Вестник БГУ. Серия 1. Физика. Математика. Информатика

This paper presents the developed training and research laboratory equipment in laser physics including an yttrium aluminum garnet laser, continuous-wave and pulsed semiconductor lasers, systems for recording the temporal and energy characteristics of lasing, high-speed photodetectors, current generators of light-emitting and laser diodes, photodiode current meters, original sets of mechanic, optic, and fiber-optic elements. All the devices feature the latest trends in design and offer the possibilities for the electronic control enabling one to perform 13 laboratory works in laser physics, nonlinear and fiber optics. In the process of laboratory works students can study the modes of free running, active and passive Q-switching, mode locking; the methods of the lasing frequency detuning with the use of a dispersive-resonator dye laser; to investigate such nonlinear-optical phenomena as second harmonic generation and stimulated Raman scattering. During the laboratory works in fiber optics students can study the operating principles of fiber-optic communication lines and functioning of some components in fiber-optic and optoelectronic elements or analyze the features of radiation input into single- and multimode waveguides as well as the factors responsible for decay of laser radiation in the process of its propagation along the fiber; can breadboard fiber-optic transmission systems.

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In the paper the possibilities of using double-pulse laser atomic-emission spectroscopy for layer-by-layer analysis of silver coins are considered. A new method to establish the authenticity of silver-copper antique coins using the in-depth concentration distribution is suggested. It is found that double laser pulses provide minimum destruction of the sample surface and high analytical sensitivity required for nondestructive investigation of virtu and artefacts. The subjects of inquiry were ancient coins from a treasure dated the second half of the XVII century. The treasure was found in 1978 in Grichino village (Dzerzhinski district, Minsk region) by a local woman. 207 coins from this treasure were handed over to the numismatic museum of the Historic Faculty of the Belarusian State University. It was revealed that in authentic coins the concentration of silver was constant at all points of the sample within the range 25÷45 %. In the fake coins a silver coating with a thickness of 30÷50 μm was deposited on the copper base.

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To elucidate the photrodestruction mechanism in media with low dielectric permeability, the spectral-luminescant properties and photodestruction of the indotricarbocyanine dye HITC in dichlorobenzene and dioxane have been studied on oxygen saturation and in hypoxic conditions. It has been found that HITC dye in dioxane is in the form of an equilibrium mixture of contact ion pairs and free radicals. The differences in deformation of absorption spectra for the dye in the oxygen saturated solutions and at hypoxic conditions revealed upon the photoeffect point to the formation of different photoproducts and to the differing photodestruction mechanisms. The increased quantum yield of HITC photodestruction has been found when the ionic equilibrium was shifted to the increased numbers of the contact ion pairs of the dye in oxygenless solutions. Based on the study of the spectral, luminescent, and photophysical properties of the indotricarbocyanine dye HITC with different counter-ions, the possibility for concurrency of a radical photodestruction mechanism of polymethine dyes and of the principal mechanism of self-sensitized oxidation with a singlet oxygen has been demonstrated.

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Vibrational (IR absorption and Raman scattering) spectra for the reaction products of uranyl nitrate hexahydrate with NaOH and КОH have been studied. As a result of exchange reactions, the uranyl-ion coordinated nitrate groups are completely replaced by hydroxyl ions and various uranium and uranyl oxides or hydrates are formed. An analysis of the vibrations has been performed in terms of the frequencies of a free or coordinated nitrate group; comparison with the vibrations of the well-known uranium oxides and of the uranyl group 22 UO + has been carried out. Vibrational spectra of a free nitrate group are characterized by four vibrational frequencies 1050, 724, 850, and 1380 cm–1, among which the frequencies at 724 and 1380 cm–1 are doubly degenerate and attributed to E' symmetry of the point group Dзh. When this group is uranium coordinated, its symmetry level is lowered to C2v, all vibrations of this group being active both in Raman and IR spectra. The doubly degenerate vibrations are exhibited as two bands and a frequency of the out-of-plane vibration is lowered to 815 cm

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The effect of potassium and sodium hydrates on the spatial distribution of calcium, magnesium, and aluminum when the drops of aqueous solution of egg albumin are drying on the surface of a porous body (paper filter) has been studied using the multichannel atomic-emission laser spectrometry. It has been shown that previous coating of the substrate with albumin and potassium or sodium hydrates leads to a considerable decrease in the cationic motion of aluminum, calcium, and magnesium to the periphery on drying of the biologic liquid and to its reduced size. Varying the composition of hydroxides and the solution application procedure, one can reduce significantly the drop diameter thus improving the analytical sensitivity. At the same time, the possibility of competing reactions associated with reformation of more soluble metal compounds should be taken into consideration.

