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25 August 2005, Volume 25 Issue 4 Previous Issue    Next Issue

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Alternating Direction Finite Element Method for Semiconductor Problem LIU Wen-Xian Acta mathematica scientia,Series A. 2005, 25 (4):  433-444.  Abstract ( 1678 )   RICH HTML Save The energy transport model of semiconductor problem, including both elliptic and parabolic equations, is solved by an alternating direction method. The elliptic equation for the electrostatic potential is solved by an alternating direction iterative method, the convectiondominated diffusion quations for the conservation of electron and hole concentrations are solved by an characteristic alternating direction finite element method, and the heat conduction equation is solved by an alternating direction finite element method with patch approximation. Using the theory and technique of a priori estimate of differential equation, the author obtains the optimal order error estimates in H+1norm and L+2 norm of the elliptic equation and parabolic equations respectively.  References | Related Articles | Metrics

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Existence of Positive Singular Solutions for a Class of Quasilinear Elliptic Equations  YANG Zuo-Dong Acta mathematica scientia,Series A. 2005, 25 (4):  445-450.  Abstract ( 1581 )   RICH HTML PDF (333KB) ( 1308 )   Save The existence of singluar positive radial  solutions of quasilinear elliptic equ ations is considered in a finite ball ( Ω=B_R={x∈R^N:|x|<R} ) or N dimension Euclidean space (Ω=B_∞=R^N, N≥3). The  nonlinear function f∈C^1(R)  has supercritical growth.  References | Related Articles | Metrics

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The Initial Value Problem of the Seventh Order Weakly Dispersi ve Equations DAO Shuang-Beng, CUI Chang-Bin Acta mathematica scientia,Series A. 2005, 25 (4):  451-460.  Abstract ( 2014 )   RICH HTML PDF (398KB) ( 1285 )   Save This paper is devoted to studying the initial value problem of a class of  seventh order weakly nonlinear dispersive equations:∂u/∂t + au(∂u/∂x) +β(∂^3 u /∂x^3) +γ(∂^5 u/∂x^5) + μ(∂^7 u/∂x^7)=0, (x,t)∈R^2.By using recently established decay estimates for oscillatory integrals, the authors  firs t establish several Strichartz type estimates for the fundamental solution of the corresponding linear problem. Then the authors prove that a local solution exists if t he initial function u_0(x)∈H^s(R), s≥2/13,  and a global solution exists if  s≥1. References | Related Articles | Metrics

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Global Stabilization Control of Multivariable MRAC Systems with Disturbances in Input Channel WU Yu-Jiang, ZHOU Ying Acta mathematica scientia,Series A. 2005, 25 (4):  461-472.  Abstract ( 1591 )   RICH HTML PDF (427KB) ( 1150 )   Save A design scheme of variable structure model tracking controller using only input and output measurements is presented for a class of multi input and multi output (MIMO) uncertain model reference adaptive control (MRAC) systems with disturbances in  input channel. By introducing  the auxiliary signals and normalized signals with memory functions and appropr iate choice of controller parameters,the variable structure controller developed guarantees the global stability of the closed loop system, and the tracking error can be arbitrarily small. References | Related Articles | Metrics

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Global Existence of Classical Solution with Slowly Decaying Initial Data for Quasilinear Linearly Degenerate Hyperbolic Systems YAN Ping, CHENG Ji-Rong, LV Teng- Acta mathematica scientia,Series A. 2005, 25 (4):  473-481.  Abstract ( 1513 )   RICH HTML PDF (372KB) ( 1161 )   Save In this paper, the authors prove the global existence ofclassical solution to the Cauchy problem with slowly decaying initial data with small initial total variation for general first order quasilinear linearlydegenerate hyperbolic systems. This generalizes the corresponding result of A Bressan for initial data with compactsupport. References | Related Articles | Metrics

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Multiple Nonnegative Solutions for a Class of Two point Bound ary Value Problems CHENG Jian-Gang Acta mathematica scientia,Series A. 2005, 25 (4):  482-488.  Abstract ( 1632 )   RICH HTML PDF (331KB) ( 1286 )   Save This paper deals with the existence of nonnegative solutions to two point boundary value problem [1/q(t)][q(t)y′(t)]′+p(t)f(y(t))= 0,λ_1 y(α)-λ_2 y′(α)=0 and y(β)=B,where p(t) may be singular at t=α or t=β, f(0)≥0,lim_(y→+∞)f(y)/y=+∞, and  there exists y>0 such that f(y)<0. References | Related Articles | Metrics

