Cohomology of the complement of a free divisor

We prove that if is a ``strongly quasihomogeneous" free divisor in the Stein manifold , and is its complement, then the de Rham cohomology of can be computed as the cohomology of the complex of meromorphic differential forms on with logarithmic poles along , with exterior derivative. The class of strongly quasihomogeneous free divisors, introduced here, includes free hyperplane arrangements and the discriminants of stable mappings in Mather's nice dimensions (and in particular the discriminants of Coxeter groups).

     

Synthesis of Enantiopure Primary Amines by Stereoselective Ring Opening of Chiral Octahydro-1,3-benzoxazines by Grignard and Organoaluminum Reagents

Chiral 1,3-perhydrobenzoxazines 1, 2, and 9-14, prepared by condensation of 8-(benzylamino)menthol with different aldehydes, react with alkylmagnesium bromides and trimethylaluminum leading to the open amino alcohols 3a-d, 4a-d, and 15-20 in excellent chemical yields and good to excellent diastereomeric excess. The sequential elimination of the menthol appendage by heating with P(2)O(5) and the benzyl group by hydrogenolysis lead to primary amines 7a-d, 8a-d, and 27-30 in excellent chemical yields and ee. The addition of the alkyl group from the Grignard derivatives and the methyl group from the trimethylaluminum occurs from opposite sides of the heterocycle, yielding the final primary amines with the same stereochemistry.     

An Efficient and Simple Entry to N-Substituted beta-Enamino Acid Derivatives from 2-Alkyl-2-oxazolines and 2-Alkyl-2-thiazolines

Reaction of azaenolates of 2-alkyl-oxa(thia)zolines 6 with imidoyl chlorides 7 as electrophiles to furnish masked N-substituted beta-enamino acid derivatives 1-2 in 70-90% yield is described. Alternative routes are discussed. Compounds 1-2 generally appear in one tautomeric form, imino or enamino, depending on the nature of the imidoyl chloride. The configuration of the enamino moiety (Z) and the conformation (s-cis) of compounds 1-2 obtained were established by an NMR study and unequivocally set by nuclear Overhauser effect difference experiments. An X-ray structure of compound 1e is also reported, showing a strong intramolecular NH.N hydrogen bond. Ab initio calculations (HF/3-21G and HF/3-21+G) have been carried out on several representative examples (1e, 1p, and 1l) in an attempt to support and provide the correct geometry of these derivatives. Structural considerations among the possible isomers of compounds 1 are discussed. From these studies it was concluded that the theoretical calculations agree with the experimental results. In addition, a very simple one-pot procedure for the preparation of masked N-substituted alpha-alkylated beta-enamino acid derivatives 2 from 6, 7, and different alkyl halides (R(3)Y) is described.     

Analysis of Open Discrete Time Queueing Networks: A Refined Decomposition Approach

This paper deals with approximate analysis methods for open queueing networks. External and internal flows from and to the nodes are characterized by renewal processes with discrete time distributions of their interarrival times. Stationary distributions of the waiting time, the queue size and the interdeparture times are obtained using efficient discrete time algorithms for single server (GI/G/1) and multi-server (GI/D/c) nodes with deterministic service. The network analysis is extended to semi-Markovian representations of each flow among the nodes, which include parameters of the autocorrelation function.     

Project Management Duration/Resource Tradeoff Analysis: an Application of the Cut Search Approach

The paper presents an application oriented procedure for solving the project management duration/resource tradeoff problem. A procedure is presented for reducing a project from a normal to a crash duration state at a minimum amount of additional resource expenditure assuming a linear utilization functions. The procedure is network based using a graphical Cut Search Approach to locate the minimal resource level at each reduction in total project duration. Activity-on-arc networks and flow networks are utilized. The paper is presented for practical application and for conceptual development as compared to a theoretical treatment.     

Electroweak tests with τ leptons at LEP

We report on two sensitive tests of lepton universality carried out by the 4 LEP experiments at the Z⁰ pole. From measurements of the τ polarization in e⁺ e^?→τ ⁺ τ ^?, the ratios of the vector and axial vector coupling constants of the electron and the tau lepton to the weak neutral current are obtained to beg _{v e} /g _{a e} =0.066±0.015 andg _{V τ} /g _{A τ} =0.070±0.009 respectively. From measurement of the τ lifetime and the τ leptonic branching ratios, the ratio of the coupling constants describing weak leptonic decays of the τ and the μ is measured to beG _τ /G _μ =0.996±0.008.     

Standard<Emphasis Type="Italic">SU</Emphasis>(5) supergravity grand unification model and predictions

A review is given of the StandardSU(5) supergravity model. This model has passed an important check regarding unification of the electro-weak and the strong couplings using high precision LEP data. It is shown that for a significant domain of the parameter space the model also satisfies constraints on the SUSY spectrum from CDF and LEP, as well as proton stability and cosmological relic density constraints.