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26 February 2020, Volume 40 Issue 1 Previous Issue   

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Reverse Order Law of the Drazin Inverse for Bounded Linear Operators Hua Wang,Jinfeng Li,Junjie Huang Acta mathematica scientia,Series A. 2020, 40 (1):  1-9.  Abstract ( 115 )   RICH HTML PDF (268KB) ( 129 )   Save In this paper, we discuss the Drazin invertibility and reverse order law of the Drazin inverse for the product of two bounded linear operators. Under the assumptions that P commutes with PQP and Q commutes with QPQ, respectively, we derive the Drazin invertibility of PQ and some equivalent conditions for the reverse order law (PQ)D=QDPD to hold by using space decomposition technique. References | Related Articles | Metrics

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The Squared Eigenfunction Symmetries and Miura Transformations for the KP and mKP Hierarchies Lumin Geng,Huizhan Chen,Na Li,Jipeng Cheng Acta mathematica scientia,Series A. 2020, 40 (1):  10-19.  Abstract ( 108 )   RICH HTML PDF (271KB) ( 104 )   Save In this paper, we discuss the relations of the squared eigenfunction symmetry and the Miura and auti-Miura transformations for the KP and mKP hierarchies and their constrained cases. References | Related Articles | Metrics

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Strong Fenchel-Lagrange Duality for Convex Optimization Problems with Composite Function Donghui Fang,Liping Tian,Xianyun Wang Acta mathematica scientia,Series A. 2020, 40 (1):  20-30.  Abstract ( 68 )   RICH HTML PDF (316KB) ( 72 )   Save In this paper, we consider a convex composite optimization problem which consists in minimizing the sum of a convex function and a convex composite function. By using the properties of the epigraph of the conjugate functions, some sufficient and necessary conditions for the strong and stable strong Fenchel-Lagrange dualities are provided. References | Related Articles | Metrics

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Quantum Asymptotic Estimation of the Optimal Eigenvalues of DE Operators in Riemannian Manifolds Kaiguang Wang,Yuelin Gao Acta mathematica scientia,Series A. 2020, 40 (1):  31-43.  Abstract ( 68 )   RICH HTML PDF (485KB) ( 72 )   Save In this paper, the geometric relations of differential evolution algorithm in Riemannian manifolds are analyzed and discussed. The convergence of populations in Riemannian manifolds with P-ε is analyzed. A quantum uncertain asymptotic estimation of the convergence accuracy and convergence speed of the iterative individual is obtained as follows $\Delta_{v}^{2}\cdot \Delta_{x_{\beta}^{\varepsilon}}^{2}\geq\Big(\frac{\sqrt{(\lambda_{\varepsilon})_{1}}+\cdots +\sqrt{(\lambda_{\varepsilon})_{n}}}{2}\Big)^{2},$ where, Δv2 is speed resolution of individual populations, Δxβε2 is position resolution with error ε of individual populations, (λε)i, i=1, 2, …, n. The theorem expression essentially shows that the local eigenvalues of iterated individuals in Riemann manifolds can not achieve high convergent accuracy and convergent speed at the same time. References | Related Articles | Metrics

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On the Sole Solvability of General Absolute Value Equation Cuixia Li,Shiliang Wu Acta mathematica scientia,Series A. 2020, 40 (1):  44-48.  Abstract ( 69 )   RICH HTML PDF (240KB) ( 89 )   Save In this paper, we focuss on the existence of the sole solvability of the general absolute value equation. Based on the regularity of interval matrices, along with the consistent matrix 2-norm, some new and useful results are presented to ensure the sole solvability of the general absolute value equation. References | Related Articles | Metrics

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The Perturbed Riemann Problem for the Pressureless Euler Equations with a Flocking Dissipation Qingling Zhang,Ying Ba Acta mathematica scientia,Series A. 2020, 40 (1):  49-62.  Abstract ( 58 )   RICH HTML PDF (464KB) ( 74 )   Save In this paper, the wave interactions involving the delta shock waves for the pressureless Euler equations with a flocking dissipation is considered and two kinds of perturbed Riemann problems are studied. The global existence of the generalzied solutions is obtained constructively by using the generalized Rankine-Hugoniot conditions and the entropy condition when the initial data are three piecewise constant states. By analyzing the global structure and the limit under the stability theory of weak solutions, the global soution for the delta inital data problem are constructively obtained. Moreover, a new kind of nonclassical wave -delta contact discontinuity has appeared in it. Figures and Tables | References | Related Articles | Metrics

