Deterministic chaos in one-dimensional maps—the period doubling and intermittency routes

This paper is a review of the present status of studies relating to occurrence of deterministic chaos and its characterization in one-dimensional maps. As our primary aim is to introduce the nonspecialists into this fascinating world of chaos we start from very elementary concepts and give sufficient arguments for clarity of ideas. The two main scenarios during onset of chaos viz. the period doubling and intermittency are dealt with in detail. Although the logistic map is often discussed by way of illustration, a few more interesting maps are mentioned towards the end.     

Large 2-transitive arcs

The projective planes of order n with a collineation group acting 2-transitively on an arc of length v, with n>v?n/2, are investigated and several new examples are provided.     

Dirac cohomology of unitary representations of equal rank exceptional groups

In this paper, we consider the unitary representations of equal rank exceptional groups of type E with a regular lambda-lowest K-type and classify those unitary representations with the nonzero Dirac cohomology.     

Dominions in varieties generated by simple groups

We determine the dominion (in the sense of Isbell) of a subgroup H of a finite nonabelian simple group S in Var(S). We also obtain necessary and suficient conditions for H to be epimorphically embedded in S, and derive several examples, which generalize an example of B. H. Neumann. Finally, we extend the results to a variety generated by a family of finite nonabelian simple groups. Received May 12, 1999; accepted in final form April 9, 2002.     

非可换的奇异l-群

通过建立奇异元以及奇异l-群的刻划，研究了一般非可换的奇异l-群的性质及相关的结构．     

Crystallized structure for level 0 part of modified quantum affine algebra Uq (sl2)

Crystal base of the level 0 part of the modified quantum affine algebra Uq(sl2)_0 is given by path. Weyl group actions, extremal vectors and crystal structure of all irreducible components are described explicitly.     

微分流形上的变换群

本文主要讨论如何把仿射Ｋｉｌｌｉｎｇ向量场、共形Ｋｉｌｌｉｎｇ向量场和射影Ｋｉｌｌｉｎｇ向量场推广成为四种张量场．我们得到了仿射Ｋｉｌｌｉｎｇｐ（≥１）形式和射影Ｋｉｌｌｉｎｇｐ（≥１）形式的多种定义，文献［１］中的定义仅是其中之一．     

最小二乘—红外光谱法定量测定羟基化合物

根据羟基伸缩振动吸收带的特性，用最小二乘法有效消除了溶液中羟基间的缔合作用对测定结果的影响。此方法已用于聚合物中羟基含量的测定。     

STABILIZATION OF UNITARY GROUPSOVER POLYNOMIAL RINGS

ＳＴＡＢＩＬＩＺＡＴＩＯＮＯＦＵＮＩＴＡＲＹＧＲＯＵＰＳＯＶＥＲＰＯＬＹＮＯＭＩＡＬＲＩＮＧＳ￥ＹＯＵＨＯＮＧＡｂｓｔｒａｃｔ：Ｔｈｅａｕｔｈｏｒｓｔｕｄｉｅｓｔｈｅｓｔａｂｉｌｉｚａｔｉｏｎｆｏｒｔｈｅｕｎｉｔａｒｙｇｒｏｕｐｓｏｖｅｒｐｏｌｙｎｏ...     

从复流形到对称空间的多重调和映射

本文首先证明了从复流形到对称空间的多重调和映射空间与扩张提升空间之间在相差一规范变换下存在一一对应,并给出确定的环路群在扩张提升空间的作用,因而也给出多重调和映射空间上的作用.其次,利用环路群及其代数的Iwasawa分解给出从Cn到对称空间的有限型的多重调和映射不同于文[1]中的刻划.