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20 July 2008, Volume 28 Issue 3 Previous Issue    Next Issue

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BOUNDARY LAYER ASYMPTOTIC BEHAVIOR OF INCOMPRESSIBLE NAVIER-STOKES EQUATION IN A CYLINDER WITH SMALL VISCOSITY Duan Zhiwen; Han Shuxia; Zhou Li Acta mathematica scientia,Series B. 2008, 28 (3):  449-468.  DOI: 10.1016/S0252-9602(08)60047-8 Abstract ( 1414 )   RICH HTML PDF (236KB) ( 1667 )   Save The object of this article is to study the boundary layer appearing at large Reynolds number (small viscosity ε) incompressible Navier-Stokes Equation in a cylinder in space dimension three. These are Navier-Stokes equations linearized around a fixed velocity flow: the authors study the convergence as ε→ 0 to the inviscid type equations, the authors define the correctors needed to resolve the boundary layer and obtain convergence results valid up to the boundary and the authors also study the behavior of the boundary layer when, simultaneously, time and the Reynolds number tend to infinity, in which case the boundary layer tends to pervade the whole domain. Related Articles | Metrics

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HARDY-SOBOLEV INEQUALITIES WITH GENERAL WEIGHTS AND REMAINDER TERMS Chen Zhihui; Shen Yaotian Acta mathematica scientia,Series B. 2008, 28 (3):  469-478.  DOI: 10.1016/S0252-9602(08)60048-X Abstract ( 1215 )   RICH HTML PDF (179KB) ( 1572 )   Save The Hardy-Sobolev inequality with general weights is established, and it is shown that the constant is optimal. The two weights in this inequality are determined by a Bernoulli equation. In addition, the authors obtain the Hardy-Sobolev inequality with general weights and remainder terms. By choosing special weights, it turns to be many versions of the Hardy-Sobolev inequality and the Caffarelli-Kohn-Nirenberg inequality with remainder terms in the literature. Related Articles | Metrics

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STEADY-STATE SOLUTIONS FOR A ONE-DIMENSIONAL NONISENTROPIC #br# HYDRODYNAMIC MODEL WITH NON-CONSTANT LATTICE TEMPERATURE Li Yeping Acta mathematica scientia,Series B. 2008, 28 (3):  479-488.  DOI: 10.1016/S0252-9602(08)60049-1 Abstract ( 1135 )   RICH HTML PDF (156KB) ( 1265 )   Save A one-dimensional stationary nonisentropic hydrodynamic model for semiconductor devices with non-constant lattice temperature is studied. This model consists of the equations for the electron density, the electron current density and electron temperature, coupled with the Poisson equation of the electrostatic potential in a bounded interval supplemented with proper boundary conditions. The existence and uniqueness of a strong subsonic steady-state solution with positive particle density and positive temperature is established. The proof is based on the fixed-point arguments, the Stampacchia truncation methods, and the basic energy estimates. Related Articles | Metrics

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ON MEAN CURVATURES OF A PARALLEL CONVEX BODY Zhou Jiazu; Jiang Deshuo Acta mathematica scientia,Series B. 2008, 28 (3):  489-494.  DOI: 10.1016/S0252-9602(08)60050-8 Abstract ( 1253 )   RICH HTML PDF (134KB) ( 1884 )   Save n this article, we obtain some results about the mean curvature integrals of the parallel body of a convex set in Rn. These mean curvature integrals are generalizations of the Santalo's results. Related Articles | Metrics

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THE SOLVABILITY FOR A CLASS OF SINGULARLY PERTURBED QUASI-LINEAR DIFFERENTIAL SYSTEM Mo Jiaqi; Wang Hui; Lin Wantao Acta mathematica scientia,Series B. 2008, 28 (3):  495-500.  DOI: 10.1016/S0252-9602(08)60051-X Abstract ( 1232 )   RICH HTML PDF (132KB) ( 1365 )   Save The solvability for a class of singularly perturbed Robin problem of quasi-linear differential system is considered. Using the boundary layer corrective method the formal asymptotic solution is constructed. And using the theory of differential inequality the uniform validity of the asymptotic expansions for solution is proved. Related Articles | Metrics

