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The decreasing conditions of an energy function are investigated by the use of convex function. By utilization of the primal convex function, the conditions are analyzed under which its conjugate function minus a quadratic function is also convex.

利用凸函数的定义研究了能量函数下降的条件，根据凸函数的性质分析它的共轭函数减去二次函数之差仍为凸函数的条件。

Basics of convex set theory and the convex analysis method are introduced. A comparison of probabilistic method and convex method is made with designed examples.

介绍了凸集理论的基本定理、定义和凸分析方法，并结合例题比较了概率方法和凸分析方法。

Chapter 5 is devoted the study of fuzzy optimization in fuzzy convex analysis structure given in chapter 4. We consider the problems of minimizing and maximizing a convex fuzzy mapping over a convex set and develop necessary and/or sufficient optimality conditions.

在第5章中，首先，在第4章所建立模糊凸分析的结构基础上，考虑了凸模糊映射的极值问题，得到了凸模糊映射取得极值的充分/必要条件。

An improved algorithm of two dimensional convex hull based on included angle is proposed, and all the convex points are achieved through the maximal included angle by the increasing counter-clockwise direction. When more than one point satisfies the maximal included angle, the most distant point to the previous point is regarded as the next convex point.

提出了基于夹角的平面点集凸包改进算法，以最大夹角，按顺时针的方向可得到所有的凸点，当满足最大夹角的点不唯一时，以离当前凸点最远的点为凸点。

For satisfying to process to keep a mother line, arc mother line, whole convex degree, half convex degree, ligarithmic curve cone, cylinder roll son of demand, ability according to design whet to submit have already corresponded form noodles of spiral lead a round, spiral lead Gun, double the song lead Gun, three convex Fengs to lead Gun, and arc plank and other similar of work piece etc..

为满足加工直母线、圆弧母线、全凸度、半凸度、对数曲线圆锥、圆柱滚子的需要，能根据设计磨出具有相应形面的螺旋导轮、螺旋导辊、双曲导辊、三凸峰导辊、以及圆弧支板以及其他类似的工件等。

In this project, the theory of convex models is generalized from convex domain to non-convex domain, from small-range algorithm based on Taylor's series to large-range one so that the range of its application is extended and the computational precision is improved.

本项目将凸区域的凸模型理论推广到非凸区域上，将小范围泰勒展式算法拓广到大范围问题的求解中，扩大了凸模型理论的适用范围，提高了运算精度。

In this paper, by using the kinematic measure for a segment of fixed length within a special convex domain, we obtain the Buffon probability formula of grid whose basic regional are two different convex domains, and its outreach to various convex domain cases.

本文通过利用凸域内定长线段的运动测度，给出了以两个不同凸域的并为基本区域的网格的Buffon概率公式，并将其推广到多个不同凸域的情形。

In the first part, convex duality method linearizes convex wealth equation, and the introduction of Lagrange multiplier converts original problem to an unconstrained static optimum problem. At last, we obtain another equivalent optimum problem with convex control domain.

文章前一部分运用凸对偶的方法先将财富方程线性化，Lagrange乘子的引入使最优问题等价与一个无约束的静态最优问题，最后转化为一个凸控制域的最优问题。

There are a lot of conclusions about properties of convex set and convex function, which have full application in convex programming.

相应于凸规划的凸集和凸函数的性质已有很多结论，并且在凸规划的研究中得到了充分应用。

To increase the running speed of the collision detection algorithm, a new approach is proposed, which uses convex Bounding Volume Hierarchies to express convex polyhedron. Thus the distance problem of two convex polyhedrons is come down to a nonlinear programming problem with constraints. The nonlinear programming problem can be solved by simulated annealing genetic algorithm.

为了提高碰撞检测算法的速度，提出用顶点的凸包表示凸多面体，将两个凸多面体间距离的问题归结为一个带约束条件的非线性规划问题，利用模拟退火遗传算法对该问题进行求解。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。