数学物理学报(英文版)

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STRONG CONVERGENCE RATES OF SEVERAL ESTIMATORS IN SEMIPARAMETRIC VARYING-COEFFICIENT PARTIALLY LINEAR MODELS

周勇, 尤进红, 王晓婧

数学物理学报(英文版). 2009 (5): 1113-1127. DOI: 10.1016/S0252-9602(09)60090-4

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This article is concerned with the estimating problem of semiparametric varying-coefficient partially linear regression models. By combining the local polynomial and least squares procedures Fan and Huang (2005) proposed a profile least squares estimator for the parametric component and established its asymptotic normality. We further show that the profile least squares estimator can achieve the law of iterated logarithm. Moreover, we study the estimators of the functions characterizing the non-linear part as well as the error variance. The strong convergence rate and the law of iterated logarithm are derived for them, respectively.

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METHOD OF CENTERS ALGORITHM FOR MULTI-OBJECTIVE PROGRAMMING PROBLEMS

Tarek Emam

数学物理学报(英文版). 2009 (5): 1128-1142. DOI: 10.1016/S0252-9602(09)60091-6

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In this paper, we consider a method of centers for solving multi-objective programming problems, where the objective functions involved are concave functions and the set of feasible points is convex. The algorithm is defined so that the sub-problems that must be solved during its execution may be solved by finite-step procedures. Conditions are given under which the algorithm generates sequences of feasible points and constraint multiplier vectors that have accumulation points satisfying the KKT conditions. Finally, we establish convergence of the proposed method of centers algorithm for solving multi-objective programming problems.

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BRUNN-MINKOWSKI INEQUALITY FOR VARIATIONAL FUNCTIONAL INVOLVING THE P-LAPLACIAN OPERATOR

胡华香, 周树清

数学物理学报(英文版). 2009 (5): 1143-1154. DOI: 10.1016/S0252-9602(09)60092-8

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In this paper, we investigate the following elliptic problem involving the P-Laplacian
(P) {

-Div(| u|^p-2 u) =|u|^q-1u  in  K,
u>0                                    in  K,
  u=0                                    on  ∂K,

where p>1, 0<q<p-1, K     Rⁿ with K ∈ Kⁿ, and prove that the energy integral of the problem (P) satisfies a Brunn-Minkowski type inequality.

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LOCAL TIME ANALYSIS OF ADDITIVE L\'EVY PROCESSES WITH DIFFERENT LÉVY EXPONENTS

钟玉泉

数学物理学报(英文版). 2009 (5): 1155-1164. DOI: 10.1016/S0252-9602(09)60093-X

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Let X₁,…,X_N be independent, classical Lévy processes on R^d with Lévy exponents Ψ₁,…,Ψ_N, respectively. The
corresponding additive Lévy process is defined as the following $N$-parameter random field on R^d, X(t)=X₁(t₁)+…+X_N(t_N), ∨t ∈ R^N+. Under mild regularity conditions on the Ψ_i's, we derive estimate for the local and uniform moduli of continuity of local times of X={X(t);t ∈ R^N+}.

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EXISTENCE OF GLOBAL ATTRACTORS FOR A NONLINEAR EVOLUTION EQUATION IN SOBOLEV SPACE H^k

张引娣, 李开泰

数学物理学报(英文版). 2009 (5): 1165-1172. DOI: 10.1016/S0252-9602(09)60094-1

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In this paper we prove that the initial-boundary value problem for the nonlinear evolution equation u_t=Δ_u+λ_u-u³ possesses a global attractor in Sobolev space H^k for all k≥0, which attracts any bounded domain of H^k(Ω) in the H^k-norm. This result is established by using an iteration technique and regularity estimates for linear semigroup of operator, which extends the classical result from the case k∈ [0,1] to the case k∈ [0, ∞).

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ON THE CONVERGENCE OF CIRCLE PACKINGS TO THE QUASICONFORMAL MAP

黄小军, 沈良

数学物理学报(英文版). 2009 (5): 1173-1181. DOI: 10.1016/S0252-9602(09)60095-3

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Rodin and Sullivan (1987) proved Thurston's conjecture that a scheme based on the Circle Packing Theorem converges to the Riemann mapping, thereby proved a refreshing geometric view of the Riemann Mapping Theorem. Naturally, we consider to use the ellipses to pack the bounded simply connected domain and obtain similarly a sequence simplicial homeomorphism between the ellipse packing and the circle packing. In this paper, we prove that these simplicial homeomorphism approximate a quasiconformal mapping from the bounded
simply connected domain onto the unit disk with the modulus of their complex dilatations tending to 1 almost everywhere in the domain when the ratio of the longer axis and shorter axis of the ellipse tending to ∞.