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Limiting Behavior of Weighted Sums of Negatively Associated Random Variables CHEN Beng-Tan Acta mathematica scientia,Series A. 2005, 25 (4):  489-495.  Abstract ( 1453 )   RICH HTML PDF (317KB) ( 1216 )   Save The Marcinkiewcz Zygmund strong laws of large numbers an d complete convergence are established for weighted sums of negatively associate d random variables under certain moments  both on the weights and the distributi on. These complement  extend the results of Cuzick(1995) and Bai and Cheng(2000) .  References | Related Articles | Metrics

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Singular Semipositone Boundary Value Problems of Second Order Delay Differential Equations LIN Xiao-Ning, XU Xiao-Jie Acta mathematica scientia,Series A. 2005, 25 (4):  496-502.  Abstract ( 1634 )   RICH HTML PDF (330KB) ( 1442 )   Save In this paper the authors present a new existence result for singular semiposito ne bopund ary value problems of second order delay differential equations. Through out their paper the nonlinearity may be singular in its dependent variable. References | Related Articles | Metrics

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Some Generalizations of a Classical Ergodic Property for IFS MA Dong-Kuai, XU Zhi-Ting Acta mathematica scientia,Series A. 2005, 25 (4):  503-508.  Abstract ( 1359 )   RICH HTML PDF (328KB) ( 1166 )   Save In this paper, the authors  give some  ergodic properties for the  contractive  iterated  function systems(IFS) with probabilities. These results generalize the correspo nding result of Elton's paper. One is similar to the results of Furstenber g and Assani's papers in weakly mixing system in a sense. References | Related Articles | Metrics

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Weighted Composition Operators Between Hardy-Orlicz Spaces WANG Mao-Fa, ZHOU Shao-Bei Acta mathematica scientia,Series A. 2005, 25 (4):  509-515.  Abstract ( 1700 )   RICH HTML PDF (348KB) ( 1223 )   Save In this paper, some sufficient and necessary conditions  for  weighted  composition operators between Hardy-Orlicz  spaces to be bounded or compact are given respectively. As a corollary,  the authors obtain that  the boundedness or compactness for weighted composition operators between Hardy-Orlicz spaces is equivalent to corresponding ones on associated Hardy spaces. In addition, the authors also characterize the inducing maps which induce invertible or Fredholm composition operators on N_p.  References | Related Articles | Metrics

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g-functions, Weak Base g-functions and Metrizability o f Spaces GAO Zhi-Min Acta mathematica scientia,Series A. 2005, 25 (4):  516-521.  Abstract ( 1224 )   RICH HTML PDF (332KB) ( 1146 )   Save In this paper, the author  gives some metrization theorems and characterie some  generaliz ed metric spaes. And the author will give very immediate proofs of two the orems in [12]. References | Related Articles | Metrics

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The Base Function of the Irreducible Representation for Point Groups in the Expansion of Free Energy ZHOU Guo-Xiang, HE Wen-Chen, GUO Ge-Xin, LI Jia- Acta mathematica scientia,Series A. 2005, 25 (4):  522-537.  Abstract ( 1798 )   RICH HTML PDF (417KB) ( 1561 )   Save There are many choices for the selection of the base functions (BF) of the irreducible representations for point groups. The different BF corresponds to the different representative matrix. Although under the same matrix, there are different choices for BF. The expansion of the free energy can be constructed by BF when the phenomenological phase transition theory is used. So the table of the BF of the irreducible representations is significant.In the literatures before, the BF is up to the second order. Furthermore, in some literature, the different BF for the same irreducible representations corresponds to different representative matrix. It is wrong by using such BF toobtain the invariant. The thirdorder BF was supplemented in this paper. The table of BF given in this paper is very helpful for obtaining he expansion of the free energy correctly and rapidly. Eighteen kinds of pointgroups were found having thirdorder invariant. If the group of the hightemperature crystal structure is one of these points groups, then the ferroelectrics undertake the first order phase transition when temperature is lowed. References | Related Articles | Metrics

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The Bifurcation of Limit Cycle for a Class of Cubic System with Two Imaginary Invariant Line XIE Xiang-Dong, CHEN Feng-De Acta mathematica scientia,Series A. 2005, 25 (4):  538-545.  Abstract ( 1680 )   RICH HTML PDF (381KB) ( 1445 )   Save  This paper considers the bifurcation of limit cycle of a class of cubic system with two imaginary invariant line, and  gives the focus valus of each order at O(0,0). It is proved that the system with δlmn=0  has at most one limit cycle surrounding O. With the bifurcation theory, the authors  give the bifurcation curve of homoclinic cycle and semistable cycle. It means that the system has at  most two limit cycles surrounding O References | Related Articles | Metrics

