October - KhorezmScience.uz

INVERSE SCATTERING TRANSFORM FOR A NONAUTONOMOUS TODA HIERARCHY FLOW

Bunyod — Sat, 03 Oct 2026 22:12:00 +0500

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 coefficient and norming constants are derived, while the discrete eigenvalues remain invariant.

TRACE FORMULAS FOR THE PERIODIC ABLOWITZ–LADIK SPECTRAL PROBLEM

Bunyod — Sat, 03 Oct 2026 22:11:00 +0500

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 derived.

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

Bunyod — Sat, 03 Oct 2026 22:10:00 +0500

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 the problem under consideration is obtained in the class of rapidly decaying functions.

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

Bunyod — Sat, 03 Oct 2026 22:09:00 +0500

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 monotonically (4.36 → 2.21 eV), whereas Te-containing configurations show a nonmonotonic response (2.66 to 1.12 eV) controlled by the local Te coordinationrather thanbythe defect count. The in-gap states do not by themselves establish a conducting filament.

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

Bunyod — Sat, 03 Oct 2026 22:08:00 +0500

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 recorded in the 0-25 cm layer during summer. Under strong salinity, the reduction in nitrogen-fixing microorganisms reached 78.8-86.2%, while correlation coefficients ranged from r = 0.989 to 0.993.

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

Bunyod — Sat, 03 Oct 2026 22:07:00 +0500

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 values were recorded in the non-saline 0-25 cm layer, particularly during summer.

STAGES OF HISTORICAL DEVELOPMENT OF THE PUBLIC EDUCATION SYSTEM IN UZBEKISTAN

Bunyod — Sat, 03 Oct 2026 22:06:00 +0500

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 territory of Uzbekistan from ancient times, including the period of Islamic cultural advancement, the Timurid era, the Jadid movement, and the Soviet education system. Particular attention is devoted to the formation and modernization of the national education system during 1991–2026, the improvement of its legal framework, implementation of the National Program for Personnel Training, development of lifelong learning, large-scale reforms after 2017, improvement of educational quality, strengthening the professional status of teachers, introduction of international educational standards, and digital transformation. The findings demonstrate that modernization of the education system has become one of the strategic priorities of state policy in Uzbekistan during the years of independence.

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

Bunyod — Sat, 03 Oct 2026 22:05:00 +0500

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 material was produced by compression molding at 130–160°Cand250–300 MPa. Its tribological, mechanical, and physical properties were evaluated using experimental methods. Industrial trials demonstrated up to a threefold increase in component service life, a 40% reduction in installation downtime, and a 12–25% decrease in energy consumption. These findings indicate that UVKP composites offer a promising solution for improving wear resistance and reducing operating costs in demanding industrial environments.

VOCABULARY GROWTH IN UZBEK TEXTS: A REGRESSION STUDY

Bunyod — Sat, 03 Oct 2026 22:04:00 +0500

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. The scientific significance of the study lies in providing empirically grounded evidence on this regularity specifically for the Uzbek language, where it has not previously been examined in this form. The practical motivation arises from the author’s broader dissertation research on text similarity, text summarisation, text classification, and text clustering using TF-IDF, whose vector dimensionality is determined by vocabulary size and therefore affects memory requirements. The study analysed a corpus of 132 Uzbek-language texts of different sizes, calculated token counts and unique-token shares, and modelled their relationship using linear and Heaps’-law-type power-law regression. The results show that Heaps’ law describes the relationship considerably more accurately than the linear model, with goodness of fit of approximately 94% compared with 69%, respectively. The findings demonstrate that unique-token growth is sublinear rather than proportional to text length. This provides a basis for forecasting vocabulary size, vector dimensionality, and memory requirements of TF-IDF-based applications in advance, helping to anticipate and mitigate the curse of dimensionality in Uzbeklanguage text processing.

APPLICATION OF ADVANCED CERAMIC COMPOSITES IN CUTTING TOOL INDUSTRY

Bunyod — Sat, 03 Oct 2026 22:03:00 +0500

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, performance requirements, and key properties of ceramic composite materials. It also provides information on the primary processes involved in the machining of metals using these materials.