The Transformation Matrix of Vibrational Waves

The general theory on the transformation of elastic waves at a rigid nodal junction of an arbitrary number of thin plates is considered. The notion of transformation marix is introduced, and a way for computing it and numerical examples are given. Properties of the transformation matrix resulted from the reciprocity principle and the energy conservatin law are studied. In particular, a new relation that expresses the energy conservation low for the case where a wave damped in the direction of the joint of plates is a source of a field is obtained. Bibliography: 18 titles.     

Preparation of colloidal solutions of noble metals stabilized by polyoxometalates and supported catalysts based on these solutions

Conditions for the preparation of stable aqueous monometallic and bimetallic colloidal solutions (sols) of noble metals (Ru, Rh, Pd, Pt, Ir, Ag, and Au) in the presence of polyoxometalates containing W, Mo, V, and Nb were found. The stability of sols against coagulation at room temperature was studied. The metal/C samples prepared by metal adsorption from sols were studied by powder X-ray diffraction analysis and transmission electron microscopy. The following factors of importance for the preparation of a stable sol are discussed: (1) the formation of a sol of a metal polyhydroxo complex stabilized by a polyoxometalate (preliminary stage) and (2) the formation of polyoxometalate-metal clusters in the course of reduction of polyhydroxo complexes.Translated from Kinetika i Kataliz, Vol. 45, No. 6, 2004, pp. 921–929.Original Russian Text Copyright © 2004 by Maksimova, Chuvilin, Moroz, Likholobov, Matveev.     

Near-Optimal Controls of Discrete-Time Dynamic Systems Driven by Singularly-Perturbed Markov Chains

This work is devoted to near-optimal controls of large-scale discrete-time nonlinear dynamic systems driven by Markov chains; the underlying problem is to minimize an expected cost function. Our main goal is to reduce the complexity of the underlying systems. To achieve this goal, discrete-time control models under singularly-perturbed Markov chains are introduced. Using a relaxed control representation, our effort is devoted to finding near-optimal controls. Lumping the states in each irreducible class into a single state gives rise to a limit system. Applying near-optimal controls of the limit system to the original system, near-optimal controls of the original system are derived.     

Tensor Products of Quantum Structures and Their Applications in Quantum Measurements

Tensor products of quantum logics and effect algebras with some known problems are reviewed. It is noticed that although tensor products of effect algebras having at least one state exist, in the category of complex Hilbert space effect algebras similar problems as with tensor products of projection lattices occur. Nevertheless, if one of the two coupled physical systems is classical, tensor product exists and can be considered as a Boolean power. Some applications of tensor products (in the form of Boolean powers) to quantum measurements are reviewed.     

Two scenarios for phase-transformation in disordered media

The reasons for the existence of various scenarios for structural transformations in disordered condensed media, such as liquids and amorphous substances, where both smeared transformations and sharp first-order transitions may occur, were analyzed. The ratio between the spatial scale of structural correlations and the size of the smallest possible region occupied by a new phase in the matrix of initial modification is the key parameter determining the scenario for equilibrium phase transformations in liquids. In amorphous substances, the experimentally observed transformations occur far from equilibrium, and the possible size of the region occupied by the new phase corresponds to the minimal nucleus size. For some amorphous solids, quantitative analysis of the transformation width was carried out and the main classes of covalent substances, in which the smeared or sharp transitions occur, were revealed. Specific features of the interparticle interactions determining various transformation scenarios are discussed.     

Potent New Heterogeneous Asymmetric Catalysts

A set of new, air‐stable, Rh^I‐based heterogeneous asymmetric hydrogenation catalysts have been synthesised, characterised, and tested. Individual members of this new family all exhibit good enantioselectivity.     

High-resolution infrared spectra of NCCN and NCCN

High-resolution spectra of ¹⁵N¹²C¹²C¹⁵N and ¹⁴N¹³C¹³C¹⁴N have been measured and analyzed from 200 to 3600 cm⁻¹. All the vibrational levels below 900 cm⁻¹ have been observed and characterized. The Fermi resonance between ν₂ and 2ν₄ has been studied and the resonance constant has been determined for several cases. Several Σ⁻ states have been directly observed for the first time for each isotopomer, the (0001111)0f, (0011111)0f, and (0002222)0f states. The pattern of the energy levels for clusters of l-type resonance coupled levels, such as 0001131,3, has been determined for cyanogen for the first time. Among other things this involved the determination of the vibrational l-type resonance constant, r₄₅. Many of the power series constants, α_i and x_ij, and higher order constants have been determined.     

Semiconductor Detectors, Mixers, and Frequency Multipliers for the Terahertz Band

The state of the art in the development of semiconductor detectors, mixers, and frequency multipliers based on Schottky-barrier diodes (SBDs) and heterojunction structures for uncooled terahertz receivers is reviewed. The present status of this field features a transition from quasi-optical designs based on dot-matrix, whisker-contacted SBDs to the designs with hybrid-integrated and monolithic constructions on the planar SBD base, which are positioned in a waveguide mount. The high-level performance of these planar devices is achieved by partially or completely removing or changing semiconductor substrates and/or using membrane constructions incorporated in the waveguide.     

Pressure induced transitions in calcium: a tight-binding approach

A tight-binding (TB) hamiltonian for calcium is built with a high precision parametrization technique based on density functional calculations of the energy bands and the total energy at various lattice volumes. The new set of TB parameters is appropriate to study phenomena under pressures as high as 20 GPa. Specifically, both the metal to nonmetal transition at 4 GPa and the structural transition fcc to bcc at 19 GPa are well reproduced. These transitions and several static properties are in excellent agreement with experiments. Phonon frequencies, plasmon energy, melting temperature and the coefficient of thermal expansion were calculated with a molecular dynamics scheme of this TB hamiltonian.