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Full-Text Articles in Physical Sciences and Mathematics

Some Properties Of A(Z)-Subharmonic Functions, Shohruh Khursanov Dec 2020

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 Dec 2020

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 Dec 2020

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 Dec 2020

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.


Self-Aggregation Of C60 Particles In A Volume Of Evaporating Droplets On A Flat Surface, Urol Makhmanov, Abdulmutallib Kokhkharov, Sagdilla Bakhramov, Donats Erts Sep 2020

Self-Aggregation Of C60 Particles In A Volume Of Evaporating Droplets On A Flat Surface, Urol Makhmanov, Abdulmutallib Kokhkharov, Sagdilla Bakhramov, Donats Erts

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

The experimental results on the self-aggregation of fullerene C60 particles in a microvolume of drying droplets of a colloidal solution of fullerene on a solid substrate are presented. Using methods of scanning electron microscopy and atomic force microscopy, it was shown that in the volume of an evaporating droplet of a solution of fullerene C60 in xylene, deposited on the surface of a flat silicon substrate at room temperature, nanostructured and porous mC60 aggregates of quasispherical and elongated spherical shapes with geometrical sizes in average diameter up to D≈4000 nm are synthesized. It is established that an …


To The Education Of Operational Thinking In The Higher Mathematics Courses Of The Higher Technical School, Valentin Zharov, Arslan Mardanov Sep 2020

To The Education Of Operational Thinking In The Higher Mathematics Courses Of The Higher Technical School, Valentin Zharov, Arslan Mardanov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

This article is devoted to the tasks of educating Operational thinking in the courses of higher mathematics of a higher technical educational institution. In particular, it comprehensively discusses the definitions of mathematical and operational thinking. It substantiates the need for a differentiated and structural approach to teaching mathematics in higher education and higher technical school in particular.


Intermolecular Dynamics Of Condensed State: Study Of Temperature Effect On Anisotropy Relaxation By Vibration Spectroscopy, Bakhodir Eshchanov, Shavkat Otajonov, Jurat Gayipov, Dilafruz Xudoyberdiyeva, Sarvarbek Qurbanbayev Sep 2020

Intermolecular Dynamics Of Condensed State: Study Of Temperature Effect On Anisotropy Relaxation By Vibration Spectroscopy, Bakhodir Eshchanov, Shavkat Otajonov, Jurat Gayipov, Dilafruz Xudoyberdiyeva, Sarvarbek Qurbanbayev

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

As a result of the experimental study of the spectra of anisotropic scattering of light, a character of orientation movement of molecules in aromatic hydrocarbons has been analyzed. The obtained results have been interpreted from the viewpoint of a model of inhibited rotation and the contributions of the rotational and vibrational degrees of freedom to a molecule spectrum have been estimated. With increasing temperature of liquids under study and approaching a critical state, the rotational degrees of freedom "freeze", and the vibrational degrees have become more significant.


Complex Diffusion Monte-Carlo Method: Test By The Simulation Of The 2d Fermions, Bakhodir Abdullaev, Mirzayousuf Musakhanov, Atsushi Nakamura Sep 2020

Complex Diffusion Monte-Carlo Method: Test By The Simulation Of The 2d Fermions, Bakhodir Abdullaev, Mirzayousuf Musakhanov, Atsushi Nakamura

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

On the base of the diffusion Monte-Carlo method we develop the method allowing to simulate the quantum systems with complex wave function. The method is exact and there are no approximations on the simulations of the module and the phase of the system's wave function. In our method averaged value of any quantity have no direct contribution from the phase of distribution function but only from the phase of the Green function of diffusion equation. We test the method by the simulations of the ground state of fermions in two-dimensional parabolic well. Anyons are used for the representation of the …


On The Solvability Of Hypersingular Equation Of Peridynamics, Shavkat Alimov, Shukhrat Sheraliev Sep 2020

On The Solvability Of Hypersingular Equation Of Peridynamics, Shavkat Alimov, Shukhrat Sheraliev

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

The integro-differential equation of peridynamics with hyper-singular kernel is considered. The existence and uniqueness of solution is proved.


Restoring The Function Set By Integrals For The Family Of Parabolas On The Plane, Akram Begmatov, Alisher Ismoilov Jun 2020

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 …


Test Statistics Based On Independence Processes, Leyla Kakadjanova Jun 2020

Test Statistics Based On Independence Processes, Leyla Kakadjanova

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

Paper is devoted to investigating classical normalized empirical process of independence. Processes are investigated by using strong approximation methods with best rate of convergence. We also consider the problems of finding of limit distributions of certain classes of statistics for testing the hypothesis of independence of random variable and event. The application to random censoring model also considered.


