关于C^∞—字的幂

本文讨论了Ｃ＾∞－字的一些性质，并对Ｃ＾∞－字的幂证明了以下的结果，对任意Ｃ＾∞－字ω，存在一个正整数ｋ＝ｋ（ω），使ω＾ｋ是Ｃ＾∞－字，ω＾ｋ＋１不是Ｃ＾∞－字。     

再谈关于C^∞—字幂的一个猜想

设Ｗ是一个Ｃ＾∞－字，且│Ｗ│〉３，若对一切满足│Ｄ＾ｋ（Ｗ）│〉１的自然数ｋ，都有Ｄ＾ｋ（Ｗ）的首末两个循环中至少有一个循环的长为２，则称Ｗ是一个弱偶Ｃ＾∞－字，本文讨论了弱偶Ｃ＾∞－字的性质，证明了以下的结论；基Ｗ是一个弱偶Ｃ＾∞－字，则Ｗ６２不是Ｃ＾∞－字。     

m（n）^∞的代数性质及其应用

在０∈Ｒ＾ｎ的Ｃ＾∞函数芽环Ｅｎ中,存在一类称为平坦的芽,表示为ｍ（ｎ）＾∞：一个芽ｆ称为平坦的,如果ｆ（ｏ）以及其各阶偏导数在原点都是零。本文系统讨论了ｍ（ｎ）＾∞的代数性质,作为应用给出了这类芽的一些有用的分析性质。     

C^n中B^p空间,Dp空间和A^∞空间之间的关系

讨论了Ｃ＾ｎ中单位球上Ｂ＾ｐ、Ｄｐ和Ａ＾∞三空间在ｐ不同情况下的包含关系。     

非光滑系数的二阶椭圆边值问题

本文利用Ｌｉｔｔｅｒｗｏｏｄ－Ｐａｌａｙ分解及Ｂｅｓｏｖ空间理论研究了Ｃ＾∞－区域上具非光滑系数的二阶椭圆方程边值问题的Ｂｅｓｏｖ正则性问题。     

光滑映射芽关于群A的一个子群的无穷小稳定性

在「１」中,Ｃ＾∞映射芽在Ｍａｔｈｅｒ定义的群Ａ＾「２」中的一个子群下的万有开折得到了讨论,本文则刻画了开折的无穷小稳定性。     

线性算子σ（L^∞,L^1）逼近的Korovkin定理

本文给出并证明了拓扑σ（Ｌ＾∞，Ｌ＾１）下线性算子逼近Ｌ＾∞函数的Ｋｏｒｏｖｋｉｎ定理。     

关于赵君喜“R^∞N中一个幂等元的构造”一文的意见

本文证明了“Ｒ＾∞Ｎ中一个幂等元的构造”一文中幂等元Ｑ不是套代数ａｌｇＮ中的算了，因此也不是如该文作者所断言的是Ｒ＾∞Ｎ中的元。     

有限维赋范空间至$C(\Om)$-的等

本文讨论了有限维赋范空间Ｘ至无限维Ｃ（Ω）的等距逼近问题，证明了当Ｘ不足任意ｌｎ＾∞（ｎ∈Ｎ）的子空间且Ω中含无究多个孤立点时，等距逼近问题不成立；在其它情形该问题都成立。     

关于映射同伦类的拓扑熵

设ｆ：Ｔ＾ｍ→Ｔ＾ｍ为ｍ维环面自映射，Ｎ＾∞（ｆ）是ｆ的渐近Ｎｉｅｌｓｅｎ数，本文应用Ｎｉｅｌｓｅｎ不动点理论，给出了ｌｏｇＮ＾∞（ｆ）是ｆ的同伦类的拓扑熵的最好下界的一个充要条件；并通过在齐性空间上引入等价度量，将此结论推广到了幂零流形自映射的情形。     

On the Representation of Infinitely Differentiable Functions by Series of Exponentials

We consider the problem of representing elements of a weighted space of infinitely differentiable functions on the real line by series of exponentials.     

Approximation of infinitely differentiable multivariate functions is not strongly tractable

This article studies tractability and strong tractability for multivariate approximation of infinitely differentiable functions, using either standard information or continuous linear information. We prove that this approximation problem is not strongly tractable.     