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A LAW OF ITERATED LOGARITHM FOR THE MLE IN A RANDOM CENSORING MODEL WITH INCOMPLETE INFORMATION Song Fengli; Liu Luqin Acta mathematica scientia,Series B. 2008, 28 (3):  501-512.  DOI: 10.1016/S0252-9602(08)60052-1 Abstract ( 1012 )   RICH HTML PDF (186KB) ( 1234 )   Save In this article, a law of iterated logarithm for the maximum likelihood estimator in a random censoring model with incomplete information under certain regular conditions is obtained. Related Articles | Metrics

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QUASI-STATIONARY DISTRIBUTIONS FOR THE RADIAL ORNSTEIN-UHLENBECK PROCESSES Ye Jun Acta mathematica scientia,Series B. 2008, 28 (3):  513-522.  DOI: 10.1016/S0252-9602(08)60053-3 Abstract ( 1057 )   RICH HTML PDF (171KB) ( 1826 )   Save The purpose of this article is to obtain the quasi-stationary distributions of the δ(δ<2)-dimensional radial Ornstein-Uhlenbeck process with parameter -λ by using the methods of Martinez and San Martin (2001). It is described that the law of this process conditioned on first hitting 0 is just the probability measure induced by a (4-δ)-dimensional radial Ornstein-Uhlenbeck process with parameter -λ. Moreover, it is shown that the law of the conditioned process associated with the left eigenfunction of the process conditioned on first hitting 0 is induced by a one-parameter diffusion. Related Articles | Metrics

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QUENCHING PROBLEM IN SOME SEMILINEAR WAVE EQUATIONS Li Mengrong; Pai Jente Acta mathematica scientia,Series B. 2008, 28 (3):  523-529.  DOI: 10.1016/S0252-9602(08)60054-5 Abstract ( 1190 )   RICH HTML PDF (147KB) ( 1452 )   Save This article proves a quenching result of the solutions for some semi-linear wave equations. Related Articles | Metrics

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CONTINUITY AND HAUSDORFF DIMENSION OF JULIA SET CONCERNING YANG-LEE ZEROS Gao Junyang; Qiao Jianyong Acta mathematica scientia,Series B. 2008, 28 (3):  530-536.  DOI: 10.1016/S0252-9602(08)60055-7 Abstract ( 1223 )   RICH HTML PDF (142KB) ( 1244 )   Save Considering the Julia set J(Tλ) of the Yang-Lee zeros of the Potts model on the diamond hierarchical Lattice on the complex plane, the authors proved that HDJ(Tλ)>1 and discussed the continuity of J(Tλ) in Hausdorff topology for λ∈ R. Related Articles | Metrics

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CALCULATION OF HAMILTONIAN CONSTRAINT AND MANDELSTAM IDENTITIES OVER EXTENDED KNOT FAMILIES Shao Dan; Shao Liang; Shao Changgui Acta mathematica scientia,Series B. 2008, 28 (3):  535-544.  DOI: 10.1016/S0252-9602(08)60056-9 Abstract ( 1021 )   RICH HTML PDF (166KB) ( 1081 )   Save The actions of the Hamiltonian constraint onto the members of the extended knot families {ψi}22 , {ψi}34 and {ψi}46 , and the check of their invariance under the Mandelstam identities are given in the extended loop representation of loop quantum gravity. Related Articles | Metrics

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REPELLERS FOR MULTIFUNCTIONS OF SEMI-BORNOLOGICAL SPACES M.R. Molaei; T. Waezizadeh Acta mathematica scientia,Series B. 2008, 28 (3):  545-550.  DOI: 10.1016/S0252-9602(08)60057-0 Abstract ( 1009 )   RICH HTML PDF (137KB) ( 1466 )   Save In this article the notion of repeller for multifunctions from the viewpoints of semi-bornological spaces is considered. The concept of lower semi-continuous multifunctions is extended by the use of semi-bornological spaces. Semi-bornological vector spaces are studied. The notion of conjugacy for semi-bornological multifunctions is considered. The persistence of repeller under conjugate relation is proved. Related Articles | Metrics

