The flow shop problem with time lags and separated setup times

This paper generalizes Khurana-Bagga's flow-shop model which involves separated setup times and time lags where no restrictions are imposed on the processing and setup times as well as start and stop lags. It solves the two machine case and provides and approximate solution for the multimachine case. It also shows that Khurana-Bagga's algorithm is restricted to a special case of the two machine problem.     

General relativity as a generalized Hamiltonian system

A rigorous setting for Dirac's generalized Hamiltonian dynamics in an infinite number of dimensions is presented. It is shown that the dynamical formulation of general relativity fits into this scheme.Work partially supported by GNFM-CNR.     

Accurate and sensitive analysis of triplet repeat expansions by capillary electrophoresis

The reliable genetic diagnostics of triplet repeat expansions by capillary electrophoresis (CE) remains technically challenging due to the properties of the repeated GC-rich sequences. The biased base composition of the analyzed sample as compared to the commonly used DNA size standards makes the precise repeat length determination questionable. The homologous allelic ladders improve the accuracy of the repeat length analysis significantly. Their use, however, is not devoid of other complications. In the approach we propose, the allelic ladders are used only to properly calibrate the commercially available standards which serve then as internal standards in reliable and economical repeat length determination. In this study, we have also analyzed factors that could possibly increase the sensitivity of mutant allele detection by increasing the overall amplification efficiency and long-to-short product ratio.     

On the problem of field-gradient NMR measurements of intracrystalline diffusion in small crystallites--water in NaA zeolites as an example

Necessary conditions for measuring intracrystalline diffusion in small crystal size systems via field-gradient NMR are discussed. As an illustrative case self-diffusion coefficients of water adsorbed in NaA zeolites (average crystal diameter about 1 μm) have been measured by ¹H-NMR stimulated echoes in static magnetic field gradients of up to 180 T/m in the temperature range of 254–344 K. Obtaining intracrystalline diffusion coefficients necessitates a sufficiently high spatial resolution only provided by such large field gradients.     

Conditional moments of <Emphasis Type="Italic">q</Emphasis>-Meixner processes

We show that stochastic processes with linear conditional expectations and quadratic conditional variances are Markov, and their transition probabilities are related to a three-parameter family of orthogonal polynomials which generalize the Meixner polynomials. Special cases of these processes are known to arise from the non-commutative generalizations of the Lévy processes.Mathematics Subject Classification (2000): 60J25Research partially supported by NSF grant #INT-0332062, by the C.P. Taft Memorial Fund, and University of Cincinnatis Summer Faculty Research Fellowship ProgramAcknowledgementPart of the research of WB was conducted while visiting the Faculty of Mathematics and Information Science of Warsaw University of Technology. The authors thank M. Boejko for bringing to their attention several references, to Hiroaki Yoshida for information pertinent to Theorem 4.3, and to M. Anshelevich, W. Matysiak, R. Speicher, P. Szabowski, and M. Yor for helpful comments and discussions. Referees comments lead to several improvements in the paper.     

Description of All Complex Geodesics in the Symmetrized Bidisc

Effective formulae are found for the complex geodesics in thesymmetrized bidisc. 2000 Mathematics Subject Classification32F45 (primary).     

A simple one-step electrosynthesis of poly(pyrrole-sulfated β-cyclodextrin) films

A functionalized stable film of poly(pyrrole-sulfated β-cyclodextrin) has been obtained electrochemically in LiClO₄ aqueous solution using a simple 1:1 mixture of pyrrole (Py) monomer and sulfated β-cyclodextrin (SβCD). Different cyclic voltammetric behavior is obtained for polypyrrole (PPy) and poly(Py-βSCD) during electrosynthesis. Scanning electron microscopy (SEM) and energy dispersive X-ray analysis (EDAX) measurements on the two films have confirmed the presence of CD in the films and show that CD preferentially dopes the polymer even in the presence of a large excess of perchlorate supporting electrolyte. The morphology of the new polymers shows a more organized system under SEM examination. Contrary to conventional PPy films, this new polymer offers a wide potential range for electroanalytical exploration from selective electrodes to preconcentration/sampling devices. Electronic Publication     

Effect of oxidant on the reaction of [RhCl(cyclooctadiene)(phosphine)] with 1-hexene

Summary A promoting role of an oxidant, present in commercial 1-hexene, in the substitution of phosphine in the complex [RhCl(COD)(phosphine)] (1) where the phosphine is PPh₃ or 1/2 BPS-2 [bis(diphenylphosphinoethyl)tetra-methyldisiloxane] and COD=cycloocta-1,5-diene, has been detected and explained. When [oxidant]>[(1)] two reaction steps are distinguished: an oxidation of phosphine to phosphine oxide with generation of [RhCl(COD)], followed by its fast dimerization, and an oxidation of the dimer to Rh^III species. When [oxidant]<[(1)] the latter step is not observed and the reaction of [RhCl(COD)] with 1-hexene is favoured, particularly when an excess of phosphine (even at high oxidant concentration) is present. Most rate constants of the individual steps were evaluated.