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26 October 2017, Volume 37 Issue 5 Previous Issue    Next Issue

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On the Zeros of Confluent Hypergeometric Functions Lin Weichuan, Luo Xudan Acta mathematica scientia,Series A. 2017, 37 (5):  801-807.  Abstract ( 215 )   RICH HTML PDF (317KB) ( 124 )   Save There have been many applications of confluent hypergeometric functions in quantum mechanics and statistics. Furthermore, many problems in mathematical physics can be solved with the help of the location of zeros of confluent hypergeometric functions. In this paper, we study the zero sets of the confluent hypergeometric function 1F1(α;γ;z):=zn, where α,γ,γ-α∉Z ≤ 0, and show that if {zn}n=1∞ is the zero set of F(α;γ;z) with multiple zeros repeated and modulus in increasing order, then there exists a constant M > 0 such that|zn|≥ Mn for all n ≥ 1. References | Related Articles | Metrics

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Some Properties of Sensitivity in Nonautonomous Discrete Systems Lu Tianxiu, Xin Bangying, Mao Wei Acta mathematica scientia,Series A. 2017, 37 (5):  808-813.  Abstract ( 102 )   RICH HTML PDF (316KB) ( 67 )   Save This paper introduce new definitions of sensitive dependence on initial conditions, Li-Yorke sensitive, and densely Li-Yorke sensitive in nonautonomous discrete systems. The relations between these three concepts are given. Then, necessary and sufficient conditions of sensitivity of compound systems are derived. References | Related Articles | Metrics

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A New Integrable Nonlinear Lattice Equation Hierarchy and Their Integrable Symplectic Map Zhang Ning, Xia Tiecheng Acta mathematica scientia,Series A. 2017, 37 (5):  814-824.  Abstract ( 129 )   RICH HTML PDF (309KB) ( 61 )   Save In this paper, a discrete matrix spectral problem is introduced and a hierarchy of discrete integrable systems is derived. Their Hamiltonian structures are established, and it is shown that the resulting discrete systems are all Liouville integrable. Through binary nonlinearization method, the Bargmann symmetry constraint and a family of finite-dimension completely integrable systems are obtained. Finally, the representation of solutions for the discrete integrable systems are given. References | Related Articles | Metrics

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Limit Cycle Bifurcations for a Kind of Hamilton Systems of Degree Three Zhang Erli, Xing Yuqing Acta mathematica scientia,Series A. 2017, 37 (5):  825-833.  Abstract ( 120 )   RICH HTML PDF (312KB) ( 55 )   Save By using the Picard-Fuchs equation method, we obtain an upper bound of the number of zeros of Abelian integrals I(h)=∫Γhg(x,y)dx-f(x,y)dy, where Γh is the closed orbit defined by H(x,y)=x2+y2+2xy+1/a(x4+y4)=h, a>0,h∈(0,+∞),f(x,y) and g(x,y) are real polynomials in x and y of degree n. Therefore, we get the upper bound of the number of limit cycles of this system. References | Related Articles | Metrics

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Null Controllability of a Nonlinear Keller-Segel Equation Zhang Liang, Yang Guopeng Acta mathematica scientia,Series A. 2017, 37 (5):  834-845.  Abstract ( 108 )   RICH HTML PDF (375KB) ( 64 )   Save In this paper, we study the local controllability for a nonlinear Keller-Segel equation coupled by an elliptic partial differential equation and a parabolic one, in which nonlinearity lies both on its drift-diffusion term and population growth. We prove the local null controllability by Kakutani's fixed point theorem. The method is established on the nonlocal structure of the elliptic-parabolic equation so that it can be treated as a single nonlinear parabolic equation. References | Related Articles | Metrics

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Solution and Hyers-Ulam-Rassias Stability of a Mixed Type Quadratic-Additive Functional Equation with a Parameter in Quasi-Banach Spaces Wang Chun, Xu Tianzhou Acta mathematica scientia,Series A. 2017, 37 (5):  846-859.  Abstract ( 92 )   RICH HTML PDF (328KB) ( 60 )   Save This paper establishes the general solution of the mixed type quadratic-additive functional equation 2k[f(x+ky)+f(kx+y)] =k(1-s+k+ks+2k2)f(x+y)+k(1-s-3k+ks+2k2)f(x-y) +2kf(kx)+2k(s+k-ks-2k2)f(x)+2(1-k-s)f(ky)+2ksf(y) with a parameter s, and investigates the Hyers-Ulam-Rassias stability of this functional equation in quasi-Banach spaces, where k > 1 and s ≠1-2k. References | Related Articles | Metrics

