SCIENTIFIC RESEARCH, INNOVATIONS, AND MODERN APPROACHES
Welcome to the International Scientific Journal “Scientific Research, Innovations and Modern Approaches” (SRI&MA). The Scientific Research, Innovations and Modern Approaches International Scientific Journal is an international, peer-reviewed scientific journal published under the auspices of Fergana State University. This journal serves as a platform for the dissemination of significant scientific results in all fields of scientific research. Our aim is to promote the advancement of knowledge in scientific disciplines, strengthen collaboration within the global scientific community, and uphold the highest standards of scholarly publishing. Publisher’s Name and Address: Publishing House of Fergana State University. 19 Murabbiylar Street, Fergana City, Fergana Region, Republic of Uzbekistan, 150100. Tel.: (+99873) 244-44-02 Fax: (+99873) 244-44-93 E-mail: fardu_info@umail.uz Founder: Fergana State University Language(s) of Articles: Uzbek, Russian, English. Year of Establishment: January 2026. Periodicity: Monthly (12 issues per year). Specialization (Fields of Science): 01.00.00 – Physical and Mathematical Sciences; 02.00.00 – Chemical Sciences; 03.00.00 – Biological Sciences; 05.00.00 – Technical Sciences; 05.01.00 – Information Technologies, Management and Computer Graphics; 09.00.00 – Philosophy; 10.00.00 – Philology; 13.00.00 – Pedagogical Sciences; 19.00.00 – Psychological Sciences; 22.00.00 – Sociological Sciences; 07.00.00 – Historical Sciences; 08.00.00 – Economic Sciences; 11.00.00 – Geographical Sciences; 06.00.00 – Agricultural Sciences; 17.00.00 – Art Studies; 18.00.00 – Architecture; 21.00.00 – Military Sciences; 04.00.00 – Geological and Mineralogical Sciences; Other scientific fields. Peer Review: All submitted manuscripts undergo a rigorous peer-review process to ensure originality, accuracy, and scientific merit. Open Access: All articles are made freely available to readers worldwide, ensuring high visibility and broad dissemination. Ethics and Integrity: The journal follows the best practices of scholarly publishing and adheres to international standards of publication ethics. We invite scientists from all over the world to submit their manuscripts and encourage readers to explore the issues published in the journal. Medium of Publication: Electronic scientific publication (PDF format) and distribution through a web-based platform.
ERDEYI–KOBER ALMASHTIRISH OPERATORI YORDAMIDA BESSEL OPERATORI QATNASHGAN ODDIY DIFFERENSIAL TENGLAMA UCHUN KOSHI MASALASINI YECHISH
Ushbu maqolada Bessel differensial operatori qatnashgan ikkinchi tartibli oddiy differensial tenglama uchun qo‘yilgan Koshi masalasini yechishning operator-analitik usuli tadqiq qilingan. Bunda qaralayotgan singulyar tenglamani Erdeyi–Kober kasr tartibli integral almashtirish operatori yordamida ekvivalent ravishda mos klassik (singulyarliksiz) Koshi masalasiga keltirilgan. Maqolada Erdeyi–Kober operatorining xossalari, uning Bessel operatori bilan o‘zaro kompozitsiyasi batafsil bayon qilingan. Keltirilgan munosabatdan foydalanib, dastlabki masalaning yechimi oshkor ko‘rinishda topilgan. Olingan natijalar nafaqat nazariy ahamiyatga ega, balki amaliy masalalarda — issiqlik o‘tkazuvchanlik, tebranishlar nazariyasi, kvant mexanikasi va o‘qsimmetrik masalalarda uchraydigan singulyar differensial tenglamalarni yechishda ham keng qo‘llanilishi mumkin.
Bessel operatori, Erdeyi–Kober operatori, kasr tartibli integral, singulyar differensial tenglama, Koshi masalasi, almashtirish operatori, gipergeometrik funksiya.
