Actual problems of Mathematics, Physics and Mecanics
Actual problems in modern technical sciences
Actual problems of Natural Sciences
Actual problems of history, philosophy and sociology
Actual problems in modern tourizm and economics
Modern problems of Philology and Linguistics
Actual problems in modern pedogogy and pshychology
Actual problems in modern agriculture
Actual problems in modern art and architecture
October
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...
3 October 2026, 22:12
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...
3 October 2026, 22:11
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...
3 October 2026, 22:10
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...
3 October 2026, 22:09
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...
3 October 2026, 22:08
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...
3 October 2026, 22:07
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...
3 October 2026, 22:06
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...
3 October 2026, 22:05
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....
3 October 2026, 22:04
APPLICATION OF ADVANCED CERAMIC COMPOSITES IN CUTTING TOOL INDUSTRY
The unique mechanical and wear properties of ceramic composite materials drive the steadily increasing demand for them, enabling their application across various sectors such as cutting tools, electronics, aerospace, and the automotive industry. This article analyzes the manufacturing processes,...
3 October 2026, 22:03