The method of integral transformations is used to study the process of bodies heating and cooling. As a result of theoretical calculations the regime of soil freezing depending on the ambient temperature was established. Laplace transformation is practically used to determing patterns temperature of constructed concrete dams, building grounds

The article is devoted to the current problem of differential diagnosis of diseases of viral etiology in small domestic animals. Viral diseases of dogs and cats are widespread among both high-breed and outbred animals. The spread of diseases is facilitated by an increase in the number of small domestic animals, the popularization of pet keeping, and cross-border operations related to the movement of animals. The possibility of using means and methods of diagnosing adenovirus infection in cattle, tentative diagnosis and differentiation of infectious hepatitis in dogs from plague of carnivores and parvovirus enteritis is being considered. Reducing the timing of diagnosis helps to increase the effectiveness of ongoing therapeutic and antiepizootic measures. The analysis of the place of carnivorous infectious hepatitis in the structure of the incidence of dogs is given. The article describes the research in the field of the possibility of using the established antigenic relationship of representatives of the adenovirus family for the in vivo and posthumous diagnosis of infectious diseases of small pets. The authors proposed a method for performing the production of serological reactions for the diagnosis of infectious hepatitis in dogs using diagnostic tools for adenovirus infection in cattle.

The article is devoted to the current problem of differential diagnosis of diseases of viral etiology in farm animals. Viral diseases are currently widespread, occupy a leading role in the infectious pathology of farm animals, causing enormous economic damage. Given the magnitude of animal vaccine prophylaxis, in order to increase the effectiveness of antiepizootic measures, the urgent issue i s the development of methods for the rapid and effective detection and differentiation of field and vaccine strains of the infectious rhinotracheitis virus in cattle. The possibility of using a polymerase chain reaction to identify and differentiate a vacc ine strain from epizootic strains and isolators of the cattle infectious rhinotracheitis virus is considered. In the process of research, a PCR-RFLP analysis method was developed to detect the IRT virus in the test material. The PCRRFLP analysis method was used to identify and differentiate the vaccine strain TK-A form epizootic strains and isolators of the cattle IRT virus. The principle of PCR, based on repeated repetition of DNA cycles, annealing and synthesis, which leads to an increase in the number of specific DNA fragments of the pathogen, allows you to take into account the results of PCR in an agarose gel. Analysis time is about 30 hours. The sensitivity of detecting viral DNA is 1-10 picograms (102 TCD). Due to characteristics such as relative simplicity and reaction rate, high sensitivity, specificity and reproducibility, PCR has recently become widespread in basic and applied research in various fields of biological science, including veterinary virology. The results obtained during the studies show that the use of PCR-RFLP allows to differentiate field and vaccine strains and isolates of the IRT virus with a high degree of reliability. The use of PCR -RFLP analysis increases the efficiency and informativeness of studies in the molecular epizootol ogy of cattle RTI, as it allows not only to identify the DNA of different virus strains regardless of their nature, but also to differentiate between them, including differentiating the strain TK-A used for the production of attenuated vaccines against epizootic strains and isolates of the virus.

Singularly perturbed partial differential equations with small parameters with higher derivatives deserve special attention, which often arise in a variety of applied problems and are used in describing mathematical models of diffusion processes, absorption taking into account small diffusion, filtration of liquids in porous media, chemical kinetics, chromatography, heat and mass transfer, hydrodynamics and many other fields. It is necessary to consider the creation of an asymptotic classification of solutions of singularly perturbed equations using a well-known approach to solving the boundary value problem. In this case, the singular problem is understood as the problem of constructing the asymptotics of the solution of the Cauchy problem for a system of ordinary differential equations with a small parameter with a large derivative. The asymptotics of the solution in all cases is based on the last time interval or the construction of a boundary value problem for a system with a weak clot in an asymptotically large time interval. Purpose - to construct and substantiate the asymptotics of solving a singular initial problem for a system of two nonlinear ordinary differential equations with a small parameter; To date, a number of methods have been developed for constructing asymptotic expansions of solutions to various problems. This is the method of boundary functions developed in the works of A.B. Vasilyeva, M.I. Vishik, L.A. Lusternik, V.F. Butuzov; the regularization method of S. A. Lomov, methods of averaging, VKB, splicing of asymptotic decompositions of A.M. Ilyin and others. All the above methods allow us to obtain asymptotic expansions of solutions for wide classes of equations. At the same time, such singularly perturbed problems often arise, to which ready-made methods are not applicable or do not allow to obtain an effective result. Therefore, the development of methods for solving equations remains a very urgent problem. As a result of the study, an algorithm for constructing an asymptotic classification of the initial solution of the problem with a singular perturbation is given, and approaches to estimating the residual term are also shown.

