数学物理学报(英文版)

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PARTIAL REGULARITY FOR THE NAVIER-STOKES-FOURIER SYSTEM

Luisa Consiglieri

数学物理学报(英文版). 2011 (5): 1653-1670. DOI: 10.1016/S0252-9602(11)60351-2

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This paper addresses a nonstationary flow of heat-conductive incompressible Newtonian fluid with temperature-dependent viscosity coupled with linear heat transfer with advection and a viscous heat source term, under Navier/Dirichlet boundary condi-tions. The partial regularity for the velocity of the fluid is proved for each proper weak solution, that is, for such weak solutions which satisfy some local energy estimates in a similar way to the suitable weak solutions of the Navier-Stokes system. Finally, we study the nature of the set of points in space and time upon which proper weak solutions could be singular.

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AN ENLARGEMENT OF FILTRATION FOR BROWNIAN MOTION

胡耀忠

数学物理学报(英文版). 2011 (5): 1671-1678. DOI: 10.1016/S0252-9602(11)60352-4

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Let Bt be an Ft Brownian motion and Gt be an enlargement of filtration of Ft from some Gaussian random variables. We obtain equations for ht such that Bt −ht is a Gt-Brownian motion.

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COMPACT DIFFERENCES OF COMPOSITION OPERATORS ON HOLOMORPHIC FUNCTION SPACES IN THE UNIT BALL

江良英, 欧阳才衡

数学物理学报(英文版). 2011 (5): 1679-1693. DOI: 10.1016/S0252-9602(11)60353-6

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We find a lower bound for the essential norm of the difference of two compo-sition operators acting on H²(B_N) or A²_s(B_N) (s > −1). This result plays an important role in proving a necessary and sufficient condition for the difference of linear fractional composition operators to be compact, which answers a question posed by MacCluer and Weir in 2005.

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CONVERGENCE RATE OF MULTIPLE FRACTIONAL STRATONOVICH TYPE INTEGRAL FOR HURST PARAMETER LESS THAN 1/2

汪宝彬

数学物理学报(英文版). 2011 (5): 1694-1708. DOI: 10.1016/S0252-9602(11)60354-8

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In this paper, we have investigated the problem of the convergence rate of the multiple integral

{∫^T₀···∫^T₀f(t₁, ··· , t_n)dB^H, π_t1 ···dB^H^, ^π_tn^},
where f ∈ ^Cn+1([0, T]ⁿ) is a given function, π is a partition of the interval [0, T] and {B^H, ^π_ti } is a family of interpolation approximation of fractional Brownian motion B^H_t with Hurst parameter H < 1/2. The limit process is the multiple Stratonovich integral of the function f. In view of known results, the convergence rate is different for different multiplicity n. Under some mild conditions, we obtain that the uniform convergence rate is Δ^2H in the mean square sense, where Δ is the norm of the partition generating the approximations.

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EXISTENCE RESULTS FOR A CLASS OF PSEUDOMONOTONE ELLIPTIC-PARABOLIC INCLUSIONS

彭自嘉, 刘益良

数学物理学报(英文版). 2011 (5): 1709-1718. DOI: 10.1016/S0252-9602(11)60355-X

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This paper deals with the initial-value problem of nonlinear evolution inclu-sions of the form dB(u)/dt + A(u) ∋ f, v₀ ∈ B(u)(0), where the operator B is induced by a subgradient and A is pseudomonotone. Existence theorem is established via the time discretization technique and the regularization method. In contrast to the previous results, here we impose a weaker coerciveness condition on A and remove the strong monotonicity from B.

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A NOTE ON THE DIPERNA-LIONS FLOWS

刘昕, 黄文亮

数学物理学报(英文版). 2011 (5): 1719-1724. DOI: 10.1016/S0252-9602(11)60356-1

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In this note, we give a short proof for the DiPerna-Lions flows associated to ODEs following the method of Crippa and De Lellis [3]. More precisely, assume that [divb]− ∈L^∞ loc(R^d), |b|/(1 + |x| log |x|) ∈L^∞(R^d) and |∇_b| ·(|∇_b|) ∈L^∞loc(R^d), where (r) = log ··· log(r + c), c > 0. Then, there exists a unique regular Lagrangian flow associated with the ODE ˙X (t, x) = b(X(t, x)), X(0, x) = x.

