposed the concept of Poissonian pair correlations of real number sequences in [0, 1), an i.i.d. random sequence (sampled from the uniform distribution in (0, 1)) has Poissonian pair correlations. In this paper we propose a single-level statistical test for the real number sequences in (0, 1) based on the Poissonian pair correlations. We carried out PPC test on common PRNGs (Linear Congruential Generators, Mersenne Twister, Matlab.rand function, and PRNG based on the overlap of irrational numbers $\pi$, etc), introducing the selection method of convergence criterion. The test results show that the statistical test can effectively test the uniformity and independence of the pseudo-random number sequence at the same time.

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    A High Order MQ Quasi-Interpolation Method for Time Fractional Black-Scholes Model
    Shengliang Zhang,Junxian Huang
    Acta mathematica scientia,Series A. 2022, 42 (5):  1496-1505. 
    Abstract ( 32 )   RICH HTML PDF (416KB) ( 67 )   Save

    In this paper, Quasi-interpolation is a kind of high accurate meshless approximation method with shape-preserving property, which is often used in engineering. Based on cubic multiquadric (MQ) quasi-interpolation method, this paper proposes a novel meshless numerical scheme for time fractional Black-Scholes (B-S) model. The stability and convergence of the method are given. Numerical simulation shows that the method has high-order accuracy and is easy to be implemented for the nonuniform knots.

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    Algorithm with Order m + 1 Convergence for Weakly Nonlinear Complementarity Problems Derived From the Discretization of Free Boundary Problems
    Yajun Xie,Changfeng Ma
    Acta mathematica scientia,Series A. 2022, 42 (5):  1506-1516. 
    Abstract ( 28 )   RICH HTML PDF (423KB) ( 24 )   Save

    In this paper, by introducing the modulus-based nonlinear function and extending the classical Newton method, we investigate an accelerated Newton iteration method with high-order convergence for solving a class of weakly nonlinear complementarity problems which arise from the discretization of free boundary problems. Theoretically, the performance of high-order convergence is analyzed in details. Some numerical experiments illustrate the feasibility and efficiency of the proposed method.

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    Modified Subgradient Extragradient Algorithms for Solving Common Elements of Variational Inequality and Fixed Point Problems
    Liping Liu,Jianwen Peng
    Acta mathematica scientia,Series A. 2022, 42 (5):  1517-1536. 
    Abstract ( 34 )   RICH HTML PDF (516KB) ( 47 )   Save

    In this paper, we introduce a new class of inertial subgradient extragradient algorithms for solving variational inequality problems in the real Hilbert space. Under some appropriate conditions imposed on the parameters, we prove that the sequence generated by the algorithm strongly converges to a common element of the solution set for a pseudomonotone variational inequality problem and the set of fixed points for a quasinonexpansive mapping. Finally, we give numerical experiments to illustrate the effectiveness of our proposed algorithm. The results obtained in this paper extend and improve some existing results in the literature.

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    The Convergence of Nonsmooth Newton's Method
    Wending Xu,Ting Zhong
    Acta mathematica scientia,Series A. 2022, 42 (5):  1537-1550. 
    Abstract ( 39 )   RICH HTML PDF (347KB) ( 45 )   Save

    This paper studies the convergence of nonsmooth Newton's method for generalized inclusions. By applying metric regularity, a local convergence result of nonsmooth Newton's method is proved. The compactness in a known result is weakened through the measure of non-compactness. A convergence result in global version is established in which the conditions are assumed at the initial point while not the solution of the generalized inclusions.