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NEW STRUCTURES FOR NON-SELFSIMILAR SOLUTIONS OF MULTI-DIMENSIONAL CONSERVATION LAWS

杨小舟, 魏涛

数学物理学报(英文版). 2009 (5): 1182-1202. DOI: 10.1016/S0252-9602(09)60096-5

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In this article, we get non-selfsimilar elementary waves of the conservation laws in another kind of view, which is different from the usual self-similar transformation. The solution has different global structure.

This article is divided into three parts. The first part is introduction. In the second part, we discuss non-selfsimilar elementary waves and their interactions of a class of two-dimensional conservation laws. In this case, we consider the case that the initial discontinuity is parabola with u₊>0, while explicit non-selfsimilar rarefaction wave can be obtained. In the second part, we consider the solution structure of case u₊<0.

The new solution structures are obtained by the interactions between different elementary waves, and will continue to interact with other states. Global solutions would be very different from the situation of one dimension.

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GLOBAL EXISTENCE FOR QUASILINEAR |WAVE EQUATION WITH A LOCALIZED WEAKLY NONLINEAR DISSIPATION IN EXTERIOR DOMAINS

Jeong Ja Bae

数学物理学报(英文版). 2009 (5): 1203-1215. DOI: 10.1016/S0252-9602(09)60097-7

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It is proved that the global existence for the nonhomogeneous quasilinear wave equation with a localized weakly nonlinear dissipation in exterior domains.

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A NOTE ON LARGE TIME BEHAVIOUR OF SOLUTIONS FOR VISCOUS CAHN-HILLIARD EQUATION

刘长春, 周娟, 尹景学

数学物理学报(英文版). 2009 (5): 1216-1224. DOI: 10.1016/S0252-9602(09)60098-9

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This article is devoted to the discussion of large time behaviour of solutions for viscous Cahn-Hilliard equation with spatial dimension n ≤ 5. Some results on global existence of weak solutions for small initial value and
blow-up of solutions for any nontrivial initial value are established.

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DIRICHLET PROBLEMS FOR STATIONARY VON NEUMANN-LANDAU WAVE EQUATIONS

陈泽乾

数学物理学报(英文版). 2009 (5): 1225-1232. DOI: 10.1016/S0252-9602(09)60099-0

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In this article, we are concerned with the Dirichlet problem of the stationary von Neumann--Landau wave equation: { ( -Δ_x + Δ_y ) Φ (x, y) = 0, x, y ∈ Ω
Φ | _∂Ω×∂Ω = f,
where Ω is a bounded domain in Rⁿ. By introducing anti-inner product spaces, we show the existence and uniqueness of the generalized solution for the above Dirichlet problem by functional-analytic methods.

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BOUNDARY LAYER SOLUTION FOR p-SYSTEM WITH ARTIFICIAL VISCOSITY

秦晓红

数学物理学报(英文版). 2009 (5): 1233-1240. DOI: 10.1016/S0252-9602(09)60100-4

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An initial-boundary values problem in the half space (0, ∞) for p-system with artificial viscosity is investigated. It is shown that there exists a boundary layer solution. It is further proved that the boundary layer solution is nonlinear stable with arbitrarily large perturbation. The proof is given by an elementary energy method.

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POINTWISE CONVERGENCE FOR EXPANSIONS IN SPHERICAL MONOGENICS

费铭岗, 钱涛

数学物理学报(英文版). 2009 (5): 1241-1250. DOI: 10.1016/S0252-9602(09)60101-6

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We offer a new approach to deal with the pointwise convergence of Fourier-Laplace series on the unit sphere
of even-dimensional Euclidean spaces. By using spherical monogenics defined through the generalized Cauchy-Riemann operator, we obtain the spherical monogenic expansions of square integrable functions on the unit sphere. Based on the generalization of Fueter's theorem inducing monogenic functions from holomorphic functions in the complex plane and the classical Carleson's theorem, a pointwise convergence theorem on the new expansion is proved. The result is a generalization of Carleson's theorem to the higher dimensional
Euclidean spaces. The approach is simpler than those by using special functions, which may have the advantage to induce the singular integral approach for pointwise convergence problems on the spheres.