关于多元角形区域上的无穷可微函数的广义准解析性

本文将关于角形闭区域中无穷可微函数类的广义准解析性的结果推广到了多维情形。     

Factor space of functions with a singularity

Spaces of rapidly decreasing functions on a line, which are infinitely differentiable everywhere except at zero, where there is a fixed singularity for the given space, are considered. It is proved that all such spaces are homeomorphic to each other and homeomorphic to the space of infinitely differentiable functions on a circle.     

ON THE COEFFICIENTS OF DIFFERENTIATED EXPANSIONS AND DERIVATIVES OF CHEBYSHEV POLYNOMIALS OF THE THIRD AND FOURTH KINDS

Two new analytical formulae expressing explicitly the derivatives of Chebyshev polynomials of the third and fourth kinds of any degree and of any order in terms of Chebyshev polynomials of the third and fourth kinds themselves are proved.Two other explicit formulae which express the third and fourth kinds Chebyshev expansion coefficients of a general-order derivative of an infinitely differentiable function in terms of their original expansion coefficients are also given.Two new reduction formulae for summing some terminating hypergeometric functions of unit argument are deduced.As an application of how to use Chebyshev polynomials of the third and fourth kinds for solving high-order boundary value problems,two spectral Galerkin numerical solutions of a special linear twelfth-order boundary value problem are given.     

Goursat problem for two-dimensional second-order hyperbolic operator-differential equations with variable domains

We develop a modification of the energy inequality method and use it to prove the well-posedness of the Goursat problem for linear second-order hyperbolic differential equations with operator coefficients whose domains depend on the two-dimensional time. An energy inequality for strong solutions of this Goursat problem is derived with the help of abstract smoothing operators, and we prove that the range of the problem is dense by using properties of a regularizing Cauchy problem whose inverse operator is a family of smoothing operators of a new type. We give an example of a well-posed boundary value problem for a two-dimensional complete second-order hyperbolic partial differential equation with Goursat conditions and with a boundary condition depending on the two-dimensional time.     

MULTIDIMENSIONAL GOURSAT PSOBLEM FOR SEMILINEAR WAVE EQUATIONS

ＭＵＬＴＩＤＩＭＥＮＳＩＯＮＡＬＧＯＵＲＳＡＴＰＳＯＢＬＥＭＦＯＲＳＥＭＩＬＩＮＥＡＲＷＡＶＥＥＱＵＡＴＩＯＮＳＦＡＮＧＤＡＯＹＵＡＮＡｂｓｔｒａｃｔ：ＩｎｔｈｉｓｐａｐｅｒｗｅｓｔｕｄｙｔｈｅＧｏｕｒｓａｔｐｒｏｂｌｅｍｆｏｒｓｅｍｉｌｉｎｅａｒｗ...     

Riemann and Goursat step data problems for extensible strings

Riemann and Goursat step data problems for extensible nonlinear elastic strings are solved in the class of regulated functions. In the first paragraph, the solution to the simplest initial and boundary value problem, i.e., Goursat problem in strains, is constructed. This solution points out four vector-valued functions of a vector variable, which are the tools used in solving the Goursat problem in velocity and the Riemann problem.     

Rarefaction Wave Interaction and Shock-Rarefaction Composite Wave Interaction for a Two-Dimensional Nonlinear Wave System

In order to construct global solutions to two-dimensional(2 D for short)Riemann problems for nonlinear hyperbolic systems of conservation laws,it is important to study various types of wave interactions.This paper deals with two types of wave interactions for a 2 D nonlinear wave system with a nonconvex equation of state:Rarefaction wave interaction and shock-rarefaction composite wave interaction.In order to construct solutions to these wave interactions,the authors consider two types of Goursat problems,including standard Goursat problem and discontinuous Goursat problem,for a 2 D selfsimilar nonlinear wave system.Global classical solutions to these Goursat problems are obtained by the method of characteristics.The solutions constructed in the paper may be used as building blocks of solutions of 2 D Riemann problems.     

On existence and nonexistence of global solutions of Cauchy–Goursat problem for nonlinear wave equations

We consider the Cauchy–Goursat initial characteristic problem for nonlinear wave equations with power nonlinearity. Depending on the power of nonlinearity and the parameter in an equation we investigate the problem on existence and nonexistence of global solutions of the Cauchy–Goursat problem. The question on local solvability of the problem is also considered.