On the convergence of the affine-scaling algorithm

The affine-scaling algorithm, first proposed by Dikin, is presently enjoying great popularity as a potentially effective means of solving linear programs. An outstanding question about this algorithm concerns its convergence in the presence of degeneracy. In this paper, we give new convergence results for this algorithm that do not require any non-degeneracy assumption on the problem. In particular, we show that if the stepsize choice of either Dikin or Barnes or Vanderbei, et al. is used, then the algorithm generates iterates that converge at least linearly with a convergence ratio of , wheren is the number of variables and (0,1] is a certain stepsize ratio. For one particular stepsize choice which is an extension of that of Barnes, we show that the cost of the limit point is within O(/(1–)) of the optimal cost and, for sufficiently small (roughly, proportional to how close the cost of the nonoptimal vertices are to the optimal cost), is exactly optimal. We prove the latter result by using an unusual proof technique, that of analyzing the ergodic convergence of the corresponding dual vectors. For the special case of network flow problems with integer data, we show that it suffices to take = 1/(6mC), wherem is the number of constraints andC is the sum of the cost coefficients, to attain exact optimality.This research is partially supported by the U.S. Army Research Office, contract DAAL03-86-K-0171 (Center for Intelligent Control Systems), by the National Science Foundation, grant NSF-ECS-8519058, and by the Science and Engineering Research Board of McMaster University.     

Rapid determination of underivatized pyroglutamic acid, glutamic acid, glutamine and other relevant amino acids in fermentation media by LC-MS-MS

Determination of amino acids in a complex matrix without derivatization is advantageous, however, difficulties are found in both the detection and the separation of those compounds. In this study, a rapid and reliable LC-MS-MS method for the quantitation of underivatized amino acids in exocellular media was established. Injections were made directly after centrifugation of the samples, without further preparation. The separation of seven underivatized amino acids was achieved on a reversed-phase C18 column with pentadecafluorooctanoic acid as a volatile ion-pair reagent, and the specific detection of most amino acids was achieved by MS-MS of the specific transitions [M + H]+-->[M + H - 46]+. The calibration curves of all analytes were linear over the range of 1.0-1000 microg ml(-1) and the detection limits ranged from 0.1 to 5 ng ml(-1), with an injection volume of 20 microl. The inter-day and intra-day precisions ranged from 2.6 to 5.7% and 4.8 to 8.2%, respectively; the mean recoveries of the seven analytes were 81-104%, 91-107% and 93-101% respectively at the spiked level of 10, 40 and 200 microg ml(-1). A large number of fermentation samples were analysed using this method. The technique is simple, rapid, selective and sensitive, and shows potential for the high-throughput quantitation of amino acids from other biological matrices.     

Synthesis,spectroscopy and crystal structure of a new heterodinuclear silver(I)—copper(I) cryptate

A new heterodinuclear cryptate [AgCuL](ClO₄ ^–)₂ was synthesized by transmetallation via its precursor [Ag₂L](ClO₄ ^–)₂ (L = ligand). The electrospray mass spectrum (ES-MS) showed that the heterodinuclear entity exists in the solution. The X-Ray structure analysis shows that the Ag^I ion has tetrahedral geometry while Cu^I lies in a three-coordinate environment.     

Studies on Hydroiodination and Deconjugation of 5—Aryloxy—（thiophenyl）—3—pentyn—2—one

One-pot hydroiodination and deconjugation of 5-aryloxy(or thiophenyl)-3-pentyn-2-one with a reagent system of sodium iodide/trimethylsilyl chloride/water in acetonitrile at 25℃ have been described.The plasuible mechanism was discussed.The reaction provided a simple and useful method for the preparation of (Z)-β-substituted β，γ-enones and (Z)-β-substituted α，β-unsaturated ketones.     

LapRLSR for NIR spectral modeling and its application to online monitoring of the column separation of Salvianolate

A novel near infrared (NIR) modeling method—Laplacian regularized least squares regression (LapRLSR) was presented, which can take the advantage of many unlabeled spectra to promote the prediction performance of the model even if there are only few calibration samples. Using LapRLSR modeling, NIR spectral analysis was applied to the online monitoring of the concentration of salvia acid B in the column separation of Salvianolate. The results demonstrated that LapRLSR outperformed partial least squares (PLS) significantly, and NIR online analysis was applicable.