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- A(z)-analytic function (4)
- Cayley tree (4)
- A(z)-harmonic function (3)
- Eigenvalue (3)
- Algebra of measurable functions (2)
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- Banach module (2)
- Cyclically compact set (2)
- Fourier transform (2)
- Gibbs measure (2)
- Green function (2)
- Holomorphic function (2)
- Laplace operator (2)
- M-polar set (2)
- M-regular compact (2)
- Strongly m-subharmonic functions (2)
- (m (1)
- *-automorphism. (1)
- A(z)-analytic functions (1)
- A(z)-barier (1)
- A(z)-lemniscate (1)
- A(z)-subharmonic functions (1)
- A-analytic function (1)
- Admissible control (1)
- Analogue of Fatou's theorem for the Hardy class of functions H1A (1)
- Automorphism (1)
- Banach ideal of compact operators (1)
- Banach-Kantorovich space. (1)
- Beltram equation (1)
- Bochner-Martinelli integral (1)
- Boundary control (1)
Articles 1 - 30 of 41
Full-Text Articles in Analysis
Holomorphic Motion Of Julia Sets Of Polynomial-Like Maps, And Continuity Of Compact Sets And Their Green Functions, Bazarbaev Sardor, Sobir Boymurodov
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
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 × Vr = 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
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
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
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
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.
A New Capacity In The Class Of ShM Functions Defined By Laplace Operator, Nurali Akramov, Khakimboy Egamberganov
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 Δm on the class of shm functions, which is defined by Laplace operator. We prove that Δm-capacity satisfies Choquet’s axioms of measurability. Moreover, we compare our capacity with Sadullaev-Abdullaev capacities. In particular, it implies that Δm-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
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
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.
Some Properties Of The Quartic Numerical Range For 4x4 Operator Matrices, Hakimboy Latipov
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
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
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
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
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
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.
Cyclically Compact Sets In Banach Modules Over Algebra L0, Jasurbek Karimov
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.
Strongly M-Subharmonic Functions On Complex Manifolds, Sukrotbek Kurbonboyev
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 (shm) functions on complex manifolds. A definition of strongly m-subharmonic functions on a Stein manifold is introduced and some basic properties are proven.
Analogue Of The Mittag-Leffler Theorem For A(Z)-Analytic Functions, Muhayyo Ne'matillayeva
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
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 H1A, 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 H1A is proven.
On The Hartogs Theorem For A-Analytic Functions In ℂN, Tolib Otaboev
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.
M-Subharmonic Functions On The Projective Space PN, Gokhan Gogus, Azimbay Sadullaev
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 Vqm*(z,K,ℙn), ��m-measure ωqm*(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 …
Dirichlet Problem In The Class Of A(Z)-Harmonic Functions, Shohruh Khursanov
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
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
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
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 Vm*(z,K,ψ,δ), defined by the class ℒmδ = {u(z)∈shm(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 ⊂ ℂn …
Ergodic Theorems For D-Dimensional Flows In Ideals Of Compact Operators, Azizkhon Azizov
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 CE be the symmetric ideal of compact operators in H generated by the fully symmetric sequence space E ⊂ c0. If Tu: 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 ∈ CE the net At(y) = …
Some Properties Of A(Z)-Subharmonic Functions, Shohruh Khursanov
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.
The Fokas' Unified Transformation Method For Airy Equation On Simple Open Star Graph, Zarifboy Sobirov, Mardonbek Eshimbetov
The Fokas' Unified Transformation Method For Airy Equation On Simple Open Star Graph, Zarifboy Sobirov, Mardonbek Eshimbetov
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
We considered the Airy equation on the simple star graph with three semi-infinite bonds. At the branching point of the graph we used second kind vertex conditions. Exact integral representation of the solution is obtained via Fokas unified transformation method.
The Ψ-Harmonic Measure And Its Properties, Nurbek Narzillaev, Kobiljon Kuldoshev
The Ψ-Harmonic Measure And Its Properties, Nurbek Narzillaev, Kobiljon Kuldoshev
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
It is known that, the harmonic measure of a set E, relative to a domain D, is defined by means of subharmonic functions on D. In this article we define a generalization of a harmonic measure and prove some of its properties.
Geometric Properties Of A-Harmonic Functions, Shokhrukh Khursanov
Geometric Properties Of A-Harmonic Functions, Shokhrukh Khursanov
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
This paper is devoted to geometric properties of A(z)-harmonic functions and the corresponding Laplace operator Δ A(u). It is proved that the generalized A(z)-harmonic function is generated by the usual A(z)-harmonic function.