Евразийский журнал математической теории и компьютерных наук

Mazkur maqolada tovush tebranishlari va uning to‘lqin xossalari o‘rganiladi. Tovush – bu tebranayotgan jism tomonidan hosil qilinadigan mexanik to‘lqin bo‘lib, u havoda yoki boshqa muhitlarda tarqaladi va inson qulog‘i orqali qabul qilinadi. Tadqiqotda tovushning chastota diapazoni, uni inson eshitish sezgisi bilan bog‘liqligi, shuningdek infratovush va ultratovush tushunchalari yoritilgan. Tovush to‘lqinlarining gaz, suyuqlik va qattiq jismlarda tarqalish xususiyatlari, tovushning sub’ektiv xususiyatlari (balandlik, tembr, qattiqlik) va ularning fizikaviy asoslari haqida ma’lumot berilgan. Real tovushlarning garmonik tebranishlar yig‘indisidan iboratligi va akustik spektr tushunchasi ham ko‘rib chiqilgan.

В данной статье анализируются возможности использования геометрических методов при решении квадратных уравнений. Эти подходы важны не только для закрепления теоретических знаний, но и для решения практических задач.

В статье представлена методика расчета масляного фильтра дизеля тепловоза с учетом повышения его фильтрующей способности, надежности и работоспособности, выполнено математическое моделирование, численные исследования проведены в среде программирования MATHCAD 15.

Ushbu maqola semantik qidiruv tizimlarining ilmiy asoslari, texnologik arxitekturasi va amaliy qo‘llanilish sohalari haqida tahliliy ma’lumot taqdim etadi. Semantik qidiruvning an’anaviy kalit so‘zga asoslangan tizimlardan farqi, tabiiy tilni ishlab chiqarish (NLP), ontologiyalar va graf bilimlari kabi texnologiyalarning roli yoritiladi. Maqolada tibbiyot, ta’lim, elektron tijorat va huquq sohalari misolida semantik qidiruvning amaliy qo‘llanilishi tahlil qilinadi. Shuningdek, tizimning texnik cheklovlari (hisoblash resurslari, ma’lumot sifati, til cheklovlari) va kelajakdagi rivojlanish yo‘nalishlari (ko‘p modal qidiruv, personalizatsiya, kvantsal hisoblashlar) ko‘rib chiqiladi. O‘zbekiston kontekstida semantik qidiruvni mahalliy tillarga moslashtirish va ilmiy tadqiqotlarni qo‘llab-quvvatlash bo‘yicha tavsiyalar beriladi. Maqola ilmiy jurnallar va amaliyot uchun qimmatli manba sifatida xizmat qiladi.

This article discusses the conditions under which a topological space is metrizable and how this relates to compactness. Key metrization theorems, such as those by Urysohn and Nagata-Smirnov, are examined. The article also explores the role of compactness in metrizable spaces, supported by examples like the Sorgenfrey line and Cantor set. Applications in analysis, computer science, and control theory demonstrate the practical importance of these concepts.

Maqolada timsollarni aniqlashning muhim masalalaridan biri informativ fazoni qurish usuli va algoritmi taklif etilgan. Timsollarni aniqlashning muammolari bilan bog‘liq bo‘lgan barcha tushunchalar mantiqiy mukammal, matematik aniq va sodda ko‘rinishda ifodalashga harakat qilingan. Timsollarni asosiy masalasi – sinflashtirish, informativ belgilar fazosini shakllantirish, o‘quv tanlanma ob’yekt va belgilarining muhimlik darajalarini aniqlash kabi masalalar chuqur tahlil etilgan. Informativ belgilar fazosida yaqinlik funksiya qiymatlarini aniqlashda Fisher funksionali elementlaridan foydalanilgan. Ob’yektlar aro o‘xshashlik funksiyasining yuqori va quyi chegaralari aniqlangan hamda ularni tasdiqlovchi ma’lumotlar keltirilgan

This paper explores how artificial intelligence (AI) can be applied to enhance user interface (UI) and user experience (UX) design in web applications. By analyzing real-time user interaction data such as mouse movements, click patterns, and session time, machine learning models identify usability issues and recommend interface improvements. The study compares traditional heuristic evaluation with AI-driven approaches and demonstrates how data-informed UX redesigns significantly improve engagement metrics. Experimental results suggest that AI integration leads to reduced bounce rates and more efficient user navigation, validating its role in next-generation UX design workflows.

This article explores the integration of large language models (LLMs), such as ChatGPT, into modern web applications. It discusses the practical benefits—enhanced user interaction, automation, and intelligent response generation—alongside potential security risks including data exposure, bias propagation, and misuse. A technical prototype is implemented to assess the impact of LLMs on performance and user experience metrics. Empirical analysis shows measurable gains in task efficiency but highlights challenges in privacy and latency. The study provides a framework for ethical, efficient, and secure deployment of LLMs in dynamic web environments