Copyright (c) 2026 SCIENTIFIC RESEARCH, INNOVATIONS, AND MODERN APPROACHES
INTEGRATING REFLECTIVE AND DIGITAL PEDAGOGIES FOR THE ASSESSMENT OF CREATIVE COMPETENCE IN PRE-SERVICE PRIMARY TEACHER EDUCATION
Developing creative competence in pre-service teachers requires assessment approaches that capture reflective thinking, pedagogical decision-making, and the ability to design meaningful learning experiences. However, assessment in teacher education often remains focused on knowledge acquisition rather than on the complex competencies required for professional practice. This paper presents a pedagogical framework for assessing creative competence in pre-service primary teacher education through the integration of reflective and digital pedagogical approaches. The framework was developed for the course “Primary Education Pedagogy, Innovation and Integration” and combines two complementary methods: Learning from Creative Errors (LCE) and Digital Creative Tool (DCT). The LCE method employs the Problem Solving and Omni-directional Methodology (PSOM) to support systematic analysis of authentic pedagogical situations, while the DCT method draws on the Technological Pedagogical Content Knowledge (TPACK) framework to guide the design of digital learning resources. Assessment is embedded within both methods through structured rubrics, including the Digital Tool Didactic Effectiveness Analysis (DTDEA) instrument and a Padlet-based reflective portfolio system. The proposed framework is grounded in principles of alignment, embeddedness, iteration, social visibility, and transparency. By integrating analytical, reflective, creative, and digital dimensions of learning, it provides a coherent approach to assessing professional competence in teacher education. The framework offers a transferable model for higher education practitioners seeking to design assessment systems that support the development and documentation of creative competence in future teachers.
creative competence; pre-service primary teachers; teacher education; reflective practice; digital pedagogy; competency-based assessment; TPACK; digital portfolio
LUCAS TIPIDAGI KUCHLI BO‘LINUVCHAN REKURRENT KETMA-KETLIKLAR
Maqolada Fibonachchi sonlari uchun ma'lum bo'lgan EKUB xossasining Lucas tipidagi rekurrent ketma-ketliklarga umumlashishi bayon qilinadi. Asosiy e’tibor ikkinchi tartibli chiziqli rekurrent ketma-ketliklar, ayniqsa birinchi tur Lucas ketma-ketligi U(P,Q) ga qaratiladi. Kuchli bo‘linuvchan ketma-ketlik tushunchasi, Lucas ketma-ketliklarining bo‘linuvchanlik xossasi, asosiy teorema va sodda misollar keltiriladi.
Fibonachchi sonlari, Lucas ketma-ketligi, rekurrent ketma-ketlik, EKUB, kuchli bo‘linuvchanlik, bo‘linuvchan ketma-ketlik.
DIFFERENSIAL TENGLAMALARNI SONLI YECHISHDA RUNGE-KUTTA VA CHEKLI FARQLAR USULLARINING SAMARADORLIGINI QIYOSIY TAHLILI
Ushbu maqolada differensial tenglamalarni sonli yechishda Runge–Kutta va chekli farqlar usullarining samaradorligi qiyosiy tahlil qilinadi. Tadqiqotning asosiy maqsadi ushbu usullarning aniqlik, barqarorlik, hisoblash murakkabligi hamda amaliy qoʻllanilish imkoniyatlari nuqtayi nazaridan farqlarini aniqlashdan iborat. Tadqiqot jarayonida turli boshlangʻich va chegaraviy shartlarga ega boʻlgan test tenglamalar yordamida sonli hisoblashlar amalga oshirildi hamda olingan natijalar matematik va grafik tahlil asosida solishtirildi. Bundan tashqari, sonli usullarni kompyuter dasturlari orqali modellashtirish jarayonlari ham koʻrib chiqildi va hisoblash natijalarining nazariy yechimlarga yaqinligi tahlil qilindi. Runge–Kutta usulining, ayniqsa 4-tartibli koʻrinishi, yechimning yuqori aniqligini ta’minlashi, xatolik darajasining kichikligi va murakkab differensial tenglamalarni yechishda samarali ekanligi aniqlandi. Ushbu usulning afzalligi shundaki, u kichik qadam uzunligida juda aniq natijalar beradi hamda koʻplab ilmiy va muhandislik masalalarida keng qoʻllaniladi. Chekli farqlar usuli esa algoritmik soddaligi, dasturiy jihatdan qulayligi va katta hajmdagi hisoblashlarda tezkor natija berishi bilan ajralib turishi koʻrsatildi. Ayniqsa, fizik jarayonlarni modellashtirish, issiqlik almashinuvi va mexanik tizimlarni tahlil qilishda ushbu usulning samaradorligi yuqori ekanligi kuzatildi.