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Extremal Problems of Hardy-Littlewood-Sobolev Inequalities on Compact Riemannian Manifolds: the Approximation Method from Subcritical to Critical Shutao Zhang,Yazhou Han Acta mathematica scientia,Series A. 2020, 40 (1):  63-71.  Abstract ( 73 )   RICH HTML PDF (331KB) ( 47 )   Save Let $(M^n,g)$ be a $n$-dimensional compact Riemannian manifolds, $0<\alpha<n$ and $q>\frac{n}{n-\alpha}$. This paper is mainly devoted to study the extremal problems of the following HLS inequalities: $\|I_\alpha f\|_{L^q(M^n)}\leq C\|f\|_{L^p(M^n)},\quad\mbox{with}\quad I_\alpha f(x)=\int_{M^n}\frac{f(y)}{|x-y|_g^{n-\alpha}}{\rm d}V_y,\ p\geq\frac{nq}{n+\alpha q}.$ Firstly, we prove that $I_\alpha: L^p(M^n)\rightarrow L^q(M^n)$ with $p>\frac{nq}{n+\alpha q}$ is compact and then get the existence of extremal functions $f_p, p>\frac{nq}{n+\alpha q}$. Secondly, we find that the function sequence $\{f_p\}$ is a maximizing sequence for the sharp constant of HLS inequality with $p=\frac{nq}{n+\alpha q}$. Finally, by the Concentration-Compactness principle established in [32], we can prove that there exists a convergence subsequence of $\{f_p\}$ and then give the existence of extremal function for critical case. References | Related Articles | Metrics

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Traveling Waves in a Nonlocal Dispersal SIR Epidemic Model with Treatment Dong Deng,Yan Li Acta mathematica scientia,Series A. 2020, 40 (1):  72-102.  Abstract ( 85 )   RICH HTML PDF (897KB) ( 91 )   Save This paper is concerned with the existence and nonexistence of traveling wave solutions of a nonlocal dispersal epidemic model with treatment. The existence of traveling wave solutions is established by Schauder's fixed point theorem as well as a limiting argument, while the nonexistence of traveling wave solutions is proved by two-sided Laplace transform and Fubini's theorem. From the results, we conclude that the minimal wave speed is an important threshold to predict how fast the disease invades. Figures and Tables | References | Related Articles | Metrics

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Solvability of BVPs for Impulsive Fractional Langevin Type Equations Involving Three Riemann-Liouville Fractional Derivatives Yuji Liu Acta mathematica scientia,Series A. 2020, 40 (1):  103-131.  Abstract ( 94 )   RICH HTML PDF (413KB) ( 60 )   Save Let $n,l,k$ be positive integers and $\alpha\in (n-1,n)$, $\beta\in (l-1,l)$ and $\gamma\in (k-1,k)$. Firstly the continuous general solutions of the Langevin equation with three fractional derivatives $[D_{0^+}^\alpha D_{0^+}^\beta -\lambda D_{0^+}^\gamma ] x(t)=P(t)$ are presented by using iterative method. Secondly the piecewise continuous general solutions of the impulsive Langevin equation with three fractional derivatives $[D_{0^+}^\alpha D_{0^+}^\beta -\lambda D_{0^+}^\gamma ] x(t)=P(t),t\in (t_i,t_{i+1}],i\in {\Bbb N} _0^m$ are given by using mathematical in{\rm d}uction method. Thirdly, by using the obtained results, a boundary value problem for the impulsive Langevin fractional differential equation with three Riemann-Liouville fractional derivatives of order $\alpha,\beta\in (1,2),\gamma\in (0,1)$ is converted to an integral equation. Existence results for solutions of the mentioned problem are established. Some examples are given to show readers the applications of the main results. References | Related Articles | Metrics

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Positive Solutions for a System of Boundary Value Problems of Fractional Difference Equations Involving Semipositone Nonlinearities Jiafa Xu Acta mathematica scientia,Series A. 2020, 40 (1):  132-145.  Abstract ( 69 )   RICH HTML PDF (356KB) ( 89 )   Save In this paper, we use the fixed point index to investigate the existence of positive solutions for a system of boundary value problems of fractional difference equations involving semipositone nonlinearities. References | Related Articles | Metrics

