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On A Fundamental Polyhedron Of A Hyperbolic Cone-Manifold, Lilya Grunwald, Aydos Qutbaev

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper we propose to consider two different solutions having a common problem of establishing hyperbolic structure on a 3-manifold. Under the consideration will be a cone 3-manifold with underlying space as a 3-sphere and a singular set nested in it. Furthermore, this paper is divided into two cases: a singular set as the 3₁ knot with a bridge and a singular set as the 6₁³ link. The hyperbolic space $H³ for the analytical examination in the first case will be a hyperboloid model, in the second using the upper-half space model. To show that …

On Jacobian Group Of The Δ-Graph, Alexander Mednykh, Ilya Mednykh, Ivan Yudin

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In the present paper we suggest an approach for counting Jacobian group of the Δ-graph Δ(n; k, l, m). The notion of Δ-graph arises as a continuation of the families of I-, Y- and H-graphs well-known in the graph theory. In particular, graph Δ(n; 1, 1, 1) is isomorphic to discrete torus C₃xC_n. It this case, the structure of the Jacobian group will be find explicitly.

Usual, Quadratic And Cubic Numerical Ranges Corresponding To A $3\Times 3$ Operator Matrices, Mubina Sharipova

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In the present paper we consider bounded self-adjoint 3x3 operator matrices A. An alternative formula for the calculating the cubic numerical range of the operator matrices A is derived. The components of the quadratic numerical range with respect to the expansion of the Hilbert space are found.

Cyclically Compact Sets In Banach Modules Over Algebra L0, Jasurbek Karimov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper some properties of cyclic compact sets in Banach modules over the algebra of measurable functions are given. The convergence of the cyclic subnet of any convergent sequence, and to the same limit is proved. It is also shown that if we multiply the cyclic compact set to any measurable function it will be cyclic compact set too.

On Sufficient Criteria For The Möbius Property, Tatiana Kergilova (Turtueva)

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

This paper is a survey of state of mathematical sciences related to the question on investigation of characterization of Möbius transformations under minimal assumptions.

Mappings With Bounded Distortion And Geometric Structures, Boris Apanasov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

We survey recent results on connections of mappings with bounded distortion and dynamics of discrete action in different geometries. Our new tool based on quasiconformal and conformal dynamics of discrete group actions in 3-geometries at infinity of negatively curved symmetric rank one spaces is used to construct new types of quasiconformal, quasiregular and quasisymmetric mappings in space. This tool has close relations to new effects in Teichmüller spaces of conformally flat structures on closed hyperbolic 3-manifolds/orbifolds and non-trivial hyperbolic 4-cobordisms, to the hyperbolic and conformal interbreedings, as well as to non-faithful discrete representations of uniform hyperbolic 3-lattices.

Leaving applications of …

On Fractal Squares Possessing Finite Intersection Property, Dmitriy Drozdov, Andrei Tetenov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

We consider fractal squares and obtain the conditions under which they possess finite intersection property. If the fractal square is a dendrite we find the exact estimates for the intersection number for pairs of their pieces and the orders of their points.

On The Solvability Of Some Nonlinear Differential Equations, Aleksandr Chueshev, Nadejda Chuesheva

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

We find explicit exact solutions of some nonlinear partial differential equations related to Korteweg–de Vries equation and other nonlinear equations.

Some Properties Of Condensers With Uniformly Perfect Plates, Oxana Lazareva

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

The paper contains proof of equicontinuity of the conformal modulus of a condenser in Rⁿ with respect to its α-uniformly perfect plate and the solution of the problem of constructing a lower bound for the conformal capacity of a condenser with α-uniformly perfect plates.

Goursa Type Problem For A System Of Equations Of Poroelasticity, Kholmatzhon Imomnazarov, Lochin Khujayev, Zoyir Yangiboev

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper, in the description of the test process, we assume that the change in the temperature field of the environment will not affect the acoustic characteristics of the system are determined by the compressibility and viscosity of the fluid. Let us consider the effects caused by the shear modulus and coefficient of interfacial friction.

