Physical Sciences and Mathematics Commons^™

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.

Mathematical Modeling Of Nonlinear Problem Biological Population In Not Divergent Form With Absorption, And Variable Density, Maftuha Sayfullayeva

Acta of Turin Polytechnic University in Tashkent

В работе установлены критические и двойные критические случаи, обусловленные представлением двойного нелинейного параболического уравнения с переменной плотностью с поглощением в "радиально-симметричной" форме.Такое представление исходного уравнения дало возможность легко построить решения типа Зельдовоч-Баренбатт-Паттл для критических случаев в виде функций сравнения.

Influence Of The Nature Of The Medium On The Conformational States Of Macromolecules Of Anionic Polyelectrolytes And Their Flocculating Effect, Mapruza Dzhumamuratova, Amanbay Pirniyazov, Oleg Dormeshkin, Akhmed Reymov, Tleumuratov Kuanish, Saparbay Kalbaev

Karakalpak Scientific Journal

The properties of surfactants of anionic polyelectrolytes are investigated depending on the nature of the medium, conformational states neutralized by organic bases, differing in the length of the hydrocarbon radical. The concept of the role of the state of macromolecules in solution in the indicated processes has been developed. The anionic carboxyl-containing polyelectrolytes synthesized on the basis of methacrylic acid differed not only in the length of the hydrocarbon radical of the organic base - counterion, but also in their branching. The relationship between the state of polyelectrolyte macromolecules in solution and their ability to regulate the properties of natural …

Numerical And Analytical Solutions Of The Integral Geometry Problem On The Families Of Parabola And Broken Lines, N.U Uteuliev, Gafur Djaykov, Seidullaev Abat

Karakalpak Scientific Journal

In this paper, the problem of reconstructing the function in the strip on the known integrals from it with a given weight function on the family of parabola and broken lines. Inversion formulas for the family of broken lines were obtained, on their basis the theorems of uniqueness and existence of the solution were proved. Estimations of stability of problem solving in Sobolev spaces are obtained, from which weak ill-posed of problems follows. For the problems of integral geometry on the parabola family we obtained a regularized solution. On the basis of these obtained results the numerical results of experiments …

Features Of Heart Activity Of Cattle In The Conditions Of Southern Aral Sea Region, Svetlana Mambetullaeva, Khayratdin Seytkamalov

Karakalpak Scientific Journal

In this article, the results of comparative analysis of electrocardiogram are shown for the cows of different breeds in the Aral Sea region. It is set that the high temperature of the environment and sunny insolation render a negative influence on the functional parameters of the cardiac vascular system of animals. There are facts about the cows of different breeds at the influence of different temperatures that have unidirectional functional changes in the operation of the heart. At the same time, we will mark that these changes are less expressed for the cows of the improved zebu visible cattle, what …

Photoelectric Injection Amplification Of Al–Al2o3–P-Cdte–Mo Structures At Low Bias Voltages, A K. Uteniyazov

Karakalpak Scientific Journal

The results of studies of photoelectric injection enhancement of the Al–Al₂O₃–p-CdTe –Mo structure upon application of low bias voltages. It has been shown that the studied Al-Al₂O₃–p-CdTe-Mo structure under can be represented as a n⁺-p-R_ом structure with a long base. Conducted researches show that Al-Al₂O₃–p-CdTe-Mo structure has unique properties. It has very high photocurrent and photosensitivity at both direct and reverse dias voltage under even small bias voltage (up to 500mV).

