数学物理学报(英文版)

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ON ALMOST SURE CONVERGENCE OF WEIGHTED SUMS OF RANDOM ELEMENT SEQUENCES

甘师信

数学物理学报(英文版). 2010 (4): 1021-1028. DOI: 10.1016/S0252-9602(10)60099-9

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We mainly study the almost sure limiting behavior of weighted sums of the form ∑ⁿ_i₌₁a_iX_i/ _bn, where {X_n, n ≥ 1} is an arbitrary Banach space valued random element sequence or Banach space valued martingale difference sequence and {a_n, n ≥ 1} and {b_n, n ≥ 1} are two sequences of positive constants. Some new strong laws of large numbers for such weighted sums are proved under mild conditions.

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THE P-COTORSION DIMENSIONS OF MODULES AND RINGS

耿玉仙

数学物理学报(英文版). 2010 (4): 1029-1043. DOI: 10.1016/S0252-9602(10)60100-2

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Let R be a ring. We define a dimension, called P-cotorsion dimension, for modules and rings. The aim of this
article is to investigate P-cotorsion dimensions of modules and rings and the relations between P-cotorsion dimension and other homological dimensions. This dimension has nice properties when the ring in consideration is generalized morphic.

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INEQUALITIES FOR L_p-MIXED CURVATURE IMAGES

卢峰红, 王卫东

数学物理学报(英文版). 2010 (4): 1044-1052. DOI: 10.1016/S0252-9602(10)60101-4

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Lutwak, Yang, and Zhang posed the notion of L_p-curvature images and established several L_p analogs of the
affine isoperimetric inequality. In this article, the notion of L_p-mixed curvature images is introduced, L_p-curvature images being a special case. The properties and L_p analogs of the affine isoperimetric inequality are established for L_p-mixed curvature images.

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A NOTE ON THE MEAN CURVATURE FLOW IN RIEMANNIAN MANIFOLDS

陈旭忠, 沈一兵

数学物理学报(英文版). 2010 (4): 1053-1064. DOI: 10.1016/S0252-9602(10)60102-6

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Under the hypothesis of mean curvature flows of hypersurfaces, we prove that the limit of the smooth rescaling of the singularity is weakly convex. It is a generalization of the result due to G.Huisken and C. Sinestrari in [5]. These a-priori bounds are satisfied for mean convex hypersurfaces in locally symmetric Riemannian manifolds with
nonnegative sectional curvature.

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EXTINCTION OF POPULATION-SIZE-DEPENDENT BRANCHING CHAINS IN RANDOM ENVIRONMENTS

王伟刚, 李燕, 胡迪鹤

数学物理学报(英文版). 2010 (4): 1065-1072. DOI: 10.1016/S0252-9602(10)60103-8

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We consider a population-size-dependent branching chain in a general random environment.We give sufficident
conditions for certain extinction and for non-certain extinction.The chain exhibits different asymptotic according to sup_k, θ m_k_, _θ<1, m_k_, θn→1 as k → ∞, n → ∞ , inf_k, θm_k_, θ>1.

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ONE LINEAR ANALYTIC APPROXIMATION FOR STOCHASTIC INTEGRODIFFERENTIAL EQUATIONS

Svetlana Jankovic, Dejan Ilic

数学物理学报(英文版). 2010 (4): 1073-1085. DOI: 10.1016/S0252-9602(10)60104-X

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This article concerns the construction of approximate solutions for a general stochastic integrodifferential
equation which is not explicitly solvable and whose coefficients functionally depend on Lebesgue integrals and stochastic integrals with respect to martingales. The approximate equations are linear ordinary stochastic differential equations, the solutions of which are defined on sub-intervals of an arbitrary partition of the time
interval and connected at successive division points. The closeness of the initial and approximate solutions is measured in the L_p-th norm, uniformly on the time interval. The convergence with probability one is also given.

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TOPOLOGICAL CHARACTERIZATIONS OF THE EXTENDING PROPERTY OF RINGS

卢丹诚, 武同锁

数学物理学报(英文版). 2010 (4): 1086-1092. DOI: 10.1016/S0252-9602(10)60105-1

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A commutative ring R is called extending if every ideal is essential in a direct summand of R_R. The following results are proved: (1) C(X) is an extending ring if and only if X is extremely disconnected; (2) Spec(R) is extremely disconnected and R is semiprime if and only if R is a nonsingular extending ring; (3) Spec(R) is extremely disconnected if and only if R/N}(R) is an extending ring, where N(R) consists of all nilpotent elements of R. As an application, it is also shown that any Gelfand nonsingular extending ring is clean.

