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.      

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 .     

Hydroxide ion initiated reactions under phase transfer catalysis conditions II. The roles of water and quat

The effects of water molecules and quat structure are shown to be significant in determining the behavior of alkylation reactions of weakly acidic carbon acids under PTC/OH^? conditions.     

SEARCH THEORY IN NATURAL RESOURCE MODELING

The role of search theory in the exploitation of natural resources is discussed in this paper. After a brief history and taxonomy of search problems, the mathematics of search is discussed. This includes underlying probability distributions, the differential equations of search, Bayesian use of search information and optimization problems in search theory. The theory is illustrated by applications in fisheries, pest control, animal foraging, and oil and mineral exploration.     

Amidinoethylation—a new reaction—IV : The amidinoethylation of alcohols: a facile synthesis of 3-alkoxy-N,N'-substituted-propanamidines

The amidinoethylation of alcohols takes place by the addition of sodium alkoxides 2 (R¹ = Me, Et) to the CC double bond of a variety of N,N'-substituted-propenamidines 1 (Method A). This illustrates the activation of the CC double bond by the conjugated amidine function and provides a new class of Michael acceptors for alcohols. However, this activation is poorer than with other nucleophiles or Michael acceptors. The amidinoethylation makes available 3-alkoxy-N,N'-substituted-amidines not easily accessible by other classical methods. However, it is demonstrated that the general N,N'-substituted-amidine synthesis via the nitrilium salts can also apply to nitrile compounds having an alkoxygroup present on the molecule (method B). Since the cyanoethylation of alcohols (4) is a very fast and facile reaction the method B is the preferred strategy for the synthesis of 3-alkoxy-N,N'-substituted-propanamidines 3.     

Modification de la position 8 des purines nucleosides et de l'adenosine monophosphate cyclique-3′,5′. Reactions de couplage catalytique des organo-magnesiens avec les bromo-8 purines ribosides et bromo-8 adenosine monophosphate cyclique-3′,5′ silyles en presence de dichloro-bis-triphenylphosphine palladium

The palladium catalysed condensation of Grignard reagents with silyl derivatives of 8-bromopurine nucleosides and 8-bromoadenosine-3′,5′ cyclic monophosphate is a convenient method for the preparation of free 8-alkylpurine nucleosides and 8-alkyladenosine-3′,5′ cyclic monophosphate.     

Oligomérisation anionique de l'ethylène. I. Etude cinétique

A kinetic study of ethylene oligomerization in hexane, in the presence of n-BuLi–TMEDA complexes, allowed us to suggest a new mechanism for anionic ethylene oligomerization. n-BuLi and n-Bu(CH₂CH₂)Li species have the same reactivity. The RLi–TMEDA complex in a 1-to-1 stoichiometry is the active species. The following kinetic equation has been established: It reflects the intervention of associated species (n-BuLi–TMEDA)₂ as well as the influence of the concentration of the complexing agent on the kinetics of oligomerization.     

Efficient and practical Ag-catalyzed cycloadditions between arylimines and the Danishefsky diene

An efficient Ag-catalyzed method for asymmetric addition of the Danishefsky diene to various aryl imines to afford cycloadducts in > or =89% ee and > or =85% isolated yield is reported. Reactions are effected with 0.1-1 mol % catalyst (4 degrees C), and the chiral ligand is readily prepared from commercially available materials, including the inexpensive i-Leu. These catalytic asymmetric cycloadditions can be carried out without the use of solvent or with undistilled THF in air. A first generation supported chiral catalyst that effectively promotes the cycloaddition reaction and can be recycled (five cycles) is described.