数学物理学报(英文版)

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CAUCHY PROBLEM FOR SEMILINEAR HYPERBOLIC EQUATION OF HIGHER ORDER WITH DISCONTINUOUS INITIAL DATA CAUCHY PROBLEM FOR SEMILINEAR HYPERBOLIC EQUATION OF HIGHER ORDER WITH DISCONTINUOUS INITIAL DATA

陈恕行

数学物理学报(英文版). 1994 (2): 121-129.

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In this paper the following Cauchy problem is under considerabon,
Lu=F(t,x₁,…,u,x_m,…,∂^m-1u) ∂^m-1u_t=0=q (j=1,…,m) where L is a strictly hyperbolic operator of m-th Order with respect to direction t, F is a C^∞ function of its arguments, the initial data have discontinuity along a smooth submanifold with codimentional 1 on initial plane and some conormal regularity with respect to manifold.

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AN HARMONIC ANALYSIS FOR OPERATORS IN THE CASE OF A LOCALLY COMPACT ABELIAN GROUP: F.AND M.RIESZ THEOREMS

于树模

数学物理学报(英文版). 1994 (2): 130-138.

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Let G be a locally compact Abelian group, B a homogeneous Banach algebra without the order on G.L_B¹ at denotes the set of all integrable operators with respect to right translation on B(see[1]). Under some convenient conditions we obtain the following results:both the first F. and M. Riesz Theorem for operators in L_L¹(G)¹ and the second F. and M. Riesz Theorem for operators in L_A₂(G)¹ hold.

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A BRANCH-AND-BOUND ALGORITHM IN THE TOURING-PATH PROBLEM AND ITS COMPUTER IMPLEMENTATION

徐绪松

数学物理学报(英文版). 1994 (2): 139-145.

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This paper provides a branch-and-bound algorithm for seeking the best touring-path. Using the reduction method, this algorithm found cost low-limits of a set of the paths. As a branch-node, the live node having minimum low-limit has been expanded and a state space tree has been generated. The best touring-path has been found. Moreover, combining algorithm with data structure, the author studied many details about this problem, and gave its computer implementation.

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A NOTE ON THE STRONG CONSISTENCY OF ESTEMATES IN PARTIALLY LINEAR MODELS

朱力行, 安鸿志

数学物理学报(英文版). 1994 (2): 146-152.

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In this note, a sort of partially linear models, Y=β^τX+g(T)+ε is considered, where T and X are, respectively, one-dimensional and d-dimen-sional, and independent each other. Under the least restrictions for the distributions of X and ε, a strong consistent estimate of parameter β based on the method of An and Zhu is proposed, and under mild conditions, an estimate of g(T) is proved to be consistent to g(T).

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ON STEFAN PROBLEM WITH PRESCRIBED CONVECTION

易法槐, 邱宜坪

数学物理学报(英文版). 1994 (2): 153-166.

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This paper deals with the equation:
∂β(u)+▽[vβ(u)-▽u]=f in D'(Q_T) where Q_T=Ω×(0,T], Ω is a bounded domain with piecewise smooth boundary, β is maximal monotone graph,v:Q_T→R^m There are weak solutions to the evloutionary and seady-state problems associated with this equation, provided the boundary conditions on u are chosen appropriately. We also prove the uniqueness of both problems.

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CRITICAL STOPPING TIMES AND SEMIMARTINGALESOF STOCHASTIC PROCESSES

胡必锦

数学物理学报(英文版). 1994 (2): 167-173.

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This paper discusses the property of semimartingales of B-valued R. R. C. process W, and the relation between this property and critical stopping time σ_ẇ of W after giving the definition of σ_ẇ and the structural approach to σ_ẇ. A conclusion is drawn from this paper that the process W being a non-semimartingale is characterized by P(σ_ẇ<∞) > 0.
Finally, two kinds of vector valued processes with R-control process are discussed, and they are shown to be non-semimartingales by the use of Theorem 2 in this paper.

