Separation of Nitrogen Isotopes by Thermal Diffusion

The prototype of a thermal diffusion column for the use as basic unit in a N¹⁴N¹⁵ cascade is described. The hot wire separation column consists of a brass tube of effective length of 250 cm and inner diameter of 10 mm. Four columns are connected in series on a square cascade, the separation factors of which are compared with the values obtained by other investigators.     

Separation of Variables in the Kovalevskaya–Goryachev–Chaplygin Gyrostat

We construct separation variables for the Kovalevskaya–Goryachev–Chaplygin gyrostat for arbitrary values of the parameters. We show that different separation variables can be constructed for the same integrable system if different integrals of motion are chosen.     

Primal separation algorithms

Given an integer polyhedron , an integer point , and a point , the primal separation problem is the problem of finding a linear inequality which is valid for P _I , violated by x ^*, and satisfied at equality by . The primal separation problem plays a key role in the primal approach to integer programming. In this paper we examine the complexity of primal separation for several well-known classes of inequalities for various important combinatorial optimization problems, including the knapsack, stable set and travelling salesman problems.Received: November 2002, Revised: March 2003,     

Economic Equilibrium: Optimality and Price Decentralization

Mathematical economics has a long history and covers many interdisciplinary areas between mathematics and economics. At its center lies the theory of market equilibrium. The purpose of this expository article is to introduce mathematicians to price decentralization in general equilibrium theory. In particular, it concentrates on the role of positivity in the theory of convex economic analysis and the role of normal cones in the theory of non-convex economies.     

Symbolical Algebra as a Foundation for Calculus: D. F. Gregory's Contribution

Duncan Farquharson Gregory (1813–1844) was a mathematician and founder of the Cambridge Mathematical Journal. His 1841 Examples of the Processes of the Differential and Integral Calculus was an extensive revision of Peacock's 1820 textbook of a similar title. Among the new material in Gregory's version is an exposition of symbolical algebra, prominently featuring the method of “separation of symbols.” We examine Gregory's career; the mathematicians he influenced; and Servois and Murphy, who influenced him. We consider Gregory's use of separation of symbols in the Examples and consider whether he believed these techniques to be capable of providing an adequate foundation for calculus. © 2002 Elsevier Science (USA).Le mathématicien Duncan Farquharson Gregory (1813–1844) fut également fondateur du Cambridge Mathematical Journal. Son ouvrage publié en 1841, Examples of the Processes of the Differential and Integral Calculus, constitue une révision substantielle du livre de Peacock au titre similaire. L'un des apports du livre de Gregory est un exposé de l'algèbre symbolique, et en particulier de la méthode de séparation des symboles. Dans cet article nous passons en revue la carrière de Gregory et nous parlons des mathématiciens qu'il a influencés, ainsi que de l'influence que Servois et Murphy ont eu sur ses travaux. Nous considérons son usage de la séparation des symboles dans ses Examples, et nous examinons si Gregory croyait que ses techniques pouvaient constituer un fondement pour le calcul différentiel. © 2002 Elsevier Science (USA).MSC 1991 subject classifications: 01A55, 01A70, 01A50, 26-03, 26A03, 34-03, 34A30.     

阻尼最小二乘法用于激光诱导击穿光谱重叠特征谱线分离提取

近年来,激光诱导击穿广谱技术发展迅速。作为一种用于物质成分探测的新技术,它具有简单、快速、无需复杂样品制备、多种元素同时检测等优点,可实现待测样品物质成分现场、在线的检测,在很多领域都极具应用前景。激光诱导击穿光谱特征谱线的分离拟合提取是光谱特征识别与后续元素浓度定量反演研究的基础。为实现激光诱导击穿光谱重叠特征谱线的有效分离拟合提取,采用阻尼最小二乘法,分析并确定了迭代前的初始拟合参数值,实现了在重叠特征谱线情况下对某火力发电厂粉煤灰中的铬元素特征谱线的分离提取。阻尼最小二乘法基于高斯-牛顿迭代,在迭代步长中引入阻尼因子,在迭代的过程中根据每一步迭代后所反馈的信息动态的调整迭代步长,从而有效防止了迭代的发散,保证了迭代的快速收敛,最终使得元素特征谱线拟合提取的效果更佳、所得到的特征谱线强度值更准确。分别采用阻尼最小二乘法和最小二乘法对不同浓度的样品中铬元素特征谱线进行分离拟合提取并给出特征谱线的强度值,作出特征谱线强度值关于元素浓度的定标曲线并对比两种方法所得结果的线性相关性。结果表明,阻尼最小二乘法所得结果的线性相关性更高,该方法稳定、可靠,适用于激光诱导击穿光谱重叠特征谱线的分离拟合提取。     

K_(0.8)Fe_2Se_2晶体c轴向载流子输运特性的研究

成功制备了超导临界温度为27 K的K0.8Fe2Se2晶体,并详细研究了晶体c轴向的载流子输运特性.结合X射线衍射、光学显微镜下的形貌、变温电阻率的测试结果表明,样品存在有"相分离",但是这类层状铁基超导体材料的两个相不是简单沿c轴向层状交替排布的,而应该是沿着c轴向存在弱联系的金属相链接通路,金属相部分形成近3维的空间网状链接模式.热导率测试和复阻抗谱z(ω,T0)的研究表明超导晶体沿着c轴方向存在有大量的相界面,所束缚的极化电荷致使相对介电常数达到106数量级,相应地在10 MHz附近出现负的相位特征.     

基于光谱诊断的热源间距对激光-脉冲GMAW复合焊等离子体物理特性影响研究

激光电弧复合焊中,热源间距会影响到等离子体物理特性,进而影响到焊接过程的稳定性及焊接质量。 基于Boltzmann作图法和Stark展宽法研究了不同热源间距下的激光-脉冲GMAW复合焊峰值阶段的温度场和电子密度分布,并结合高速摄影手段分析了热源间距对温度和电子密度的影响规律。 光谱诊断结果表明,随着热源间距的增大,激光等离子体的温度和电子密度都没有明显的变化;电弧温度出现下降,电弧电子密度则呈现先增高后降低的趋势。     

二维抛物型方程简单实用的显格式

提出了一个解二维抛的型方程初边值问题的简单实用的显格式，证明了其截断误差阶是Ｏ，稳定性条件是α＋β≠１／２且ｍａｘ｛α，β｝≤１／４，其中，α＝α．Δｔ／Δｘ＾２．β＝α．Δｔ／Δｙ＾２。