For nearly 40 years " development , genetic algorithms has made great achievements in both theory research and practical applications . however , its mathematical foundation is still incomplete compared with the distinctive and sound biologic foundation 经过近40年的发展，遗传算法在理论研究与实际应用中取得了巨大的成功，但相对其鲜明的生物基础，其数学基础还是相对不完善的。
Multisource information fusion is a changeable , opening and nonlinear system , in which , many uncertainties are found in the form of information , dynamic features of objects in surveillance area and the processing of multisource information . for decades , although we have made remarkable progress in this field in theory and in practice , the difficulties in dealing with uncertainties and the lack of feasible mathematical foundation of information fusion have made the unified methods of describing multisource information with uncertainties and the general system model and fusion algorithms not found . therefore , the basic theoretical framework of fusion is not yet established to this day 几十年来,虽然多源信息融合在理论上和应用中都取得了长足的进展,但是由于多源信息的复杂性及系统中存在的诸多不确定性因素,加之缺乏坚实而实用的数学基础,从而导致这一领域至今仍没能建立起描述多源不确定信息的统一方式以及有效的广义系统模型和融合算法,因而也就未能形成统一的基本理论框架,所以在多源信息融合理论研究和技术开发中,其首要问题就是如何能有效地给出多源不确定性信息的统一描述和建立反映其动态变化的系统模型。
Fractal dimension structure form of the cosmos are explored , and the mathematical foundation , which include the expressions of fractal dimension differential and calculus , regular space integral solutions of fractal dimension differential equations , the fractal calculus definitions of fractal measure as well as the measure computational equation of self - similar fractal , of fractal dimension calculus and fractal measure are given 摘要探讨了宇宙分维构造的形式，给出了分维微积分及分形测度的数学基础，包括分维导数及分维微积分的表述形式、分维微分方程的规整空间积分解、分形测度的分维微积分定义及自相似分形的测度计算方程。
It combines boolean algebra expression with time information to describe behavior of a digital circuit . it has made substantive progress at path sensitization , power dissipation estimation , iddt and delay fault diagnosis . theoretically , it is necessary to establish some mathematical foundation in order to define distance , limit and continuity based on boolean process 它将布尔代数与时间结合起来，为异步性描述提供了比较形式的理论基础，并在通路敏化、电源消耗的计算、动态电流测试方法( i _ ( ddt ) ) 、时延故障诊断等方面取得了实质性的进展。
They think that " geometric design " is not able to describe such a branch of learning such as cagd , which has a rigorous mathematical foundation as well as important applied background . and yet , " geometric design and calculation " not only widens the studying range in the field , but also gives it new vigor 他们认为仅有“几何设计”的概念还不足以刻画cagd这样的一个既有严格的数学基础，又有重要应用背景的学科，而“几何设计与计算”的概念不仅拓宽了该领域研究的覆盖面，也为该学科赋予了新的生命力。
Domain theory provides the mathematical foundation for denotation semantics of computer program languages . it is characterized by the close connection between order and topology , which makes it the common study field of both computer experts and mathematicians . weight , character and density are generally called cardinal functions 一种domain范畴要成为某种语言的语义学模型其基本条件是笛卡尔闭的，因而研究domain范畴的笛卡尔闭性或者说寻找笛卡尔闭的domain范畴就自然成了domain理论中一个十分基本的问题。
This algorithm laid the foundations of other sampling inference algorithms , such as importance sampling algorithm and like - hood weight sampling algorithm . in this paper , the description of accurate and complexities of some kinds of sampling algorithms are presented on the basis of introduction to basic concepts of bayesian networks . first , the mathematical foundations of them are given here in view of statistics 本文首先介绍了bayesian网的一般概念及推理任务,并主要着眼于bayesian网推理算法的数学原理,提出了样本平均值算法,对几种推理算法从数学角度做出本质性的刻画,给出各自的复杂度和精确度的理论分析,证明了他们在各种情况下的推理效率。
In consideration of the viewpoint of superposition theorem being only for linear circuits , starting from mathematical foundation of superposition theorem , substitutional theorem is used to conduct an equivalent conversion on the nonlinear circuits , and application of superposition theorem in the nonlinear - resisting circuits is innovatively proposed and basic procedures for its solution are provided 摘要针对叠加定理只能用于线性电路的观点，从叠加定理的数学基础出发，通过应用替代定理等效变换非线性电路，创造性地提出了叠加定理在非线性电阻电路中应用的方法，给出了求解的基本步骤。
