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26 August 2016, Volume 36 Issue 4 Previous Issue    Next Issue

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Abstract Multi-Term Fractional Differential Equations with Riemann-Liouville Derivatives Marko Kostić, Li Chenggang, Li Miao Acta mathematica scientia,Series A. 2016, 36 (4):  601-622.  Abstract ( 115 )   RICH HTML PDF (542KB) ( 226 )   Save In this paper, we investigate the following abstract multi-term fractional differential equation Dtαnu（t）+AjDtαju(t)=ADtαu(t)+f(t),t∈(0,τ), where n∈N\{1}, A and A1,…,An-1 are closed linear operators on a complex Banach space E, 0≤α1<…<αn, 0≤α<αn, 0<τ≤∞, f(t) is an E-valued function, and Dtα denotes the Riemann-Liouville fractional derivative of order α ([5]). We introduce and systematically analyze several new types of k-regularized (C1,C2)-existence and uniqueness (propagation) families for (0.1), continuing in such a way our previous researches raised in [22, 24-25] and [34]. Plenty of various examples illustrates our abstract results. References | Related Articles | Metrics

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Viscosity Iterative Algorithm for Variational Inequality Problems and Fixed Point Problems of Strict Pseudo-Contractions in q-Uniformly Smooth and Uniformly Convex Banach Spaces Cai Gang, Yekini Shehu Acta mathematica scientia,Series A. 2016, 36 (4):  623-638.  Abstract ( 107 )   RICH HTML PDF (354KB) ( 147 )   Save The purpose of this paper is to investigate a viscosity iterative algorithm based on a generalized contraction for finding a common element of the set of solutions of a general variational inequality problem for two inverse-strongly accretive mappings and the set of common fixed points for infinite strict pseudo-contractions in q-uniformly smooth and uniformly convex Banach spaces. Strong convergence theorems are proved under some appropriate conditions. The results obtained in this paper improve and extend many recent ones announced by many others in this literature. References | Related Articles | Metrics

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Liouville Type Theorems of Solutions for the Nonlinear Hénon Equations Hu Lianggen Acta mathematica scientia,Series A. 2016, 36 (4):  639-648.  Abstract ( 178 )   RICH HTML PDF (310KB) ( 159 )   Save In this paper, Liouville theorem of finite Morse index solutions for the second order and fourth order nonlinear Hénon-Lane-Emden equations is considered. Adopting a new method, i.e., the monotonicity formula, Pohozaev identity combining with doubling lemma, the main results is proved. References | Related Articles | Metrics

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Hardy Inequalities for Jacobi Operators and Applications He Ruirui, Liu Hengxing Acta mathematica scientia,Series A. 2016, 36 (4):  649-655.  Abstract ( 142 )   RICH HTML PDF (273KB) ( 124 )   Save In this paper we consider the Hardy inequalities for Jacobi operators. We compute the sharp constants of these inequalities. As an application, we show the Hardy inequalities on hyperbolic spaces can be globally refined by adding remainder terms like the Brezis-Vázquez improvement, which is contrary to the case of Euclidean spaces. References | Related Articles | Metrics

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Superconvergence Analysis of a Lower Order Mixed Finite Element Method for Nonlinear Fourth-Order Hyperbolic Equation Zhang Houchao, Shi Dongyang Acta mathematica scientia,Series A. 2016, 36 (4):  656-671.  Abstract ( 164 )   RICH HTML PDF (470KB) ( 158 )   Save Based on the bilinear element Q11 and the Q01×Q10 element, a lower order conforming mixed finite element approximation scheme is proposed for nonlinear fourth-order hyperbolic equation. With the help of the known high accuracy results of the about two elements, by use of derivative delivery techniques and the post-processing technique, the superclose and superconvergence with order O(h2) for both scalar original variable u and the intermediate variable v=-Δu in H1 norm and the flux =-▽u in (L2)2 norm are derived in semi-discrete schemes through interpolation and Ritz projection approach, respectively. Meanwhile, the superclose and superconvergence with order O(h2+(Δt)2) for both u and v in HM1 norm and ???20160405-1??? in (L2)2 norm are proved in fully-discrete schemes, which cannot be deduced by the interpolation and Ritz projection alone. References | Related Articles | Metrics