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Homogenization of Degenerate Quasilinear Elliptic Equations Zhao Leina Acta mathematica scientia,Series A. 2017, 37 (5):  860-868.  Abstract ( 105 )   RICH HTML PDF (289KB) ( 62 )   Save In this paper, the homogenization of degeneration quasilinear elliptic equations -div a(x/ε,u,▽ u)+g(x/ε,u)=f(x), are studied, where a(y, α, λ) and g(y, α) is periodic in y. References | Related Articles | Metrics

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Infinitely Many High Energy Solutions of p-Kirchhoff-Type System with Sign-Changing Weight Li Qin, Yang Zuodong Acta mathematica scientia,Series A. 2017, 37 (5):  869-876.  Abstract ( 131 )   RICH HTML PDF (315KB) ( 62 )   Save In this paper, we study a p-Kirchhoff-type system with sign-changing weight. Under some more general assumptions, we obtain the existence of infinitely many high energy solutions by using the Symmetric Mountain Pass Theorem of Rabinowitz[10, Theorem 9.12], which unifies and generalizes the recent results of Zhou et al[3], Wu[4] and Li et al[6]. References | Related Articles | Metrics

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Existence of Solutions to Some Singular Elliptic Problems with Degenerate Coercivity Li Qingwei, Gao Wenjie, Han Yuzhu Acta mathematica scientia,Series A. 2017, 37 (5):  877-894.  Abstract ( 100 )   RICH HTML PDF (416KB) ( 57 )   Save In this article, the authors consider the existence of solutions for the following elliptic boundary value problem with degenerate coercivity and a singular lower order term with natural growth with respect to the gradient of the following form ???20170509???, where Ω⊂RN(N ≥ p) is a bounded domain, B,γ,θ>0 and p > 1, and f is a non-negative function belonging to some Lebesgue space Lm(Ω) with m ≥ 1. By combining the truncation methods with several delicate test functions, the existence and regularity of solution is proved. The results show that the lower order term has some regularizing effects on the solution, even if it is singular. References | Related Articles | Metrics

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Generalized Picone's Identity and Its Applications for Heisenberg-Greiner Operators Wang Shengjun, Han Yazhou Acta mathematica scientia,Series A. 2017, 37 (5):  895-901.  Abstract ( 107 )   RICH HTML PDF (282KB) ( 66 )   Save In this paper, a generalized version of the Picone's identity is established for Heisenberg-Greiner operators. As applications, Hardy type inequality, Sturmian Comparison principle and strict monotonicity of the principal eigenvalue are given. Finally, quasilinear system with singular nonlinearity also is studied. References | Related Articles | Metrics

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Unilateral Global Interval Bifurcation and One-Sign Solutions for the Half-Linear Periodic Problems Shen Wenguo Acta mathematica scientia,Series A. 2017, 37 (5):  902-916.  Abstract ( 93 )   RICH HTML PDF (402KB) ( 46 )   Save In this paper, we establish a unilateral global bifurcation result from interval for a class of periodic problems with nondifferentiable nonlinearity. By applying the above result, we shall prove the existence of the principal half-eigenvalues for a class of half-linear periodic boundary problems. Moreover, we also investigate the existence of one-sign solutions for the following half-linear periodic problems. -x"+q(t)x=αx++βx-+ra(t)f(x),0< t< T, x(0)=x(T),x'(0)=x'(T), where r≠0 is a parameter, q,a∈C([0,T],(0,∞)),α,β∈C[0,T],x+=max{x,0},x-=-min{x,0};f∈C(R,R), sf(s)>0 for s≠0, and f0∈[0,∞) and f∞∈(0,∞) or f0∈[0,∞] and f∞=0, where f0=???20170511-1???f(s)/s,f∞=???20170511-2???f(s)/s. References | Related Articles | Metrics

