数学物理学报(英文版)

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ON EXCHANGE ALGORITHM FOR NONLINEAR BEST CHEBYSHEV APPROXIMATION WITH LGH CONDITION

熊规景, 韦旦

数学物理学报(英文版). 1994 (4): 361-370.

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In this paper, exchange algorithm and its convergence, quadratic convergence are given for nonlinear best chebyshev approximaton with LGH condition.

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ON THE CLASS Φ_p^*(α,β,γ,ε,η;A) of p-VALENT FUNCTIONS WITHREFERENCE TO THE BERNARDI INTEGRAL OPERATOR

蹇明

数学物理学报(英文版). 1994 (4): 371-376.

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Bernardi has proved that if f(z) is starlike univalent in the unit disk △, then so is the function g(z) given by
g(z)=(c+1)z^-1∫0^zt^c-1f(t)dt,c=1,2….In this paper, we extend Bernardi's theorem to certain class Φ_p^*(α,β,γ,ε,η;A) of p-valent starlike functions for operators. We prove that if f(A)∈Φ_p^*(α,β,γ,ε,η;A), then g(A), defined by
g(_A)=(p+c)∫₀¹t^c-1f(tA)dt,c=1,2,… also belongs to Φ_p^*(α,β,γ,ε,η;A) and give a sufficient and necessary vondition with reference to f(A) ∈Φ_p^*(α,β,γ,ε,η;A).

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CONDITIONS OF ORTHOGONALITY AND STABILITY ASSOCIATED WITH THE GENERAL REFINEMENT EQUATION

张青

数学物理学报(英文版). 1994 (4): 377-383.

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Given a sequence {b(j), j ∈ Z}, let φ be the compactly supported distribution solution to following refinement equation:
φ=∑_j∈Zb(j)φ(r·-j) we derive necessary and sufficient conditions for orthogonality, stability and linear independence of integer translates of φ. These conditions are mainly based on the location of the zeros of symbol b(z)=∑_j∈Zb(j)z'. Such φ can generate a multiresolution analysis.

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PIECEWISE CONTINUOUS SOLUTIONS OF NONLINEAR ELLIPTIC EQUATIONS IN THE PLANE

戴道清

数学物理学报(英文版). 1994 (4): 384-392.

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The Riemann boundary value problem is solved for the nonlinear elliptic equation in the plane
W_z=H(z,W,W_z) + f(z,W).The function H is Lipschitz continuous with respect to the last two variables, with the Lipschitz constant for the last variable being strictly less than one (ellipticity condition). While the function f satisfies a natural growth condition with σ > 0.
|f(z,W)| ≤ F(z)|W|^σ.

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EXCESSIVE FUNCTIONS OF A CLASS OF SUPERPROCESSES

赵学雷

数学物理学报(英文版). 1994 (4): 393-399.

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In this paper, we investigate the excessive functions of a class of superprocesses. We establish some relationships between excessive functions with respect to a superprocess and those with respect to its underlying process.

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SINGULARITY AND QUADRATURE REGULARITY OF(0,1,…,m-2,m)-INTERPOLATION ON THE ZEROS OF(1-x) P_n-1^(α,β)(x)

史应光

数学物理学报(英文版). 1994 (4): 400-408.

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In this paper, we show that if a problem of (0, 1,..,m-2, m) -interpolation on the zeros of (1 -x)P_m-1^(α,β)(x)(α>1,β ≥ -1) has an infinity of solutions then the general form of the solutions is f₀(x) +Cf(x) with an arbitrary constant C,where P_m-1^(α,β)(x) stands for the (n-1)th Jacobi polynomial, and f₀ (x) and f(x) are fixed polynomials of degree ≤ mn-1,and, meanwhile. the explicit form of f(x) is given. Moreover, a necessary and sufficient condition of quadrature regularity of the interpolation in a manageable form is established.

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THE GENERALIZED EINSTEIN RELATION ON A COMPACT ORIENTABLE RIMANNIAN MANIFOLD

方海涛, 龚光鲁

数学物理学报(英文版). 1994 (4): 409-416.

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A generalized Einstein relation is established for a drifted Brownian motion on a compact orientable Remannian manifole. The original form of such relation comes from an explicit formula of diffusion coeffcient by using the autocorrelation function of the velocity of the Einstein fluctuation theory of the diffusion process.

