数学物理学报(英文版)

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SOME CHARACTERS OF A CLASS OF ORNSTEIN-UHLENBECK TYPE MARKOV PROCESSES WITH STABLE PROCESSES

王永进

数学物理学报(英文版). 1997 (2): 121-128.

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This article concerns a class of Ornstein-Uhlenbeck type Markov processes and for which the level sets will be approached. By constructing a new class f processes,we shall obtain an inequality on the Hausdorff dimensions of the level sets for the Ornstein-Uhlenbeck type Markov processes. Based on this result, we finally verify that any two independent O-U.M.P with α-stable processes could collide with probability one.

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DEFORMING CONVEX HYPERSURFACES BY THE LINEAR COMBINATION OF THE MEAN CURVATURE AND THE N-TH ROOT OF THE GAUSS-KRONECKER CURVATURE

沈一兵, 盛卫民

数学物理学报(英文版). 1997 (2): 129-142.

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In this paper a flow of convex hypersurfaces in the Euclidean space by the linear combination of the mean curvature and the n-th root of the Gauss-Kronecker curvature is considererd. It is proved that such deforming convex hypersurfaces converge to a round sphere in the Huisken's sense.

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SOME PATH PROPERTIES OF BROWNIAN MOTION AND SUPER-BROWNIAN MOTION ON THE SIERPINSKI GASKET

郭军义

数学物理学报(英文版). 1997 (2): 143-150.

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We study in this paper the path properties of the Brownian motion and super-Brownian motion on the fractal structure-the Sierpinski gasket. At first some results about the limiting behaviour of its increments are obtained and a kind of law of iterated logarithm is proved. Then A Lower bound of the spreading speed of its corresponding super-Brownian motion is obtained.

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A MAXIMUM PRINCIPLE FOR DISTRIBUTED PARAMETER SYSTEMS WITH MIXED PHASE-CONTROL CONSTRAINTS ANDENDPOINT CONSTRAINTS

张平健

数学物理学报(英文版). 1997 (2): 151-158.

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This paper considered the optimal control problem for distributed parameter systems with eded phase-control constraints and end-point constraints. Pontryagin's maximum principle for optimal control are derived via Duboviskij-Milujin theorem.

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REGULARITY OF WEAK SOLUTIONS TO QUASILINEAR ELLIPTIC OBSTACLE PROBLEMS

杨健夫

数学物理学报(英文版). 1997 (2): 159-166.

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This paper obtain C^1,α-regularity of weak solutions to the p-Laplacian obstacle problem with C^1,β-obstacle function under controllable growth conditions.

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SINGULAR PERTURBATIONS OF A HIGHER-ORDER SCALAR NONLINEAR BOUNDARY VALUE PROBLEM

史玉明, 高灿柱

数学物理学报(英文版). 1997 (2): 167-179.

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In the present paper, the singular perturbations for the higher-order scalarnonlinear boundary value problem
ε²y=f(t,ε,y,y',…,y^(n-2),εy(n-1)),t∈[0,1] H₁(y(0,ε),…,y^(n-3)(0,ε),εy^(n-2))(0,ε),εy^(n-1))(0,ε),ε)=0,H₂(y(0,ε),…,y^(n-1)(0,ε),y(1,ε),…,y^(n-1)(1,ε),ε)=0 are studied, where ε > 0 is a small parameter, n ≥ 2. Under some mild assumptions,we prove the existence and local uniqueness of the perturbed solution and give out the uniformly valid asymptotic expansions up to its nth-order derivative function by employing the Banach/Picard fixsed-point theorem. Then the existing results are extended and improved.

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SELF-SIMILAR SOLUTIONS OF A CLASS OF NONLINEAR PAPTIAL DIFFERENTIAL EQUATION

严国政

数学物理学报(英文版). 1997 (2): 180-189.

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In this paper, we investigate the following partial differential equation, u_t-a(x·▽u)|u|^p-1=△u+|u|^p-1u, where a ≥ 0 and p> 1. When n(p-1)/2 > 1 and p > 3, we obtained a nontrivial non-negative global solution. Furthermore, on Sobolev space W^1,s(W^2,s) with s > 1. a nonuniqueness result is established which shows that there exists a positive solution u(t,x) with u(t,x)→0 as t→0 in W^1,s(W^2,s). On the other hand, our result can be regarded as a generalization of conclusion of Haraux, A.and Weissler, F.B. in[5].

