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11 March 2024

INTERNATIONAL SCIENTIFIC AND PRACTICAL CONFERENCE ON “MODERN PROBLEMS OF APPLIED MATHEMATICS AND INFORMATION TECHNOLOGY (MPAMIT2022)”

11–12 May 2022

Bukhara, Uzbekistan

All Issues

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In this Issue

PRELIMINARY
MATHEMATICAL ANALYSIS
ALGEBRA AND GEOMETRY
DIFFERENTIAL EQUATIONS AND MATHEMATICAL PHYSICS
ARTIFICIAL INTELLIGENCE
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL MODELING
DIGITAL TECHNOLOGIES IN EDUCATION

PRELIMINARY

Dedication: To the 90th Anniversary of the Birth of Professor Gaybulla Nazrullaevich Salikhov

AIP Conf. Proc. 3004, 010001 (2024) https://doi.org/10.1063/12.0025282

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Preface: International Scientific and Practical Conference on “Modern Problems of Applied Mathematics and Information Technology (MPAMIT2022)”

AIP Conf. Proc. 3004, 010002 (2024) https://doi.org/10.1063/12.0024643

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MATHEMATICAL ANALYSIS

Hausdorff dimension of invariant measure of piecewise linear circle maps with two breaks

Abdurakhmon Aliyev; Gulasal Tirkasheva

AIP Conf. Proc. 3004, 020001 (2024) https://doi.org/10.1063/5.0199650

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On the spectrum of the Shrödinger operator

Sanjar Bakirov

AIP Conf. Proc. 3004, 020002 (2024) https://doi.org/10.1063/5.0200422

Abstract

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Uniformly linked space and its hyperspace

Ruzinazar Beshimov; Dilnora Safarova

AIP Conf. Proc. 3004, 020003 (2024) https://doi.org/10.1063/5.0202939

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New equivalent conditions for the boundedness of Hardy-Volterra operator

Mohlaroyim Eshimova

AIP Conf. Proc. 3004, 020004 (2024) https://doi.org/10.1063/5.0200036

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Dynamics of a discrete SIRD model based on Lotka-Volterra mappings

Dilfuza Eshmamatova

AIP Conf. Proc. 3004, 020005 (2024) https://doi.org/10.1063/5.0199863

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Non-tangential boundary values for A(z)−analytic functions

Behzod Husenov

AIP Conf. Proc. 3004, 020006 (2024) https://doi.org/10.1063/5.0199861

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On the existence of eigenvalues of the one particle discrete Schrödinger operators

Ahmad Khalkhuzhaev; Shakhobiddin Khamidov; Habibullo Mahmudov

AIP Conf. Proc. 3004, 020007 (2024) https://doi.org/10.1063/5.0200550

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2-local -antiautomorphism of B(H) is an inner -antiautomorphism

Sayyora Kholbekova; Abdugafur Rakhimov

AIP Conf. Proc. 3004, 020008 (2024) https://doi.org/10.1063/5.0200749

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Estimates for the norm of an integral operator with Oinarov’s kernel

Komil Kuliev; Gulchehra Kulieva; Normurod Ismatov

AIP Conf. Proc. 3004, 020009 (2024) https://doi.org/10.1063/5.0200753

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The problem of integral geometry in three-dimensional space with a weight function of a special form

Mukhiddin Muminov; Zarifjon Ochilov

AIP Conf. Proc. 3004, 020010 (2024) https://doi.org/10.1063/5.0200484

Abstract

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Invariant sets of Lotka-Volterra mappings acting in a four-dimensional simplex

Dilfuza Eshmamatova; Mokhbonu Tadzhieva; Rasul Ganikhodzhaev

AIP Conf. Proc. 3004, 020011 (2024) https://doi.org/10.1063/5.0199936

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Representation of a max-plus-gauge of the set of idempotent probability measures by the guage of the set of probability measures

Abror Tagaymurotov

AIP Conf. Proc. 3004, 020012 (2024) https://doi.org/10.1063/5.0200258

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ALGEBRA AND GEOMETRY

On asymptotic distributions of members of variational series for a random sample size

Igamnazar Mamurov

AIP Conf. Proc. 3004, 030001 (2024) https://doi.org/10.1063/5.0200828

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A variant of the Banach-Steinhaus theorem for weakly additive, order-oreserving operators

