数学物理学报(英文版)

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WU WEN-TSÜN——AN OUTSTANDING MATHEMATICIAN

李邦河

数学物理学报(英文版). 1989 (4): 361-365.

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GLOBAL EXISTENCE OF SOLUTION TO NONLINEAR INTEGRODIFFERENTIAL EQUATION IN A BANACH SPACE

庄万, 于洪义

数学物理学报(英文版). 1989 (4): 367-372.

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Using Daher's fixed point theorem, we obtain a local existence theorem, in which the assumption is weaker than That in the Theorem 2.1 in[2]. Based on this theorem, we get a global existence theorem which is an extension of certain results for ordinary differential equations.

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EXISTENCE OF GENERALIZED SOLUTION AND ORBITAL STABILITY OF STANDING WAVES FOR NONLINEAR SINGULAR SCHRÖDINGER EQUATION

张波

数学物理学报(英文版). 1989 (4): 373-383.

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The existence of generalized solution to the initial value problem iu_t+△u+k/(x_N)u_{X_N}+q(x)u+|u|^p-1u=0 on R^N is studied, By Galerkin method, we prove that the solution always exists for every initial value in H¹(R^N; k) if 1 < p < (N+k)/(N+k-2), N ≥ 2. Finally, we prove orbital stability of standing waves for nonlinear singular Schrödinger equation.

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THE EXISTENCE AND NODAL CHARACTER OF THE SOLUTIONS IN Rⁿ FOR SEMILINEAR ELLIPTIC EQUATION INVOLVING CRITICAL SOBOLEV EXPONENT

邓引斌

数学物理学报(英文版). 1989 (4): 385-402.

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This paper is concerned with the existence and the nodal character of the nontrivial solutions in the entire space for some semilinear elliptic equation involving critical Sobolev exponent.

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THE CONVERGENCE RATES OF EMPIRICAL BAYES ESTIMATION FOR PARAMETERS OF TWO-SIDED TRUNCATION DISTRIBUTION FAMILIES

韦来生

数学物理学报(英文版). 1989 (4): 403-413.

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Consider the two-sided truncation distribution families written in the form f(x,θ)=w(θ₁, θ₂)·h(x)I_{[θ₁,θ₂]}(x)dx, where θ=(θ₁,θ₂). T(X)=(t₁(X), t₂(X))=(min(X₁, …, X_m), max(X₁, …, X_m)) is a sufficient statistic and we denote its marginal density by f(t)dμ^T. The prior distribution of θ belong to the famlly J={G:∫∫_Θ||θ||2dG(θ)<∞}. In this paper, we have constructed the empirical Bayes (EB) estimator of θ, φ_n(t), by using the kernel estimation of f(t) and established its convergence rates. Under suitable conditions it is shown that the rates of convergenc of EB estimator are O(N-^{((λk-1)(k+1))/(2(k+2)k))}, where the neural number k > 1 and 1/2 < λ < 1-(1/2k). Finally an example about this result is given.

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STABLE HARMONIC MAPS FROM COMPLETE MANIFOLDS

忻元龙

数学物理学报(英文版). 1989 (4): 415-420.

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Recently, the Liouville theorem for stable harmonic maps is proved from Euclidean space into sphere. The technique employed in this paper allows the researchers to consider stable harmonic maps from complete manifolds.

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SOME KINDS OF SINGULAR INTEGRAL EQUATIONS OF HILBERT KERNEL WITH CONVOLUTION

沈永祥

数学物理学报(英文版). 1989 (4): 421-426.

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In this paper, some kinds of singular integral equations of Hilbert kernel with convolution will be set up and discussed. The general solution and conditions of solvability in class L₂[-π, π] (or{0}) are obtained.

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ON SOME INEQUALITIES WITH WEIGHTS

丁夏畦, 罗佩珠

数学物理学报(英文版). 1989 (4): 427-436.

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This note is a continuation of[1] and[4]. We get further completions and new applications of the power weight inequalities in[1] and[4].

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REMARKS ON BOUNDS ON THE DISCREPANCY OF APPROXIMATE SOLUTIONS CONSTRUCTED BY GODUNOV'S SCHEME

王靖华

数学物理学报(英文版). 1989 (4): 437-452.

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The bounds on the discrepancy of approximate solutions constructed by Gedunov's scheme to IVP of isentropic equations of gas dynamics are obtained, Three well-knowu results obtained by Lax for shock waves with small jumps for general quasilinear hyperbolic systems of conservation laws are extended to shock waves for isentropic equations of gas dynamics in a bounded invariant region with ρ=0 as one of boundries of the region. Two counterexamples are given to show that two inequalities given by Godunov do not hold for all rational numbers γ∈(1, 3]. It seems that the approach by Godunov to obtain the forementioned bounds may not be possible.

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SOME NOTES ON MULTIPLE STRA TONOVITCH INTEGRALES

胡耀忠

数学物理学报(英文版). 1989 (4): 453-462.

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Tn this paper we point out some similarities of multiple Stratonovitch integrale series with Talor series and prove some properties and a convergence theorem.

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APPROXIMATE ISOMETRIES ON (F)-NORMED SPACES

黄森忠

数学物理学报(英文版). 1989 (4): 463-477.

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By considering the connection of approximate isometry with isometry we study the following problem "For what subclass of (F)-normed spaces the metric structure completely determines the linear constructure and further, what form can be taken when we represent an approximate isometry as a perturbation of isometry. We introduce a subclass of so-called midpoint p-constracted (F)-normed spaces. For this subclass some new results are obtained and especially the known results of Mazur-Ulam and Gervitz-Gruber are extended.

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