Effect of trapping centers of luminescent properties of bismuth orthogermanate

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 54, No. 6, pp. 970–975, June, 1991.     

Some new results on superimposed codes

A (w,r) cover‐free family is a family of subsets of a finite set such that no intersection of w members of the family is covered by a union of r others. A (w,r) superimposed code is the incidence matrix of such a family. Such a family also arises in cryptography as the concept of key distribution pattern. In the present paper, we give some new results on superimposed codes. First we construct superimposed codes from super‐simple designs which give us results better than superimposed codes constructed by other known methods. Next we prove the uniqueness of the (1,2) superimposed code of size 9 × 12, the (2,2) superimposed code of size 14 × 8, and the (2,3) superimposed code of size 30 × 10. Finally, we improve numerical values of upper bounds for the asymptotic rate of some (w,r) superimposed codes. © 2004 Wiley Periodicals, Inc.     

Effects of localization of the areas of sound scattering by surface wind waves

Experimental studies of the scattering of a monochromatic sound signal by a rough sea surface are carried out. The signal is produced by a point source in a shallow-water basin. The measurements are performed with the use of horizontal and vertical linear receiving arrays. The experimental data are compared with the estimates obtained on the basis of the model developed by the authors for resonant sound scattering by surface roughness. A satisfactory agreement between the experiments and the calculations is achieved. It is shown that the scattered signal is formed within small surface areas, whose sizes have the same order of magnitude as the first Fresnel zone with respect to the source and the receiving system.     

Method of linear prediction in the ultrasonic spectroscopy of rock

The possibility of using the resonant acoustic spectroscopy method for testing the internal state of rock is considered. This method can be used for the determination of the concentration of defects and their spatial distribution. A rock specimen with defects is characterized by a high loss of vibrational energy, which leads to the overlapping of the resonant responses. In this case, the complex resonant frequencies are determined as the parameters of a model that describes the measured transfer function of the response of the mechanical system. The linearity of the vibratory system is used as the a priori information for presetting the functional dependences of the model. An algorithm is developed for the determination of the parameters of the resonances in conditions of their partial overlapping. Examples are presented to demonstrate the possibility of analyzing the complex elastic constant tensor of rock by the acoustic spectroscopy method. The proposed method of experimental data processing provides the possibility for the determination of the weak anisotropy that occurs in the velocity of sound because of a partial fracture of rock.     

Fractional Hamiltonian Monodromy

We introduce fractional monodromy in order to characterize certain non-isolated critical values of the energy–momentum map of integrable Hamiltonian dynamical systems represented by nonlinear resonant two-dimensional oscillators. We give the formal mathematical definition of fractional monodromy, which is a generalization of the definition of monodromy used by other authors before. We prove that the 1:( − 2) resonant oscillator system has monodromy matrix with half-integer coefficients and discuss manifestations of this monodromy in quantum systems. Communicated by Eduard Zehnder Submitted: February 25, 2005; Accepted: November 17, 2005     

Three-dimensional flow of supersonic jets past bodies

Translated from Aktual'nye Voprosy Prikladnoi Matematiki, pp. 228–235, 1989.     

Application of hydroacoustic radiators for the generation of seismic waves

To excite seismic waves with a high coherence, powerful hydroacoustic radiators placed in a natural reservoir were used. Theoretical estimates and the test data demonstrate a high efficiency of the proposed method of seismic wave excitation. The calculations are in good agreement with the results of measurements. The results of phasing the radiation with the use of two monopole sources separated by a quarter-wave distance are presented. It is shown that the use of the proposed scheme of excitation makes it possible to control the radiation pattern while obtaining a high coherence of seismic waves.