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SINGULAR INTEGRAL EQUATIONS ON THE REAL AXIS WITH SOLUTIONS HAVING SINGULARITIES OF HIGHER ORDER

钟寿国

数学物理学报(英文版). 2010 (4): 1093-1099. DOI: 10.1016/S0252-9602(10)60106-3

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We transform the singular integral equations with solutions simultaneously having singularities of higher order at infinite point and at several finite points on the real axis into ones along a closed contour with solutions having singularities of higher order, and for the former obtain the extended Neother theorem of complete equation as well as the solutions and the solvable conditions of characteristic equation from the latter. The conclusions drawn by
this article contain special cases discussed before.

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ON REFLEXIVITY OF HYPONORMAL AND WEIGHTED SHIFT OPERATORS

M. Faghih Ahmadi, K. Hedayatian

数学物理学报(英文版). 2010 (4): 1100-1104. DOI: 10.1016/S0252-9602(10)60107-5

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By an elementary proof, we use a result of Conway and Dudziak to show that if A is a hyponormal operator with spectral radius r(A) such that its spectrum is the closed disc {z:|z| ≤ r(A)} then A is reflexive. Using this result, we give a simple proof of a result of Bercovici, Foias, and Pearcy on reflexivity of shift operators. Also, it is shown that every power of an invertible bilateral weighted shift is reflexive.

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SOME PROPERTIES OF GALTON-WATSON BRANCHING PROCESSES IN VARYING ENVIRONMENTS

余旌胡, 许芳

数学物理学报(英文版). 2010 (4): 1105-1114. DOI: 10.1016/S0252-9602(10)60108-7

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This article deals with some properties of Galton-Watson branching processes in varying environments. A
necessary and sufficient condition for relative recurrent state is presented, and a series of ratio limit properties of the transition probabilities are showed.

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IMPROVED ESTIMATES OF THE COVARIANCE MATRIX IN GENERAL LINEAR MIXED MODELS

叶仁道, 王松桂

数学物理学报(英文版). 2010 (4): 1115-1124. DOI: 10.1016/S0252-9602(10)60109-9

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In this article, the problem of estimating the covariance matrix in general linear mixed models is considered. Two new classes of estimators obtained by shrinking the eigenvalues towards the origin and the arithmetic mean,
respectively, are proposed. It is shown that these new estimators dominate the unbiased estimator under the squared error loss function. Finally, some simulation results to compare the performance of the proposed estimators with that of the unbiased estimator are reported. The simulation results indicate that these new shrinkage estimators provide a substantial improvement in risk under most situations.

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MODERATE DEVIATIONS FOR PARAMETER ESTIMATORS IN FRACTIONAL ORNSTEIN-UHLENBECK PROCESS

高付清, 蒋辉, 汪宝彬

数学物理学报(英文版). 2010 (4): 1125-1133. DOI: 10.1016/S0252-9602(10)60110-5

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We study moderate deviations for estimators of the drift parameter of the fractional Ornstein-Uhlenbeck process. Two moderate deviation principles are obtained.

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QUANTIZATION OF LIE ALGEBRAS OF BLOCK TYPE

程永胜, 苏育才

数学物理学报(英文版). 2010 (4): 1134-1142. DOI: 10.1016/S0252-9602(10)60111-7

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In this article, we use the general method of quantization by Drinfeld's twist to quantize explicitly the Lie bialgebra structures on Lie algebras of Block type.

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LORENTZ MARTINGALE SPACES AND INTERPOLATION

范利萍, 焦勇, 刘培德

数学物理学报(英文版). 2010 (4): 1143-1153. DOI: 10.1016/S0252-9602(10)60112-9

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In this article, the authors introduce some new Lorentz spaces for martingales, which are extensions of Hardy spaces of martingales. Then they discuss their basic properties, embedding relationships, and interpolation spaces between them, during which the use of rearrangement good-λ-inequality plays an important role.

