Poisson Morphisms and Reduced Affine Poisson Group Actions

We establish the concept of a quotient affine Poisson group, and study the reduced Poisson action of the quotient of an affine Poisson group G on the quotient of an affine Poisson-G-variety V. The Poisson morphisms (including equivariant cases) between Poisson affine varieties are also discussed. Received April 5, 1999, Accepted March 5, 2001     

蕴含K5-e图的度序列

设σ（G，n）是具有下述性质的最小正偶数，每一项和至少为σ（G．n）的n项可图序列π都有一个实现包台G作为于图．本文给出σ（K5-e，7）=32,σ（K5-e,8）=36。以及当n≥9时．σ（K5-e,n）=2[（5n/6）/2]．     

Types of two-dimensionalN = 4 superconformal field theories

Various types ofN = 4 superconformal symmetries in two dimensions are considered. It is proposed that apart from the well-known cases ofSU (2)and SU(2) × SU(2) ×U (1), their Kac-Moody symmetry can also be SU(2) × (U (1))⁴. Operator product expansions for the last case are derived. A complete free field realization for the same is obtained     

The Realization of 4-dimensional 3-Lie Algebras

In this paper, we mainly investigate the realization of 3-Lie algebras from a family of Lie algebras. We prove the realization theorem, offer a concrete example realizing all type of 4-dimensional 3-Lie algebras, and also give some properties about semi-simple n-Lie algebras.     

Generating multi-layer nested chaotic attractor and its FPGA implementation

Complex chaotic sequences are widely employed in real world, so obtaining more complex sequences have received highly interest. For enhancing the complexity of chaotic sequences, a common approach is increasing the scroll-number of attractors. In this paper, a novel method to control system for generating multi-layer nested chaotic attractors is proposed.At first, a piecewise(PW) function, namely quadratic staircase function, is designed. Unlike pulse signals, each level-logic of this function is square constant, and it is easy to realize. Then, by introducing the PW functions to a modified Chua's system with cubic nonlinear terms, the system can generate multi-layer nested Chua's attractors. The dynamical properties of the system are numerically investigated. Finally, the hardware implementation of the chaotic system is used FPGA chip.Experimental results show that theoretical analysis and numerical simulation are right. This chaotic oscillator consuming low power and utilization less resources is suitable for real applications.     

The automorphism group of a rigid affine variety

An irreducible algebraic variety X is rigid if it admits no nontrivial action of the additive group of the ground field. We prove that the automorphism group of a rigid affine variety contains a unique maximal torus . If the grading on the algebra of regular functions defined by the action of  is pointed, the group  is a finite extension of . As an application, we describe the automorphism group of a rigid trinomial affine hypersurface and find all isomorphisms between such hypersurfaces.     

到2020年我国能全面建成小康社会吗

以国家统计局统计科学研究所制定的全面建设小康指标体系为基础,采用变异系数法确定权重,构建我国全面建成小康社会指标体系,测算了我国2007-2012年全面建成小康社会的实现程度,测算结果表明2012年我国全面建成小康社会实现程度达84.9%.与此同时,利用一次线性预测模型、对数曲线预测模型和灰色预测模型构建变权重组合预测模型对2013-2020年我国全面建成小康社会实现程度进行预测,预测结果表明我国将在2019年实现全面建成小康社会的目标.     

Divisible designs with dual translation group

Many different divisible designs are already known. Some of them possess remarkable automorphism groups, so called dual translation groups. The existence of such an automorphism group enables us to characterize its associated divisible design as being isomorphic to a substructure of a finite affine space.      

Fourier frequencies in affine iterated function systems

We examine two questions regarding Fourier frequencies for a class of iterated function systems (IFS). These are iteration limits arising from a fixed finite families of affine and contractive mappings in Rd, and the “IFS” refers to such a finite system of transformations, or functions. The iteration limits are pairs (X,μ) where X is a compact subset of Rd (the support of μ), and the measure μ is a probability measure determined uniquely by the initial IFS mappings, and a certain strong invariance axiom. The two questions we study are: (1) existence of an orthogonal Fourier basis in the Hilbert space L²(X,μ); and (2) explicit constructions of Fourier bases from the given data defining the IFS.