类函数

In Chapter 4,we obtain the optimality for the quasi-score function 〓in a more general class of estimation functions〓,where〓and〓or〓This result is a extension of Gauss-Markov theorem of the linear model to the nonlin-eaar model.

在本章中，我们得到拟得分函数〓在一种较大的估计函数类〓中的最优性，其中〓而〓或〓于是，我们得到类似于线性模型中的Gauss-Markov定理和拟得分函数的拟Fisher信息上界及达到上界的充要条件：〓，其中〓为真实未知的得分函数，〓为模型均值。

In chapter 3, we introduce a new family of functions with negative coefficients T,...

第五章根据α螺旋形函数的定义及算子D~λ定义一族新的解析函数类S_α，导出族中函数的积分表达式；研究了S_α中函数的某种积分运算及卷积定理。

According to the structured element representation theorem of fuzzy number and fuzzy-valued function, we obtained one-to-one isometric mapping from the family of standard bounded monotone function with same monotonic formal on [-1, 1] to the fuzzy number space, and proved they are homeomorphic.

在模糊值函数的模糊结构元表述理论的基础上，利用[-1，1]上同序标准单调函数类上的距离诱导出模糊值函数空间上的距离，证明了模糊实数空间与[-1，1]上同序单调函数类同胚。

Secondly, we introduce the integral operator , where is an operator-valued functions, and derive some argument properties of the integral operator and some interesting corollaries as the special case.

二、将一类被积函数为复值函数的积分算子推广到被积函数为解析算子值函数的情况，并讨论了这类积分算子的辐角性质。

Quantifying similarity/difference between two objects plays an important role in many contexts The quality of the similarity/difference scores can be improved by considering the semantic information related to the features of objects A flexible semantic distance function called X Dist is proposed, which can utilize the semantic information to measure the difference between two objects based on a solution to the transportation problem from linear optimization With a ground distance function for single features being a metric, X Dist is also a metric This property is very useful for making searching efficient, but is not investigated in the previous research Moreover, the experimental results show X Dist can be as good as the previously studied similarity measures in nearest neighbor searching, discriminative power and computing speed

量化对象间相似性/差别的方法具有广泛的用途，利用相关的语义信息能够得到更好的量化结果提出了一个量化对象间语义差别的距离函数XDist，它基于线性优化中的运输问题模型和相关的语义信息量化两个对象之间的差别在量化特征的差别函数是度量的情况下，XDist是一个度量，在提高搜索的效率方面具有优势，弥补了以往研究的不足，而且实验初步表明，此函数在最近邻查询效果、差别分辨力和计算速度方面能与已有函数相媲美1 引言量化对象间相似性/差别的方法具有广泛的用途，例如数据挖掘中的聚类；信息检索中的相似文档查询；协同过滤中的相似用户查询；CBR中的相似案例查询集合是对象特征表示的常用结构，集合的元素是与对象特征相关的项，它们可以

To generalize convex functions, Zalinescu introduced the concepts of uniformly convex functions in 1983, and discussed some properties for them;under the conditions of upper semicontinuity and lower semicontinuity, some equivalent conditions were given by Yang in 1998, so that criteria for uniformly convex functions are simplified.

作为对凸函数的推广，1983年Zalinescu提出了一致凸函数的概念，并讨论了它们的一些性质特点；1998年Yang在上半连续和下半连续条件下给出了一致凸函数的一些等价条件，简化了一致凸性函数类的判别条件。

Results of analysis show that Generalized Paris Law can consider the complex crack propagation in the material of the pavement structure. The fatigue life of the pavement increases with increasing thickness of surface layer in a power function. Use of a thicker surface layer may extend the service life of the asphalt pavement. The fatigue life increases with decreasing modulus of surface layer in a power function with a negative exponent. However, since reduced modulus would scarify the structural strength and might cause rutting-related distress, caution should be taken when using low modulus materials for improving fatigue performance of asphalt pavements. The fatigue life increases with increasing modulus of base material in a power function. However, the fatigue life can not infinitely increases with increasing modulus of the base.

计算与分析表明：广义Paris公式可以考虑沥青路面结构内材料复杂的裂缝扩展：沥青面层的疲劳寿命随着面层厚度的增加以幂函数的形式增加，适当增加沥青面层厚度可以提高路面的使用寿命；沥青面层的疲劳寿命随着面层材料模量的降低以负指数的幂函数形式增加；由于材料模量的降低将牺牲路面的整体强度并可能引起路面车辙类损坏，以此提高疲劳寿命的方法应慎重对待；沥青面层的疲劳寿命随着基层材料模量的增加呈幂函数的形式增加，但由疲劳方程可以看出，寿命并不是随基层材料模量的增加而无限的增加，疲劳曲线在经过一个上升段后，逐渐趋于一个常数值，这说明，这时基层模量对寿命已不作关键性贡献；随着底基层厚度的增加，面层的疲劳寿命近似地呈线性函数增加，但效果并不很明显。

Based on the mind of perturbation,a method which combines transitive closure method with the objective function method is introduced,and the steps of the method is presented.

分析了传统的模糊聚类方法，基于摄动思想，将传递闭包聚类法与目标函数法相结合，得出了一种既满足聚类效果要求又减小聚类失真的简便算法，同时给出了该聚类方法的步骤。

In Chapter 2,we investigate the construction and dimension character-ization of fractal curves in the plane.The method proposed by Bush et al,yielding nondifferentiable continuous functions,is first extended to more gen-eral cases.

第二章研究平面分形曲线的构造及维数刻划问题，首先将Bush等人利用实数的b进制小数构造无处可微函数的方法发展到更一般的情形，借助于实数的Cantor级数表达式，构造了一类广泛的无处可微连续函数，使得Bush等人所构造的函数成为本文所构造函数类的特殊形式。

After all the angular integrations and spin summations completed, the needed parameters in the non-relativistic wave functions have been acquired using the variational method and so the functions themselves have been established in this way.

在第三章中，利用对角和法则，导出了类硼离子基态及第一激发态非相对论能量的解析表达式，完成涉及到的角向积分和自旋求和后，利用变分原理求出了非相对论性波函数中的待定参数，从而确定了非相对论性波函数，并获得类硼离子基态及第一激发态非相对论能量。

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。