Head of sector, acting head of the Computational Geophysics Division of the M.V. Keldysh Institute for Applied Mathematics, RAS. Assistant professor. Finished the Electrodynamics and Quantum Theory Department of Faculty of Physics, MSU in 1962.
Ph.D. thesis — “On the asymptotic of transport equations”, 1965.
Ill-posed problems, stochastic processes, theory of approximation.
Mechanics and physics of multi-phase media, phenomena in porous media, difference schemes for some classes of mathematical physics problems (filtration, elasticity theory).
The Ph.D. thesis of Pergament (Rakhmatulina) was dedicated to the diffusion approximation validation and refinement for the neutron and electromagnetic field particle transport equation. By the same token she has constructed the uniform-in-a-segment asymptotic expansions of the integrals with the δ-function-like and decreasing kernels.
A.Kh. Pergament has developed the method that is based on the deployment of optimal approximations that ensure the minimal error for the given number of the approximation parameters. In addition the approximation accuracy corresponds by order of magnitude to values of diameter of compactums the solutions belong to. For determining the number of parameters the testing criteria of statistical hypotheses were used. On the basis of proposed algorithms the program complexes were created for processing the data received by means of the Roentgen methods of plasma diagnostics that were applied in the Kurchatov Institute.
She has carried out a work on the creation of program complexes for the mathematical modeling of the oil-gas field's evolution processes, including the man-caused consequences connected with the tangential tensions initiation.
About 100 published papers. [List (in Russian) of publications]
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