数学物理学报(英文版)

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UNIQUENESS OF MEROMORPHIC FUNCTIONS WHOSE NONLINEAR DIFFERENTIAL POLYNOMIALS SHARE ONE VALUE OR HAVE THE SAME FIXED POINTS IN AN ANGULAR DOMAIN

李效敏, 仪洪勋

数学物理学报(英文版). 2014 (3): 593-609. DOI: 10.1016/S0252-9602(14)60032-1

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In this article, we study the uniqueness question of nonconstant meromorphic functions whose nonlinear differential polynomials share 1 or have the same fixed points in an angular domain. The results in this article improve Theorem 1 of Yang and Hua [26], and improve Theorem 1 of Fang and Qiu [6].

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POSITIVE SOLUTIONS FOR PARAMETRIC EQUIDIFFUSIVE p-LAPLACIAN EQUATIONS

Leszek GASINSKI, Nikolaos S. PAPAGEORGIOU

数学物理学报(英文版). 2014 (3): 610-618. DOI: 10.1016/S0252-9602(14)60033-3

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We consider a parametric Dirichlet problem driven by the p-Laplacian with a Carath´eodory reaction of equidiffusive type. Our hypotheses incorporate as a special case the equidiffusive p-logistic equation. We show that if λ₁ > 0 is the principal eigenvalue of the Dirichlet negative p-Laplacian and λ > λ₁ (λ being the parameter), the problem has a unique positive solution, while for λ ∈(0, λ₁], the problem has no positive solution.

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APPLICATIONS OF HYPERGEOMETRIC SUMMATION THEOREMS OF KUMMER AND DIXON INVOLVING DOUBLE SERIES

H. M. SRIVASTAVA, M. I. QURESHI, Kaleem A. QURAISHI, Ashish ARORA

数学物理学报(英文版). 2014 (3): 619-628. DOI: 10.1016/S0252-9602(14)60034-5

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Using series iteration techniques, we derive a number of general double series identities and apply each of these identities in order to deduce several hypergeometric reduc-tion formulas involving the Srivastava-Daoust double hypergeometric function. The results presented in this article are based essentially upon the hypergeometric summation theorems of Kummer and Dixon.

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PSEUDOHYPERBOLIC METRIC AND UNIFORMLY DISCRETE SEQUENCES IN THE REAL UNIT BALL

任广斌, Uwe KAHLER

数学物理学报(英文版). 2014 (3): 629-638. DOI: 10.1016/S0252-9602(14)60035-7

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We present an overview of the properties of the pseudohyperbolic metric in sev-eral real dimensions and study uniformly discrete sequences for the real unit ball in Rⁿ.

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APPROXIMATE DUALITY OF g-FRAMES IN HILBERT SPACES

Amir KHOSRAVI, Morteza MIRZAEE AZANDARYANI

数学物理学报(英文版). 2014 (3): 639-652. DOI: 10.1016/S0252-9602(14)60036-9

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In this article, we introduce and characterize approximate duality for g-frames. We get some important properties and applications of approximate duals. We also obtain some new results in approximate duality of frames, and generalize some of the known results in approximate duality of frames to g-frames. We also get some results for fusion frames, and perturbation of approximately dual g-frames. We show that approximate duals are stable under small perturbations and they are useful for erasures and reconstruction.

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ON THE DIFFERENCE COUNTERPART OF BRÜCK´S CONJECTURE

陈宗煊

数学物理学报(英文版). 2014 (3): 653-659. DOI: 10.1016/S0252-9602(14)60037-0

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In this article, for a transcendental entire function f(z) of finite order which has a finite Borel exceptional value α we utilize properties of complex difference equations to prove the difference counterpart of Br¨uck´s conjecture, that is, if Δf(z) = f(z + η) − f(z) and f(z) share one value a (≠ ) CM, where η ∈ C is a constant such that f(z + η) ≠ f(z), then
Δf(z) − a/f(z) − a =a/a −α.

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MATCHING PURSUITS AMONG SHIFTED CAUCHY KERNELS IN HIGHER-DIMENSIONAL SPACES

钱涛, 王晋勋, 杨燕

数学物理学报(英文版). 2014 (3): 660-672. DOI: 10.1016/S0252-9602(14)60038-2

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Appealing to the Clifford analysis and matching pursuits, we study the adaptive decompositions of functions of several variables of finite energy under the dictionaries con-sisting of shifted Cauchy kernels. This is a realization of matching pursuits among shifted Cauchy kernels in higher-dimensional spaces. It offers a method to process signals in arbitrary
dimensions.

