Physical Sciences and Mathematics Commons^™

Difference Schemes Of High Accuracy For Equation Of Spin Waves In Magnets, Mirsaid Aripov, Dauletbay Utebaev, Zhusipbay Nurullaev

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

Three-parameter difference schemes of the finite element method with a high order of accuracy are considered in the article for a mathematical model of spin waves in magnets (Sobolev-type equations). Discretization of time and space variables is conducted on the basis of the finite element method. The parameters of the scheme allow choosing the best approximation and accuracy, and an economic algorithm for numerical implementation. Theorems on the stability and convergence of the considered difference schemes are obtained.

M-Subharmonic Functions On The Projective Space PN, Gokhan Gogus, Azimbay Sadullaev

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

We consider a class of quasi m-subharmonic functions in the projective space ℙⁿ. Similarly to the m-subharmonic functions, we will show a number of potential properties of quasi m-subharmonic functions. We introduce the concepts of Green’s function V_qm^*(z,K,ℙⁿ), ��_m-measure ω_qm^*(z,E,D) and study m-regularities of compact sets K ⊂ ℙⁿ. In contrast to the complex space ℂⁿ, we will prove that in the projective space ℙⁿ the locally …

Interpretation Of De Sitter Space Of Second Kind, Abdulaziz Artikbaev, Botirjon Mamadaliyev

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In a five-dimensional pseudo-Euclidean space of index two, the geometry on its sphere is studied. The equivalence of the geometry on a sphere of imaginary radius on de Sitter space is shown. The interpretation of the geometry on a sphere of imaginary radius, inside the sphere of imaginary radius of the Minkowski four-dimensional space, is implemented. We study a curve in a five-dimensional pseudo-Euclidean space of index two and determine the membership condition of the curve to a sphere of imaginary radius.

Dirichlet Problem In The Class Of A(Z)-Harmonic Functions, Shohruh Khursanov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

This paper work is devoted to the study of the Dirichlet problem in the class of A(z)-harmonic functions.

Duality For L1-Spaces Associated With The Maharam Measure, Botir Zakirov, Khabibulla Umarov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

Dual space for the Banach-Kantorovich space L¹(m) of all functions integrable with respect to a Maharam measure m is described and its pre-dual space is constructed.

On Extensions And Restrictions Of Τ-Smooth And Τ-Maxitive Idempotent Measures, Muzaffar Eshimbetov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In the paper we investigate maps between idempotent measures spaces, τ-maxitive idempotent measures and their extensions and restrictions. For an idempotent measure we prove that its extension is τ-maxitive if and only if its restriction is τ-maxitive.

Weighted (M, Δ)-Green Functions In CN, Nurbek Narzillaev

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this work some extremal function and its properties are studied for the class of m-subharmonic functions. We study weighted (m,δ)-Green function V_m^*(z,K,ψ,δ), defined by the class ℒ_m^δ = {u(z)∈sh_m(ℂⁿ): u(z)≤δ, z∈ℂⁿ}, δ > 0. We see that the regularity of the points with respect to different numbers δ differ from each other. Nevertheless, we will prove that if the compact K ⊂ ℂ^{n …}

Study Asymmetry Of Stellar Jets, Stanislav Melnikov, Karomat Mirtadjieva

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

This review article describes the diversity of astrophysical jets. The differences between relativistic and slower stellar jets are described briefly. The data on recent studies of stellar jets, which led to the discovery of the asymmetry of their emissions - a mismatch of their parameters in the opposite components. A review of the physical mechanisms that is proposed to explain the observed asymmetry is given.

On The Structure Of The Essential Spectrum For Discrete Schrödinger Operators Associated With Three-Particle System, Shukhrat Lakaev, Tirkash Radjabov, Nizomiddin Makhmasaitovich Aliev

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

We consider a family of discrete Schrödinger operators $H(K),\,K\in (-\pi,\pi]^5$ associated with a system of three quantum particles on the five-dimensional lattice ${\mathbb{Z}}^5$ interacting via short-range pair potentials and having arbitrary "dispersion functions" with not necessarily compact support.

We show that the essential spectrum of the three-particle discrete Schr\"odinger operator $H(K),\,K\in (-\pi,\pi]^5$ consists of a finitely many bounded closed intervals.

