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26 December 2019, Volume 39 Issue 6 Previous Issue   

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Property (H) and Perturbations Lihong Chen,Weigang Su Acta mathematica scientia,Series A. 2019, 39 (6):  1281-1290.  Abstract ( 74 )   RICH HTML PDF (300KB) ( 179 )   Save This paper introduces two new spectral properties (H) and (gH), and investigates the two properties in connection with Weyl type theorems. Also the preservation of the two properties are studied under commuting nilpotent, quasi-nilpotent, finite rank or Riesz perturbation. References | Related Articles | Metrics

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Equivalent Characterization of Several Quantities on Holomorphic Function Spaces Pengcheng Tang,Xuejun Zhang,Ruixin Lv Acta mathematica scientia,Series A. 2019, 39 (6):  1291-1299.  Abstract ( 118 )   RICH HTML PDF (335KB) ( 130 )   Save In this paper, the expression under the action of fractional derivative and fractional integral for a common function on the unit ball of several complex variables is improved. At the same time, the equivalent norms of the fractional differential on two holomorphic function spaces are improved, and the constraint conditions β=s+N for the fractional differential Rs, t and Rβ, t in the equivalent norms are removed, where N is a positive integer. References | Related Articles | Metrics

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The Generalized Riemann Problem for Chromatography Equations with Delta Shock Wave Lijun Pan,Xinli Han,Tong Li Acta mathematica scientia,Series A. 2019, 39 (6):  1300-1313.  Abstract ( 89 )   RICH HTML PDF (643KB) ( 119 )   Save This paper is concerned with the generalized Riemann problem for the nonlinear chromatography equations, where the delta shock wave occurs in the corresponding Riemann solution. It is quite different from the previous generalized Riemann problems which focus on classical elementary waves. We constructively solve the generalized Riemann problem in a neighborhood of the origin on the x-t plane. In solutions, we find that the generalized Riemann solutions have a structure similar to the solution of the corresponding Riemann problem for most of cases. However, a delta shock wave in the corresponding Riemann solution may turn into a shock wave followed by a contact discontinuity, which provides us with a detailed method for analyzing the internal mechanism of a delta shock wave. Figures and Tables | References | Related Articles | Metrics

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The Solvability of Dual Minkowski Problem in $\mathbb{R}$2 Na Wei Acta mathematica scientia,Series A. 2019, 39 (6):  1314-1322.  Abstract ( 60 )   RICH HTML PDF (306KB) ( 112 )   Save In this paper, we study the existence of minimum of a constrained variational problem in the Sobolev space W1, 4($\mathbb{S}$). If ∫$_\mathbb{S}$g(θ)dθ>0, the minimum is a positive solution to the related Euler-Lagrange equation ${u^{\prime \prime }} + u = \frac{{g(\theta )}}{{u\left( {{u^2} + {u^{\prime 2}}} \right)}}, \theta \in {\rm{\mathbb{S}}}$ Based on this, we prove the solvability of the dual Minkowski problem in $\mathbb{R}$2 posed by Huang-Lutwak-Yang-Zhang[Acta Math, 2016, 216(2):325-338]. References | Related Articles | Metrics

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A Constrained Variational Problem of Kirchhoff Type Equation with Ellipsoid-Shaped Potential Rongxing Li,Wenqing Wang,Xiaoyu Zeng Acta mathematica scientia,Series A. 2019, 39 (6):  1323-1333.  Abstract ( 85 )   RICH HTML PDF (330KB) ( 113 )   Save In this paper, we are considered with a constrained variational problem for certain type of Kirchhoff equation with trapping potential and the bottom of the potential is an ellipsoid. We are interested in the asymptotic behavior of solutions of variational problem and we prove that the minimizers of the minimization problem blows up at one of the endpoints of the major axis of the ellipsoid as the related parameter approaches a critical value. References | Related Articles | Metrics

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Existence of Mild Solutions for a Class of Fractional Semilinear Integro-Differential Equation of Mixed Type Bo Zhu,Baoyan Han,Lishan Liu Acta mathematica scientia,Series A. 2019, 39 (6):  1334-1341.  Abstract ( 76 )   RICH HTML PDF (301KB) ( 119 )   Save In this paper, the authors studied the existence results of the mild solutions for a class of fractional semilinear integro-differential equation of mixed type by using the measure of noncompactness, k-set contraction and β-resolvent family. It is well known that the k-set contraction requires additional condition to ensure the contraction coefficient 0 < k < 1. We don't require additional condition to ensure the contraction coefficient 0 < k < 1. An example is introduced to illustrate the main results of this paper. References | Related Articles | Metrics

