A Cutting Plane Algorithm for Linear Reverse Convex Programs

In this paper, global optimization of linear programs with an additional reverse convex constraint is considered. This type of problem arises in many applications such as engineering design, communications networks, and many management decision support systems with budget constraints and economies-of-scale. The main difficulty with this type of problem is the presence of the complicated reverse convex constraint, which destroys the convexity and possibly the connectivity of the feasible region, putting the problem in a class of difficult and mathematically intractable problems. We present a cutting plane method within the scope of a branch-and-bound scheme that efficiently partitions the polytope associated with the linear constraints and systematically fathoms these portions through the use of the bounds. An upper bound and a lower bound for the optimal value is found and improved at each iteration. The algorithm terminates when all the generated subdivisions have been fathomed.     

Er~(3+),Yb~(3+)共掺杂的NaYF_4荧光粉的制备及下转换发光研究

采用高温固相法合成了Er3+、Yb3+共掺杂的NaYF4荧光粉。XRD测量数据表明合成的样品为纯相。测量了样品的激发谱和发射谱,证明377 nm的紫外光通过量子剪裁的形式将能量传递给一个Yb3+,发射一个975 nm的红外光子,再从4F9/2能级跃迁到基态发射一个红外光子。测量了377 nm激发下,监测541 nm的发光寿命曲线,计算得到最大的量子效率为126.35%。通过监测Yb3+的975 nm的近红外发射,证明了Er3+的4F7/2和2H11/2能级通过下转换的形式将吸收的485 nm和519 nm的能量传递给Yb3+。这种将Er3+在可见光波段的多种光子能量传递给Yb3+发射975 nm的近红外光子的思想在以前的研究中从未被提出。     

下料问题的优化模型及其快速算法

结合生产实际中具体的下料问题,本文建立了该类问题的优化模型,并提出下料方式的遴选三准则,即高利用率优先准则,长度优先准则和时间优先准则.运用本文的算法对一维下料的利用率高达99.6%,机器时间4秒.对二维的利用率为98.9%,机器时间约7秒.     

金属切屑塑性流动的稳定性

对金属正交切削过程中切屑形成机制和材料塑性流动行为进行实验研究和理论分析. 通过对4 种常用金属材料正交切削过程的实验研究和切屑形貌的微观观察,确定了连续切屑转变成锯齿切屑的临界速度. 结果表明该临界速度与材料性能相关. 在实验观察基础上,提出描述材料正交切削过程的二维分析模型. 该模型假设切屑形成区为包括主剪切区和次剪切区的一个平行四边形. 载荷有主剪切区中的剪应力和次剪切区中的正压力;通过量纲分析得到描述材料正交切削过程的无量纲主控参数和无量纲形式的基本控制方程;应用线性稳定性分析方法建立平面应变状态下评价材料塑性流动稳定性的普遍准则;求得切屑形成区内材料塑性变形的速度和应力近似解. 讨论切屑形成、形貌转变以及相关的塑性失稳机制. 分析结果表明, 表征材料惯性与阻尼之比的无量纲参数— 雷诺数可以作为主控参数描述金属切削过程以及切屑材料塑性流动的稳定性.      

分段函数的分类及分离型分段函数与初等函数之间的关系

将分段函数划分为连结型分段函数 ,分离型分段函数和它们的组合形式三种类型 ,得到了分离型分段函数是初等函数的充分必要条件 ,完整地解决了分离型分段函数与初等函数之间的关系 ,并且给出了初等函数在其任一截取集上的限制函数 (截取函数 )仍然是初等函数的结果     

Parallel bucket sorting on graphics processing units based on convex optimization

We found an interesting relation between convex optimization and sorting problem. We present a parallel algorithm to compute multiple order statistics of the data by minimizing a number of related convex functions. The computed order statistics serve as splitters that group the data into buckets suitable for parallel bitonic sorting. This led us to a parallel bucket sort algorithm, which we implemented for many-core architecture of graphics processing units (GPUs). The proposed sorting method is competitive to the state-of-the-art GPU sorting algorithms and is superior to most of them for long sorting keys.     

胰岛素分子主链构象的CNDO／2计算和比较

对蛋白质分子进行量子化学计算常采用如下方法:以肽基和残基侧链为基本计算单元,使对蛋白质分子的计算分解成各次单元的计算(图10)。计算时往往根据构象图选择代表点以减少工作量。例如,计算木瓜蛋白酶时,根据其构象图,212个肽基被分为10组,每组中选取1个代表点进行计算。用同样的方法处理残基侧链的计算。但该方法     

线型聚能装药的理论研究

本文提出了一端起爆的线型聚能装药射流形成的不定常理论模型。根据这一模型,当金属罩在爆轰波作用下的运动速度为已知时,则不论此速度是否是时间或初始位置的函数,都能得到射流形成时的速度,质量和位置等参数。 按照本文模型,Defourneaux.M.的定常射流形成定常模型是一个简单的特例。我们利用本文的模型对等厚度装药的情况进行了计算,并与实验结果比较,两者符合良好。同时计算结果表明,考虑射流形成的不定常因素,可以较好地解释射流头部的质量堆积和射流内部的反向速度梯度等实验现象。本文的模型可以为线型聚能切割索的设计提供较为准确的理论指导。     

On Global Optimality Conditions and Cutting Plane Algorithms

We discuss global optimality conditions and cutting plane algorithms for DC optimization. The discussion is motivated by certain incorrect results that have appeared recently in the literature on these topics. Incidentally, we investigate the relation of the Tikhonov reciprocity theorem to the optimality conditions for general nonconvex global optimization problems and show how the outer-approximation scheme developed earlier for DC programming can be used to solve a wider class of problems.     

Effcient Near-Infrared Quantum Cutting in Tm3+/Yb3 Codoped LiYF4 Single Crystals for Solar Photovoltaic

Downconversion (DC) with emission of two near-infrared photons about 1000 nm for each blue photon absorbed was obtained in thulium (Tm³⁺) and ytterbium (Yb³ ) codoped yt-trium lithium fluoride (LiYF₄) single crystals grown by an improved Bridgman method. The luminescent properties of the crystals were measured through photoluminescence excitation, emission spectra and decay curves. Luminescence between 960 and 1050 nm from Yb³ : ²F_5/2→²F_7/2 transition, which was originated from the DC from Tm³ ions to Yb³ ions, was observed under the excitation of blue photon at 465 nm. Moreover, the energy transfer processes were studied based on the Inokuti-Hirayama model, and the results indicated that the energy transfer from Tm³ to Yb³ was an electric dipole-dipole interaction. The max-imum quantum cutting effciency approached up to 167.5% in LiYF₄ single crystal codoped with 0.49mol% Tm³ and 5.99mol% Yb³ . Application of this crystal has prospects for increasing the energy e ciency of crystalline Si solar cells by photon doubling of the high energy part of the solar spectrum