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Asymptotic Stability of Weak Solutions to Wave Equation with Variable Exponents and Strong Damping Term Menglan Liao,Bin Guo Acta mathematica scientia,Series A. 2020, 40 (1):  146-155.  Abstract ( 74 )   RICH HTML PDF (360KB) ( 98 )   Save This paper deals with the following wave equation with strong damping term: $u_{tt}-{\rm div}(|\nabla{u}|^{p(x)-2}\nabla{u})-\Delta u_t=|u|^{q(x)-2}u$ under initial and Dirichlet boundary value condition. By constructing a new control function and applying the Sobolev embedding inequality, the authors establish the relationship between source term and energy functional, and then decay estimates are obtained by means of Komornik's inequality and energy estimates. At last, we prove that u(x, t)=0 is asymptotic stable. References | Related Articles | Metrics

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Liouville Type Theorems for Stable Solutions of the Degenerate Elliptic System with Weight Qianqiu Wu,Lianggen Hu Acta mathematica scientia,Series A. 2020, 40 (1):  156-168.  Abstract ( 60 )   RICH HTML PDF (350KB) ( 64 )   Save We study the degenerate elliptic system with weight $\left\{\begin{array}{ll}-\Delta_{G} u=\omega (x) v, \\-\Delta_{G} v=\omega (x) u^q, \end{array}\right.\quad \mbox{in}\;\ \mathbb{R} ^N=\mathbb{R} ^{N_1}\times \mathbb{R} ^{N_2}, $ where $\Delta_{G} u=\Delta_{x} u+(a+1)^2|x|^{2a}\Delta_{y} u$ is the Grushin operator, $a, \beta\ge0$, $q>1$, $\omega(x)=\left (1+\| x \|^{2(a+1)}\right)^{\frac{\beta}{2(a+1)}}$. Liouville type results for positive stable solutions in the supercritical exponent are established. References | Related Articles | Metrics

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Philos-Type Criteria for Second-Order Delay Differential Equations with Nonlinear Neutral Term Jimeng Li,Jiashan Yang Acta mathematica scientia,Series A. 2020, 40 (1):  169-186.  Abstract ( 56 )   RICH HTML PDF (417KB) ( 62 )   Save We study the oscillatory behavior of Emden-Fowler-type differential equations with a nonlinear neutral term $\{a(t)|[x(t)+p(t)x^\alpha(\tau(t))]'|^{\beta-1}[x(t)+p(t)x^\alpha(\tau(t))]'\}'+q(t)f(|x(\delta(t))|^{\gamma-1}x(\delta(t)))=0, t\geq t_0$ in this article. By using the generalized Riccati transformation, and Bernoulli inequality, Yang inequality and integral averaging technique, we establish some new oscillation criterions for the equations. The illustrative examples are provided to show that our results obtained extend and improve those reported in the literature, and have practicability and maneuverability. References | Related Articles | Metrics

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A New Integrable Generalization of Super Soliton Hierarchy and Its Self-Consistent Sources and Conservation Laws Hanyu Wei,Tiecheng Xia,Beibei Hu,Yan Zhang Acta mathematica scientia,Series A. 2020, 40 (1):  187-199.  Abstract ( 53 )   RICH HTML PDF (345KB) ( 70 )   Save Based on a Lie super algebra B(0, 1), a new generalized super soliton hierarchy is obtained. By making use of the super trace identity, the resulting super soliton hierarchy can be put into a super bi-Hamiltonian form. Then, the self-consistent sources of the generalized super soliton hierarchy is established. Furthermore, we present the infinitely many conservation laws for the integrable super soliton hierarchy. References | Related Articles | Metrics

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SDE Driven by Fractional Brown Motion and Their Coefficients are Locally Linear Growth Qikang Ran Acta mathematica scientia,Series A. 2020, 40 (1):  200-211.  Abstract ( 114 )   RICH HTML PDF (390KB) ( 66 )   Save In this paper, we discuss the existence and uniqueness of a class of stochastic differential equations driven by fractional Brown motion with Hurst parameter H ∈ ($\frac{1}{2}$, 1) and their coefficients are local linear growth. So far, there are several ways to define stochastic integrals with respect to FBM. In this paper, we define stochastic integrals with respect to FBM as a generalized Stieltjes integral. We give the existence and uniqueness theorems respectively for SDEs driven by fractional Brown motion and their coefficients are local linear growth. References | Related Articles | Metrics

