Necessary Conditions for Differentiability of Distance Functions

Necessary conditions for the Gâteaux differentiability of the distance function to a set are considered. A series of characterizing results is obtained.     

AGE method simulations of a turbulent far‐wake compared to spectral DNS

Turbulent flow simulation methods based on finite differences are attractive for their simplicity, flexibility and efficiency, but not always for accuracy or stability. This paper demonstrates that a good compromise is possible with the advected grid explicit (AGE) method. Starting from the same initial field as a previous spectral DNS, AGE method simulations of a planar turbulent wake were carried out as DNS, and then at three levels of reduced resolution. The latter cases were in a sense large‐eddy simulations (LES), although no specific sub‐grid‐scale model was used. Results for the two DNS methods, including variances and power spectra, were very similar, but the AGE simulation required much less computational effort. Small‐scale information was lost in the reduced resolution runs, but large‐scale mean and instantaneous properties were reproduced quite well, with further large reductions in computational effort. Quality of results becomes more sensitive to the value chosen for one of the AGE method parameters as resolution is reduced, from which it is inferred that the numerical stability procedure controlled by the parameter is acting in part as a sub‐grid‐scale model. Copyright © 2002 John Wiley & Sons, Ltd.     

Coxeter Transformation and Quasiquivers

Mathematical Notes -     

一类机器人系统的最优控制

本文通过把结构阻尼系数当作控制变量来讨论一类弹性机器人系统的最优控制问题 ,并利用Banach空间几何性质证明了最优控制元的存在唯一性     

理想气体在热力学中的作用

指出热力学理论是普遍的,不依赖于理想气体.理想气体为热力学理论提供了一个简单的实例,为测量热力学温度提供了一种简单的温度计.     

Remote stereocontrol by the sulfinyl group: Mukaiyama aldol reactions of (S)-2-[2-(p-tolylsulfinyl)phenyl]acetaldehyde in the asymmetric synthesis of β-hydroxyacids and 1,3-diols

(S)-2-[2-(p-Tolylsulfinyl)phenyl]acetaldehyde reacts with different O-silylated ketenethioacetals in the presence of Yb(OTf)₃ yielding β-hydroxythioesters in high yields and diastereoselectivities. The obtained compounds were readily transformed into β-hydroxyacids and their corresponding diols. These Mukaiyama aldol reactions are a direct evidence of the ability of the sulfinyl group to control 1,5- and 1,6-asymmetric induction processes.     

Maximizing a Linear Fractional Function on a Pareto Efficient Frontier

We consider the problem of maximizing a linear fractional function on the Pareto efficient frontier of two other linear fractional functions. We present a finite pivoting-type algorithm that solves the maximization problem while computing simultaneously the efficient frontier. Application to multistage efficiency analysis is discussed. An example demonstrating the computational procedure is included.     

Investigations of Solid State Dynamics at the NRSSR Beamline at PETRA II. An Overview

The present status of the new nuclear resonance beamline PETRA 1 at HASYLAB, DESY, Hamburg is described. Besides an overview of the experimental setup some examples of recent experiments are given. Those cover the main applications, i.e., inelastic scattering from iron alloys and quasielastic scattering from glass-forming liquids. This revised version was published online in August 2006 with corrections to the Cover Date.     

A solution of the DGLAP equation for gluon at low x

We obtain a solution of the DGLAP equation for the gluon at low x first by expanding the gluon in a Taylor series and then using the method of characteristics. We test its validity by comparing it with that of Glück, Reya and Vogt. The convergence criteria of the approximation used are also discussed. We also calculate εF ₂(x,Q)²/ε In Q ² using its approximate relations with the gluon distribution at low x. The predictions are then compared with the HERA data.     

超临界流体触媒作用下石墨-金刚石转变

 研究了超临界流体CO₂在石墨-金刚石转变中的触媒作用。实验中，采用Ag₂O作为流体触媒的先驱材料，在7.7 GPa压力下，Ag₂O在1 200 ℃分解成Ag和O₂，O₂与石墨套管在高温高压下反应形成CO₂超临界流体。研究结果表明，在7.7 GPa和1 500 ℃以上温度条件下，石墨在CO₂流体触媒的作用下可转变为金刚石晶体，在1 500～1 700 ℃温度范围内合成出的金刚石具有完好的八面体形貌，与天然金刚石的生长特征非常相似。