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Let A" denote the commutant of a bounded linear operator S on H and R denote the collection of all operators in A" which are compact and upper triangular operators with diagonal sequence being zeros. In this paper, we show that if A"= CI + R, the K_0-group of A" is isomorphic to the integer group.

本文指出若H上的有界线性算子S的换位代数A′=CI+R，其中C是复数域，I是H上的单位算子，R是所有与S可交换的对角线为0的紧上三角有界线性算子的集合，则K_0A′

To develop a branch and bound method for this problem,a nonlinear integer-programming model was constructed.

为设计求解该问题的分支定界算法，建立了非线性整数规划模型。

Solutions using Matlab branch and bound method for integer programming proc...

matlab解用分支定界法解整数规划的程序。

Solutions using Matlab branch and bound method for integer programming procedures.

matlab解用分支定界法解整数规划的程序。

Magnetic Resonance Imaging, Integer Programming, Branch and Bound Method, Shimming

磁共振成像；整数规划；分支定界法；匀场

Reverse logistics ; recycling ; mixed integer linear programming ; branch and bound method

反向物流；再循环；混合整数线性规划；分枝定界法

At first the typical die and mould components and their standard processing technique,and the types of facilities were defined.Then the integer programming model of the facility planning was established and the branch and bound method was used to give a solution to the model cases.

定义了模具典型零件、设备类及模具典型零件标准工艺；建立了设备资源规划的整数规划数学模型；采用分枝—定界法对给定实例进行求解；计算结果证明了模型的有效性及实用性。

Although departed methods such as dynamic programming, integer programming, and branch bound method can solve small scale problems, the rise in execution time of these methods is exponential with the number of generating units.

虽然在以往的研究中，已有许多方法使用在此问题上，例如动态规划法、整数规划法及支界法等，但是由於这些方法所需的求解时间会随机组数的增加呈指数关系成长，因此都比较适合於小规模系统上使用。

When problem scale is small, we can adopt many classical algorithms such as linear programming integer programming, branch and bound method to solve this problem.

当问题规模较小时，可用线性规划、整数规划、动态规划等经典算法求解。

Second, according to model characteristic, such as non-linear, non-convex, multiple-peaked and so on, the paper discusses limitation of traditional solving algorithm, such as branch and bound method, GBD method and OA method, puts forward penalty function-makeup integer algorithm and genetic algorithm, analyses procedures of genetic algorithm, such as selection, crossover and mutation, brings forward modifications for specific realized problems of genetic algorithm, such as selection of initial points, operator design, adoptive value adjustment, constraint treatment and so on, and works out correlated solving program.

其次针对该模型非线性、非凸、多峰等特点，讨论了分支定界法、GBD法和OA法等传统求解算法的局限性，提出了罚函数一凑整算法和遗传算法的求解思路，对遗传算法的选择、交叉、变异等过程进行分析，对遗传算法初始点选择、算子设计、适应值调整和约束处理等具体实现问题提出了改进措施，并编制了相关的求解程序。

Fostering the concept of multi-culture firmly and mastering the development of advanced culture correctly are conductive to resisting terrorism, separatism of nationalities and ultraism of religion, which is of great academic theoretical, immediate and profound historical si...

牢固树立多元文化的理念和正确把握先进文化的发展方向，有助于在世界范围内自觉地抵制恐怖主义，民族分裂主义和宗教极端主义。不仅具有重大的学术理论意义，而且也具有重大的现实意义和深远的历史意义。

But if anyone walks in the night, he stumbles, because the light is not in him.

11：10 若在黑夜行走，就必碰跌，因为那光不在他里面。