Differensial tenglamalar, sonli yechim usullari, Runge–Kutta usuli, chekli farqlar usuli, Eyler usuli, matematik modellashtirish, sonli tahlil, aniqlik, barqarorlik, hisoblash samaradorligi, algoritmik murakkablik, kompyuter modellashtirish, muhandislik hisoblari, matematik analiz, dasturiy ta’minot, iteratsion usullar, ilmiy hisoblash, differensial tenglamalarni modellashtirish, hisoblash tezligi, xatolik tahlili.
LOGISTIKA JARAYONLARINI OPTIMALLASHTIRISHDA GREEDY VA 2-OPT ALGORITMLARINING QOʻLLANILISHI
Mazkur maqolada logistika jarayonlarini optimallashtirishda amaliy matematika, graf nazariyasi va kombinatorik optimallashtirish usullarining qoʻllanilishi tadqiq etilgan. Tadqiqotning asosiy maqsadi kuryerlik va yetkazib berish xizmatlari uchun optimal marshrutlarni aniqlash hamda transport xarajatlarini kamaytirishga qaratilgan dasturiy model ishlab chiqishdan iborat. Tadqiqot jarayonida logistika tizimlarida keng uchraydigan marshrutlashtirish muammosi Sayohatchi tijoratchi masalasi (Traveling Salesperson Problem — TSP) asosida matematik modellashtirilgan. Optimal marshrutlarni hosil qilishda Greedy (“Yaqin qoʻshni”) va 2-opt evristik algoritmlarining kombinatsiyasidan foydalanilgan. Geografik koordinatalar orasidagi real masofalarni aniq hisoblash maqsadida Haversine formulasi qoʻllanilgan. Dasturiy model Python dasturlash tilida ishlab chiqilib, OpenStreetMap xarita tizimi bilan integratsiya qilingan. Tadqiqot natijalari ishlab chiqilgan model yordamida kuryerlarning umumiy harakat masofasini oʻrtacha 22.5% ga qisqartirish, yoqilgʻi xarajatlarini kamaytirish hamda yetkazib berish vaqtini optimallashtirish mumkinligini koʻrsatdi. Taklif etilgan yondashuv logistika kompaniyalarining iqtisodiy samaradorligini oshirish, resurslardan oqilona foydalanish va ekologik zararlarni kamaytirishda muhim amaliy аҳамиятга ega.
Logistika, graf nazariyasi, Sayohatchi tijoratchi masalasi, TSP, Greedy algoritmi, 2-opt algoritmi, optimallashtirish, Haversine formulasi, marshrutlash, Python dasturlash, OpenStreetMap, evristik algoritmlar.
LESSONPLANNER — BAYES BILIM IZLASH MODELI ASOSIDAISHLOVCHI ADAPTIV BILIM PROGNOZI PLATFORMASI
Ushbu maqolada raqamli taʼlim muhitida oʻquvchilarning bilim darajasini aniq prognozlash va ularga moslashtirilgan (adaptiv) taʼlim traektoriyalarini taklif qilish imkonini beruvchi “LessonPlanner” platformasi va uning ishlash mexanizmi yoritilgan. Platformaning asosi hisoblangan Bayes bilim izlash modeli (Bayesian Knowledge Tracing - BKT) talabalarning topshiriqlarni bajarish ketma-ketligiga tayanib, ularning muayyan koʻnikmalarni oʻzlashtirish ehtimolini dinamik tarzda hisoblab boradi. Maqolada platformaning arxitekturasi, maʼlumotlarni qayta ishlash algoritmlari hamda bilim prognozi aniqligini oshirish usullari tahlil qilingan. Tadqiqot natijalari shuni koʻrsatadiki, Bayes modeliga asoslangan adaptiv yondashuv anʼanaviy test tizimlariga qaraganda oʻquvchining haqiqiy bilim darajasini va kelgusi natijalarini yuqori aniqlikda prognozlash hamda individual taʼlim sifatini oshirish imkonini beradi.
