Limiting behavior of the affine scaling continuous trajectories for linear programming problems

We consider the continuous trajectories of the vector field induced by the primal affine scaling algorithm as applied to linear programming problems in standard form. By characterizing these trajectories as solutions of certain parametrized logarithmic barrier families of problems, we show that these trajectories tend to an optimal solution which in general depends on the starting point. By considering the trajectories that arise from the Lagrangian multipliers of the above mentioned logarithmic barrier families of problems, we show that the trajectories of the dual estimates associated with the affine scaling trajectories converge to the so called centered optimal solution of the dual problem. We also present results related to asymptotic direction of the affine scaling trajectories. We briefly discuss how to apply our results to linear programs formulated in formats different from the standard form. Finally, we extend the results to the primal-dual affine scaling algorithm.     

苯丙醇对映体在酰胺型手性固定相上的分离

对于手性对映体苯丙醇在3种Pirkk型手性固定相（CSP）Whelk-O 1、DNB-Leu和DNB-Pg上直接分离进行了研究。考察了流动相极性以及温度对分离的影响，发现在常用的范围内无法获得分离，仅有Whelk-O1在流动相极性的极端条件下（正己烷／异丙醇=99．5／0．5，V/V）能够被直接分离。在较低温度0℃和流速1mL／min的优化条件下能获得基线分离。用旋光检测器与液相色谱串联的方式确定了手性拆分结果，并确定了（-）苯丙醇优先洗脱的顺序。针对这种流动相极性极端条件下的分离，结合有关理论，进一步探讨了分离机理。     

Capillary gas chromatographic properties of three new mono-ester permethylated β-cyclodextrin derivatives

2^I-O-Methoxycarbonylmethyl-2^II–VII,3^I–VII,6^I–VII-eicosa-O-methyl-cyclodextrin (20Me/P2OCH₂COOMe), 6^I-O-methoxycarbonylmethyl-2^I–VII,3^I–VII,6^II–VII-eicosa-O-methyl-cyclodextrin (20Me/P6OCH₂COOMe), 6^I-O-methoxycarbonyl-6^I-deoxy-2^I–VII,3^I–VII,6^II–VII-eicosa-O-methyl-cyclodextrin (20Me/P6COOMe) have been evaluated as chiral stationary phases (CSPs) for capillary gas chromatography. General chromatographic properties of the corresponding columns have been investigated in terms of efficiency, polarity and inertness. More than 60 solutes have been used for studying their enantioselectivity by comparison with permethylated β-cyclodextrin as a reference. Similar enantioseparation ability was established for the four studied CSPs, the 20Me/P2OCH₂COOMe exhibiting in most cases a better enantioselectivity than the other selectors.     

Future independent times and Markov chains

Summary A random timeT is a future independent time for a Markov chain (X _n ) ₀ ifT is independent of (X _T+n ) _n ^/ =0 and if (X _T+n ) _n ^/ =0 is a Markov chain with initial distribution and the same transition probabilities as (X _n ) ₀ . This concept is used (with the conditional stationary measure) to give a new and short proof of the basic limit theorem of Markov chains, improving somewhat the result in the null-recurrent case.This work was supported by the Swedish Natural Science Research Council and done while the author was visiting the Department of Statistics, Stanford University     

Stationary Boltzmann equation for a degenerate gas in a slab: Boundary value problem and hydrodynamics

The boundary value problem for the stationary Boltzmann equation for a model gas in a plane slab is solved in full generality. The asymptotic behavior as the size of the slab goes to infinity is studied via a Chapman-Enskog expansion.     

A mean-field limit for a class of queueing networks

A model of centralized symmetric message-switched networks is considered, where the messages having a common address must be served in the central node in the order which corresponds to their epochs of arrival to the network. The limitN is discussed, whereN is the branching number of the network graph. This procedure is inspired by an analogy with statistical mechanics (the mean-field approximation). The corresponding limit theorems are established and the limiting probability distribution for the network response time is obtained. Properties of this distribution are discussed in terms of an associated boundary problem.     

Strong stationary duality for continuous-time Markov chains. Part I: Theory

LetX(t), 0t<, be an ergodic continuous-time Markov chain with finite or countably infinite state space. We construct astrong stationary dual chainX ^* whose first hitting times yield bounds on the convergence to stationarity forX. The development follows closely the discrete-time theory of Diaconis and Fill.^(2,3) However, for applicability it is important that we formulate our results in terms of infinitesimal rates, and this raises new issues.     

A new class of libraries

In this paper we give the stationary measure and a sufficient condition of positive recurrence for a new class of linear libraries. These libraries are built by juxtaposing McCabe's libraries and Tsetlins libraries in an appropriate way: Their policy is not classical, by the fact that instead of a circular permutation, ₁ can be the product of several disjoint circular permutations.     

Chromatographic Properties for Enantiomeric Separation of Amino Acid Derivatives on the Molecularly Imprinted Monoliths

Since their introduction in 1992 by Fréchet and Svec[1], monolithic supports as stationary phases in high performance liquid chromatography (HPLC) and capillary electrochromatography (CEC) have gained significant interest due to a number of unique properties. Their ease of preparation, high reproducibility, versatile surface chemistry and fast mass transport are advantageous in a variety of applications[2-4]. Separations in diverse chromatographic modes have been performed in either HPLC or CEC, showing their strong point for high-speed separations of biological and synthetic molecules[5-12]. Although a number of papers have been reported on the application of monolithic supports as chiral stationary phases in CEC and pressure-assisted capillary electrochromatography (p-CEC)[13-19], few reports have so far been published on chiral monolithic stationary phases for liquid chromatography[20].