应用函数

Since the lengths of the line segments and the angles between line segments are treated as representation parameters, it is convenient to construct energy function and to deal with displacement and length constraints. Based on this advantage, a parametrical model for human body is proposed, which can easily produce human body models with different feature sizes. The above method is just suitable for polylines. Therefore, a generic deformation method for both discrete curves and surfaces is presented. The energy function is constructed by analyzing the relationship of the points before and after deformation. Together with the displacement constraints, the deformation problem is converted to a convex quadratic programming. A necessary condition for constraint points and a sufficient condition for the uniqueness of solution are given. The proposed method can be combined with skeleton-driven animation to control the deformation.

将线段长度与线段之间的角度作为表示参数，既有利于能量函数的构造，又便于处理位移约束和长度内蕴约束条件，利用这一优势，将其应用于三维人体的参数化建模，可以方便地产生具有不同特征尺寸参数的人体模型，由于这种方法只适用于折线变形，具有较大局限性，因此，本文进一步提出一种较通用的离散曲线曲面变形方法，通过分析变形前后的位置关系来构造能量函数，再加上位移约束条件，将变形问题转化为一个凸二次规划问题，并且给出了约束点应满足的必要条件及模型解唯一的充分条件，这种方法还可以与骨架驱动变形的思想相结合，能更好的控制变形。

Further I make use of the conclusion to solve a storage problem, get an optimal control policy between storage and need, and give the corresponding numerical results.And we also discuss the key word that dissolve this kind of problem: the construct and analysis of variational equation.

本论文的主要工作时对原问题的费用函数进行了扩展，使其归结到一类更广泛的函数上去，从而拓宽了其应用；并且将得出的结论引入存储问题，得到储量与需求间平衡的最佳效益模型的最优控制策略，并给出相应的数值结果。

Derive the requirement to strain and displacement of Patch Test. Give the relationship between weak form of continuity equation and the Patch Test, through which the hybrid element method and quasi-conform element method are analyzed. Refined direct stiffness method and generalized conforming elements are also analyzed about why they can pass patch test. At last, as an example of using the requirement of patch test for displacement, improved the BCIZ Element.

得出分片试验对位移函数和应变函数的要求，这些要求便是一个好的有限元法所应保证的；分析了几何方程弱形式与分片试验的关系，借此分析了杂交元、拟协调元如何满足这些要求，以及在满足这些要求的同时产生的对其他条件的影响；分析了精化直接刚度法、广义协调元和双参数法如何保证分片试验的满足；最后作为位移条件的应用例子，改进了BCIZ元。

A Multi-Species Cooperative PSO algorithm is developed using the ideas of species dividing in the bionomical world. The algorithm is shown to have guaranteed convergence to the global optimum. Furthermore, the training strategies of RBF network structures and weights based on the MCPSO aigorithm is proposed. Simulation results show that the algorithm is effective in such fields as chaotic time-sequence forecasting, system identification, speech signal processing and etc.

在分析基本微粒群算法和协同微粒群算法特点的基础上，借鉴生态学中的种群划分思想，设计出一种多种群协同进化微粒群算法，并分析了该算法的收敛性能；在分析径向基函数神经网络结构的基础上，提出了基于多种群协同进化微粒群算法的径向基函数神经网络结构和权值优化设计策略，并在混沌序列预测、系统辨识、语音信号处理等应用仿真实验中验证了算法的有效性。

The main achievements of the project are as follows: 1 the hypothesis that a decrease in seed mass causes an increase in mean dispersal distance has been tested based on the experiments of weed dispersal by wind. The experimental results partly support the hypothesis. The results will help farmers to make an optimal strategy of weed control; 2 a statistic method for inferring probabilistic distribution function of a random variable has been developed, by which probabilistic distribution functions of weed species dispersal have been determined; 3 the reproduction structure of Bromus sterilis has been studied; 4 a more complex CA model with 25 neighborhood cells were built, which can simulate spread of a weed population. This work promotes developments in both theory and application of CA models; 5 the "mean law" in weed control has been proposed. Accordingly, the algorism of patch spring may be calibrated; 6 the "patch" and "true patch" have been mathematically defined so that herbicide can be efficiently applied; 7 simulation validates that initial configurations of weed will affect dispersal of its population and strategies of controlling it, or its distribution patterns affect its dispersal progresses.