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Multi-Samples Testing for Second Stochastic Dominance Against Unrestricted Alternative Jianling Zhang Acta mathematica scientia,Series A. 2020, 40 (1):  212-220.  Abstract ( 56 )   RICH HTML PDF (343KB) ( 48 )   Save In this paper, we will study test problem of multi-sample second order stochastic dominance against no restriction by using isotonic regression estimates and bootstrap method. The specific steps are as follows:Firstly, a test statistic is constructed with the isotonic regression estimators and empirical distribution functions. Then, the critical value and p value of the test are given by bootstrap method. Finally, simulation results are presented to illustrate the proposed test method. Figures and Tables | References | Related Articles | Metrics

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Dynamics of a Nonautonomous SIRI Epidemic Model with Random Perturbations Zhongwei Cao,Xiangdan Wen,Wei Feng,Li Zu Acta mathematica scientia,Series A. 2020, 40 (1):  221-233.  Abstract ( 85 )   RICH HTML PDF (616KB) ( 68 )   Save In this paper, we study the dynamics of a stochastic nonautonomous Susceptible-Infective-Removed-Infective (SIRI) epidemic model. By employing the Lyapunov function method, we show that there exists at least one nontrivial positive T-periodic solution of the system. Moreover, sufficient conditions for extinction of the disease are established. Some numerical simulations are carried out to illustrate the theoretical results. Figures and Tables | References | Related Articles | Metrics

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Well-Posedness of the Solution of Schwinger-Dyson Equation in Quantum Chromodynamics Feng Hu,Ruifeng Zhang Acta mathematica scientia,Series A. 2020, 40 (1):  234-242.  Abstract ( 60 )   RICH HTML PDF (362KB) ( 66 )   Save In this paper, we study the Schwinger-Dyson integral equation in quantum chromodynamics under the condition of the finite-temperature. Applying the theory of integral equation and functional analysis, we get the well-posedness of the solution of Schwinger-Dyson integral equation. Furthermore, we prove the existence and uniqueness of critical temperature Tc, which separates the low-temperature phase where the chiral symmetry is spontaneously broken from the high-temperature phase where the chiral symmetry restores in quantum chromodynamics. References | Related Articles | Metrics

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Dynamical Mechanism and Energy Conversion of Couette-Taylor Flow Heyuan Wang Acta mathematica scientia,Series A. 2020, 40 (1):  243-256.  Abstract ( 81 )   RICH HTML PDF (1761KB) ( 65 )   Save There have been a lot of investigations which concern with rotating flow between two concentric cylinders (abbreviate frequently as Couette-Taylor Flow), Couette-Taylor flow is the typical rotation flow problems, It provides a paradigm from laminar to turbulent transition. Dynamical mechanism and energy conversion of Couette-Taylor flow are investigated in this paper, the Couette-Taylor flow chaotic system is transformed into Kolmogorov type system, which is decomposed into four types of torques:inertial torque, internal torque, dissipation and external torque. By the combinations of different torques, key factors of chaos generation and the physical meaning of Couette-Taylor Flow are studied. The conversion among Hamiltonian energy, kinetic energy and potential energy is investigated. The relationship between the energies and the Reynolds number is discussed. It concludes that the combination of the four torques is necessary conditions to produce chaos, and only when the dissipative torques matches the driving (external) torques can the system produce chaos, any combination of three types of torques cannot produce chaos. The external torque, which is provided by the rotation of the cylinder, supply the energy of the system, and that leads to Taylor vortex and chaos, the physical meaning and energy conversion of Couette-Taylor flow system are investigated. The Casimir function is introduced to analyze the system dynamics, and its derivation is chosen to formulate energy conversion. The bound of chaotic attractor is obtained by the Casimir function and Lagrange multiplier. The Casimir function reflects the energy conversion and the distance between the orbit and the equilibria. These relationships are illustrated by numerical simulations. Figures and Tables | References | Related Articles | Metrics