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CONVERGENCE ANALYSIS OF THE JACOBI SPECTRAL-COLLOCATION METHOD FOR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS

杨银, 陈艳萍, 黄云清

数学物理学报(英文版). 2014 (3): 673-690. DOI: 10.1016/S0252-9602(14)60039-4

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We propose and analyze a spectral Jacobi-collocation approximation for frac-tional order integro-differential equations of Volterra type. The fractional derivative is de-scribed in the Caputo sense. We provide a rigorous error analysis for the collection method, which shows that the errors of the approximate solution decay exponentially in L^∞ norm and weighted L²-norm. The numerical examples are given to illustrate the theoretical results.

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SIGN-CHANGING SOLUTIONS FOR SCHRÖDINGER EQUATIONS WITH VANISHING AND SIGN-CHANGING POTENTIALS

吴元泽, 黄毅生, 刘增

数学物理学报(英文版). 2014 (3): 691-702. DOI: 10.1016/S0252-9602(14)60040-0

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In this article, we study the existence of sign-changing solutions for the following Schr¨odinger equation
−Δu + λV (x)u = K(x)|u|^p−2u x ∈R^N, u →0 as |x| →+∞,
where N ≥ 3, λ > 0 is a parameter, 2 < p < 2N/N−2 , and the potentials V (x) and K(x) satisfy some suitable conditions. By using the method based on invariant sets of the descending flow, we obtain the existence of a positive ground state solution and a ground state sign-changing solution of the above equation for small λ, which is a complement of the results obtained by Wang and Zhou in [J. Math. Phys. 52, 113704, 2011].

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PERTURBATION METHODS IN SEMILINEAR ELLIPTIC PROBLEMS INVOLVING CRITICAL HARDY-SOBOLEV EXPONENT

蓝永艺, 唐春雷

数学物理学报(英文版). 2014 (3): 703-712. DOI: 10.1016/S0252-9602(14)60041-2

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In this article, we deal with a class of semilinear elliptic equations which are perturbations of the problems with the critical Hardy-Sobolev exponent. Some existence results are given via an abstract perturbation method in critical point theory.

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ON A KÄHLER VERSION OF CHEEGER-GROMOLL-PERELMAN´S SOUL THEOREM

傅小勇, 葛剑

数学物理学报(英文版). 2014 (3): 713-718. DOI: 10.1016/S0252-9602(14)60042-4

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In this note, we will prove a K¨ahler version of Cheeger-Gromoll-Perelman´s soul theorem, only assuming the sectional curvature is nonnegative and bisectional curvature is positive at one point.

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THE VALUE DISTRIBUTION AND UNIQUENESS OF ONE CERTAIN TYPE OF DIFFERENTIAL-DIFFERENCE POLYNOMIALS

张克玉, 仪洪勋

数学物理学报(英文版). 2014 (3): 719-728. DOI: 10.1016/S0252-9602(14)60043-6

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In this article, we investigate the distribution of the zeros and uniqueness of differential-difference polynomials
G(z) = (fⁿ(f^m(z) − 1)∏^d_j₌₁f(z + c_j)^v_j)^(k)− α(z),
H(z) = (fⁿ(f(z) − 1)^m∏^d_j₌₁f(z + c_j )^v_j)^(k)− α(z),
where f is transcendental entire function of finite order, c_j(j = 1, 2, · · · , d), n, m, d, and vj (j = 1, 2, · · · , d) are integers, and obtain some theorems, which extended and improved many previous results.

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GENERAL DECAY FOR A DIFFERENTIAL INCLUSION OF KIRCHHOFF TYPE WITH A MEMORY CONDITION AT THE BOUNDARY

Jum-Ran KANG

数学物理学报(英文版). 2014 (3): 729-738. DOI: 10.1016/S0252-9602(14)60044-8

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In this article, we consider a differential inclusion of Kirchhoff type with a memory condition at the boundary. We prove the asymptotic behavior of the corresponding solutions. For a wider class of relaxation functions, we establish a more general decay result, from which the usual exponential and polynomial decay rates are only special cases.