LessonPlanner, Bayes bilim izlash modeli, adaptiv taʼlim, bilim prognozi, raqamli platforma, Bayesian Knowledge Tracing, individual oʻquv traektoriyasi, sunʼiy intellekt taʼlimda.
BO‘LAJAK MATEMATIKA O‘QITUVCHILARINING INTELLEKTUAL-IJODIY KOMPETENTLILIGINI RIVOJLANTIRISHNING AMALIYOTDAGI HOLATI
Mazkur maqolada bo‘lajak matematika o‘qituvchilarining intellektual-ijodiy kompetentligini rivojlantirishning amaliyotdagi holati tahlil qilingan. Ta’lim jarayonida talabalarning mustaqil fikrlashi, kreativ yondashuvi, muammoli vaziyatlarni hal etish ko‘nikmalari hamda kasbiy kompetentligini shakllantirish masalalari yoritilgan. Shuningdek, oliy ta’lim muassasalarida matematika o‘qituvchilarini tayyorlash jarayonida innovatsion pedagogik texnologiyala foydalanishning ahamiyati ochib berilgan. Tadqiqot natijalari asosida bo‘lajak matematika o‘qituvchilarining intellektual-ijodiy kompetentligini rivojlantirishga oid amaliy tavsiyalar ishlab chiqilgan.
intellektual kompetentlik, ijodiy kompetentlik, bo‘lajak matematika o‘qituvchisi, kreativ fikrlash, pedagogik texnologiyalar, kasbiy kompetensiya, innovatsion yondashuv, matematik tafakkur, ta’lim sifati, ijodkorlik
DESIGNING AN INTELLECTUAL CALCULATOR THAT CONTROLS THE SHELF LIFE OF FOOD PRODUCTS USING THE EXAMPLE OF THE "FRESHFOOD" RESTAURANT.
This article explores the design of an intelligent food storage calculator aimed at ensuring food safety and reducing waste in public catering establishments. Using the "Freshfood" restaurant as a case study, an algorithm was developed to automatically calculate the shelf life of products based on their type, storage conditions, and temperature regimes. The research employs mathematical modeling and FIFO (First-In, First-Out) principles. The results indicate that the implementation of an intelligent calculator can reduce food disposal by 15-20% and enhance compliance with sanitary standards.
Oddiy differensial tenglamalar uchun qo'yilgan Koshi masalasini taqribiy yechishda Eyler va Runge–Kutta usullarini qo'shish
Koshi masalasi, takomillashtirilgan Eyler usuli, oddiy differensial tenglama, sonli usullar, aniqlik, barqarorlik.
PROCESSING FINANCIAL INFORMATION IN TELEGRAM BOTS: EXPERIENCE OF YAHOO FINANCE AND FINNHUB API INTEGRATION
The article examines the technical aspects of processing and presenting financial information in real time within the Telegram bot environment. The experience of integrating the free APIs Yahoo Finance (yfinance) and Finnhub.io, as well as a comparison of their capabilities and limitations, is discussed. Methods for calculating and visually presenting technical analysis indicators such as RSI and moving averages within the bot are described. As a result of the study, an optimal API strategy for financial bots is proposed.
Development of a Bot System for Providing Stock Market Information Based on the Telegram Messenger
This article describes StockBot, a stock market information bot system developed using the Python programming language and the Telegram Bot API. The article presents the system architecture, the technologies used, the main functionalities, and the testing results. StockBot provides free real-time services such as stock prices, technical analysis indicators, company information, and financial news. The system uses the Yahoo Finance and Finnhub APIs to provide information on more than 500 stocks.