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Life Span of Solutions for a Class of Parabolic System with Large Initial Data Xiao Feng Acta mathematica scientia,Series A. 2016, 36 (4):  672-680.  Abstract ( 140 )   RICH HTML PDF (325KB) ( 104 )   Save We are concerned with the life span of solutions of the initial-boundary value problem  ut-Δu=eav,(x,t)∈Ω×(0,T), vt-Δv=ebu,(x,t)∈Ω×(0,T),u(x,t)=v(x,t)=0,(x,t)∈∂Ω×(0,T), u(x,t)=ρφ(x),v(x,t)=ρψ(x),(x,t)∈Ω×{t=0}, Here a>0, b>0 are constants, Ω is a bounded domain in RN with smooth boundary ∂Ω, ρ>0 is a parameter, and φ(x) and ψ(x) are nonnegative continuous functions on Ω. To this end, we first deduce a asymptotic lower bound on its life span by constructing a upper solution of the above initial-boundary value problem which is based on the analysis of a new ODE system, then by the comparison principle and Kaplan's method[3], we can further show that such a lower bound is indeed a asymptotic upper bound and thus we obtain the asymptotic expression of the life span of the solutions for the problem concerned. References | Related Articles | Metrics

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Plane Wave Solutions to the Euler Equations for Chaplygin Gases Huang Shoujun, Wang Rui Acta mathematica scientia,Series A. 2016, 36 (4):  681-689.  Abstract ( 135 )   RICH HTML PDF (346KB) ( 167 )   Save In this paper, we consider the plane wave solutions to the Euler equations for isentropic Chaplygin gases. Some interesting properties enjoyed by plane wave solutions are explored. In particular, the reduced system for the plane wave solutions of Chaplygin gases can be solved successively. Based on this, we are able to obtain the global existence of smooth plane wave solutions for isentropic Chaplygin gases. Some results on the blow up phenomena are also discussed. References | Related Articles | Metrics

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General Continuous Solutions of a Dhombres Type Functional Equation Chen Kai Acta mathematica scientia,Series A. 2016, 36 (4):  690-702.  Abstract ( 126 )   RICH HTML PDF (313KB) ( 108 )   Save In this paper, we consider the real continuous solutions of functional equation f(x[f(x)]p)=(f(x))r, where p, r∈R. We get the general continuous solutions of the equation, and answer an open problem proposed in 1996 by Kahlig P, Matkowska A and Matkowski J partly. References | Related Articles | Metrics

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The Stability of a Transport Equations Solution with Abstract Boundary Condition in Slab Geometry Wu Hongxing, Wang Shenghua, Cheng Guofei Acta mathematica scientia,Series A. 2016, 36 (4):  703-714.  Abstract ( 117 )   RICH HTML PDF (382KB) ( 103 )   Save First, the objective of this paper is to discuss the transport equation of anisotropic, continuous energy and inhomogeneous medium with abstract boundary condition in slab geometry. Second, it is to prove that the transport operator generates a C0 semigroup and the ninth-order remained term of the Dyson-phillips expansion of the C0 semigroup is weakly compact, and it obtains that the spectrum of the transport operator only consists of finite isolated eigenvalues with a finite algebraic multiplicity in the trip Γ0. Finally, it discusses the solution of transport equation is asymptotic stability. The paper relies on the theory of linear operators, resolvent operator, and comparison operator methods. References | Related Articles | Metrics

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Blow-Up of Smooth Solutions to the Compressible MHD Equations Bian Dongfen, Tang Tong Acta mathematica scientia,Series A. 2016, 36 (4):  715-721.  Abstract ( 94 )   RICH HTML PDF (325KB) ( 108 )   Save In this paper, we prove the blow-up phenomena of smooth solutions to the Cauchy problem for the full compressible MHD equations in arbitrary dimensions, under the assumption that the initial density and magnetic have compact support. Here the coefficients are generalized to a general case which depend on density and temperature. References | Related Articles | Metrics