主要完成的工作和取得的成果有：1）用实验证实了重量较轻的杂草种子并不一定飞得比较重的远，其结果有助于农民制订杂草的优化控制策略；2）发展了一种推断随机变量分布函数的统计方法并用它来获得了几个杂草种的扩散分布函数；3）对杂草Bromus sterilis的繁殖结构进行了研究；4）建立了一个具有25邻的较复杂的能模拟杂草扩散的CA模型，并在理论和应用方面促进了CA模型的发展；5）在杂草控制方面提出了&平均法则&，据此可对按块施药方法进行校正；6）精确地定义了&块&和&真块&以便在杂草控制中能更有效地使用除草剂；7）模拟证实杂草种群的初始配置影响其扩散和控制策略，或者格局影响过程。

It is an important branch of mathematics and it has developed into a bulky subject and has been extensively applied in other natural sciences such as mechanics, calorifics, theoretical physics and other branches of mathematics.

复变函数论是数学的重要分支之一，它本身在发展中已成为一门庞大的学科，而对其它的自然学科，如力学、热学、理论物理及数学的其它分支，复变函数论均有重要的应用。

In this paper w e derived the optimum form of important function by variation method, with that proposed percepts to improve impor tant function; by utilizing the result of delaminateˉ sample theory, the improving direction of reˉsampling was determine d, and with that the double weight selecting partiˉ cle filtering was proposed.

为解决粒子滤波算法在实际应用中出现的滤波发散、粒子退化问题，文中利用变分法证明了重要性函数取法的最优形式，并由此提出重要性函数的改进方案；利用分层抽样原理，确定了重采样方法的改进方向，并由此提出双权重重采样方法。

According the experiential formulas of headbox to design the stepped diffuser headbox's geometry parameters. Supposing Paper suspension flow as potential flow and basing on hydrokinetic and computational fluid dynamics theories, we can solve the elliptoid partial differential equations which are followed by the flow functions and the potential functions by finite element method and simulate the flow's speed distribution with pde toolbox of matlab software. The simulate results and the flow analysis have good precision.

按照流浆箱的经验设计公式，设计阶梯扩散式流浆箱的各组件几何参数，以流体动力学、计算流体力学等理论为基础，假定浆流的流动为势流，采用有限元法求解浆流流动时其流函数和速度势函数所符合的椭圆型偏微分方程，应用matlab软件的偏微分方程工具包pde toolbox，模拟出所设计的流浆箱各组件内的浆流的流场流速分布，模拟结果与数值计算流动分析结果吻合。

On the basis of engine idiocratic mathematical model, using the origin underway accelerate time and the oil consumption at the cycle of multi-working conditions as the objective functions of the power performance and the economy performance respectively, and then transform it to a single objective function by using the linear adding.

在建立发动机特性数学模型的基础上，以原地起步连续换档加速时间和多工况循环使用油耗作为衡量动力性和燃油经济的2个分目标，采用线性加权组合的方法将其转换成单一目标函数，建立了汽车动力传动系优化数学模型，利用惩罚函数法对此模型进行了优化，实例计算表明，应用该方法对汽车动力传动系进行优化匹配分析时，整车综合性能均有显著改善。

The semivariogram models built by former analysis used as the input functions for Kriging that making isohyetal maps by integrating GIS.

为具体表现本区之台风降雨空间分布之情形，遂以前项所得之半变异函数作为克利金推估之输入函数，并应用地理资讯系统建立等雨量线分布图。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。