Laboratory Staff

Apakov Yusupjon Pulatovich

Yetakchi ilmiy xodim More details →

Arzikulov Farhodjon Nematjonovich

Bosh ilmiy xodim More details →

Egamov Dilshod Odiljonovich

Kichik ilmiy xodim More details →

Irgashev Bahrom Yusuphanovich

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Karimjonov Iqboljon Abdulazizovich

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Karimov Erkinjon To‘qinovich

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Karimov Kamoliddin To‘ychiboyevich

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Rahmatullayev Muzaffar Muhammadjonovich

Matematika instituti Namangan bo’linmasi mudiri More details →

Rasulova Muhayyo Akbarjon qizi

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Sattarov Iskandar Abu-Aliyevich

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Xakimov Rustam Maxmudovich

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Xodjibayev Vali Raximdjanovich

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Scientific Activity

Researchers at the Namangan Branch of the V.I. Romanovskiy Institute of Mathematics conduct scientific research on "Gibbs measures on Cayley trees, Non-associative algebras, integer and fractional order differential equations" within a planned framework, devoted to direct and inverse problems for integer and fractional order differential equations, non-associative algebras, some two-boundary problems in probability theory, and Gibbs measures on Cayley trees.

Direct and inverse problems for integer and fractional order differential equations. A second boundary value problem in a rectangular domain is considered for a non-homogeneous third-order partial differential equation with constant coefficients and multiple characteristics. The uniqueness of the solution to the posed problem is proven using the energy integrals method. An example is constructed for the case where the conditions of the uniqueness theorem are violated. The unique solvability of an initial-boundary value problem for a diffusion equation involving a generalized fractional order operator (Hilfer) on a star-shaped graph is proven. A modified Cauchy problem is studied for a non-homogeneous hyperbolic-type equation of the second kind that degenerates in a characteristic triangle. It is proven that the obtained solutions actually satisfy the equation and initial conditions.

Non-associative algebras. An algorithm for obtaining the general form of the matrix of weak left multiplication operators and an algorithm for obtaining the general form of the matrix of local weak left multiplication operators in five-dimensional naturally graded 2-filiform indecomposable associative algebras of type μ(1,2) over an algebraically closed field F of zero characteristic are constructed. The general form of the matrices of automorphisms and local automorphisms of n-dimensional filiform and null-filiform associative algebras is determined. Additionally, it is proven that every 2-local automorphism of a null-filiform associative algebra is an automorphism, and that the filiform associative algebras mentioned above have 2-local automorphisms that are not automorphisms.

Some boundary problems in probability theory. The probability of first exit through the upper (lower) boundary from a strip bounded by parallel straight lines is studied for traces of a homogeneous independent increment random process (Lévy process). Two-sided inequalities are proven for the probability under study by imposing restrictions only on moments. For a certain class of processes, the loss probability is found in explicit form.

Gibbs measures on Cayley trees. For three-state HC-models on Cayley trees, conditions for periodic Gibbs measures to be translation-invariant are found for the first time for "Triangle"-type graphs. A complete description of two-periodic Gibbs measures for the two-state HC-model is obtained, and for the first time, using the reconstruction method on trees, conditions for periodic Gibbs measures to be limiting measures are found. A complete description of translation-invariant Gibbs measures is obtained for the three-state Hard-Core model when the generating graphs are "Comb" and "Brush," and for the first time, existence conditions for non-translation-invariant alternating Gibbs measures are found for the case when the generating graph is "Comb."

International Cooperation

Seminars