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Two photon Jaynes Cummings Model Governed by the Milburn Equation with Phase Damping CHEN Chang-Yong, YANG Xi-Shu Acta mathematica scientia,Series A. 2005, 25 (4):  546-553.  Abstract ( 1474 )   RICH HTML PDF (390KB) ( 1016 )   Save In this paper, the authors  find an analytic solution of the master equation of  a non resonant two photon Jaynes cummings model (JCM) with phase damping with  the help of the super operator technique. The authors  study the influence of phase damping  on non classical effects in the JCM, such as oscillations of the photon number  distribution, revivals of the atomic inversion, and sub Possion photon statistics . It is demonstrated that the phase damping suppresses the revivals of the atomi c inversion and non classical effects of the cavity field in the JCM. References | Related Articles | Metrics

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Positive Solutions of Singular Boundary Value Problems of Differential Equations LIU Li-Shan, SUN Pan Acta mathematica scientia,Series A. 2005, 25 (4):  554-563.  Abstract ( 2010 )   RICH HTML PDF (374KB) ( 1367 )   Save The authors  consider  the existence of  positive solutions for the singular boundary value problem using fixed point  theory in cones, the authors   derive an explicit interval for λ such that for any λ in  this  interval,  the existence of at  least one positive solution  to the boundary value problem is guaranteed.  The results significantly  extend and improve many known results even for non singular cases References | Related Articles | Metrics

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Computation of the Orders of Unitary Groups Over Finite Local |Rings GAO You Acta mathematica scientia,Series A. 2005, 25 (4):  564-568.  Abstract ( 1922 )   RICH HTML PDF (291KB) ( 1230 )   Save Assume that K=F_(q^2),where q=p^α, Let  G be a p-group of order p^β and R=KG. Define an  involutive automorphism of K by ω:a→a^q.Denote by ω′ the involutive automorphism extended from K to R. For any a∈R, write ~a=ω′(a). Define unitary groups of degree 2n over R by U_(2n)R={A∈GL_(2n)R|A(0,I^n,I^n,0)~A^t=(0,I^n,I^n,0)} .In this paper, the author  computes the order of  U_(2n)R. References | Related Articles | Metrics

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On Approximation by Neural and Translation Networks in B_a Spaces ZHOU Guan-Zhen Acta mathematica scientia,Series A. 2005, 25 (4):  569-576.  Abstract ( 1681 )   RICH HTML PDF (365KB) ( 1103 )   Save The characteristic theorem  as well as the degree of approximating by neural ne tworks and translation networks, with a single hidden layer in B_a spaces  is established. The Favard type estimate is obtained as well. The correspondences of Orlicz spaces are given by one of the applications of B_a spaces.  References | Related Articles | Metrics

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Minimax Estimation and Admissible Estimation Under Normal MANOVA Model CHEN Qing-Ping, LI Na-Na, XIAO Zhi-Hong Acta mathematica scientia,Series A. 2005, 25 (4):  577-583.  Abstract ( 1490 )   RICH HTML PDF (341KB) ( 959 )   Save Let random matrix Y_(n×m) be distributed according to N(XΘ, σ^2Σ×V),Where X is a known n×k matrix of rank k, n≥k≥3, σ^2 is unknown  and σ^(-2)S_p has a χ square distribution with degree of freedom p. When f(t) is differentiable and f′(t)≥0,0≤f(t)≤2(k-2)/m(p+2), the estimator whose ithcolumn vector has the formΔ_i(Y)=[I_k- f(V′_iY′(X′Σ^(-1)X)^(-2)YV_iS_p_(-1)S_p (X′Σ^(-1)X)^(-1) /V′_iY′(X′Σ^(-1)X)^(-2)YV_i](X′Σ^(-1)X)^(-1)X′Σ^(-1)Y_i where V_i is the ith column vector of  V^(-1/2),can improve the maximum likelihood estimator (X′Σ^(-1)X)^(-1)X′Σ^(-1)Y of Θ. Moreover, some  classes  of admissible linear estimators for Θ or  CXΘ  are obta ined too References | Related Articles | Metrics

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Nonlinear Transformation and Non selfsimilar Solution of Conservation Laws YANG Xiao-Zhou Acta mathematica scientia,Series A. 2005, 25 (4):  584-592.  Abstract ( 1598 )   RICH HTML PDF (368KB) ( 1433 )   Save The author proposes a kind of nonlinear transformation, u nder which the n dimensional scalar conservation laws and its initial value  are  transformed into one dimensional situation at the same time. The non selfsimilar global solution and the expression of elementary wave are obtained. The author  also discovers the essential difference and connection between non selfsimilar and selfsimilar solutions. References | Related Articles | Metrics