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On the basis of the even irradiation simulation onto the surface of the silicon wafer, covering formation of the phantom and actual images of the irradiation sources, the expressions were derived, describing distribution of the photon flow on the wafer area in dependence with on the geometrical dimensions of the camera and the distance from the wafer to the irradiation sources. On the basis of the conducted calculations there were determined the geometrical dimensions of the chamber and the place of the wafer positioning in it, ensuring the minimum unevenness of the photon flow onto its area. Meanwhile, it was indicated, that for each diameter of a wafer the appropriate geometrical dimensions of the chamber are required.

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In the given paper one can find description of the features of the instrument specifically designed to realize DOAS technique. The above device can be used as ground-based measuring equipment. The experimental registration of the spectra of scattered solar radiation at different angles of elevation has been performed at the Minsk ozone station. On the basis of data on slant column density, the estimation of nitrogen dioxide total amount is made. The instrument possesses a better relative aperture if compared to devices with fiber optic lens which is regarded as the main advantage. The data collected with this instrument can be used for remote monitoring of air quality in Minsk.

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The problem of definition of optimal locations for the Wi-Fi access points in the buildings, which is quite urgent at the present stage of the local information network modernization within enterprises, demands the assessment of the Wi-Fi signal level in various parts of the enterprise premises. To perform this assessment the effects of radio waves weakening when passing through obstacles (walls, partitions, etc.) should be considered, and this is connected with multiple repetition of a number of computing steps. In this article, various effects occurring from passing through the obstacles are considered, as well as the primary effects are highlighted and the abstraction from the secondary effects is performed (in order to reduce the computing complexity); the way of fast assessment of Wi-Fi signal power at the given distance is offered and the accuracy of received ratings is experimentally determined. The experiment on measurement of Wi-Fi signal power weakening is performed.

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Modern software development is based on the methods of its intellectualization. Software should solved not only well-posed problems, and determine the best ways to solve a variety of problems. Therefore it is need using special software with intelligent component responsible for the behavior and evolution of the program in different situations. Technology for creating software of medical images analysis and processing based on the using of tables interpreter with an intelligent agent, which is equipped with appropriate properties of communicating tags and functions. Such software can modify by yourself or with a simple user, without the intervention of specialists. The data table for each commands shell corresponds to estimates set, which are calculated on the basis of commands performance. Comparing table interpreter with the calculated estimates allow to intelligent agent makes a decision about formation of a new script. This script consists of image processing and analysis commands. Now, such an organization of software is unique and can to solve many problems of image processing and analysis. If intelligent agent has work mistake, developers or users can change interpreter script and influence to work of software. This technology has been successfully tested for analysis of histological images, and will be adapted to other problems that related to image processing. It is developing as pilot software QTIP, which is used for the diagnosis of disease on base histological images, and will be adapted for nanoscale imaging, aerial photography and satellite images.

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The paper describes the main approaches for creating interactive web environment for building 3D-applications. The modern development of graphics systems and technologies is urgent transferring of imaging to the next level, which greatly simplifies the development of 3D-objects. Scientific novelty of the approach is to create an integrated system for the implementation of graphics applications that abstracts the end user from the intermediate levels graphics creation and provides the ability to directly construct graphic scenes through a graphical interface on modern platforms such as Windows 7 and Android. The main concept of the proposed solution involves the creation of a set of classes and utilities that implement a common approach to graphics rendering and hide by the direct use of various mathematical models and graphics algorithms. This will allow a wider range of stakeholders to create the desired 3D-objects and scenes, spending minimal time to develop the necessary solutions.