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MULTIRESOLUTION ANALYSIS, SELF-SIMILAR TILINGS AND HAAR WAVELETS ON THE HEISENBERG GROUP

刘和平, 刘宇, 王海辉

数学物理学报(英文版). 2009 (5): 1251-1266. DOI: 10.1016/S0252-9602(09)60102-8

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In this article, the properties of multiresolution analysis and self-similar tilings on the Heisenberg group are
studied. Moreover, we establish a theory to construct an orthonormal Haar wavelet base in $L^2({\mathbb H}^d)$ by using self-similar tilings for the acceptable dilations on the Heisenberg group.

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SOLVING COLORED YANG-BAXTER EQUATION BY WU'S METHOD

任新安, 王世坤, 吴可

数学物理学报(英文版). 2009 (5): 1267-1294. DOI: 10.1016/S0252-9602(09)60103-X

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In this article, we discuss nonsymmetric solutions of the colored Yang-Baxter equation dependent on spectral as well as colored parameters and give all seven-vertex solutions by Wu's method. It is also proved that the solutions are composed of six groups of basic solutions up to five solution transformations. Moreover, all solutions can be classified into two categories called Baxter type and free-fermion type.

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GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR FOR AN 1-D COMPRESSIBLE ENERGY TRANSPORT MODEL

黎勇

数学物理学报(英文版). 2009 (5): 1295-1308. DOI: 10.1016/S0252-9602(09)60104-1

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In this article, the global existence and the large time behavior of smooth solutions to the initial boundary value problem for a degenerate compressible energy transport model are established.

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UNIQUENESS, ERGODICITY AND UNIDIMENSIONALITY OF INVARIANT MEASURES UNDER A MARKOV OPERATOR

唐军民, 张继宏, 章雄鹰

数学物理学报(英文版). 2009 (5): 1309-1322. DOI: 10.1016/S0252-9602(09)60105-3

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Let X be a compact metric space and C(X) be the space of all continuous functions on X. In this article, the authors
consider the Markov operator T:C(X)^N → C(X)^N defined by
Tf = (∑_j=1^Np_1jf_j ο w_1j, …, ∑_j=1^Np_Njf_jο w_Nj)
for any f =(f ₁, f ₂, …, f _N), where (p _ij) is a N × N transition probability matrix and {w _ij} is an family of continuous transformations on X. The authors study the uniqueness, ergodicity and unidimensionality of T*-invariant measures where T* is the adjoint operator of T.

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MULTIPLE SOLUTIONS FOR THE SCHRÖDINGER EQUATION WITH MAGNETIC FIELD

彭超权, 杨健夫

数学物理学报(英文版). 2009 (5): 1323-1340. DOI: 10.1016/S0252-9602(09)60106-5

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The authors consider the semilinear Schrödinger equation
-Δ_Au+ V_λ(x)u=Q(x)|u|^γ-2u in R^N,
where 1< γ < 2* and γ≠ 2, V_λ= V⁺ - λV^-. Exploiting the relation between the Nehari manifold and fibrering maps, the existence of nontrivial solutions for the problem is discussed.

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A NOTE ON CONVOLUTION-TYPE CALDERÓN-ZYGMUND OPERATORS

杨占英, 杨奇祥

数学物理学报(英文版). 2009 (5): 1341-1350. DOI: 10.1016/S0252-9602(09)60107-7

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For convolution-type Calderón-Zygmund operators, by the boundedness on Besov spaces and Hardy spaces, applying interpolation theory and duality, it is known that Hörmander condition can ensure the boundedness on
Triebel-Lizorkin spaces F_p^0,q(1< p, q < ∞) and on a party of endpoint spaces F₁^0,q(1 ≤ q ≤ 2), but this idea is invalid for endpoint Triebel-Lizorkin spaces F₁^0,q(2 < q ∞). In this article, the authors apply wavelets and interpolation theory to establish the boundedness on F₁^0,q(2 < q ≤ ∞) under an integrable condition which
approaches Hörmander condition infinitely.

