Estimates of the rate of convergence of a dynamic reconstruction algorithm under incomplete information about the phase state

In this paper, we study a dynamic reconstruction algorithm which reconstructs the unknown unbounded input and all unobservable phase coordinates from the results of measurements of part of the coordinates. An upper and a lower bound for the accuracy of the reconstruction is obtained. We determine the class of inputs for which the upper bound is uniform. We give a condition for optimally matching the algorithm parameters, ensuring the highest order of the upper bound and equating the orders of the upper and lower bounds. Thus, we establish the sharpness of the upper bound.     

A local characterization of the johnson scheme

Within the Johnson schemeI(m, d) we find the graphK(m, d) ofd-subsets of anm-set, two such adjacent when disjoint. Among all connected graphs,K(m, d) is characterized by the isomorphism type of its vertex neighborhoods providedm is sufficiently large compared tod. Partial support provided by NSF (USA), SERC (UK), ZWO (NL).     

Stereochemical aspects of the formation of toxisterols A

Mechanisms for the formation of toxisterol A are suggested. The connection between the conformation of the initial previtamin and the stereochemistry of the reaction products is discussed.Lensoviet Leningrad Technological Institute. Translated from Khimiya Prirodnykh Soedinenii, No. 2, pp. 225–229, March–April, 1989.     

Mg 2p shallow core-level and local atomic structure of i-ZnMgRE quasicrystals

We present a detailed analysis of the Mg 2p shallow core-levels measured on icosahedral single-grain ZnMgY, ZnMgHo, and ZnMgEr quasicrystals during a photoelectron microscopy study. The synchrotron radiation photoemission measurements were performed on in situ cleaved samples at a pressure of 10⁻¹⁰ mbar and at low temperature, typically 90-150 K. The Mg 2p photoemission lines are essentially broadened as compared to those of the Mg 2p spin-orbit doublet recorded on the Zn₂Mg crystalline Laves phase. The broadening is associated to the coordination shifts of the Mg 2p level due to the inequivalent magnesium sites in the quasicrystalline lattice. The coordination shifts are calculated on the basis of i-ZnMg(Ho, Y) atomic structure data, recently determined from the pair distribution function analysis. The coordination shifts obtained are up to 0.2 eV. The Mg 2p experimental spectral intensity is nicely reproduced by a superposition of coordination-shifted Mg 2p spin-orbit doublets.     

Improvement of least-squares finite difference method on simulating slider air bearings in head disk systems

Least-squares finite difference (LSFD) method, one of mesh-free methods, is used to solve slider air bearings problem through discritizing the generalized Reynolds equation into nonlinear systems of algebraic equations. Two approximation schemes for the linearization of these equations are presented and compared. And, some new techniques to search supporting points for the reference node in the mesh-free method were proposed and explored. Therefore, these improvements eliminate some potential limitation of the LSFD method previously published and further facilitate its employment in complex slider models. Advanced step slider as an example of negative pressure sliders is simulated and verified using the improved LSFD mesh-free method in head disk systems.     

A comparison of spin relaxation and local motion between symmetrically and asymmetrically ring-substituted bisphenol units in dissolved polycarbonates

Carbon-13 and proton spin-lattice relaxation times were measured at two field strengths on solutions 10% by weight of two polycarbonates in C₂D₂Cl₄ from ?20 to +120°C. The first polycarbonate is an asymmetrically substituted form with one chlorine on one of the two phenylene aromatic rings of the bisphenol unit, whereas the second polycarbonate is symmetrically substituted with two chlorines on each of the two rings. The nuclear spin relaxation data are interpreted in terms of several local motions likely in these polymers. Segmental motion was described by the Hall–Helfand correlation function. Segmental motion in the monosubstituted polycarbonate is somewhat slower than in unsubstituted polycarbonate, whereas segmental motion in the tetrasubstituted polycarbonate is considerably slower. Phenylene ring rotation is observed in unsubstituted polycarbonate and in the monosubstituted polycarbonate above 40°C. Below 40°C in the monosubstituted species, and at all temperatures in the tetrasubstituted species, ring rotation is replaced by ring libration as the predominant motion contributing to spin lattice relaxation. In addition, the rotational motion of the two types of rings in the asymmetric monosubstituted form are very similar although not identical. The substituted ring is slightly less mobile than the rings of unsubstituted polycarbonate. This indicates a strong coupling of ring motion, although the coupling leads to less than synchronous motion. Methyl group rotation is present in both polymers and is little affected by the various structural modifications.     

Near-infrared laser photoacoustic detection of methane: the impact of molecular relaxation

A photoacoustic sensor has been developed for trace-gas monitoring using a near-infrared semiconductor laser emitting in the 2ν₃ band of methane at 1.65 μm. The apparatus was designed for on-line process control in the manufacturing of the novel low-water-peak fibres developed for optical telecommunications. The importance of collisional relaxation processes in the generation of the photoacoustic signal is reported in the particular case of CH₄ detection in dry O₂ and O₂–N₂ mixtures. The negative influence of these effects results in a strongly reduced and phase-shifted photoacoustic signal, induced by a fast resonant coupling between the vibrational states of methane and oxygen, associated with the slow relaxation of the excited oxygen molecules. An unusual parabolic response of the sensor with respect to the methane concentration has been observed and is discussed. Finally, the beneficial effect of several species, including water vapour and helium, acting as a catalyst to hasten the relaxation of the CH₄–O₂ system, is demonstrated. PACS 42.62.Fi; 33.20.Ea; 34.50.Ez     

Nonlinear Theory of the Plasma Wave Excitation in a Bounded Beam-Plasma System

The excitation of symmetric and antisymmetric plasma waves by a beam layer that moves within a homogeneous plasma enclosed by a metallic wall was dealt with theoretically. Investigations were carried out for the magnetic field free case and for a magnetized electron beam. In the latter case, the beam electrons are assumed to be unable to move in the perpendicular direction. The theoretical model bases upon an extension of the well known single wave theory to a two-dimensional beam-plasma system. Special emphasis should be paid to the fact that the perpendicular wave profile of the excited waves was determined self-consistently. Energy and momentum balance equations are derived for this system. The theoretical method outlined in this paper which is based on a Green's-function technique can be extended easily to three-dimensional systems or to beam-plasma systems with other boundary conditions. The main features of the saturation process of the basic unstable wave types are discussed. Several interesting effects were found in the magnetic field free case: (i) numerical solutions describe an increasing steepening of the wave amplitudes in perpendicular direction near the center of the system for the symmetric potential wave; (ii) for the antisymmetric wave, a smoothing tendency was found in the development of the perpendicular wave potential profile; (iii) spatial separation of the slow and fast beam electrons was observed; (iv) it is shown for the antisymmetric potential wave type that, under certain conditions, a very efficient beam particle retardation mechanism occurs which is connected with a strong reduction of the formation of a fast particle group; (v) generally it was shown that the conversion of the kinetic energy of the beam electrons into the plasma wave energy may be more effective as compared with the case of the magnetized beam.