水电站有压管道水击波数值模拟十分重要，其计算方法一直都是重点研究方向，TVD格式是数值模拟水击波的新方法，特别适合数值模拟强间断问题。其限制函数是该格式的核心问题，具有四种不同形式，将其运用于水击方程，数值模拟阀门突然关闭时水击波压力变化，与解析解进行对比，以此探究限制函数类型对TVD数值模拟水击波结果的影响。结果表明：四种限制函数TVD格式的计算结果，在间断处避免了非物理振荡，Superbee型TVD格式的分辨率最高，推荐该限制函数数值模拟水电站水击波。

The numerical simulation of water hammer waves in pressure pipes of hydropower stations is very important .Its calculation method has always been a key research issue .TVD scheme is a new method to simulate water hammer waves with its strength in simulating strong discontinutity problems .The limiter function which possesses four different forms is the essence of the scheme .Here ,they were applied to the water hammer equation to simulate the variations of surge pres-sure when the valve suddenly closed .In order to discuss the effect that the type of limiter function had on the results of water hammer waves’ numerical simulation with TVD scheme ,the results of numerical simulation were compared with that of the analytical solutions .It indicates that the calculations of TVD scheme with four limiter functions can avoid nu-merical oscillations at discontinuity point .The TVD scheme with Superbee limiter fountion has the highest resolution and it is recommended for simulating w

在Bernt利用Picard迭代给出的随机积分方程解的存在唯一性定理基础上，通过定义本性有界可测函数作为核函数并对核函数的积分进行限制，给出了带核函数随机积分方程解的存在唯一性定理。

Bernt uses Picard iteration to give the existence and uniqueness theorem about the solution of stochastic integral equations.On this basis,we define the essential bounded function as the kernel func-tion and limit the integral of kernel function,then we give the existence and uniqueness theorem of the solution of stochastic integral equations with kernel function.

在利用智能化方法实现辅助决策的过程中，为提高模糊规则在使用中的准确度和可靠性，定义C-E模型，引入语义限制函数描述模糊规则的倾向程度。通过对专家意见的量化转换，初始化拟合规则的语义限制函数，并提出一种误差校正方法，在规则匹配过程中校正语义限制函数误差，进而构建可自适应调整的模糊规则。借鉴框架表达法的设计思想，采用框架-模糊规则组的设计思路，完成基于语义限制的模糊规则结构的设计，为该结构的吻合度计算提出一套较为科学的计算方法，以此达到挖掘专家的深度认知和潜在经验、降低专业知识影响、提高模糊集下精细化计算的目的。某采油厂的应用实例表明，利用基于语义限制的模糊规则结构可有效地实现对于故障井诊断的专家知识设计。

In the process of achieving decision by intelligent method, in order to improve accuracy and reliability in using fuzzy rules,this paper defines the C-E model as the basis,bringing in the semantic restriction function to describe the fuzzy rules tendency. By quantitatively transformating for expert opinions,initializiting semantic restriction function for fitting rules,it raises an error-correction method that can correct errors of semantic restriction function. In the process of matching rules,it builds the fuzzy rules that can be self-adjusted. To use the design idea of frame expression method for reference,the design thought of the frame-fuzzy rules group is adopted,and the design that based on the fuzzy rule structure with semantic restriction is accomplished. A more scientific set of calculation method for the structure coincidence is brought out. On this account,to excavate experts’ depth cognition and the potential experience,lower the impact of specialized knowledge,

基于统计学习理论,核被看做是一种相似度测量模型.核函数是支持向量机算法的核心,利用核函数可以将低维不可分数据映射到高维空间,并进行最优分类研究.但孤立点或噪声数据都会影响最优分类平面和最优分类函数,所以提出利用相似度测量构建模糊核函数.相比高斯核函数和模糊sigmoid核函数的分类支持向量模型,本文提出的模糊相似核函数在支持向量机运算中计算成本最低,可以提供更高的准确率,同时可以避免传统模糊核函数的限制.

Based on the statistical learning theory ,kernels are often presented as measures of similarity measure . Kernels play a very important role in support vector machine (SVM ) algorithms , which can mapper the un-classification data to high dimensional space ,to get the optimal classification result .Unfortunately ,SVM lacks ability to deal with the system or data with ambiguous characters .So this paper proposes to SVM with fuzzy kernel , which is obtained by similarity measure method .Compared to Gaussian RBF kernel function and fuzzy sigmoid kernel function ,SVM with fuzzy similarity kernel gets more accuracy results with less computation requirements , and alleviates current limitation of the fuzzy kernel function .

Della Vecchia等引进一种修正的Bernstein算子，它可以用来逼近端点具有奇性的函数。文章利用加权光滑模ω2φλ（ f，t） w和加权K 泛函K2φλ（ f，t2） w ，建立了该算子的导数与其目标函数的光滑性之间的等价关系，所得结论对权函数的参数a，b无上界限制，只要求a， b ＞0。

In the present paper,we establish the equivalent relation between the derivatives of a modified Bernstein operators and the smoothness of the functions which approximate in the weighted approximation,by using the weighted modulus of smoothness and the weighted K?functional.All the results involved have no re?striction on the upper bounds of the parameters a and b.