Physical Sciences and Mathematics Commons^™

Boundary Value Problem With The Bitsadze-Samarsky Condition For A Loaded Equation Of Parabolic-Hyperbolic Type In A Doubly Connected Region, Bozor Islomov, Oybek Yunusov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

This paper is devoted to the study of a nonlocal boundary value problem for a loaded equation of parabolic-hyperbolic type in a special domain.Using representations of the general regular solution, are proven the unique solvability of the problem posed.

Holomorphic Motion Of Julia Sets Of Polynomial-Like Maps, And Continuity Of Compact Sets And Their Green Functions, Bazarbaev Sardor, Sobir Boymurodov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper, we study holomorphic motion of Julia sets of polynomial-like maps. In particular, we prove that in the stable family of polynomial-like maps if all the continuos functions move continuously by parameter then the Julia sets move holomorphically. Moreover, we also study the relation between continuity of regular compact sets and their Green functions.

An Analogue Of Hartogs Lemma For Separately Harmonic Functions With Variable Radius Of Harmonicity, Sevdiyor Imomkulov, Sultanbay Abdikadirov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this note we prove that if a function u(x,y) is separately harmonic in a domain D × V_r = D × {y∈ℝ²:|y|<r,  r>1} ⊂ ℝⁿ × ℝ² and for each fixed point x⁰ ∈ D the function u(x⁰,y) of variable y continues harmonically into the great circle {y∈ℝ²:|y|<R(x⁰),  R(x⁰)>r}, then it continues harmonically into a domain {(x …

Investigating Bremsstrahlung Radiation In Tungsten Targets: A Geant4 Simulation Study, Sindor Ashurov, Satimboy Palvanov, Abror Tuymuradov, Dilmurod Tuymurodov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

Bremsstrahlung radiation, a pivotal phenomenon in high-energy physics, presents numerous applications and implications in both theoretical studies and practical scenarios. This article explores the Bremsstrahlung radiation of electrons in tungsten (W) targets of varying widths subjected to different energy beams using GEANT4 simulations. By systematically altering the target widths and electron beam energies, we assess the corresponding effects on radiation yield and spectrum. The findings contribute to a deeper understanding of Bremsstrahlung processes in high-$Z$ materials and offer valuable insights for applications ranging from radiation therapy to materials analysis.

On Geometry Of Two Dimensional Surfaces In Four Dimensional Euclid Space, Abdigappar Narmanov, Bekzod Diyarov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

Geometry of two-dimensional surfaces in E⁴ is an essential part of differential geometry and studied by many authors [4, 5, 6, 10]. In this paper, we give some surface in four dimensional Euclid space E⁴ with nonzero Gauss curvature which is a orbit of the system of two vector fields. Smoothness is the smoothness of the class C^∞.

Computer Simulation Of Adsorption Of C60 Fullerene Molecule On Reconstructed Defective Si(100) Surfacee Content Of The Body Element Is Displayed In Your Browser, I. Urolov, Ishmumin Yadgarov, Ganiboy Raxmanov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this work, based on the molecular dynamics (MD) method, the adsorption processes of C₆₀ fullerene molecules on the reconstructed defective silicon Si(100) surface with different configurations were simulated in the LAMMPS open package program. Second-order Brenner interatomic potential was used to determine interactions between Si-Si, C-C and Si-C atoms. The interaction of various shaped defect areas with the C₆₀ molecule on the surface of reconstructed silicon Si(100) was studied. As a result of calculations, stable adsorption states were determined by comparing the energy of C₆₀ molecule adsorption to the defective silicon Si(100) surface and the Si-C …

Translation-Invariant Gibbs Measures For Potts Model With Competing Interactions With A Countable Set Of Spin Values On Cayley Tree, Zarinabonu Mustafoyeva

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In the present paper we consider of an infinite system of functional equations for the Potts model with competing interactions and countable spin values Φ = {0, 1, ..., } on a Cayley tree of order k. We study translation-invariant Gibbs measures that gives the description of the solutions of some infinite system of equations. For any k ≥ 1 and any fixed probability measure ν we show that the set of translation-invariant splitting Gibbs measures contains one and two points for odd k and even k, respectively, independently on parameters of the Potts model with a countable …

Cyclically Compact Operators In Banach Modules Over L0(B), Jasurbek Karimov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper the properties of linear cyclically compact operators in Banach modules over space L⁰(B) are given.

