Allocation of jobs and identical resources with two pooling centers

We examine the resource allocation problem of partitioning identical servers into two parallel pooling centers, and simultaneously assigning job types to pooling centers. Each job type has a distinct Poisson arrival rate and a distinct holding cost per unit time. Each pooling center becomes a queueing system with an exponential service time distribution. The goal is to minimize the total holding cost. The problem is shown to be polynomial if a job type can be divided between the pooling centers, and NP-hard if dividing job types is not possible. When there are two servers and jobs cannot be divided, we demonstrate that the two pooling center configuration is rarely optimal. A heuristic which checks the single pooling center has an upper bound on the relative error of 4/3. The heuristic is extended for the multiple server problem, where relative error is bounded above by the number of servers.      

Random walks generated by affine mappings

This article is concerned with Markov chains on ^m constructed by randomly choosing an affine map at each stage, and then making the transition from the current point to its image under this map. The distribution of the random affine map can depend on the current point (i.e., state of the chain). Sufficient conditions are given under which this chain is ergodic.     

BRST cohomology in classical mechanics

The classical (non-quantum) cohomology of the Becchi-Rouet-Stora-Tyutin (BRST) symmetry in phase space is defined and worked out. No group action for the gauge transformations is assumed. The results cover, therefore, the general case of an open algebra and are valid off-shell. Each cohomology class contains all BRST invariant functions with fixed ghost number (an integer) which differ from each other by a BRST variation. If the ghost number is negative there is only the trivial class whose elements are equivalent to zero. If the ghost number is positive or zero there is a bijective correspondence between the BRST classes and those of the exterior derivative along the gauge orbits. These gauge orbits lie in the phase space surface on which the gauge generators are constrained to vanish. The BRST invariant functions of ghost numberp are then related to closedp-forms along the orbits. The addition of a BRST variation corresponds to the addition of an exact form. Some comments about the quantum case are included. The physical meaning of the classes with ghost number greater than zero is not discussed.Chercheur qualifié du Fonds National de la Recherche Scientifique (Belgium)     

Finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple Lie algebra

Let be a complex simple Lie algebra. We show that whent is not a root of 1 all finite dimensional representations of the quantum analogU _t are completely reducible, and we classify the irreducible ones in terms of highest weights. In particular, they can be seen as deformations of the representations of the (classical)U .     

Influence of the Presence of CO2 in the Feed of an Indirect Heating TSA Process for VOC Removal

This work deals with an experimental study of an indirect temperature swing adsorption process for VOC removal from air or for gas purification. A 1 m long and 70 mm diameter column with an internal heat exchanger has been filled with Ambersorb 600 carbonaceous adsorbent. This column is equipped with sensors to measure temperature at several points inside the bed, as well as the inlet and outlet gas concentration, pressure, temperature and mass flow. In a first step, CO₂ or ethane/dry nitrogen mixtures were used to simulate a single VOC in air, with different concentrations (350 ppm, 1% and 10%). As a first results very effective gas purification was obtained and an advantage of this process is the high pollutant concentration during the regeneration phase. Experiments were performed with various ethane/CO₂ mixtures. The influence of the presence of CO₂ on the ethane concentration breakthrough curves and on the ethane concentration during regeneration is reported. The IAS theory was used, as a first approach, to predict the adsorbed pollutants amount. Relatively good prediction is obtained with a maximum error in the order of 10%. An energy balance study is reported as well.     

The stereospecific epoxidation of olefins catalysed by ruthenium

Epoxidation of olefins by sodium periodate is effected by the catalysis of RuCl₃, (H₂O)_n associated with bipyridyl. The reaction is stereospecific for both cis and trans alkenes.     

Comparison of different fibers for the solid-phase microextraction of phthalate esters from water

Solid-phase microextraction (SPME) coupled to gas chromatography-mass spectrometry (GC-MS) has been applied to determine six phthalate esters and one adipate ester in water. The SPME parameters were optimized for several commercially available fibers. A 65-microm polydimethylsiloxane-divinylbenzene (PDMS-DVB) was the fiber selected and was applied to analysis of water from the Ebro river and the industrial port of Tarragona. The studied compounds were found at concentrations ranging from 0.4 microg l(-1) for di-n-butyl phthalate ester (DnBP) to 3.2 microg l(-1) for bis(2-ethylhexyl) phthalate ester (DEHP). The linear range for real samples was from 0.1 to 10 microg l(-1) for most phthalates, and the limits of detection of the method were between 3 and 30 ng l(-1). Repeatability and reproducibility between days (n = 5) for 1 microg l(-1) samples were below 13 and 18%, respectively.     

A method for the determination of histamine in wine by HPLC with precolumn derivatization with phenylisothiocyanate

Summary A method for determining histamine in wine by precolumn derivatization with PITC (phenylisothiocyanate) with reversed-phase HPLC and UV detection is reported. Histamine can be determined together with the 24 amino acids within 40 min, or separately in a shorter time (less than 4 min) if a prior solid phase extraction clean-up is used.