相关熵及其有限性的条件

就相关熵的性质进行了讨论，证明了在pp密度逼近中使用的作为“距离”的相关熵不满足距离定义中的第三个条件，并给出了三角不等式成立的条件。     

Desargues定理的推广

本文将射影几何著名的Desargues透视三点形定理推广到四面体和三维射影空间的完全n(n≥4)点形(体)中。     

Application of Hilbert＇s Projective Metric on Symmetric Cones

Let Ω be a symmetric cone. In this note, we introduce Hilbert＇s projective metric on Ω in terms of Jordan algebras and we apply it to prove that, given a linear invertible transformation g such that g（Ω） = Ω and a real number p, ｜p｜ 〉 1, there exists a unique element x ∈ Ω satisfying g（x） = x^p.     

Projection of Markov Measures May Be Gibbsian

We study the induced measure obtained from a 1-step Markov measure, supported by a topological Markov chain, after the mapping of the original alphabet onto another one. We give sufficient conditions for the induced measure to be a Gibbs measure (in the sense of Bowen) when the factor system is again a topological Markov chain. This amounts to constructing, when it does exist, the induced potential and proving its Hölder continuity. This is achieved through a matrix method. We provide examples and counterexamples to illustrate our results.     

Gauss Algebras

A special class of associative algebras is introduced and studied. A criteria of semisimplicity for suitable category of modules is obtained.     

ON THE SINGULAR DIRECTIONS OF VALUE DISTRIBUTION OF HOLOMORPHIC CURVES IN P^n（C）

This article proves the existence of singular directions of value distribution theory for some transcendental holomorphic curves in the n-dimensional complex projective space Pn(C). An example is given to complement these results.     

On the spectral sequence constructors of Guichardet and Stefan

The concept of a spectral sequence constructor is generalised to Hopf Galois extensions. The spectral sequence constructions that are given by Guichardet for crossed product algebras are also generalised and shown to provide examples. It is shown that all spectral sequence constructors for Hopf Galois extensions construct the same spectral sequence.     

计算机画法几何的研究与应用

以AutoCAD2000i为图形支撑平台，构建一种计算机辅助画法几何方法以直观、精确、高效地求解三维空间几何度量与定位问题，该方法适合于传统画法几何求解，也可用于曲柄滑块机构的行程、运动轨迹等内容的设计。     

On structure of small contractions of odd dimensional projective varieties

Let X be a smooth projective variety of dimension 2k-1 (k≥3) over the complex number field. Assume that fR: X→Y is a small contraction such that every irreducible component Ei of the exceptional locus of fR is a smooth subvariety of dimension k. It is shown that each Ei is isomorphic to the k-dimensional projective space Pk, the k-dimensional hyperquadric surface Qk in Pk 1, or a linear Pk-1-bundle over a smooth curve.