Delta and singular delta locus for one‐dimensional systems of conservation laws

This work gives a condition for existence of singular and delta shock wave solutions to Riemann problem for 2×2 systems of conservation laws. For a fixed left‐hand side value of Riemann data, the condition obtained in the paper describes a set of possible right‐hand side values. The procedure is similar to the standard one of finding the Hugoniot locus. Fluxes of the considered systems are globally Lipschitz with respect to one of the dependent variables. The association in a Colombeau‐type algebra is used as a solution concept. Copyright © 2004 John Wiley &Sons, Ltd.     

A simple stereoselective one-pot synthesis of C-nucleosides by 1,3-dipolar cycloaddition of chiral azomethine imines prepared in situ

The NH,NH-dihydrocycloadduct 1 (6-chloro-9,9-dimethyl-7,8-dihydro-9H-pyrazolo[4,3-d]tetrazolo[1,5-b]-pyridazine) obtained by the cycloaddition of 2-diazopropane to 6-chlorotetrazolo[1,5-b]pyridazine, is transformed with protected or unprotected carbohydrates 2, 5, 7,9, 11, 13 and 15 in the presence of methyl acrylate ( 3 ) into the corresponding C-nucleosides 4,6,8,10,12,14 and 16 . In this one-pot synthesis two new chiral centers are formed stereoselectively, dependent on the chirality at C-atom next to aldehydo group in the carbohydrate.     

Microbial Baeyer-Villiger Oxidation of Ketones by Cyclohexanone and Cyclopentanone Monooxygenase – A Computational Rational for Biocatalyst Performance

Summary. Recombinant Escherichia coli overexpressing Pseudomonas sp. NCIMB 9872 cyclopentanone monooxygenase (CPMO, EC 1.14.13.16) and Acinetobacter sp. NCIMB 9871 cyclohexanone monooxygenase (CHMO, EC 1.14.13.22) have been utilized in whole-cell Baeyer-Villiger biotransformations of prochiral bicycloketones. A significant difference in substrate acceptance and stereoselectivity was observed for bicyclo[3.3.0] and bicyclo[4.3.0] substrates. A plausible mechanism of these transformations was established by means of high level DFT/B3LYP calculations suggesting an essential difference in electronic requirements for a successful enzymatic conversion, which was similarly encountered in recombinant whole-cell mediated biooxidations. Some of the lactones produced in the biocatalytic Baeyer-Villiger oxidation represent key intermediates for the synthesis of indole alkaloids.     

A one‐dimensional CdII coordination polymer: catena‐poly[cadmium(II)‐bis(μ‐6‐methylpicolinato)]

In the title compound, [Cd(C₇H₆NO₂)₂]_n, the Cd^II ion has a distorted octahedral geometry. The 6‐methylpyridine‐2‐carboxylate anions are perpendicular to one another and act as bidentate and bridging ligands. Two carboxylate O atoms bridge the Cd^II ions, forming centrosymmetric dinuclear units. These units are further connected via carboxylate O atoms into a one‐dimensional polymeric chain which extends in the [100] direction.     

On a characterization of the normal distribution by means of identically distributed linear forms

Let X₁, X₂,…, be independent, identically distributed random variables. Suppose that the linear forms L₁ = Σ_j=1^∞a_jX_j and L₂ = Σ_j=1^∞b_jX_j exist with probability one and are identically distributed; necessary and sufficient conditions assuring that X₁ is normally distributed are presented. The result is an extension of a theorem of Linnik (Ukrainian Math. J.5 (1953), 207–243, 247–290) concerning the case that the linear forms L₁ and L₂ have a finite number of nonvanishing components. This proof only makes use of elementary properties of characteristic functions and of meromorphic functions.     

Antioxidants and stabilizers: Part IC—Hydroperoxide deactivation by aliphatic sulfides. A model study

The hydroperoxide decomposing efficiencies of dioctadecylsulfide (I), dioctadecyldisulfide (IV) and dioctadecyl 3,3-thio-dipropionate (VII) have been compared at 75°C and 85°C. The formation of oxidation products from (I) and (IV) has been checked. Experimental evidence is given of the important rôle of the activation of the molecule of (IV) by the presence of two sulfidic sulfur atoms compared with the activation of the sulfur atom in (VII) by the alkoxycarbonyl group in the beta position. The explanation of the high efficiency of disulfide has been based on the formation of thiosulfinate—the key intermediate for the generation of peroxidolytic species—in the first reaction step.