Competitive [2,3]- and [1,2]-oxonium ylide rearrangements. Concerted or stepwise?

The axial-equatorial conformational isomer distribution of the reactant diazoacetoacetate or its metal carbene intermediate is reflected in Rh(II) catalyzed oxonium ylide forming reactions of 3-(trans-2-arylvinyl)tetrahydropyranone-5-diazoacetoacetates that afford diastereoisomeric products for both the symmetry-allowed [2,3]- and the formally symmetry-forbidden [1,2]-oxonium ylide rearrangements.     

Simultaneous liquid-liquid extraction of dibenzyl disulfide, 2,6-di-tert-butyl-p-cresol, and 1,2,3-benzotriazole from power transformer oil prior to GC and HPLC determination

2,6-Di-tert-butyl-p-cresol (DBPC), dibenzyl disulfide (DBDS), and 1,2,3-benzotriazole (BTA) are additives that may be found concomitantly in the oil matrix of power transformer. DBPC and DBDS act as antioxidants while, BTA is a corrosion inhibitor that protects copper conductors inside the transformer unit from corrosion. A powerful analytical method is, therefore, required to determine these additives at trace levels in the transformer oil. This work describes a unique single liquid-liquid extraction pretreatment step prior to the determination of the components by gas chromatography (GC) and high-performance liquid chromatography (HPLC) techniques. The optimum volume ratio used in the pretreatment step was determined as 5:2:5 for mineral oil/n-hexane/acetonitrile, respectively. Relatively, the method is simple and quick with a minimal use of solvents. Analytical results indicate that the method is relatively sensitive, accurate, and precise for each of the three components in fresh and used mineral oil. The calibration curves for the three components demonstrate a significant increase in sensitivities. Detection limits found were, 100 mg L(-1) (0.01% w/v), 0.80 mg L(-1) , and 2.04 mg L(-1) for DBPC, DBDS, and BTA, respectively. The Student's t values determined at 95% confidence level indicate that there is no significant difference between the experimental means obtained by this method and the standard method for each component.     

Two-product inventory management with fixed costs and supply uncertainty

This paper determines the optimal ordering policy for a two-product, periodic-review inventory problem in which the probability of supply availability is unknown. Moreover, there are two different fixed costs assigned to each product. Demand rates are random variables with known probability density functions, and the supply availability for each product is updated at the beginning of each time period. We prove the optimality of (s,S) policy with a monotone switching curve that indicates the priority of production, where the order-up-to levels and the reorder points are functions of supply availability information. A simple computation is proposed to calculate the two threshold levels. Bayesian updating helps to manage the optimal ordering policy by updating supply disruption information. Numerical results show that improving the accuracy of the forecast leads to making a better ordering decision and eliminating the negative effect of supply disruption on the total cost.     

Largeur et nilpotence

The notion of a large set in an arbitrary group is introduced in analogy to the generic sets in an algebraic or stable group. The question is studied which properties “satisfied largely” by a group hold on the entire group.

ZUSAMMENFASSUNG. Wir definieren den Begriff einer groβen Teilmenge einer be-liebigen Gruppe in Analogie zu den generischen Mengen einer algebraischen oder stabilen Gruppe und untersuchen, welche “grofiteils erfullten” Gruppeneigenschaften fur die ganze Gruppe gelten müssen.     

Crystal structure of a silver(I) complex with the 1,2,4,5-benzenetetracarboxylic acid (pyromellitic acid)

The reaction between freshly precipitated silver oxide Ag₂O and an aqueous solution of tetrabenzenecarboxylic acid H₄L leads to the anhydrous Ag₂H₂L complex. It crystallizes in the space groupP2₁/c, witha=6.457(1),b=8.180(1),c=9.982(1) Å, β=97.83(1)°,V=522.3(1) ?³,Z=2,d=2.976 g cm⁻³. This structure is a three dimensional polymeric network polymer without any silver...silver interaction. The silver environment is a bipyramid trigonal polyhedron with three short bond distances in the equatorial plane (Ag−O=2.255(2), 2.295(2), and 2.499(2) Å) and two longer bond distances in axial positions (Ag−O=2.558(2) and 2.617(2) Å). Thus, the silver polyhedron involves five different ligands. It is noteworthy that the (H₂L₂)²⁻ ligand is located around an inversion centre.     

Stereoselectivity and regioselectivity in the segment-coupling Prins cyclization

The scope of the segment-coupling Prins cyclization has been investigated. The method is outlined in Scheme 1 and involves esterification of a homoallylic alcohol (1), reductive acetylation to give the alpha-acetoxy ether (3), and cyclization on treatment with a Lewis acid to produce a tetrahydropyran (4). Alkene geometries dictate the product configurations, with E-alkenes leading to equatorial substituents and Z-alkenes leading to axial substituents (Table 1). Not unexpectedly, applying the method to allylic alcohols leads to fragmentation rather than a disfavored 5-endo-trig cyclization. Dienols in which one alkene is allylic and the other alkene is homoallylic cyclize efficiently and produce the tetrahydropyrans 49-54, Table 3. Dienols with two homoallylic alkenes cyclize with modest to high regioselectively, generating tetrahydropyrans 40-45, Table 2. The relative rates for cyclization decrease in the order of vinyl > Z-alkene > E-alkene > alkyne. The configurations of the products are consistent with cyclization via a chair conformation, Figure 1. The 2-oxonia Cope rearrangement may be a factor in the regioselectivity of diene cyclizations and in the erosion of stereoselectivity with Z-alkenes. This investigation establishes the stereoselectivity and regioselectivity for a number of synthetically useful segment-coupling Prins cyclizations.