NUMERICAL SIMULATION OF HEAT TRANSFER DYNAMICS IN SMART RESIDENTIAL ENVIRONMENTS USING FINITE DIFFERENCE METHODS
This article investigates the numerical simulation of two-dimensional heat transfer processes within a room modeled after a smart home environment. The governing equation is the classical parabolic heat diffusion partial differential equation , discretized over a 30×50 spatial grid using the Forward Euler finite difference scheme. Dirichlet boundary conditions represent three physically distinct zones: a radiator as the primary heat source, a window as the principal heat sink, and a door modeling ambient ventilation exchange. The computational model is implemented using HTML5 Canvas, CSS3, and JavaScript, enabling real-time interactive visualization. The influence of the thermal diffusivity coefficient on solution stability is analyzed, and the role of stochastic perturbations in achieving physical realism is discussed. Results confirm that the discrete model reproduces the expected steady-state thermal profile consistent with theoretical predictions.
heat diffusion equation, finite difference method, Forward Euler scheme, Dirichlet boundary conditions, 2D Laplacian, Canvas API, smart home thermal modeling, thermal diffusivity, stochastic perturbation, temperature field visualization
Surface acoustic wave propagation model based on the Runge-Kutta method
The simulation of acoustic wave propagation in the surface layer region is carried out by obtaining a positive acoustic velocity gradient, so that the wave phenomenon in the surface layer region is left in this simulation. In this study, the emission of acoustic rays was carried out by changing the angle of incidence and length of the used beam, and the determination of the acoustic velocity gradient was carried out using the 2nd order Runge-Kutta procedure. The results showed that with an acoustic velocity of 1405 m/s at a depth of 0 to 40 meters, a minimum angle of incidence of 0.09 radians was obtained with a wave propagation of 250 meters at a length of 1 meter and a gradient pattern of +2.5. The comparison of analytical and computational results for wave propagation in the surface layer region is 4.51% error.
Acoustic modeling Gradient, Runge-Kutta method, Surface layer, Transmission loss
ENSURING NETWORK SECURITY BASED ON BLOCKCHAIN TECHNOLOGY
This article analyzes the role of blockchain technology in ensuring the security of modern computer networks. The decentralized architecture of blockchain, immutable ledger, and consensus mechanisms are examined as a foundation for protecting network infrastructure. The capabilities of blockchain in defending against DDoS attacks, managing user identity, and ensuring data integrity are highlighted. The article presents conclusions on the application of blockchain-based security systems in corporate networks, IoT environments, and government information infrastructure.
Blockchain, network security, decentralized system, consensus mechanism, smart contract, DDoS protection, IoT security, data integrity, cryptographic hash, PKI.
MATHCAD DASTURIDA TENGLAMALARNI SIMVOLIK VA SONLI YECHISH USULLARINING TAHLILI
Ushbu maqolada Mathcad dasturida tenglamalarni simvolik va sonli yechish usullarining nazariy asoslari, algoritmik xususiyatlari hamda amaliy qo‘llanilish imkoniyatlari keng tahlil qilingan. Zamonaviy kompyuterli matematik tizimlarning ilmiy tadqiqotlar va muhandislik hisoblaridagi o‘rni yoritilib, Mathcad dasturining matematik hisoblashlarni avtomatlashtirishdagi samaradorligi asoslab berilgan. Maqolada algebraik, transcendеnt va tenglamalar sistemasini yechish jarayonlari ko‘rib chiqilib, simvolik usullar yordamida aniq analitik yechimlarni olish hamda sonli usullar orqali murakkab tenglamalarning taqribiy ildizlarini topish usullari misollar asosida tahlil etilgan. Tadqiqot davomida Mathcad dasturining algebraik ifodalarni soddalashtirish, matematik modellarni tahlil qilish, funksiyalar grafiklarini qurish va iteratsion algoritmlar asosida sonli hisoblashlarni bajarish imkoniyatlari o‘rganilgan. Xususan, Newton usuli va boshqa iteratsion metodlarning qo‘llanilishi orqali murakkab matematik masalalarni tezkor hamda aniq yechish imkoniyatlari yoritilgan. Shuningdek, simvolik va sonli usullarning o‘zaro farqli jihatlari, afzalliklari hamda qo‘llanish sohalari ilmiy jihatdan taqqoslangan. Maqola natijalari shuni ko‘rsatadiki, Mathcad dasturi matematik modellashtirish, ilmiy izlanishlar, texnik va iqtisodiy hisoblashlarni samarali tashkil etishda muhim vositalardan biri hisoblanadi. Dastur yordamida murakkab matematik hisoblashlarni qisqa vaqt ichida yuqori aniqlik bilan bajarish mumkin bo‘lib, bu esa ta’lim jarayoni va amaliy tadqiqotlarda undan keng foydalanish imkoniyatini yaratadi.