Synthesis Of Supramolecular Complex L– (-) – Menthol, Ziyada Djumanova Dr, Lolaxan Ettibaeva, Ugilay Abduraxmonova, Zulfiya Khalmuratova

Karakalpak Scientific Journal

In this article glycyrrhizic acid content with menthol in several various proportions (2:1; 4:1; 9:1), information was given on synthesis and physical and chemical properties of new supermolecular complexes. Received supramolecular complexes concerning 4:1 it was chemically defined and also studied the structure of supramolecular complexes by physical methods on the basis of interaction of organic molecules with electromagnetic radiation, in particular their range IR – of spectroscopy. Our work of the near future will be turned to check its recent supramolecular complexes on the basis of GA: Menthol for growth of a plant and biotic elasticity of tension …

Spectrophotometric Characterization Of The Complexation Of Gossypol Acetic Acid With Cobalt Ion, Ugilay Abdurahmanova, Habibjon Kushiev, Maral Askarova, Dilafruz Allanazarova

Karakalpak Scientific Journal

The authors of the article suggest simple and express method of spectrophotometric determination of cobalt with the help of derivatives of gossypol. Optimal conditions of determining cobalt are found. Under optimal conditions there was created a graded graph, which is more linear in the range for cobalt concentration of 10.0 – 50.0 microgram/25 ml, contents and constants of cobalt complex with gossypol vinegar acid.

Fuzzy Synergetic Control Nonlinear Dynamic Objects, Isomiddin Sidikov, Noilakhon Yakubova, Komil Usmanov, Saparbay Kazakhbayev

Karakalpak Scientific Journal

The article deals with the synthesis of effective algorithms for controlling a chemical reactor and developed a fuzzy synergistic controller for a class of indefinite nonlinear dynamic systems. A synergetic control scheme is proposed for solving the control problem for nonlinear systems. Non-linear systems with configurations and parameters that change over time require a completely non-linear model and adaptive control scheme for a practical operating environment. The synthesis of control laws is performed by the method of analytical design of aggregated controllers (ACAR). Fuzzy logic systems are used to evaluate the unknown nonlinear behavior of the system, and a new …

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 …

Local And 2-Local Derivation On Solvable Leibniz Algebras Whose Nilradical Is A Quasi-Filiform Leibniz Algebra Of Maximum Length, Shavkat Ayupov, Bakhtiyor Yusupov

Karakalpak Scientific Journal

We show that any local derivation on the solvable Leibniz algebras whose nilradical is a quasi-filiform Leibniz algebra of maximum length with the maximal dimension of complementary space to the nilradical is a derivation. Moreover, a similar problem concerning 2-local derivations of such algebras is investigated.

Boundary Theorem Of Morera In The Space Of Rectangular Matrices, B. T. Kurbanov

Karakalpak Scientific Journal

In the theory of functions of one complex variable, Morer's theorem is known, which is inverse in some sense to the classical Cauchy theorem. On the complex plane, results on functions with the one-dimensional property of holomorphic continuation are trivial, and Morer's boundary theorems are absent. We note that the ordinary (non-boundary) Morera theorems in domains of space are well known. The first result related to our topic was obtained by Agranovsky M.L. and Valsky R.E. [1], who studied functions with the one-dimensional property of holomorphic continuation in a ball. The proof was based on the properties of the automorphism …

Boundary Value Problem For The Fourth-Order Degenerate Equation Of Mixed Type, Zh. A. Otarova

Karakalpak Scientific Journal

In this paper, we study a boundary value problem for degenerate fourth-order mixed type partial differential equation in a rectangular domain. The unique regular solvability of the boundary value problem posed is investigated. The solution is constructed in the form of the sum of the biorthogonal series in an explicit form, and the rationale for the convergence of the series in the class of regular solutions is given. To prove the solution of this problem, the estimates of the coefficients of the series and the system of eigenfunctions are used, which are established by asymptotic formulas for the Bessel function …

String Oscillations With Impulse Effects, K. K. Yelgondiyev, O. O. Kurbanbaev, S. R. Matmuratova

Karakalpak Scientific Journal

The problem of existence of periodic solutions to the equation of oscillations of a pulse stuny impact soft moments. Necessary and sufficient conditions of existence of periodic solutions in such oscillatory systems.