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SEPARABLE CONDITIONS AND SCALARIZATION OF BENSON PROPER EFFICIENCY

丘京辉, 郝媛, 王璀

数学物理学报(英文版). 2010 (4): 1154-1166. DOI: 10.1016/S0252-9602(10)60113-0

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Under the assumption that the ordering cone has a nonempty interior and is separable (or the feasible set has a
nonempty interior and is separable), we give scalarization theorems on Benson proper efficiency. Applying the results to vector optimization problems with nearly cone-subconvexlike set-valued maps, we obtain scalarization theorems and Lagrange multiplier theorems for Benson proper efficient solutions.

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DURATION OF NEGATIVE SURPLUS FOR A TWO STATE MARKOV-MODULATED RISK MODEL

马学敏, 袁海丽, 胡亦钧

数学物理学报(英文版). 2010 (4): 1167-1173. DOI: 10.1016/S0252-9602(10)60114-2

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We consider a continuous time risk model based on a two state Markov process, in which after an exponentially distributed time, the claim frequency changes to a different level and can change back again in the same way. We derive the Laplace transform for the first passage time to surplus zero from a given negative surplus and for the duration of negative surplus. Closed-form expressions are given in the case of
exponential individual claim. Finally, numerical results are provided to show how to estimate the moments of duration of negative surplus.

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INITIAL TRACE OF SOLUTIONS FOR A DOUBLY NONLINEAR DEGENERATE PARABOLIC EQUATIONS

王淑娟, 赵俊宁

数学物理学报(英文版). 2010 (4): 1174-1188. DOI: 10.1016/S0252-9602(10)60115-4

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In this note, we study the existence of an initial trace of nonnegative solutions for the following problem
u_t-div(|\bigtriangledown u^m|^p-2\bigtriangledownu^m)+u^q=0 in Q_T=Ω×(0, T).
We prove that the initial trace is an outer regular Borel measure, which may not be locally bounded for some values of parameters p, q, and m. We also study the corresponding Cauchy problems with a given generalized Borel measure as initial data.

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ESTIMATES OF THE DOUBLE DETERMINANTS OF QUATERNION MATRICES

冯良贵, 程薇

数学物理学报(英文版). 2010 (4): 1189-1198. DOI: 10.1016/S0252-9602(10)60116-6

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An estimate of the upper bound is given for the double determinant of the sum of two arbitrary quaternion matrices, and meanwhile the lower bound on the double determinant is established especially for the sum of two quaternion matrices which form an assortive pair. As applications, some known results are obtained as corollaries and a question in the matrix determinant theory is answered completely.

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MULTIPLE SOLUTIONS AND THEIR LIMITING BEHAVIOR OF COUPLED NONLINEAR SCHRÖDINGER SYSTEMS

万优艳

数学物理学报(英文版). 2010 (4): 1199-1218. DOI: 10.1016/S0252-9602(10)60117-8

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We study the multiplicity of positive solutions and their limiting behavior as ε tends to zero for a class of coupled nonlinear Schr\"odinger system in R^N. We relate the number of positive solutions to the topology of the set of minimum points of the least energy function for ε sufficiently small. Also, we verify that these solutions concentrate at a global minimum point of the least energy function.

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THE BANACH-LIE GROUP OF LIE TRIPLE AUTOMORPHISMS OF AN |H*-ALGEBRA

A. J.Calderon Martí, C.Martín González

数学物理学报(英文版). 2010 (4): 1219-1226. DOI: 10.1016/S0252-9602(10)60118-X

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We study the Banach-Lie group Ltaut}(A) of Lie triple automorphisms of a complex associative H*-algebra A. Some consequences about its Lie algebra, the algebra of Lie triple derivations of A, Ltder(A), are obtained. For a topologically simple A, in the infinite-dimensional case we have Ltaut(A)₀=Aut(A) implying Ltder(A)= Der(A). In the finite-dimensional case Ltaut(A)₀ is a direct product of aut(A) and a certain subgroup of Lie derivations δ from A to its center, annihilating commutators.