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LARGE TIME BEHAVIORS OF THE ISENTROPIC BIPOLAR COMPRESSIBLE NAVIER-STOKES-POISSON SYSTEM

邹晨

数学物理学报(英文版). 2011 (5): 1725-1740. DOI: 10.1016/S0252-9602(11)60357-3

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The isentropic bipolar compressible Navier-Stokes-Poisson (BNSP) system is investigated in R3 in the present paper. The optimal time decay rate of global strong solution is established. When the regular initial data belong to the Sobolev space H^l(R³)∩˙B^−s_1,1(R³) with l ≥ 4 and s ∈ (0, 1], it is shown that the momenta of the charged particles decay at the optimal rate (1+t)^−1/4−s/2 in L²-norm, which is slower than the rate (1+t)^−3/4−s/2 for the compressible Navier-Stokes (NS) equations [14]. In particular, a new phenomenon on the charge transport is observed. The time decay rate of total density and momentum was both (1 + t)^−3/4 due to the cancellation effect from the interplay interaction of the charged particles.

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ON THE HEAT FLOW EQUATION OF SURFACES OF CONSTANT MEAN CURVATURE IN HIGHER DIMENSIONS

谭忠, 吴国春

数学物理学报(英文版). 2011 (5): 1741-1748. DOI: 10.1016/S0252-9602(11)60358-5

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In this paper, we consider the heat flow for the H-system with constant mean curvature in higher dimensions. We give sufficient conditions on the initial data such that the heat flow develops finite time singularity. We also provide a new set of initial data to
guarantee the existence of global regular solution to the heat flow, that converges to zero in W^{1, n} with the decay rate t^2/2−nas time goes to infinity.

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A MATHEMATICAL MODEL OF ENTERPRISE COMPETITIVE ABILITY AND PERFORMANCE THROUGH A PARTICULAR EMDEN-FOWLER EQUATION

Pai Jente, Li Mengrong, Chang Yueloong, Chiu Sumiao

数学物理学报(英文版). 2011 (5): 1749-1764. DOI: 10.1016/S0252-9602(11)60359-7

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In this paper we work with the ordinary diffential equation u′′− u³ = 0 and obtain some interesting phenomena concerning blow-up, blow-up rate, life-spann, zeros and critical points of solutions to this equation.

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A REDUCED MFE FORMULATION BASED ON POD FOR THE NON-STATIONARY CONDUCTION-CONVECTION PROBLEMS

罗振东, 谢正辉, 陈静

数学物理学报(英文版). 2011 (5): 1765-1785. DOI: 10.1016/S0252-9602(11)60360-3

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In this article, a reduced mixed finite element (MFE) formulation based on proper orthogonal decomposition (POD) for the non-stationary conduction-convection problems is presented. Also the error estimates between the reduced MFE solutions based
on POD and usual MFE solutions are derived. It is shown by numerical examples that the results of numerical computation are consistent with theoretical conclusions. Moreover, it is shown that the reduced MFE formulation based on POD is feasible and efficient in finding numerical solutions for the non-stationary conduction-convection problems.

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EXISTENCE OF PERIODIC SOLUTIONS FOR A DIFFERENTIAL INCLUSION SYSTEMS INVOLVING THE p(t)-LAPLACIAN

葛斌, 薛小平, 周庆梅

数学物理学报(英文版). 2011 (5): 1786-1802. DOI: 10.1016/S0252-9602(11)60361-5

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We study a nonlinear periodic problem driven by the p(t)-Laplacian and hav-ing a nonsmooth potential (hemivariational inequalities). Using a variational method based on nonsmooth critical point theory for locally Lipschitz functions, we first prove the exis-tence of at least two nontrivial solutions under the generalized subquadratic and then estab-lish the existence of at least one nontrivial solution under the generalized superquadratic.

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UNIFORM ATTRACTOR FOR NONAUTONOMOUS INCOMPRESSIBLE NON-NEWTONIAN FLUID WITH A NEW CLASS OF EXTERNAL FORCES

赵才地, 贾晓琳, 杨新波

数学物理学报(英文版). 2011 (5): 1803-1812. DOI: 10.1016/S0252-9602(11)60362-7

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This paper is joint with [27]. The authors prove in this article the existence and reveal its structure of uniform attractor for a two-dimensional nonautonomous incom-pressible non-Newtonian fluid with a new class of external forces.

