乘法群

This paper researches linear maps preserving orthogonality,obtains the linear maps preserving othrogonality,it is either a rank -declining or rank -keeping map or a map with nilpotent element in its codomain.

利用分块成向量的方法证明了MnMn(F为域F上所有n×n矩阵构成的乘法半群上的n×n拟正交矩阵组至多含有n个矩阵，利用方程组的解的理论证明了Mn中与给定矩阵A构成两两拟正交矩阵组的矩阵个数不超过n-Rank+1，从而得到Mn上保持拟正交性的线性映射φ要么是降秩的或者保秩的映射，要么φ的值域中含有幂零元。

Aim In order to prove a semiring whose additive reduct is a semilattice and multiplicative reduct is a inverse semigroup to be a distributive lattice.

摘要目的求证加法导出是半格、乘法导出是逆半群的半环成为分配格的充要条件。

For this purpose, the compactly supported radial basis function and the moving least squares approximation based ones are integrated into the aforementioned two global optimizers. As a result, two novel hybrid algorithms are introduced.

其次，为解决电磁场逆问题分析、计算中由于随机类优化算法需进行数以千计次电磁场的数值分析，以致计算时间和计算量难以满足工程分析实际要求的难题，本文将表面响应模型法引入电磁场逆问题的求解，研究了基于紧支径向基函数和基于移动最小二乘法的两种表面响应模型，并将其分别与改进的遗传算法和粒子群算法相结合，提出两种不同的混合快速全局优化算法。

We will study 〓-quantum groups and multiplicative unitary operators in this paper.

本文主要目的是研究〓量子群和乘法酉算子。

That is to utilize general MPI programming environment, program on the NHBL parallel computational model, analyze and predicate the running cost of program by using the cost function of this model, and analyze the scalability of program by using the time-scale scalability metric. Finally, we analyze the numeric algorithm example---matrix multiplication and the nonnumeric algorithm example---PSRS sorting on Dawning-1000 MPP and NHPCC-cluster NOW system by using the integrative method.

提出了将并行计算模型、算法、编程进行一体化的研究的方法，即利用通用的标准的MPI编程环境，将编程建立在NHBL并行计算模型上，并且利用该并行计算模型的评价函数进行分析、预测程序的运行代价，再利用时间比例的可扩放性分析方法来分析程序的可扩放性性能；最后我们用PSRS排序算法和矩阵乘法这两个典型的数值和非数值的算法，在曙光-1000并行机和NHPCC-Cluster工作站集群上进行了一体化的分析。

A two-layer framework with particle swarms cooperative optimization and a mutation parameter is introduced by the QPSCO algorithm for larger searching scale and quicker convergence. Moreover I the residual sum of squares in least-square principle is introduced into the fitness function to enhance the fitting precision of the sensor position curve.

在QPSCO算法中，采用双层的多粒子群协同优化结构，同时引入参数变异策略，在扩大搜索范围的同时加快该算法收敛；将加权最小二乘法的误差平方和引入适应度函数中，以提高传感器位置曲线的拟合精度，从而实现传感器的优化配置。

Several models of cylindricity error evaluation,such as MZC,LSC,MCC and MIC,were given,a constriction factor model of the Particle Swarm Optimization was introduced.

建立了圆柱度误差评价的最小区域法、最小二乘法、最小外接圆柱法和最大内接圆柱法的数学模型，将一种含收敛因子的粒子群优化算法应用于圆柱度误差的目标函数的优化问题。

A Green's relation of the a dditive redect of an idempotentsemiring S is a congruence of the semiring S, but Green's relation of the multiplicative redect of S need not be.

幂等元半环S的加法半群上的Green关系是半环S的同余，然而S的乘法半群上的Green关系未必是S上的同余。

And it is proved that a semiring S in ■°■l is a subdirect product of a member of ■° and a member of ■l if and only if the multiplicative reduct of S is a subdirect product of a group and a semilattice by using the concept of sturdy frame of type(2,2) algebras.

O∩■°■B和■∩■°■中成员的次直积分解，并利用&(2，2)型代数的坚固构架&的概念，证明了半环S∈■°■l是■与■l中成员的次直积当且仅当S的乘法半群是群与半格的次直积。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。