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Vanishing Pressure Limit of Riemann Solutions to the Aw-Rascle Model for Generalized Chaplygin Gas Li Huahui, Shao Zhiqiang Acta mathematica scientia,Series A. 2017, 37 (5):  917-930.  Abstract ( 102 )   RICH HTML PDF (383KB) ( 69 )   Save The Riemann problem for the Aw-Rascle (AR) traffic model with generalized Chaplygin gas is considered. Its first eigenvalue is genuinely nonlinear and the second eigenvalue is linearly degenerate, but the nonclassical solutions appear. The Riemann solutions are constructed, and the generalized Rankine-Hugoniot conditions and the δ-entropy condition are clarified. In particular, the existence and uniqueness of δ-shock waves are established under the generalized Rankine-Hugoniot conditions and entropy condition. The delta shock may be useful for description of the serious traffic jam. More importantly, it is proved that the limits of the Riemann solutions of the above AR traffic model are exactly those of the pressureless gas dynamics system with the same Riemann initial data as the traffic pressure vanishes. References | Related Articles | Metrics

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Dependence Measure:A Comparative Study Jiang Hangjin, Shan Yan, Wu Qiongli Acta mathematica scientia,Series A. 2017, 37 (5):  931-949.  Abstract ( 140 )   RICH HTML PDF (5628KB) ( 64 )   Save Dependence measure plays a fundamental role in statistical analysis, such as fMRI data analysis, variable selection, network analysis, genetical analysis, PPI network analysis. The aim of this paper is to provide a state of the art on the topic of dependence measure and to show their properties. We classified all these dependence measures into 3 classes:(1) Extension of correlation coefficient; (2) Dependence measures based on independent conditions; (3) Dependence measures in learning framework; As showed in our analysis, there is no such a dependence measure has the best performance over all kinds of functional types. However, according to the properties that a dependence measure should have combing with our results, CDC[4] is the best one. Furthermore, CDC2-ρ2 or CDC-|ρ|is proposed as a measure of non-linearity, which is better than MIC-ρ2, as showed in our analysis, where ρ is the Pearson correlation coefficient. References | Related Articles | Metrics

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Distributional Chaos on Complex Sectors Yao Yuwu, Chen Xiu, Niu Xin Acta mathematica scientia,Series A. 2017, 37 (5):  950-961.  Abstract ( 97 )   RICH HTML PDF (331KB) ( 52 )   Save We characterize the densely distributional chaos for the translation semigroup, with a sector in the complex plane as index set, defined on a weighted function space. A sufficient condition is given for the translation semigroup to be distributionally chaotic in terms of the the integrability of the admissible weight function, and in terms of the upper density of a subset of the index set. In addition, we study the index set and show that the translation semigroup is also distributionally chaotic on some subsets of the index set. References | Related Articles | Metrics

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A Two-Grid Finite Volume Element Approximation for One-Dimensional Nonlinear Parabolic Equations Chen Chuanjun, Zhang Xiaoyan, Zhao Xin Acta mathematica scientia,Series A. 2017, 37 (5):  962-975.  Abstract ( 108 )   RICH HTML PDF (368KB) ( 50 )   Save In this paper, a two-grid finite volume element approximation for one-dimensional nonlinear parabolic equations is derived and studied. We develop a finite volume element approximation for one-dimensional nonlinear parabolic equations and study its existence and error analysis. Optimal error estimates in the L2-norm and H1-norm are proved. We study the two-grid method based on the finite volume element method and optimal error estimate in the H1-norm is proved. It is shown that we can achieve asymptotically optimal approximation when the size of grids satisfies h=O(H2). Numerical examples are presented to verify the theoretical results. References | Related Articles | Metrics

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A Formally Second-Order BDF Compact ADI Difference Scheme for the Two-Dimensional Fractional Evolution Equation Chen Hongbin, Gan Siqing, Xu Da, Peng Yulong Acta mathematica scientia,Series A. 2017, 37 (5):  976-992.  Abstract ( 121 )   RICH HTML PDF (455KB) ( 72 )   Save In this paper, we will consider a formally second-order backward differentiation formula (BDF) compact alternating direction implicit (ADI) difference scheme for the twodimensional fractional evolution equation. To obtain a fully discrete implicit scheme, the integral term is treated by means of the second order convolution quadrature suggested by Lubich and the second order space derivatives are approximated by the fourth-order accuracy compact finite difference. The stability and convergence of the compact difference scheme in a new norm are proved by the energy method. The verification of stability and convergence is based on the nonnegative character of the real quadratic form associated with the convolution quadrature. A numerical experiment in total agreement with our analysis is reported. References | Related Articles | Metrics