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.