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Traveling Wave Solutions of the Generalized Hyperelastic-Rod Wave Equation Yongyi Gu,Wenjun Yuan,Yonghong Wu Acta mathematica scientia,Series A. 2019, 39 (6):  1342-1351.  Abstract ( 60 )   RICH HTML PDF (385KB) ( 109 )   Save In this paper, we study the generalized hyperelastic-rod wave equation. We changed the generalized hyperelastic-rod wave equation into a complex differential equation by using traveling wave transform and show that meromorphic solutions of the complex differential equation belong to the class W by the weak $ \left\langle {h, k} \right\rangle $ condition and the Fuchs index. Furthermore, we find out all meromorphic solutions of the complex differential equation, then we obtain the traveling wave solutions of the generalized hyperelastic-rod wave equation. We can apply the idea of this study to some related mathematical physics equations. References | Related Articles | Metrics

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Polynomial Solutions of the Polynomial-Like Iterative Equation Zhiheng Yu,Xiaobing Gong Acta mathematica scientia,Series A. 2019, 39 (6):  1352-1364.  Abstract ( 77 )   RICH HTML PDF (382KB) ( 114 )   Save Most of known results for the polynomial-like iterative equation were given for monotone functions. In this paper, we discuss this equation for a polynomial function, which is non-monotonic. In one-dimensional case, we apply the method of computer algebra system SINGULAR decomposing algebraic varieties to find a sufficient and necessary condition for the polynomial-like iterative equation of orders 2 and 3 having quadratic polynomial solutions respectively and give quadratic polynomial solutions of both two equations. Then we give a procedure for computing polynomial solutions of the polynomial-like equation. In two-dimensional case, applying the idea of one-dimensional case we obtain several sufficient and necessary conditions for second order polynomial-like iterative equation having quadratic degree-preserving polynomial solutions when the given function is a two-dimensional homogeneous polynomial mapping of degree 2. References | Related Articles | Metrics

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A Revisit on Multiple-Pulse Homoclinic Solutions in a Generalized Gierer-Meinhardt Equation Kun Zhu,Jianhe Shen Acta mathematica scientia,Series A. 2019, 39 (6):  1365-1375.  Abstract ( 77 )   RICH HTML PDF (529KB) ( 80 )   Save In paper[1] (Indiana Univ Math J, 2001, 50:443-507), the authors studied the existence and stability of multiple-pulse homoclinic solutions in a generalized Gierer-Meinhardt equation. However, in this paper, a general integral measuring the distance of the stable and unstable manifolds of the critical manifold of the layer system, i.e., the Melnikov integral, was not computed explicitly. So we have two aims in this manuscript. Firstly, we give an elementary method to solve a second-order nonlinear conservative system and hence obtain the explicit representation of the homoclinic orbit. Secondly, we substitute the explicit representation of the homoclinic orbit into the the Melnikov integral. By computing such a general integral, we obtain a more explicitly parametric condition on the existence of multiple-pulse homoclinic solutions in such a generalized Gierer-Meinhardt equation. Figures and Tables | References | Related Articles | Metrics

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Singularity and Decay of Solutions for a Degenerate Semilinear Elliptic Equation Dongyan Li,Yan Dong Acta mathematica scientia,Series A. 2019, 39 (6):  1376-1380.  Abstract ( 67 )   RICH HTML PDF (259KB) ( 85 )   Save In this paper, we establish a singularity and decay of solutions for a degenerate semilinear elliptic equation based on re-scaling arguments combined with a doubling property. As an application, we derive a priori bounds of solutions of a boundary value problem. References | Related Articles | Metrics

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Global Existence and Stability to a Prey-Taxis Model with Porous Medium Diffusion and Indirect Signal Production Limin Zhang,Haiyan Xu,Chunhua Jin Acta mathematica scientia,Series A. 2019, 39 (6):  1381-1404.  Abstract ( 86 )   RICH HTML PDF (441KB) ( 107 )   Save In this paper, we consider the following prey-taxis model with nonlinear diffusion and indirect signal production $\left\{ \begin{array}{l}{u_t} = \Delta {u^{{m_1}}} - \chi \nabla \cdot \left( {u\nabla w} \right),\\{w_t} = \Delta w - \mu w + \alpha v{F_0}\left( u \right),\\{v_t} = \Delta {v^{{m_2}}} + \lambda v\left( {1 - \frac{v}{k}} \right) - v{F_0}\left( u \right)\end{array} \right.$ in a bounded domain of $ {{\mathbb{R}}^{3}}$ withzero-flux boundary condition. It is shown that for any m1>1, m2>1, there exists a global bounded weak solution for any large initial datum. Based on the uniform boundedness property, we also studied the large time behavior of solutions, and the global asymptotically stability of the constant steady states are established. More precisely, we showed that when λ=0, α ≥ 0, the global weak solution converges to (ū0, 0, 0) in the large time limit; when λ>0, α=0, the global weak solution converges to (ū0, 0, 0) if λ < F0(ū), and the global weak solution converges to $\left( {{{\bar u}_0}, 0, k\left( {1 - \frac{{{F_0}(\bar u)}}{\lambda }} \right)} \right) $ if λ > F0(ū). References | Related Articles | Metrics

