Three kinds of generalized convexity

This paper gives some properties of quasiconvex, strictly quasiconvex, and strongly quasiconvex functions. Relationships between them are discussed.This research was supported in part by the National Natural Science Foundation of China. The author would like to thank Professor M. Avriel for valuable comments about this paper.     

关于Ponomarev-系统的一些注记(英文)

本文给出一个反例,证明了在一个Ponomarev-系统(f,M,X,P)中,P是点有限不蕴涵f是紧有限.这纠正了有关Ponomarev-系统的一个错误命题.作为Ponomarev-系统(f,M,X,P)的进一步结果,本文分别给出了f是紧映射以及P是点有限的充分必要条件.此外,本文还给出了Ponomarev-系统中映射与网络的一些其他关系.     

La valeur d'un entier classique en \lambda\mu-calcul

In this paper, we present three methods to give the value of a classical integer in -calculus. The first method is an external method and gives the value and the false part of a normal classical integer. The second method uses a new reduction rule and gives as result the corresponding Church integer. The third method is the M. Parigot's method which uses the J.L. Krivine's storage operators.

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Re?u le 4 Septembre 1995     

The stability theorem for smooth pseudoisotopies

The stability theorem states that the suspension map C(M) C(M X I) defined on the pseudoisotopy space C(M)=Diff(M X I rel M X O U M X I) of a compact smooth n-manifold M is n/3-connected. This implies that C(M) has the R~ n/3-homotopy type of the stable pseudoisotopy space P(M) which is related to Waldhausen's algebraic K-theory of spaces by Waldhausen's formula A(X) S(X₊) X B2P(X). This paper gives a detailed proof of the smooth stability theorem following ideas by Hatcher for the proof of a PL stability theorem.Supported by NSF Grant No. MCS-85-02317.     

Stability of Functional Equations in Several Variables

We prove a generalization of Hyers＇ theorem on the stability of approximately additive mapping and a generalization of Badora＇s theorem on an approximate ring homomorphism. We also obtain a more general stability theorem, which gives the stability theorems on Jordan and Lie homomorphisms. The proofs of the theorems given in this paper follow essentially the D. H. Hyers-Th. M. Rassias approach to the stability of functional equations connected with S. M. Ulam＇s problem.     

Remark on the weierstrass points on curves

We give a treatment of the Weiertrass points of curves which is a little different from the treatment by Laksov. We introduce the notion of theith weight which makes the treatment easier and gives an algorithm for computing the gap sequence of an effective divisor and the weight at a point. Supported in part by NNSF of China.     

奇数阶亚循环p-群分类的一个证明

一个有限p群p称为亚循环的,如果P有一个循环的正规子群A,使得PA是循环的.1973年King在文[2]中对亚循环p群进行了分类;在文[4,5]中M.F.NewmanandMingYaoXu发现了这些群的新的表示,给出了新的分类方法,这种方法是由p群生成算法(见文[3])得到的.本文的目的是给这些结果的另一种证明,与p群生成算法是不相关的.     

Erratum to: “Travelling waves for a system of equations” [Nonlinear Anal. 68(12) (2008) 3909–3912]

We correct an oversight in the proof of Theorem 1.1 in [Shair Ahmad, Alan C. Lazer, Antonio Tineo, Traveling waves for a system of equations, Nonlinear Analysis 68 (12) (2008)], which, in addition to considerably reducing the assumptions made in [M.M. Tang, P.C. Fife, Propagating fronts for competing species equations with diffusion, Arch. Ration. Mech. Anal. 73 (1980). [2]], gives a better derivation and a sharper estimate of the wave speed.     

“三焦点”广义椭圆曲线及其传导特性

提出了三焦点广义椭圆的概念,给出了三焦点广义椭圆的画法及其轨迹方程,建立了三焦点广义椭圆的重心M到三焦点广义椭圆轨迹曲线上动点P的距离d的数学模型,研究了三焦点广义椭圆构件对力与速度的传动特性及其在工业上的应用.