Problems Of Classification Of Globular Clusters And Their Systems, Nuritdinov Saloxutdin, Ikram Tadjibaev

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

A review is carried out mainly of the classification problems of globular clusters (GC) of our Galaxy. Classification of GC has a rich history, since it was first considered by Shapley and Sawyer [1] over 90 years ago. After them, a number of authors [2-8] tried to classify GC in various ways, but however, before our work no one was able to solve this problem to the desired level. We first studied the physical characteristics of the GC of our Galaxy by constructing diagrams of the relationship between these characteristics. Next, we decided to answer the question of whether it …

Numerical Calculation Of Lyapunov Stable Solutions Of The Hyperbolic Systems, Dilfuza Ne'matova, Aziza Akbarova

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

We give numerical examples demonstrating and confirming the theoretical results obtained for systems of two linear hyperbolic equations.

Choice Of Feature Space For Classification Of Network Ip-Traffic By Machine Learning Methods, Avazjon Marakhimov, Ulugbek Ohundadaev

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

IP-protocol and transport layer protocols (TCP, UDP) have many different parameters and characteristics, which can be obtained both directly from packet headers and statistical observations of the flows. To solve the problem of classification of network traffc by methods of machine learning, it is necessary to determine a set of data (attributes), which it is reasonable to use for solving the classification problem.

Negative Representability Degree Structures Of Linear Orders With Endomorphisms, Nadimulla Kasymov, Sarvar Javliyev

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

The structure of partially ordered sets of degrees of negative representability of linear orders with endomorphisms is studied. For these structures, the existence of incomparable, maximum and minimum degrees, infinite chains and antichains is established,and also considered connections with the concepts of reducibility of enumerations, splittable degrees and positive representetions.

Nonlocal Problems For A Fractional Order Mixed Parabolic Equation, Azizbek Mamanazarov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In the present work nonlocal problems with Bitsadze-Samarskii type conditions, with the first and the second kind integral conditions for mixed parabolic equation involving Riemann-Liouville fractional differential operator have been formulated and investigated. The uniqueness and the existence of the solution of the considered problems were proved. To do this, considered problems are equivalently reduced to the problems with nonlocal conditions with respect to the trace of the unknown function and its space-derivatives. Then using the representation of the solution of the second kind of Abel's integral equation, it was found integral representations of the solutions of these problems. Necessary …

Nonlocal Boundary Value Problem For A System Of Mixed Type Equations With A Line Of Degeneration, Kudratillo Fayazov, Ikrombek Khajiev

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

This work is devoted to the study of a nonlocal boundary value problem for a system of two-dimensional parabolic equations with changing direction of time. A priori estimate is obtained for the solution of the problem under consideration, and theorems on stability and conditional stability are proved depending on the parameters of the nonlocal condition. As a result, the uniqueness of the solution to the problem is presented.

A Development Of A Polyhedron In The Galilean Space, Abdulaziz Artykbaev, Jasur Sobirov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper, we study the development of a polyhedron in the Galilean space. A development of a polyhedron is an isometric mapping of a polyhedron to a plane, in which the gluing sides are indicated. Since the motion of the Galilean space differs significantly from the motion of the Euclidean space, the development of a polyhedron of the Galilean space will also differ from the development of a polyhedron of the Euclidean space. We prove that the total angle around the vertex of the polyhedral angle is preserved in the development. We also give illustrations of the developments for …

Ergodic Theorems For D-Dimensional Flows In Ideals Of Compact Operators, Azizkhon Azizov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

Let H be an infinite-dimensional complex Hilbert space, let (B(H), ||.||_∞ be the C^⚹-algebra of all bounded linear operators acting in H, and let C_E be the symmetric ideal of compact operators in H generated by the fully symmetric sequence space E ⊂ c₀. If T_u: B(H)→ B(H), u=(u_1,...,u_d)∈ R₊^d, is a semigroup of positive Dunford-Schwartz operators, which is strongly continuous on C₁, then the following versions of individual and mean ergodic theorems are true: For each y ∈ C_E the net A_t(y) = …

On Time-Optimal Control Problem Associated With Parabolic Equation, Farrukh Dekhkonov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

The boundary control problem for heat equation in a right rectangle domain is considered. The control parameter is equal to the temperature on some part of the border of the considered domain The estimate of a minimal time for achieving the given average temperature over some subdomain is found.