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 the Frequency of Zeros of Solutions of Second Order Linear Differential Equations

We consider the equation \(\rm f^{\prime\prime}+{A}(z){f}=0\) with linearly independent solutions f₁,₂, where A(z) is a transcendental entire function of finite order. Conditions are given on A(z) which ensure that max{λ(f₁),λ(f₂)} = ∞, where λ(g) denotes the exponent of convergence of the zeros of g. We show as a special case of a further result that if P(z) is a non-constant, real, even polynomial with positive leading coefficient then every non-trivial solution of \(\rm f^{\prime\prime}+{e}^P{f}=0\) satisfies λ(f) = ∞. Finally we consider the particular equation \(\rm f^{\prime\prime}+({e}^Z-K){f}=0\) where K is a constant, which is of interest in that, depending on K, either every solution has λ(f) = ∞ or there exist two independent solutions f₁, f₂ each with λ(f_i) ≤ 1.     

Electrospray ionization mass spectrometric studies of nucleophilic carbenes derived from pyrazolium and indazolium carboxylates

Pyrazolium-3-carboxylate and indazolium-3-carboxylate, which belong to the class of pseudo-cross-conjugated mesomeric betaines and which represent the electronically relevant partial structures of the betaine alkaloid Nigellicin, were examined by electrospray ionization mass spectrometry. These compounds decarboxylate to pyrazol-3-ylidene and indazol-3-ylidene. The formation of adducts of these new nucleophilic carbenes under the measurement conditions was examined.     

The influence of different InsP(3) receptor isoforms on Ca(2+) signaling in tracheal smooth muscle cells

In airway myocytes, like in many cells, Ca(2+) signaling is controlled by inositol 1,4,5-trisphosphate (InsP(3)) via InsP(3) receptors (InsP(3)R) located in the sarco-endoplasmic reticulum. Three types of InsP(3)R exist, labeled Types 1, 2, and 3, which differ in their gating kinetics. We analyze a possible impact of the different gating kinetics of Type 1 and Type 3 InsP(3)R on the time course of cytosolic Ca(2+) concentration in tracheal smooth muscle cells upon agonist stimulation. Previous experimental data in rat tracheal myocytes showed that upon gradually increased stimulation with acetylcholine (ACh), a contractile agonist that acts via InsP(3) production, signal spikes, several spikes with declining maxima, and sustained oscillations appear. Our model reproduces the time courses of cytosolic Ca(2+) measured in tracheal myocytes. Moreover, by postulating slight variations in the model parameters which determine the total number of receptors expressed and the ratio between Type 1 and Type 3 InsP(3)R, it offers an explanation to the experimental observation of qualitatively different responses of cells within a presumably homogeneous tissue.     

Influence of biomass on hydrodynamics of an internal loop airlift reactor

The effect of the biomass presence on the overall circulation velocity, the linear velocities both in the riser and the downcomer and the overall gas hold-up was studied in a three-phase internal loop airlift reactor (ILALR). The measured data were compared with those obtained using a two-phase system (air—water). All experiments were carried out in a 40 dm³ ILALR at six different biomass concentrations (ranging from 0 g dm⁻³ to 7.5 g dm⁻³), at a temperature of 30°C, under atmospheric pressure. Air and water were used as the gas and liquid model media, respectively. Pellets of Aspergillus niger produced during the fermentation of glucose to gluconic acid in the ILALR were considered solid phase. In addition, liquid velocities were measured during the fermentation of glucose to gluconic acid using Aspergillus niger. All measurements were performed in a bubble circulation regime. At given experimental conditions the effect of the biomass on the circulation velocities in the ILALR was negligible. However, increasing of the biomass concentration led to lower values of the total gas hold-up. Presented at the 33rd International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 22–26 May 2006.