约束

Classifying the system constraints as basic constraints and variable constraints,a model of flexible multibody with changing topologies is developed.

将系统约束分为基本约束和条件约束，建立了变拓扑结构柔性多体动力学模型。

How to deal with the restrictions of deep excavation is a very difficult problem. This paper analyzes the restrictions of pile-support structure detailedly, uses a castigatory function to deal with the restrictions, and adds the castigation to the function. Now the problem has changed to solve a minimal problem, and GA can be used to the optimal design successfully.

束条件的处理是遗传算法应用到深基坑支护结构优化的难题和重点，本文详细分析了桩撑支护结构的约束条件，采用了罚函数法对约束条件进行处理并反映到适应度函数上，使其变为无约束的极小值问题，从而使遗传算法得以顺利实施。

By transforming the nonlinear saturation constraint into the special linear constraint, the problem of solving the feedback controller with saturated actuator is converted to the design of controller with linear constraint. The stochastic stability is ensured by using the intersection of ellipsoid invariant set of different modes existing in the attraction domain of the closed loop system. In this case, solving controllers can be equivalent to a solvability problem of linear matrix inequalities.

通过将非线性饱和约束转化为特殊的线性约束，使具有饱和执行器的控制器求解问题转化为线性约束控制器的求解问题，利用位于闭环系统吸引域内的不同模态下椭圆不变集的交集来保证系统的随机稳定性，此时控制器的求解可等效为线性矩阵不等式的可解性问题。

They include the fundamental concepts of jet bundle geometry needed in describing time-dependent mechanical systems, decomposition of jet bundles into a direct sum according to the constraints, horizontal distributions on constraint mainifolds, the global formulation of D'Alembert-Lagrange's equations and Chaplygin's equations, and nonholonomic mechanics on a Riemann-Cartan manifold. Meanwhile, the geometric significance of Chetaev's conditions and $\rd$-$\delta$ commutation relation are discussed in depth.

本文主要综述非完整约束系统几何动力学的外附型和内禀型Lagrange理论，包括非定常力学系统所需要的射丛几何学的基本概念、射丛按约束的直和分解、约束流形上的水平分布、 D'Alembert-Lagrange方程与Chaplygin方程的整体描述、以及Riemann-Cartan流形上的非完整力学，文中对Chetaev条件和d-δ交换关系的几何意义作了深入讨论。

The primary work of this paper includes: 1 The general process and the fundamental theory of genetic algorithm is introduced systematically, which is also be applied to an example; 2 The penalty function method and the constraint tournament method are introduced in the paper, which are used to process the constraint limit. Via analyzing the basic principle of NSGA-II ,which is elaborated in the paper, the fast non- dominated sorting method, congestion distance and its comparison operator, the elite strategy and the main process of NSGA-II is researched particularly. 3 Via modeling the fire distribution problem, the model is computed by the algorithm of NSGA-II, which is combined with both the penalty function method and the restraint league tournament method The optimization of two goals are also realized in the paper. The results derived from the VC++6.0 indicate that, two algorithms both have the high convergence, simultaneously the Pareto optimal solution also maintain the variety of distribution.

本文所作的主要工作如下：系统地介绍了遗传算法的一般流程和基本理论，并应用于一个函数优化的实例；研究了用于处理约束限制的罚函数法和约束联赛法，论述了NSGA-II的基本原理，并对其提出的快速非支配排序法、拥挤度及其比较算子、精英策略及NSGA-II的主要流程作了详细的研究；建立了火力分配问题的模型，并将NSGA-II算法分别与罚函数法和约束联赛法相结合对该模型进行了计算，实现了对两个目标的最优化；用VC++6.0编程计算后所得的结果表明，两种算法均具有很好的收敛性，同时Pareto最优解也保持了好的多样性分布。

The nonholonomic system is controllable when the dimension of input space is less than that of configuration space.

这类问题通常是由于机械系统受到对速度的不可积约束引起的，这种约束不可通过积分的方法表示成位形空间的约束形式。

The F-P structure, especially the thermal-strain mechanism of thermal bimetal sheets were investigated deeply in the paper, the Finite Element Analysis results for both the "four nodes" and the "ring" confinements were given; the size of the ring hole can be simply changed to agilely meet the requirement of the different measurement range; the materials match and the parameters selection of the thermal bimetal sheets were analyzed and discussed, and some available suggestions were given; the F-P temperature sensors with the two developed bimetal sheets confinement mechanism were designed and fabricated, the practical measurements were carried out, and the experiment results were analyzed and discussed.

文中对所提出的F-P腔结构，特别是热双金属片的应变机制进行了较系统深入的研究，给出四点约束和环状约束具体有限元分析结果；提出的环状约束可以简单改变环孔大小灵活适应不同量程的需要；对热双金属片材料配对和参数选择进行了分析讨论，并给出有益的建议；实际制作了两种约束机制的光纤热双金属片F-P腔温度传感器，进行了相关实际测试，并对实验结果进行了讨论。

Extensive research has been carried out under the hypothesises such as fixed number of constraints in one dynamic system, nondegenerative Jacobian of constraints, ideal and bilateral constraints. If one or more of these hypothesises are violated, inconsistency in state space may appear.

然而，目前有待发展的经典力学理论中有一些假设性的前提，例如约束的数目保持不变，约束的Jacobian非退化，约束是理想的，同时对含单边约束的系统研究甚少。

This method changes the generation process of the constrained texture synthesis, first of all it synthesises textures, and then constraints regionals, it makes the binding process easy and separate the synthesis process, overcomes the constraints of regional boundaries and repeated to determine synthesis methods used interchangeably cumbersome, then speeds the process.

该方法改变了以往的生成过程，首先进行纹理合成，再进行区域约束，使得约束过程与合成过程分开，从而减弱了约束边界在多样图纹理合成时对合成算法的约束，克服了反复判断区域边界的繁琐，进而加快了合成速度。

In this paper, the Hestenes-Powell augmented Lagrangian function is again considered, for solving equality constrained problems via unconstrained minimization techniques.

在适当的条件下，我们建立了Hestenes-Powell 增广拉格朗日函数在原问题变量空间上的无约束极小与原约束问题的解之间的关系，并且也给出了Hestenes-Powell 增广拉格朗日函数在原问题变量和乘子变量的积空间上的无约束极小与原约束问题的解之间的一个关系。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。