数学物理学报(英文版)

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2012年, 第32卷, 第5期　刊出日期：2012-09-20 上一期下一期

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POINTWISE ESTIMATES OF SOLUTION FOR NON-ISENTROPIC NAVIER-STOKES-POISSON EQUATIONS IN MULTI-DIMENSIONS

吴志刚, 王维克

数学物理学报(英文版). 2012 (5): 1681-1702. DOI: 10.1016/S0252-9602(12)60134-9

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The Cauchy problem of the non-isentropic Navier-Stokes-Poisson equations in multi-dimensions is considered. The global existence and pointwise estimates of the classical solution are given, which extend the optimal decay rate in L²-norm in [27] to the L^p(Rⁿ) (p > n/n−1 )-norm.

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MARKOV CHAIN INVERSION APPROACH TO IDENTIFY THE TRANSITION RATES OF ION CHANNELS

向绪言, 邓迎春, 杨向群

数学物理学报(英文版). 2012 (5): 1703-1718. DOI: 10.1016/S0252-9602(12)60135-0

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We consider how to identify the transition rates of ion channels with the underlying scheme which is kinetically modelled as time-homogeneous Markov chain. A Markov chain inversion approach is developed to perform a difficult inversion to identify the transition rates from the parameters characterizing the lifetime distributions at a small number of states, although it is straightforward to derive the lifetime distribution. The general explicit equations relating the parameters of the lifetime distribution to the tran-sition rates are derived and transition rates are then obtained as roots to this system of equations. The concrete solutions are proposed to the basic and regular schemes such as linear, star-graph branch and loop. Useful conclusions and solutions to realistic schemes are also included to show its efficiency.

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THE DISTRIBUTION OF VALUES OF TAYLOR SERIES

余家荣

数学物理学报(英文版). 2012 (5): 1719-1726. DOI: 10.1016/S0252-9602(12)60136-2

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Clarify some classical results and their proofs on the distribution of values of simple Taylor series and extend them to multiple Taylor series.

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THE HOMOGENEOUS DIRICHLET PROBLEM FOR QUASILINEAR ANISOTROPIC DEGENERATE PARABOLIC-HYPERBOLIC EQUATION#br# WITH L^p INITIAL VALUE

王志刚, 李亚纯

数学物理学报(英文版). 2012 (5): 1727-1742. DOI: 10.1016/S0252-9602(12)60137-4

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The aim of this paper is to prove the well-posedness (existence and uniqueness) of the L^pentropy solution to the homogeneous Dirichlet problems for the anisotropic degenerate parabolic-hyperbolic equations with Lp initial value. We use the device of doubling variables and some technical analysis to prove the uniqueness result. Moreover we can prove that the Lp entropy solution can be obtained as the limit of solutions of the corresponding regularized equations of nondegenerate parabolic type.

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DEGENERATE BOUNDARY LAYER SOLUTIONS TO THE GENERALIZED BENJAMIN-BONAMAHONY-BURGERS EQUATION

肖清华, 陈正争

数学物理学报(英文版). 2012 (5): 1743-1758. DOI: 10.1016/S0252-9602(12)60138-6

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This paper is concerned with the convergence rates of the global solutions of the generalized Benjamin-Bona-Mahony-Burgers (BBM-Burgers) equation to the cor-responding degenerate boundary layer solutions in the half-space. It is shown that the convergence rate is t^−α/4 as t →1 provided that the initial perturbation lies in H¹α for α < α(q) := 3+ 2/q , where q is the degeneracy exponent of the flux function. Our analysis is based on the space-time weighted energy method combined with a Hardy type inequality with the best possible constant introduced in [1].

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REGULARITY AND SYMMETRY OF SOLUTIONS OF AN INTEGRAL SYSTEM

陈晓莉, 杨健夫

数学物理学报(英文版). 2012 (5): 1759-1780. DOI: 10.1016/S0252-9602(12)60139-8

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In this paper, we are concerned with the regularity and symmetry of positive solutions of the following nonlinear integral system
u(x) = ∫_RⁿG (x − y)v(y)^q/|y| dy, v(x) = ∫_RⁿG (x − y)u(y)^p/|y| dy
for x ∈ Rⁿ, where G (x) is the kernel of Bessel potential of order α, 0 ≤β < α< n, 1 < p, q < n− β/β and 1 /p + 1+1/q + 1>n −α + β/n.
We show that positive solution pairs (u, v) ∈ L^p⁺¹(Rⁿ)×L^q⁺¹(Rⁿ) are H¨older continuous, radially symmetric and strictly decreasing about the origin.

