RANDOM EDGE can be exponential on abstract cubes

We prove that RANDOM EDGE, the simplex algorithm that always chooses a random improving edge to proceed on, can take a mildly exponential number of steps in the model of abstract objective functions (introduced by Williamson Hoke [Completely unimodal numberings of a simple polytope, Discrete Appl. Math. 20 (1988) 69-81.] and by Kalai [A simple way to tell a simple polytope from its graph, J. Combin. Theory Ser. A 49(2) (1988) 381-383.] under different names). We define an abstract objective function on the n-dimensional cube for which the algorithm, started at a random vertex, needs at least exp(const·n^1/3) steps with high probability. The best previous lower bound was quadratic. So in order for RANDOM EDGE to succeed in polynomial time, geometry must help.     

Optimal design of a convergent-barrel cold spray nozzle by numerical method

A convergent-barrel (CB) cold spray nozzle was designed through numerical simulation. It was found that the main factors influencing significantly particle velocity and temperature include the length and diameter of the barrel section, the nature of the accelerating gas and its pressure and temperature, and the particle size. Particles can achieve a relatively low velocity but a high temperature under the same gas pressure using a CB nozzle compared to a convergent-divergent (CD) nozzle. The experiment results with Cu powder using the designed CB nozzle confirmed that particle deposition can be realized under a lower gas pressure with a CB nozzle.     

Hilbert Space of Probability Density Functions Based on Aitchison Geometry

The set of probability functions is a convex subset of L1 and it does not have a linear space structure when using ordinary sum and multiplication by real constants. Moreover, difficulties arise when dealing with distances between densities. The crucial point is that usual distances are not invariant under relevant transformations of densities. To overcome these limitations, Aitchison＇s ideas on compositional data analysis are used, generalizing perturbation and power transformation, as well as the Aitchison inner product, to operations on probability density functions with support on a finite interval. With these operations at hand, it is shown that the set of bounded probability density functions on finite intervals is a pre-Hilbert space. A Hilbert space of densities, whose logarithm is square-integrable, is obtained as the natural completion of the pre-Hilbert space.     

SILEX-1装置上等离子体尾场加速电子初步实验

激光等离子体加速电子机制可以产生准单能的高能电子束, 近年来成为国际上的研究热点. 中国工程物理研究院激光装置已经能够达到286TW的输出功率, 为国内在该领域的研究提供了实验条件. 文章介绍了在SILEX-1装置上开展的激光等离子体加速电子的初步实验, 并对测得结果进行讨论, 为下一步实验的进行提供了准备条件.     

基于单纯形方法的双层线性规划全局优化算法

通过分析双层线性规划可行域的结构特征和全局最优解在约束域的极点上达到这一特性,对单纯形方法中进基变量的选取法则进行适当修改后,给出了一个求解双层线性规划局部最优解方法,然后引进上层目标函数对应的一种割平面约束来修正当前局部最优解,直到求得双层线性规划的全局最优解.提出的算法具有全局收敛性,并通过算例说明了算法的求解过程.     

Extension of a combined analytical/numerical initial value problem solver for unsteady periodic flow

Here we describe analytical and numerical modifications that extend the Differential Reduced Ejector/ mixer Analysis (DREA), a combined analytical/numerical, multiple species ejector/mixing code developed for preliminary design applications, to apply to periodic unsteady flow. An unsteady periodic flow modelling capability opens a range of pertinent simulation problems including pulse detonation engines (PDE), internal combustion engine ICE applications, mixing enhancement and more fundamental fluid dynamic unsteadiness, e.g. fan instability/vortex shedding problems. Although mapping between steady and periodic forms for a scalar equation is a classical problem in applied mathematics, we will show that extension to systems of equations and, moreover, problems with complex initial conditions are more challenging. Additionally, the inherent large gradient initial condition singularities that are characteristic of mixing flows and that have greatly influenced the DREA code formulation, place considerable limitations on the use of numerical solution methods. Fortunately, using the combined analytical–numerical form of the DREA formulation, a successful formulation is developed and described. Comparison of this method with experimental measurements for jet flows with excitation shows reasonable agreement with the simulation. Other flow fields are presented to demonstrate the capabilities of the model. As such, we demonstrate that unsteady periodic effects can be included within the simple, efficient, coarse grid DREA implementation that has been the original intent of the DREA development effort, namely, to provide a viable tool where more complex and expensive models are inappropriate. Copyright © 2002 John Wiley & Sons, Ltd.     

胶束薄层色谱法测定食品及药用胶囊中的合成食用色素

在聚酰胶片上以13%SDBS(十二烷基苯磺酸钠)+7%Triton X-100〔聚乙二醇-对-(1.1,3,3-四甲基)丁基苯基醚〕+(2+3)氨水(1+5+1)为展开剂,用胶束薄层色谱法分离和测定了柠檬黄、亮蓝、苋菜红、胭脂红和赤藓红。测定波长分别为440、632、535、525和528 nm,线性范围分别为0.1～2、0.05～1、0.05～1、0.05～1和0.05～1μg/斑点。方法用于测定软饮料糖果及药用胶囊中的合成色素,获得了满意的结果。此外,还对展开剂的最佳组成进行了单纯形法优化。     

用模糊综合评价值作为单纯形优化指标

本文介绍了一个模糊综合评价方法,讨论了模糊运算方法对运算结果即综合评价值的影响,并将模糊综合评价值用作单纯形优化指标。     

A competitive (dual) simplex method for the assignment problem

Where there is abundance of mystery and confusion in every direction, the truth seldom remains hidden for long. It's a matter of having plenty of angles to go at it from. Only the utterly simple crimes - the simplex crimes, you may say - have the trick of remaining baffling. - Sir John (from Michael Innes,The Open House (A Sir John Appleby Mystery), Penguin Books, 1974).A dual simplex method for the assignment problem leaves open to choice the activity (i,j) of rowi and columnj that is to be dropped in pivoting so long asx _ij < 0. A choice (i,j) over columnsj having at least 3 basic activities that minimizesx _ij is shown to converge in at most ( ₂ ^n-1 ) pivots, and at most O(n ³) time, and it is argued that on average the number of pivots is at mostn logn. Dedicated with affection to George B. Dantzig on the occasion of his seventieth birthday.     

On the average length of lexicographic paths

A bound is given for the average length of a lexicographic path, a definition that is motivated by degeneracies encountered when using the randomized simplex method.