Solutions of logarithmic type for elliptic and hypoelliptic equations

LetK be an algebraically closed field withp:=char (K)>0 andX a bielliptic curve over Spec(K) with genus≥6 and such that the canonical model ofX is ordinary. In this paper we determine all the possible gap sequences of Weierstrass points on such curves.     

Λ-Shaped Policies to Schedule Deteriorating Jobs

We study a problem of scheduling deteriorating jobs, i.e. jobs whose processing times are an increasing function of their starting times. We consider the case of a single machine and linear job-independent deterioration. The objective is to minimize the sum of weighted completion times, with weights proportional to the basic processing times. The optimal schedule is shown to be Λ-shaped, i.e. the sequence of the basic processing times has a single local maximum. Moreover, we show that the problem is solved in O(N log N) time. In the last section we test heuristics for the case of general weights.     

Synthesis of Six-Membered Compounds by Environmentally Friendly Cyclization Using Indirect Electrolysis

[Ni(cyclam)](ClO(4))(2)-catalyzed indirect electroreduction of olefinic bromides produced six-membered compounds in low to high yields. The synthetic intermediate 49 of Ipecac and Corynanthe alkaloids was obtained in 88% yield in a highly stereoselective manner. Lactam 66, the synthetic precursor of tacamonine, was prepared in 49% yield as a mixture of two diastereoisomers. The electrolysis of the bromoacetates gave the debrominated compounds in good yields.     

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.     

Identification of Shiga toxins in Shiga toxin-producing Escherichia coli using immunoprecipitation and high-performance liquid chromatography-electrospray ionization mass spectrometry

We developed a rapid and reliable identification method for Shiga toxins in Shiga toxin-producing Escherichia coli (STEC) using immunoprecipitation and high-performance liquid chromatography-electrospray ionization mass spectrometry (HPLC-ESI-MS). Polyclonal antisera specific for Shiga toxin 1 (Stx1) and Shiga toxin 2 (Stx2) were raised in rabbits so as to be used for the immunoprecipitation. The immunoprecipitaion was carried out by mixing sample solutions with 50 microl each of the antisera to Stx1 and Stx2 followed by allowing the mixed solutions to stand for 30 min. The quantity required to obtain the immunoprecipitate was more than 0.5 microg of Shiga toxins. HPLC-ESI-MS analysis of the resulting immunoprecipitates provided accurate molecular weight information on Shiga toxins, leading to direct evidence for the presence of these toxins. It requires at most two days to perform our procedure from toxin extraction to measurement of HPLC-ESI-MS whereas the previous method using isolation procedures required about two weeks to complete. The usefulness of the present method has been demonstrated by identifying Stx1, Stx2 and a variant of Stx2 (Stx2e) in the immunoprecipitates prepared from STEC strains.     

Development of versatile cis- and trans-dicarbon-substituted chiral cyclopropane units: synthesis of (1S,2R)- and (1R,2R)-2-aminomethyl-1-(1H-imidazol-4-yl)cyclopropanes and their enantiomers as conformationally restricted analogues of histamine

The cyclopropane ring can be used effectively in restricting the conformation of biologically active compounds to improve activity and also to investigate bioactive conformations. We designed (1S,2R)- and (1R,2R)-2-aminomethyl-1-(1H-imidazol-4-yl)cyclopropanes (1 and 2, respectively) and their enantiomers (ent-1 and ent-2) as conformationally restricted analogues of histamine. The four types of chiral cyclopropanes bearing two differentially functionalized carbon substituents in a cis or trans relationship on a cyclopropane ring, (1S,2R)-2-(tert-butyldiphenylsilyloxy)methyl-1-formylcyclopropane (7) and (1R,2R)-2-(tert-butyldiphenylsilyloxy)methyl-1-formylcyclopropane (8) and their enantiomers (ent-7 and ent-8), were developed as the key intermediates for synthesizing 1, 2, ent-1, and ent-2. The reaction between (R)-epichlorohydrin [(R)-12] and phenylsulfonylacetonitrile (13a) in the presence of NaOEt in EtOH followed by treatment with acid gave the chiral cyclopropane lactone 11a with 98% ee in 82% yield. Compound 11a was converted into both the cis- and trans-chiral cyclopropane units 7 and 8, respectively, via reductive desulfonylation with Mg/MeOH as the key step. The corresponding enantiomers, the cis-substituted ent-7 and the trans-substituted ent-8, were also prepared starting from (S)-epichlorohydrin [(S)-12]. The four conformationally restricted target histamine analogues 1, 2, ent-1, and ent-2 were successfully synthesized from 7, 8, ent-7, and ent-8, respectively. The chiral cyclopropane units 7, 8, ent-7, and ent-8 should be useful as versatile intermediates for synthesizing various compounds having an asymmetric cyclopropane structure.