数学物理学报(英文版)

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INVERSE SCATTERING BY AN INHOMOGENEOUS PENETRABLE OBSTACLE IN A PIECEWISE HOMOGENEOUS MEDIUM

刘晓东, 张波

数学物理学报(英文版). 2012 (4): 1281-1297. DOI: 10.1016/S0252-9602(12)60099-X

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This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is first established by using the in-tegral equation method. We then proceed to establish two tools that play important roles for the inverse problem: one is a mixed reciprocity relation and the other is a priori esti-mates of the solution on some part of the interfaces between the layered media. For the inverse problem, we prove in this paper that both the penetrable interfaces and the possible inside inhomogeneity can be uniquely determined from a knowledge of the far field pattern for incident plane waves.

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LOCAL EXISTENCE OF SOLUTION TO FREE BOUNDARY VALUE PROBLEM FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS

刘健

数学物理学报(英文版). 2012 (4): 1298-1320. DOI: 10.1016/S0252-9602(12)60100-3

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This paper is concerned with the free boundary value problem for multi-dimensional Navier-Stokes equations with density-dependent viscosity where the flow den-sity vanishes continuously across the free boundary. Local (in time) existence of a weak solution is established; in particular, the density is positive and the solution is regular away from the free boundary.

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GENERAL DECAY FOR A QUASILINEAR SYSTEM OF VISCOELASTIC EQUATIONS WITH NONLINEAR DAMPING

Jong Yeoul Park, Sun Hye Park

数学物理学报(英文版). 2012 (4): 1321-1332. DOI: 10.1016/S0252-9602(12)60101-5

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In this paper, we consider a system of coupled quasilinear viscoelastic equa-tions with nonlinear damping. We use the perturbed energy method to show the general decay rate estimates of energy of solutions, which extends some existing results concerning a general decay for a single equation to the case of system, and a nonlinear system of viscoelastic wave equations to a quasilinear system.

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ON THE GENERALIZATIONS OF DENJOY-WOLFF THEOREM

徐丽芳, 杨欢欢

数学物理学报(英文版). 2012 (4): 1333-1337. DOI: 10.1016/S0252-9602(12)60102-7

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We consider generalizations of Denjoy-Wolff theorem on strongly pseudo-convex domains. Beardon [3] gave a general Denjoy-Wolff theorem in hyperbolic domain in the complex plane. Our main results are generalizations of Beardon's result in a higher dimensional setting.

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PULLBACK ATTRACTORS FOR THE NON-AUTONOMOUS BENJAMIN-BONA-MAHONY EQUATIONS IN H²

秦玉明, 杨新光, 刘欣

数学物理学报(英文版). 2012 (4): 1338-1348. DOI: 10.1016/S0252-9602(12)60103-9

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In this paper, we prove the existence of the pullback attractor for the non-autonomous Benjamin-Bona-Mahony equations in H² by establishing the pullback uni-formly asymptotical compactness.

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LOWER INEQUALITIES OF HEAT SEMIGROUPS BY USING PARABOLIC MAXIMUM PRINCIPLE

胡二彦

数学物理学报(英文版). 2012 (4): 1349-1364. DOI: 10.1016/S0252-9602(12)60104-0

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Using parabolic maximum principle, we apply the analytic method to obtain lower comparison inequalities for non-negative weak supersolutions of the heat equation associated with a regular strongly ρ-local Dirichlet form on the abstract metric measure space. As an application, we obtain lower estimates for heat kernels on some Riemannian manifolds.

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GLOBAL ATTRACTOR FOR A DENSITY-DEPENDENT SENSITIVITY CHEMOTAXIS MODEL

陈学勇, 刘伟安

数学物理学报(英文版). 2012 (4): 1365-1375. DOI: 10.1016/S0252-9602(12)60105-2

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In this paper, a chemotaxis model with reproduction term in a bounded do-main Ω( Rⁿ is discussed. The existence of a global-in-time solution and a global attractor for this model are obtained.