Fractional Differentiation Of The Grunwald-Letnikov-Hadamard Type And The Difference Of The Fractional Order With A Multiplicative Step, Mahmadiyor Yakhshiboev Jun 2020

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 Jun 2020

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.


On The New Nonlinear Properties Of The Nonlinear Heat Conductivity Problem In Nondivergence Form, Mersaid Aripov, Maftuha Sayfullayeva Jun 2020

On The New Nonlinear Properties Of The Nonlinear Heat Conductivity Problem In Nondivergence Form, Mersaid Aripov, Maftuha Sayfullayeva

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this article, we discuss one problem of nonlinear thermal conductivity with double nonlinearity; an exact analytical solution has been found for it, the analysis of which allows revealing a number of characteristic features of thermal processes in nonlinear media. The following nonlinear effects have been established: the inertial effect, the finite propagation velocity of thermal disturbances, the spatial localization of heat, and the effect of the finite time of the existence of a thermal structure in an absorption medium.


The Entrance Times For Circle Maps With A Break, Akhtam Dzhalilov, Javlon Karimov Jun 2020

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 …


The Method Of Potentials For The Airy Equation Of Fractional Order, Kamoliddin Rakhimov Jun 2020

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 Jun 2020

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 Jun 2020

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 Jun 2020

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 ecX and enX. 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 Apr 2020

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.


Photocatalytic Performance Of V2O5 Nanoparticles Incorporated Tio2 Nanotubes As A Visible-Light Active Photoelectrodefor Water Splitting, Ulugbek Shaislamov, Kamil Mukimov, Turgunali Akhmadjanov Apr 2020

Photocatalytic Performance Of V2O5 Nanoparticles Incorporated Tio2 Nanotubes As A Visible-Light Active Photoelectrodefor Water Splitting, Ulugbek Shaislamov, Kamil Mukimov, Turgunali Akhmadjanov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

Herein we demonstrate brief investigation results of photoelectrochemical performance of TiO2 nanotube (NT) based photoelectrode incorporated with V2O5 nanopaerticles (NP). Photoelectrodes were composed of TiO2 NTs with a diameter of 100 nm and length of 8µm,that were prepared by electrochemical anodization process at 35V in a formamade based electrolyte. The V2O5 nanoparticles were formed on the walls of the TiO2 NTs by deep coating technique with an average size of ∼5-10 nm. The V2O5NP incorporated TiO2NTs show superior light absorption properties in the …


On Negative Eigenvalues Of The Discrete Schrödinger Operator With Non-Local Potential, Zahriddin Muminov, Shukhrat Lakaev Apr 2020

On Negative Eigenvalues Of The Discrete Schrödinger Operator With Non-Local Potential, Zahriddin Muminov, Shukhrat Lakaev

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

On the d-dimensional lattice 𝕋d, d= 1, 2 the discrete Schrödinger operator Hλµ with non-local potential constructed via the Dirac delta function and shift operator is considered. The dependency of negative eigenvalues of the operator on the parameters is explicitly derived.


On The Number Of The Discrete Spectrum Of Two-Particle Discrete Schröodinger Operators, Zahriddin Muminov, Utkir Kuljanov, Shukhrat Alladustov Apr 2020

On The Number Of The Discrete Spectrum Of Two-Particle Discrete Schröodinger Operators, Zahriddin Muminov, Utkir Kuljanov, Shukhrat Alladustov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

We consider a family of discrete Schrö dinger operators hd(k), where k is the two-particle quasi-momentum varying in 𝕋d=(−π,π]d , associated to a system of two-particles on the d - dimensional lattice ℤd, d>1. The CwikelLieb-Rozenblum (CLR)-type estimates are written for hd(k) when the Fermi surface Ek-1(𝔢m(k)) of the associated dispersion relation is a one point set at em(k), the bottom of the essential spectrum. Moreover, when the Fermi surface Ek-1(𝔢m(k)) is of dimension d−1 or d−2, we …


On Negative Eigenvalues Of The Discrete Schrödinger Operator With Non-Local Potential, Zahriddin Muminov, Shukhrat Lakaev Apr 2020

On Negative Eigenvalues Of The Discrete Schrödinger Operator With Non-Local Potential, Zahriddin Muminov, Shukhrat Lakaev

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

On the d-dimensional lattice 𝕋d, d= 1, 2 the discrete Schrödinger operator Hλµ with non-local potential constructed via the Dirac delta function and shift operator is considered. The dependency of negative eigenvalues of the operator on the parameters is explicitly derived.