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COMPLETE CONVERGENCE OF ERROR VARIANCE ESITIMATES UNDER φ-MIXING ERROR IN LINEAR MODELS

薛留根

数学物理学报(英文版). 1994 (4): 417-425.

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In this paper,we consider the estimates σ_m² of error variance σ²=Var(e_i) in the linear models Y_i=x'_iβ+e_i(i=1, 2,…). We study the complete convergence of σ_m²-σ² when the error {e_i }is a sequence of identically distributed φ-mixing variables. And we also obtain the better convergence rates when {e_i} is not identically distribution.

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FREDHOLM DETERMINANT SOLUTION FOR NONLINEAR EQUATIONS ASSOCIATED WITH ISOSPECTRAL SCHRÖDINGER EICENVALUE PROBLEM

黄烈德, 夏忠奂

数学物理学报(英文版). 1994 (4): 426-437.

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The explicit solution of a large class of nonlinear evolution equations associated with the isospectral Schröding equation is given in terms of the Fedholm determinant of a family of linear integral operators,whose kernels solve the corresponding base equations. Using Fredholm theory,the relation between the Fredholm determinant method and the inverse scattering method is clarified. Moreover,it is also shown that the Cauchy problems for these nonlinear evolution equations can be solved by the Fredholm determinant method.

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A CLASS OF SINGULARLY PERTURBED NONLINEAR ROBIN PROBLEMS

赵为礼

数学物理学报(英文版). 1994 (4): 438-445.

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In this paper, taking the search of steady state solutions of one-dimension reactiondiffusion problems as the background, we study the existence and asymptotic estimates of solutions of the singularly perturbed Robin problem
a (x, ε)y"=f(x,y,y',ε),
a₀y(0,ε)-b₀y' (0 ε)=A₀, a₁y(1,ε) + b₁y' (1,ε)=A₁,where it is assumed that f_y'≡0 or f_y'≢0 and f_y' ≤ 0.

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A J-CONVEX SUBSET WHICH IS NOT PSH-CONVEX

步尚全

数学物理学报(英文版). 1994 (4): 446-450.

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In this paper, we show that J-convex and PSH-convex are different notions for closed bounded subsets in complex Banach space. Precisely, we show that a complex Banach space X is infinite dimensional if and only if there exists a closed bounded J-convex subset which is not PSH-convex.

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PARABOLIC EQUATIONS WITH BOTH NON-CONVEXITY NONLINEARITIES AND STRONG DEGENERACY

尹景学

数学物理学报(英文版). 1994 (4): 451-460.

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This paper is devoted to a strongly degenerate or singular quasilinear parabolic equation.We first extend Kalashnikov's ekistence results[6] to a general situation for the equation without convexity. As a supplementation, we also discuss the regularity and uniqueness of solutions.

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THE PATHWISE SOLUTION FOR A CLASS OF QUASILINEAR STOCHASTIC DIFFERENTIAL EQUATION IN BANACH SPACES I

胡耀忠

数学物理学报(英文版). 1994 (4): 461-474.

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In this paper we will first get some results about Banach valued stochastic integral.Then we will discuss the linear stochastic equations of evolution with random coefficients,and obtain the existence and uniqueness theorem as well as the perturbation theorem.

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A REMARK ON L₁ SUBSPACES OF L₁ (^μ,^X)

定光桂, 黄森忠

数学物理学报(英文版). 1994 (4): 475-478.

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Let (Ω, ∑,μ) be a measure space and (X_ω)_ω∈Ω a family of closed linear subspaces of some Banach space X. Let L₁ (μ, (X_ω)) be the linear subspace of the Bochner space L₁ (μ,X) given by L₁ (μ, (X_ω)):={f ∈ L₁ (μ,X):f(ω) ∈ X_ω for all ω ∈ Ω}. Suppose that each X_ω is of type p with constant 1 for some fixed p > 1. Two results are obtained:(1) If E ⊆ L₁ (μ, (X_ω)) is isomorphic to some L₁ space with constant less than 2^1-1/p, then there is a projection from L₁ (μ,X) onto E. (2) If E ⊆ L₁ (μ, (X_ω)) is a L_1,λ space with λ small enough then E is complemented in L₁ (μ, (X_ω)). These results generalize early results of Dor[3], Alspach and Johnson[1].

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