Physical Sciences and Mathematics Commons^™

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.

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.

Behavior And Dynamics Of The Set Of Absolute Nilpotent And Idempotent Elements Of Chain Of Evolution Algebras Depending On The Time, Anvar Imomkulov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper we construct some families of three-dimensional evolution algebras which satisfies Chapman-Kolmogorov equation. For all of these chains we study the behavior of the baric property, the behavior of the set of absolute nilpotent elements and dynamics of the set of idempotent elements depending on the time.

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.

The Entrance Times For Circle Maps With A Break, Akhtam Dzhalilov, Javlon Karimov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In present work we study the entrance times for circle homeomorphisms with one break point and universal renormalization properties. Consider the set X of all orientation preserving circle homeomorphisms T with one break point and golden mean rotation number. It is well known that the renormalization group transformation has a unique periodic point T _b with period 2. Denote by B the set of all circle maps C¹ -conjugated to T _b . Consider the map T ∈ B and its unique probability invariant measure μ . Denote by E(x) the first entrance times of x to interval defined …

Restoring The Function Set By Integrals For The Family Of Parabolas On The Plane, Akram Begmatov, Alisher Ismoilov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

Integral geometry is one of the most important sections of the theory of ill-posed problems of mathematical physics and analysis. The urgency of the problems of integral geometry is due to the development of tomographic methods, which raise the requirements for the depth of the applied results, the fact that the solution of problems of integral geometry reduces a number of multidimensional inverse problems for partial differential problems, as well as the internal development needs of the theory of ill-posed problems of mathematical physics and analysis. In this work we consider the problem of reconstructing a function from a family …

Fractional Differentiation Of The Grunwald-Letnikov-Hadamard Type And The Difference Of The Fractional Order With A Multiplicative Step, Mahmadiyor Yakhshiboev

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

The properties of ''convolution-type'' operators that are invariant with respect to dilation and to their approximation using a unity in weighted mixed Lebesgue spaces are studied in this paper. Integral representations are obtained for the Marchaud-Hadamard and Marchaud-Hadamard type truncated fractional derivatives (by direction and mixed ones). This paper introduces the concept of a mixed difference of a vector fractional order with a multiplicative step and its properties. Some of these properties are proven using the Mellin transform. In this paper, we give the proof of theorems on coincidence of the definition domains of two different forms of fractional differentiation …

The Symmetric Form Of A Poroelasticity System In Terms Of Velocities, Stresses And Pressure, Sayyora Tuychieva

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

The form for representing the equation of motion for porous media in terms of velocities, stresses, and pressure as a symmetric hyperbolic Friedrechs system has been obtained. A two-dimensional initial- boundary value problem in a half-space is considered, the excitation source is a point source. For its numerical solution, an explicit predictor-corrector scheme is used. A series of numerical calculations for a test model of media is presented.

The Method Of Potentials For The Airy Equation Of Fractional Order, Kamoliddin Rakhimov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this work initial-boundary value problems for time-fractional Airy equation are considered on the different intervals. We studied properties of potentials for this equation and using these properties found the solutions of the considered problems. The uniqueness of problems proved using the analogue of Grö nwall–Bellman inequality and apriory estimate.

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.

Damped Oscillatory Integrals And Weierstrass Polynomials, Azimbay Sadullaev, Isroil Ikromov, Shaxriddin Muranov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper we consider the Sogge- Stein problem related to the damped oscillatory integrals. We show that in three-dimensional Euclidean spaces minimal exponent, which guarantees optimal decaying of the Fourier transform of the surfaces-carried measures with mitigating factor is bounded by 3/2. A proof of the main theorem is based on Weierstrass type results.

Generalized Metric Spaces And Hyperspaces, Ruzinazar Beshimov, Dilnora Safarova

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper, we investigate the heredity of some kind of generalized metric spaces to e_cX and e_nX. We will study the connection between a σ-space, Σ-space, a stratifiable space, ℵ-space, ℵ₀-space and its hyperspace.

On The Application Of Multidimensional Logarithmic Residue To Systems Of Non-Algebraic Equations, Barlikbay Prenov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper, the residue integrals over cycles associated with a system of non-algebraic equations and formulas for their calculation are given. Their connection with the power sums of the roots of the system is established. Some examples are considered.

Jump Theorems For The Bochner-Martinelli Integral In Domains With A Piecewise Smooth Boundary, Alexander Kytmanov, Davlatbay Dzhumabaev, Bayrambay Utemuratov, Barlikbay Prenov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

Jump theorems for the Bochner-Martinelli integral in domains with a piecewise smooth boundary are obtained. Moreover, theorem for the Bochner-Martinelli integral in domains with a piecewise smooth boundary is proved for continuous functions and also for functions from the class 𝓛^p.

Research Of Parabolic Surface Points In Galilean Space, Abdullaaziz Artykbaev, Bekzod Sultanov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

The paper studies the surfaces of the Galilean space $R_3^1$. First, we consider the geometry of the surface in a small neighborhood of a point on the surface. Basically, we studied the points of the surface where at least one of the principal curvature appeals to zero. Two classes of points are defined where at least one of the principal curvature is zero. These points are divided into two types, parabolic and especially parabolic. It is proved that these neighborhoods using the movement of space is impossible to move each other. A sweep of surfaces with parabolic and especially parabolic …

2-Local Derivations On Virasoro Algebras, Shavkat Ayupov, Bakhtiyor Yusupov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

The present paper is devoted to study 2-local derivations on infinite-dimensional Lie algebras over a field of characteristic zero. We show that every derivation on Virasoro algebra is inner and prove that all 2-local derivations on this algebra is a derivation. We give an example of infinite-dimensional Lie algebra with a 2-local derivation which is not a derivation.

