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Convergence on the iteration of Halley family in weak conditions

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Chinese Science Bulletin 1997年第7期42卷 552-555页

作者： WANG XinghuaDepartment of Mathematics, Hangzhou University, Hangzhou 310028, China Department of Mathematics Hangzhou University Hangzhou China

WE have obtained the convergence theorems of the iteration of Halley family by the point estimate of Smale. In the point estimate, map f which is desired to be solved is presumed to be analytic in some proper neighbor... 详细信息

关键词： operator equations Banuch space the iteration of Halley family convergence weak conditions.

A weak equivalence theorem for weak random elements with values in weakly compactly generated Banach spaces and its applications

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Chinese Science Bulletin 1996年第1期41卷 6-10页

作者：郭铁信 Department of Mathematics Xiamen University Xiamen 361005 China

1 Introduction and preliminaries The aim of this note is to prove the following basic theorem: Let (Ω, σ, u) be a probability space, (B, ‖·‖) a weakly compactly generated Banach space, and a mapping V from Ω to B be a weak random element, then there exists a unique strongly measurable random element V from Ω to B under the sense of almost sure equality such that (?) is weakly equivalent to the weak random dement V. This theorem itself not only removes the limitation that the weak random element considered in a theorem due to Lewis is bounded, but also has many applications to probability theory in Banach spacest. As an example of applications, we give a theorem of properties of the reproducing kernel Hilbert spaces for weak twofold weak random elements.

关键词： weak random elements strongly measurable random elements weak equivalence theorems reproducing kernel Hilbert spaces.

Existence of weak solution for a doubly degenerate parabolic equation with Radon measures as data

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Chinese Science Bulletin 1995年第20期40卷 1677-1680页

作者：甘筱青 Department of Basic Courses Nanchang University Nanchang 330029 China

Recently, some scholars such as Boccardo, Callout and Rakotoson, studied studied the second-order partial differential equation u=f, where f∈L^1(Ω) (non-reflexive), more generally f∈M(Ω), M(Ω)=[C_c(Ω)]＇, the topological dual of C_c(Ω), is also called the set of Radon-measures. A classical example is f=δ(the measure of Dirac), δ∈M(Ω). In brief, they proved the existence of weak solution for a quasilinear elliptic problem: -div((x, u, Du))=f∈M(Ω), u|_αΩ=0, in which ΩR^N, is

关键词： Radon-measure weak solution priori estimate approximation.

ON weak STABILITY OF DISCRETIZATION FOR OPERATOR EQUATION

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Science China Mathematics 1989年第8期32卷 897-907页

作者：郭本瑜 Shanghai University of Science and Technology

The discretization of operator equation is considered. The weak stability is defined, which is the generalization of stabilities by Strang, Stetter, Keller and the author. Under some conditions, such stability implies the existence of approximate solution and the convergence for the operator equation with isolated solutions. Two examples show how to. use the theorems here.

关键词： weak stability discretization operator equation.

Convergence rates to nonlinear diffusion waves for weak entropy solutions to p-system with damping

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Science China Mathematics 2003年第4期46卷 562-575页

作者：朱长江 Laboratory of Nonlinear Analysis Department of MathematicsCentral China Normal UniversityWuhan 430079China

This paper studies the asymptotic behavior ofweak entropy solutions to the Cauchy problem of the so-called p-system with damping. The convergence rates to nonlinear diffusion waves for weak entropy solutions are obtained in L∞-norm or L2-norm. These convergence rates are the same to the decay rates of smooth solution obtained by Nishihara. They are proved by using the vanishing viscosity method and the elementary L2-energy method.

关键词： weak entropy solution, diffusion wave, convergence rate, vanishing viscosity method, energy method.

THE BEST weak t-NORM OF PROBABILISTIC METRIC SPACE

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Chinese Science Bulletin 1991年第23期36卷 1937-1939页

作者：游兆永朱林户 Department of Mathematics Xi'an Jiaotong University Xi'an 710049 PRC The Air Force Institute of Engineering Xi'an 710038 PRC

1. Introduction In [1], let (E, F)be a probabilistic metric (PM) space, and then (E. F, T_W) be a generalized Menger (GM) space, where T_W(a, b)= It follows that all Menger’s triangle inequalities can be given with G... 详细信息

关键词： probabilistic metric space best weak t-norm

A CLASS OF PLANAR n (EVEN NUMBER)-POLY-NOMIAL SYSTEM WITH A weak FOCUS OF ORDER n^2-n

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Chinese Science Bulletin 1992年第19期37卷 1590-1593页

作者：白敬新刘一戎 Ebian Dongfeng Wood Factory Ebian 614300 PRC Institute of Mathematics Nankai University Tianjin 300071 PRC

For any second order autonomous differential system with a polynomial of degree n on its right-hand side, what the maximum order of fineness of its weak focal point, weak saddle point in real domain and weak critical singular point in complex domain is (M(n)=?)? This problem relates to Hilbert’s 16th problem closely. Inequality M(3)≥7 have

关键词： weak focus fineness

Growth of the Fourier transforms of the weak Hardy spaces

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Chinese Science Bulletin 1995年第12期40卷 976-980页

作者：刘和平 Department of Mathematics Peking University Beijing 100871 China

Interest in the weak Hardy spaces comes from the careful consideration of the sharp-ness of some basic operators in harmonic analysis. In the past twenty years thenoncommutative Fourier transform becam a useful tool i... 详细信息

关键词： Heisenberg group weak Hardy space Fourier transform.

PARTIAL REGULARITY FOR weak SOLUTIONS OF QUASILINEAR ELLIPTIC SYSTEMS

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Chinese Science Bulletin 1991年第9期36卷 705-709页

作者：严树森李工宝 Wuhan Institute of Mathematical Sciences Academia Sinica Wuhan 430071 PRC

In this note, we study the partial regularity for the weak solutions of the elliptic systems:Dα(Aαβij（x,u）Dβuj)=fi（x,u,Du）, x∈Ω,i=1,2,…,N, （1）where Ω is a bounded domain in Rn, n≥3 and N≥1. Here, the repeated Latin letters andrepeated Greek letters are summed from 1 to N and 1 to n respectively. We assume thefollowing conditions:

关键词： elliptic systems weak solution regularity.