Mathcad, kompyuterli matematik tizimlar, simvolik hisoblash, sonli hisoblash, tenglama yechish, Newton usuli, iteratsion algoritmlar, matematik modellashtirish, algebraik hisoblashlar.
ANALYSIS OF MATHEMATICAL BASIS OF REPETITION OPERATORS AND COMPUTATIONAL EFFICIENCY IN MATHCAD
This article analyzes the mathematical essence and practical significance of repetition operators in the Mathcad program. The principles of the for and while operators, their role in calculating recurrent formulas, implementing numerical methods, and mathematical modeling are discussed. The advantages of iterative algorithms in improving computational accuracy and efficiency, as well as the negative effects of improperly organized loops, are also examined. The research results show that the effective use of repetition operators in Mathcad increases the speed, reliability, and accuracy of mathematical and engineering calculations.
Mathcad, repetition operators, iteration, for operator, while operator, mathematical modeling, numerical methods, algorithm, computational efficiency, computer mathematical systems, iterative processes, engineering calculations.
Talabalarning bilim darajasiga qarab individual dars rejasini tuzuvchi AI tizimlari
Talabalarning bilim darajasiga qarab individual dars rejasini tuzuvchi AI tizimlari ta'lim dunyo uchun katta yangilik. Ular har bir talabani alohida qaraydi, vaqtda tejaydi va doimiy taraqqiyotni kuzatadi. Lekin texnik muammolar va ijtimoiy murakkabliklar ham bor.
EFFECTIVENESS OF VR (VIRTUAL REALITY) TECHNOLOGIES IN DEVELOPING COGNITIVE PROCESSES OF CHILDREN WITH INTELLECTUAL DISABILITIES.
This article analyzes the effectiveness of Virtual Reality (VR) technologies in developing the cognitive processes of children with intellectual disabilities. It examines the role of VR-based learning in improving attention, memory, thinking, and perception, as well as its advantages in providing individualized instruction, increasing learning motivation, and enhancing special education effectiveness. The findings confirm that VR is an important innovative tool for strengthening cognitive activity, improving knowledge acquisition, and supporting social adaptation.
children with intellectual disabilities, cognitive processes, virtual reality (VR), innovative educational technologies, special pedagogy, attention, memory, thinking, perception, interactive learning, psychological development, individualized approach, digital technologies, effectiveness of special education.
METHODOLOGICAL BASIS OF COORDINATES ON A PLANE
This article provides a scientifically grounded examination of the coordinate system on a plane and its methodological significance in school mathematics education. The origin and development of coordinate systems, their fundamental concepts, effective teaching methods, and their role in modern educational methodology are analyzed. The article highlights the advantages of using visual approaches, didactic games, and real-life examples in teaching the topic of coordinates. The research findings confirm that the methodology of coordinates plays an essential role in developing students' mathematical thinking.