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ON CERTAIN CLASS OF MEROMORPHIC FUNCTIONS WITH POSITIVE COEFFICIENTS

J. DZIOK, G. MURUGISUNDARAMOORTHY, J. SOKóL

数学物理学报(英文版). 2012 (4): 1376-1390. DOI: 10.1016/S0252-9602(12)60106-4

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In the present investigation we define a new class of meromorphic functions on the punctured unit disk Δ* := {z ∈C : 0 < |z| < 1} by making use of the generalized Dziok–Srivastava operator H^l_m[α₁]. Coefficient inequalities, growth and distortion inequal-ities, as well as closure results are obtained. We also establish some results concerning the partial sums of meromorphic functions and neighborhood results for functions in new class.

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ELEMENTARY BIFURCATIONS FOR A SIMPLE DYNAMICAL SYSTEM UNDER NON-GAUSSIAN LÉVY NOISES

陈慧琴, 段金桥, 张诚坚

数学物理学报(英文版). 2012 (4): 1391-1398. DOI: 10.1016/S0252-9602(12)60107-6

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Nonlinear dynamical systems are sometimes under the influence of random fluctuations. It is desirable to examine possible bifurcations for stochastic dynamical sys-tems when a parameter varies.
A computational analysis is conducted to investigate bifurcations of a simple dynamical system under non-Gaussian α-stable L´evy motions, by examining the changes in station-ary probability density functions for the solution orbits of this stochastic system. The
stationary probability density functions are obtained by solving a nonlocal Fokker-Planck equation numerically. This allows numerically investigating phenomenological bifurcation, or P-bifurcation, for stochastic differential equations with non-Gaussian L´evy noises.

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ON A CLASS OF ANALYTIC FUNCTIONS RELATED TO CONIC DOMAINS AND ASSOCIATED WITH CARLSON-SHAFFER OPERATOR

S. HUSSAIN, J. SOKóL

数学物理学报(英文版). 2012 (4): 1399-1407. DOI: 10.1016/S0252-9602(12)60108-8

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Making use of the Carlson–Shaffer convolution operator, we introduce and study a new class of analytic functions related to conic domains. The main object of this paper is to investigate inclusion relations, coefficient bound for this class. We also show that this class is closed under convolution with a convex function. Some applications are also discussed.

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POSITIVE UPPER DENSITY POINTS AND CHAOS

尹建东, 周作领

数学物理学报(英文版). 2012 (4): 1408-1414. DOI: 10.1016/S0252-9602(12)60109-X

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In this work, we mainly investigate the problem of complexity for a topologi-cally dynamical system (X, f). We prove that f has a full measure center if there exists a countable base {U_i}^∞_i=0 of X satisfying that, for any i, there is y in X such that N(y,U_i) is a positive Banach upper density set. Moreover, we consider the chaotic property of (X, f). We show that such a system is chaotic in the sense of Takens-Ruelle if it is transitive but not minimal.

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A CLASS OF COMPACTLY SUPPORTED ORTHOGONAL SYMMETRIC COMPLEX WAVELETS WITH DILATION FACTOR 3

杨守志, 沈延锋, 李尤发

数学物理学报(英文版). 2012 (4): 1415-1425. DOI: 10.1016/S0252-9602(12)60110-6

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When approximation order is an odd positive integer, a simple method is given to construct compactly supported orthogonal symmetric complex scaling function with dilation factor 3. Two corresponding orthogonal wavelets, one is symmetric and the other is antisymmetric about origin, are constructed explicitly. Additionally, when approximation order is an even integer 2, we also give a method to construct compactly supported orthogonal symmetric complex wavelets. In the end, there are several examples that illustrate the corresponding results.