Laterally Complete Regular Modules, Jasurbek Karimov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper we introduce the notion laterally complete regular modules and study some properties of theese modules.

Asymptotic Results For Empirical Processes In Informative Model Of Random Censorship From Both Sides, Abdurakhim Abdushukurov, Dilshod Mansurov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In the paper, the empirical process in informative model of random censorship from both sides is investigated. For it, the limit Gaussian process with mean zero is founded. Under investigating of empirical process, the characterization properties of the considered informative model is used. The properties of the semiparametric estimator by using methods of numerical modeling are discussed.

Identification Of Sources In A Boundary Value Problem For Benney-Luke Type Differential Equation With Integral Conditions, Farhod Rakhmonov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In three-dimensional domain a problem of identification of recourses for Benney-Luke type partial differential equation of the even order with integral form conditions, spectral parameter and small positive parameters in mixed derivatives is considered. The solution of this partial differential equation is studied in the class of regular functions. The Fourier series method is used. Using this Fourier method, is obtained a countable system of ordinary differential equations. So, the nonlocal boundary value problem is integrated as an ordinary differential equation. When we define the arbitrary integration constants there are possible five cases with respect to the spectral parameter. By …

Error Estimation For The Third-Order Accuracy Approximate Solution Of The Cauchy Problem By The Taylor Formula, Abdugani Abdullaev

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

A method based on the Taylor formula for the approximate solution of the Cauchy problem for the ordinary differential equation is studied. The problem of estimating the accuracy of the approximate solution generated by this method is considered, and an estimate of high accuracy is obtained for the difference of the exact and approximate solution. Here, different from the known values, an exact expression for the estimation coefficient is found.

Evasion Differential Game Of Two Pursuers And One Evader, Toychivoy Tursunaliev

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

We study a linear evasion differential game of two pursuers and one evader. We impose geometric constraints on the control parameters of players. The control sets of pursuers are unit balls, and that of evader is the ball of radius σ,σ>1. Evasion is said to be possible if the state of the evader doesn't coincide with the state of any pursuer for all time. We construct an evasion strategy for the evader that guarantees the evasion from any initial positions of players. Also, we introduce the concept of approach times. We show that the number of approach times doesn't …

A New Capacity In The Class Of ShM Functions Defined By Laplace Operator, Nurali Akramov, Khakimboy Egamberganov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper, we define a new capacity Δ_m on the class of sh_m functions, which is defined by Laplace operator. We prove that Δ_m-capacity satisfies Choquet’s axioms of measurability. Moreover, we compare our capacity with Sadullaev-Abdullaev capacities. In particular, it implies that Δ_m-capacity of a set E is zero if and only if E is a m-polar set.

Gibbs Measures Of Models With Uncountable Set Of Spin Values On Lattice Systems, Farhod Haydarov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper, we shall discuss the construction of Gibbs measures for models with uncountable set of spin values on Cayley trees. It is known that "translation-invariant Gibbs measures" of the model with an uncountable set of spin values can be described by positive fixed points of a nonlinear integral operator of Hammerstein type. The problem of constructing a kernel with non-uniqueness of the integral operator is sufficient in Gibbs measure theory. In this paper, we construct a degenerate kernel in which the number of solutions does not exceed 3, and in turn, it only gives us a chance to …

Local And 2-Local Derivations On Small Dimensional Zinbiel Algebras, Bakhtiyor Yusupov, Sabohat Rozimova

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In the present paper we investigate local and 2-local derivations on small dimensional Zinbiel algebras. We give a description of derivations and local derivations on all three and four-dimensional Zinbiel algebras. Moreover, similar problem concerning 2-local derivations on all three and four-dimensional Zinbiel algebras are investigated.