Oscillatory Integrals And Weierstrass Polynomials, Azimbay Sadullaev, Isroil Ikromov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this work we consider some applications of the Weierstrass preparation theorem and Weierstrass pseudopolynomials to study of behavior of the oscillatory integrals and Fourier transforms with analytic and smooth phases with critical points.

On A Control Problem Associated With Fast Heating Of A Thin Rod, Shavkat Alimov, Farrukh Dekhkonov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this work, we consider boundary control problem associated with a parabolic equation on a interval. On the part of the border of the considered segment, the value of the solution with control parameter is given. Restrictions on the control are given in such a way that the average value of the solution in some part of the considered interval gets a given value. The auxiliary problem is solved by the method of separation of variables, while the problem in consideration is reduced to the Volterra integral equation of the second kind. The control parameter is defined on one. The …

Solvable Leibniz Superalgebras Whose Nilradical Is A Lie Superalgebra Of Maximal Nilindex, Abror Khudoyberdiyev, Manuel Ladra, Khosiat Muratova

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper, we investigate solvable Leibniz superalgebras whose nilradical is a Lie superalgebra with maximal nilindex.It should be noted that Lie superalgebra with a maximal nilindex only exists in the variety of Lie_2,m when m is odd. We give the classification of all solvable Leibniz superalgebras such that even part is a Lie algebra and nilradical is a Lie superalgebra with a maximal index of nilpotency.

Topological Properties Of Hyperspaces, Ruzinazar Beshimov, Dilnora Safarova

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In the work, it is given the normal functor F acting in the category of compacts and their continuous mappings. This functor does not preserve the Souslin number (or hereditary cellularity), the hereditary density, the hereditary π-weight and the hereditary Shanin number, the hereditary caliber, the hereditary precaliber, the hereditary preshanin number, the hereditary weak density, the hereditary Lindelöf number, and the hereditary extent of a compact. The example of the normal functor and the compact of Aleksandorv's two arrows are given. We study the action of functors exp_n, exp_ω, exp_c and exp on …

The Waiting Time And Dynamic Partitions, Akhtam Dzhalilov, Mukhriddin Khomidov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In the present paper we study the behaviour of normalized waiting times for linear irrational rotations. D.Kim and B.Seo investigated the waiting times for equidistance partitions. We consider waiting times with respect to dynamical partitions. The results show that limiting behaviour of waiting times essentially depend on type of partitions.

On The Continuation Of The Hartogs Series With Holomorphic Coefficients, Takhir Tuychiev, Jurabay Tishabaev

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper we consider the question of continuation of the sums of the Hartogs series that admit holomorphic continuation along a fixed direction with “thin” singularities, assuming only the holomorphic of the coefficients of the series and investigate the convergence region of such series. The results of the work develop a well-known result of A.Sadullaev and E.M.Chirka on the continuation of functions with polar singularities.

Ill-Posed Boundary Value Problem For Operator-Differential Equation Of Fourth Order, Kudratillo Fayazov, Ikrom Khajiev, Z. Fayazova

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

We prove the correctness of the conditional boundary value problem for an operator differential equation of the fourth order. A priori estimate is get. Uniqueness and conditional stability of solution are proved. The approximate solution is construct and get estimates of the norm of the difference between the exact and approximate solution.

Translation-Invariant Gibbs Measures Of A Model On Cayley Tree, Golibjon Botirov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

We consider a model where the spin takes values in the set [0,1]^d, and is assigned to the vertexes of the Cayley tree. We reduce the problem of describing the “splitting Gibbs measures” of the model to the description of the solutions of some non-linear integral equation. For a concrete form of the Kernel of the integral equation we show the uniqueness of solution.

Using An A Priori Estimate For Constructing Difference Schemes For Quasi-Linear Hyperbolic Systems, Rakhmatillo Aloev, Mirzoali Khudayberganov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper we consider a class of quasi-linear hyperbolic systems, which allows the construction of a dissipative energy integrals. In the basis of the design and investigation the stability of difference schemes for the numerical solution of the initial boundary value problems for the above class of quasi-linear hyperbolic systems, we put the existence of a discrete analogue of the dissipative energy integrals.

Some Cardinal And Topological Properties Of The $N$-Permutation Degree Of A Topological Spaces And Locally $\Tau$-Density Of Hyperspaces, Farkhod Mukhamadiev

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In the paper we investigate some cardinal and topological properties of the $n$-permutation degree of a topological spaces and locally $\tau$-density of hyperspaces. It is proved that the functors $\exp_n$ and $SP^n$ preserves locally $\tau$-density of any infinite $T_1$-spaces.

Using An A Priori Estimate For Constructing Difference Schemes For Quasi-Linear Hyperbolic Systems, Rakhmatillo Aloev, Mirzoali Khudayberganov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper we consider a class of quasi-linear hyperbolic systems, which allows the construction of a dissipative energy integrals. In the basis of the design and investigation the stability of difference schemes for the numerical solution of the initial boundary value problems for the above class of quasi-linear hyperbolic systems, we put the existence of a discrete analogue of the dissipative energy integrals.

Carleman’S Formula For The Matrix Upper Half-Plane, Gulmirza Khudayberganov, Zokirbek Matyakubov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this work the Carleman’s formula for the matrix upper half-plane is obtained.