数学规划

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。

The research of this paper is began with the analysis the geographic spatial character of the UPTN, and designs the UPTN data mode based on GIS. Then, based on the good exhibiting all kinds of topology of the UPTN, and combined with the technology evaluation standards of the UPTN, this paper builds the UPTN planning mathematic model, and puts forward the quantitative calculation of the UPTN evaluation standards based on GIS; brings forward the arithmetic of the optimal path of the UPTN based on the public traffic network storage structure; designs the bus lines grouping management model, and realizes the contradistinctive evaluation of the UPTN planning projects based on GIS.

论文研究的重点内容是从分析城市公交网络中地理空间实体的特征开始，设计基于GIS的城市公交网络数据模型，在有效表现公交网络拓扑关系的基础上，根据公交线网技术评价指标，建立基于GIS的公交线网规划的数学模型，并给出公交线网评价指标的GIS量化计算方法；提出以公交线网数据存储结构为基础的公交网络最优路径算法；设计公交线路分组管理模型，实现公交线网规划方案对比分析。

In this paper, The power grid planning system that utilize the computer network, share the information of SCADA, Customer Information System, Production Management System, explore new mathematics model, help the user planning based on GIS technology, space load-forecast and decision making will be discussed. The system will help the power supply company to allocate power substation appropriate, bring great economic benefit with limited investment and improve its planning level.

本文探讨了如何通过计算机网络，共享自动化系统、营销系统、输配电管理系统等系统的已有资源，采用适当的数学模型，实现基于GIS的空间负荷预测和电网规划辅助决策功能，合理和适时地配置电源，优化网络的结构，使电网具有可扩展性和可持续发展的能力，从而使有限的投资可以发挥最大的经济效益，使目前的电网规划工作提高至一个新的水平，适应新形势的要求。

In this paper,several continuous variables are introduced to replace the discrete decision variable s,most importantly the pipe .

在数学模型中，引入连续变量代替离散的决策变量，这些连续变量是管道的"分段长度"，将混合整数非线性规划问题转化成连续的非线性规划问题。

Water deficiency sensitive index; water production function; optimal irrigation schedule; dynamic planning model; non-linear model

农业科技，农业基础科学，农业数学缺水敏感指数；水分生产函数；灌溉制度优化；动态规划模型；非线性规划

XEX ~ Arg min{FIy E ~2} where the upper level is about topological structure optimization(a~ is a topological structure varable), and the lower level is a constrained programming about continuous variable y. 2 Apply graph, the action of permutation group on a graph, equiva- lent class, orbit etc.

取得的主要成果有： 1 依点到集的映射、集值映射、二元映射和分离定理等理论首次建立了具有拓扑结构双层规划的数学模型 min F s.t.x∈X y∈Arg min｛F|y∈Ω｝其上层规划为关于离散变量x的拓扑结构优化，下层规划是关于连续变量的约束规划。

All the sub-plans are described by a group of general mathematic formulae. The computation of the sub- plan can be decomposed into two sub-problems by relaxing the constraint that production level at production period of a sub-plan must be more than zero. Based on the properties of an optimal solution, two polynomial algorithms are devised to solve sub-problems and reintegrate the relaxed constraint. Finally, a dynamic programming algorithm with complexity O(T^4) is developed to solve the global problem, where T is number of periods in planning horizon.

给出了所有子计划的通用数学描述，并通过松弛正生产量约束将子计划的计算分成两个子问题；依据子问题和子计划最优解的性质，设计了求解子问题和重新集结松弛约束的多项式算法；在此基础上提出了一个复杂性为O(T^4)的求解整个规划问题的多项式动态规划算法，这里T是规划时段上的周期数。

Aiming at researching on the theory of the shaft-kind parts form error evaluation and its application, on the basis of the analysis for the geometric model of the roundness error and cylindricity error, the linear programming models of the enclosure evaluation were proposed. According to the features of the proposed models, the solution of the optimization algorithms of linear planning was discussed to obtain accurate evaluation results.

为了对轴类零件形状误差评定理论及应用进行研究，在分析轴类零件的圆度、圆柱度误差评定几何模型的基础上，建立了包容拟合评定的规划数学模型，并针对模型的特点，探讨了使用线形规划的单纯形优化算法进行规划模型的求解，从而获得精确的形状误差评定结果。

In this paper, we provide an improved form of MPEC model for data classification first proposed in Ref.

对基于均衡约束数学规划的数据分类模型进行改进。

Besides FPS, the proposed GCA approach can also be used to solve a class of network communication problems.

通常的梯度下降法等数学规划方法，本质上是串行的优化方法，不能满足

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