数学物理学报(英文版)

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THE SERIES SOLUTION OF THE GEL'FAND-LEVITAN-MARCHENKO EQUATION

徐邦清, 邵常贵

数学物理学报(英文版). 1987 (1): 1-8.

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The convergence of the Neumann series solution of the Gel'fand-Levitan-Marchenko equation in L^∞[0, ∞), L¹[0, ∞) and L²[0, ∞) is proved and the explicit expression of the series solution is given.

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SOME NEW RESULTS IN MULTIVARIABLE LINEAR SYSTEM——Some Achievements in China, 1980-1984

黄琳

数学物理学报(英文版). 1987 (1): 9-23.

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From 1980-1984 some new results on multivariable linear system had been obtained by Chinese authors. The author of this paper gave out in 5 section the concept of (A, B)-characteristic subspace and its applications, the minimal polynomial matrix and its properties and the equivalence between state-space model and polynomial matrix and other corresponding results, some applications of Yokoyama canonical form especially in solving the disturbance decoupling problem, the properties of external skew prime polynomial matrices and their applications to output regulation, the internal model principle in frequence domain and robust control, and finally some other results were introduced.

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EXISTENCE THEOREMS FOR LINEAR GROWTH PROCESSES WITH DIFFUSION

郑小谷, 丁万鼎

数学物理学报(英文版). 1987 (1): 25-42.

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In this paper, we have obtained the existence and uniqueness theorems in the case of the reactions being birth-death type with linear rates.

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CONTINUOUS-TIME STOCHASTIC APPROXIMATION PROCEDURE WITH RANDOMLY VARYING TRUNCATIONS

陈翰馥, 吴春涛, 朱允民

数学物理学报(英文版). 1987 (1): 43-55.

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In this paper a continuous-time stochastic approximation (S.A.) procedure with randomly varying truncations is proposed, and for its convergence to the value to be sought for it is proved that the conditions imposed on the regression function are rather weak and neither the independence of the increment of the error process nor the boundedness of the procedure are required. The convergence rate and the asymptotic properties for a class of measurement errors are also concerned.

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STRUCTURAL STABILITY OF ASYMPTOTICALLY ELEMENTARY SYSTEMS

姚勇

数学物理学报(英文版). 1987 (1): 57-62.

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In this paper, an elementary system proves constructively to be structurally stable provided the system is asymptotically stable on some region. This conclusion favors system modelling because Lyapunov and gradient systems are all elementary.

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NONTRIVIAL SOLUTIONS OF THE DIRICHLET PROBLEM FOR A CLASS OF NONLINEAR ELLIPTIC EQUATIONS

陈祖墀, 沈尧天

数学物理学报(英文版). 1987 (1): 63-74.

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Under the mild conditions by using the theory of the generalized Sobolev space and minimax theory we get the existence of solutions for a wide class of nonlinear Dirichlet problem as follows
d/dx_i[G_i(x,Du)]+f(x,u)=0, x∈Q, u|_∂Q=0,
where Q is a bounded domain in Rⁿ,G_i(x,q)=∂G/∂q_i, q=(q₁,q₂,…,q_n). This equation is the Euler equation of the functional
I(u)=∫_Q[G(x,Du)-F(x,u)]dx,
where
F(x,s)=∫₀^xf(x,t)dt.

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DECOMPOSITION, REPRESENTATION AND EXTENSION OF THE HARMONIC FUNCTIONS

李志阐

数学物理学报(英文版). 1987 (1): 75-83.

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In this paper, by using the probabilistic method, we obtained a decomposition theorem for the harmonic functions, generalized and strengthened some theorems:Doob's theorem on the limit behaviors of the superharmonic functions, Bocher's theorem on the representation of the harmonic functions and the extension theorem of the harmonic functions etc.

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SOME SYSTEMS OF ORTHOGONAL POLYNOMIALS ASSOCIATED WITH SINGULAR INTEGRAL EQUATIONS

杜金元

数学物理学报(英文版). 1987 (1): 85-96.

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In this paper, some systems of orthogonal polynomials associated with singular integral equation of the form
a(t)φ(t)+b(t)/π∫_-1¹φ(t)/(τ-t)dτ=f(t),-1 < t <1
is derived, and some properties of such polynomials will are discussed.

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DEGENERATE ELLIPTIC SYSTEMS OF CLASS Ⅰ

邓志兵

数学物理学报(英文版). 1987 (1): 97-108.

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In this paper, we considered the first class (class Ⅰ) of elliptic systems of partial differential equations with a special kind of lower-order terms which are one-order singular. For the classical well-posedness of Dirichlet problem and skew derivative problem in the unit circle, we gave a discussion in full detail, and obtained complete results.

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ON THE GROWTH AND VALUE DISTRIBUTION OF ANALYTIC SOLUTIONS OF A CLASS OF ALGEBRAIC DIFFERENTIAL EQUATIONS

何育赞, 高仕安

数学物理学报(英文版). 1987 (1): 109-120.

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In this paper, we show that the growth of meromorphic or algebroidal solutions of some algebraic differential equations can be estimated in terms of the growth of the coefficients in tho equation and the counting functions of some value points. We point simulteneously out that the growth of algebroid solutions of certain class of differential equations can be estimated using only the growth of coefficients in the equation, and give an example which is not belonging to this class to show that the above conclusion is not true.

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