数学物理学报(英文版)

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WEIGHTED ESTIMATES FOR COMMUTATORS OF OPERATORS CALDERÓN-ZYGMUNDWITH NON-DOUBLING MEASURES

林海波, 孟岩, 杨大春

数学物理学报(英文版). 2010 (1): 1-18. DOI: 10.1016/S0252-9602(10)60017-3

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Let μ be a nonnegative Radon measure on R^d, which only satisfies the polynomial growth condition. Under this assumption, the authors obtain some weighted weak-type estimates for the commutators generated by the multilinear Calder\'on-Zygmund operators and RBMO(μ) functions.

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CYCLOTOMIC ELEMENTS IN K₂F, REVISITED

Jerzy Browkin

数学物理学报(英文版). 2010 (1): 19-26. DOI: 10.1016/S0252-9602(10)60018-5

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Basing on results of Xu and Qin [10], and Guo [12] on cyclotomic elements in K₂F for local fields F, we prove that every element in K₂Q
is a finite or infinite product of cyclotomic elements. Next, we extend this result to finite extensions of Q satisfying some additional conditions.

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ADMISSIBILITY IN THE GENERAL GROWTH CURVE MODEL WITH RESPECT TO RESTRICTED |PARAMETER SETS UNDER MATRIX LOSS FUNCTION

张尚立, 覃红

数学物理学报(英文版). 2010 (1): 27-38. DOI: 10.1016/S0252-9602(10)60019-7

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In this paper, we study the issue of admissibility in the growth curve model with respect to restricted parameter sets under matrix loss function. We obtain some necessary and sufficient conditions that the linear estimators of $KBL$ are admissible in the class of
homogeneous linear estimators and in the class of non-homogeneous linear estimators under the growth curve model with respect to
restricted parameter sets, respectively.

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PHASE RETRIEVAL OF TIME-LIMITED SIGNALS

付应雄, 李落清

数学物理学报(英文版). 2010 (1): 39-46. DOI: 10.1016/S0252-9602(10)60020-3

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The problem of reconstructing a signal φ(x) from its magnitude |φ(x)| is of considerable interest to engineers and physicists. This article concerns the problem of determining a time-limited signal f with period 2π when |f(e^ix)| is known for x ∈[-π, π]. It is shown that the conditions |g(e^ix)|=|f(e^ix)| and |g(e^i(x+b))-g(e^ix)|=|f(e^i(x+b))-f(e^ix)|, b≠2π, together imply that either g=wf or g=vf, where both w and v have period b. Furthermore, if b/2π is irrational then the functions w and v reduce to some constants c₁ and c₂, respectively; if b/2π is rational then w takes the form w=e^iαB₁(e^ix}B₂(e^ix) and v takes the form e^{i(x2πN/b+α)}B₁(e^ix)B₂(e^ix), where B₁ and B₂ are Blaschke products.

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DECAY RATES OF PLANAR VISCOUS RAREFACTION WAVE FOR MULTI-DIMENSIONAL SCALAR CONSERVATION LAW #br# WITH DEGENERATE VISCOSITY ON HALF SPACE

刘艳红

数学物理学报(英文版). 2010 (1): 47-54. DOI: 10.1016/S0252-9602(10)60021-5

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We investigate the decay rates of the planar viscous rarefaction wave of the initial-boundary value problem to scalar conservation
law with degenerate viscosity in several dimensions on the half-line space, where the corresponding one-dimensional problem
admits the rarefaction wave as an asymptotic state. The analysis is based on the standard L²-energy method and L¹-estimate.

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INFINITELY MANY SOLUTIONS FOR ELLIPTIC SYSTEMS WITH STRONGLY INDEFINITE VARIATIONAL STRUCTURE

刘朝霞

数学物理学报(英文版). 2010 (1): 55-64. DOI: 10.1016/S0252-9602(10)60022-7

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Based on the multiplicity results of Benci and Fortunato [4], we consider some elliptic systems with strongly indefinite quadratic part, and establish the existence of infinitely many nontrivial solutions in a suitable family of products of fractional Sobolev spaces.

