Thermodynamic equilibrium of the solute distribution in size-exclusion chromatography

Our understanding of the nature of solute retention in size-exclusion chromatography (SEC) is predicated upon an equilibrium, entropy-controlled, size-exclusion mechanism. The entropic nature of the separation depends, in turn, upon the solute distribution coefficient (K(SEC) being at (or close to) thermodynamic equilibrium. Classic experiments to confirm this assumption were performed over thirty years ago. Here, we combine information obtained from both flow and static mixing SEC experiments to show that the solute distribution in SEC is in thermodynamic equilibrium over a molar mass range extending one order of magnitude higher than previously measured (from 2 x 10(3) to 1.1 x 10(6) Da) using crosslinked polystyrene packing material of identical pore size (10(4) A). The differences between our observations and previous ones conducted over three decades ago are ascribed, principally, to advances in stationary phase synthesis and column technology for SEC in particular and, secondarily, to improvements in the performance of the various instrumental components of liquid chromatographic systems in general.     

Thermodynamic Equilibrium in the System of Chaotic Quantized Vortices in a Weakly Imperfect Bose Gas

In the example of a weakly imperfect Bose gas, we discuss the mechanism of establishing thermodynamic equilibrium for a chaotic set of quantum vortex filaments. We assume that the dynamics of the Bose condensate is described by the Gross–Pitaevsky equation with an additional noise satisfying the fluctuation–dissipation theorem. In considering a vortex filament as the intersection line of surfaces on which the real and imaginary parts of the order parameter (x,t) vanish, we obtain an equation of the Langevin type for elements of the vortex filament with an appropriately transformed random force. The Fokker–Planck equation for the probability density has a solution given by the Gibbs distribution at the temperature of the Bose condensate. In other words, when the Bose condensate is in thermal equilibrium and no other random actions exist, the system of vortices is also in thermal equilibrium.     

战略性绩效管理系统设计中的决策问题

战略性绩效管理系统的设计中存在很多决策问题,本以一家制造业公司为例,介绍了应用Nash均衡建立绩效监察博弈模型。确定组织的绩效系统规模;通过AHP方法的创新应用,确定组织的关键业务领域,同时对组织关键业绩指标分类分层设计的思路做了简要阐述。     

An empirical fit to estimated neutron emission cross sections from proton induced reactions

Neutron emission cross section for various elements from⁹Be to²⁰⁹Bi have been calculated using the hybrid model code ALICE-91 for proton induced reactions in the energy range 25 MeV to 105 Me V. An empirical expression relating neutron emission cross section to target mass number and incident proton energy has been obtained. The simple expression reduces the computation time significantly. The trend in the variation of neutron emission cross sections with respect to the target mass number and incident proton energy has been discussed within the framework of the model used.     

Borel stay-in-a-set games

Consider an n-person stochastic game with Borel state space S, compact metric action sets A ₁,A ₂,,A _n , and law of motion q such that the integral under q of every bounded Borel measurable function depends measurably on the initial state x and continuously on the actions (a ₁,a ₂,,a _n ) of the players. If the payoff to each player i is 1 or 0 according to whether or not the stochastic process of states stays forever in a given Borel set G _i , then there is an -equilibrium for every >0. AMS (1991) subject classification: 60G40, 91A60, 60E15, 46A55.     

On existence of undominated pure strategy Nash equilibria in anonymous nonatomic games: a generalization

In this paper, we generalize the exitence result for pure strategy Nash equilibria in anonymous nonatomic games. By working directly on integrals of pure strategies, we also generalize, for the same class of games, the existence result for undominated pure strategy Nash equilibria even though, in general, the set of pure strategy Nash equilibria may fail to be weakly compact. Received August 2001     

Thermodynamics and Hydrodynamics (Statistical Foundations): 2. Thermodynamic Equilibrium

We show that the BBGKY hierarchy in thermodynamic equilibrium degenerates into an equilibrium hierarchy. In turn, the latter can be used to obtain both the fundamental system of equations describing the state of matter inside a correlation sphere of the radius R10^-7cm and the canonical Gibbs distribution, which, according to the current concepts, describes the state of the entire macroscopic system. We show that the Gibbs distribution is indeed also local, i.e., describes the state of matter only inside the correlation sphere; in the thermostat surrounding this sphere, the Gibbs distribution degenerates into a constant. We state that these two approaches are equivalent to each other.     

Vector Equilibrium Problems Under Asymptotic Analysis

Given a closed convex set K in Rⁿ; a vector function F:K×K R^m; a closed convex (not necessarily pointed) cone P(x) in ^m with non-empty interior, PP(x) Ø, various existence results to the problemfind xK such that F(x,y)- int P(x) y K under P(x)-convexity/lower semicontinuity of F(x,) and pseudomonotonicity on F, are established. Moreover, under a stronger pseudomonotonicity assumption on F (which reduces to the previous one in case m=1), some characterizations of the non-emptiness of the solution set are given. Also, several alternative necessary and/or sufficient conditions for the solution set to be non-empty and compact are presented. However, the solution set fails to be convex in general. A sufficient condition to the solution set to be a singleton is also stated. The classical case P(x)=^m ₊ is specially discussed by assuming semi-strict quasiconvexity. The results are then applied to vector variational inequalities and minimization problems. Our approach is based upon the computing of certain cones containing particular recession directions of K and F.     

期货合约的简单创新

本文通过观察代办收入最大化交换,提出期货合约创新的一个简单两阶段模型. 经济代理商具有均值-方差偏好,按代理买卖量的大小,在期货合约过程中收取交易费用.期货交易过程中存在价差.代办收入最大化交换促成期货合约的创新.     

离子通道中环形束流分布与场解的自洽理论

考虑环形束流的空间电荷效应与相对论状态下的自磁效应对离子通道——环形束流系统的影响，研究了通道中环形束流的轨道与场解的自洽平衡态.利用动力学理论得到了电子平衡态分布函数以及环形束流的径向位置和通道内电磁场的自洽解.研究发现，相对论束流的自场对系统平衡态有很大影响，并证实了系统自洽平衡态的存在.数值计算给出了束流位置与通道半径间随能量的分布关系以及通道内场随半径分布的规律，为相关器件的设计提供了重要的理论数据. 关键词： 离子通道 环形束流 动力学理论 自洽平衡态