Feruz Aktamov

AIP Conf. Proc. 3004, 030002 (2024) https://doi.org/10.1063/5.0200264

Abstract

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Homomorphisms of arens algebras of measurable operators

Akrom Alimov

AIP Conf. Proc. 3004, 030003 (2024) https://doi.org/10.1063/5.0200676

Abstract

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Topological transformation groups on hyperspace and Dugundji compacta

Dilorom Beshimova

AIP Conf. Proc. 3004, 030004 (2024) https://doi.org/10.1063/5.0200321

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Structure of essential spectra and discrete spectrum of the energy operator of four-electron systems in the impurity Hubbard model. Quintet state. In the two- and three-dimensional lattice

Sa’dulla Tashpulatov; Rukhsat Parmanova

AIP Conf. Proc. 3004, 030005 (2024) https://doi.org/10.1063/5.0201559

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Clean-cut pairs (F(X ), η_F (X )) compacts of type F(X )

Shavkat Ayupov; Tursunbay Zhuraev

AIP Conf. Proc. 3004, 030006 (2024) https://doi.org/10.1063/5.0201549

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Generalized extrinsic curvature of a surface

Abdullaaziz Artykbaev; Nafisa Ibodullaeva

AIP Conf. Proc. 3004, 030007 (2024) https://doi.org/10.1063/5.0200171

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Classification of geometry of orbits of killing vector fields

Jasurbek Aslonov; Abdigappar Narmanov

AIP Conf. Proc. 3004, 030008 (2024) https://doi.org/10.1063/5.0199581

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On asymptotic properties of the perimeter of a convex hull generated by a uniformly distributed sampling in a convex polygon

Isakjan Khamdamov

AIP Conf. Proc. 3004, 030009 (2024) https://doi.org/10.1063/5.0201923

Abstract

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On the group of homeomorphisms foliated manifolds

Anvarjon Sharipov

AIP Conf. Proc. 3004, 030010 (2024) https://doi.org/10.1063/5.0199811

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On defects of polyhedra isometric on sections at vertices

Fayzulla Topvoldiyev; Anvarjon Sharipov

AIP Conf. Proc. 3004, 030011 (2024) https://doi.org/10.1063/5.0199937

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DIFFERENTIAL EQUATIONS AND MATHEMATICAL PHYSICS

Predator-prey model with a free boundary

Alimardon Elmurodov; Ibodat Khaldibaeva; Nurila Yuldoshev

AIP Conf. Proc. 3004, 040001 (2024) https://doi.org/10.1063/5.0201883

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On some linear two-point inverse problems for a three-dimensional wave equation with nonlocal conditions

Sirojiddin Dzhamalov; Shokhrukh Khudoykulov

AIP Conf. Proc. 3004, 040002 (2024) https://doi.org/10.1063/5.0200324

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On a nonlocal boundary value problem for a three-dimensional mixed-type equation of the second kind in an unbounded parallelepiped

Sirojiddin Dzhamalov; Biybinaz Sipatdinova

AIP Conf. Proc. 3004, 040003 (2024) https://doi.org/10.1063/5.0200325

Abstract

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Investigation of initial-boundary value problem for integro-differential fractional diffusion equation

Jonibek Jumaev; Zavqiddin Bozorov; Istam Shadmanov; Dilshod Atoev

AIP Conf. Proc. 3004, 040004 (2024) https://doi.org/10.1063/5.0199967

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A quasilinear parabolic equation of the reaction-diffusion type with free boundary

Mirojiddin Rasulov; Abdurakhmon Norov

AIP Conf. Proc. 3004, 040005 (2024) https://doi.org/10.1063/5.0201572

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Application of the Fourier method to the study of a hyperbolic integro-differential equation in a rectangular domain

Jurabek Safarov; Askar Rakhmonov; Maftunakhon Safarova

AIP Conf. Proc. 3004, 040006 (2024) https://doi.org/10.1063/5.0201252

Abstract

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Determination of a diffusion coefficient and a source control term for a time fractional diffusion equation with integral type overdetermining conditions

Kibriyo Amrilloyeva; Dilshoda Akramova; Shuhrat Juraev; Jamshid Ergashov

AIP Conf. Proc. 3004, 040007 (2024) https://doi.org/10.1063/5.0200382

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Vector fields and invariant solutions of two dimensional heat equation