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An implementation of Actor – Role design pattern by means of languages with static types is considered. The proposed approach is based on a realization of the association between roles and actors by means of the association class. The implementation of the association class is based on idioms of type promotion. The programming language C++ is used as a model language for the proposed implementation of Actor – Role design pattern. The source code of two frameworks for realization of role assignment and role choosing is presented. Dynamic type identification mechanism of the programming language C++ is used to determine which role is chosen for the actor.

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The article deals with a mixed problem for the vibration equation of a finite string with a time dependent oblique derivative in the boundary condition. It’s mean that dynamic force applies to the end of a finite string. Consider a case where a derivative in the boundary condition is not directed along the characteristics. There exists a unique classical solution of the mixed problem which is represented as a restriction of some function. This function is build by special method using the results which were obtained for the solution of a problem for a semi-bounded string. The method is similar with a reflection method for the solution of a mixed problem for a finite string with fixed ends. This method has a unique nature and it is considered for the first time in the article. Formulas of the solution of this problem and matching conditions between initial and boundary conditions have been found.

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A theorem on the stability and the totally stability of the zero solution for the system of nonautonomous differential equations is proved. The results are based on the method of semi definite Lyapunov’s functions. The resulting synthesis of known results of the direct method A. M. Lyapunov, I. G. Malkin and N. N. Krasovskii is based on the concept of B-stability. The B-stability of the equilibrium introduced by the author. It is «stronger» than the known properties of stability, but the «weaker» of asymptotic stability. Article provides an illustrative example.

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The stability properties of the essentially regular operators and of the corresponding essential spectrum under compact perturbations are discussed in this article. It is proved that the essentially regular operators occupy the intermediate position between Fredholm and normally solvable operators in Banach space but the stability properties of the essentially regular operators are different from the operators above. The reasons for instability of the essentially regular operators under compact perturbations are revealed and confirmed by the counterexamples. The addition conditions for the essentially regular operator and for the perturbing compact operator which provides the stability of the essentially regular operator under compact perturbation are displayed. The result for the stability of the essential spectrum corresponding to the essentially regular operators under compact perturbations in Banach space is given.

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We consider the problem of bandwidth selection in kernel estimation of the marginal probability density on the basis of sample from a stationary Markov process. Our criterion for bandwidth selection is the mean integrated square difference between the kernel estimator and the true marginal density. For dependent sample data this criterion contains an unknown joint probability density of the sample values. This considerably complicates the estimation problem. The paper suggests an approximation for the mean integrated square difference. This approximation takes into account the presence of dependence in the sample data, but at the same time does not contain the joint probability density. We also obtain an expression for the bandwidth that does not require any assumptions about the functional form of the unknown marginal probability density. The possibility of the practical application of the proposed approximation is demonstrated by the example of bandwidth selection in kernel estimation of marginal probability densities for the interest rates processes, which are described by three well-known models (Vasicek model, Cox – Ingersoll – Ross model and Ahn – Gao model). In addition, we obtain the explicit expression for bandwidth in a case of Gaussian kernel and Vasicek model. It is shown that for the models of interest rates processes, the proposed approximation has a significant advantage over the approximation of the mean integrated square difference, which is commonly used for bandwidth selection in the case of independent sample data.

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An m-ring, in which any superposition of its elements to be preserved under the even substitutions, is called 3-commutative. It is shown, that the class of such m-rings is a subvariety of the variety of null-symmetric m-rings, strictly containing the variety of commutative m-rings. It is proved, that any 3-commutative m-ring is an extension of a 3 commutative nil-m-ring by a direct sum of two ideals, the first of them being a commutative idempotent m-ring, where the multiplication coincides with the superposition, the other has null multiplication and respective to addition and superposition is an commutative reduced ring. For finite 3-commutative m-rings the above description is refined using extensions and semidirect products with participation of 3-commutative 0-nilpotent m-rings and commutative reduced rings or Boolean rings.

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Based on Markowitz’s portfolio theory we build a multicriteria Boolean problem with Wald’s maximin efficiency criteria. We obtained lower and upper bounds for the stability radius of a Pareto optimal portfolio of the problem in the case of the Chebychev norm l∞ in the portfolio and financial market state spaces and the Hölder norm lp , 1 ≤ p ≤ ∞, in the criteria space.

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