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CONVERGENCE RATES FOR THE COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH GENERAL FORCE

钱建贞, 尹慧

数学物理学报(英文版). 2009 (5): 1351-1365. DOI: 10.1016/S0252-9602(09)60108-9

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For the viscous and heat-conductive fluids governed by the compressible Navier-Stokes equations with external force of general form in R³, there exist nontrivial stationary solutions provided the external forces are small in suitable norms, which was studied in article [15], and there we also proved the global in time stability of the stationary solutions with respect to initial data in H³-framework. In this article, the authors investigate the rates of
convergence of nonstationary solutions to the corresponding stationary solutions when the initial data are small in H³ and bounded in L_6/5.

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GENERALIZATIONS AND CARTESIAN CLOSED SUBCATEGORIES OF SEMICONTINUOUS LATTICES

李庆国, 伍秀华

数学物理学报(英文版). 2009 (5): 1366-1374. DOI: 10.1016/S0252-9602(09)60109-0

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In this article, the authors mainly study how to obtain new semicontinuous lattices from the given semicontinuous lattices and discuss the conditions under which the image of a semicontinuous projection operator is also
semicontinuous. Moreover, the authors investigate the relation between semicontinuous lattices and completely distributive lattices. Finally, it is proved that the strongly semicontinuous lattice category is a Cartesian closed category.

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THE APPLICATION OF THE KINETIC FORMULATION TO A SYSTEM OF QUADRATIC FLUX

成志新

数学物理学报(英文版). 2009 (5): 1375-1382. DOI: 10.1016/S0252-9602(09)60110-7

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In this article, the author uses the compensated compactness method coupled with some basic ideas of the kinetic formulation developed by Lions, Perthame, Souganidis and Tadmor to give a refined proof for the
existence of global entropy solutions to a system of quadratic flux. The fire-new method of reduction of Young measures is a pith of this work.

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LYAPOUNOV EXPONENTS AND LAW OF LARGE NUMBERS FOR RANDOM WALK IN RANDOM ENVIRONMENT WITH HOLDING TIMES

毛明志, 韩东

数学物理学报(英文版). 2009 (5): 1383-1394. DOI: 10.1016/S0252-9602(09)60111-9

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In this article, the authors mainly discuss the law of large number under Kalikow's condition for multi-dimensional random walks in random environment with holding times. The authors give an expression to the escape speed of random walks in terms of the Lyapounov exponents, which have been precisely used in the context of large deviation.

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SOME NEW FAMILIES OF FILTRATION FIVE IN THE STABLE HOMOTOPY OF SPHERES

林金坤

数学物理学报(英文版). 2009 (5): 1395-1404. DOI: 10.1016/S0252-9602(09)60112-0

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This study proves a general result on convergence of α₂ x ∈ Ext_A^s^{+2, tq+2q+1}(Z_p, Z_p) in the Adams spectral sequence and as a consequence, the study detects some new families in the stable homotopy groups of spheres π_tq+2q-4S which is represented in the Adams spectral sequence by α₂f_n, α₂f'_n^, ，α₂h_uh_mh_n ∈ Ext_A^{5, tq+2q+1}(Z_p, Z_p) with tq = pⁿ^+1q+2pⁿq, 2pⁿ⁺¹q+pⁿq, p^uq+p^mq+pⁿq, respectively, where α₂ ∈Ext_a^{2, 2q+1}Z_p, Z_p), f_n ∈ Ext_A3,^_pn+1q+2pⁿq(Z_p, Z_p), f'_n ∈ Ext_A3, 2pⁿ⁺¹q+pⁿq (Z_p, Z_p), h_n ∈ Ext_A1,pⁿq(Z_p, Z_p) and p ≥ 5 is a prime, q = 2(p-1), n ≥ 2.

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NONTRIVIAL SOLUTIONS FOR SCHRÖDINGER EQUATIONS

刘芳, 杨健夫

数学物理学报(英文版). 2009 (5): 1405-1420. DOI: 10.1016/S0252-9602(09)60113-2

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The authors prove the existence of nontrivial solutions for the Schrödinger equation -Δu + V(x) u = λ f(x, u) in R^N, where f is superlinear, subcritical and critical at infinity, respectively, V is periodic.

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COBORDISM CLASSES OF FIBERINGS OVER PRODUCT OF PROJECTIVE SPACES

王彦英, 李京艳

数学物理学报(英文版). 2009 (5): 1421-1429. DOI: 10.1016/S0252-9602(09)60114-4

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Let RP(k) denote the k-dimensional real projective space. This article determines which cobordism classes are represented by the total space of a fibering with prescribed base space RP(3)\times RP(1), RP(2)×RP(1), RP(2)\times RP(1)×RP(1) or $RP(3)\times RP(2).