Abdigappar Narmanov; Eldor Rajabov

AIP Conf. Proc. 3004, 040008 (2024) https://doi.org/10.1063/5.0199818

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Propagation of skew-symmetric nonstationary waves in an elastic spherical layer

Amon Shukurov; Ma’mura Musurmonova

AIP Conf. Proc. 3004, 040009 (2024) https://doi.org/10.1063/5.0199588

Abstract

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The problem of finding the kernels in the system for integro-differential acoustic equations

Zavqiddin Bozorov; Halim Turdiev

AIP Conf. Proc. 3004, 040010 (2024) https://doi.org/10.1063/5.0199964

Abstract

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Inverse problem of determining the coefficient and kernel in an integro - differential equation of parabolic type

Jonibek Jumaev; Durdimurod Durdiev; Shakhnoza Ibragimova; Bekhzod Zaripov

AIP Conf. Proc. 3004, 040011 (2024) https://doi.org/10.1063/5.0199968

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A 2D inverse problem for a fractional-wave equation

Askar Rahmonov; Durdimurod Durdiev; Dilshoda Akramova

AIP Conf. Proc. 3004, 040012 (2024) https://doi.org/10.1063/5.0199843

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Uniqueness of one inverse problem for heat equation with a variable thermal conductivity

Durdimurod Durdiev; Javlon Nuriddinov

AIP Conf. Proc. 3004, 040013 (2024) https://doi.org/10.1063/5.0201320

Abstract

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Kernel determination problem for a integro–differential heat equation with a variable thermal conductivity

Durdimurod Durdiev; Javlon Nuriddinov

AIP Conf. Proc. 3004, 040014 (2024) https://doi.org/10.1063/5.0201318

Abstract

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The problem of determining the one-dimensional kernel for the system of viscoelasticity in the anisotropic medium

Durdimurod Durdiev; Halim Turdiev; Asliddin Boltaev

AIP Conf. Proc. 3004, 040015 (2024) https://doi.org/10.1063/5.0199987

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Nonlocal boundary value problems for a third order equation of elliptic-hyperbolic type

Bozor Islomov; Bakhtiyor Usmonov

AIP Conf. Proc. 3004, 040016 (2024) https://doi.org/10.1063/5.0200357

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On convergence of trajectories of a non-volterra quadratic stochastic operator

Bobokhon Mamurov

AIP Conf. Proc. 3004, 040017 (2024) https://doi.org/10.1063/5.0199878

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Convergence test statistic of kernel estimators of a density function from stationary sequence of strongly linearly positive quadrant dependent random variables

Abdurakhman Muhamedov

AIP Conf. Proc. 3004, 040018 (2024) https://doi.org/10.1063/5.0201723

Abstract

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ARTIFICIAL INTELLIGENCE

UzRoberta: A pre-trained language model for Uzbek

Rifkat Davronov; Fatima Adilova

AIP Conf. Proc. 3004, 050001 (2024) https://doi.org/10.1063/5.0199871

Abstract

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Comparative analysis of QSAR feature selection methods

Rifkat Davronov; Samariddin Kushmuratov

AIP Conf. Proc. 3004, 050002 (2024) https://doi.org/10.1063/5.0199872

Abstract

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Problematic issues in the organization of customs control related to the application of artificial intelligence methods

Abdusobir Saidov; Alisher Dustmukhamedov; Fazilat Khakimova

AIP Conf. Proc. 3004, 050003 (2024) https://doi.org/10.1063/5.0199812

Abstract

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COMPUTATIONAL MATHEMATICS AND MATHEMATICAL MODELING

Asymptotic behavior of solutions to the reaction-diffusion problem with double nonlinearity with variable density and source

Mersaid Aripov; Dilobar Nigmanova

AIP Conf. Proc. 3004, 060001 (2024) https://doi.org/10.1063/5.0199607

Abstract

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Modeling of cross-diffusion systems

Abrorjon Mamatov; Aziza Nurumova

AIP Conf. Proc. 3004, 060002 (2024) https://doi.org/10.1063/5.0200124

Abstract

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The equation of the driving torque generated by the concave surface rotor blade under the influence of wind pressure

Ulugbek Dekhkanov; Yodgorjon Tillaboev

AIP Conf. Proc. 3004, 060003 (2024) https://doi.org/10.1063/5.0201798

Abstract

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Development of a mathematical model of aerosol particles’ distribution process in the surface layer of the atmosphere taking into account the earth’s heterogeneous surface