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Lorentz Estimates for Nondivergence Parabolic Equations with Partially BMO Coefficients Junjie Zhang,Shenzhou Zheng,Haiyan Yu Acta mathematica scientia,Series A. 2019, 39 (6):  1405-1420.  Abstract ( 49 )   RICH HTML PDF (413KB) ( 79 )   Save In this paer, we prove an interior Lorentz estimate for Hessian of the strong solutions to nondivergence linear parabolic equations ut -aij(x, t)Diju(x, t)=f(x, t). Here, the leading coefficients aij(x, t) are assumed to be merely measurable in one spatial variable and have small BMO semi-norms with respect to the remaining variables. References | Related Articles | Metrics

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Pointwise Estimates for Systems of Wave Equations with Viscosity Zhigang Wu,Xiaofang Miao Acta mathematica scientia,Series A. 2019, 39 (6):  1421-1442.  Abstract ( 54 )   RICH HTML PDF (473KB) ( 108 )   Save The Cauchy problem for two systems of wave equations with viscosity in dimension three is considered. By using the long wave and short wave decomposition method together with energy method and Green function, the pointwise estimates of the time-asymptotic shape of the solution are given, which exhibit two kinds of generalized Huygens' waves. As a byproduct, the optimal Lp-decay rates with p ≥ 1 of the solutions of these systems are also established. References | Related Articles | Metrics

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Decay Estimates of the Global Solution for the Landau-Lifshitz-Gilbert Equation in Three Dimensions Junyu Lin,Minglian Wan,Muhua Cao Acta mathematica scientia,Series A. 2019, 39 (6):  1443-1455.  Abstract ( 56 )   RICH HTML PDF (324KB) ( 103 )   Save In this paper, the authors consider the Cauchy problem for the Landau-Lifshitz-Gilbert equation in $\mathbb{R}$3. By energy method and standard continuity argument, the authors obtain the global existence and uniqueness of smooth solution under suitable small initial data firstly. After establishing a monotone inequality for this solution, the authors built the time decay rates for this solution by the Fourier splitting method. References | Related Articles | Metrics

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Blow-Up Phenomenon for a Coupled Diffusion System with Exponential Reaction Terms and Space-Dependent Coefficients Danni Ma,Zhongbo Fang Acta mathematica scientia,Series A. 2019, 39 (6):  1456-1475.  Abstract ( 59 )   RICH HTML PDF (450KB) ( 90 )   Save Blow-up phenomena for the Dirichlet initial boundary value problem of a coupled diffusion system with exponential reaction terms and space-dependent coefficients is considered. By virtue of the Bernoulli equation, the method of super-and-sub solutions and the modified differential inequality techniques, we founded the influence of space-dependent coefficients on the existence of global solution or blow-up solution at finite time. Moreover, upper and lower bounds for the blow-up time of the solution are derived under different measures in whole dimensional spaces (N ≥ 1). References | Related Articles | Metrics

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Fixed Points of Meromorphic Functions and Their Differences Zhaojun Wu Acta mathematica scientia,Series A. 2019, 39 (6):  1476-1482.  Abstract ( 100 )   RICH HTML PDF (264KB) ( 107 )   Save Let f be a transcendental meromorphic function in the complex plane C, k is a positive integer, Δf=f(z+1)-f(z), Δk+1 f=Δk f(z+1)-Δk f, k=1, 2, …. The author prove some results concerning the fixed points of the differences Δk f. The results obtained in this paper generalize some relative results. References | Related Articles | Metrics

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Order-Preservation of Solution Correspondence for Generalized Vector Equilibrium Problems on Chain-Complete Posets Yuehu Wang,Baoqing Liu Acta mathematica scientia,Series A. 2019, 39 (6):  1483-1491.  Abstract ( 46 )   RICH HTML PDF (356KB) ( 70 )   Save In this paper, we explore the upper order-preservation of solution correspondence for parametric generalized vector equilibrium problems on chain-complete posets. In contrast to the previous results which mainly focus on the existence, topological continuity and algorithms, the order-preservation is a new subject for generalized vector equilibrium problems and it is useful for predicting the changing trend of solutions. Since our approaches are order-theoretic fixed point theorems and isotone selection theorems, neither convexity nor continuity is required for the mapping F. References | Related Articles | Metrics