Smoothness Of Riesz Potential Out Of The Set Of Small Lebesgue Measure, A. Daujanov

Karakalpak Scientific Journal

We deals with the differential properties of the potential to some Borel measure of order, where Riesz kernel. The smoothness of Riesz potential out of some set of small Lebesgue measure is proved. The method of proof is based on the representation theorem of subharmonic function with the help of potential associated with a Borel measure. The result complements the well-known theorem of Cartan.

A Problem Of Solute Transport In A Cylindrical Porous Media With A Fractal Structure Taking Into Account Adsorption Phenomena, B. X. Xujayorov, J. M. Maxmudov, A. I. Usmanov, B. O. Saidov

Scientific Journal of Samarkand University

The process of anomalous solute transport in a coaxial cylindrical porous media is modelled by differential equations with a fractional derivative. The problem of solute transport in a two-zone cylindrical media consisting of macro- and micropores taking into account adsorption effectshas been numericallyposed and solved. The concentration profiles of suspended particles and the adsorbed solute in the macropore and micropore, the surface of the local concentration in the micropore are determined. The influence of adsorption phenomena and the order of the derivative with respect to the coordinate, i.e. fractal dimension of the media, on the characteristics of the solute transport …

On A Two-Speed Mathematical Model Of Two-Fluid Medium With One Pressure, X. X. Imomnazarov, S. B. Kuyliyev

Scientific Journal of Samarkand University

An overdetermined stationary system of second-order differential equations is obtained. For the two-dimensional system, a variational statement of the problem is established. It is shown that the variational problem for the system of equations of two-speed hydrodynamics is well-posed in the corresponding Sobolev space

The Cauchy Problem For The System Of The Elasticity, I. E. Niyozov, O. Karshiboyev

Scientific Journal of Samarkand University

In this paper we consider the problem of analytical continuation of solutions to the system of the elasticity in a bounded domain from their values and values of their strains on a part of the boundary of this domain, i.e., we study the Cauchy problem

On Estimates For The Damped Oscillatory Integrals, I. A. Ikromov, Sh. A. Muranov

Scientific Journal of Samarkand University

In this paper we consider estimates of the Fourier transform measures, concentrated on analytic hypersurfaces containing the of damping factor. The paper presents the solution of the problem S.D.Soggi and I.M. Stein about the optimal decay of the transformation Fourier measures with a damping factor for any analytic surfaces in three-dimensional Euclidean space.

Of The Cauchy Problem For Thelaplace Equations On A Plane, D. S. Shodiyev

Scientific Journal of Samarkand University

In this paper, a uniqueness theorem is proved, and an estimate of conditional stability is obtained, and an approximate solution is constructed by the method of quasi-derivation and Tikhonov regularization.

The Problem Of Integral Geometry In A Strip With Weight Function, A. X. Begmatov, A. S. Ismoilov

Scientific Journal of Samarkand University

In this work we consider the problem of reconstructing a function from a family of parabolas in the upper half-plane with a weight function having a singularity. The uniqueness of theorem for the solution of equation is proved and the inversion formula is derived. It is shown that the solution of the problem posed is weakly ill-posed, that is, stability estimates are obtained in spaces of finite smoothness.

Uniqueness And Stability Problem Of Integral Geometry With Indignation, Akram Begmatov, Zarifjon Ochilov, Abduroziq Xusanov

Scientific Journal of Samarkand University

Рассматривается новый класс задач интегральной геометрии типа Вольтерра с функцией специального веса. Доказаны теоремы единственности и существования решения, получены оценки устойчивости и формула обращения в пространствах Соболева, что свидетельствует о слабой некорректности решения задачи интегральной геометрии. Постановка задачи интегральной геометрии с возмущением на семейство парабол в полосе считается. Теорема единственности ее решения доказана в классе дважды непрерывно дифференцируемых функций с компактным носителем, а оценки устойчивости получены в пространствах конечной гладкости.