Independence of vectors in codes over rings

We study codes over Frobenius rings. We describe Frobenius rings via an isomorphism to the product of local Frobenius rings and use this decomposition to describe an analog of linear independence. Special attention is given to codes over principal ideal rings and a basis for codes over principal ideal rings is defined. We prove that a basis exists for any code over a principal ideal ring and that any two basis have the same number of vectors. Hongwei Liu is supported by the National Natural Science Foundation of China (10571067).     

理想单子在非标准饱和模型下的若干应用

通过利用非标准分析中的饱和模型,对其中的理想进行了讨论,从而得到了理想的非标准特征,并进一步利用这一特征证明了单子论中的一些相关定理．     

素数p在Q（6√u）中的素理想分解问题

利用局部域的方法,研究素数p在有理数域的6次根扩张中的素理想分解问题,并完全确定了素数p在Q（6√u）中分解所可能有的形式（pα︱︱u）.为进一步研究素数p在Q（2l√u）中（l为素数）的分解提供了途径.     

On the ideal centre of the space of vector valued integrable functions

Let E be a Banach lattice and L¹(μ, E) be the space of E-valued Bochner integrable functions. Some order properties of L¹(μ, E) are given. It is shown that L_s^∞(μ, Z(E)) is the ideal centre of L¹(μ, E) and it is obtained a Radon-Nikodym type theorem for B -integrable functions.      

关于nZ的理想及商环

给出了nZ的全部理想、极大理想和素理想,并研究了nZ的商环的构造以及为域的条件,解决了Z<,n>的子域的存在和个数问题.     

The spontaneous formation of inhomogeneity in a classical one-particle “gas”: An example in silico

A single classical isoergic particle was placed in a cube and allowed to propagate for 100 ns to 10 ms. The interaction of the particle with the inner wall of the cube was modeled as a linear combination of specular and random reflection, the extent of the combination being governed by a user-defined “roughness” parameter α. As a function of α, the particle’s relative pressure and density spontaneously took on an inhomogenous distribution.     

HBa(D)空间的内插定理

研究了一类由H^p空间构成的Ba空间的内插性质，给出了H^Ba(D)空间的三个内插定理。     

Mixed multiplicities,Hilbert polynomials and homaloidal surfaces

We investigate the relationship among several numerical invariants associated to a (free) projective hypersurface V : the sequence of mixed multiplicities of its Jacobian ideal, the Hilbert polynomial of its Milnor algebra, and the sequence of exponents when V is free. As a byproduct, we obtain explicit equations for some of the homaloidal surfaces in the projective 3‐dimensional space constructed by C. Ciliberto, F. Russo and A. Simis.