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CONVERGENCE ANALYSIS OF RUNGE-KUTTA METHODS FOR A CLASS OF RETARDED DIFFERENTIAL ALGEBRAIC SYSTEMS

肖飞雁, 张诚坚

数学物理学报(英文版). 2010 (1): 65-74. DOI: 10.1016/S0252-9602(10)60023-9

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This article deals with a class of numerical methods for retarded differential algebraic systems with time-variable delay. The methods can be viewed as a combination of Runge-Kutta methods and Lagrange interpolation. A new convergence concept, called $D_A$-convergence, is introduced. The D_A-convergence result for the methods is derived. At the end, a numerical example is given to verify the computational effectiveness and the theoretical result.

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SUBNORMAL SOLUTIONS OF DIFFERENTIAL EQUATIONS WITH PERIODIC COEFFICIENTS

陈宗煊, 孙光镐

数学物理学报(英文版). 2010 (1): 75-88. DOI: 10.1016/S0252-9602(10)60024-0

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In this article, we apply the concept of hyper-order to higher order linear differential equations with periodic
coefficients, investigate the existence and the form of its subnormal solution, and estimate the growth of all other solutions, and answer the question raised by Gundersen and Steinbart for more general periodic differential equations.

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BOCHNER TECHNIQUE ON STRONG KÄHLER-FINSLER MANIFOLDS

肖金秀, 钟同德, 邱春晖

数学物理学报(英文版). 2010 (1): 89-106. DOI: 10.1016/S0252-9602(10)60025-2

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By using the Chern-Finsler connection and complex Finsler metric, the Bochner technique on strong Kähler-Finsler manifolds is studied. For a strong Kähler-Finsler manifold M, the authors first prove that there exists a system of local coordinate which is normalized at a point v ∈M=T^1,0M \ o(M), and then the horizontal Laplace operator ΟH for differential forms on PTM is defined by the horizontal part of the Chern-Finsler connection and its curvature tensor, and the horizontal Laplace operator ?H on holomorphic vector bundle over PTM is also defined. Finally, we get a Bochner vanishing theorem for differential forms on PTM. Moreover, the Bochner vanishing theorem on a holomorphic line bundle over PTM is also obtained.

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FINITENESS OF HIGHER CODIMENSIONAL DISJOINT MINIMAL GRAPHS

东瑜昕, 嵇庆春, 张玮

数学物理学报(英文版). 2010 (1): 107-112. DOI: 10.1016/S0252-9602(10)60026-4

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We estimate the number of disjoint open subsets in Rⁿ, which can support area-decreasing minimal graphs. This result generalizes the related results of Li-Wang and Tkachev for minimal hypersurfaces to higher codimensional case.

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MULTIPLE AND SIGN-CHANGING SOLUTIONS FOR NONLINEAR ELLIPTIC EQUATION WITH CRITICAL POTENTIAL AND CRITICAL PARAMETER

王友军, 沈尧天

数学物理学报(英文版). 2010 (1): 113-124. DOI: 10.1016/S0252-9602(10)60027-6

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Some embedding inequalities in Hardy-Sobolev space are proved. Furthermore, by the improved inequalities and the linking theorem, in a new k-order Sobolev-Hardy space, we obtain the existence of sign-changing solutions for the nonlinear elliptic equation
\left\{\begin{array}{ll}
\disp -\Delta_{(k)}u:=-\Delta
u-\frac{(N-2)^2}{4}\frac{u}{|x|^2}-\frac{1}{4}\sum\limits_{i=1}^{k-1}\frac{u}{|x|^2(\ln_{(i)}R/|x|)^2}
=f(x,u),&\quad x\in\Omega,
u=0,&\quad x\in\partial\Omega, \end{array} \right.
where 0\in \Omega \subset B_a(0)\subset {\Bbb R}^N, N\geq 3, \ln_{(i)}=\prod\limits_{j=1}^i\ln^{(j)}, and R=ae^{(k-1)}, where e^{(0)}=1, e^{(j)}=e^{e^{(j-1)}} for j\geq 1, \ln^{(1)}=\ln, \ln^{(j)}=\ln\ln^{(j-1)} for j\geq 2. Besides, positive and negative solutions are obtained by a variant mountain pass theorem.

