Geometric properties of homogeneous parabolic geometries with generalized symmetries

We investigate geometric properties of homogeneous parabolic geometries with generalized symmetries. We show that they can be reduced to a simpler geometric structures and interpret them explicitly. For specific types of parabolic geometries, we prove that the reductions correspond to known generalizations of symmetric spaces. In addition, we illustrate our results on an explicit example and provide a complete classification of possible non-trivial cases.     

On the asymptotic number of inequivalent binary self-dual codes

Let Ψn be the number of inequivalent self-dual codes in . We prove that , where . Let Δn be the number of inequivalent doubly even self-dual codes in . We also prove that .     

The Invariant and Quasi-invariant Transformations of the Stable Lévy Processes

Let ξ(t),t∈[0,1] be a strictly stable Lévy process with the index of stability α∈(0,2). By ℘ _ξ we denote the law of ξ in the Skorokhod space . For arbitrary ξ we construct ℘ _ξ -quasi-invariant semigroup of transformations of . Under some nondegeneracy condition on the spectral measure of the stable process we construct ℘ _ξ -quasi-invariant group of transformations of . In symmetric case this group is a group of the invariant transformations.      

The Noether map II

Let be a faithful representation of a finite group . In this paper we proceed with the study of the image of the associated Noether map

In our 2005 paper it has been shown that the Noether map is surjective if is a projective -module. This paper deals with the converse. The converse is in general not true: we illustrate this with an example. However, for -groups (where is the characteristic of the ground field ) as well as for permutation representations of any group the surjectivity of the Noether map implies the projectivity of .

     

具有不依赖于时间的不变量的三维常微分方程组的Hamilton结构

本文证明了具有不依赖于时间的不变量的三维常微分方程组所描述的动力系统相对于一广义Poisson括号可以改写为Hamilton系统,并且这些不变量就是Hamilton量。作为例子,我们讨论了Kermack-Mckendrick传染病模型,所得结果推广了Y.Nutku的结果。     

GLOBAL TOPOLOGICAL PROPERTIES OF HOMOGENEOUS VECTOR FIELDS IN R^3

In this paper the authors prove that the flows of homogeneous vector field     

The admissible interval for the invariant factors of a product of matrices

It is well known that Littlewood-Richardson sequences give a combinatorial characterization for the invariant factors of a product of two matrices over a principal ideal domain. Given partitions a and c, let LR(a,c) be the set of partitions b for which at least one Littlewood - Richardson sequence of type (a,b,c) exists. I. Zaballa has shown in [20] that LR(a, c) has a minimal element w and a maximal element n, with respect to the order bf majorization, depending only on a and c;. In generalLR(a, c) is not the whole interval [w, n]. Here a combinatorial algorithm is provided for constructing all the elements of LR(a, c). This algorithm consists in starting with the minimal Littlewood-Richardson sequence of shape c/a and successively modifying it until the maximal Littlewood - Richardson sequence of shape c/a is achieved. Also explicit bijections between Littlewood - Richardson sequences of conjugate shape and weight and between Littlewood - Richardson sequences of dual shape and equal weight are presented. The bijections are denned by means of permutations of Littlewood - Richardson sequences.     

Dulac函数的构造及其应用(Ⅰ)

本文研究（Ⅰ）和（Ⅱ）类系统Dulac函数的构造问题,作为应用,讨论此两类系统的极限环的不存在性问题,得到了一些新结果．     

The Qualitative Study of Space Quadratic Systems with a First Integral

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