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ANTI-PERIODIC SOLUTIONS FOR DIFFERENTIAL INCLUSIONS IN BANACH SPACES AND THEIR APPLICATIONS

刘贵方, 刘益良

数学物理学报(英文版). 2012 (4): 1426-1434. DOI: 10.1016/S0252-9602(12)60111-8

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We deal with anti-periodic problems for differential inclusions with nonmono-tone perturbations. The main tools in our study are the maximal monotone property of the derivative operator with anti-periodic conditions and the theory of pseudomonotone perturbations of maximal monotone mappings. We then apply our results to evolution hemivariational inequalities and parabolic equations with nonmonotone discontinuities, which generalize and extend previously known theorems.

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ZEROS OF BRAUER CHARACTERS

王慧群, 陈晓友, 曾吉文

数学物理学报(英文版). 2012 (4): 1435-1440. DOI: 10.1016/S0252-9602(12)60112-X

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The authors obtain a sufficient condition to determine whether an element is a vanishing regular element of some Brauer character. More precisely, let G be a finite group and p be a fixed prime, and H = G'′O^p' (G); if g ∈ G⁰− H⁰ with o(gH) coprime to the number of irreducible p-Brauer characters of G, then there always exists a nonlinear irreducible p-Brauer character which vanishes on g. The authors also show in this note that the sums of certain irreducible p-Brauer characters take the value zero on every element of G⁰− H⁰.

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ON THE NEVANLINNA DIRECTION OF ALGEBROID FUNCTIONS

张洪申, 孙道椿

数学物理学报(英文版). 2012 (4): 1441-1448. DOI: 10.1016/S0252-9602(12)60113-1

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In this paper, we prove that for an algebroid function w(z), the singular direction arg z = φ₀, satisfying that for arbitrary ε(0 < ε < π/2 ) and any given a α ∈C , lim _r→∞n(r,φ₀−ε, φ₀+ε, w=a)/log r= +∞ holds with at most 2v possible exceptional values of a, is the Nevanlinna direction of w(z).

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REPETITIVE CLUSTER-TILTED ALGEBRAS

张顺华, 张跃辉

数学物理学报(英文版). 2012 (4): 1449-1454. DOI: 10.1016/S0252-9602(12)60114-3

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Let H be a finite-dimensional hereditary algebra over an algebraically closed field k and C_F^m be the repetitive cluster category of H with m ≥1. We investigate the properties of cluster tilting objects in CFm and the structure of repetitive cluster-tilted algebras. Moreover, we generalize Theorem 4.2 in [12] (Buan A, Marsh R, Reiten I. Cluster-tilted algebra, Trans. Amer. Math. Soc., 359(1)(2007), 323-332.) to the situation of CFm, and prove that the tilting graph KCFm of CFm is connected.

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INITIAL BOUNDARY VALUE PROBLEM FOR MODIFIED ZAKHAROV EQUATIONS

游淑军, 郭柏灵, 宁效琦

数学物理学报(英文版). 2012 (4): 1455-1466. DOI: 10.1016/S0252-9602(12)60115-5

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In this paper the authors consider the existence and uniqueness of the solution to the initial boundary value problem for a class of modified Zakharov equations, prove the global existence of the solution to the problem by a priori integral estimates and Galerkin method.

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GLOBAL EXISTENCE OF STRONG SOLUTIONS OF NAVIER-STOKES EQUATIONS WITH NON-NEWTONIAN POTENTIAL FOR ONE-DIMENSIONAL ISENTROPIC#br# COMPRESSIBLE FLUIDS

袁洪君, 柳洪志, 乔节增, 李梵蓓

数学物理学报(英文版). 2012 (4): 1467-1486. DOI: 10.1016/S0252-9602(12)60116-7

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The aims of this paper are to discuss global existence and uniqueness of strong solution for a class of isentropic compressible navier-Stokes equations with non-Newtonian in one-dimensional bounded intervals. We prove two global existence results on strong solutions of isentropic compressible Navier-Stokes equations. The first result shows only the existence. And the second one shows the existence and uniqueness result based on the first result, but the uniqueness requires some compatibility condition.

