Stress–Strain Analysis of Rectangular Plates with a Variable Thickness and Constant Weight

The stress–strain state of rectangular plates with a variable thickness and constant weight is analyzed. The laws of variation in the thickness are specified to depend on parameters so that the plate weight remains constant for any of their values. To solve the problem, discrete Fourier series are used, which makes it possible to reduce a two-dimensional problem to one-dimensional. Calculation results are presented.     

Surface grating formation and erasing on a-Se films

Surface relief formation at holographic recording on amorphous selenium films was demonstrated and investigated. The presence of this optical phase modulation component is essential for ensuring significant, stable and erasable optical recording in a-Se films at 290–320 K temperatures, where conventional photodarkening was known as insignificant and unstable. Photocrystallization can only be observed in super-exposed a-Se films at the given experimental conditions of hologram recording. Erasing behavior of surface relief gratings under heat treatment was also investigated in order to reveal further details of the mechanism. Photoinduced structural transformations within the amorphous phase, connected to local ordering under the condition of light-induced fluidity, are proposed as an explanation for the relief formation and erasing. The observed reversible optical recording process may be useful for the various optoelectronic applications of photoconductive a-Se layers. Received: 12 June 2000 / Accepted: 6 June 2001 / Published online: 30 August 2001     

Quantum-well states and resonances in thin single-crystal layers of noble metals on W(110) substrates

This paper reports on the first experimental observation of quantum-well states and sp-type resonances in thin single-crystal gold, silver, and copper layers formed on single-crystal W(110) surfaces, which result from spatial localization of Bloch-type electronic wave functions in a quantum well with potential barriers at the vacuum/metal and metal/W(110) interfaces. The quantization of the valence-band electronic structure in Au/W(110), Ag/W(110), and Cu/W(110) systems was studied experimentally using angle-resolved photoelectron spectroscopy.     

Study of the charge-exchange reactions\pi ^ - p \to (\pi ^0 ,\eta ,\eta \prime )n at 63 GeV

Muon electron pairs were detected in an Al multiplate spark chamber, exposed to a neutrino beam from the CERN PS. The leptons were not accompanied by other particles, except occasionally by protons. The background came mainly from muon associated π⁰ production, with one decay gamma lost. It was determined empirically, together with the small contribution from υ _e reactions. For electron energies above 2 GeV the background is 5.7±1.5 events, whereas 18 (μe)-candidates have been observed. Hence the effect is established, with a rate of about 10^?4 as compared to the muonic reactions above 3 GeV. Charm creation as the origin of this (μe)-production process is excluded; heavy neutral lepton production does not fit the kinematics observed. Instead the events are compatible with the two-body decay of an object with variable invariant mass of order 1 GeV, possibly resulting from axion interactions.     

Numerical algorithm for the Mayer problem for nonlinear dynamic systems

An algorithm is proposed for numerical construction of optimal programmed controls in the Mayer problem for a nonlinear dynamic system. In each step of the optimization process, the algorithm uses the method of successive linearization with subsequent projection of the objective functional gradient on the constraints and recovery of violated boundary conditions and constraints. Solutions of some test problems are reported.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 56, pp. 107–114, 1985.     

A comparison of steady-state evoked potentials to modulated tones in awake and sleeping humans.

Steady-state evoked potential responses were measured to binaural amplitude-modulated (AM) and combined amplitude- and frequency-modulated (AM/FM) tones. For awake subjects, AM/FM tones produced larger amplitude responses than did AM tones. Awake and sleeping responses to 30-dB HL AM/FM tones were compared. Response amplitudes were lower during sleep and the extent to which they differed from awake amplitudes was dependent on both carrier and modulation frequencies. Background EEG noise at the stimulus modulation frequency was also reduced during sleep and varied with modulation frequency. A detection efficiency function was used to indicate the modulation frequencies likely to be most suitable for electrical estimation of behavioral threshold. In awake subjects, for all carrier frequencies tested, detection efficiency was highest at a modulation frequency of 45 Hz. In sleeping subjects, the modulation frequency regions of highest efficiency varied with carrier frequency. For carrier frequencies of 250 Hz, 500 Hz, and 1 kHz, the highest efficiencies were found in two modulation frequency regions centered on 45 and 90 Hz. For 2 and 4 kHz, the highest efficiencies were at modulation frequencies above 70 Hz. Sleep stage affected both response amplitude and background EEG noise in a manner that depended on modulation frequency. The results of this study suggest that, for sleeping subjects, modulation frequencies above 70 Hz may be best when using steady-state potentials for hearing threshold estimation.     

Flatness in analytic mappings I. On an announcement of Hironaka

We present a stratification by “normal flatness” associated to an analytic mapping, analogous to Hironaka's classical result for analytic spaces. Our construction is based on a generic normal flatness theorem for mappings, proved using techniques concerning the variation of modules of meromorphically parametrized formal power series [1]. The existence of such a stratification was announced by Hironaka [13], but the other claims made in [13] are false. Counterexamples are also presented here.     

Reducing systems of linear differential equations to a passive form

In this paper, an application of the Riquer-Thomas-Janet theory is described for the problem of transforming a system of partial differential equations into a passive form, i.e., to a special form which contains explicitly both the equations of the initial system and all their nontrivial differential consequences. This special representation of a system markedly facilitates the subsequent integration of the corresponding differential equations. In this paper, the modern approach to the indicated problem is presented. This is the approach adopted in the Knuth-Bendix procedure [13] for critical-pair/completion and then Buchberger's algorithm for completion of polynomial ideal bases [13] (or, alternatively, for the construction of Groebner bases for ideals in a differential operator ring [14]). The algorithm of reduction to the passive form for linear system of partial differential equations and its implementation in the algorithmic language REFAL, as well as the capabilities of the corresponding program, are outlined. Examples illustrating the power and efficiency of the system are presented.     

A statistical approach to the solution of ill-posed problems in geophysics

The article surveys the main results of the statistical approach to the solution of ill-posed problems of mathematical physics, in application to specific ill-posed inverse problems in geophysics.Invited paper presented at the International Seminar on Mathematical Foundations of the Interpretation of Geophysical Fields, Moscow, May–June 1972.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 79, pp. 67–81, 1978.