Laboratory Staff

Arziev Allabay Djalgasovich

Qoraqalpog‘iston bo‘linmasi mudiri More details →

Kalenbaev Kamalatdin

Kichik ilmiy xodim More details →

Nurjanov Berdax Orinbayevich

Katta ilmiy xodim More details →

Orinbaev Paraxatdiin Raxman o‘g‘li

Kichik ilmiy xodim More details →

Uzakbaev Nawriz Esengeldievich

Kichik ilmiy xodim More details →

Scientific Activity

Currently, the Karakalpakstan Branch conducts research in the following directions:

Kaplansky-Hilbert modules over the ring of measurable functions. Partial integral operators in Kaplansky-Hilbert modules over the ring of measurable functions are investigated. A variant of the Bukhvalov-type theorem for partial integral operators defined in ideal functional spaces of measurable real functions is considered. The spectrum of self-adjoint operators in Kaplansky-Hilbert modules over the ring of measurable functions is characterized.

JBW-algebras with strongly symmetric edges. The properties of Pierce projections in JBW-algebras with strongly symmetric edges are studied, showing that linear isometries map mutually orthogonal geometric tripotents to mutually orthogonal tripotents, and surjective isometries are characterized. It is shown that the geometric Pierce space corresponding to a minimal geometric tripotent is linearly isometric to a Hilbert space.

Non-associative algebras. The derivations and local derivations of these algebras are investigated. It is proven that arbitrary almost inner derivations of simple Leibniz algebras are inner derivations. Four-dimensional complex nilpotent Leibniz dialgebras are characterized. It is proven that local derivations of Leibniz and Lie algebras are derivations.

n-separately harmonic functions. The analytic continuation of such functions and their removable singularities are investigated. A theorem on the analytic continuation of n-separately harmonic functions in a specified direction and an analogue of the Osgood-Brown theorem for n-separately harmonic functions are proven.

Various models of random censoring. Statistical estimation of unknown parameters and their computation using numerical methods are investigated in these models. The asymptotic normality, uniform strong consistency, efficiency of estimates, and weak convergence properties of empirical processes are studied.

Compact difference schemes. High-accuracy compact (4+4) difference schemes are constructed and investigated for parabolic equations with constant and variable coefficients based on the finite element method. A priori estimates are obtained in classes of smooth and non-smooth solutions. Theorems on the convergence and accuracy of difference schemes are proven. Compact schemes are constructed and investigated for local and nonlocal boundary conditions posed for pseudoparabolic equations. Numerical experiments are conducted.

Quasiclassical approximation of functional integrals. Functional integrals are a fundamental tool in quantum mechanics, quantum field theory, statistical physics, chemistry, and other fields. They describe the dynamics of systems through summation over all possible trajectories or field configurations. The quasiclassical approximation method is used for approximate calculation of functional integrals with special types of potentials.

Integral geometry problem. The uniqueness, existence, and stability of the solution to this problem for families of hyperbolas are investigated. The application of the exact inversion formula for the integral geometry problem on families of hyperbolas in seismic data reconstruction is studied. The Fourier transform of the solution with respect to the first variable is obtained, and an exact inversion formula is derived through regularization.

International Cooperation

The branch actively collaborates scientifically with numerous institutes and universities, including:

• University of New South Wales (Sydney, Australia);
• Institute of Mathematics of the National Academy of Sciences of Belarus.

Seminars