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.     

Multiple scattering in the high-frequency limit with second-order shadowing function from 2D anisotropic rough dielectric surfaces: I. Theoretical study

In this paper the first- and second-order Kirchhoff approximation is applied to study the backscattering enhancement phenomenon, which appears when the surface rms slope is greater than 0.5. The formulation is reduced to the geometric optics approximation in which the second-order illumination function is taken into account. This study is developed for a two-dimensional (2D) anisotropic stationary rough dielectric surface and for any surface slope and height distributions assumed to be statistically even. Using the Weyl representation of the Green function (which introduces an absolute value over the surface elevation in the phase term), the incoherent scattering coefficient under the stationary phase assumption is expressed as the sum of three terms. The incoherent scattering coefficient then requires the numerical computation of a ten- dimensional integral. To reduce the number of numerical integrations, the geometric optics approximation is applied, which assumes that the correlation between two adjacent points is very strong. The model is then proportional to two surface slope probabilities, for which the slopes would specularly reflect the beams in the double scattering process. In addition, the slope distributions are related with each other by a propagating function, which accounts for the second-order illumination function. The companion paper is devoted to the simulation of this model and comparisons with an 'exact' numerical method.     

Multiple scattering in the high-frequency limit with second-order shadowing function from 2D anisotropic rough dielectric surfaces: II. comparison with numerical results

This second part presents illustrative examples of the model developed in the companion paper, which is based on the first- and second-order optics approximation. The surface is assumed to be Gaussian and the correlation height is chosen as anisotropic Gaussian. The incoherent scattering coefficient is computed for a height rms range from 0.5λ 1λwhere λ is the electromagnetic wavelength), for a slope rms range from 0.5 to 1 and for an incidence angle range from 0 to 70°. In addition, simulations are presented for an anisotropic Gaussian surface and when the receiver is not located in the plane of incidence. For a metallic and dielectric isotropic Gaussian surfaces, the cross- and co-polarizations are also compared with a numerical approach obtained from the forward.backward method with a novel spectral acceleration algorithm developed by Torrungrueng and Johnson (2001, JOSA A 18). (Some figures in this article are in colour only in the electronic version)     

Shadowing function with single reflection from anisotropic Gaussian rough surface. Application to Gaussian, Lorentzian and sea correlations

In this paper, the monostatic (transmitter and receiver are located at the same place) and bistatic (transmitter and receiver are distinct) statistical shadowing functions from an anisotropic two-dimensional randomly rough surface are presented. This parameter is especially important in the case of grazing angles for computing the bistatic scattering coefficient in optical and microwave frequencies. The objective of this paper is to extend the previous work (Bourlier C, Berginc G and Saillard J 2002 Waves Random Media 12 145-74), valid for a one-dimensional surface, to a two-dimensional anistropic surface by considering a joint Gaussian process of surface slopes and heights separating two points of the surface. The monostatic average (statistical shadowing function average over the statistical variables) shadowing function is then performed in polar coordinates with respect to the incidence angle, the azimuthal direction and the surface height two-dimensional autocorrelation function. In addition, for a bistatic configuration, it depends on the incidence angle and azimuthal direction of the receiver. For Gaussian and Lorentzian correlation profiles and practically important power-type spectra such as the Pierson-Moskowitz sea roughness spectrum, the numerical solution, obtained from generating the surface Gaussian elevations (Monte Carlo method), is compared with the uncorrelated and correlated models. The results show that the correlation underestimates the shadow slightly, whereas the uncorrelated results weakly overpredict the shadow and are close to the numerical solution.     

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.     

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.