The Ramifications of the Centres: Quantised Function Algebras at Roots of Unity

This paper continues the study of quantised function algebrasO[G] of a semisimple group G at an lth root of unity . Thesealgebras were introduced by De Concini and Lyubashenko in 1994,and studied further by De Concini and Procesi and by Gordon,amongst others. Our main purpose here is to increase understandingof the finite-dimensional factor algebras O[G](g), for g G.We determine the representation type and block structure ofthese factors, and (for many g) describe them up to isomorphism.A series of parallel results is obtained for the quantised Borelalgebras and . 2000 Mathematical Subject Classification: 16W35,17B37.     

New weighted Rogers-Ramanujan partition theorems and their implications

This paper has a two-fold purpose. First, by considering a reformulation of a deep theorem of Göllnitz, we obtain a new weighted partition identity involving the Rogers-Ramanujan partitions, namely, partitions into parts differing by at least two. Consequences of this include Jacobi's celebrated triple product identity for theta functions, Sylvester's famous refinement of Euler's theorem, as well as certain weighted partition identities. Next, by studying partitions with prescribed bounds on successive ranks and replacing these with weighted Rogers-Ramanujan partitions, we obtain two new sets of theorems - a set of three theorems involving partitions into parts (mod 6), and a set of three theorems involving partitions into parts (mod 7), .

     

An Expansion Formula for q-Series and Applications

In this paper the author proves a q-expansion formula which utilizes the Leibniz formula for the q-differential operator. This expansion leads to new proofs of the Rogers–Fine identity, the nonterminating ₆₅ summation formula, and Watson's q-analog of Whipple's theorem. Andrews' identities for sums of three squares and sums of three triangular numbers are also derived. Other identities of Andrews and new identities for Hecke type series are also discussed.     

Commutativity of rings with polynomial constraints

Let p, q and r be fixed non-negative integers. In this note, it is shown that if R is left (right) s-unital ring satisfying , respectively) where , then R is commutative. Moreover, commutativity of R is also obtained under different sets of constraints on integral exponents. Also, we provide some counterexamples which show that the hypotheses are not altogether superfluous. Thus, many well-known commutativity theorems become corollaries of our results.     

匿名无线认证协议的匿名性缺陷和改进

分析了朱建明,马建峰提出的匿名无线认证协议的匿名性安全缺陷,提出了一种改进的匿名无线认证协议(IWAA),并用对其匿名性进行了形式化的安全分析。分析表明改进后的协议不仅实现了身份认证,而且具有很强的匿名性,满足无线网络环境匿名性的安全需求。     

电子邮件认证技术

主要讨论电子邮件认证技术的相关问题，详细介绍了目前互联网中新出现的几种电子邮件认证技术，如发件人策略框架、发件人身份标识、域密钥以及互联网电子邮件标识技术，通过对这些技术的分析指出电子邮件认证技术面临的主要问题及未来的发展趋势。     

基于Harn签名方案的远距离通行字认证方案

本文首先利用Ｓｈａｍｉｒ的秘密共享方法将Ｃｈａｎｇ－Ｌｉａｏ通行字认证方案转变成（ｔ，ｎ）共享认证方案，从而使ｎ个认证者中任意ｔ个人能够认证通行字的正确性。其次提出了一个基于Ｈａｒｎ数字签名方案的远距离通行字认证方案。     

The electrostatics of Einstein’s unified field theory

When sources are added at their right-hand sides, and g_(ik) is a priori assumed to be the metric, the equations of Einstein’s Hermitian theory of relativity were shown to allow for an exact solution that describes the general electrostatic field of n point charges. Moreover, the injunction of spherical symmetry of g_(ik) in the infinitesimal neighbourhood of each of the charges was proved to yield the equilibrium conditions of the n charges in keeping with ordinary electrostatics. The tensor g_(ik), however, cannot be the metric of the theory, since it enters neither the eikonal equation nor the equation of motion of uncharged test particles. A physically correct metric that rules both the behaviour of wave fronts and of uncharged matter is the one indicated by Hély.In the present paper it is shown how the electrostatic solution predicts the structure of the n charged particles and their mutual positions of electrostatic equilibrium when Hély’s physically correct metric is adopted.