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ON THE LOWER BOUND FOR A CLASS OF HARMONIC FUNCTIONS IN THE HALF SPACE

张艳慧, 邓冠铁, 高洁欣

数学物理学报(英文版). 2012 (4): 1487-1494. DOI: 10.1016/S0252-9602(12)60117-9

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The main objective is to derive a lower bound from an upper one for harmonic functions in the half space, which extends a result of B. Y. Levin from dimension 2 to dimension n ≥ 2. To this end, we first generalize the Carleman's formula for harmonic functions in the half plane to higher dimensional half space, and then establish a Nevanlinna's representation for harmonic functions in the half sphere by using H¨ormander's theorem.

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ESTIMATES OF N-FUNCTION AND m-FUNCTION OF MEROMORPHIC SOLUTIONS OF SYSTEMS OF COMPLEX DIFFERENCE EQUATIONS

高凌云

数学物理学报(英文版). 2012 (4): 1495-1502. DOI: 10.1016/S0252-9602(12)60118-0

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We apply Nevanlinna theory of the value distribution of meromorphic func-tions to study the properties of Nevanlinna counting function and proximity function of
meromorphic solutions of a type of systems of complex difference equations. Our results can give estimates on the proximity function and the counting function of solutions of systems of difference equations. This implies that solutions have a relatively large number of poles. It extend some result concerning difference equations to the systems of difference equations.

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NORMAL FAMILIES OF MEROMORPHIC FUNCTIONS SHARING A HOLOMORPHIC FUNCTION AND THE CONVERSE OF THE BLOCH PRINCIPLE

姜云波, 高宗升

数学物理学报(英文版). 2012 (4): 1503-1512. DOI: 10.1016/S0252-9602(12)60119-2

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In this paper, we investigate normal families of meromorphic functions, prove some theorems of normal families sharing a holomorphic function, and give a counterex-
ample to the converse of the Bloch principle based on the theorems.

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SOME TOPOLOGICAL AND GEOMETRICAL PROPERTIES OF THE SEQUENCE SPACE e^r(u, p)

Serkan Demiriz, Celal Cakan

数学物理学报(英文版). 2012 (4): 1513-1528. DOI: 10.1016/S0252-9602(12)60120-9

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In this paper, we introduce the sequence space e^r(u, p) and investigate its some topological and geometrical properties such as basis, α-, β-,γ- duals and the uniform
Opial property.

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WEIGHTED ESTIMATES WITH GENERAL WEIGHTS FOR MULTILINEAR CALDER´|ON-ZYGMUND OPERATORS

胡国恩

数学物理学报(英文版). 2012 (4): 1529-1544. DOI: 10.1016/S0252-9602(12)60121-0

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In this paper, some weighted estimates with general weights are established for the m-linear Calder´on-Zygmund operator and the corresponding maximal operator. It is proved that, if p₁, · · · , p_m ∈ [1,∞] and p ∈ (0,∞) with 1/p =∑^m_k₌₁1/p_k, then for any weight w, integer l with 1 ≤ l ≤ m, these operators are bounded from L^p¹ (Rⁿ, M_Bw) ×· · ·×L^pl(Rⁿ, M_Bw)×L^pl⁺¹ (Rⁿ, Mw)×· · ·×L^pm(Rⁿ, Mw) to L^p^,∞(Rⁿ, w) or Lp(Rn,w), where B is a Young function and MB is the maximal operator associated with B.

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NONTRIVIAL SOLUTIONS FOR ASYMPTOTICALLY LINEAR HAMILTONIAN SYSTEMS WITH LAGRANGIAN BOUNDARY CONDITIONS

刘春根, 张清业

数学物理学报(英文版). 2012 (4): 1545-1558. DOI: 10.1016/S0252-9602(12)60122-2

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In this article, we study the existence of nontrivial solutions for a class of asymptotically linear Hamiltonian systems with Lagrangian boundary conditions by the Galerkin approximation methods and the L-index theory developed by the first author.

