Eurasian Journal of Mathematical Theory and Computer Sciences

XXI аср - рақамли иқтисодиёт асри бўлиб, ахборот технологиялари (АТ) жамият ҳаётининг барча жабҳаларига, жумладан, иқтисодиёт, таълим, соғлиқни сақлаш ва давлат бошқарувига чуқур кириб бормоқда. Бугунги кунда АТ нафақат муайян соҳалар учун мутахассислар тайёрлашнинг асосий воситаси, балки рақобатбардош кадрлар тайёрлашнинг муҳим омили ҳамдир. Шу муносабат билан ушбу макола, олий таълим муассасаларида (ОТМ) АТ фанини ўқитишнинг самарадорлигини ошириш долзарб аҳамият касб этади. Мазкур мақолада биз ОТМларда АТ фанини ўқитишнинг ҳозирги ҳолатини таҳлил қиламиз, мавжуд муаммоларни аниқлаймиз ва уларнинг ечимларини таклиф қиламиз, шунингдек, АТ соҳасида таълимнинг келажак истиқболларини кўриб чиқамиз.

The advancement and growing efficiency of computing technologies necessitate operation under increasingly noisy environments. These conditions may result in imbalanced heat dissipation, reduced signal strength, and, consequently, system malfunctions and errors in output data. This study focuses on the issue of unauthorized information leakage. The core of the problem is analyzed through graphical models, which are subsequently transformed into a matrix representation. The findings of this research can be utilized for evaluating and enhancing information security measures.

Ushbu maqolada   fazosida logarifmik qoldiq tushunchasi, uning asosiy xossalari va Bochner–Martinelli yadrosi asosida hisoblash usullari tadqiq qilinadi. Mualliflar integral formulalar yordamida logarifmik qoldiqni hisoblash metodlarini tahlil qiladi va Yuzhakov–Roos teoremasini qo‘llab, turli holomorf funksiyalar uchun nollar to‘plami va ularning kattaliklarini (multiplicity) aniqlaydi. Maqolada keltirilgan misollar orqali izolyatsiyalangan nollar, ikkilik nollar va ildizli ifodali nollar tizimli tarzda o‘rganiladi, ularning logarifmik qoldiqqa ta’siri ko‘rsatib beriladi. Xususan,  ​ va  ​ kabi funksiyalar misolida Jakobi matritsasining singulyarlik shartlari va qoldiqning qiymati tushuntiriladi. Tadqiqot natijalari ko‘p o‘lchovli kompleks analizning nazariy va amaliy masalalariga qo‘llanilishi mumkinligini ko‘rsatadi.

This article studies one of the important issues in analytical geometry - methods for determining the shortest distance from a point to a straight line. From a geometric point of view, this distance is considered as the length of the perpendicular drawn from the point to the straight line. The article discusses in detail the basic formula used to calculate this distance, its mathematical foundations and the rules for its use. During the study, the formula for calculating the distance given the general equation of a straight line (Ax+By+C=0) and an arbitrary point (  . is analyzed. This topic is of great importance not only theoretically, but also in practical areas. In particular, it is widely used in engineering to determine the optimal distance between structures, and in the fields of computer graphics and physics to calculate spatial relationships between objects. The article can be a useful guide in mastering this formula and applying it to real problems.

For several decades, the economically unfavorable state of the country was associated with the difficulties of the transition period. We are so clinging to the conviction that happiness can be achieved not through material well-being, but through spiritual maturity, as a result of which both the state and society found themselves in a maelstrom of problems. Finally, they realized the truth: without elementary living conditions, a person will not achieve not so much happiness, but even just calmness. For many years, the problem of poverty in the country was considered a closed topic. Instead of the prescribed term, they used the concepts of "poor", "in need of protection."

Ta'lim sifati olingan bilim darajasi, ijtimoiy va professional funktsiyalarni bajarishga qaratilgan shaxsning ijodiy fazilatlarini shakllantirish bo'yicha baholanadi. Intellektual shaxsning umumiy ta'limida geometriya asosiy o'rinni egallaydi. Ushbu maqola geometrik masalalarni yechishda o’quvchilarning mustaqil ijodiy tafakkurini rivojlantirish muammolari va imkoniyatlariga bag‘ishlangan.

This article discusses various types of malicious software that have become well-known on a global scale, their classifications, and the methods they use to operate or cause damage to computer systems.

The article discusses the word2vec model, which is an effective method for learning vector representations of words, widely used in natural language processing tasks. The main architectures of the model - Skip-gram and CBOW, as well as key parameters that affect the quality of the resulting vector representation are described. It is shown that the use of word2vec allows transforming words into dense vectors that reflect their semantic and syntactic properties, which significantly improves the results compared to traditional text representation methods.

This article analyzes advanced foreign and national experiences related to the development of creative activities. In particular, it examines programs, methods, and environments aimed at supporting creativity in education in advanced countries such as the USA, Finland, Japan, and South Korea. Additionally, it explores the work being done in the education system of Uzbekistan to develop creative potential, existing approaches, and national experiences. The role of teaching methodologies that promote creative thinking, problem-based learning, project-based activities, the STEAM approach, and other modern technologies is highlighted. Based on the analysis, possibilities for adapting foreign experiences to the national context, practical recommendations, and prospective directions are identified. This work serves as a valuable resource for educators, researchers, and participants in the education system.