The binomial conditional autoregressive model of spatio-temporal data is constructed. The probabilistic properties of the model constructed are studied. The maximum likelihood estimators of parameters of the model based on the observed spatiotemporal data are calculated. The results of computer experiments are presented.

For any sufficiently large positive integer Q≥Q₀(n)we prove that there exist complex circles K₁, K₂ є C of radii r₁ and r₂, max(r₁, r₂)<c₁(n)Q ^-1/4 , c1>c₀₁(n), containing no algebraic numbers αєK₁, βєK₂ with heights bounded by Q, max(H(α), H(β))≤Q. We also show that if the radii of the circles K₁ and K₂ obey the condition min(r₁, r₂) >c₂ (n)Q ^-1/4, c₂>c₀₂(n), then the number of algebraic numbers lying in these circles is bounded from below by c₃(n)Q⁵r₁²r₂².

In the article we obtain an upper bound of the amount of integral polynomials from a special class of bounded degree and height with small value of derivative at а root of the polynomial on a given interval.

In this article we show that the clustering minimum biclique completion problem is NP-complete in the class of P₄-free bipartite graphs. We have also proposed a dynamic programming algorithm for that problem restricted to 2K₂-free bipartite graphs.

This article considers three mixed problems in the cylindrical area for the second-order linear hyperbolic equation with an operator which is weakly loaded with an operator of the same type. Coefficients of the loading operator are small enough. This demand is expressed through the estimates of the characteristic polynomial. The research of problems reduces to solving operator equations in suitable functional spaces. Existence and uniqueness of strong solutions were proved with the use of functional analysis methods.

The article is devoted to a perspective of optimization of the integrated and characteristic base of modular arithmetics (MA). It is shown that at the minimum code redundancy, this problem is successfully solved for a class of non-modular operations which are realized by means of interval and index characteristics and the interval and modular form of integers. Proposed is a new expanded algorithm of calculation of integrated characteristics of the minimally reductant modular code allowing one to build MA configurations both over the ranges of non-negative numbers and over the symmetric ranges. With a length of the minimally redundant modular code from 8 to 64 figures, the synthesized algorithm is superior to the known analogs for calculations connected with interval and index characteristics in time-consuming by a factor of 6–34.4 and in table memory-consuming by a factor 3.5–31.5.

Within the framework of premetric electrodynamics, it is shown that the macroscopic field equations are invariant under generalized gauge transformations of Cabibbo–Ferrari type, the special case of which are the "Serdyukov–Fedorov transformations". However, the invariance of the complete system of equations, including the linear equations of general form and potentials, takes place only under the additional condition that has been found in most general form.

Classification bases of the synthesis of optical systems are presented: a classification of optical schemes, modules, elements; their types; cataloguing optical systems; a method of formalization of knowledge by means of decision tables; an index of complexity of an optical scheme, and some heuristic rules of formalization of transition from requirements of a preliminary specification to a choice of the element base of an optical system.

The photoluminescence (PL) of the chalcogenide semiconductor compound CaGa₂S₄:Pr³⁺ was studied in the temperature range 10–300 K under nanosecond pulsed laser excitation at 456 nm. The PL spectrum consists of a number of intense lines at 494, 631, 654 and 741 nm, formed by electronic transitions in praseodymium ions from ³P₀ to ³H₄, ³H₆, ³F₂ and ³F₄ levels, respectively. It was found that the rise in the concentration of praseodymium ions in CaGa₂S₄:Pr³⁺ from 3 to 7 at. % resulted in a double increase of the PL intensity. Temperature quenching only by 50 and 75 % of the PL intensity of CaGa₂S₄:Pr³⁺ with 7 and 3 at. % Pr³⁺ ions concentration, respectively, was obtained in the range 10–300 K. It is shown that at 10 K the decay time constants of the most intense lines of the PL are between 3.9–4.8 μs. The decrease of the PL decay time constants by less than 0.1 μs with increasing the temperature up to 300 K and the appearance of a fast component with a duration constant of about 2.15–1.1 μs in the temperature range 220–300 K were obtained.

Calcium pectinate microparticles with a hydrodynamic diameter of 2–6 μm were synthesized by the spray drying technique. The approach allowing one to entrap in them up to 30 wt. % of miramistin has been developed. It has been shown that all miramistin entrapped in microparticles fully releases in 2 hours in the acidic medium (pH 2.0). In the physiological solution, about 66 % of miramistin releases in 48 hours. In the alkali solution, less than 5 % of miramistin releases in 2 days.

This article presents the research results of tetrazolation of a commercial copolymer of acrylonitrile, methyl acrylate and 2-acrylamido-2-methylpropanesulfonic acid. Transformation of nitrile groups into tetrazole-5-yl moieties was found to proceed smoothly in dimethylformamide using NaN₃–NH₄Cl as an azidation system reaching 90–95 % conversion of nitrile groups. Alkylation of poly-5-vinyltetrazole with halogen and hydroxyl substituted bis-alkylating agents have been found to produce cross-linked polymers. The degree of cross-linking can be regulated by changing the polymer – alkylating agent ratio.