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EXISTENCE OF SOLUTIONS FOR NON-PERIODIC SUPERLINEAR SCHRÖDINGER EQUATIONS WITHOUT (AR) CONDITION

万莉莉, 唐春雷

数学物理学报(英文版). 2012 (4): 1559-1570. DOI: 10.1016/S0252-9602(12)60123-4

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The existence of solutions is obtained for a class of the non-periodic Schr¨odinger equation −Δu + V (x)u = f(x, u), x ∈ R^N, by the generalized mountain pass theorem, where V is large at infinity and f is superlinear as |u| →∞.

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A NEW CLASS OF BILEVEL GENERALIZED MIXED EQUILIBRIUM PROBLEMS IN BANACH SPACES

丁协平

数学物理学报(英文版). 2012 (4): 1571-1583. DOI: 10.1016/S0252-9602(12)60124-6

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A new class of bilevel generalized mixed equilibrium problems involving set-valued mappings is introduced and studied in a real Banach space. By using the auxiliary principle technique, new iterative algorithms for solving the generalized mixed equilibrium problems and bilevel generalized mixed equilibrium problems involving set-valued map-pings are suggested and analyzed. Existence of solutions and strong convergence of the iterative sequences generated by the algorithms are proved under quite mild conditions. The behavior of the solution set of the generalized mixed equilibrium problems and bilevel generalized mixed equilibrium problems is also discussed. These results are new and gen-eralize some recent results in this field.

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ON CRITICAL CASES OF SOBOLEV'S INEQUALITIES FOR HEISENBERG GROUPS

杨乔华

数学物理学报(英文版). 2012 (4): 1584-1592. DOI: 10.1016/S0252-9602(12)60125-8

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We prove some Trudinger-type inequalities and Brezis-Gallouet-Wainger in-equality on the Heisenberg group, extending to this context the Euclidean results by T. Ozawa.

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UNIQUENESS RESULTS OF MEROMORPHIC FUNCTIONS WHOSE DERIVATIVES SHARE FOUR SMALL FUNCTIONS

李效敏, 仪洪勋, 胡海燕

数学物理学报(英文版). 2012 (4): 1593-1606. DOI: 10.1016/S0252-9602(12)60126-X

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We prove an oscillation theorem of two meromorphic functions whose deriva-tives share four values IM. From this we obtain some uniqueness theorems, which improve the corresponding results given by Yang [16] and Qiu [10], and supplement results given by
Nevanlinna [9] and Gundersen [3, 4]. Some examples are provided to show that the results in this paper are best possible.

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APPROXIMATION OF COMMON SOLUTIONS OF VARIATIONAL INEQUALITIES VIA STRICT PSEUDOCONTRACTIONS

Sun Young Cho, Shin Min Kang

数学物理学报(英文版). 2012 (4): 1607-1618. DOI: 10.1016/S0252-9602(12)60127-1

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In this paper, a convex feasibility problem is considered. We construct an iter-ative method to approximate a common element of the solution set of classical variational inequalities and of the fixed point set of a strict pseudocontraction. Strong convergence theorems for the common element are established in the framework of Hilbert spaces.

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THE OPTIMAL GENERALIZED LOGARITHMIC MEAN BOUNDS FOR SEIFFERT'S MEAN

褚玉明, 王淼坤, 王根娣

数学物理学报(英文版). 2012 (4): 1619-1626. DOI: 10.1016/S0252-9602(12)60128-3

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For p ∈ R, the generalized logarithmic mean L_p(a, b) and Seiffert's mean T(a, b) of two positive real numbers a and b are defined in (1.1) and (1.2) below respectively. In this paper, we find the greatest p and least q such that the double-inequality L_p(a, b) <T(a, b) < L_q(a, b) holds for all a, b > 0 and a ≠ b.