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INEQUALITIES OF EIGENVALUES FOR BI-KOHN LAPLACIAN ON |HEISENBERG GROUP

黄广月, 陈文艺

数学物理学报(英文版). 2010 (1): 125-131. DOI: 10.1016/S0252-9602(10)60028-8

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In this article, we consider the eigenvalue problem for the bi-Kohn Laplacian and obtain universal bounds on the
(k+1)-th eigenvalue in terms of the first k eigenvalues independent of the domains.

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ON MÜNTS FORMULA

丁夏畦, 罗佩珠

数学物理学报(英文版). 2010 (1): 132-136. DOI: 10.1016/S0252-9602(10)60029-X

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In the theory of Riemann Zeta-function, there is an important formula called M\"{u}nts formula. In this note we will give its general form.

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EXISTENCE OF A COOPERATIVE ELLIPTIC SYSTEM INVOLVING PUCCI OPERATOR

杨健夫, 余小辉

数学物理学报(英文版). 2010 (1): 137-147. DOI: 10.1016/S0252-9602(10)60030-6

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The authors study the existence of solutions for the nonlinear elliptic system

{ -M\⁺_λ, ∧(D²u)=f(u, v) in Ω,

-M\⁺_λ, ∧(D²v)=f(u, v) in Ω,

u ≥ 0, v ≥ 0 in Ω,

u=v=0 on ∂Ω,

where Ω is a bounded convex domain in R^N, N ≥ 2. It is shown that under some assumptions on f and g, the problem has at least one positive solution (u,v).

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AVERAGE ONESIDED WIDTHS OF SOBOLEV AND BESOV CLASSES

杨柱元, 杨宗文, 刘永平

数学物理学报(英文版). 2010 (1): 148-160. DOI: 10.1016/S0252-9602(10)60031-8

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The article concerns the average onesided widths of the Sobolev and Besov classes and the classes of functions with bounded moduli of smoothness. The weak asymptotic results are obtained for the corresponding quantities.

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ON LINEAR EXTENSION OF 1-LIPSCHITZ MAPPING FROM HILBERT SPACE INTO A NORMED SPACE

王瑞东

数学物理学报(英文版). 2010 (1): 161-165. DOI: 10.1016/S0252-9602(10)60032-X

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In this article, we prove that an into 1-Lipschitz mapping from the unit sphere of a Hilbert space to the unit sphere of an arbitrary normed space, which under some conditions, can be extended to be a linear isometry on the whole
space.

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NORMALITY CRITERIA FOR FAMILIES OF MEROMORPHIC ALGEBROID FUNCTIONS

孙道椿

数学物理学报(英文版). 2010 (1): 166-172. DOI: 10.1016/S0252-9602(10)60033-1

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By using the definition of Hausdorff distance, we prove some normality criteria for families of meromorphic algebroid functions. Some examples are given to complement the theory in this article.

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A CLASS OF COMPOUND VECTOR-VALUED PROBLEM AND FACTORIZATION OF MATRIX FUNCTION

郭国安, 杜金元

数学物理学报(英文版). 2010 (1): 173-179. DOI: 10.1016/S0252-9602(10)60034-3

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In this article, we consider a class of compound vector-valued problem on upper-half plane C₊, which consists of vector Riemann problem along a closed contour in C₊ with matrix coefficient in Hölder class and vector Hilbert problem on the real axis with essential bounded measurable matrix coefficient. Under appropriate assumption we obtain its solution by use of Corona theorem and factorization of matrix functions in decomposed Banach algebras.