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Upper Semi-Continuity of Pullback Attractors for the 2D Non-Autonomous Navier-Stokes Equations with Weak Damping Yang Xinguang, Zhao Mingxia, Hou Wei Acta mathematica scientia,Series A. 2016, 36 (4):  722-739.  Abstract ( 127 )   RICH HTML PDF (449KB) ( 132 )   Save In this paper, the upper semi-continuity of pullback attractors for the 2D non-autonomous Navier-Stokes equations with weak damping and external force perturbation terms which describes the motion of fluid with weak damping was considered. By decomposition of process (semigroup) and some estimates, we obtained the pullback attractors Aε(t) of equation (1.1) with ε>0 converges to the global attractor A of equation (1.1) with ε=0 for any t∈R. References | Related Articles | Metrics

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Borel Directions and Uniqueness of Analytic Functions Xuan Zuxing, Xu Hongyan Acta mathematica scientia,Series A. 2016, 36 (4):  740-749.  Abstract ( 92 )   RICH HTML PDF (332KB) ( 131 )   Save In view of Nevanlinna theory, we deal with the relationship between Borel directions and uniqueness of analytic functions. Some theorems of analytic functions sharing four distinct values in an angular domain containing a Borel directions are obtained. Our theorems are improvement of the results given by Long and Wu[10]. References | Related Articles | Metrics

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On Meromorphic Functions of Infinite Order Zhang Hongshen, Ge Yuli Acta mathematica scientia,Series A. 2016, 36 (4):  750-762.  Abstract ( 118 )   RICH HTML PDF (340KB) ( 91 )   Save By using Nevanlinna theory of the angular domain and the type function of characteristic T(r,f), we study the value distribution of meromorphic functions of infinite order, obtain the existences of Borel direction and Hayman direction of proximate order dealing with small functions, at the same time prove existences of T direction and Hayman-T direction dealing with small functions, from which we can easily deduce the existing results. References | Related Articles | Metrics

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A System of Split Equilibrium Problems for Sequences of Bifunctions Deng Weiqi Acta mathematica scientia,Series A. 2016, 36 (4):  763-770.  Abstract ( 96 )   RICH HTML PDF (303KB) ( 91 )   Save The purpose in this paper is to introduce an up-to-date method for the approximation of an element of the set of solutions to the split common fixed point problem for countable families of nonlinear operators, by which an iterative algorithm is developed for solving a new type of problems, namely, a system of split equilibrium problems for two sequences of bifunctions. A strong convergence theorem is established in the framework of Hilbert spaces. References | Related Articles | Metrics

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Itô Formula for Multidimensional Continuous-Time Quantum Random Walk Kang Yuanbao Acta mathematica scientia,Series A. 2016, 36 (4):  771-782.  Abstract ( 133 )   RICH HTML PDF (337KB) ( 106 )   Save In the paper, following [5-6] we present an Itô formula for the multidimensional continuous-time quantum random walk (CQRW, for short) based on [18]. As an application we then establish a Tanaka's formula for the high-dimensional CQRW. References | Related Articles | Metrics

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Decomposition of Noise and Trend Based on EMD and Non-Stationarity Measure Tan Qiuheng, Wu Liang, Li Bo Acta mathematica scientia,Series A. 2016, 36 (4):  783-794.  Abstract ( 156 )   RICH HTML PDF (2437KB) ( 116 )   Save In this paper, we study the decomposition of trend and noise based on empirical mode decomposition algorithm and non-stationarity measure, and propose a criterion to choose intrinsic mode function for trend. Numerical simulation results show that the proposed criterion can overcome drawback of continuous mean square error criterion, achieve a good effect in different noise intensity and complex trend. References | Related Articles | Metrics

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New Differential Formulae Related to Hermite Polynomials and Their Applications in Quantum Optics Sun Yun, Wu Jianguang, Wang Dong, Tang Xubing Acta mathematica scientia,Series A. 2016, 36 (4):  795-808.  Abstract ( 113 )   RICH HTML PDF (571KB) ( 143 )   Save In this work, based on quantum operator Hermite polynomials and Weyl's mapping rule, we find a generation function of the two-variable Hermite polynomials. And then, noting that the Weyl ordering is invariant under the similar transformations, we obtain another generalized differential expression related to the Hermite polynomials. Those identites can be applied to investigate the nonclasscial properties of quantum optical fields. References | Related Articles | Metrics