Normakhmad Ravshanov; Shakhzod Nazarov; Erkin Nazarov; Bakhtiyor Boborakhimov

AIP Conf. Proc. 3004, 060004 (2024) https://doi.org/10.1063/5.0200769

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Development of a mathematical model and an efficient computational algorithm for predicting atmospheric pollution in industrial regions

Tursun Shafiev

AIP Conf. Proc. 3004, 060005 (2024) https://doi.org/10.1063/5.0199817

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Asymptotic behavior of solutions for a doubly nonlinear parabolic non-divergence form equation with density

Mersaid Aripov; Makhmud Bobokandov

AIP Conf. Proc. 3004, 060006 (2024) https://doi.org/10.1063/5.0199587

Abstract

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Issues on using modern platforms in the process of assembling sumorobots in robotics curriculums

Gulnora Buronova

AIP Conf. Proc. 3004, 060007 (2024) https://doi.org/10.1063/5.0200564

Abstract

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Statistical and mathematical model of the process of extracting pumpkin seeds by #x0421;O₂-extraction

#x041A;arim Gafurov; Jura Jumayev

AIP Conf. Proc. 3004, 060008 (2024) https://doi.org/10.1063/5.0199923

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Mathematical model for information monitoring system of fat and oil enterprises

Khamza Eshankulov; Nazokat Sayidova; Gulbahor Zaripova; Shafoat Imomova; Dildora Fayzieva

AIP Conf. Proc. 3004, 060009 (2024) https://doi.org/10.1063/5.0199814

Abstract

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Post-pass regime at stationary functioning of main gas pipelines

Ismatilla Khujaev; Khusniddin Mamadaliev; Khayotjon Aminov; Ziyomat Shirinov

AIP Conf. Proc. 3004, 060010 (2024) https://doi.org/10.1063/5.0200002

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Application of the conditions of imama bukhariy to modern information challenges

Fazilat Khakimova; Takhir Abduraxmonov; Abdusobir Saidov

AIP Conf. Proc. 3004, 060011 (2024) https://doi.org/10.1063/5.0199990

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On one efficient method for calculating three-dimensional turbulent jets of reacting gases

Safar Khodjiev

AIP Conf. Proc. 3004, 060012 (2024) https://doi.org/10.1063/5.0199840

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Modeling and algorithm for calculation the mixing and propagation of co-current flows in channels

Safar Khodjiev

AIP Conf. Proc. 3004, 060013 (2024) https://doi.org/10.1063/5.0199839

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Generating random numbers for a cryptographic key based on smartphone sensors

Mirkhon Nurullaev

AIP Conf. Proc. 3004, 060014 (2024) https://doi.org/10.1063/5.0199570

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Modeling of combustion processes in cylindrical chambers using modern package programs

Ismatulla Khujaev; Jurabek Jumayev; Muzaffar Hamdamov

AIP Conf. Proc. 3004, 060015 (2024) https://doi.org/10.1063/5.0199986

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Algorithms for constructing a finite element mesh of compound domains

Askhad Polatov; Sultan Gaynazarov; Akhmat Ikramov; Sardor Jumaniyozov

AIP Conf. Proc. 3004, 060016 (2024) https://doi.org/10.1063/5.0199609

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Optimal coefficients of the quadrature formulas in the space K_3,ω

Kholmat Shadimetov; Gayratjon Akhmadaliev

AIP Conf. Proc. 3004, 060017 (2024) https://doi.org/10.1063/5.0199926

Abstract

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Interpolation splines minimizing semi-norm in S₂(P₂) space

Kholmat Shadimetov; Siroj Azamov

AIP Conf. Proc. 3004, 060018 (2024) https://doi.org/10.1063/5.0200119

Abstract

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To construct basis functions in $W_{2}^{(1, 0)}$ space to finite element method for 1D two-point boundary-value problems

Samandar Babaev; Javlon Davronov; Jakhongir Mirzakulov; Gulchekhra Mirzaeva; Nilufar Amonova

AIP Conf. Proc. 3004, 060019 (2024) https://doi.org/10.1063/5.0199590

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Construction of optimal quadrature formulas for Fourier coefficients in the Hilbert space

Kholmat Shadimetov; Nurali Boltaev

AIP Conf. Proc. 3004, 060020 (2024) https://doi.org/10.1063/5.0199930

Abstract

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Construction of natural L spline in $W_{2, σ}^{(2, 1)}$ space

Samandar Babaev; Nurali Olimov; Shafoat Imomova; Bekhruzjon Kuvvatov

AIP Conf. Proc. 3004, 060021 (2024) https://doi.org/10.1063/5.0199595

Abstract

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Construction of an optimal quadrature formula for the approximation of fractional integrals

Samandar Babaev

AIP Conf. Proc. 3004, 060022 (2024) https://doi.org/10.1063/5.0199596

Abstract

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On an optimal formula for approximate integration

Kholmat Shadimetov; Fotima Davlatova

AIP Conf. Proc. 3004, 060023 (2024) https://doi.org/10.1063/5.0199935

Abstract

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Optimization of difference formulas for solving differential equations in the Hilbert space

Kholmat Shadimetov; Shermamat Esanov

AIP Conf. Proc. 3004, 060024 (2024) https://doi.org/10.1063/5.0199940

Abstract

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One new method for constructing compound optimal quadrature formulas

Kholmat Shadimetov; Otabek Gulomov

AIP Conf. Proc. 3004, 060025 (2024) https://doi.org/10.1063/5.0199943

Abstract

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Construction of the optimal cubature formula in the space ${\tilde{H}}_{p}^{μ}$ (T_n)

Farhod Jalolov; Bekzodjon Isomiddinov

AIP Conf. Proc. 3004, 060026 (2024) https://doi.org/10.1063/5.0199850

Abstract

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An approximate solution method of Abel’s integral equation in the Hilbert space

Abdullo Hayotov; Bobomurod Boytillayev

AIP Conf. Proc. 3004, 060027 (2024) https://doi.org/10.1063/5.0199912

Abstract

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Asymptotically optimal lattice cubature formulas with a regular boundary layer in the space $H_{p}^{μ}$ (Ω)

Ozodjon Jalolov

AIP Conf. Proc. 3004, 060028 (2024) https://doi.org/10.1063/5.0199854

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On determination of optimal coefficients of a quadrature formula of Hermite type in the Sobolev space ${\tilde{W}}_{2}^{(m)}$ (T₁)

Hakim Rustamov; Islomjon Jalolov; Bekzodjon Isomiddinov

AIP Conf. Proc. 3004, 060029 (2024) https://doi.org/10.1063/5.0199865

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Optimal coefficients of an implicit difference formula in the Hilbert space

Kholmat Shadimetov; Rozik Karimov

AIP Conf. Proc. 3004, 060030 (2024) https://doi.org/10.1063/5.0200065

Abstract

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Coefficients and norms of error functionals of optimal difference formulas

Kholmat Shadimetov; Ravshan Mirzakabilov

AIP Conf. Proc. 3004, 060031 (2024) https://doi.org/10.1063/5.0200004

Abstract

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On an optimal method for the approximate solution of singular integral equations

Dilshod Akhmedov; Kholmat Shadimetov; Khakim Rustamov

AIP Conf. Proc. 3004, 060032 (2024) https://doi.org/10.1063/5.0199829

Abstract

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Approximate solution of a class of singular integral equations of the first kind

Dilshod Akhmedov

AIP Conf. Proc. 3004, 060033 (2024) https://doi.org/10.1063/5.0199828

Abstract

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Numerical modeling of the eigenvalue problem for a linear ordinary differential equation with homogeneous boundary conditions using the second kind Chebyshev polynomials

Chori Normurodov; Barno Tursunova

AIP Conf. Proc. 3004, 060034 (2024) https://doi.org/10.1063/5.0200331

Abstract

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Coefficients of optimal quadrature formulas in the space of differentiable functions

Kholmat Shadimetov; Farhod Nuraliev; Siroj Azamov; Shukurillo Ulikov

AIP Conf. Proc. 3004, 060035 (2024) https://doi.org/10.1063/5.0200106

Abstract

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System for finding the optimal coefficients of an interpolation spline

Kholmat Shadimetov; Aziz Boltaev

AIP Conf. Proc. 3004, 060036 (2024) https://doi.org/10.1063/5.0199834

Abstract

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An optimal quadrature formula in the space ${\tilde{W}}_{2}^{(2, 1)}$ of periodic complex-valued functions

Umedjon Khayriev; Mohinur Usmonova; Gavhar Turdieva

AIP Conf. Proc. 3004, 060037 (2024) https://doi.org/10.1063/5.0199582

Abstract

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Algorithm for finding the norm of the error functional of a Hermite type cubature formula in the Sobolev space ${\tilde{W}}_{2}^{(m)}$ (T_n)

Ozodjon Jalolov; Khurshidjon Khayatov

AIP Conf. Proc. 3004, 060038 (2024) https://doi.org/10.1063/5.0199855

Abstract

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Construction of the optimal quadrature formula in $L_{2}^{(2, 0)}$ (0, 1) space by Sobolev’s method

Kholmat Shadimetov; Javlon Davronov

AIP Conf. Proc. 3004, 060039 (2024) https://doi.org/10.1063/5.0199831

Abstract

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Cubature formulas in the parabolic domain

Gaybulla Ismatullaev; Ravshan Mirzakabilov; Rozik Karimov

AIP Conf. Proc. 3004, 060040 (2024) https://doi.org/10.1063/5.0200066

Abstract

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Optimal quadrature formulas for the approximate calculation of the Riemann-Liouville fractional order integral

Kholmat Shadimetov; Farhod Nuraliev; Otajon Toshboev

AIP Conf. Proc. 3004, 060041 (2024) https://doi.org/10.1063/5.0199830

Abstract

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The norm of the error functional for the Euler-Maclaurin type quadrature formulas in the space $W_{2}^{(2 k, 2 k - 1)} (0, 1)$

Rashidjon Rasulov; Diyorakhon Mahkamova

AIP Conf. Proc. 3004, 060042 (2024) https://doi.org/10.1063/5.0200255

Abstract

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An explicit expression of ordinary difference schemes for differential equations by the moved node method

Umurdin Dalabaev; Dilfuza Khasanova

AIP Conf. Proc. 3004, 060043 (2024) https://doi.org/10.1063/5.0201793

Abstract

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Approximate solution of a system of Volterra integral equations of the second kind using number-theoretic grids

Imamali Abiraev

AIP Conf. Proc. 3004, 060044 (2024) https://doi.org/10.1063/5.0203049

Abstract

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Approximate solution of the system of integral equations Volterra of the 2nd kind using uniform grids

Imamali Abirayev

AIP Conf. Proc. 3004, 060045 (2024) https://doi.org/10.1063/5.0203050

Abstract

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An optimal quadrature formula for approximating Fourier integrals in a Hilbert space

Abdullo Hayotov; Umedjon Khayriev

AIP Conf. Proc. 3004, 060046 (2024) https://doi.org/10.1063/5.0199913

Abstract

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On finding the norm of the error functional of interpolation formulas in the Sobolev space of periodic functions

Khurshidjon Khayatov

AIP Conf. Proc. 3004, 060047 (2024) https://doi.org/10.1063/5.0199928

Abstract

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A representation of the optimal quadrature formula in the Hörmander space $H_{2}^{μ}$ (R)

Kholmat Shadimetov; Ikrom Jalolov

AIP Conf. Proc. 3004, 060048 (2024) https://doi.org/10.1063/5.0199860

Abstract

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Numerical integration of Fourier integrals by the optimal quadrature formula exact for hyperbolic functions

Abdullo Hayotov; Abdimumin Kurbonnazarov; Sarvarbek Polvonov

AIP Conf. Proc. 3004, 060049 (2024) https://doi.org/10.1063/5.0199915

Abstract

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Quadrature method for linear integral equations in $L_{2}^{(1)}$ (0,1) space

Kholmat Shadimetov; Khojiakbar Usmanov

AIP Conf. Proc. 3004, 060050 (2024) https://doi.org/10.1063/5.0201819

Abstract

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Construction of an optimal interpolation formula exact for trigonometric functions

Abdullo Hayotov; Negmurod Doniyorov

AIP Conf. Proc. 3004, 060051 (2024) https://doi.org/10.1063/5.0199916

Abstract

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DIGITAL TECHNOLOGIES IN EDUCATION

Mathematical model for early prediction of learning success

Michail Noskov; Irina Fedotova; Marina Somova; Yulia Vainshtein

AIP Conf. Proc. 3004, 070001 (2024) https://doi.org/10.1063/5.0202515

Abstract

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