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A DELAY-DEPENDENT STABILITY CRITERION FOR NONLINEAR STOCHASTIC DELAY-INTEGRO-DIFFERENTIAL EQUATIONS

牛原玲, 张诚坚, 段金桥

数学物理学报(英文版). 2011 (5): 1813-1822. DOI: 10.1016/S0252-9602(11)60363-9

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A type of complex systems under both random influence and memory effects is considered. The systems are modeled by a class of nonlinear stochastic delay-integrodifferential equations. A delay-dependent stability criterion for such equations is derived under the condition that the time lags are small enough. Numerical simulations are presented to illustrate the theoretical result.

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DETERMINISTIC HOMOGENIZATION OF QUASILINEAR DAMPED HYPERBOLIC EQUATIONS

Gabriel Nguetseng, Hubert Nnang, Nils Svanstedt

数学物理学报(英文版). 2011 (5): 1823-1850. DOI: 10.1016/S0252-9602(11)60364-0

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Deterministic homogenization is studied for quasilinear monotone hyperbolic problems with a linear damping term. It is shown by the sigma-convergence method that the sequence of solutions to a class of multi-scale highly oscillatory hyperbolic problems converges to the solution to a homogenized quasilinear hyperbolic problem.

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EXACT MAXIMUM LIKELIHOOD ESTIMATOR FOR DRIFT FRACTIONAL BROWNIAN MOTION AT DISCRETE OBSERVATION

胡耀忠, Nualart David, 肖炜麟, 张卫国

数学物理学报(英文版). 2011 (5): 1851-1859. DOI: 10.1016/S0252-9602(11)60365-2

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This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both the central limit theorem and the Berry-Ess´een bounds for these estimators are obtained by using the Stein’s method via Malliavin calculus.

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REMARKS ON SUB-FRACTIONAL BESSEL PROCESSES

申广君, 陈超, 闫理坦

数学物理学报(英文版). 2011 (5): 1860-1876. DOI: 10.1016/S0252-9602(11)60366-4

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Let S = {(S¹_t, ···, S^d_t)}_t≥0 denote a d-dimensional sub-fractional Brownianmotion with index H ≥ 1/2. In this paper we study some properties of the process X of the form
X_t :=∑^d_i₌₁∫ ^t₀Sⁱ_s/R_sdSⁱ_s, d ≥ 1,
where R_t=√(S¹_t )²+ ··· + (S^d_t)² is the sub-fractional Bessel process.

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REMARKS ON THE NONLINEAR INSTABILITY OF INCOMPRESSIBLE EULER EQUATIONS

谢华朝, 訾瑞昭

数学物理学报(英文版). 2011 (5): 1877-1888. DOI: 10.1016/S0252-9602(11)60367-6

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In this paper, we consider the nonlinear instability of incompressible Euler equations. If a steady density is non-monotonic, then the smooth steady state is a non-linear instability. First, we use variational method to find a dominant eigenvalue which is important in the construction of approximate solutions, then by energy technique and analytic method, we obtain the dynamical instability result.

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CONSTRUCTION OF HOMOGENEOUS MINIMAL 2-SPHERES IN COMPLEX GRASSMANNIANS

费杰, 焦晓祥, 许小卫

数学物理学报(英文版). 2011 (5): 1889-1898. DOI: 10.1016/S0252-9602(11)60368-8

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In this paper, we construct a class of homogeneous minimal 2-spheres in com-plex Grassmann manifolds by applying the irreducible unitary representations of SU(2). Furthermore, we compute induced metrics, Gaussian curvatures, Kähler angles and the square lengths of the second fundamental forms of these homogeneous minimal 2-spheres in G(2, n + 1) by making use of Veronese sequence.

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INFINITELY MANY SOLUTIONS FOR A CLASS OF DEGENERATE ELLIPTIC EQUATIONS

李珂, 魏红军

数学物理学报(英文版). 2011 (5): 1899-1910. DOI: 10.1016/S0252-9602(11)60369-X

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Let X = (X₁, … , X_m) be an infinitely degenerate system of vector fields. The aim of this paper is to study the existence of infinitely many solutions for the sum of operators Δ_X =∑^m_j₌₁X^*_j X_j.