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APPLICATION OF MINIMUM PROJECTION UNIFORMITY CRITERION IN COMPLEMENTARY DESIGNS

宋硕, 覃红

数学物理学报(英文版). 2010 (1): 180-186. DOI: 10.1016/S0252-9602(10)60035-5

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In this article, we consider the characterization problem in design theory. The objective is to characterize minimum
projection uniformity for two-level designs in terms of their complementary designs. Here, the complementary design means a design in which all the Hamming distances of any two runs are the same, which generalizes the concept of a pair of complementary designs in the literature. Based on relationships of the uniformity pattern between a pair of complementary designs, we propose a minimum projection uniformity (MPU) rule to assess and compare two-level factorials.

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VISCOSITY SOLUTIONS OF HJB EQUATIONS ARISING FROM THE VALUATION OF EUROPEAN PASSPORT OPTIONS

边保军, 王杨, 张寄洲

数学物理学报(英文版). 2010 (1): 187-202. DOI: 10.1016/S0252-9602(10)60036-7

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The passport option is a call option on the balance of a trading account. The option holder retains the gain from trading, while the issuer is liable for the net loss. In this article, the mathematical foundation for pricing the
European passport option is established. The pricing equation which is a fully nonlinear equation is derived using the dynamic programming principle. The comparison principle, uniqueness and convexity preserving of the viscosity solutions of related HJB equation are proved. A relationship between the passport and lookback options is discussed.

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FUNDAMENTAL GROUPS OF CLOSED POSITIVELY CURVED MANIFOLDS WITH ALMOST DISCRETE ABELIAN GROUP ACTIONS

王雨生

数学物理学报(英文版). 2010 (1): 203-207. DOI: 10.1016/S0252-9602(10)60037-9

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Let M be a closed n-manifold of positive sectional curvature. Assume that $M$ admits an effective isometrical
T¹× Z_p^k-action with p prime. The main result of the article is that if k=1 for n=3 or k>n+1/4 for n ≥ 5, then there exists a positive constant $p(n)$, depending only on n, such that π₁(M) is cyclic if p ≥ p(n).

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LOCAL REGULARITY RESULT IN OBSTACLE PROBLEMS

高红亚, 郭静, 左亚丽, 褚玉明

数学物理学报(英文版). 2010 (1): 208-214. DOI: 10.1016/S0252-9602(10)60038-0

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We obtain a local regularity result for solutions to K_ψ，θ-obstacle problem of A-harmonic equation divA(x, u(x), ∨ u(x))=0, where A: Ω×R×Rⁿ→ Rⁿ is a Carath\'eodory function satisfying some coercivity and growth conditions with the natural exponent 1<p<n, the obstacle function ψ≥0$, and the boundary data θ ∈W^1, ^p(Ω).

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SLANT SUBMANIFOLDS OF A RIEMANNIAN PRODUCT MANIFOLD

Mehmet Atceken

数学物理学报(英文版). 2010 (1): 215-224. DOI: 10.1016/S0252-9602(10)60039-2

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In this article, the geometry of the slant submanifolds of a Riemannian product manifold is studied. Some necessary and sufficient conditions on slant, bi-slant and semi-slant submanifolds are given. We research fundamental properties of the distributions which are involved in definitions of semi- and bi-slant submanifolds
in a Riemannian product manifold.

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LIE SUPER-BIALGEBRA STRUCTURES |ON GENERALIZED SUPER-VIRASORO ALGEBRAS

杨恒云, 苏育才

数学物理学报(英文版). 2010 (1): 225-239. DOI: 10.1016/S0252-9602(10)60040-9

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In this article, Lie super-bialgebra structures on generalized super-Virasoro algebras L are considered. It is proved that all such Lie super-bialgebras are coboundary triangular Lie super-bialgebras if and only if H¹(L, L{\cal L})=0.