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ON THE EMDEN-FOWLER EQUATION u"(t)u(t)=c₁+c₂u' (t)²WITH c₁≥0, c₂ ≥0

李明融

数学物理学报(英文版). 2010 (4): 1227-1234. DOI: 10.1016/S0252-9602(10)60119-1

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In this article, we study the following initial value problem for the nonlinear equation
{ u"u( t) =c₁+c₂u' (t)², c₁≥ 0, c₂≥ 0,
u(0)=u₀, u' (0)=u₁.
We are interested in properties of solutions of the above problem. We find the life-span, blow-up rate, blow-up constant and the regularity, null point, critical point, and asymptotic behavior at infinity of the solutions.

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L² DECAY OF THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DAMPING

蔡晓静, 雷利华

数学物理学报(英文版). 2010 (4): 1235-1248. DOI: 10.1016/S0252-9602(10)60120-8

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In this article, we show large time behavior of weak solutions to the Cauchy problem of the Navier-Stokes equations with damping α|u|^β-1u (α>0).

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V-BILIPSCHITZ DETERMINACY OF WEIGHTED HOMOGENEOUS ANALYTIC FUNCTION-GERMS ON WEIGHTED HOMOGENEOUS REAL ANALYTIC VARIETIES

刘恒兴, 张敦穆

数学物理学报(英文版). 2010 (4): 1249-1256. DOI: 10.1016/S0252-9602(10)60121-X

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In this article, we provide estimates for the degree of V-bilipschitz determinacy of weighted homogeneous function germs defined on
weighted homogeneous analytic variety V satisfying a convenient Lojasiewicz condition.The result gives an explicit order such that the geometrical structure of a weighted homogeneous polynomial function germs is preserved after higher order perturbations.

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MATHEMATICAL PROGRAMS WITH SYSTEM OF GENERALIZED VECTOR QUASI-EQUILIBRIUM CONSTRAINTS IN FC-SPACES

丁协平

数学物理学报(英文版). 2010 (4): 1257-1268. DOI: 10.1016/S0252-9602(10)60122-1

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In this article, four new classes of systems of generalized vector quasi-equilibrium problems are introduced and studied in FC-spaces without convexity structure. The notions of C_i(x)-FC-partially diagonally quasiconvex, C_i(x)-FC-quasiconvex, and C_i(x)-FC-quasiconvex-like for set-valued mappings are also introduced in FC-spaces. By applying these notions and a maximal element theorem, the nonemptyness and compactness of solution sets for four classes of systems of generalized vector quasi-equilibrium problems are proved in
noncompact FC-spaces. As applications, some new existence theorems of solutions for mathematical programs with system of generalized vector quasi-equilibrium constraints are obtained in FC-spaces. These results improve and generalize some recent known results in literature.

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CONVERGENCE THEOREMS AND MAXIMAL INEQUALITIES FOR MARTINGALE ERGODIC PROCESSES

罗光洲, 马璇, 刘培德

数学物理学报(英文版). 2010 (4): 1269-1279. DOI: 10.1016/S0252-9602(10)60123-3

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In this article, we study two types of martingale ergodic processes. We prove that a.e. convergence and L^p convergence as well as maximal inequalities, which are established both in ergodic theory and martingale setting, also hold well for these new sequences of random variables. Moreover, the corresponding theorems in the former two areas turn out to be degenerate cases of the martingale
ergodic theorems proved here.

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STRONG SOLUTIONS OF THE COUPLED NAVIER-STOKES-POISSON EQUATIONS FOR ISENTROPIC COMPRESSIBLE FLUIDS

谭忠, 张映辉

数学物理学报(英文版). 2010 (4): 1280-1290. DOI: 10.1016/S0252-9602(10)60124-5

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In this article, we are concerned with the strong solutions of the coupled Navier-Stokes-Poisson equations for isentropic compressible fluids in a domain Ω R³. We prove the local existence of unique strong solutions provided that the initial data ρ₀ and u₀satisfy a nature compatibility condition. The important point in this article is that we allow the initial vacuum: the initial density may vanish in an open subset of Ω. This is achieved by getting some uniform estimates and using a Schauder fixed point theorem.

