连续

Based on the decided configurations, the continuity condition of combined Bezier curve in Euclidean space and De Casteljau algorithm on Lie group SO(3) are integrated to construct a combined Bezier positioning path of C^2 continuity at junctional configuration, and an illustration of different positioning path planning is analyzed in detail based on a liver tumor case.

根据确定的位姿，把组合Bezier曲线的连续条件和SO(3)的De Casteljau算法结合，构造出了一条在衔接位姿C^2连续的组合Bezier曲线路径用於定位，并且根据一例肝脏肿瘤病例对各种连续路径作了详细分析。

In this paper,several continuous variables are introduced to replace the discrete decision variable s,most importantly the pipe .

在数学模型中，引入连续变量代替离散的决策变量，这些连续变量是管道的"分段长度"，将混合整数非线性规划问题转化成连续的非线性规划问题。

Week 5 The definition and nature of derivative, the geometric meaning of derivative, the relation between the derivability and the integral, derivation rule.

第4周 连续的定义，连续函数的性质，初等函数的连续性，闭区间上连续函数的性质。

The identity and difference in the expressional patterns between distribution functions of discrete random variables and distribution functions of continuous random variables are elaborated,and the main expressional patterns of distribution functions of continuous random variables are summarized,and the derivability of distribution functions of continuous random variables is discussed.

0引言在概率论中，连续型随机变量分布函数的表达形式及其可导性是一难点。其一，离散型随机变量的分布函数有较明显的性质和统一的表达形式，而连续型随机变量，由于其概率密度函数一般为分段函数，根据其分段区间的差异，表达形式差异较大，不容易总结其规律，本文主要比较连续型随机

Surface blending in terms of geometric continuous is more practical and welcome with view of geometric interpretation which is different to the traditional differential method based on algebra.

几何连续是对参数曲面中参数连续度量进一步深刻的认识和研究。它是可微性的代数概念的几何抽象，克服了参数连续对曲面苛刻，高阶及结果失真等缺点。

The intermediate value theorem for discontinuous function is studied,the problem of discontinuous points when the left and right limit exists is considered by ZHU Le-min.

研究了非连续函数的介值定理，受朱乐敏等考虑的具有左、右极限存在的跳跃间断点的非连续函数的介值性定理的启发，利用上、下极限把介值定理推广到具有一般间断点的非连续函数的情况。

The authors studied carefully two numerical differential methods, finite difference method and rational polynomial technique, and pointed that FDM is the special ease of RPT when the limit state function is linear. Accordingly, FDM3 can be used for the continuous linear limit state function and RPT5 for the continuous nonlinear limit state function. For the discontinuous limit state function, RPT should be used because of the large error of FDM.

对于可靠度分析中常用的有限差分法及有理多项式法这两种数值微分方法，本文详细研究了二者间的异同及其求导结果与步长的关系，指出了对于相同的步长控制系数及取样方式，FDM是RPT在线性情况下的特例；对于连续的线性功能函数，可直接用3点FDM求导；对于连续的非线性功能函数，可用5点RPT求导；对于非连续的功能函数，应采用RPT求导。

In spite of the granular nature, soil has traditionally been modeled as a continuum. This continuum mechanics cannot get the precise solution while soil\'s nonlinear, discontinuous, large deformation, and strain localization behavior are considered. The discrete element method is based on discontinuum theory, and is pioneered by Cundall.

土是由多相介质组成的离散颗粒集合体，尽管研究者早已在土的散粒状属性上达成共识，但关于土体力学性质的研究还经常沿用连续介质力学方法，这种基于连续体小变形假设的方法在求解实际土体非线性、非连续、大变形、应变局部化问题时往往无法得到精确解答。

A novel hybrid algorithm, which combines predictor-corrector primal-dual interior point method and genetic algorithm, is presented for dynamic and static reactive optimization in this dissertation. The algorithm fully make use of the advantage of interior point method in solving successive optimization problem and the advantage of genetic algorithm in solving discrete optimization problem. The original problem is divided into three parts: total successive problem, discrete problem and successive problem.

结合内点法和遗传算法，本文提出了一种新颖的混合算法用于求解动、静态无功优化问题，算法充分利用了内点法易于求解连续优化问题和遗传算法易于求解离散优化问题的优势，将原优化问题分解为初步的连续优化问题、离散变量优化问题、连续变量优化问题这三个子问题分别求解。

Based on the ICMmethod,the discrete topological optimization problem about spot-weld's existence or not is transformed into the continuous optimization problem on[0,1].The optimization model is founded with maximizing the structural stiffness as objective and structural strength as constraints.The problem of multi-objectives and multi-constraints is transformed into the problem of single-objective and single-constraint with the K-S function.The displacement and stress are transformed into the explicit function of design variables with the Response Surface Methodology.The optimization model is solved with Sequential Quadratic Program.

基于ICM（Independent Continuous Mapping，即独立、连续、映射）方法，将焊点有无的离散拓扑优化问题转化为[0，1]区间上的连续优化问题；建立了以结构刚度最大为目标、结构强度为约束的连续拓扑优化模型；采用K-S函数将多目标和多约束问题转化为单目标和单约束问题；运用响应面方法将位移和应力转化为设计变量的显式函数，采用序列二次规划方法求解优化模型。

It is also known as one of the most poisonous naturally occurring substances.

它也被称为一个最自然发生的有毒物质。

The greatest stress is found at the location on the cross section where V is the largest.

最大应力出现在横截面上V为最大的地方。