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ON WEAK MINIMUM ABERRATION AND NUMBER OF CLEAR TWO-FACTOR INTERACTION COMPONENTS IN s_IV^m-p DESIGNS

杨贵军

数学物理学报(英文版). 2010 (1): 240-246. DOI: 10.1016/S0252-9602(10)60041-0

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This article obtains some theoretical results on the number of clear two-factor interaction components and weak minimum aberration in an s_IV^m-p design, by considering the number of not clear two-factor interaction components of the design.

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ON THE OPERATIONS OF ALGEBROID FUNCTIONS

孙道椿, 高宗升

数学物理学报(英文版). 2010 (1): 247-256. DOI: 10.1016/S0252-9602(10)60042-2

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In this article, we first investigate the operational properties of algebroid functions. Then we prove two uniqueness theorems for algebroid functions.

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WHITE NOISE APPROACH TO SCATTERING SOLUTION OF Φ₄⁴ WAVE EQUATION

让光林

数学物理学报(英文版). 2010 (1): 257-268. DOI: 10.1016/S0252-9602(10)60043-4

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Under the framework of white noise analysis, the existence of scattering solutions to the abstract dynamical φ₄⁴ wave equations in terms of generalized operators (see Section 3 below) is proven via a combination of the characterization for the symbol of generalized operators and the classical scattering results. In addition, some properties (Poincar\'{e} invariance and irreducibility) of the solutions are discussed.

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AN EFFICIENT SEQUENTIAL DESIGN FOR SENSITIVITY EXPERIMENTS

田玉斌, 房永飞

数学物理学报(英文版). 2010 (1): 269-280. DOI: 10.1016/S0252-9602(10)60044-6

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In sensitivity experiments, the response is binary and each experimental unit has a critical stimulus level that cannot be observed directly. It is often of interest to estimate extreme quantiles of the distribution of these
critical stimulus levels over the tested products. For this purpose a new sequential scheme is proposed with some commonly used models. By using the bootstrap repeated-sampling principle, reasonable prior
distributions based on a historic data set are specified. Then, a Bayesian strategy for the sequential procedure is provided and the estimator is given. Further, a high order approximation for such an estimator is explored and its consistency is proven. A simulation study shows that the proposed method gives superior performances over the existing methods.

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GLOBAL SOLUTION TO THE CAUCHY PROBLEM ON A UNIVERSE FIREWORKS MODEL

姜正禄, 田红炯

数学物理学报(英文版). 2010 (1): 281-288. DOI: 10.1016/S0252-9602(10)60045-8

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We prove existence and uniqueness of the global solution to the Cauchy problem on a universe fireworks model with finite total mass at the initial state when the ratio of the mass surviving the explosion, the probability of the explosion of fragments and the probability function of the velocity change of a surviving particle satisfy the corresponding physical conditions. Although the nonrelativistic Boltzmann-like equation modeling the universe
fireworks is mathematically easy, this article leads rather theoretically to an understanding of how to construct contractive mappings in a Banach space for the proof of the existence and uniqueness of the solution by means of methods taken from the famous work by DiPerna & Lions about the Boltzmann equation. We also show both the
regularity and the time-asymptotic behavior of solution to the Cauchy problem.

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MAXIMAL ATTRACTORS FOR THE COMPRESSIBLE NAVIER--STOKES EQUATIONS OF VISCOUS AND HEAT CONDUCTIVE FLUID

秦玉明, 宋锦萍

数学物理学报(英文版). 2010 (1): 289-311. DOI: 10.1016/S0252-9602(10)60046-X

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This article is concerned with the existence of maximal attractors in Hⁱ (i=1,2,4) for the compressible Navier--Stokes equations for a polytropic viscous heat conductive ideal gas in bounded annular domains Ω_n in Rⁿ (n=2,3). One of the important features is that the metric spaces H⁽¹⁾, H⁽²⁾, and H⁽⁴⁾ we work with are three incomplete
metric spaces, as can be seen from the constraints θ >0 and u>0, with θ and u being absolute temperature and specific volume respectively. For any constants δ₁, δ₂, ^…, δ₈verifying some conditions, a sequence of closed subspaces H_δ⁽ⁱ⁾ H⁽ⁱ⁾;(i=1, 2, 4) is found, and the existence of maximal (universal) attractors in H_δ⁽ⁱ⁾; (i=1, 2, 4) is
established.