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AN INFEASIBLE-INTERIOR-POINT PREDICTOR-CORRECTOR ALGORITHM FOR THE SECOND-ORDER CONE PROGRAM Chi Xiaoni; Liu Sanyang Acta mathematica scientia,Series B. 2008, 28 (3):  551-559.  DOI: 10.1016/S0252-9602(08)60058-2 Abstract ( 1354 )   RICH HTML PDF (167KB) ( 1856 )   Save A globally convergent infeasible-interior-point predictor-corrector algorithm is presented for the second-order cone programming (SOCP) by using the Alizadeh--Haeberly--Overton (AHO) search direction. This algorithm does not require the feasibility of the initial points and iteration points. Under suitable assumptions, it is shown that the algorithm can find an ε-approximate solution of an SOCP in at most O(\sqrt{n}\ln(ε0/ε)) iterations. The iteration-complexity bound of our algorithm is almost the same as the best known bound of feasible interior point algorithms for the SOCP. Related Articles | Metrics

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HOLOMORPHIC HARMONIC ANALYSIS ON COMPLEX REDUCTIVE GROUPS An Jinpeng; Qian Min; Wang Zhengdong Acta mathematica scientia,Series B. 2008, 28 (3):  560-572.  DOI: 10.1016/S0252-9602(08)60059-4 Abstract ( 1196 )   RICH HTML PDF (195KB) ( 1167 )   Save The authors define the holomorphic Fourier transform of holomorphic functions on complex reductive groups, prove some properties such as the Fourier inversion formula, and give some applications. The definition of the holomorphic Fourier transform makes use of the notion of K-admissible measures. The authors prove that K-admissible measures are abundant, and the definition of holomorphic Fourier transform is independent of the choice of K-admissible measures. Related Articles | Metrics

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PERIODIC BOUNDARY VALUE PROBLEM AND CAUCHY PROBLEM OF THE GENERALIZED CUBIC DOUBLE DISPERSION EQUATION Chen Guowang; Xue Hongxia Acta mathematica scientia,Series B. 2008, 28 (3):  573-587.  DOI: 10.1016/S0252-9602(08)60060-0 Abstract ( 1281 )   RICH HTML PDF (213KB) ( 1363 )   Save In this article, the existence, uniqueness and regularities of the global generalized solution and global classical solution for the periodic boundary value problem and the Cauchy problem of the general cubic double dispersion equation utt-uxx-auxxtt+bux4-duxxt=f(u)xx are proved, and the sufficient conditions of blow-up of the solutions for the Cauchy problems in finite time are given. Related Articles | Metrics

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A CHARACTERIZATION OF LOCALLY COMPACT INNER AMENABLE GROUPS Ali Ghaffari Acta mathematica scientia,Series B. 2008, 28 (3):  588-594.  DOI: 10.1016/S0252-9602(08)60061-2 Abstract ( 1112 )   RICH HTML PDF (146KB) ( 2422 )   Save For locally compact groups G, Kuan Yuan studied a notion of inner amenability groups, that is, if there exists an inner invariant mean on G. In this article, among other things, the author investigates the inner amenability on a locally compact group G. The author gives sufficient conditions and some necessary conditions about G to have an inner invariant mean. Related Articles | Metrics

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THE EXISTENCE AND GLOBAL OPTIMAL ASYMPTOTIC BEHAVIOUR OF LARGE SOLUTIONS FOR A SEMILINEAR ELLIPTIC PROBLEM Zhang Zhijiun Acta mathematica scientia,Series B. 2008, 28 (3):  595-603.  DOI: 10.1016/S0252-9602(08)60062-4 Abstract ( 1338 )   RICH HTML PDF (174KB) ( 1257 )   Save By Karamata regular variation theory and constructing comparison functions, the author shows the existence and global optimal asymptotic behaviour of solutions for a semilinear elliptic problem △u=k(x)g(u), u>0, x in Omega, u|_{\partial \Omega}=+∞, where Omega is a bounded domain with smooth boundary in RN; g ∈ C1[0,∞), g(0)=g'(0)=0, and there exists p>1, such that $\lim\limits_{s\rightarrow \infty}\frac {g(s \xi)}{g(s)}=\xi^p$, $\forall \ \xi>0$, and $k \in C_{\rm loc}^\alpha(\Omega)$ is non-negative non-trivial in Omega which may be singular on the boundary. Related Articles | Metrics

