准晶体中八方晶系点群的对称性与矩阵表示

从理论上对准晶体中八方晶系各点群进行了研究.运用八方晶系各点群的极赤投影图,列出了各点群的所有对称操作;填出了固有点群822的群乘表.运用坐标变换和群论在自定义的八方坐标系中,推导出八方晶系点群所有对称操作的矩阵.这32个3×3矩阵的结构是相当简洁的,它们的矩阵元只有5种可能取值:0,±1,±2.其中2是反映八方晶系准晶体所具有的准周期性的特殊无理数.     

All-optical frequency multiplication/recovery based on a semiconductor optical amplifier ring cavity

A novel scheme for all-optical frequency multiplication/recovery based on a semiconductor optical amplifier ring cavity is proposed and investigated numerically. The results show, for a 2.5 GHz driving pulse train, it can be generated 5-25 GHz repetition rate pulse trains with low clock amplitude jitter, polarization independence and high peak power. Furthermore, the extraction of the clock signal from a pseudorandom bit sequence signal can be realized based on the proposed scheme.     

INTERSECTION OF PRIME SUBMODULES AND DIMENSION OF MODULES

The aim of this paper is to study the conditions by which a P-prime submodule can be expressed as a finite intersection or union of P-prime submodules. Also corresponding to dimension and rank of modules, some equivalent conditions for a ring to be a Dedekind domain are given.     

Weak Multiplication Modules

In this paper we characterize weak multiplication modules.     

Montgomery Multiplication in GF(2k)

We show that the multiplication operation c=a · b · r^-1 in the field GF(2^k can be implemented significantly faster in software than the standard multiplication, where r is a special fixed element of the field. This operation is the finite field analogue of the Montgomery multiplication for modular multiplication of integers. We give the bit-level and word-level algorithms for computing the product, perform a thorough performance analysis, and compare the algorithm to the standard multiplication algorithm in GF(2^k. The Montgomery multiplication can be used to obtain fast software implementations of the discrete exponentiation operation, and is particularly suitable for cryptographic applications where k is large.     

Adaptive application of operators in standard representation

Recently adaptive wavelet methods have been developed which can be shown to exhibit an asymptotically optimal accuracy/work balance for a wide class of variational problems including classical elliptic boundary value problems, boundary integral equations as well as certain classes of noncoercive problems such as saddle point problems. A core ingredient of these schemes is the approximate application of the involved operators in standard wavelet representation. Optimal computational complexity could be shown under the assumption that the entries in properly compressed standard representations are known or computable in average at unit cost. In this paper we propose concrete computational strategies and show under which circumstances this assumption is justified in the context of elliptic boundary value problems. Dedicated to Charles A. Micchelli on the occasion of his 60th birthday Mathematics subject classifications (2000) 41A25, 41A46, 65F99, 65N12, 65N55. This work has been supported in part by the Deutsche Forschungsgemeinschaft SFB 401, the first and third author are supported in part by the European Community's Human Potential Programme under contract HPRN-CT-202-00286 (BREAKING COMPLEXITY). The second author acknowledges the financial support provided through the European Union's Human Potential Programme, under contract HPRN-CT-2002-00285 (HASSIP) and through DFG grant DA 360/4–1.     

Winograd矩阵乘法算法用于任意阶矩阵时的一种新处理方法

摘要t矩阵乘法StraSsen算法及其变形winograd算法用分而治之的方法把矩阵乘法时间复杂性由传统的D(n。)改进到0(佗kg。n.但是对于奇数阶矩阵,在划分子矩阵时,要作特殊处理才能继续使用此算法.本文提出了一种非等阶“十”字架划分方法,可以最少化填零,最大化性能,使得奇数阶矩阵乘法的时间复杂性更加接近偶数阶矩阵乘法的效果.计算实例显示该方法是有效的.     

On the field of definition for modularity of CM elliptic curves

The purpose of this paper is to decide the conditions under which a CM elliptic curve is modular over its field of definition.     

双峰倍增配平法用于同步、导数-同步荧光法同时测定邻羟基苯甲酸和间羟基苯甲酸

邻羟基苯甲酸（ｏＨＢＡ）和间羟基苯甲酸（ｍＨＢＡ）荧光光谱严重重叠，同步及导数技术虽使选择性有所改善，但仍不能完全分辨开重叠谱。用双峰倍增配平计算法结合同步、一阶导数－同步荧光法对双组分体系（邻羟基苯甲酸／间羟基苯甲酸，ｐＨ１２介质）同时测定。结合计算的两种测定方法精密度、回收率和不同组分间浓度比范围均优于一阶导数－同步荧光法。     

X=Y=ZH Systems as potential 1,3-dipoles. Part 58: Cycloaddition route to chiral conformationally constrained (R)-pro-(S)-pro peptidomimetics

Imines of (1S,9S)-t-butyl-9-amino-octahydro-6,10-dioxo-6H-pyridazino[1,2-a][1,2]diazepine-1-carboxylate undergo thermal (toluene, 110°C) or LiBr-DBU catalysed (MeCN, room temperature) regio- and stereo-specific cycloaddition to a range of chiral dipolarophiles giving enantiopure spiro-cycloadducts in excellent yield. The reactions proceed via intermediate NH azomethine ylides and litho azomethine ylides, respectively and results in the multiplication of chiral centres from 2 (one of which is lost in the process) to 5.