特殊函数

To deal with data containing time drift, orthogonal polynomials fitting instead of least squares method is used.

研究了一种适用于这种过程的数据处理方法，利用权函数为1的特殊正交多项式做最佳平方逼近，从而避免求解病态方程组，得到较好的处理结果。

Based on the local parametric representation of a curve, the mathematical models of planar mechanism optimum synthesis for the local path generation are built. Objective functions are constructed generally and for some special cases as well.

在平面曲线局部参数表示的基础上建立平面机构局部轨迹优化综合的数学模型，构造了一般情况下及常见特殊情形的优化目标函数。

By making use of the definition of derivative ,one can calculate the derivative of demarcation point ,the derioative of the special elementary function,the derivative of parametric equation.

利用导数的定义可求分界点的导数，特殊初等函数的导数和某些参数方程的导

A new technique of free-form deformation about parametric surface through so-called extension factor is presented in this article.

提出一种新的参数曲面自由变形方法：构造出特殊的伸缩因子函数，用它去作用待变形曲面，从而使曲面发生形变。

The detailed algorithm on analyzing cracks exploration inside blocks is: enriched approximations which describe singular crack tips fields and discontinuous crack faces are employed under the Partition of Unity theory; the enriched nodes surrounding crack tips or faces are respectively mapped with corresponding enriched degrees of freedom, and the solution of all these degrees of freedom is uniformly proceeded by the implicit iteration algorithm of DDA, then fracture and breakage of DDA blocks can be analyzed. The numeric examples show this algorithm is rational and efficient.

为此建立的无网格法裂纹扩展分析算法，采用满足单位分解条件的特殊增强型函数表达裂纹周围应力场的非连续、奇异特性，将对应的扩展自由度动态映射到裂纹周围的节点上，统一按DDA法隐式迭代方式求解，实现块体裂纹扩展和强度分析，相关算例结果显示该算法是合理有效的。

This paper introduces the game theory and sets up, based on it, the choice model for the public transportation priority by identifying the function of the payoff and the muster of attendee and stratagem. In addition, it analyses the existence of NASH equilibrium, and puts forward the arithmetic of Iterated Elimination of Strictly Dominated Strategies in the general condition, the Integrated Strategies in the special condition and the flow chart of the model. At last, it verifies the feasibility of the model with the given example.

本文采用了博弈论的理论，通过对公交优先系统中参与者集合N、战略集合S和收益函数u的确定，建立了一种基于博弈论的公交优先技术方案选择博弈模型来量化方案选择问题；在此基础上分析了NASH均衡的存在性，并且给出了一般情况下的重复剔除劣战略和特殊情况下的混合策略两种模型求解方法以及公交优先技术方案选择博弈模型的流程图；最后通过算例分析，验证了博弈模型应用于公交优先技术方案选择的可行性。

Nextly, the definition of Perron integral and Denjoy integral for fuzzy-number-valued functions in the plane are given, and by using them, we discuss the characterization theorems of the primitive functions for fuzzy Henstock integral in the sense of the special derivate bases.

其次，定义了平面上的模糊Perron积分及模糊Denjoy积分，并利用这两种积分对平面上两种特殊形式的导数基意义下的模糊Henstock积分原函数进行了刻划。

The results show that the linear birefringence will modulate the scale factor of the system with a Sa function, it can also affect the extent of the influence of the incident polarizing angle, taking －sin2;(δ/2) as the influence factor, at the same time. When the incident polarizing angle has some special values such as 0,45, or 90 degree, the effect to the system will be zero.

结果表明，线性双折射会以Sa函数的形式调制理想光学玻璃电流传感器输出信号的尺度因子，同时以－sin2(δ／2)为影响因子决定入射起偏角对系统影响的大小；当入射起偏角取某些特殊值时其对系统的影响为零。

We consider Theorem 1 to be highly significant and apply it to obtaining the rank of a certain augmentation quotient group by proposing Theorem 3 and giving its complete proof.

应用具有Np-序列有限p-群的特殊性质和重量函数，基本序列等概念以及已有的一些结果，分别研究了类为1的pk(k 2)阶A bel基本p-群和类为2的p4阶基本p-群之增广商群Qn的结构，得到了当n足够大时Qn作为A bel基本p-群的秩。

In this paper, the theories of generation function and recursive relation in combinatorics is used to analyze the time complexity of some special recursive algorithm, with three conclusions reached simultaneously, which is of valuable reference to the analysis and research on algorithm.

提出了用组合数学中的母函数与递推关系理论来分析一些特殊的递归算法的时间复杂度，并同时得出三个推论，在算法的分析与研究方面具有一定的参考价值。

It has been put forward that there exists single Ball point and double Ball points on the symmetrical connecting-rod curves of equilateral mechanisms.

从鲍尔点的形成原理出发，分析对称连杆曲线上鲍尔点的产生条件，提出等边机构的对称连杆曲线上有单鲍尔点和双鲍尔点。

The factory affiliated to the Group primarily manufactures multiple-purpose pincers, baking kits, knives, scissors, kitchenware, gardening tools and beauty care kits as well as other hardware tools, the annual production value of which reaches US$ 30 million dollars.

集团所属工厂主要生产多用钳、烤具、刀具、剪刀、厨具、花园工具、美容套等五金产品，年生产总值3000万美元，产品价廉物美、选料上乘、质量保证，深受国内外客户的青睐