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AREA INTEGRAL FUNCTIONS FOR SECTORIAL OPERATORS ON L^p SPACES

陈泽乾, 孙牧

数学物理学报(英文版). 2014 (3): 739-747. DOI: 10.1016/S0252-9602(14)60045-X

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Area integral functions are introduced for sectorial operators on Lp-spaces. We establish the equivalence between the square and area integral functions for sectorial operators on Lp spaces. This follows that the results of Cowling, Doust, McIntosh, Yagi, and Le Merdy on H1 functional calculus of sectorial operators on Lp-spaces hold true when the square functions are replaced by the area integral functions.

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PROPERTIES OF POSITIVE SOLUTIONS FOR A NONLOCAL NONLINEAR DIFFUSION EQUATION WITH NONLOCAL NONLINEAR BOUNDARY CONDITION

李玉环, 米永生, 穆春来

数学物理学报(英文版). 2014 (3): 748-758. DOI: 10.1016/S0252-9602(14)60046-1

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This article deals with the global existence and blow-up of positive solution of a nonlinear diffusion equation with nonlocal source and nonlocal nonlinear boundary condition. We investigate the influence of the reaction terms, the weight functions and the nonlinear terms in the boundary conditions on global existence and blow up for this equation. Moreover, we establish blow-up rate estimates under some appropriate hypotheses.

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GLOBAL EXISTENCE AND EXPONENTIAL STABILITY OF SOLUTIONS TO THE QUASILINEAR THERMO-DIFFUSION EQUATIONS WITH SECOND SOUND

秦玉明, 李海燕

数学物理学报(英文版). 2014 (3): 759-778. DOI: 10.1016/S0252-9602(14)60047-3

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This article is devoted to the study of global existence and exponential stability of solutions to an initial-boundary value problem of the quasilinear thermo-diffusion equations with second sound by means of multiplicative techniques and energy method provided that the initial data are close to the equilibrium and the relaxation kernel is strongly positive definite and decays exponentially.

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ATOMIC DECOMPOSITION OF μ-BERGMAN SPACE IN Cⁿ

张学军, 席利华, 范海霞, 李俊锋

数学物理学报(英文版). 2014 (3): 779-789. DOI: 10.1016/S0252-9602(14)60048-5

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Let μ be a normal function on [0, 1). The atomic decomposition of the μ-Bergman space in the unit ball B is given for all p > 0.

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ON COLEMAN OUTER AUTOMORPHISM GROUPS OF FINITE GROUPS

海进科, 李正兴

数学物理学报(英文版). 2014 (3): 790-796. DOI: 10.1016/S0252-9602(14)60049-7

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Let G be a finite group and Out_Col(G) the Coleman outer automorphism group of G(for the definition, see below). The question whether Out_Col(G) is a p′-group naturally arises from the study of the normalizer problem for integral group rings, where p is a prime. In this article, some sufficient conditions for Out_Col(G) to be a p′-group are obtained. Our results generalize some well-known theorems.

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SHARP BOUNDS FOR NEUMAN-SÁNDOR MEAN IN TERMS OF THE CONVEX COMBINATION OF QUADRATIC AND FIRST SEIFFERT MEANS

褚玉明, 赵铁洪, 宋迎清

数学物理学报(英文版). 2014 (3): 797-806. DOI: 10.1016/S0252-9602(14)60050-3

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In this article, we prove that the double inequality
αP(a, b) + (1 − α)Q(a, b) < M(a, b) < βP(a, b) + (1 − β)Q(a, b)
holds for any a, b > 0 with a ≠b if and only if α ≥ 1/2 and β ≤ [π(√2 log(1 + √2) −1)]/[(√2π−2) log(1+√2)] = 0.3595 · · · , where M(a, b), Q(a, b), and P(a, b) are the Neuman-S´andor, quadratic, and first Seiffert means of a and b, respectively.

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A NOTE ON COMPLETE MANIFOLDS WITH FINITE VOLUME

邓洪存

数学物理学报(英文版). 2014 (3): 807-813. DOI: 10.1016/S0252-9602(14)60051-5

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In this article, we concern on complete manifolds with finite volume. We prove that under some assumptions about scalar curvature and the Yamabe constant, the manifolds must be compact, and we also give the diameter estimates in terms of the scalar curvature and the Yamabe constant.