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STABILITY AND SUPERSTABILITY OF JORDAN HOMOMORPHISMS AND JORDAN DERIVATIONS ON BANACH ALGEBRAS AND C*-ALGEBRAS: A FIXED POINT APPROACH

M. Eshaghi Gordji, A. Najati, A. Ebadian

数学物理学报(英文版). 2011 (5): 1911-1922. DOI: 10.1016/S0252-9602(11)60370-6

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Using fixed point methods, we prove the Hyers–Ulam–Rassias stability and su-perstability of Jordan homomorphisms (Jordan *-homomorphisms), and Jordan derivations (Jordan *-derivations) on Banach algebras (C*-algebras) for the generalized Jensen–type
functional equation
rf(x + y/r ) + rf(x − y/r) = 2f(x),
where r is a fixed positive real number in (1,1).

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ON THE CONCENTRATION PROPERTIES FOR THE NONLINEAR SCHRÖDINGER EQUATION WITH A STARK POTENTIAL

朱世辉, 张健

数学物理学报(英文版). 2011 (5): 1923-1938. DOI: 10.1016/S0252-9602(11)60371-8

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In this paper, we study blow-up solutions of the Cauchy problem to the L² critical nonlinear Schr¨odinger equation with a Stark potential. Using the variational char-acterization of the ground state for nonlinear Schr¨odinger equation without any potential, we obtain some concentration properties of blow-up solutions, including that the origin is the blow-up point of the radial blow-up solutions, the phenomenon of L²-concentration and rate of L²-concentration of blow-up solutions.

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INVERTIBLE SEQUENCES OF BOUNDED LINEAR OPERATORS

臧丽丽, 孙文昌

数学物理学报(英文版). 2011 (5): 1939-1944. DOI: 10.1016/S0252-9602(11)60372-X

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In this paper, we study the invertibility of sequences consisting of finitely many bounded linear operators from a Hilbert space to others. We show that a sequence of operators is left invertible if and only if it is a g-frame. Therefore, our result connects the invertibility of operator sequences with frame theory.

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STABLE SUB-GAUSSIAN MODELS CONSTRUCTED BY POISSON PROCESSES

戴洪帅, 李育强

数学物理学报(英文版). 2011 (5): 1945-1958. DOI: 10.1016/S0252-9602(11)60373-1

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In this paper, we first prove that one-parameter standard -stable sub-Gaussian processes can be approximated by processes constructed by integrals based on the Poisson process with random intensity. Then we extend this result to the two-parameter processes. At last, we consider the approximation of the subordinated fractional Brownian motion.

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GLOBAL ASYMPTOTICAL PROPERTIES FOR A DIFFUSED HBV INFECTION MODEL WITH CTL IMMUNE RESPONSE AND#br# NONLINEAR INCIDENCE

王绍利, 冯新龙, 何银年

数学物理学报(英文版). 2011 (5): 1959-1967. DOI: 10.1016/S0252-9602(11)60374-3

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This article proposes a diffused hepatitis B virus (HBV) model with CTL immune response and nonlinear incidence for the control of viral infections. By means of different Lyapunov functions, the global asymptotical properties of the viral-free equi-librium and immune-free equilibrium of the model are obtained. Global stability of the positive equilibrium of the model is also considered. The results show that the free diffu-sion of the virus has no effect on the global stability of such HBV infection problem with Neumann homogeneous boundary conditions.

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GLOBAL WELL-POSEDNESS OF THE STOCHASTIC 2D BOUSSINESQ EQUATIONS WITH PARTIAL VISCOSITY

蒲学科, 郭柏灵

数学物理学报(英文版). 2011 (5): 1968-1984. DOI: 10.1016/S0252-9602(11)60375-5

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This paper deals with the stochastic 2D Boussinesq equations with partial viscosity. This is a coupled system of Navier-Stokes/Euler equations and the transport equation for temperature under additive noise. Global well-posedness result of this system under partial viscosity is proved by using classical energy estimates method.

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ANALYTIC HARDY SPACES ON THE QUANTUM TORUS

陈泽乾, 尹智

数学物理学报(英文版). 2011 (5): 1985-1996. DOI: 10.1016/S0252-9602(11)60376-7

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Analytic Hardy and BMO spaces on the quantum torus are introduced. Some basic properties of these spaces are presented. In particular, the associated H1-BMO duality theorem is proved. Finally, we discuss some possible extensions of the obtained results.

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THE CLASSIFICATION OF NILPOTENT LEIBNIZ 3-ALGEBRAS

白瑞蒲, 张杰

数学物理学报(英文版). 2011 (5): 1997-2006. DOI: 10.1016/S0252-9602(11)60377-9

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The notions of the nilpotent and the strong-nilpotent Leibniz 3-algebras are defined. And the three dimensional two-step nilpotent, strong-nilpotent Leibniz 3-algebras are classified.