Change In The Physical And Chemical Properties Of Oil-Contaminated Soil In The Steppe Zone, Zafarjon Jabbarov, Tokhtasin Abdrakhmanov, Shavkat Akhmedov, Urol Nomozov, Muqaddas Abdurahmonova Apr 2020

Change In The Physical And Chemical Properties Of Oil-Contaminated Soil In The Steppe Zone, Zafarjon Jabbarov, Tokhtasin Abdrakhmanov, Shavkat Akhmedov, Urol Nomozov, Muqaddas Abdurahmonova

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

Today, around the world as a result of the activities of industrial enterprises, mining, their use, as well as other anthropogenic factors, there is a chemical pollution of the soil cover, a change in soil properties and fertility. Pollution of soils of various types leads to the formation of problems such as soil degradation, a decrease in the qualitative and quantitative level of fertility, as well as other problems associated with the ecosystem. Today, the urgent task is to create remediation measures for soils contaminated to varying degrees with oil and oil products, corresponding to the climatic conditions of the …


On The Asymptotic Behavior Of Branching Processes With Stationary Immigration, Yakubjan Khusanbaev, Sadulla Sharipov Apr 2020

On The Asymptotic Behavior Of Branching Processes With Stationary Immigration, Yakubjan Khusanbaev, Sadulla Sharipov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper, we consider nearly critical branching processes with immigration. We study the convergence of a sequence of nearly critical branching processes with immigration when immigration is a stationary in wide sense. Moreover, we derive an asymptotic for characteristic function of this process.


Fixing Mobile Desert Sands: Definition Of Water Resistance, Mechanical Strength And Mechanism Of Fixing, Shakhnoza Kuldasheva, I. L. Ahmadjonov, N. Z. Adizova, I. D. Eshmetov, Kh. I. Akbarov Apr 2020

Fixing Mobile Desert Sands: Definition Of Water Resistance, Mechanical Strength And Mechanism Of Fixing, Shakhnoza Kuldasheva, I. L. Ahmadjonov, N. Z. Adizova, I. D. Eshmetov, Kh. I. Akbarov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

The possibility of the formation of a water-resistant structures in dispersions of saline soils by using a composition of additives combining a surfactant and a fixing agent, generally providing the effect of dispersed hardening, is considered. The data by investigation of method of fixing the sands of the Surkhandarya region with complex additives obtained on the basis of the waste of the Kungrad soda plant are presented. It is shown that the basis of the proposed method of fixing saline soils with complex additives is the process of converting their surface layers (up to 5 cm) from free-dispersed state to …


Choosing The Structure Of Convolutional Neural Networks For Face Recognition, Kabul Khudaybergenov Apr 2020

Choosing The Structure Of Convolutional Neural Networks For Face Recognition, Kabul Khudaybergenov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

Evaluating the number of hidden neurons and hidden layers necessary for solving of face recognition, pattern recognition and classification tasks is one of the key problems in artificial neural networks. In this note, we show that artificial neural network with a two hidden layer feed forward neural network with d inputs, d neurons in the first hidden layer, 2d+2 neurons in the second hidden layer, k outputs and with a sigmoidal infinitely differentiable function can solve face recognition tasks. This result can be applied to design pattern recognition and classification models with optimal structure in the number of hidden neurons …


Sequential Estimation By Intervals Of A Fixed Width Of The Asymptotic Variance Of Rank Estimates Of The Shift Parameter, Gulnoza Rakhimova Apr 2020

Sequential Estimation By Intervals Of A Fixed Width Of The Asymptotic Variance Of Rank Estimates Of The Shift Parameter, Gulnoza Rakhimova

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper, we consider a sequential interval estimation by intervals of a fixed width of the asymptotic variance of rank estimates of the shift parameter. Reviewed the asymptotical properties of estimates of functionals of an unknown probability density and the conditions of the asymptotical consistency of a confidence interval of a fixed width and the asymptotical efficiency of the stopping time. The convergence rate of consistency of the fixed width interval for the asymptotic variance of rank estimates of the shift parameter is obtained.


Death Line For Radio Pulsars In Braneworlds, Djavlanbek Rayimbaev, Satimbay Palvanov, Maksud Umaraliyev, Malika Khudoyberdiyeva Apr 2020

Death Line For Radio Pulsars In Braneworlds, Djavlanbek Rayimbaev, Satimbay Palvanov, Maksud Umaraliyev, Malika Khudoyberdiyeva

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

We investigate the effects of braneworlds on energetic processes in plasma. magnetosphere of neutron stars. Obtained that the presence of brane charge causes an increase in the size of the polar cap region. It has shown that the polar capsize of neutron stars with larger rotation period and compactness parameter is also larger. We have studied deathline of radio pulsar in braneworld. Obtained that the deathline shifted down and the pulsars which lying on the deathline become visible in radio band. Moreover, we have extended particle acceleration in polar cap of neutron stars in the presence of the brane charge, …