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GENERALIZED DERIVATIONS ON PARABOLIC SUBALGEBRAS OF GENERAL LINEAR LIE ALGEBRAS

陈正新

数学物理学报(英文版). 2014 (3): 814-828. DOI: 10.1016/S0252-9602(14)60052-7

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Let P be a parabolic subalgebra of a general linear Lie algebra gl(n, F) over a field F, where n ≥ 3, F contains at least n different elements, and char(F) ≠ 2. In this article, we prove that generalized derivations, quasiderivations, and product zero derivations of P coincide, and any generalized derivation of P is a sum of an inner derivation, a central quasiderivation, and a scalar multiplication map of P. We also show that any commuting automorphism of P is a central automorphism, and any commuting derivation of P is a central derivation.

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CYCLIC AND NEGACYCLIC CODES OF LENGTH 2p^s OVER Fp^m + uFp^m

刘修生, 许小芳

数学物理学报(英文版). 2014 (3): 829-839. DOI: 10.1016/S0252-9602(14)60053-9

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In this article, we focus on cyclic and negacyclic codes of length 2p^s over the ring R = Fp^m+ uFp^m, where p is an odd prime. On the basis of the works of Dinh (in J.Algebra 324,940-950,2010), we use the Chinese Remainder Theorem to establish the alge-braic structure of cyclic and negacyclic codes of length 2p^sover the ring Fp^m +uFpm in terms of polynomial generators. Furthermore, we obtain the number of codewords in each of those cyclic and negacyclic codes.

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ON GROUND STATE SOLUTIONS FOR SUPERLINEAR DIRAC EQUATION

张健, 唐先华, 张文

数学物理学报(英文版). 2014 (3): 840-850. DOI: 10.1016/S0252-9602(14)60054-0

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This article is concerned with the nonlinear Dirac equations
-i∂_t φ= ich φ −mc²β φ + R φ(x, φ ) in R³.
Under suitable assumptions on the nonlinearity, we establish the existence of ground state solutions by the generalized Nehari manifold method developed recently by Szulkin andWeth.∑³_k=1α_k∂_k

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LOCAL WELL-POSEDNESS TO THE CAUCHY PROBLEM OF THE 3-D COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY

叶嵎林, 窦昌胜, 酒全森

数学物理学报(英文版). 2014 (3): 851-871. DOI: 10.1016/S0252-9602(14)60055-2

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In this article, we prove the local existence and uniqueness of the classical solution to the Cauchy problem of the 3-D compressible Navier-Stokes equations with large initial data and vacuum, if the shear viscosity μ is a positive constant and the bulk viscosity λ(ρ) = ρ^βwith β ≥0. Note that the initial data can be arbitrarily large to contain vacuum states.

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A POD REDUCED-ORDER SPDMFE EXTRAPOLATING ALGORITHM FOR HYPERBOLIC EQUATIONS

罗振东, 李宏

数学物理学报(英文版). 2014 (3): 872-890. DOI: 10.1016/S0252-9602(14)60056-4

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In this article, a proper orthogonal decomposition (POD) method is used to study a classical splitting positive definite mixed finite element (SPDMFE) formulation for second-order hyperbolic equations. A POD reduced-order SPDMFE extrapolating algorithm with lower dimensions and sufficiently high accuracy is established for second-order hyperbolic equations. The error estimates between the classical SPDMFE solutions and the reduced-order SPDMFE solutions obtained from the POD reduced-order SPDMFE extrapolating algorithm are provided. The implementation for solving the POD reduced-order SPDMFE extrapolating algorithm is given. Some numerical experiments are presented illustrating that the results of numerical computation are consistent with theoretical conclusions, thus validating that the POD reduced-order SPDMFE extrapolating algorithm is feasible and efficient for solving second-order hyperbolic equations.

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BOUNDEDNESS OF STEIN´S SQUARE FUNCTIONS ASSOCIATED TO OPERATORS ON HARDY SPACES

闫雪芳

数学物理学报(英文版). 2014 (3): 891-904. DOI: 10.1016/S0252-9602(14)60057-6

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Let (X, d, μ) be a metric measure space endowed with a metric d and a nonneg-ative Borel doubling measure μ. Let L be a second order non-negative self-adjoint operator on L²(X). Assume that the semigroup e−^tL generated by L satisfies the Davies-Gaffney estimates. Also, assume that L satisfies Plancherel type estimate. Under these conditions, we show that Stein´s square function G_δL) arising from Bochner-Riesz means associated to L is bounded from the Hardy spaces H^p_L(X) to L^p(X) for all 0 < p ≤1.