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OPTIMAL CONVERGENCE RATE OF THE LANDAU EQUATION WITH FRICTIONAL FORCE

刘双乾, 刘红霞

数学物理学报(英文版). 2012 (5): 1781-1804. DOI: 10.1016/S0252-9602(12)60140-4

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The Cauchy problem of the Landau equation with frictional force is investi-gated. Based on Fourier analysis and nonlinear energy estimates, the optimal convergence rate to the steady state is obtained under some conditions on initial data.

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BOREL RADIUS AND T-RADIUS OF THE ALGEBROIDAL FUNCTION IN THE UNIT DISC

孔荫莹

数学物理学报(英文版). 2012 (5): 1805-1812. DOI: 10.1016/S0252-9602(12)60141-6

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Using Ahlfors’ theory of covering surface and a type-function, we confirm the existence theorem of a Borel radius and a T-radius for the algebroidal function dealing with multiple values in the unit disc, which briefly extend some results for the algebroidal functions in the complex plane.

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RANDOM APPROXIMATION OF AN ADDITIVE FUNCTIONAL EQUATION OF m-APPOLLONIUS TYPE

Hassan Azadi Kenary

数学物理学报(英文版). 2012 (5): 1813-1825. DOI: 10.1016/S0252-9602(12)60142-8

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In this paper, using the fixed-point and direct methods, we prove the Hyers-Ulam stability of the following m-Appolonius type functional equation:
∑^m_i₌₁f(z − x_i) = mf(z −1/m²∑^m_i₌₁x_i)−1/m∑_1≤i<j≤mf(x_i + x_j),
where m is a natural number greater than 1, in random normed spaces.

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RELATIVE ENTROPY AND LARGE DEVIATIONS UNDER SUBLINEAR EXPECTATIONS

高付清, 徐明周

数学物理学报(英文版). 2012 (5): 1826-1834. DOI: 10.1016/S0252-9602(12)60143-X

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We give a definition of relative entropy with respect to a sublinear expectation and establish large deviation principle for the empirical measures for independent random variables under the sublinear expectation.

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ON THE DECAY AND SCATTERING FOR THE KLEIN-GORDON-HARTREE EQUATION WITH RADIAL DATA

毋海根, 张军勇

数学物理学报(英文版). 2012 (5): 1835-1850. DOI: 10.1016/S0252-9602(12)60144-1

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In this paper, we study the decay estimate and scattering theory for the Klein-Gordon-Hartree equation with radial data in space dimension d 3. By means of a compactness strategy and two Morawetz-type estimates which come from the linear and nonlinear parts of the equation, respectively, we obtain the corresponding theory for energy subcritical and critical cases. The exponent range of the decay estimates is extended to 0 < γ ≤4 and γ < d with Hartree potential V (x) = |x|^−γ.

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ON RUBIN´S HARMONIC ANALYSIS AND ITS RELATED POSITIVE DEFINITE FUNCTIONS

Néji Bettaibi, Kamel Mezlini, Moufida El Guénichi

数学物理学报(英文版). 2012 (5): 1851-1874. DOI: 10.1016/S0252-9602(12)60145-3

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In this paper, a new formulation of the Rubin´s q-translation is given, which leads to a reliable q-harmonic analysis. Next, related q-positive definite functions are introduced and studied, and a Bochner´s theorem is proved.

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EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO A SINGULAR PARABOLIC EQUATION

夏莉, 李敬娜, 姚正安

数学物理学报(英文版). 2012 (5): 1875-1882. DOI: 10.1016/S0252-9602(12)60146-5

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In this paper, we study the initial-boundary value problem for a class of sin-gular parabolic equations. Under some conditions, we obtain the existence and asymptotic behavior of solutions to the problem by parabolic regularization method and the sub-super solutions method. As a byproduct, we prove the existence of solutions to some problems with gradient terms, which blow up on the boundary.

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A BLOW-UP CRITERION FOR 3-D NON-RESISTIVE COMPRESSIBLE HEAT-CONDUCTIVE MAGNETOHYDRODYNAMIC EQUATIONS#br# WITH INITIAL VACUUM

徐新英

数学物理学报(英文版). 2012 (5): 1883-1900. DOI: 10.1016/S0252-9602(12)60147-7

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In this paper, we prove a blow-up criterion of strong solutions to the 3-D vis-cous and non-resistive magnetohydrodynamic equations for compressible heat-conducting flows with initial vacuum. This blow-up criterion depends only on the gradient of velocity and the temperature, which is similar to the one for compressible Navier-Stokes equations.

