Embedding and wavelet decomposition of spaces of minimal splines

On a sequence of embedded nonuniform grids, chains of embedded spaces of minimal splines (not necessarily polynomial) are constructed. The wavelet decomposition is given. The basis wavelets are compactly supported and admit simple analytic representation. The corresponding decomposition and reconstruction formulas are derived. The variety of spaces under consideration is identified with the variety of complete sequences of points of the direct product of an interval and a projective plane. Bibliography: 20 titles. __________ Translated from Problemy Matematicheskogo Analiza, No. 35, 2007, pp. 15–31     

Inhomogeneous configurations of magnetization of ferromagnetic films with biaxial anisotropy

The system of the Landau-Lifshitz equations and magnetostatic equations for a ferromagnetic film with biaxial anisotropy and a Q-factor smaller than unity is reduced to a single scalar equation for the magnetostatic potential. Such a procedure is possible if the magnetization modulation scale in the sample considerably exceeds the characteristic magnetic length. The solutions to this equation describing inhomogeneous periodic magnetic configurations are obtained. The energy analysis of these configurations is carried out.     

There does not exist an enumerable family of context-free grammars that generates the class of single-valued languages

Translated from Matematicheskie Zametki, Vol. 50, No. 1, pp. 34–40, July, 1991.     

Calculation of the Radiating Characteristics of a Thermodynamically Nonuniform Gas Medium

Passive methods of remote analysis of waste gases of industrial enterprises and aircrafts engines and gases ejected in eruptions of volcanos, in fires, and in other processes disturbing the atmosphere are now of limited utility because of the lack of well-developed mathematical techniques for solving the inverse problems of gas analysis. However, the advantage of these methods is obvious, since the equipment is limited to a receiving device and the gas medium serves as a radiator. At the same time, in modern techniques, the interpretation of measurements of emissivities of gases is performed using a phenomenological approach such that experimental data on radiation characteristics of various objects are approximated by simple polynomial relations whose coefficients are determined by minimization methods. This approach does not allow one to investigate the mechanism of the processes occurring in a radiating medium and gives no way of solving the inverse problem of monitoring the composition and thermodynamic parameters of a medium which disturbs the atmosphere by thermal effects. In elaborating theoretical methods of gas analysis, the elaboration of the direct problem of calculation of radiating characteristics of gases is of importance, since it is not clear how the emissivity of a gas medium depends on its thermodynamic parameters. This paper is devoted to the above problem. Here, the error is estimated that arises in modeling a nonuniform gas medium with an actual temperature distribution, which linearly depends on coordinate, by a uniform gas layer. It is shown that the difference between the radiation intensities calculated for uniform and nonuniform media can be significant in the practically important case where the recording device is in a zone of normal temperatures. This implies that the error of reconstruction of the spectroscopic and molecular parameters of gaseous compounds from high-temperature measurements of the radiating and absorbing characteristics should take into account the thermodynamic nonuniformity of the medium.     

Testing exponentiality against a class of alternatives which includes the RNBUE distributions based on the empirical laplace transform

A scale-free test for exponentiality is proposed which is consistent within an extended set of models, including, but not limited to, the “renewal new better than used in expectation” (RNBUE) class of life distributions. The limiting null distribution of the test statistics is derived, and the approximate local Bahadur efficiency is calculated for several families of alternatives. Finite-sample properties of the proposed procedures are investigated via simulation. Bibliography: 24 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 339, 2006, pp. 63–77.     

On the dynamical Casimir effect in a one-dimensional contracting cavity

The dynamical Casimir effect is analyzed in the framework of the S-matrix formulation for a one-dimensional cavity that exhibits contraction at a constant rate over a finite time interval. The exact solution to the problem is presented. It is demonstrated that the efficiency of the creation of pairs nonmonotonically depends on the contraction time. This is due to the fact that the particles are only created at the moments corresponding to the acceleration and stopping of the moving boundary, so that the contributions of these processes on the number of the created particles interfere with each other. The parameters that correspond to the optimal creation of pairs and the stability of a vacuum are presented. The effect of the finiteness of the cavity-boundary acceleration on the results obtained is studied.     

On the effect of magnetic fields on alloys with isothermal kinetics of martensitic transformation

The effect of magnetic treatment on the isothermal martensitic transformation in the Fe-24% Ni-4% Mn alloy has been investigated. The martensitic transformation in a dc magnetic field at liquid-helium temperature has been analyzed.