It is known that an increase in the volume of production in any sphere of production as a consequence increases the intensity of anthropogenic impact on the environment, including the atmosphere. This problem is especially typical for oil refineries. On the one hand, this is due to the complexity of oil refining processes and the release of various hydrocarbon compounds into the atmosphere during processing. Therefore, when implementing sustainable ecological and economic development in the Azerbaijani regions that are associated with oil refining, an increase in the volume of products should not create an increase in environmental impact. This problem is considered one of the factors directly affecting the economic situation of the enterprise, as well as creating certain environmental, social and economic problems for society as a whole. The purpose is to study the possibility of using the correlation-regression method in solving the problem of determining the presence of the decapling effect. The relationship between the volume of petroleum products produced and the amount of pollutants released into the atmosphere is random and is characterized by stochastic and statistical dependence. At the same time, on the basis of a mutual comparison of the methods of correlation and regression analysis and the method of production function, the effectiveness of correlation and regression analysis is determined. The methodological basis of the work was the scientific works of scientists-economists, mathematicians providing the definition of the decoupling effect at industrial enterprises. In the presented methodology, the obtained estimates of the performed in real time vary depending on the values of the set parameter. When developing the presented methodology, the STATISTIKA software package was used. This program was developed by StatSoft. Based on the obtained and experimentally verified data, the equation of linear regression dependence is determined. During the research, it was found that in some cases it is not possible to evaluate the statistical characteristics of a random variable or it is accompanied by serious errors. Therefore, when processing data, instead of mathematical expectations and variances, we used selective mathematical expectations and variances. The analysis of the ecological and economic situation of oil refineries based on correlation and regression analysis allows us to determine the presence of the decapling effect. The obtained correlation coefficient between the volume of production oil products and the volume of emissions into the atmosphere shows that there is no statistically significant relationship between these parameters. Thus, there is an achievement of the decoupling effect between the production of petroleum products and the volume of emissions of pollutants into the atmosphere.

Main problem: the article is devoted to the issue of designing basic recipes for dairy products using mathematical modeling methods. The author analyzed the problems in the field of food technology and concluded that mathematical modeling is used in the following areas: clarification of technological process modes, designing recipes and assessing the quality of finished products, as well as predicting the shelf life of new products when they are put into production. The use of dihydroquercetin as a drug that prevents the oxidation of milk fat in the design of dairy products is substantiated. Mathematical modeling was carried out on the basis of experimental and analytical material obtained in laboratory and production conditions. Based on the maximum value of the objective functions, the optimal normalized mixtures and the maximum allowable concentration of dihydroquercetin were selected. The analysis of the received mathematical dependences and models is carried out, the system of linear equations is made. Purpose: to study the effect of natural bioflavonoid antioxidant on the oxidative processes of milk fat and the viability of lactic acid cultures and their associations by mathematical modeling in order to use it in the technology of a new product; conduct an analysis of mathematical dependencies and models, compose a system of linear equations. Methods: the article uses the method of mathematical analysis and the matrix method. Results and their significance: a mathematical model was developed for the dependence of the viability of probiotic cultures on the mass fraction of dihydroquercetin when designing recipes for a creamy-protein curd product, a matrix of the chemical composition of dairy ingredients was presented, and a system of linear equations for basic recipes was compiled. In the course of the study, the spatial configurations of dihydroquercetin, as well as its effect on the oxidative processes of milk fat, were studied. Mathematical modeling of experimental data on the study of the effect of dihydroquercetin on the viability of microorganisms with probiotic properties was carried out. The normalization of the complex of obtained results on the study of the influence of the mass fraction of dihydroquercetin on the fermentation process was studied. Controlled factors characterizing the process of fermentation of model media with dihydroquercetin have been determined. A rationing of the dihydroquercetin complex of more than 0.50% was established; the target function decreases to its minimum value of 0.53 with a mass fraction of dihydroquercetin of 1.00%.

The present stage of development of power systems is characterized by the need to increase their intelligence, that is, the formation of an environment capable of solving the problems of effective management of all components included in the power system. One of the features of modern energy systems is an active consumer, that is, a consumer who has the opportunity to optimize the schedule of loading their capacities, planning energy consumption, intellectualization of energy consumption. In addition to the fact that there are digital systems for collecting, processing and presenting information, as well as transmitting this information via the Internet, to solve the most difficult task of managing power systems, it is necessary to develop a large number of models adequate to real processes that can describe the processes taking place in the power system under consideration. The purpose is to develop models capable of adequately describing the interrelated processes occurring in the considered elements of the power system, as well as in the aggregate of related elements; development of methods that allow solving problems of effective control of elements of energy systems on the basis of the proposed intelligent models. To solve the problem of increasing the intelligence of the power system, nonlinear adaptive models of electrical complexes of an energy-intensive enterprise included in the power system were developed on the basis of balance equations and artificial intelligence methods. The production of alumina with the properties of inertia, nonlinearity and closure is chosen as the production under consideration. This type of production was chosen as the most difficult to predict due to the unpredictability of changes in energy consumption during the transition to other modes of its operation, associated, for example, with the receipt of raw materials with a different chemical composition for processing. Static and dynamic models of energy consumption of electrotechnical complexes with continuous inertial nonlinear closed production based on artificial intelligence methods have been developed, which makes it possible to eliminate the need to use long time series of retrospective data. For the considered type of continuous energy-intensive production, dynamic characteristics of energy consumption and technological processes are obtained from the main controlled parameters, which make it possible to predict emergency situations and partly man-made disasters. On the basis of a genetic algorithm, a multiparametric optimization problem of energy management of continuous production has been solved, taking into account technological parameters and cost factors.