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25 April 2016, Volume 36 Issue 2 Previous Issue    Next Issue

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Differential Subordination and Differential Superordination for Analytic Functions in the Upper Half-Plane Tang Huo, Srivastava H, Deng Guantie Acta mathematica scientia,Series A. 2016, 36 (2):  201-214.  Abstract ( 188 )   RICH HTML PDF (336KB) ( 1442 )   Save Let Ω be a set in the complex plane C. Also let p be analytic in the upper half-plane Δ={z:z∈C and Im(z)>0} and suppose that ψ: C3×Δ→C. In this paper, we consider the problem of determining properties of functions p that satisfy the following differential superordination Ω⊂{ψ(p(z), p'(z), p"(z);z): z∈Δ}. Applications of these results to differential subordination and differential superordination for analytic functions in Δ are also presented. References | Related Articles | Metrics

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New Estimates of Lower Bound for the First Eigenvalue on Compact Manifolds with Positive Ricci Curvature He Yue Acta mathematica scientia,Series A. 2016, 36 (2):  215-230.  Abstract ( 157 )   RICH HTML PDF (439KB) ( 145 )   Save In this paper we study the lower bound for the first (closed, or Dirichlet, or Neumann) eigenvalue of the Laplace operator on compact Riemannian manifolds with its Ricci curvature bounded below by nonnegative constant, and give a new estimate of lower bound for the first (closed, or Neumann) eigenvalue and also an easy proof of Ling's an estimate[16]. Although we use Ling's methods on the whole, to some extent we deal with the singularity of test functions and greatly simplify many of the calculations involved. Maybe we provide a new way for estimating eigenvalues. References | Related Articles | Metrics

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Iteration of Upper Semi-Continuous Multifunctions on Interval Zhang Pingping, Li Lin Acta mathematica scientia,Series A. 2016, 36 (2):  231-243.  Abstract ( 222 )   RICH HTML PDF (347KB) ( 117 )   Save In this paper we study a class of upper semi-continuous multifunctions with a unique set-valued point on compact interval. By classifying the monotonicity on each subinterval, we give a completed relation between the coordinate of the set-valued points and their n-th iteration. Moreover, our method is available for the upper semi-continuous multifunctions with finitely many set-valued points, as well as those ones defined on the whole real line. References | Related Articles | Metrics

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Uniqueness Theorem of Meromorphic Functions with Non-Integer Luo Jie, Lin Weichuan Acta mathematica scientia,Series A. 2016, 36 (2):  244-253.  Abstract ( 134 )   RICH HTML PDF (311KB) ( 163 )   Save In this paper, we discuss the problem of uniqueness of meromorphic functions and obtain that if two meromorphic functions with non-integer order that share a, b, c IM, and d is a generalized Picard exceptional value of them, then they are identically equal. In addition, we provide some examples to show that the conditions of our theorem are necessary. References | Related Articles | Metrics

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Uniqueness of Meromorphic Functions Concerning Nonlinear Differential Polynomials Sharing a Polynomial Zeng Juanjuan, Liu Huifang Acta mathematica scientia,Series A. 2016, 36 (2):  254-266.  Abstract ( 223 )   RICH HTML PDF (286KB) ( 217 )   Save In this paper, we prove some uniqueness theorems of meromorphic functions whose certain nonlinear differential polynomials share a polynomial weakly. Those results in this paper generalize and improve some previous results obtained by Li and Yi (Comput Math Appl, 2011, 62: 539-550), Chen and Zhang et al (Comput Math Appl, 2008, 56: 3000-3014). References | Related Articles | Metrics

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Iterative Learning Control for Distributed Parameter Systems in Space W1,2 Fu Qin Acta mathematica scientia,Series A. 2016, 36 (2):  267-286.  Abstract ( 149 )   RICH HTML PDF (438KB) ( 161 )   Save In space W1,2, the problem of iterative learning control algorithm for a class of distributed parameter systems is considered. Here, the considered distributed parameter systems are composed of parabolic partial differential equations or hyperbolic partial differential equations. According to system properties, iterative learning control laws are proposed for such distributed parameter systems based on P-type learning scheme. Further, it is shown that the scheme can guarantee the output tracking errors on W1,2 space converge along the iteration axis. Simulation examples show the feasibility and effectiveness of the conclusion. References | Related Articles | Metrics

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Existence and Successively Iterative Method of Singular Solution to a Nonlinear Fractional Differential Equation Yao Qingliu Acta mathematica scientia,Series A. 2016, 36 (2):  287-296.  Abstract ( 195 )   RICH HTML PDF (341KB) ( 176 )   Save The existence and the iterative method of solutions are studied for the nonlinear fractional differential equation Dαu(t)=f(t, u(t)), 0≤t≤1, t1-αu(t)|t=0=c, where 0< α< 1. The solutions of the equation are singular if c≠0. By constructing two successively iterative sequences which converge to the solutions in the Banach space Cα[0, 1], the existence of solutions is proved. The main result in [8] is improved by this work. References | Related Articles | Metrics

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Entire Solutions of a Certain Type of Nonlinear Differential-Difference Equation Chen Minfeng, Gao Zongsheng Acta mathematica scientia,Series A. 2016, 36 (2):  297-306.  Abstract ( 125 )   RICH HTML PDF (271KB) ( 228 )   Save In this paper, we investigate the differential-difference equations f'(z)2+P(z)2f(z+c)2=Q(z) and f'(z)2+P(z)2(f(z+c)-f(z))2=Q(z), where P(z) and Q(z) are nonzero polynomials. If the differential-difference equations admit a transcendental entire solution of finite order, then we can obtain the exact expression of the solution. References | Related Articles | Metrics

