Issue 1, 2018

Yu. P. Pyt'ev

A mathematical formalism for subjective modeling, based on modelling of uncertainty, ref lecting unreliability of subjective information and fuzziness that is common for its content, is presented in the article. The model of subjective judgments on values of an unknown uncertain parameter x ∈ X of the model M(x) of a research object is defined by the researcher–modeler as a spacea (X,𝒫(X), Pl˜x, Bel˜x) with plausibility Pl˜x and believability Bel˜x measures, where x is an uncertain element taking values in X that models researcher–modeler’s uncertain propositions about an unknown x ∈ X, measures Pl˜x and Bel˜x model modalities of a researcher–modeler’s subjective judgments on the validity of each x ∈ X: the value of Pl˜x( ˜x = x) determines how relatively plausible, in his opinion, the equality ˜x = x is, while the value of Bel˜x( ˜x ̸= qx) determines how the inequality ˜x ̸= qx should be relatively believed in see Subsection 1.3. Versions of plausibility Pl and believability Bel measures and pl- and bel-integrals that inherit some traits of probabilities, psychophysics and take into account interests of researcher–modeler groups are considered. It is shown that the mathematical formalism of subjective modeling, unlike “standard” mathematical modeling, ∙ enables a researcher–modeler to model both precise formalized knowledge and non-formalized unreliable knowledge, from complete ignorance to precise knowledge of the model of a research object, to calculate relative plausibilities and believabilities of any features of a research object that are specified by its subjective model M( ˜x) , and if the data on observations of a research object is available, then it: ∙ enables him to estimate the adequacy of subjective model to the research objective, to correct it by combining subjective ideas and the observation data after testing their consistency, and, finally, to empiric-ally recover the model of a research object. aA space (X,𝒫(X), Pl˜x, Bel˜x) , is formally equivalent to a fuzzy space (X,𝒫(X), P, N) with possibility P and necessity N measures, see remark 1.1 in [1]

V. L. Frolov$^{1,2}$, V. O. Rapoport$^1$, E. A. Shorokhova$^1$, M. Parrot$^3$, J. -. Rauch$^3$

The results of the DEMETER satellite mission for 2005–2010 are summarized. The characteristics of electromagnetic and plasma perturbations induced in the F2 layer of the Earth’s ionosphere by the high-power HF radio waves from the SURA heating facility are analyzed.

Structural, electronic and optical properties of cubic Y2O3: First-principles calculations

W. Zeng$^1$, Q. Liu$^2$, Z. Liu$^3$

Structural, electronic and optical properties of cubic Y$_2$O$_3$ were studied using the plane-wave ultrasoft pseudopotential technique based on the first-principles density-functional theory (DFT). The ground-state properties were calculated and these results were in good agreement with the previous work. Furthermore, in order to understand the optical properties of cubic Y2O3, the complex dielectric function, refractive index, extinction coefficient, optical reflectivity, absorption coefficient, energy-loss function and complex conductivity function were calculated, which were in favorable agreement with the theoretical and experimental values. We explained the origin of the absorption peaks using the theories of crystal-field and molecular-orbital bonding and investigated the relation between electronic structure and optical properties.

P. Zhang

Gaussian profile is conventionally assumed as the probe shape of the incident electron beam in theoretical analysis of dimensional measurements by a scanning electron microscope (SEM). However, it is not suitable for samples with small and tiny structure. In this paper, a model of a focusing electron beam with finite width due to aberration was used in simulating the SEM image of gold particles/balls on a carbon substrate. An effective electron beam shape (EEBS) was displayed and was found that it deviates significantly from the Gaussian profile. The difference between images simulated by Monte Carlo method with ideal electron incident beam, electron beam focusing model and with ideal beam incident then convoluted by Gaussian profile were discussed in detail. Furthermore, the influence of external electric field effect: full extraction and no extraction for imaging were studied.

A. G. Khundjua, A. Ptitsin, E. A. Brovkina

The internal structure of experimentally observed self-accommodation complexes of martensite crystals, which is determined by the system of twinning planes, is studied in this work. The direct correlation of the construction type of the complexes with the subgroups of the austenite lattice symmetry group is shown.

V. I. Kozlov

It is shown that the effective uniaxial anisotropy field that is usually applied in thin magnetic films (TMFs), which is noncollinear to the magnetization vector, is insufficient for deeper understanding of these processes, although it explains many physical processes in films. The analysis of the magnetization discontinuity in films under certain conditions yields the component of the effective uniaxial anisotropy field collinear to the magnetization vector. This component explains the magnetization discontinuity and allows one to speak of the total effective uniaxial anisotropy field in TMFs.

E. E. Shalygina, A. V. Makarov, A. M. Kharlamova

The results of investigation of the structural and magnetic characteristics of Co/Cu/Co thin-film systems obtained by magnetron sputtering on glass substrates are presented. The thickness of the cobalt layer in all samples was 5 nm and the thickness of the copper layer was varied from 0.5 to 4 nm. The saturation field HS of the studied samples was found to oscillate in magnitude with changes in the copper-layer thickness with a period on the order of 1 nm. The maximum values of HS are observed for the thin-film systems with t$_{Cu}$ = 1.4, 2.2, and 3.2 nm. The hysteresis loops measured for these systems in a magnetic field applied along the easy magnetization axis of the samples have a two-stage shape, while for the samples with other values of t$_{Cu}$ the hysteresis loops are rectangular. These data are explained by the presence of exchange coupling between the ferromagnetic layers through a copper spacer and its oscillating behavior with changing t$_{Cu}$.

