Volume 10 » KhorezmScience.uz

INVERSE SCATTERING TRANSFORM FOR A NONAUTONOMOUS TODA HIERARCHY FLOW

We investigate a nonautonomous system generated by a timedependent linear combination of two commuting Toda hierarchy flows. Using the inverse scattering transform, we establish the Lax representation and determine the time evolution of the scattering data. Explicit formulas for the reflection...

Actual problems of Mathematics, Physics and Mecanics / 2026 / October

Eshchanova Gulchehra Sheribbayevna

Volume 10 | Issue 10

3 October 2026, 22:12

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TRACE FORMULAS FOR THE PERIODIC ABLOWITZ–LADIK SPECTRAL PROBLEM

We study the periodic Ablowitz-Ladik spectral problem under the focusing reduction. The associated hyperelliptic spectral curve and auxiliary divisor are constructed from the monodromy matrix. Trace formulas and spatialshift relations connecting the periodic potential with the spectral data are...

Actual problems of Mathematics, Physics and Mecanics / October / 2026

Babadjanova Aygul Kamildjanovna

Volume 10 | Issue 10

3 October 2026, 22:11

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RAPIDLY DECREASING SOLUTIONS OF THE NEGATIVE ORDER MODIFIED KORTEWEG-DE VRIES EQUATION

In this work, an algorithm for constructing solutions to the negative order modified Korteweg–de Vries equation is proposed, based on the application of the inverse scattering theory to the Zakharov–Shabat system. Within the framework of the developed algorithm, an explicit one-soliton solution of...

Actual problems of Mathematics, Physics and Mecanics / 2026 / October

Atanazarova Shoira Erkinovna

Volume 10 | Issue 10

3 October 2026, 22:10

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CONFIGURATION-DEPENDENT ELECTRONIC STRUCTURE OF OXYGEN-VACANCY- AND TE-RELATED DEFECTS IN Α-AL2O3: A FIRSTPRINCIPLES STUDYAuthor information

Using DFT (GGA-PBE), we calculate the electronic structureofa120-atom α-Al2O3 supercell for four defect families: Frenkel-pair-like defects, oxygen vacancies, vacancies around an interstitial Te atom, and substitution of O by Te. The pristine gap is 6.17 eV. Oxygen vacancies narrow the gap...

Actual problems of Mathematics, Physics and Mecanics / 2026 / October

Khasanov Asrorbek

Volume 10 | Issue 10

3 October 2026, 22:09

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CHANGES IN THE ACTIVITY OF NITROGEN-FIXING MICROORGANISMS IN IRRIGATED TAKYR IN THE KARAKUL DISTRICT UNDER THE INFLUENCE OF SOIL AND ECOLOGICAL FACTORS

The study investigated the effects of salinity level, soil profile depth, and seasonal conditions on the abundance of nitrogen-fixing microorganisms in irrigated takyr-meadow soils. The number of nitrogen fixers decreased consistently with increasing salinity and soil depth. The highest values were...

Actual problems in modern agriculture / 2026 / October

Umarov Otabek Rafoilovich, Ochilova Muyassar Alisher qizi

Volume 10 | Issue 10

3 October 2026, 22:08

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THE EFFECT OF SEASONAL VARIATIONS, TYPE AND DEGREE OF SALINITY ON THE ACTIVITY OF CELLULOSE-DEGRADING MICROORGANISMS IN IRRIGATED SEROZEM-MEADOW SOILS OF THE ARID ZONE

The study evaluated the effects of soil salinity, profile depth, and seasonal conditions on the abundance of cellulose-decomposing microorganisms in irrigated sierozem-meadow soils. The results showed that microbial abundance decreased with increasing salinity and soil depth, while the highest...

Actual problems in modern agriculture / 2026 / October

Umarov Otabek Rafoilovich, Ochilova Muyassar Alisher qizi

Volume 10 | Issue 10

3 October 2026, 22:07

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STAGES OF HISTORICAL DEVELOPMENT OF THE PUBLIC EDUCATION SYSTEM IN UZBEKISTAN

This article systematically analyzes the historical stages of development of the public education system of the Republic of Uzbekistan, with particular attention to the reforms implemented after independence. The study examines the historical development of education and enlightenment in the...

Actual problems of history, philosophy and sociology / 2026 / October

Sadullayev Mirzobek Baxtiyarovich

Volume 10 | Issue 10

3 October 2026, 22:06

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ENHANCING THE WEAR RESISTANCE OF THE WORKING SURFACES OF MILL AND PUMP COMPONENTS USING AN ULTRAHIGH-MOLECULAR-WEIGHT POLYMER COMPOSITE: A COMBINED TRIBOLOGICAL, MATHEMATICAL, AND INDUSTRIAL STUDY

Working components of mills and slurry pumps in mining, metallurgy, and mineral processing are exposed to abrasive wear, erosion, and cavitation. This study presents a UVKP polymer composite based on ultra-highmolecular-weight polyethylene (UHMWPE), reinforced with graphite and short fibers. The...

Actual problems in modern technical sciences / 2026 / October

Sarvar Parmonov, Bekhzod Abdurafikov, Sherzodjon Rakhimboev

Volume 10 | Issue 10

3 October 2026, 22:05

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VOCABULARY GROWTH IN UZBEK TEXTS: A REGRESSION STUDY

This study investigates the relationship between the number of tokens in Uzbek-language texts and the percentage share of unique tokens. The purpose is to determine the form of this relationship under a linear model and a Heaps’-law-type power-law model and to compare their descriptive performance....

Actual problems in modern technical sciences / 2026 / October

Madatov Khabibulla Akhmedovich

Volume 10 | Issue 10

3 October 2026, 22:04

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