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ANALYSIS OF FDTD TO UPML FOR MAXWELL EQUATIONS IN POLAR COORDINATES

方能胜, 应龙安

数学物理学报(英文版). 2011 (5): 2007-2032. DOI: 10.1016/S0252-9602(11)60378-0

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An FDTD system associated with uniaxial perfectly matched layer (UPML) for an electromagnetic scattering problem in two-dimensional space in polar coordinates is considered. Particularly the FDTD system of an initial-boundary value problems of the
transverse magnetic (TM) mode to Maxwell’s equations is obtained by Yee’s algorithm, and the open domain of the scattering problem is truncated by a circle with a UPML. Besides, an artificial boundary condition is imposed on the outer boundary of the UPML.
Afterwards, stability of the FDTD system on the truncated domain is established through energy estimates by the Gronwall inequality. Numerical experiments are designed to ap-prove the theoretical analysis.

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SUBALGEBRAS AND FINITISTIC DIMENSIONS OF ARTIN ALGEBRAS

张爱平, 张顺华

数学物理学报(英文版). 2011 (5): 2033-2040. DOI: 10.1016/S0252-9602(11)60379-2

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Let A be an Artin algebra. We investigate subalgebras of A with certain conditions and obtain some classes of algebras whose finitistic dimensions are finite.

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SOME RESULTS ON GENERALIZED EQUILIBRIUM PROBLEMS INVOLVING STRICTLY PSEUDOCONTRACTIVE MAPPINGS

Jong Kyu Kim, Sun Young Cho, Xiaolong Qin

数学物理学报(英文版). 2011 (5): 2041-2057. DOI: 10.1016/S0252-9602(11)60380-9

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In this paper, we consider an iterative sequence for generalized equilibrium problems and strictly pseudocontractive mappings. We show that the iterative sequence converges strongly to a common element of the solution set of generalized equilibrium problems and of the fixed point set of strictly pseudocontractive mappings.

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NECESSARY AND SUFFICIENT CONDITION OF THE STRONG CONVERGENCE FOR TWO FINITE FAMILIES OF UNIFORMLY#br# L-LIPSCHITZIAN MAPPINGS

谷峰

数学物理学报(英文版). 2011 (5): 2058-2066. DOI: 10.1016/S0252-9602(11)60381-0

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The purpose of this paper is to study necessary and sufficient condition for the strong convergence of a new parallel iterative algorithm with errors for two finite families of uniformly L-Lipschitzian mappings in Banach spaces. The results presented in this paper
improve and extend the recent ones announced by [2–7].

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THE DUAL OF NONCOMMUTATIVE LORENTZ SPACES

韩亚洲, Turdebek N. Bekjan

数学物理学报(英文版). 2011 (5): 2067-2080. DOI: 10.1016/S0252-9602(11)60382-2

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We prove some noncommutative analogues of the classical results about dual spaces of the classical Lorentz spaces.

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ROUGH MULTIPLE SINGULAR INTEGRALS ALONG HYPERSURFACES

邓浏睿, 李中凯, 马柏林, 伍火熊

数学物理学报(英文版). 2011 (5): 2081-2098. DOI: 10.1016/S0252-9602(11)60383-4

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In this paper, the authors study the mapping properties of singular integrals on product domains with kernels in L(log+L)^ε(S^m⁻¹× Sⁿ⁻¹) (ε = 1 or 2) supported by hyper-surfaces. The L^p bounds for such singular integral operators as well as the related
Marcinkiewicz integral operators are established, provided that the lower dimensional max-imal function is bounded on L^q(R³) for all q > 1. The condition on the integral kernels is known to be optimal.

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ERRATA TO: "λ-Statistical Convergence of Order α”Acta Mathematica Scientia 2011, 31B(3): 953–959

R. Colak, C. A. Bektas

数学物理学报(英文版). 2011 (5): 2099-2100. DOI: 10.1016/S0252-9602(11)60384-6

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The sequences defined in Example 3 and Example 4 do not serve our purpose for any λ = (λ_n). Because this sequences are just the sequences x = (x_k) = (k) and x = (x_k) =(1) respectively and any term of these sequences can not be 0. In this short not we give Example
3* and Example 4* to show that the inclusions given in Theorem 2.4 and Theorem 2.9 are strict for some λ = (λ_n) , α and β such that 0 < α < β≤ 1.

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