Characterization of solutions of a class of ultraparabolic equations of the Kolmogorov type

For a class of ultraparabolic equations of the Kolmogorov type, we prove the theorems on the correct solvability and the integral representation of solutions of the Cauchy problem, whose initial data belong to special weight spaces of functions and generalized Borel measures. On the basis of these theorems, we obtained the full characterization of appropriate classes of solutions of the equations under consideration.     

The construction of an algebraically reduced system for the acceleration of preconditioned conjugate gradients

In this paper we show how an algebraically reduced system can be constructed, for which the preconditioned conjugate gradient method converges faster than for the original system. For this method it is necessary that the original matrix is symmetric positive-definite. Our approach is based on an efficient projection on a well-chosen subspace and we show an application in which a cyclically reduced system is one step further reduced by this novel technique.     

A New Method to Examine Interfacial Reactions of a Multilayered System NiAl–Hf–hBN on a Sapphire Fibre

Fibre reinforced NiAl offers new possibilities for the development of high strength structural materials of low density applicable in gas turbines at high operating temperatures. The properties of composite materials are strongly influenced by the strength of the fibre–matrix interface. In addition, if fibre and matrix differ in their thermal expansion coefficients, a well controlled interface reaction at high temperature changes is demanded. Therefore, two layers consisting of BN and Hf were embedded between a sapphire fibre and NiAl and heated at 1350 °C to find a compromise between adhesion and ductility. The control and characterization of the reaction zone is essential for the development of these new materials. Especially, the characterization of the fibre-coating interface is a challenge. The different hardness of fibre and coating makes it nearly impossible to use a conventional cross-section preparation. Further, the small dimension of the reaction zone requires the use of analytical techniques providing high lateral resolution. In order to accomplish these requirements, a newly developed technique FIB (Focused Ion Beam)-EPMA (Electron Probe Microanalysis) was combined with XRD (X-ray diffraction). XRD was performed for the identification of the phases. The reaction zone was exposed by a special FIB preparation technique and examined by surface-sensitive EPMA. This allowed to determine the spatial distribution of the different phases.     

(n‐Nitrophenyl)acetonitrile,with n = 2, 3 and 4

The molecular structures of the three title nitro‐substituted phenyl­aceto­nitriles, C₈H₆N₂O₂, at 123 K show that the mol­ecules are linked together very differently. In the 2‐ and 4‐nitro compounds, there are both O?H and N_cyano?H interactions, whereas the crystal lattice of the 3‐nitro compound is essentially built up by O?H interactions. The O atoms seem to prefer the aromatic H atoms, while the cyano N atoms prefer the methyl­ene H atoms. The phenyl–nitro torsion angles are ?19.83 (13), ?5.69 (12) and ?2.88 (12)°, while the phenyl–cyano­methyl torsion angles are ?62.27 (12), ?147.99 (9) and ?16.75 (14)° in the 2‐, 3‐ and 4‐NO₂‐substituted compounds, respectively.     

Gas chromatography-mass spectrometry analysis of alkylphenols in cod (Gadus morhua) tissues as pentafluorobenzoate derivatives

A highly selective and sensitive method for the determination of 30 meta- and para-substituted alkylphenols from phenol (C0) to nonylphenol (C9) in biota is described. Dichloromethane extracts of spiked cod liver and muscle samples are cleaned up by gel permeation chromatography, derivatised with pentafluorobenzoyl chloride and analysed by gas chromatography-mass spectrometry with negative-ion chemical ionisation. Quantification is done with isotope dilution of five internal standards of different chain length. The detection limits were in the low microg/kg levels. There were encountered problems with background levels of 4-nonylphenol. 4-Nonylphenol isomers were found in a number of plastic and rubber products used in the laboratory.     

Schwinger-Dyson equations for <Emphasis Type="Italic">N</Emphasis> = 1 supersymmetric Yang-Mills theory

The Schwinger-Dyson equations for the N = 1 supersymmetric Yang-Mills theory are constructed.     

Influence on the Energy of the Covalent Bond of the Isotopic Composition of its Nuclei

Russian Physics Journal - Based on the classical quantum-mechanical approach, the physical mechanism of isotope fractionation is proposed associated with the predominance of a certain number of...