Weighted M-Subharmonic Measure And (M, 𝜓)-Regularity Of Compacts, Kobiljon Kuldoshev, Nurbek Narzillaev

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

It is known that, the m−subharmonic measure of a set E ⊂ D,  related to a domain D ⊂ ℂⁿ, is defined by m−subharmonic functions in D. In this article we define a generalization of the m−subharmonic measures and prove some of their properties.

Limit Theorems For Weakly Dependent Random Variables With Values In Stable Type P Banach Spaces, Olimjon Sharipov, Utkir Kobilov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

We consider stable type p Banach spaces. We extend results known for independent random variables to the mixing random variables.

In particular we prove moment in equalities, low of large numbers and almost sure convergence of the series in the case of mixing random variables.

Search For The Least Massive Objects In The Hyades Open Cluster With The Help Of A Wide Stellar View, Stanislav Melnikov, Karamat Mirtadjieva

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

No abstract provided.

On Specifications Of Positive Data Models With Effectively Separable Kernels Of Algorithmic Representations, Nodira R. Karimova

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

It is established that any effectively separable multi-sorted positively representable model with an effectively separable representation kernel has an enrichment that is the only (up to isomorphism) model constructed from constants for a suitable computably enumerable set of sentences.

Some Properties Of The Quartic Numerical Range For 4x4 Operator Matrices, Hakimboy Latipov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In the present paper we consider self-adjoint 4x4 operator matrices A. For some special cases the alternative formulas for the calculating the quartic numerical range of 4x4 operator matrices A are derived. Using the obtained alternative formula for the quartic numerical range of A we estimate the lower and upper bound of A.

Inverse Source Problem For The Heat Equation On A Metric Star Graph With Integral Over-Determination Condition, Zarif Sobirov, Ariuxan Turemuratova

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this work we investigated an initial boundary value problem for the heat equation on a metric star graph in Sobolev space. The existence and uniqueness of the generalized solution are proved with the classical functional method based on a priori estimates. Also, we considered the inverse source problem with the integral over-determination condition. We reduced the inverse problem to the operator-based equation and proved that the corresponding resolvent operator is well-defined.

A Characterization Of Approximately Inner Automorphisms Of Aw*-Factor Of Type Ii1, Dmitriy Kim

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

Approximately inner *-automorphisms of AW*-algebra of type II₁ are considered. Faithful normalized quasitraces of AW*-algebras are studied and the inequality connecting ||.||₁ and ||.||₂ norms generated by quasitrace is obtained. It is showed the characterization of approximately inner *-automorphisms of AW*-algebra of type II₁.

On The Negative Order Loaded Modified Korteweg–De Vries Equation, Praveen Agarwal, Bakhrom Abdullaev, Iroda Baltaeva, Shoira Atanazarova

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this study, we establish the integration of the negative order loaded modified Korteweg-de Vries equation using the inverse scattering transform method. The main result is included in deriving the evolution equations for scattering data of the Dirac operator which is associated with the considered problem. Moreover, it was described the process of the construction of one-soliton solution of the negative order loaded modified Korteweg-de Vries equation.

On Generalizations Of The Upper Half Plane In A Multidimensional Complex Space, Bukharbay Kurbanov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

The paper considers an unbounded realization of a polydisk and a unit ball: the group of holomorphic automorphisms is described, and the Cauchy-Szego and Poisson kernels are calculated explicitly.

Integration Of The Negative Order Korteweg-De Vries Equation With Self-Consistent Source, Michal Fečkan, Gayrat Urazboev, Iroda Baltaeva, Oxunjon Ismoilov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper, we show that the negative-order Korteweg-de Vries equation with a self-consistent source can be solved by the inverse scattering method. The evolution of the spectral data of the Sturm-Liouville operator with the potential associated with the solution of the negative order Korteweg-de Vries equation with a self-consistent source is determined. The results obtained make it possible to apply the method of the inverse scattering problem to solve the problem under consideration.

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 …

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.

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.

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.