Strongly M-Subharmonic Functions On Complex Manifolds, Sukrotbek Kurbonboyev

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

This article is devoted to the definition and study of strongly m-subharmonic (sh_m) functions on complex manifolds. A definition of strongly m-subharmonic functions on a Stein manifold is introduced and some basic properties are proven.

75-Th Anniversary Of V.V.Aseev, Azimbay Sadullaev, Azizjon Varisov, Alexander Mednykh, Tetenov Andrey

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

No abstract provided.

Analogue Of The Mittag-Leffler Theorem For A(Z)-Analytic Functions, Muhayyo Ne'matillayeva

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

We consider A(z)-analytic functions in case when A(z) is antiholomorphic function. For A(z)-analytic functions analog of the Mittag-Leffler theorem is proved.

Existence Of Boundary Values Of Hardy Class Functions H1A, Nasridin Zhabborov, Shokhruh Khursanov, Behzod Husenov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

We consider A(z)-analytic functions in case when A(z) is antianalytic function. In this paper, the Hardy class for A(z)-analytic functions are introduced and for these classes, the boundary values of the function are investigated. For the Hardy class of functions H¹_A, an analogue of Fatou's theorem was proved about that the bounded functions have the boundary values. As the main result, the boundary uniqueness theorem for Hardy classes of functions H¹_A is proven.

Algorithmic Criterion Of Locally Finite Separability Of Algebras Represented Over Equivalence Α2 ∪ Id Ω, Sarvar Zhavliev

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

It has been established that for equivalences of the form α² ∪ id ω, the locally finite separability of any universal algebra represented over it is equivalent to the immune of the complement α. It is shown that for finitely separable algebras this criterion does not meet.

The Pursuit–Evasion Problems In A Differential Game With Ggr-Constraints On Controls, Bahrom Samatov, Bakhodirjon Juraev

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In the present paper, we consider pursuit and evasion problems in a simple motion differential game when Pursuer's control is subjected to geometric constraint and Evader's control is subjected to Grönwall type constraint. In order to solve the pursuit problem, the parallel convergence strategy (the П-strategy) for the Pursuer is constructed, and sufficient conditions of pursuit are obtained. Also, we prove that the П-strategy is an optimal strategy of Pursuer. In solving of the evasion problem, we propose an admissible control function to the Evader, and we obtaine sufficient conditions of evasion. In addition, an estimation of the distance between …

Problems Of Formation And Evolution Of Bulges Of Spiral Galaxies, Farkhodjon Botirov, Salakhutdin Nuritdinov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this work, we develop the theory of the origin of galactic bulges, and gravitational instability of the bending, as well as modes of perturbation based on the background of a nonlinear non-stationary model. As a result, here, we propose critical diagrams and determine increments of instabilities for such types of perturbations. In addition, we also consider relationships between the masses of the bulge and the central black hole, which is of great importance in studying the evolution of the bulges of spiral galaxies. Moreover, problems on the evolution of bulges in spiral galaxies, together with discussions of their main …

Theoretical Study Of The Mechanisms Of Absorption Of Semiconductor Spherical Quantum Dots In The Framework Of Quantum Mechanics, Kamoliddin Qoraboyev, Usmon Sapayev

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

Analytical expressions for the linear and nonlinear optical susceptibilities of spherical quantum dots are obtained using the Schrödinger equation. To solve the Schrödinger equation, the Nikiforov-Uvarov method was used, assuming that electrons isolated in the medium are associated with the Gelman inverse quadratic potential. Using the density matrix formalism, analytical expressions were obtained for the coefficients of linear and nonlinear absorption and changes in the refractive index of quantum dots. Elements of the matrix of the electric dipole moment l=± 1 and m = 0 are obtained according to the selection rules. To demonstrate the results obtained, we used the …

On The Hartogs Theorem For A-Analytic Functions In ℂN, Tolib Otaboev

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper, we define a separately A-analytic and an A-analytic function of several variables as a solution of system of equations of Beltrami in the space ℂⁿ. It is proved an analogue of the Cauchy integral formula for an A-analytic function of several variables. It is proved a theorem on the expansion of an A-analytic function of several variables into a multiple series. When the function is bounded, it is proved an analogue of the Hartogs’ theorem for A-analytic functions of several variables.