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COMPOSITION TYPE OPERATORS FROM HARDY SPACES TO μ-BLOCH SPACES ON THE UNIT BALL

王雄亮, 刘太顺

数学物理学报(英文版). 2009 (5): 1430-1438. DOI: 10.1016/S0252-9602(09)60115-6

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Let φ be a holomorphic self-map of B_n and Ψ ∈ H(B_n). A composition type operator is defined by T_Ψ, φ(f)= Ψf ο φ for f ∈ H(B_n), which is a generalization of the multiplication operator and the composition operator. In this article, the necessary and sufficient conditions are given for the composition type operator T_Ψ_, φ to be bounded or compact from Hardy space H_p(B_n) to μ-Bloch space B(_Bn). The conditions are some supremums concerned with Ψ, φ, their derivatives and Bergman metric of $\Bn$. At the same time, two corollaries are obtained.

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ATOMIC DECOMPOSITIONS AND |DUALS OF WEAK HARDY SPACES OF B-VALUED MARTINGALES

马涛, 刘培德

数学物理学报(英文版). 2009 (5): 1439-1452. DOI: 10.1016/S0252-9602(09)60116-8

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In this article, several weak Hardy spaces of Banach-space-valued martingales are introduced, some atomic decomposition theorems for them are established and their duals are investigated. The results closely depend on the geometrical properties of the Banach space in which the martingales take values.

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ON A NEW SINGULAR DIRECTION OF QUASIMEROMORPHIC MAPPINGS

吴昭君, 孙道椿

数学物理学报(英文版). 2009 (5): 1453-1460. DOI: 10.1016/S0252-9602(09)60117-X

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By applying Ahlfors' theory of covering surface, we establish a fundamental inequality for quasimeromorphic mapping in an angular domain. As an application, we prove the existence of a new singular direction for quasimeromorphic mapping f, namely, a precise S direction, for which the spherical characteristic function S(r, f) is used as a comparison function.

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CONVEX CONCENTRATION INEQUALITIES FOR CONTINUOUS GAS AND STOCHASTIC DOMINATION

马宇韬

数学物理学报(英文版). 2009 (5): 1461-1468. DOI: 10.1016/S0252-9602(09)60118-1

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In this article, we consider the continuous gas in a bounded domain ∧of R⁺ or R^ddescribed by a Gibbsian probability measure
μ^η_∧associated with a pair interaction Φ, the inverse temperature β, the activity z>0, and the boundary condition η. Define F=∫f(s)ω∧(ds). Applying the generalized Ito's formula for forward-backward martingales (see Klein et al. [5]), we obtain convex concentration inequalities for F
with respect to the Gibbs measure μ^η_∧. On the other hand, by FKG inequality on the Poisson space, we also give a new simple argument for the stochastic domination for the Gibbs measure.

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REGULARITY OF THE SOLUTIONS FOR NONLINEAR BIHARMONIC EQUATIONS IN |R^N

邓引斌, 李亦

数学物理学报(英文版). 2009 (5): 1469-1480. DOI: 10.1016/S0252-9602(09)60119-3

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The purpose of this article is to establish the regularity of the weak solutions for the nonlinear biharmonic equation
{Δ²u+a(x)u=g(x, u),

u∈ H² (R^N), （1.1）

where the condition u ∈ H²(R^N) plays the role of a boundary value condition, and as well expresses explicitly that the differential equation is to be satisfied in the weak sense.

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RIEMANN BOUNDARY VALUE PROBLEM WITH RESPECT TO THE PERTURBATION OF BOUNDARY CURVE TO BE AN OPEN ARC

林娟, 王传荣

数学物理学报(英文版). 2009 (5): 1481-1488. DOI: 10.1016/S0252-9602(09)60120-X

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By dint of the stability of Cauchy-type integral with kernel density of class H* for an open arc, this paper discusses the stability of the solution of Riemann boundary value problem with respect to the perturbation of boundary curve to be an open arc.

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EIGENVALUE PROBLEM OF ELLIPTIC EQUATIONS WITH HARDY POTENTIAL

谢朝东, 沈尧天, 姚仰新

数学物理学报(英文版). 2009 (5): 1489-1496. DOI: 10.1016/S0252-9602(09)60121-1

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Consider the eigenvalue problem of elliptic equations with Hardy potential. Improve the results of references by introducing a new Hilbert space and using integral inequality.

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