A. L. Delitsyn$^{1,2}$

The distribution of special points of dispersion curves for an anisotropic filled waveguide is considered. The existence of special curves is substantiated for some relationship between anisotropy coefficients. These points are connected with complex and backward waves. It is proven that the curve of special points is an ellipse.

K. V. Zhukovsky

A particular solution of the hyperbolic heat-conduction equation was constructed using the method of operators. The evolution of a harmonic solution is studied, which simulates the propagation of electric signals in long wire transmission lines. The structures of the solutions of the telegraph equation and of the Guyer–Krumhansl equation are compared. The influence of the phonon heat-transfer mechanism in the environment is considered from the point of view of heat conductivity. The fulfillment of the maximum principle for the obtained solutions is considered. The frequency dependences of heat conductivity in the telegraph equation and in an equation of the Guyer–Krumhansl type are studied and compared with each other. The influence of the Knudsen number on heat conductivity in the model of thin films is studied.

E. E. Bukzhalev

A sequence converging to the solution of the Cauchy problem for a singularly perturbed weakly nonlinear first-order differential equation is constructed. This sequence is asymptotic in the sense that the distance (with respect to the norm of the space of continuous functions) between its nth element and the solution to the problem is proportional to the (n+1)th power of the perturbation parameter. Such a sequence can be used to justify asymptotics obtained by the boundary function method.

A. V. Borisov, E. A. Stepanova

A simple phenomenological formula for the gluon distribution function in a proton is proposed. The reported results of calculations of the cross section of Higgs boson production via gluon fusion with higher-order QCD radiative corrections are reproduced using this formula and the one-loop amplitude.

V. A. Gazaryan$^{1,2}$, J. A. Kurbatova$^3$, T. A. Ovsyannikov$^1$, N. E. Shapkina$^{1,4}$

A statistical analysis of periodic and cyclical components of time series of meteorological parameters was conducted for the 40-year observation period in the southwest of the Valdai Hills by classic seasonal decomposition and Fourier analysis. The dependence of the obtained OLS estimates of linear-regression models of meteorological parameters on a length of the smoothing interval was analyzed. Cyclical fluctuations in the time series of temperature with periods of 8 and 3 years and those of rainfall with periods of 3.5 and 10.5 years were detected and analyzed.

V. V. Varlamov$^1$, V. D. Kaydarova$^2$, M. E. Stepanov$^2$

The cross sections of partial photoneutron reactions for 98Mo were evaluated. These cross sections are free from the shortcomings of various methods for neutron multiplicity determination used at the beams of quasimonoenergetic annihilation photons and bremsstrahlung radiation. New data on the cross sections of reactions ($\gamma$, 1n), ($\gamma$, 2n), and ($\gamma$, 3n) were obtained using the experimental–theoretical method for evaluation of cross sections of partial reactions satisfying the introduced physical reliability criteria. It is demonstrated that considerable deviations of the experimental cross sections from the evaluated ones result from an inaccurate sorting of neutrons between channels with a multiplicity of 1, 2, and 3.

V. P. Zarubin$^{1,2}$, A. S. Bychkov$^{1,2}$, A. A. Karabutov$^{1,2}$, V. A. Simonova$^{1,3}$, I. A. Kudinov$^1$, E. B. Cherepetskaya$^2$

Laser ultrasound tomography for profilometry of solid objects is proposed. This approach provides high spatial resolution, high efficiency and ability to profilometry contaminated objects or submerged in liquids objects. Algorithms for tomograms reconstruction and recognition of objects profiles using the NVIDIA CUDA parallel programming technology are investigated and implemented. A prototype of the real-time laser ultrasonic profilometer is tested on solids of revolution. The proposed method allows determining the position of solids surfaces with approximation accuracy of up to 16 microns in real time.

M. G. Milkov$^1$, V. B. Voloshinov$^1$, L. I. Isaenko$^{2,3}$, V. N. Vedenyapin$^2$

Acousto-optic interaction in an optically biaxial crystalline medium under propagation of light close to one of the optical axes of a potassium arsenate titanyl KTiOAsO4 crystal has been studied. The experimental dependences of the intensity of a diffracted optical beam on the angle of light incidence on an ultrasonic wave have been obtained. It has been shown that a flat cut of a wave-vector surface provides development of an ultra-wide-aperture and ultra-wide-band acousto-optic def lector to control radiation in the visible and infrared electromagnetic spectral ranges.

K. I. Deshko, V. A. Chernikov

The operation of a miniature magneto-plasma compressor with low-voltage power-supply system was studied experimentally and the current and voltage drop under discharge were measured. It was found that the voltage drop remains practically constant during discharge and amounts to a few tens of volts. The performed electrotechnical analysis made it possible to determine the efficiency of the power-supply system depending on the initial voltage of the energy storage, the discharge burning voltage and the discharge circuit parameters (capacitance, inductance, and resistance).