Latroids and their representation by codes over modules

It has been known for some time that there is a connection between linear codes over fields and matroids represented over fields. In fact a generator matrix for a linear code over a field is also a representation of a matroid over that field. There are intimately related operations of deletion, contraction, minors and duality on both the code and the matroid. The weight enumerator of the code is an evaluation of the Tutte polynomial of the matroid, and a standard identity relating the Tutte polynomials of dual matroids gives rise to a MacWilliams identity relating the weight enumerators of dual codes. More recently, codes over rings and modules have been considered, and MacWilliams type identities have been found in certain cases.

In this paper we consider codes over rings and modules with code duality based on a Morita duality of categories of modules. To these we associate latroids, defined here. We generalize notions of deletion, contraction, minors and duality, on both codes and latroids, and examine all natural relations among these.

We define generating functions associated with codes and latroids, and prove identities relating them, generalizing above-mentioned generating functions and identities.

     

一类更新序列的母函数

数列f={f_1,f_2,…,f_n,…}称为f-序列,如果■(1)由f产生的更新序列u={u_0,u_1,u_2,…,u_n,…}依下式定义■记f=■,如果f=1,则称更新序列u为常返的.周知,u常返的充要条件是     

The Hamming weight of the non-adjacent-form under various input statistics

The Hamming weight of the non-adjacent form is studied in relation to the Hamming weight of the standard binary expansion. In particular, we investigate the expected Hamming weight of the NAF of an n-digit binary expansion with k ones where k is either fixed or proportional to n. The expected Hamming weight of NAFs of binary expansions with large (≥ n/2) Hamming weight is studied. Finally, the covariance of the Hamming weights of the binary expansion and the NAF is computed. Asymptotically, these Hamming weights become independent and normally distributed. Communicated by Attila Pethő     

Hsu-Riordan 阵/partial monoid

本文首先对Shapiro的Riordan群进行了推广。给出了Hsu-Riordan partial monoid的概念，然后在此框架内，对徐利治先生的两类扩展型广义Stirling数偶进行了统一处理；建立了Hsu-Wang转换定理。Brown-Sprugnoli转换公式，以及广义Brown转换引理-它揭示了一些不同类型的Hsu-Riordan阵之间转换的方法。由此可产生大量的恒等式。     

有理B样条曲线的快速逐点生成算法

给出了有理B样条曲线的快速逐点生成算法。对均匀有理参数曲线或非均匀有理参数曲线（NURBS），对低次有理B样条曲线和高次有理B样条曲线都适用，算法速度快，效率高，具有广泛的应用价值。     

Hilbert-generated spaces

We classify several classes of the subspaces of Banach spaces X for which there is a bounded linear operator from a Hilbert space onto a dense subset in X. Dually, we provide optimal affine homeomorphisms from weak star dual unit balls onto weakly compact sets in Hilbert spaces or in c₀(Γ) spaces in their weak topology. The existence of such embeddings is characterized by the existence of certain uniformly Gâteaux smooth norms.     

基于蒙特卡洛-马尔科夫链(MCMC)的ARMA模型选择

AIC与SIC等准则函数方法是ARMA模型选择过程中经常使用的方法。但是,当模型的阶数很高时,无法计算并比较每一个备选模型的准则函数值。本文提出了一个基于蒙特卡洛-马尔科夫链方法的随机模型生成方法,以产生准则函数值最小的备选模型。实际应用表明本文的方法在处理拥有大量备选模型的ARMA模型选择问题时有很好的效果。     

有关重复排列的一类计数问题

利用生成函数解决了从n个元素的集合中任意重复选取r个元素且这r个元素中含有不同元素的个数一定时，所构成的不同r-序列的方法数．     

Joint Distributions of Numbers of Runs of Specified Lengths in a Sequence of Markov Dependent Multistate Trials

Let Z ₀, Z ₁,...,Z _n be a sequence of Markov dependent trials with state space Ω = {F ₁,...,F _λ, S ₁,...,S _ν}, where we regard F ₁,...,F _λ as failures and S ₁,...,S _ν as successes. In this paper, we study the joint distribution of the numbers of S _i -runs of lengths k _ij (i = 1,2,...,ν, j = 1,2,...,r _i ) based on four different enumeration schemes. We present formulae for the evaluation of the probability generating functions and the higher order moments of this distribution. In addition, when the underlying sequence is i.i.d. trials, the conditional distribution of the same run statistics, given the numbers of success and failure is investigated. We give further insights into the multivariate run-related problems arising from a sequence of the multistate trials. Besides, our results have potential applications to problems of various research areas and will come to prominence in the future. This research was partially supported by the ISM Cooperative Research Program (2004-ISM·CRP-2007).     

非均匀随机数产生

本文详细介绍了产生非均匀随机数的一般方法,常用连续分布(正态分布,Gamma分布,Beta分布,χ2分布和F分布)的抽样法及利用R软件产生随机数的方法。