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EXISTENCE OF SOLUTIONS TO THE PARABOLIC EQUATION WITH A SINGULAR POTENTIAL OF THE SOBOLEV-HARDY TYPE

韩军强, 王永达, 钮鹏程

数学物理学报(英文版). 2012 (5): 1901-1918. DOI: 10.1016/S0252-9602(12)60148-9

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We study the existence of solutions to the following parabolic equation
{ut − Δ_pu =λ/|x|^s |u|^q−2 u,    (x, t) ∈ Ω × (0,∞),
u(x, 0) = f(x),                          x ∈Ω,
u(x, t) = 0,                               (x, t) ∈ ∂Ω × (0,∞),                   (P)
where −Δ_pu ≡ −div(|∇u|^p−2 ∇u), 1 < p < N, 0 < s ≤ p, p ≤ q ≤ p*(s) = N−s/N−p p, Ω is a bounded domain in RN such that 0 ∈ Ω with a C¹boundary ∂Ω, f ≥ 0 satisfying some convenient regularity assumptions. The analysis reveals that the existence of solutions for (P) depends on p, q, s in general, and on the relation between and the best constant in the Sobolev-Hardy inequality.

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S_p-CLASS (0 <p < ∞) TOEPLITZ OPERATOR WITH UNBOUNDED SYMBOL ON DIRICHLET SPACE

夏锦, 王晓峰, 曹广福

数学物理学报(英文版). 2012 (5): 1919-1928. DOI: 10.1016/S0252-9602(12)60149-0

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In this paper, we construct a function u in L^2,1(B_n, dA), which is unbounded on any neighborhood of each boundary point of Bn, such that Toeplitz operator T_u is com-pact on Dirichlet space D(B_n, dA). Furthermore, Schatten p-class (0 < p < ∞) Toeplitz operators on Dirichlet space D(B_n, dA) with unbounded symbols are also obtained.

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THE EXTREME POINTS OF A CLASS OF ANALYTIC FUNCTIONS WITH POSITIVE REAL PART AND A PRESCRIBED SET OF VALUES

彭志刚

数学物理学报(英文版). 2012 (5): 1929-1936. DOI: 10.1016/S0252-9602(12)60150-7

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Let ζ = (0, z₁, z₂, · · · , z_n) with |z_j| < 1 for 1 ≤ j ≤ n, ! = (1, w₁, w₂, · · · , w_n), and P(ζ, ω) denote the set of functions p(z) that are analytic in D = {z : |z| < 1} and satisfy Rep(z) > 0 (|z| < 1), p(0) = 1, p(z_j) = w_j, j = 1, 2, · · · , n. In this article we investigate the extreme points of P(ζ, ω).

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REGULARITY FOR NONLINEAR ELLIPTIC SYSTEMS WITH DINI COEFFICIENTS UNDER NATURAL GROWTH CONDITION FOR THE CASE: 1 <m <2

邱亚林

数学物理学报(英文版). 2012 (5): 1937-1958. DOI: 10.1016/S0252-9602(12)60151-9

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In this article, we consider interior regularity for weak solutions to nonlinear elliptic systems of divergence type with Dini continuous coefficients under natural growth condition for the case 1 < m < 2. All estimates in the case of m ≥ 2 is no longer suitable, and we can’t obtain the Caccioppoli’s second inequality by using these techniques developed in the case of m ≥ 2. But the Caccioppoli’s second inequality is the key to use A-harmonic approximation method. Thus, we adopt another technique introduced by Acerbi and Fcsco to overcome the difficulty and we also overcome those difficulties due to Dini condition. And then we apply the A-harmonic approximation method to prove partial regularity of weak solutions.

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EMDEN-FOWLER TYPE SYSTEM: NOETHER SYMMETRIES AND FIRST INTEGRALS

B. Muatjetjeja, C. M. Khalique

数学物理学报(英文版). 2012 (5): 1959-1966. DOI: 10.1016/S0252-9602(12)60152-0

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We classify a generalized coupled singular Emden-Fowler type system ¨u +a(t)vⁿ = 0, ¨v + b(t)u^m = 0 with respect to the standard first-order Lagrangian according to the Noether point symmetries which it admits. First integrals of the various cases which admit Noether point symmetries are then obtained. This system was discussed in the literature from the view-point of existence and uniqueness of positive solutions.

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ON SOLUTIONS OF QUATERNION MATRIX EQUATIONS XF-AX = BY AND XF-AX = BY

宋彩芹, 陈果良, 王晓东

数学物理学报(英文版). 2012 (5): 1967-1982. DOI: 10.1016/S0252-9602(12)60153-2

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In this paper, the quaternion matrix equations XF − AX = BY and XF −AX= BY are investigated. For convenience, they were called generalized Sylvester-quaternion matrix equation and generalized Sylvester-j-conjugate quaternion matrix equa-tion, which include the Sylvester matrix equation and Lyapunov matrix equation as special cases. By applying of Kronecker map and complex representation of a quaternion matrix, the sufficient conditions to compute the solution can be given and the expressions of the explicit solutions to the above two quaternion matrix equations XF − AX = BY and XF − AX = BY are also obtained. By the established expressions, it is easy to compute
the solution of the quaternion matrix equation in the above two forms. In addition, two practical algorithms for these two quaternion matrix equations are give. One is complex representation matrix method and the other is a direct algorithm by the given expression. Furthermore, two illustrative examples are proposed to show the efficiency of the given method.

