Analytic Properties of the Transition Admittance of an Infinite Plate in a medium and the Regularization of Boundary-Contact Integrals in Acoustics

A condition for regularization of boundary-contact integrals in two-dimensional problems of acoustics is considered. With an example of the simplest boundary-contact problem of acoustics, it is shown that a known sufficient condition for regularization is also a necessary one. The study of analytic properties of the transition admittance of an infinite plate that is in contact with a medium is conducted in order to obtain this statement. The considerations are carried out in general terms. The results obtained may be used in arbitrary models of plate theory, and they also may be adapted to boundary-contact problems of another physical nature. Bibliography: 9 titles.     

High energy asymptotics of the scattering amplitude for the Schrödinger equation

We find an explicit function approximating at high energies the kernel of the scattering matrix with arbitrary accuracy. Moreover, the same function gives all diagonal singularities of the kernel of the scattering matrix in the angular variables. This paper is dedicated to Jean-Michel Combes on the occasion of his sixtieth birthday.     

Likelihood Ratio Processes for Markovian Particle Systems with Killing and Jumps

We consider Markov processes built from pasting together pieces of strong Markov processes which are killed at a position dependent rate and connected via a transition kernel. We give necessary and sufficient conditions for local absolute continuity of probability laws for such processes on a suitable path space and derive an explicit formula for the corresponding likelihood ratio process. The main tool is the consideration of the process between successive jumps – what we call ‘elementary experiments’ – and criteria for absolute continuity of laws of the process there. We apply our results to systems of branching diffusions with interactions and immigrations. This revised version was published online in June 2006 with corrections to the Cover Date.     

Modified Three-Dimensional Formulations of Bending Problems of Homogeneous Plates and Beams under Complex Fixing Conditions

Modified three-dimensional formulations of bending problems of homogeneous elastic plates and beams are considered. Modification of the known three-dimensional formulations reduces to using additional constraints imposed on displacement functions. An advantage of the formulations proposed is that complex fixing conditions of plates and beams can be taken into account.     

Dynamic holograms and optical limiting: Asymmetric two-wave interactions

The conditions for obtaining a high efficiency of energy exchange upon two-wave interactions in dynamic holograms are found by analysis and numerical simulation of a system of nonlinear equations. Use of an asymmetric scheme of beam interaction in a medium with two nonlinearities, one of which determines the amplitude and relaxation time of a grating and the other of which provides phase modulation of the interacting beams, is proposed. It is shown that such a scheme in combination with the specific properties of a medium makes it possible to radically reduce the requirements for the nonlinearity of a medium and the intensity of a light flux in limiting systems, as well as to significantly decrease the time of the transition process. As a result, it becomes possible to attain an efficiency of energy transfer higher than 90% and to increase the corresponding attenuation of a high-power beam by almost two orders of magnitude, which is of interest for optical limiting of intense light fluxes.     

Higher Order Peak Algebras

Using the theory of noncommutative symmetric functions, we introduce the higher order peak algebras (Sym(N))_N≥1, a sequence of graded Hopf algebras which contain the descent algebra and the usual peak algebra as initial cases (N=1 and N=2). We compute their Hilbert series, introduce and study several combinatorial bases, and establish various algebraic identities related to the multisection of formal power series with noncommutative coefficients. Received November 19, 2004     

The effect of traffic noise on sleep of young adults in their homes

The disturbance of sleep by traffic noise is a major problem area in noise pollution. Extensive laboratory tests using multichannel electroencephalograms (EEG) have been carried out by many workers to determine the general response of people when exposed to noise during sleep. An experimental technique for obtaining results in people's homes has been developed using a simplified one-channel EEG. The responses of six people in the age range 19-24 were measured. A significant correlation was found between sleep disturbance and traffic noise when the noise is expressed in EPNdB. In the home experiments the subjects appeared to be approximately 10 dB less sensitive to noises than laboratory subjects for similar noise exposure. There also appeared to be some adaptation to the noise exposure; however, only one subject was tested for a period of 20 days and was insufficient to give definite results on adaptation.     

Development of a quantitative FI-MS technique for the characterization of high- and nonboiling saturated hydrocarbon mixtures

Summary Using a saturated non-boiling hydrocarbon mixture, the influence of two parameters on the results of field ionization mass spectrometry (FI-MS) measurements was studied: (a) the potential difference between the FI emitter and the counterelectrode; (b) the emitter temperature.Variation of the potential difference had only a minor effect on the average molecular mass measured and had no evident effect on the relative ring number distribution in the sample. In contrast, when the emitter temperature was increased, higher average molecular masses were recorded. Moreover, the average molecular masses shifted to higher ring numbers. In order to control the relationship between the described influences during mixture analysis, measuring instructions have been developed that enable the quantitative analysis of unknown saturated samples. However, average molecular mass of the mixture must be known.

---

Entwicklung einer quantitativen FI-MS-Methode zur Charakterisierung von gesättigten hoch- und nichtsiedenden Kohlenwasserstoffgemischen

     

Investigation of multicomponent fluoride optical materials in the UV spectral region: I. Single crystals of Ca1−x R xF2+x (R = Sc, Y, La, Yb, Lu) solid solutions

Crystalline materials that are transparent in the vacuum UV spectral region and currently used have been reviewed. Transmission of crystals of solid solutions with the fluorite structure Ca_1?x R _xF_2+x (R = Sc, Y, La, Yb, Lu) in the UV and vacuum UV spectral regions has been investigated. It is shown that application of different methods of purification of fluorides from some impurities can significantly improve the optical quality of fluoride multicomponent crystals in the short-wavelength spectral region.