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OBLIQUE DERIVATIVE PROBLEMS FOR SECOND ORDER NONLINEAR MIXED#br# EQUATIONS WITH DEGENERATE LINE Wen Guochun Acta mathematica scientia,Series B. 2008, 28 (3):  604-612.  DOI: 10.1016/S0252-9602(08)60063-6 Abstract ( 1021 )   RICH HTML PDF (170KB) ( 1396 )   Save The present article deals with oblique derivative problems for some nonlinear mixed equations with parabolic degeneracy, which include the Tricomi problem as a special case. First, the formulation of the problems for the equations is given; next, the representation and estimates of solutions for the above problems are obtained; finally, the existence of solutions for the problems is proved by the successive iteration and the compactness principle of solutions of the problems. In this article, the author uses the complex method, namely, the complex functions in the elliptic domain and the hyperbolic complex functions in hyperbolic domain are used. Related Articles | Metrics

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TESTING OF CORRELATION AND HETEROSCEDASTICITY IN NONLINEAR REGRESSION MODELS WITH DBL(p,q,1) RANDOM ERRORS Liu Yingan; Wei Bocheng Acta mathematica scientia,Series B. 2008, 28 (3):  613-632.  DOI: 10.1016/S0252-9602(08)60064-8 Abstract ( 1153 )   RICH HTML PDF (218KB) ( 1369 )   Save Chaos theory has taught us that a system which has both nonlinearity and random input will most likely produce irregular data. If random errors are irregular data, then random error process will raise nonlinearity (Kantz and Schreiber (1997)). Tsai (1986) introduced a composite test for autocorrelation and heteroscedasticity in linear models with AR(1) errors. Liu (2003) introduced a composite test for correlation and heteroscedasticity in nonlinear models with DBL(p,0,1) errors. Therefore, the important problems in regression model are detections of bilinearity, correlation and heteroscedasticity. In this article, the authors discuss more general case of nonlinear models with DBL(p,q,1) random errors by score test. Several statistics for the test of bilinearity, correlation, and heteroscedasticity are obtained, and expressed in simple matrix formulas. The results of regression models with linear errors are extended to those with bilinear errors. The simulation study is carried out to investigate the powers of the test statistics. All results of this article extend and develop results of Tsai (1986), Wei, et al (1995), and Liu, et al (2003). Related Articles | Metrics

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ON SELF-DUAL PERMUTATION CODES Fan Yun; Yuan Yuan Acta mathematica scientia,Series B. 2008, 28 (3):  633-638.  DOI: 10.1016/S0252-9602(08)60065-X Abstract ( 987 )   RICH HTML PDF (138KB) ( 1535 )   Save Permutation codes over finite fields are introduced, some conditions for existence or non-existence of self-dual permutation codes are obtained. Related Articles | Metrics

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TESTING SPHERICITY IN A GMANOVA-MANOVA MODEL WITH NORMAL ERROR Bai Peng; Shi Lei Acta mathematica scientia,Series B. 2008, 28 (3):  639-650.  DOI: 10.1016/S0252-9602(08)60066-1 Abstract ( 1118 )   RICH HTML PDF (178KB) ( 1212 )   Save This article presents a statistic for testing the sphericity in a GMANOVA-MANOVA model with normal error. It is shown that the null distribution of this statistic is beta and its nonnull distribution is given in series form of beta distributions. Related Articles | Metrics

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BOUNDARY VALUE PROBLEM FOR DEGENERATE AND SINGULAR p-LAPLACIAN SYSTEMS Chen Zuchi; Li Du Acta mathematica scientia,Series B. 2008, 28 (3):  651-664.  DOI: 10.1016/S0252-9602(08)60067-3 Abstract ( 1116 )   RICH HTML PDF (184KB) ( 1266 )   Save In this article, using the contraction mapping principle and the shooting method, the authors obtain the existence and uniqueness of the local solution and the global solution to a class of quasilinear elliptic systems with p-Laplacian as its principal. They also obtain the continuous dependence of the solutions on the boundary data. Related Articles | Metrics

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MODERATE DEVIATIONS AND LARGE DEVIATIONS FOR A TEST OF SYMMETRY#br# BASED ON KERNEL DENSITY ESTIMATOR He Xiaoxia; Gao Fuqing Acta mathematica scientia,Series B. 2008, 28 (3):  665-674.  DOI: 10.1016/S0252-9602(08)60068-5 Abstract ( 1312 )   RICH HTML PDF (173KB) ( 1425 )   Save Let fn be a non-parametric kernel density estimator based on a kernel function K. and a sequence of independent and identically distributed random variables taking values in <b>R</b>. The goal of this article is to prove moderate deviations and large deviations for the statistic $\sup\limits_{x\in{{\Bbb R}}}| {f_{n}(x)-f_{n}(-x)}|$. Related Articles | Metrics