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SUBGEOMETRIC RATES OF CONVERGENCE OF THE GI/G/1 QUEUEING SYSTEM

李晓花, 侯振挺

数学物理学报(英文版). 2012 (5): 1983-1996. DOI: 10.1016/S0252-9602(12)60154-4

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The article deals with the waiting time process of the GI/G/1 queueing sys-tem. We shall give that the rate of convergence to the stationary distribution and the decay of the stationary tail only depend on the tail of the service distribution, but not on the interarrival distribution. We shall also give explicit criteria for the rate of con-vergence and decay of stationary tail for three specific types of subgeometric cases (Case
1: the rate function r(n) = exp(sn ^1/1+α ), α > 0, s > 0; Case 2: polynomial rate function r(n) = n^α, α > 0; Case 3: logarithmic rate function r(n) = log^αn, α > 0).

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A REDUCED FE FORMULATION BASED ON POD METHOD FOR HYPERBOLIC EQUATIONS

罗振东, 欧秋兰, 吴加荣, 谢正辉

数学物理学报(英文版). 2012 (5): 1997-2009. DOI: 10.1016/S0252-9602(12)60155-6

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A proper orthogonal decomposition (POD) method was successfully used in the reduced-order modeling of complex systems. In this paper, we extend the applications of POD method, namely, apply POD method to a classical finite element (FE) formulation for second-order hyperbolic equations with real practical applied background, establish a reduced FE formulation with lower dimensions and high enough accuracy, and provide the error estimates between the reduced FE solutions and the classical FE solutions and the implementation of algorithm for solving reduced FE formulation so as to provide scientific theoretic basis for service applications. Some numerical examples illustrate the fact that the results of numerical computation are consistent with theoretical conclusions. Moreover,
it is shown that the reduced FE formulation based on POD method is feasible and efficient for solving FE formulation for second-order hyperbolic equations.

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QUOTIENT SPACE OF LMC-COMPACTIFICATION AS A SPACE OF z-FILTERS

Mohammad Akbari Tootkaboni

数学物理学报(英文版). 2012 (5): 2010-2020. DOI: 10.1016/S0252-9602(12)60156-8

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The left multiplicative continuous compactification is the universal semigroup compactification of a semitopological semigroup. In this paper an internal construction of a quotient space of the left multiplicative continuous compactification of a semitopological semigroup is constructed as a space of z-filters.

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A COUPLED SYSTEM OF INTEGRAL EQUATIONS IN REFLEXIVE BANACH SPACES

A. M. A. El-Sayed, H. H. G. Hashem

数学物理学报(英文版). 2012 (5): 2021-2028. DOI: 10.1016/S0252-9602(12)60157-X

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We present an existence theorem for at least one weak solution for a coupled system of integral equations of Volterra type in a reflexive Banach spaces relative to the weak topology.

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RIEMANN BOUNDARY VALUE PROBLEMS FOR SOME K-REGULAR FUNCTIONS IN CLIFFORD ANALYSIS

姜乐, 杜金元

数学物理学报(英文版). 2012 (5): 2029-2049. DOI: 10.1016/S0252-9602(12)60158-1

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In this paper, we study the R_m(m > 0) Riemann boundary value prob-lems for regular functions, harmonic functions and bi-harmonic functions with values in a universal clifford algebra C(V_n, n). By using Plemelj formula, we get the solutions of R_m (m > 0) Riemann boundary value problems for regular functions. Then transforming the Riemann boundary value problems for harmonic functions and bi-harmonic functions into the Riemann boundary value problems for regular functions, we obtain the solutions of R_m (m > 0) Riemann boundary value problems for harmonic functions and bi-harmonic functions.

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ON GRAPH MEASURES IN BANACH SPACES AND DESCRIPTION OF ESSENTIAL SPECTRA OF MULTIDIMENSIONAL TRANSPORT EQUATION

Boulbeba Abdelmoumen, Aref Jeribi, Maher Mnif

数学物理学报(英文版). 2012 (5): 2050-2064. DOI: 10.1016/S0252-9602(12)60159-3

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In this paper, we define new measures called respectively graph measure of noncompactness and graph measure of weak noncompactness. Moreover, we apply the obtained results to discuss the incidence of some perturbation results realized in [2] on
the behavior of essential spectra of such closed densely defined linear operators on Banach spaces. These results are exploited to investigate the essential spectra of a multidimensional neutron transport operator on L₁ spaces.

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