The stability of the state of rest of a heated infinite horizontal layer of a viscous heat-conducting fluid (the Rayleigh-Benard problem) is considered. The equation of state for the fluid takes into account the nonmonotonic temperature and pressure dependence of water density. Instability of the mechanical equilibrium with respect to small monotonic perturbations is studied. The effect of the problem parameters on the Rayleigh numbers and their corresponding critical motions is investigated numerically using linear theory. Numerical investigation of the spectral problem is based on the Godunov-Abramov orthogonalization method. The calculation results are compared with the wellknown results for the limiting case where the density is considered a quadratic function of temperature and does not depend on pressure.Introduction. Interest in the Rayleigh-Benard problem for an anomalous fluid is motivated by the recent studies performed at Lake Baikal. The results of observations obtained using modern instrumentation indicate the existence of a deep mixing mechanism in the lake due to transport of Lake Baikal surface water to bottom regions [1,2]. There are several hypotheses to explain this phenomenon. One of these hypotheses is based on the effect of anomalous thermal expansion of water.If the pressure-density relation is ignored, the water density is a nonmonotonic function of temperature. This function reaches a maximum at a temperature approximately equal to 4 • C (the so-called thermal-expansion inversion temperature). In this case, the equation of state for water can be written as

To study the seroprevalence of Lawsonia intracellularis among the pig livestock of Ukraine. The research was conducted in the laboratories of the Institute of Veterinary Medicine of NAAS and in pig farms. Were studied 653 samples of pigs’ serum of different age groups from17 pig farms with breeding stock of 40 456 sows. To study seroprevalence was used a test system for enzyme-linked immunosorbent assay based on monoclonal antibodies bioScreen Ileitis Antibody Test ELISA Svanovir®Lawsonia intracellularis (Boehringer Ingelheim Svanova). Serological tests have provided evidence that the pathogen was circulating in the herd. According to the research results, 46.4% of seropositive animals were found. Seropositive pigs were found in all studied farms, namely – among sows – 74.0%, replacement gilts – 79.6%, growing pigs – 2.5% and fattening pigs – 59.8%. The high level of seroprevalence among replacement gilts and sows of the 1st farrowing indicates the circulation of the pathogen in the herd, as well as the manifestation of morbidity in the fattening group, where was the highest rate of positive serum samples. From the 17 examined farms, only one farm was found where no seropositive animals were detected. According to our observations, proliferative enteropathy in pigs of Ukrainian pig farms has signs of chronic course, especially it is common in pig farms that import replacement gilts from abroad, where antibiotics are prohibited or restricted in donor farms. The results of serological tests allowed us to reconfirm that the spread of the disease is increasing in Ukrainian pig farms. Compared to 2015, the percentage of seropositive animals increased by almost 10%. The typical serological profile for Lawsonia intracellularis which is characteristic of our studied farms allowed us to conclude for which age groups of pigs and for which technological period of raising swine it is necessary to develop and implement measures for treatment and disease prevention. To control the disease, it is highly recommended to conduct constant monitoring of the farm’s well-being against ileitis (send, in addition to faecal samples for PCR testing, also serum for ELISA testing).