With an increase of anthropogenic transformation of the natural environment from relatively natural complexes to total agricultural and recreational-urbanized suburbs, it is revealed that the number of owl species decreases and the species composition of their assemblage changes. In this direction, the species composition as a whole shows an increase in the dominance of its relative lack of natural Paazierre forest to the absolute domination of one species in highly transformed territories, as well as the disappearance of rare species, reducing the representation of forest species and the increase of synanthropic species, and other positive and negative changes in the proportions of different species at various stages of transformation. All these changes in the species composition occur on the background of reducing the total density of populations of owls and differently directed changes in the density of populations of species of owls in the territories of different anthropogenic transformation. It is also found that with an increase of anthropogenic transformation of the natural environment, the size structure of owl assemblage changes significantly in the direction of increasing a proportion of smaller species.

The article contains the research results of the common carp influence on macrozoobenthos in lake ecosystems. The reduction of the benthos abundance and its biomass in the littoral of the fish-stocking reservoir is established. It is found that the benthos structure – the increase in a relative abundance of Diptera (Chironomidae sp.) larvae changes due to the grazing of large larvae of Odonata, Ephemeroptera, Megaloptera and Trichoptera by big carp.

In experiments on rats, the technique of application of mesenchymal cells into the region of the receptive or conductor paths of cranial nerves (I and V pair) was perfected for the natural movement of these cells to the central nucleus of the nerve, and then into the damaged areas of the brain. It is found that after the modeling of a local injury of the precentral gyrus, the mesenchymal cells implanted into the submucosa of the nasal cavity have been visualized in the olfactory bulb and in the damage area in 1 hour. After the pre-damaged areas of the cerebellar cortex, the mesenchymal cells introduced into the Meckel area are found in 1 hour in the central nuclei of the trigeminal nerve in the damage area.

The parameters of specific triidothyronine binding with lymphocytes of patients operated for highly differentiated thyroid cancer and received comprehensive treatment, on the average, for 15 years are studied. These patients have revealed a significant increase of interaction affinity and a decrease in the number of binding places in comparison with these characteristics of the persons of the control group. A relationship of the studied indices between the factors of treatment and its duration is shown. Patients with overweight have revealed a significant increase in interaction affinity and a decrease in the number of binding places as compared to patients with normal weight, which explains a decreased need in triiodothyronine in this group of patients.

Different-rank elements of the hydrocarbon accumulation system in the intersalt complex of the Pripyat basin being oil-and-gas accumulation areals and zones have been divided into regions. All the objects divided into regions have been subdivided into the traditional, non-traditional, and complex ones according to the types of their natural reservoirs.

The theoretical analysis of the influence of thermal processes on the energy separation efficiency in a Ranque vortex tube has been performed using two models of motion of a viscous incompressible medium in the approximation of a plane twisted flow. It is shown that the observed cooling effect in the vortex tube is caused, as a minimum, by three factors, viz., a radial flow in the vortex periphery zone, which is directed to the center; mechanical energy dissipation, and local flow local nonequilibrium.

A comparison of the calculated and experimental data allows one to draw a conclusion that a theoretical description of thermohydrodynamic processes occurring in a vortex tube should be based on the theory of a locally nonequilibrium flow, which takes into account the isentropic character of momentum transfer in a shear flow of a viscous medium.

A self-consistent mathematical model of nanoparticle deposition from a gas flow and a nanostructured film growth was developed. Qualitative estimates and simulation results are presented, which are in accordance with experimental data. During simulation it is found that at the inlet of the cylindrical reactor a large-scale morphology of a film thickness is formed which does not depend on its width. It is shown that the morphology of a deposited film can be optimized by controlling the width of an inlet nanoparticle beam and by an inlet gas temperature.

This article is devoted to the formation of the registry of the dictionary of the living Belarusian language in the 20 years of the twentieth century in comparison with the most important Russian, Polish, Czech, Serbian, and Ukrainian dictionaries. Special attention is drawn on the criteria for inclusion into a future dictionary of loan words, terms, narrowly regional dialect, slang, personal names, place names, and other layers of vocabulary, as well as on the structural features of the entry: combined clearance means of the entry, a lack of stylistic marks, mandatory non-anonymous illustration and linguistic passport of each lexeme or its meanings. Also, tasks have been revealed, which must decide a future academic dictionary: show the lexical composition of the Belarusian language and enrich it by including terminology and abstract vocabulary, thus allowing regulatory writings and having proved the independence of the Belarusian language.

The work is devoted to the study and a comprehensive analysis of economically useful qualities of daughters of Belarusian, Canadian, American, Swedish, and Hungarian selection sires. The influence of the origin of sires on the milk production of their daughters and the economic efficiency of milk production is examined.