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    Characterization of the Radius of the Robust Feasibility for a Class of Uncertain Convex Optimization Problems with Polynomial Constraints
    Caiyun Xiao,Xiangkai Sun
    Acta mathematica scientia,Series A. 2022, 42 (5):  1551-1559. 
    Abstract ( 37 )   RICH HTML PDF (366KB) ( 33 )   Save

    This paper deals with the lower bound of the radius of the robust feasibility for a class of convex optimization problems with uncertain convex polynomial constraints. Following the idea due to robust optimization, we first introduce the robust counterpart of the uncertain convex optimization problem and give the concept of radius of robust feasibility. By using the so-called epigraphical set and the Minkowski functions generated by the uncertain sets, we obtain the lower bound for the radius of robust feasibility of the uncertain convex optimization. Furthermore, an exact formula for the radius of the robust feasibility for an uncertain optimization problem with SOS-convex polynomial constraints is obtained. Our results extend and improve the corresponding results obtained in [10].

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    Environmental Detection and Response to a Kind of Dynamic Optimization Problem Subjected to Random Disturbance
    Jiale Nie,Jinghu Yu
    Acta mathematica scientia,Series A. 2022, 42 (5):  1560-1574. 
    Abstract ( 29 )   RICH HTML PDF (741KB) ( 54 )   Save

    Dynamic optimization problems are widespread in actual production or life, and environmental detection and response methods are the core of solving such problems. In many practical problems, due to the interference of random factors, the true optimal solution of the optimization problem will be randomly offset to a certain extent. This paper considers the stochastic dynamic optimization problem in which the random offset of the optimal solution obeys the normal distribution. First of all, this paper improves the existing interval shrinkage method based on the idea of orthogonal experimental design, and then proposes an environmental detection and response strategy for dynamic optimization problems, which avoids the blindness and randomness of the existing methods to a certain extent. Secondly, the upper limit of the standard deviation of the random perturbation corresponding to no change in the environmental detection before and after the perturbation is given. Finally, the particle swarm optimization algorithm is used for testing. And the experimental results show that the environmental detection and response method proposed in this paper can not only effectively deal with the stochastic dynamic optimization problem in which the optimal solution is disturbed by random, but also improve the ability of using particle swarm optimization to deal with other dynamic optimization problems. The improved environment detection and response method can be applied to other evolutionary algorithms besides particle swarm optimization.

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    Dynamics and Patterns for a Diffusive Leslie-Gower Predator-Prey Model with Michaelis-Menten Type Harvesting in Prey
    Zhanping Ma,Haifeng Huo,Hong Xiang
    Acta mathematica scientia,Series A. 2022, 42 (5):  1575-1591. 
    Abstract ( 50 )   RICH HTML PDF (1308KB) ( 61 )   Save

    This paper is devoted to study the dynamical properties and stationary patterns of a diffusive Leslie-Gower predator-prey model with Michaelis-Menten type harvesting in the prey population. We first prove the uniform persistence, and then study the nonnegative constant equilibrium solutions and their stabilities. Particularly, we obtain sufficient conditions of the global asymptotical stability of positive constant equilibrium solution by Lyapunov function method and the upper and lower solution method, respectively. Moreover, we investigate the stationary patterns induced (Turing pattern) by diffusion by degree theory. Our results show that Michaelis-Menten type harvesting in our model plays a crucial role in the formation of stationary patterns, which is a strong contrast to the case without harvesting.

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    Stability Analysis of an HIV Infection Dynamic Model with CTL Immune Response and Immune Impairment
    Meng Deng,Rui Xu
    Acta mathematica scientia,Series A. 2022, 42 (5):  1592-1600. 
    Abstract ( 64 )   RICH HTML PDF (393KB) ( 62 )   Save

    In this paper, we study an HIV infection model with saturation incidence rate, CTL immune response, immune impairment, and intracellular delay. Firstly, the basic reproduction ratio $ \Re_{0} $ of virus infection is obtained by using the next generation matrix method. Secondly, the local stability of feasible equilibria is proved by analyzing the distribution of the root of the corresponding characteristic equations. By constructing appropriate Lyapunov functionals and using LaSalle's invariance principle, we prove that when $ \Re_{0}<1 $, the virus infection-free equilibrium is globally asymptotically stable; when $ \Re_ {0}>1 $, the immunity-inactivated equilibrium is globally asymptotically stable. Finally, the parameter with critical influence on $ \Re_{0} $ is determined by the parameter sensitivity analysis.

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