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HOMOCLINIC ORBITS FOR A CLASS OF THE SECOND ORDER HAMILTONIAN SYSTEMS

万莉莉, 唐春雷

数学物理学报(英文版). 2010 (1): 312-318. DOI: 10.1016/S0252-9602(10)60047-1

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The existence of homoclinic orbits is obtained by the variational approach for a class of second order Hamiltonian systems q(t)+ V(t, q(t))=0, where V(t, x)=-K(t,x)+W(t, x), K(t, x) is neither a quadratic form in x nor periodic in t and W(t, x) is superquadratic in x.

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LIMITING BEHAVIOR OF RECURSIVE M-ESTIMATORS IN MULTIVARIATE LINEAR REGRESSION MODELS AND THEIR ASYMPTOTIC EFFICIENCIES

缪柏其, 吴月华, 刘东海

数学物理学报(英文版). 2010 (1): 319-329. DOI: 10.1016/S0252-9602(10)60048-3

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Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter Parameters. In this article, it is shown that for a nondecreasing u₁(t), under some mild conditions the recursive M-estimators of regression coefficients and scatter parameters are strongly consistent and the recursive M-estimator of the regression coefficients is also asymptotically normal distributed. Furthermore, optimal recursive M-estimators, asymptotic efficiencies of recursive M-estimators and asymptotic relative efficiencies between recursive M-estimators of regression coefficients are studied.

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SOME POSTERIOR DISTRIBUTIONS FOR THE LAPLACE MEAN

Saralees Nadarajah

数学物理学报(英文版). 2010 (1): 330-340. DOI: 10.1016/S0252-9602(10)60049-5

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Two posterior distributions for the mean of the Laplace distribution are obtained by deriving the distributions of the product XY and the ratio X/Y when X and Y are Student's t and Laplace random variables distributed independently of each other. Tabulations of the associated percentage points are given along with computer programs for generating them.

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THE POINCAR\'E-BERTRAND FORMULA ON THE BUILDING DOMAIN OF COMPLEX BIBALLS

龚定东, 林良裕

数学物理学报(英文版). 2010 (1): 341-349. DOI: 10.1016/S0252-9602(10)60050-1

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The Poincaré-Bertrand formula takes an important position in the study of complex singular integral. The Poincaré-Bertrand formula on the complex sphere in the multidimensional complex Euclidian spaces was given by Sheng Gong. Using the method of solid angular coefficient, the authors extend the Poincaré-Bertrand formula on the complex sphere to the building domain of the complex biballs, and obtain a more general Poincaré-Bertrand formula with the solid angular coefficients.

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MULTIPLE SOLUTIONS FOR NONAUTONOMOUS SECOND ORDER PERIODIC SYSTEMS

Zdzislaw Denkowski, Leszek Gasinski, Nikolaos S. Papageorgiou

数学物理学报(英文版). 2010 (1): 341-349. DOI: 10.1016/S0252-9602(10)60051-3

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We study nonautonomonus second order periodic systems with a nonsmooth potential. Using the nonsmooth critical theory, we establish the existence of at least two nontrivial solutions. Our framework incorporates large classes of both subquadratic and superquadratic potentials at infinity.

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INEQUALITIES OF THE QUERMASSINTEGRALS FOR THE L_p-PROJECTION BODY AND THE L_p-CENTROID BODY

王卫东, 冷岗松

数学物理学报(英文版). 2010 (1): 359-368. DOI: 10.1016/S0252-9602(10)60052-5

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Associated with the concepts of the L_p-mixed quermassintegrals, the L_p-mixed volume, and the L_p-dual mixed volume, we establish inequalities for the quermassintegrals of the L_p-projection body and the L_p-centroid body. Further, the general results for the Shephard problem of the L_p-projection body and the L_p-centroid body are obtained.

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