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DOUBLE Φ-INEQUALITIES FOR BANACH-SPACE-VALUED MARTINGALES

王迎占, 张超, 侯友良

数学物理学报(英文版). 2012 (4): 1627-1636. DOI: 10.1016/S0252-9602(12)60129-5

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Let B be a Banach space, Φ₁, Φ₂ be two generalized convex Φ-functions and ψ₁, ψ₂ the Young complementary functions of Φ₁, Φ₂respectively with
∫^t_t₀ψ₂(s)/s ds ≤ c₀ ψ₁(c₀t) (t > t0)
for some constants c₀ > 0 and t₀ > 0, where ψ₁ and ψ₂ are the left-continuous derivative functions of ψ₁ and ψ₂, respectively. We claim that: (i) If B is isomorphic to a p-uniformly smooth space (or q-uniformly convex space, respectively), then there exists a constant c > 0 such that for any B-valued martingale f = (f_n)_n≥0,

||f *||_Φ1 ≤ c||S^(p)(f)||_Φ2 (or ||S^(q)(f)||_Φ1 ≤ c||f *||_Φ2 , respectively),

where f * and S^(p)(f) are the maximal function and the p-variation function of f respec-tively; (ii) If B is a UMD space, Tvf is the martingale transform of f with respect to v = (v_n)_n≥0 (v* ≤ 1), then ||(T_vf )||_Φ1 ≤ c||f *||_Φ2 .

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NON-UNIQUENESS OF THE RECONSTRUCTION FOR CONNECTED AND SIMPLY CONNECTED SETS IN THE PLANE BY THEIR FIXED#br# FINITE PROJECTIONS

Takashi Takiguchi

数学物理学报(英文版). 2012 (4): 1637-1646. DOI: 10.1016/S0252-9602(12)60130-1

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We discuss a problem to reconstruct the measurable sets in the plane from their fixed finite projections. In the main theorem, we construct an example of connected and simply connected polygons which are not uniquely reconstructed by their fixed finite projections. We also make a comparison between our main theorem and the known results on this problem.

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MUSIC ALGORITHM FOR LOCATING POINT-LIKE SCATTERERS CONTAINED IN A SAMPLE ON FLAT SUBSTRATE

董和平, 马富明, 张德悦

数学物理学报(英文版). 2012 (4): 1647-1661. DOI: 10.1016/S0252-9602(12)60131-3

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In this paper, we consider a MUSIC algorithm for locating point-like scatterers contained in a sample on flat substrate. Based on an asymptotic expansion of the scattering amplitude proposed by Ammari et al., the reconstruction problem can be reduced to a calculation of Green function corresponding to the background medium. In addition, we use an explicit formulation of Green function in the MUSIC algorithm to simplify the calculation when the cross-section of sample is a half-disc. Numerical experiments are included to demonstrate the feasibility of this method.

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T- AND HAYMAN T-POINTS OF MEROMORPHIC FUNCTIONS FOR SMALL FUNCTIONS IN THE UNIT DISK

吴楠, 郑建华

数学物理学报(英文版). 2012 (4): 1662-1674. DOI: 10.1016/S0252-9602(12)60132-5

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In this article, we consider the singular points of meromorphic functions in the unit disk. We prove the second fundamental theorem for the Ahlfors-Shimizu's charac-teristic in the unit disk in terms of Nevanlinna theory in the angular domains, and obtain the existence of T-points and Hayman T-points dealing with small functions as target.

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DISTORTION THEOREMS FOR SUBCLASSES OF STARLIKE MAPPINGS ALONG A UNIT DIRECTION IN Cⁿ

卢金, 刘太顺, 王建飞

数学物理学报(英文版). 2012 (4): 1675-1680. DOI: 10.1016/S0252-9602(12)60133-7

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In this paper, we obtain a distortion theorem of Jacobian matrix for biholo-morphic subclasses of starlike mappings along a unit direction on the unit polydisc. These results extend the classical distortion theorem of starlike mappings to higher dimensions. We then give an upper bound estimate for biholomorphic subclasses of starlike mappings along a unit direction in a complex Banach space.

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