CENTRAL ASIAN JOURNAL OF MATHEMATICAL THEORY AND COMPUTER SCIENCES

Algorithms for Automatic Analysis of Human Foot Radiographic Images

Yusupov Ozod Rabbimovich — 2026-05-05

This article provides an overview of algorithms for processing human foot X-ray images, which are essential for diagnosing various foot conditions, including fractures, deformities, and joint diseases. The study explores several image preprocessing techniques, such as detecting structural changes, noise reduction, and contrast enhancement, all of which help improve the quality of radiographic images and increase diagnostic accuracy. In addition, the paper discusses challenges related to noise, distortions, and low contrast in X-ray images, and outlines methods to mitigate these issues. By implementing these algorithms, the study aims to enhance the effectiveness of foot-related diagnoses and support more efficient medical decision-making.

Practical Estimation and Simulation Analysis of the Kolmogorov Constant for Heavy-Tailed Noncritical Markov Branching Systems

Iskandarov S.B — 2026-05-11

This paper presents a practical estimation and simulation-based study of the Kolmogorov constant in the context of heavy-tailed, noncritical continuoustime Markov branching systems. Building on the explicit analytic form recently derived for noncritical Markov branching models, we investigate the empirical behaviour of the survival probability and related asymptotic quantities under heavy-tailed offspring distributions using Monte Carlo simulation techniques.

Global Convergence Guarantees for Adaptive Gradient Algorithms with Barzilai–Borwein and Alternative Step-Length Strategies

Alyaqdhan Ammar Abed — 2026-05-23

Motivated by recent progress in adaptive schemes for convex optimization, this work develops a proximal-gradient framework that enforces global convergence without resorting to linesearch procedures. The proposed approach accommodates widely used step-length rules, including Barzilai–Borwein updates and one-dimensional Anderson-type acceleration. Importantly, the analysis applies to problems where the smooth component admits only local Hölder continuity of its gradient. The resulting theory unifies and strengthens several existing results, while numerical experiments confirm the practical benefits of coupling aggressive step-length selection with adaptive safeguarding mechanisms.

Applications of Laplace’s Method in Asymptotic Analysis

Iskandarov S.B — 2026-06-02

This article investigates the application of Laplace’s method in asymptotic analysis. An asymptotic formula is derived showing that, as the parameter increases, the value of the integral involving powers of a function is mainly determined by the behavior of the function near its maximum point. The paper also discusses the asymptotic properties of large-parameter functions and presents related analytical results.

Vibescape: Real-Time Emotion-Based Music Recommendation Using Multimodal Analysis

P. Velavan — 2026-06-02

Vibescape is a novel emotion-based music recommender system that aims to provide a personalised and immersive music streaming experience. This system employs cutting-edge emotion detection technology to analyse the user's emotions in real time and suggest songs that fit their current mood. Vibescape combines popular music platforms such as Spotify, SoundCloud and YouTube to allow users to stream music from their preferred sources seamlessly. The app also provides personalised playlists that match the user’s mood and listening habits. Vibescape’s intuitive and user-friendly interface customises the overall music streaming experience according to the emotional journey of the listener. Vibescape uses advanced algorithms to analyse emotional signals from facial expressions, voice, or text inputs to accurately identify moods. In addition to recommendations based on emotion, the system also adapts to long-term listening patterns, fine-tuning its recommendations to make a more personalised experience over time. Its integration with multiple music sources means the platform can provide a huge library of songs for different tastes and moods. Vibescape is a new way to link emotions and music, turning passive listening into an emotionally resonant and dynamic experience.