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REPRESENTATIONS AND ENUMERATIONS OF SEMIORDERS WITH HEIGHT ONE

巫世权

数学物理学报(英文版). 1994 (2): 174-178.

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In this paper, we represent semiorders with height at most one by ordered paritions and give an analytic formula for enumerating the semiorders of an n-set. Problem 2. 21, posed by K. P. Bogart in[7], is closed for semiorders and interval orders with height at most one and cardinality n.

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AN EFFECTIVE IMPROVEMENT OF REMES ALGORITHM

熊规景, 谢四清

数学物理学报(英文版). 1994 (2): 179-187.

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In this paper, we improve Remes algorithm by simplifying the process of finding maximum points, avoiding solving linear of equations and finding zero points of error function. For an arbitrary continuous function f, we obtain the explicit formula of its nth best Chebyshev approximation on n+2 knots, at the same time, we show the explicit expression of minimal deviation in a very simple way. Finally we obtain the convergence deviation in a very simple way. Finally we obtain the convergence of the improved algorithm and give the analysis of numerical results.

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ON SOME RESULTS FOR NONLINEAR BEST CHEBYSHEV APPROXIMATION WITH LGH CONDITION

韦旦

数学物理学报(英文版). 1994 (2): 188-194.

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In this paper, some new results are given for a class of nonlinear best chebyshev approximation which satisfies LGH condition.

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NONNULL DISTRIBUTION OF THE LIKELIHOOD RATIO CRITERION FOR TESTING THE EQUALITY OF DIAGONAL BLOCKS WITH BLOCKWISE INDEPENDENCE

A. K. Gupta C. C. Chao

数学物理学报(英文版). 1994 (2): 195-203.

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In this paper, the nonnull moments and the distributions of the likelihood ratio criterion for testing the equality of diagonal blocks with blockwise independence under certain alternatives have derived.

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THE TURNPIKE IN DYNAMIC STOCHASTIC ECONOMIC GROWTH MODELS FOR STATE-CONTINGENT CAPITAL STOCKS

江胶宁, 喻小培, 何穗, 蹇明

数学物理学报(英文版). 1994 (2): 204-212.

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A stochastic economic growth model may be transformed into a deterministic economic growth model with an infiaite dimentional Banach space of state-contingent capital stocks[6]. This paper proves that under the framework, the stochastic analogUes of the asymptotic turnpike theorems in the standard deterministic economic growth model[5] will continue tO hold if we assume that essentially smooth programs satisfy uniformly essentially dominant diagonal condition.

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MAIN THEOREM ON COVERING SURFACES

孙道椿

数学物理学报(英文版). 1994 (2): 213-225.

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In this paper, we introduce the concepts of cut ratio and covered ratio of domains. Further, we give an explicit estimation of the constant in the general Ahlfors' covering theorem and Ahlfors' fundamental theorem on a sphere. Because of the importance of these theorems, it is no doubt that these rstimations is significant. Applying these yesults, we improve a series of theorems, prove that there exists a sequence of filling circles for algebroidal function. and establish a new normal criterion. (These works will be done in other papers.)

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ON CERTAIN BOUNDARY VALUE PROBLEMS FOR NONLINEAR INTEGRODIFFERENTIAL EQUATIONS

D. G. Pachpatte

数学物理学报(英文版). 1994 (2): 226-234.

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In this paper we seek sufficient conditions for the existence, uniqueness and continuous dependene on parameter of solutions of certain boundary value problems for nonlinear integrodifferential equations. The main tool employed in our analysis is based on converting the problems into equivalent Volterra integral equations by means of Green's function representation and the application of the Banach fixed point theorem.

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A GENERALIZATION OF CARATHEODORY INERUALITY

杨长森

数学物理学报(英文版). 1994 (2): 235-239.

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Let H be a Hilbert space. and f(z) is an analytic function in unit disk,|f(z)|<1, then
||f'(A)|| ≤ (||I-f^*(A)f(A)||^(1)/2||I-f(A)f^*(A)|^(1)/2)/1-||A||² where A is a proper contraction operator on H.

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