Some topics on the continuation and smoothing of vector functions

We consider problems of continuation of vector functions from a subspace to the entire space and of smoothing problems for these functions. It is shown that there exists a reflexive separable spaceX and a subspaceY such that even a very smooth mapping ofY does not extend to a uniformly continuous mapping of a neighborhood ofY.Translated fromMatematicheskie Zametki, Vol. 58, No. 6, pp. 906–916, December, 1995.     

Determination of 3-Chloro-4-(Dichloromethyl)-5-Hydroxy-2(5H)-Furanone (Toxicant MX) in Drinking Water by Chromatography–Tandem Mass Spectrometry

It is shown that toxicant MX can be reliably identified and determined quantitatively by ion-trap tandem mass spectrometry with an accuracy as high as that for high-resolution mass spectrometry.     

Studies on Rare-Earth/Iron and Actinide/Iron Multilayers

Hyperfine Interactions - Multilayers of Ce/Fe and U/Fe were fabricated by sputtering and studied by X-ray diffraction and reflectivity, Mössbauer spectroscopy and polarised neutron...     

Molecular flow and wall collision age distributions

The use of storage cells has become a standard technique for internal gas targets in conjunction with high energy storage rings. In case of spin-polarized hydrogen and deuterium gas targets the interaction of the injected atoms with the walls of the storage cell can lead to depolarization and recombination. Thus the number of wall collisions of the atoms in the target gas is important for modeling the processes of spin relaxation and recombination. It is shown in this article that the diffusion process of rarefied gases in long tubes or storage cells can be described with the help of the one-dimensional diffusion equation. Mathematical methods are presented that allow one to calculate collision age distributions (CAD) and their moments analytically. These methods provide a better understanding of the different aspects of diffusion than Monte Carlo calculations. Additionally it is shown that measurements of the atomic density or polarization of a gas sample taken from the center of the tube allow one to determine the possible range of the corresponding density weighted average values along the tube. The calculations are applied to the storage cell geometry of the HERMES internal polarized hydrogen and deuterium gas target. Received 9 July 2001 and Received in final form 18 September 2001     

Synthesis of Palladium and Nickel Complexes with Octaphenyltetraazaporphyrins

Palladium(II) and nickel(II) complexes with octaphenyltetraazaporphyrin, octakis(4-bromophenyl)tetraazaporphyrin, and octakis(4-nitrophenyl)tetraazaporphyrin were obtained by reactions of octaphenyltetraazaporphyrin, Mg octaphenyltetraazaporphyrin, octakis(4-bromophenyl)tetraazaporphyrin, and octakis(4-nitrophenyl)tetraazaporphyrin with palladium(II) and nickel(II) chlorides in DMF.     

Pattern Search Method for Discrete <Emphasis Type="Italic">L</Emphasis><Subscript>1</Subscript>–Approximation

We propose a pattern search method to solve a classical nonsmooth optimization problem. In a deep analogy with pattern search methods for linear constrained optimization, the set of search directions at each iteration is defined in such a way that it conforms to the local geometry of the set of points of nondifferentiability near the current iterate. This is crucial to ensure convergence. The approach presented here can be extended to wider classes of nonsmooth optimization problems. Numerical experiments seem to be encouraging. This work was supported by M.U.R.S.T., Rome, Italy.     

Complex projections of completely positive quaternionic maps

We show that the complex projection of a completely positive quaternionic map of quaternionic density matrices is a positive map in the space of complex density matrices, and we briefly outline some of its properties. To illustrate this result, we study the complex projection of a one-parameter quaternionic unitary dynamics of a spin-1/2 quantum system. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 3, pp. 360–370, June, 2007.     

Certain constructions of asymptotic analysis related to the Stone-Čcech compactification

The paper considers the representations of attraction sets in topological spaces and their relations with the relaxation of accessibility problems under the conditions of sequentially relaxed constraints. The author studies the structure of approximate (in essence, asymptotic) solutions and generalized elements and establishes the possibility of their real identification for a certain version (related to the Stone-Čech compactification and the Wallman relaxation) of relaxation of the initial problem. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 26, Nonlinear Dynamics, 2005.