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A Double Projection Method for Solving Variational Inequalities Yuxian Hu Acta mathematica scientia,Series A. 2019, 39 (6):  1492-1498.  Abstract ( 64 )   RICH HTML PDF (319KB) ( 98 )   Save In this paper, we introduce a new method for solving variational inequalities. The method uses a new hyperplane which differs from known ones. Under some mild conditions, we prove that the sequence produced by our method globally converges to a solution. Furthermore, the convergence rate of the iteration sequence is established. Numerical experiments are reported in section 5. Figures and Tables | References | Related Articles | Metrics

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Consistency of Least Squares Estimation to the Parameter for Stochastic Differential Equations Under Distribution Uncertainty Chen Fei,Weiyin Fei Acta mathematica scientia,Series A. 2019, 39 (6):  1499-1513.  Abstract ( 77 )   RICH HTML PDF (451KB) ( 148 )   Save Under distribution uncertainty, on the basis of discrete observation data we investigate the consistency of the least squares estimator (LSE) of the parameter for the stochastic differential equation (SDE) where the noise are characterized by G-Brownian motion. In order to obtain our main result of consistency of parameter estimation, we provide some lemmas by the theory of stochastic calculus of sublinear expectation. The result shows that under some regularity conditions, the least squares estimator is strong consistent uniformly on the prior set. An illustrative example is discussed. Figures and Tables | References | Related Articles | Metrics

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Pricing European Lookback Option in a Special Kind of Mixed Jump-Diffusion Black-Scholes Model Zhaoqiang Yang Acta mathematica scientia,Series A. 2019, 39 (6):  1514-1531.  Abstract ( 116 )   RICH HTML PDF (504KB) ( 126 )   Save This article considers the pricing problem of European fixed strike lookback options under the environment of mixed jump-diffusion fractional Brownian motion. Under the conditions of Merton assumptions, we analyze the Cauchy initial problem of stochastic parabolic partial differential equations which the risky asset satisfied, by using the perturbation method of multiscale-parameter, the approximate pricing formulae of European lookback options are given by solving stochastic parabolic partial differential equations. Then the error estimates of the approximate solutions are given by using Feynman-Kac formula. Numerical simulation illustrate that the European lookback options have exact solutions when the volatilities are constant, and as the order of simulation increases, the approximate solutions are gradually approximates the exact solutions. Figures and Tables | References | Related Articles | Metrics

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The Moderate Deviation Principle for Stochastic 3D LANS-α Model Driven by Multiplicative Lévy Noise Jianhua Huang,Zaiyun Zhang,Yong Chen Acta mathematica scientia,Series A. 2019, 39 (6):  1532-1544.  Abstract ( 46 )   RICH HTML PDF (346KB) ( 115 )   Save In this paper, we construct the moderate deviation principle for stochastic 3D LANS-α model driven by multiplicative Lévy noise by the weak convergence method. References | Related Articles | Metrics

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Dynamical Properties of a Discontinuous Models with Signal Molecules Regulation Ru Wang,Zhonghua Zhang,Yeling Liu Acta mathematica scientia,Series A. 2019, 39 (6):  1545-1554.  Abstract ( 61 )   RICH HTML PDF (585KB) ( 99 )   Save In this paper, the concentration of signal molecules is used as an indicator to establish a discontinuous model that describes the regulation of signal molecules concentration by the quorum sensing mechanism of pathogens. The existence of the sliding module region, the existence and stability of the true (false) equilibrium point and the pseudo equilibrium point are discussed. In particular, the existence of the crossing limit cycles is proved. Finally, the Matlab software is used to carry out numerical simulations to support the theoretical results. Figures and Tables | References | Related Articles | Metrics

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The Asymptotic Path Curve for Fermi Gases Optical Lattices Model Cheng Ouyang,Weigang Wang,Jiaqi Mo Acta mathematica scientia,Series A. 2019, 39 (6):  1555-1562.  Abstract ( 73 )   RICH HTML PDF (454KB) ( 83 )   Save A class of model for the Fermi gases optical lattices is investigated. Firstly, the exact solution of the path curve to typical Fermi gases optical lattices model is constructed. Then, from the generalized functional analysis variation theory it constructed a set of iterative system. The arbitrary order asymptotic solution of nonlinear disturbed model of the path curve to Fermi gases optical lattices is obtained. In this paper, there got asymptotic repressions of the path curve expediently in the method and the proposed method and with the basic theory has wide application values. Figures and Tables | References | Related Articles | Metrics