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A QUASILINEAR SINGULAR ELLIPTIC SYSTEM WITHOUT COOPERATIVE STRUCTURE

Dumitru MOTREANU, Abdelkrim MOUSSAOUI

数学物理学报(英文版). 2014 (3): 905-916. DOI: 10.1016/S0252-9602(14)60058-8

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In this article, we investigate the existence of positive solutions of a singular quasilinear elliptic system for which the cooperative structure is not required. The approach is based on the Schauder fixed point theorem combined with perturbation arguments that involve the singular terms.

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SPHERICAL SYMMETRIC SOLUTIONS FOR THE MOTION OF RELATIVISTIC MEMBRANES AND NULL MEMBRANES IN THE REISSNER-NORDSTRÖM SPACE-TIME

罗少盈, 刘琦

数学物理学报(英文版). 2014 (3): 917-931. DOI: 10.1016/S0252-9602(14)60059-X

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In this article, we concern the motion of relativistic membranes and null membranes in the Reissner-Nordstr¨om space-time. The equation of relativistic membranes moving in the Reissner-Nordstr¨om space-time is derived and some properties are discussed. Spherical symmetric solutions for the motion are illustrated and some interesting physical phenomena are discovered. The equations of the null membranes are derived and the exact solutions are also given. Spherical symmetric solutions for null membranes are just the two horizons of Reissner-Nordstr¨om space-time.

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ON A LEMMA OF BOWEN

李名田, 马际华

数学物理学报(英文版). 2014 (3): 932-940. DOI: 10.1016/S0252-9602(14)60060-6

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We are concerned with the sets of quasi generic points in finite symbolic space. We estimate the sizes of the sets by the Billingsley dimension defined by Gibbs measures. A dimension formula of such set is given, which generalizes Bowen´s result. An application is given to the level sets of Birkhoff average.

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BOUNDED TRAVELING WAVE SOLUTIONS OF VARIANT BOUSSINESQ EQUATION WITH A DISSIPATION TERM AND DISSIPATION EFFECT

张卫国, 刘强, 李正明, 李想

数学物理学报(英文版). 2014 (3): 941-959. DOI: 10.1016/S0252-9602(14)60061-8

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This article studies bounded traveling wave solutions of variant Boussinesq equa-tion with a dissipation term and dissipation effect on them. Firstly, we make qualitative analysis to the bounded traveling wave solutions for the above equation by the theory and method of planar dynamical systems, and obtain their existent conditions, number, and gen-eral shape. Secondly, we investigate the dissipation effect on the shape evolution of bounded traveling wave solutions. We find out a critical value r* which can characterize the scale of dissipation effect, and prove that the bounded traveling wave solutions appear as kink profile waves if |r| ≥ r*; while they appear as damped oscillatory waves if |r| < r*. We also obtain kink profile solitary wave solutions with and without dissipation effect. On the basis of the above discussion, we sensibly design the structure of the approximate damped oscillatory so-lutions according to the orbits evolution relation corresponding to the component u(ξ) in the global phase portraits, and then obtain the approximate solutions (u(ξ), H(ξ)). Furthermore, by using homogenization principle, we give their error estimates by establishing the integral equation which reflects the relation between exact and approximate solutions. Finally, we discuss the dissipation effect on the amplitude, frequency, and energy decay of the bounded traveling wave solutions.

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TWO-LEVEL MULTISCALE FINITE ELEMENT METHODS FOR THE STEADY NAVIER-STOKES PROBLEM

文娟, 何银年, 王学敏, 霍米会

数学物理学报(英文版). 2014 (3): 960-972. DOI: 10.1016/S0252-9602(14)60062-X

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In this article, on the basis of two-level discretizations and multiscale finite el-ement method, two kinds of finite element algorithms for steady Navier-Stokes problem are presented and discussed. The main technique is first to use a standard finite element dis-cretization on a coarse mesh to approximate low frequencies, then to apply the simple and Newton scheme to linearize discretizations on a fine grid. At this process, multiscale finite element method as a stabilized method deals with the lowest equal-order finite element pairs not satisfying the inf-sup condition. Under the uniqueness condition, error analyses for both algorithms are given. Numerical results are reported to demonstrate the effectiveness of the simple and Newton scheme.

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