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Multiple Solutions for a Class of Quasilinear Nonhomogeneous Elliptic Systems with Nonlinear Boundary Conditions Li Qin, Yang Zuodong Acta mathematica scientia,Series A. 2016, 36 (2):  307-316.  Abstract ( 158 )   RICH HTML PDF (300KB) ( 152 )   Save In this paper, we study the existence and multiplicity of nontrivial solutions for a class of quasilinear elliptic systems involving nonhomogeneous nonlinearities and nonlinear boundary conditions. By using the Mountain Pass Theorem and the Ekeland's variational principle, we prove that the system has at least two nontrivial solutions when the parameter λ belongs to a certain subset of R. References | Related Articles | Metrics

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Quasi-Periodic Solution of the Generalized Broer-Kaup-Kupershmidt Soliton Equation Wei Hanyu, Xia Tiecheng Acta mathematica scientia,Series A. 2016, 36 (2):  317-327.  Abstract ( 128 )   RICH HTML PDF (366KB) ( 168 )   Save In this paper, starting from a new spectral problem, a new (2+1)-dimensional generalized Broer-Kaup-Kupershmidt soliton equation is decomposed into systems of integrable ordinary differential equations resorting to the nonlinearization of Lax pairs. Then, a finite-dimensional Hamiltonian system is obtained and is proved to be completely integrable in Liouville sense. The Abel-Jacobi coordinates are constructed to straighten out the Hamiltonian flows, from which the quasi-periodic solution of the (2+1)-dimensional generalized Broer-Kaup-Kupershmidt soliton equation is obtained in terms of Riemann theta functions. References | Related Articles | Metrics

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Stability for Stationary Solution of Non-Isentropic Viscous Fluid Equations Xie Huazhao, Li Suli Acta mathematica scientia,Series A. 2016, 36 (2):  328-339.  Abstract ( 106 )   RICH HTML PDF (346KB) ( 301 )   Save In three dimension space, we study the stationary solutions and nonlinear stability of Navier-Stokes-Poisson equations. Using variational method, we get the existence of stationary solution of N-S-P equations when 4/3< γ< 2, the nonlinear stability of such steady states is also proved. As γ=4/3, we prove the nonlinear instability of stationary solution. References | Related Articles | Metrics

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Decay of Weak Solutions to the Multi-Dimensional Burgers' Equation with Fractional Diffusion Yu Pei Acta mathematica scientia,Series A. 2016, 36 (2):  340-352.  Abstract ( 123 )   RICH HTML PDF (362KB) ( 163 )   Save In this paper, we investigate the time decay properties of the global weak solutions to the multi-dimensional Burgers' equation with fractional diffusion. We establish the optimal decay rates in L2 or Lp norm to solutions with initial data u0∈L2∩Lp for p≠2. If u0∈L2 only, we also show that it is impossible to obtain a uniform decay. Finally, for u0∈L2∩Ln/2α-1, we obtain a uniform decay estimate of solutions in Lp norm for any p>n/2α-1. References | Related Articles | Metrics

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Convergence of Branching Process in Varying Environments when All Moments Being Finite Wang Weigang, Yang Guangyu, Gao Zhenlong Acta mathematica scientia,Series A. 2016, 36 (2):  353-361.  Abstract ( 137 )   RICH HTML PDF (319KB) ( 144 )   Save In this paper, we studied convergence theorems of the branching processes in varying environments. When the environment is not independence, at the moment conditions of the environment, we prove that WnW and W>0, a.s. firstly, and then we give the central limit theorem of the process, at last we give the law of the iterated logarithm of log Zn. Those results are very important to the other asymptotic properties and deviations of the process. References | Related Articles | Metrics

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Optimal Portfolio Problems for an Insurance Company Under Default Risk and Model Uncertainty Zheng Xiaoxiao, Sun Zhongyang, Zhang Xin Acta mathematica scientia,Series A. 2016, 36 (2):  362-379.  Abstract ( 147 )   RICH HTML PDF (514KB) ( 135 )   Save In this paper, we investigate a stochastic portfolio optimization problem with model uncertainty and default risk. We assume that an insurer can invest his money into financial market where a savings account, a stock and a corporate bond are available, and aim to maximize the CARA utility of the terminal wealth. Furthermore, to take the model uncertainty into consideration, we formulate the optimization problem as a zero-sum stochastic differential game problem between market and the insurer. By using dynamic programming principle, we derive the Hamilton-Jacobi-Bellman-Isaacs (HJBI) equation, and then find the optimal policy under the "worst-case" scenario for both jump-diffusion model and its diffusion approximation. References | Related Articles | Metrics

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Analysis of the Departure Process for Geo/G/1 Discrete-Time Queue with Single Server Vacation and Min-Policy Lan Shaojun, Tang Yinghui Acta mathematica scientia,Series A. 2016, 36 (2):  380-392.  Abstract ( 121 )   RICH HTML PDF (465KB) ( 160 )   Save In this paper we investigate the departure process for a Geo/G/1 discrete-time queueing system in which the server takes single server vacation and the system adopts Min(N, V)-policy. In this study, by employing the total probability decomposition law, renewal theory and probability generating function technique, the transient and the steady probability that the server is busy at any epoch n+ are derived. Furthermore, we also obtain the expression of the probability generating function for the expected number of departures occurring in the time interval (0+, n+] from any initial state. Meanwhile, the relationship among departure process, server busy-state process and the service renewal process in server busy period is found, which shows the especial structure of departure process. Especially, some corresponding results of departure process for special discrete-time queues are directly gained by the results obtained in this paper. Finally, the asymptotic expansion for calculating expected number of departures conveniently is presented. References | Related Articles | Metrics