Zk线性码的对称形式的MacWilliams恒等式

该文定义了Zk线性码的码字的对称重量计数公式，利用离散的Hadamard变换，建立了线性码与其对偶码之间的对称形式的MacWilliams恒等式．     

高性能音频方案配置可编程DSP及丰富软件

不知何时起, "软件为王"开始成为系统设计的基础.Wintel的时代,只有PC的零售广告说明或者那些自由市场的攒机发烧友们才会把软、硬件进行详细分类、标注和讨论.在核心操作系统软件部分,只有微软和与之有关的一切,于是,用户唯一注意并热衷讨论的是硬件的性能如何,并且几乎集中在核心处理器、内存和显卡的性能指标上.     

基于Mac OS X的多媒体外语开放式学习平台的设计研究

随着计算机信息化应用技术的发展,Mac OS X作为苹果电脑的MAC系列产品专属的操作系统,为苹果电脑用户进行外语学习提供了技术支持.基于Mac OS X的多媒体外语开放式学习平台为高校大学生更好的学习外语提供了更多的帮助.本文对Mac OS X技术进行了分析,对大学外语多媒体学习的现状进行了研究.在Mac OS X技术的基础之上对多媒体外语开放式学习平台进行了设计研究,对基于Mac OS X的多媒体外语开放式学习平台的特点和关键性应用技术进行了介绍.     

The strength of Mac Lane set theory

Saunders Mac Lane has drawn attention many times, particularly in his book Mathematics: Form and Function, to the system of set theory of which the axioms are Extensionality, Null Set, Pairing, Union, Infinity, Power Set, Restricted Separation, Foundation, and Choice, to which system, afforced by the principle, , of Transitive Containment, we shall refer as . His system is naturally related to systems derived from topos-theoretic notions concerning the category of sets, and is, as Mac Lane emphasises, one that is adequate for much of mathematics. In this paper we show that the consistency strength of Mac Lane's system is not increased by adding the axioms of Kripke–Platek set theory and even the Axiom of Constructibility to Mac Lane's axioms; our method requires a close study of Axiom H, which was proposed by Mitchell; we digress to apply these methods to subsystems of Zermelo set theory , and obtain an apparently new proof that is not finitely axiomatisable; we study Friedman's strengthening of , and the Forster–Kaye subsystem of , and use forcing over ill-founded models and forcing to establish independence results concerning and ; we show, again using ill-founded models, that proves the consistency of ; turning to systems that are type-theoretic in spirit or in fact, we show by arguments of Coret and Boffa that proves a weak form of Stratified Collection, and that is a conservative extension of for stratified sentences, from which we deduce that proves a strong stratified version of ; we analyse the known equiconsistency of with the simple theory of types and give Lake's proof that an instance of Mathematical Induction is unprovable in Mac Lane's system; we study a simple set theoretic assertion—namely that there exists an infinite set of infinite sets, no two of which have the same cardinal—and use it to establish the failure of the full schema of Stratified Collection in ; and we determine the point of failure of various other schemata in . The paper closes with some philosophical remarks.