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ON A PROBLEM IN COMPLEX OSCILLATION THEORY OF PERIODIC HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS

肖丽鹏, 陈宗煊

数学物理学报(英文版). 2010 (4): 1291-1300. DOI: 10.1016/S0252-9602(10)60125-7

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In this article, the zeros of solutions of differential equation

f^(k)}(z)+A(z)f(z)=0, (*)
are studied, where k>2, A(z)=B(e^z), B(ς)=g₁(1/ς)+g₂(ς), g₁and g₂ being entire functions with g₂ transcendental and ο(g₂) not equal to a positive integer or infinity. It is shown that any linearly independent solutions f₁, f₂, …, f_k of Eq.(*) satisfy λ_e(f₁… f_k) ≥ο(g₂) under the condition that f_j(z) and f_j(z+2πi )(j =1, …, k) are linearly dependent.

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THE REGULARITY OF QUASI-MINIMA AND ω-MINIMA OF INTEGRAL FUNCTIONALS

宁正元, 王秀丽

数学物理学报(英文版). 2010 (4): 1301-1317. DOI: 10.1016/S0252-9602(10)60126-9

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In this article, we have two parts. In the first part, we are concerned with the locally Holder continuity of quasi-minima of the following integral functional
∫_Ω f(x, u, Du) dx, (1)
where Ω is an open subset of Euclidean N-space (N ≥3), u: Ω→R, the Carath\'eodory function f satisfies the critical Sobolev exponent growth condition

|Du|^p-|u|^p*-a(x)l≤ f(x, u, Du)≤ L(|Du|^p+|u|^p*+a(x)), (2)
where L≤1, 1<p<N, p*=Np/N-p, and a(x) is a nonnegative function that lies in a suitable L^p space. In the second part, we study the locally H\"{o}lder continuity of ω-minima of (1). Our method is to compare the ω-minima of (1) with the minima of corresponding function determined by its critical Sobolev exponent growth condition. Finally, we obtain the regularity by Ekeland's variational principal.

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ADDITIVE HAZARDS MODEL WITH TIME-VARYING REGRESSION COEFFICIENTS

黄彬

数学物理学报(英文版). 2010 (4): 1318-1326. DOI: 10.1016/S0252-9602(10)60127-0

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This article discusses regression analysis of failure time under the additive hazards model, when the regression coefficients are time-varying. The regression coefficients are estimated locally based on the pseudo-score function [12] in a window around each time
point. The proposed method can be easily implemented, and the resulting estimators are shown to be consistent and asymptotically
normal with easily estimated variances. The simulation studies show that our estimation procedure is reliable and useful.

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OPERATOR-VALUED FREE FISHER INFORMATION OF RANDOM MATRICES

孟彬

数学物理学报(英文版). 2010 (4): 1327-1337. DOI: 10.1016/S0252-9602(10)60128-2

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The free Fisher information of an operator random matrix is studied. When the covariance of a random matrix is a conditional expectation, the free Fisher information of such a matrix is the double of this conditional expectation's Watatani index.

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BOUNDEDNESS OF CALDERÓN-ZYGMUND OPERATORS ON BESOV SPACES AND ITS APPLICATION

杨占英

数学物理学报(英文版). 2010 (4): 1338-1346. DOI: 10.1016/S0252-9602(10)60129-4

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In this article, the author introduces a class of non-convolution Calderón-Zygmund operators whose kernels are certain sums involving the products of Meyer wavelets and their convolutions. The boundedness on Besov spaces
B_p^{0, q}(1≤p, q≤ ∞) is also obtained. Moreover, as an application, the author gives a brief proof of the known result that Hörmander condition can ensure the boundedness of convolution-type Calderón-Zygmund operators on Besov spaces B_p^0, ^q(1≤p, q≤ ∞) . However, the proof is quite different from the previous one.

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STABILITY OF GASEOUS STARS IN THE NON-ISENTROPIC CASE

邓引斌, 巴娜, 谢华朝

数学物理学报(英文版). 2010 (4): 1347-1356. DOI: 10.1016/S0252-9602(10)60130-0

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The motion of the self-gravitational gaseous stars can be described by the Euler-Poisson equations. The main purpose of this article is concerned with the nonlinear stability of gaseous stars in the non-isentropic case, when
4/3 < γ <2, S(x, t) is a smooth bounded function. First, we verify that the steady states are minimizers of the energy via concentration-compactness method; then using the variational approach we obtain the stability results of the non-isentropic flow.

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