coordinates, abscissa axis, ordinate axis, coordinate plane, Cartesian coordinates, methodological approach, mathematics education, geometric concepts, student, didactics
AMIR TEMUR — BUYUK DAVLAT ARBOBI:SIYOSIY MEROSI VA DAVLAT BOSHQARUVIDAGI ISLOHOTLARI TAHLILI
Ushbu maqola Amir Temur (1336–1405) — o'rta asrlar Markaziy Osiyosining eng buyuk davlat arboblaridan birining siyosiy faoliyati, davlat boshqaruv islohotlari va diplomatik yutuqlarini tahlil etadi. Tadqiqotda Temurning davlatchilik tamoyillari, huquqiy asoslar yaratishdagi ishtiroki hamda madaniy va iqtisodiy rivojlanishga qo'shgan hissasi IMRAD metodologiyasi asosida o'rganiladi. Manbalar tahlili va tarixiy-qiyosiy metodlar qo'llangan holda, Amir Temurning boshqaruv tizimi nafaqat zamonasida, balki keyingi davr davlatchiligi uchun ham namuna bo'lganligi isbotlanadi. Tadqiqot natijalari shuni ko'rsatadiki, Temur davlati markazlashgan boshqaruv, adolatli qonunchilik va kuchli diplomatiya asoslariga qurilgan bo'lib, uning «Temur tuzuklari» asari davlat boshqaruvining noyob dasturulamal hujjati hisoblanadi. Shuningdek, Temurning Samarqandni jahon madaniyati markaziga aylantirish borasidagi sa'y-harakatlari va Buyuk Ipak yo'lini nazorat qilishdagi strategik ahamiyati ham ko'rib chiqiladi.
Amir Temur, Temuriylar davlati, davlat boshqaruvi, «Temur tuzuklari», Markaziy Osiyo tarixi, siyosiy islohotlar, diplomatiya, markazlashgan hokimiyat, o'rta asrlar, adolat tamoyillari
NEGATIVE AND POSITIVE CONSEQUENCES OF USING AN ELECTRONIC DIGITAL SIGNATURE
This article analyzes the role of electronic digital signature (EDS) technology in the modern process of information exchange, as well as its legal, economic, and technical aspects. The research highlights the positive impacts of EDS, such as the acceleration of document workflow, ensuring confidentiality, and the efficiency of remote services. At the same time, negative consequences associated with the use of EDS, including the risks of cyberattacks, theft of private keys, and dependence on technical infrastructure, are systematically demonstrated. The article concludes with practical recommendations for enhancing system security.
Electronic digital signature, information security, cryptography, electronic document management, cybersecurity, remote authentication, identification, digital economy.
Intelligent reflecting surfaces (IRS), phase shift, energy efficiency, artificial intelligence, wireless communication, spectral efficiency, virtual channel.
Ushbu maqolada kelajak simsiz aloqa tizimlarida energiya va spektral samaradorlikni oshirishga qaratilgan intellektual aks ettiruvchi yuzalar (IRS) texnologiyasi tadqiq etilgan. IRSning ishlash tamoyillari, faza siljishini optimallashtirish muammolari hamda uning anʼanaviy faol retlyanslyatorlardan afzalliklari matematik modellar orqali tahlil qilingan. Shuningdek, texnologiyani Oʻzbekistonning chekka hududlarida qamrovni kengaytirish uchun joriy etish istiqbollari va mavjud muammolar koʻrib chiqilgan.
This article investigates intelligent reflective surfaces (IRS) technology aimed at increasing energy and spectral efficiency in future wireless communication systems. The operating principles of the IRC, the problems of optimizing phase shift, and its advantages over traditional active relays were analyzed using mathematical models. The prospects for implementing the technology to expand coverage in remote areas of Uzbekistan and existing challenges are also considered.
KVANT KRIPTOGRAFIYASINING KOMPYUTER TARMOQLARIDA QO'LLANILISHI ISTIQBOLLARI
Ushbu tadqiqotning maqsadi kvant kriptografiyasining zamonaviy kompyuter tarmoqlarida qo'llanilishi istiqbollarini tahlil qilishdir. