Physical Sciences and Mathematics Commons^™

Sufficient Condition For The Possibility Of Completing The Pursuit, Nodirbek Umrzaqov

Scientific Bulletin. Physical and Mathematical Research

In this paper, the problem of chase is represented by a system of linear differential equations of motion dynamics. In this case, there is an integral limit to the control parameter of the evader, and a geometric limit to the control parameter of the pursuer. The pursuer is allowed to use the control that the fugitive has used so far to build his control. There are enough conditions for the game to end even if it starts from any starting point. An algorithm for constructing the control function of the pursuer is defined. It should also be noted that the …

Infinite Peirce Distribution In The Algebra Of Compact Operators And Description Of Its Local Au-Tomorphisms, Farhodjon N. Arzikulov, Rejabboy Qo’Shaqov

Scientific Bulletin. Physical and Mathematical Research

In the present paper the infinite Peirce decomposition of the algebra 𝐾(𝐻) of com-pact operators on an infinite dimensional separable Gilbert space 𝐻 is constructed, using the norm of the algebra 𝐾(𝐻) and a maximal family of mutually or-thogonal minimal projections, i.e., self-adjoint,idempotent elements. The infinite Peirce decompo-sition on the norm of a 𝐶∗-algebra is also con-structed in 2012 by the first author. But, it turns, the condition, applied then, is not sufficient for the infi-nite Peirce decomposition on the norm constructed in 2012 to be an algebra. Therefore, in the present paper, the infinite Peirce decomposition on the norm …

Effect Of Excess Tellurium And Lead On Defor-Mation - Characteristics Of Polycrystalline Pbte Films, Yu.Yu. Vaitkus, Otajonov Salimjon

Scientific Bulletin. Physical and Mathematical Research

In this work, we studied the ef-fect of excess tellurium and lead on the defor-mation characteristics of polycrystalline PbTe films obtained on different substrates. It was found that the resistance of the films first increases and reach-es a maximum, and with a further increase in the level of deformation, it decreases and the sign of the tensile resistance begins to change, which are associated with the presence of internal stresses in the films. It was also shown that with an increase in the amount of lead in the composition of the PbTe film, the electrical conductivity increases in com-parison with …

Structure And Electrophysical Properties Of A Solid Solution (Gaas1-Δbiδ)1-X-Y(Ge2)X(Znse)Y, S.Z. Zainabidinov, I.N. Karimov, Hotamjon Mansurov, Akramjon Boboev, Dilkhayotjon Pulatjon Ugli Abdurakhimov

Scientific Bulletin. Physical and Mathematical Research

This paper shows the possibility of growing a single-crystal solid solution of substitution (GaAs1-δBiδ)1-x-y(Ge2)x(ZnSe)y on GaAs substrates by liquid-phase epitaxy from a bismuthcontaining solution-melt. The grown films had a ptype of conductivity with a current carrier concentration of 1,86·1017 сm-3, a mobility of р = 300 cm2/V·s, and a resistivity of 0,13 Ohms·cm. Structural studies have shown that the epitaxial films have a sphalerite structure of the ZnS type and are monocrystalline with an orientation of (100). The crystal lattice parameter of the film was af = 0,56697 nm. Studies of current-voltage characteris-tics of n-GaAs – p-(GaAs1-δBiδ)1-x-y(Ge2)x(ZnSe)y heterostructures at different …

Simulation Of Self-Heating Effect In Mosfet Based On 2d Mos2, Atabek E. Atamuratov, Xushnudbek Sh. Saparov, A Yusupov, Frank Schwierz

Scientific Bulletin. Physical and Mathematical Research

One of the main trends of today's electronics is the decreasing the sizes of MOSFET up to nanometer scale. In this connection there are two main views to the perspective of scaling. According to one of them limit of scaling is reached at sizes 10 nm order, however according to second view, still there are opportunity to decrease transistor to more lower sizes. In accordance with second approach it is suggested to continue the size scaling by modification the transistor structure or by using the new materials, particularly one or two dimensional materials. One of such suggestions is the designing …

Method Of Characteristics For Solving The Problem Of Gas Outflow From An Elementary Sec-Tion Of A Gas Pipeline, Madaminjon K. Mahkamov, S.S. Akhmadjonov, I.K. Khujaev

Scientific Bulletin. Physical and Mathematical Research

Numerous problems based on equations of hyperbolic type are solved by the method of characteristics when boundary conditions of the first, second and third kinds are set on the boundary. These include, in particular, the problems of pipeline transportation of various media. The quasi-one-dimensional equations of conservation of mass and momentum are linearized and separate equations are drawn up for a specific indicator (flow rate, gas pressure) of the process. This approach is associated with the tradition of forming boundary conditions and solving problems only with respect to a specific indicator, in particu-lar, with respect to pressure, velocity, and flow …

Electrophysical Properties Of Supercapacitor On The Basis Of New Gel Polymer Electrolyte, J.A. Shodmanov, Azamat Boymirzaev

Scientific Bulletin. Physical and Mathematical Research

The results showed a slight increase in internal resistance under the influence of bending and confirmed that the equivalent circuit model of electrons did not change under bending conditions as indicated in graphically illustrated the results by cyclic voltamperometry (TsV) at a scanning speed of 10 mV / s under the above bending angles of the SK prepared on the basis of PG 10 GPE. From ex-periments we found that the shapes are almost rec-tangular, with no redox peaks observed. We can see that the area of the TsV curves changes slightly as the bending angle increases, but this does …

Influence Of A Strong Magnetic Field On Fermi Energy Oscillations In Two-Dimensional Semiconductor Materials, Gafur Gulyamov, Ulugbek Inayatillyevich Erkaboev, Rustam Gulomzhonovich Rakhimov, Nozimjon Sayidov Sayidov, Jasurbek Mirzaev

Scientific Bulletin. Physical and Mathematical Research

This article discusses the effect of a quantizing magnetic field and temperature on Fermi energy oscillations in nanoscale semiconductor materials. A generalized mathematical expression is obtained for calculating the dependence of the Fermi energy oscillations on the magnetic field, temperature, and thickness of the quantum well. It is shown that the Fermi energy in nanoscale semiconductor materials under a quantizing magnetic field is quantized. The proposed theory explains the experimental results in two-dimensional semiconductor structures with a parabolic dispersion law.

Determination Of The Specific Thermo Emf Of Granulated Silicon Doped With Alkaline Metals., B.M. Abdurakhmanov, Zarnigor Sohibova, M.M. Adilov

Scientific Bulletin. Physical and Mathematical Research

The value of the specific thermo EMF is one of the most important thermoelectric parameters of a material and in practice is estimat-ed mainly by two well-known methods - integral and differential. To measure the thermo EMF of granular silicon, we used a differential method. In this work, the thermoelectric properties of granular silicon containing alkali metal atoms have been studied, the presence of which, for example, in single-crystal structures makes it possible to improve the characteristics of a number of devices, and in polycrystalline ones, the effect of grain boundaries on the electrical properties, in particular, to reduce the …

The State Of Solar Energy In Uzbekistan In The Framework Of The Devel-Opment Of Renewable Energy Sources, E.Z. Imamov, Ramizulla Abdullaevich Muminov, Temur Asfandiyarovich Djalalov, I.Sh. Abdullaeva

Scientific Bulletin. Physical and Mathematical Research

The paper analyzes the possibilities of renewable energy sources to become the main sources of ener-gy that can in the future replace traditional technologies for the production of thermal and electrical energy based on the use of fossil fuels and nuclear energy.

Technological approaches are considered that make it possible to significantly increase the efficiency of solar energy, and it is also shown that such a possibility can be realized by using weakly crystalline and cheap modifications of silicon, which have previously passed the corresponding nanotechnological effect.

Properties And Applications Of Metal-Oxide Thin Films In Converters Of En-Ergy (Review), Shakhriyor Kh. Yulchiev, Akramjon Boboev, Xushruybek Mahmudov

Scientific Bulletin. Physical and Mathematical Research

Metal-oxide semiconductors (SnO2, ZnO, TiO2, etc.) have a wide band gap (~3 eV) and are trans-parent in the visible range of the optical spectrum. Therefore, transparent semiconductor devices (diodes, transistors, integrated circuits, etc.) can be made based on them. There are two peaks in the emission spectrum of the LED. One of the peaks (3.3 eV), apparently, is as-sociated with exciton recombination, and the other peak is associated with recombination through a deep impuri-ty level. The emission spectrum of the LED was ob-served at a direct current of 40 mA. The electrolumines-cence spectrum obtained on the heterostructure at room temperature …

Development And Implementation Of A Photovoltaic Power Plant With A Capacity Of 3-6 Kw With “Smart Greed” Elements In The Conditions Of The Fergana Valley, Райимжон Алиев, Жамшидбек Каххоров, Авазбек Мирзаалимов, Наврузбек Мирзаалимов, Бобур Рашидов

Scientific Bulletin. Physical and Mathematical Research

Today, solar cells are manufactured at the industrial level mainly from polycrystalline and monocrystalline silicon. Solar elements made of silicon make up more than 90% of the solar elements that are produced worldwide. Depending on the seasons of the year in the Ferghana Valley, the movement of the Sun, geographical location, air humidity, temperature changes, the intensity of light falling on the surface of solar panels and other parameters, the characteristic (I-V) of solar panels was studied. The installation of solar panels installed at Andijan State University consists of the installation, commissioning and analysis of the results obtained on sunny, …

A Cauchy-Goursat Problem For A Second Kind Degenerated Equation Of Hyperbolic Type, Doniyor Usmonov

Scientific Bulletin. Physical and Mathematical Research

In the work a Cauchy-Goursta problem has been formulated and investigated for a second kind degenerated equation of hyperbolic type. During the investigation, it was used properties of Gauss’s hyper geometric function and symbol of Pochhammer, the considered problem equivalently reduced to an integral equation with respect to trace of unknown function. Properties of Riemann-Liuvill integral-differential and generalized integral-differential operators have found solution of the taken integral equation. To find solution of the problem it was used general solution of the equation. A class of generalized solutions was introduced for the correctness of the problem. It was found necessary conditions …

Evolution Of Quantum Systems Consisting Of Mul-Tiple Various Particles Interacting With General-Ized Yukasha Potential, N.N. Bogolyubov, Rasulova Mukhayo, U.O. Avazov

Scientific Bulletin. Physical and Mathematical Research

In this paper, multi-variety densely packed par-ticle dynamic systems with the ability to interact with the shielded Yukawa potential were studied. Also, in order to study more widely the dynamics of systems containing particles interacting via shielded potential, the theoretical foundations of the dynam-ics of systems consisting of an arbitrary number of bounded - sorted multi-particles are analyzed. The dynamics of an arbitrary number of interacting par-ticle systems on a screening potential was studied using the Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY) chain of quantum kinetic equations. The BBGKY chain of quantum kinetic equations has solutions for the case that characterizes the evo-lution of …

Measurement Of Geometric Fractals On The Basis Of Hausdorf-Bezikovich And Minkovsky-Buligan Measurements, Anorova Amanbaevna Shaxzoda, Jabborov Sindorovich Jamoliddin, Meliyev Fattoevich Farxod

Scientific Bulletin. Physical and Mathematical Research

This article is devoted to the study of the future position of fractal measurements. Different methods of computer modeling of a wide range of classes of fractal geometric objects are described in detail, as well as the main methods of mathematical analysis of fractal size of virtual and real fractals are described. The article explains the differences between the concept of fractals, their properties, B. Mandelbrot's tariff, Hausdorf-Bezikovich scale, Minkowski-Buligan scale, topological measurement, the concept of fractal measurement and measurement in Euclidean geometry. This article provides basic information about fractals. A detailed description of the various methods of computer modeling …

Local And 2-Local Derivations Of Solvable Leibniz Algebras With Null-Filiform Nilradical, Sardorbek Umrzaqov

Scientific Bulletin. Physical and Mathematical Research

In the works of Ayupov, Khudoyberdiyev and Yusupov proved that the local and 2-local derivation of solvable Leibniz algebras with model nilradical are derivations. Solvable Leibniz algebras with null-filiform nilradical are the partial case of solvable Leibniz algebras with model nilradical. However, the proof in the paper is different from model nilradical case. The derivation is a fundamental notion in mathematics. Derivations play a prominent role in algebra. There are many generalizations of derivations as antiderivation, δ-derivations, ternary derivations and (α,β,γ)-derivations. One of the important generalizations of derivation is local and 2-local derivations. Local derivations defined by Kadison, Larson and …

A Linear Differential Game With Gronwall Type Constraint, Bahromjon Samatov, Ulmasjon Soyyiboev, Adhambek Akbarov

Scientific Bulletin. Physical and Mathematical Research

In the paper, it has been investigated how Gronwall`s inequality can be used in theory of Differential Games. Here a pursuit problem of linear differential game has been studied when constraints of Gronwall type generalizing geometrical constraint imposed on control parameters of players. To solve the pursuit problem it will be proposed a parallel pursuit strategy ( -strategy) and its structure will be studied in relation to parameters. In this article, the authors` previous works will be advanced and extended. As a result of the work, the new sufficiency conditions will be suggested.

Solvability Of Boundary Value Problem With A Conormal Derivative For An Equation Of Mixed Elliptic-Parabolic Type, Marguba H. Akbarova, Surayyo H. Akbarova

Scientific Bulletin. Physical and Mathematical Research

This article is devoted to the formulation and study of a nonlocal boundary value problem with a conormal derivative for an equation of mixed elliptic-parabolic type. Here the existence and uniqueness of the solution of the problem is proved. Uniqueness of the solution is shown by the method of energy integrals, and existence of a solution is based on the theory of integral equations. Existence of a solution of a nonlocal boundary value problem is equivalently led to a solvability of a system of singular integral equations of normal type with zero index.

On The Stability Of Some Non-Stationary Nonlinear Systems, Rustamjon V. Mullajonov, Shakhodathon N. Abdugapparova, Jumagul V. Mirzaahmedova

Scientific Bulletin. Physical and Mathematical Research

The objective of the theory of stability of motion is to establish signs that make it possible to judge whether the motion in question is stable or unstable. Since in reality perturbing factors always inevitably exist, it becomes clear that the problem of stability of movement assumes very important theoretical and practical significance.

Mathematical modeling of processes and phenomena in animate and inanimate nature always involves a certain classification of them in accordance with their complexity. Many processes and phenomena are modeled by large-scale systems (CMS), which consist of separate subsystems, united by communication functions. In many cases, CMS is …

Solve The Diophante`S Equations, Tulanboy T. Ibaydullayev, Alisher L. Abdulvohidov

Scientific Bulletin. Physical and Mathematical Research

This article is based on the lectures for gifted students of the faculty of Physics and Mathematics on the solution of Diophantine equations in science circles.

If the number of unknowns involved in a system of equations exceeds the number of equations, such equations are called Diophantine equations or indeterminate equations. Specifically, equations of the form

3x-5y=8, x²+3xy-y²=12,

x³+y²-3x+5=0, x³+y³=z³,… are indefinite equations.

Many of the equation or system of equations determine all the numbers to find solutions to the most common examples. Short multiplication formulas, …

Rota-Baxter Operators On 3-Dimensional Nilpotent Associative Algebras, Jamila R. Aliyeva, Hushruyahon M. Karimjanova, Ziyodahon B. Holmirzayeva

Scientific Bulletin. Physical and Mathematical Research

Associative algebras are introduced into mathematics of the 19th century and are still intensively studied. The classification of associative algebras of small dimensions first appeared in the works of Pierce in 1881. In 2018, the German scientist William de Graf gave a classification of nilpotent associative algebras of small sizes. The article describes all the Rota-Baxter operators on 3-dimensional nilpotent associative algebras.

Rota-Baxter operators were defined by Baxter to solve an analytic formula in probability. It has been related to other areas in mathematical physics and mathematics.

Throughout this paper algebras are considered over the field of complex numbers.

A …

Some Innovative Statistical Tools For Sustainability Of The Research Production Process, Kamola S. Ablazova

Scientific Bulletin. Physical and Mathematical Research

New control charts and their assessments determining the normality of the quality criterion are carried out in the article. Using these charts, the degree of stability of the production process is studied using one example.

In practice, the stability of the process under study is important. It depends on ordinary (random) and special (nonrandom) reasons. These reasons strongly affect the distribution of the process under study. Distributions may vary in position, spread, and shape. They can be checked using asymmetry and excess coefficients. If only the usual causes of variations occur, then the results of the process form a distribution …

On Abattle Over The ‘Ebbinghaus Forgetting Curve’ Using Control Charts, Sohibjon A. Ahmedov, Hushnudbek D. Yuldashev

Scientific Bulletin. Physical and Mathematical Research

Studying the laws of memorization, the German experimental psychologist German Ebbinghaus statistically proved that if a person does not repeat the material studied, then the storage of material in memory decreases almost exponentially with respect to time. He called these arcs the “Curve of Forgetting”. In this case, the information is forgotten at first very quickly, and then slower.

More than two centuries, research has been conducted on the functional abilities of the human brain. Nowadays, natural and artificial intelligence are being compared by researchers.

Our method on the “Ebbinghaus Forgetting Curve” is based on using Control Charts with exponentially …

Eigenvalue Problems For An Elliptic Equation With Two Singular Coefficients, Asror M. Shokirov

Scientific Bulletin. Physical and Mathematical Research

For the elliptic type of differential equation with two singular coefficients, the quadratic values of the Dirixle and Dirixle-Neumann problems were found in the quarter in that work. The field and boundary conditions for solving these problems are described in the polar coordinate system. The result is a rectangle in the polar coordinate system. Then, we used the method of separating variables in the right rectangle, that is, divided the variables by the equation and divided the problem into two distinct values for ordinary differential equations. The first of the ordinary differential equations is the substitution of , where the …

The Task Of Prosecuting Simple Differential Games On The Rectangle, Azizhon O. Zunnunov

Scientific Bulletin. Physical and Mathematical Research

The theory of differential games is developed and resulted from modeling technical problems. Some of the problems in differential games theory can be described as controlling two moving objects, i.e. one of them is the follower that tries to catch the other object, and obviously the other object is the runner. The runner tries to run away from the follower. Most of the practical and theoretical IT problems, planning, technical and other challenges will be derived to the differential games theory for resolution. Thus researching this theory is one of most important topics currently. A lot of researchers contributed enormous …

Description Of 2-Local Two Sided Multiplication On An Algebra Of Matrices, Farhodjon N. Arzikulov, Kamola A. Solijanova

Scientific Bulletin. Physical and Mathematical Research

The present paper is devoted to 2-local derivation on associative and Jordan matrix rings. In 1997, P. Semrl introduced the notion of 2-local derivations and described 2-local derivations on the algebra ¬B(H) of all bounded linear operators on the infinite-dimensional separable Hilbert space H. A similar description for the finite-dimensional case appeared later in 2004. In the paper Y. Lin and T. Wong 2-local derivations have been described on matrix algebras over finite dimensional division rings. In 2012 Sh. Ayupov, K. Kudaybergenov suggested a new technique and have generalized the above mentioned results for abritrary Hilbert spaces. Namely they considered …