一些约束规划问题的近似全局最优解

首先将一个具有多个约束的规划问题转化为一个只有一个约束的规划问题,然后通过利用这个单约束的规划问题,对原来的多约束规划问题提出了一些凸化、凹化的方法,这样这些多约束的规划问题可以被转化为一些凹规划、反凸规划问题．最后,还证明了得到的凹规划和反凸规划的全局最优解就是原问题的近似全局最优解．     

A new simplicial cover technique in constrained global optimization

A simplicial branch and bound-outer approximation technique for solving nonseparable, nonlinearly constrained concave minimization problems is proposed which uses a new simplicial cover rather than classical simplicial partitions. Some geometric properties and convergence results are demonstrated. A report on numerical aspects and experiments is given which shows that the most promising variant of the cover technique can be expected to be more efficient than comparable previous simplicial procedures.     

仿紧集上的拟变分不等式

本文利用T－γ－对角凹函数和我们得到的一类极大极小不等式研究了仿紧集上的拟变分不等式．     

Least Squares Convex-Concave Data Smoothing

We consider n noisy measurements of a smooth (unknown) function, which suggest that the graph of the function consists of one convex and one concave section. Due to the noise the sequence of the second divided differences of the data exhibits more sign changes than those expected in the second derivative of the underlying function. We address the problem of smoothing the data so as to minimize the sum of squares of residuals subject to the condition that the sequence of successive second divided differences of the smoothed values changes sign at most once. It is a nonlinear problem, since the position of the sign change is also an unknown of the optimization process. We state a characterization theorem, which shows that the smoothed values can be derived by at most 2n – 2 quadratic programming calculations to subranges of data. Then, we develop an algorithm that solves the problem in about O(n ²) computer operations by employing several techniques, including B-splines, the use of active sets, quadratic programming and updating methods. A Fortran program has been written and some of its numerical results are presented. Applications of the smoothing technique may be found in scientific, economic and engineering calculations, when a potential shape for the underlying function is an S-curve. Generally, the smoothing calculation may arise from processes that show initially increasing and then decreasing rates of change.     

质点从可自由移动的凹曲面上滑下的速度、加速度和时间

对于一个质点从可自由移动的光滑的凹曲面上滑下的速度、加速度和时间作了一般性讨论,建立了相应的公式.并对质点的运动平面与凹曲面的交线分别为直线、抛物线和椭圆等情况进行了具体的计算.     

凹形树突状PtCu纳米催化剂的合成及对甲醇的电催化

以邻苯二胺为表面活性剂,通过水热釜法一步制备凹形树突状PtCu双金属纳米催化剂(PtCu NCDs)。PtCu NCDs在电催化甲醇氧化(MOR)的应用中表现出非常高的活性和很强的抗有毒中间体作用。PtCu NCDs对于甲醇氧化的质量活性为(0.53 A·mg^-1 Pt)是商业Pt/C(0.26 A·mg^-1 Pt)的2.04倍。从比活性的CV曲线图对比发现PtCu NCDs(1.07 mA·cm^-2)是商业Pt/C(0.55 mA·cm^-2)的1.95倍。而且,PtCu NCDs(2.76)比商业Pt/C催化剂(1.02)表现出更高的I_f/I_b比值。这些优异的电催化活性可能归功于PtCu NCDs特殊的凹形树突状形貌。     

高效凹面聚光集热海水蒸馏淡化及供暖混合装置

在便携的高效凹面聚光集热装置基础上,通过综合利用所获得的太阳热辐射能实现海水淡化蒸馏、温差发电以及温箱供暖,从而达到太阳能高效综合利用的目的.为岛礁等特殊环境下的海水淡化与供暖需求提供一种途径.