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NEGATIVE NORM LEAST-SQUARES METHODS FOR THE INCOMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS Gao Shaoqin; Duan Huoyuan Acta mathematica scientia,Series B. 2008, 28 (3):  675-684.  DOI: 10.1016/S0252-9602(08)60069-7 Abstract ( 1169 )   RICH HTML PDF (158KB) ( 1525 )   Save The purpose of this article is to develop and analyze least-squares approximations for the incompressible magnetohydrodynamic equations. The major advantage of the least-squares finite element method is that it is not subjected to the so-called Ladyzhenskaya-Babuska-Brezzi (LBB) condition. The authors employ least-squares functionals which involve a discrete inner product which is related to the inner product in H-1(\Omega). Related Articles | Metrics

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A NEW SELF-ADAPTIVE ITERATIVE METHOD FOR GENERAL MIXED QUASI #br# VARIATIONAL INEQUALITIES Abdellah Bnouhachem; Mohamed Khalfaoui; Hafida Benazza Acta mathematica scientia,Series B. 2008, 28 (3):  685-696.  DOI: 10.1016/S0252-9602(08)60070-3 Abstract ( 1097 )   RICH HTML PDF (180KB) ( 1167 )   Save The general mixed quasi variational inequality containing a nonlinear term ψ is a useful and an important generalization of variational inequalities. The projection method can not be applied to solve this problem due to the presence of nonlinear term. It is well known that the variational inequalities involving the nonlinear term ψ are equivalent to the fixed point problems and resolvent equations. In this article, the authors use these alternative equivalent formulations to suggest and analyze a new self-adaptive iterative method for solving general mixed quasi variational inequalities. Global convergence of the new method is proved. An example is given to illustrate the efficiency of the proposed method. Related Articles | Metrics

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TIME INCONSISTENCY AND REPUTATION IN MONETARY POLICY: A STRATEGIC #br# MODELLING IN CONTINUOUS TIME Li Jingyuan; Tian Guoqiang Acta mathematica scientia,Series B. 2008, 28 (3):  697-710.  DOI: 10.1016/S0252-9602(08)60071-5 Abstract ( 1189 )   RICH HTML PDF (197KB) ( 1113 )   Save This article develops a model to examine the equilibrium behavior of the time inconsistency problem in a continuous time economy with stochastic and endogenized distortion. First, the authors introduce the notion of sequentially rational equilibrium, and show that the time inconsistency problem may be solved with trigger reputation strategies for stochastic setting. The conditions for the existence of sequentially rational equilibrium are provided. Then, the concept of sequentially rational stochastically stable equilibrium is introduced. The authors compare the relative stability between the cooperative behavior and uncooperative behavior, and show that the cooperative equilibrium in this monetary policy game is a sequentially rational stochastically stable equilibrium and the uncooperative equilibrium is sequentially rational stochastically unstable equilibrium. In the long run, the zero inflation monetary policies are inherently more stable than the discretion rules, and once established, they tend to persist for longer periods of the time. Related Articles | Metrics

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THE EXTENSION OPERATOR IN BANACH SPACES FOR LOCALLY BIHOLOMORPHIC MAPPINGS Liu Mingsheng; Zhu Yucan Acta mathematica scientia,Series B. 2008, 28 (3):  711-720.  DOI: 10.1016/S0252-9602(08)60072-7 Abstract ( 1043 )   RICH HTML PDF (172KB) ( 1454 )   Save In this article, the generalized Roper--Suffridge extension operator in Banach spaces for locally biholomorphic mappings is introduced. It is proved that this operator preserves the starlikeness on some domains in Banach spaces but does not preserves convexity for some cases. Moreover, the growth theorem, covering theorem, and the radius of starlikeness are discussed. Some results of Roper and Suffridge, Gong and Liu, Graham et al in <b> C</b>n are extended to Hilbert spaces or Banach spaces. Related Articles | Metrics