Physical Sciences and Mathematics Commons^™

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.

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 …

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 …

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 …

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.

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.

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 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.

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.

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.

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.

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.

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.

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.

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.

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 …

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 …}

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.

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.

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) = …

Some Properties Of A(Z)-Subharmonic Functions, Shohruh Khursanov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper we give a definition of A(z)-subharmonic functions and consider some properties of A(z)-subharmonic functions. Namely A(z)-subharmonicity criterion in class C².