The components of the system model describing the regulation of energy metabolism of cells in normoxia and hypoxia were developed.

Parametric models of the geometry of the lymph node were developed. Models were developed and topological properties of a network of fibroblastic reticular cells were analyzed. The features of lymph flow in the network of lymph node conduits were studied.

Joint research work with C. Dumontet, P. Nony. Mathematical modeling of variousdiseases: leukaemia, lymphoma, lymphodema, mucoviscidosis, thrombosis. Simulation of clinical trials.

Joint research work with A. Meyerhans. The study of the spread of viral infection in body tissues on the basis of reaction-diffusion and hybrid discrete-continuous models of immune response.

Joint research work with M. Koury. The mathematical model was developed, computer calculations and comparisons with experimental data of erythropoiesis functioning on the basis of erythroblastic islands were carried out. The development of multiple myeloma and its effect on erythropoiesis were investigated. Various treatment protocols of patients were modeled and compared with clinical data.

Joint research work with A. Bouchnita. Mathematical models and computer programs for describing the coagulation of blood in the stream considering biochemical reactions in the plasma and aggregation of platelets were developed. The terms of normal clot growth and thrombosis were obtained. Two articles are in print this year.

Necessary and sufficient terms for the boundedness of fractional maximal operators in general Morrie local spaces are for a wide class of admissible values of numerical parameters were obtained together with A. Gogatishvili. Sufficient and necessary terms for this kind of limitation for a certain range of parameters were obtained.

The terms that ensure the boundedness of Hausdorff operators in Morrie spaces were obtained together with E. Liflyand. The classes of Hausdorff operators for which the necessary and sufficient terms of boundedness coincide were described.

The problem of the limitation of various operators (Riesz potential, the maximum operator, Hardy operator) in local spaces of the Morrie type was studied together with the staff of this Institute (V. S. Guliyev, H. V. Guliyev, R. Mustafayev). A full list of collaborations can be found here.

Accurate stability evaluation for the variation of eigenvalues of nonnegative selfadjoint elliptic operators of arbitrary even order when changing the open sets on which they are defined were obtain with P. D. Lamberti, M. Lanza de Cristoforis, Feleqi E. This evaluation is expressed in terms of Lebesgue measure of the symmetric difference of open sets. The boundary terms of Dirichlet and Neumann were analyzed.

A full list of joint works can be found here