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A LIMINF RESULT FOR HANSON-RUSSO TYPE INCREMENTS OF FRACTIONAL BROWNIAN MOTION

张立新

数学物理学报(英文版). 1997 (2): 190-197.

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Let {X(t), t > 0} be a fractional Brownian motion of order 2α with 0 < α <1,β > 0 be a real number, a_T be a function of T and 0 < a_T ≤ T, lim_T→∞(log T/a_T)/log log T=r, (0 ≤ r ≤ ∞). In this paper, we proved that
c₁((r)/1+r)^α ≤ lim inf_T→∞(log log T)^β max_{a_T ≤ t ≤ T}(|X(T)+X(T-t)|)/t^α(log(T/t)+log logt)^β ≤ c²((r)/1+r)^α,a.s. where c₁, c₂ are two positive constants depending only on α,β.

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A CLASS OF NATURALLY ORDERED ABUNDANT SEMIGROUPS WITH A GREATEST IDEMPOTENT

曾祥金, 景奉杰

数学物理学报(英文版). 1997 (2): 198-204.

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On the base of the construction of abundant semigroups with a normal mallal idempotent[14], in this paper we consider a class of naturally ordered abundant semigroups which satisfies the regularity condition and contains a greatest idempotent.Furthermore, we give a completely description of the overall structure of such ordered semigroups via the algebraic structure of them, which generalizes known result obtainedby Blyth and McFadden^[3].

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PARALLEL MULTIPLICATIVE ITERATIVE METHODS FOR CONVEX PROGRAMMING

陈忠, 费浦生

数学物理学报(英文版). 1997 (2): 205-210.

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In this paper, we present two parallel multiplicative algorithms for convex programming. If the objective function has compact level sets and has a locally Lipschitz continuous gradient, we discuss convergence of the algorithms. The proofs are essentially based on the results of sequential methods shown by Eggermont^[1].

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A HARDY-LITTLEWOOD THEOREM FOR WEIGHTED SPACES

刘建明, 郑维行

数学物理学报(英文版). 1997 (2): 211-218.

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Let q > 2,f is measurable function on Rⁿ such that f(x)|x|^n(1-2/q) ∈L^q(Rⁿ), then its Fourier transform f can be defined and there exists a constant A_q such that the inequality||f||_q ≤ A_q||f|·|^n(1-2/q)||_q holds.This is the Hardy-Littlewood Theorem. This paper considers the corresponding result for the Fourier-Bessel transform and Fourier-Jacobi transform.It is interesting that we can deal with theses two cases in the same way,and the function corresponding to|x|ⁿ is tw(t), where w(t) is the weight,w(t)=t^2α+1 for Fourier-Bessel transform,and w(t)=(2 sinh t)^2α+1 (2 cosh t)^2β+1 for Fourier-Jacobi transform.

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ON BOUNDEDNESS OF SOLUTIONS OF IMPULSIVE INTEGRO-DIFFERENTIAL SYSTEMS WITH FIXED MOMENTS OF IMPULSE EFFECTS

傅希林, 张立琴

数学物理学报(英文版). 1997 (2): 219-229.

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Several boundedness criteria for the impulsive integro-differential systems with fored moments of impulse effects are established, employing the method of Lyapunov functions and Razumikhin technique.

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SOME LARGE SAMPLE PROPERTIES OF AN ESTIMATOR OF THE HAZARD FUNCTION FROM RANDOMLY CENSORED DATA

王启华

数学物理学报(英文版). 1997 (2): 230-240.

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In this paper, A nonparametric hazard estimtor is introduced. Weak convergence and strong uniformly coinsistency of the proposed estimator λ_n(t) are investigated on a bounded interval, respectively. An asymptotic representation of λ_n(t) is also given, and the asymptotic representation is used to prove asymptotic normality of the hazard estimator.

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