Stability of nonlinear waves and patterns and related topics.

Periodic and localized travelling waves such as wave trains, pulses, fronts and patterns of more complex structure often occur in natural and experimentally built systems. In mathematics, these objects are realized as solutions of nonlinear partial differential equations. The existence, dynamic properties and bifurcations of those solutions are of interest.

Travelling waves in the Holling-Tanner model with weak diffusion.

For a wide range of parameters, we study travelling waves in a diffusive version of the Holling-Tanner predator-prey model from population dynamics. Fronts are constructed using geometric singular perturbation theory and the theory of rotated vector fields. We focus on the appearance of the fronts in various singular limits.

[The modification of the M.D. Patsiora's operation by portal hypertension].

The direct transcutaneous transhepatic portography was performed in 85 patients with hystologically confirmed liver cirrhosis, portal hypertension and varices of the esophagus and stomach. It was found out, that the left gastric vein partakes the varicous transformation in 100% of cases. The least had an isolated division in 27% of the studied patients.

[Pathogenesis of esophageal and gastric varicose veins formation in patients with liver cirrhosis].

Research Objective: studying the features of the collateral venous blood flow and the basic ways of the formation of gastroesophageal varices in patients with cirrhosis and portal hypertension.

Methods: The following analysis is based on the interpretation of results from percutaneous transhepatic splenoportography in 85 patients. It has been established that in all 85 patients the left gastric vein plays a key role in the formation of gastroesophageal varices.

[Autonomic dysfunction syndrome and diabetic cardiac autonomic neuropathy in children with diabetes mellitus type I. The correction method].

We assessed the state of the autonomic nervous system in 90 children with diabetes mellitus type I. The autonomic dysfunction syndrome was found in 58,9% and diabetic cardiac autonomic neuropathy in 28,9% of patients. We revealed the high risk of the development of diabetic cardiac autonomic neuropathy in children with diabetes mellitus type I in the presence of the autonomic dysfunction syndrome.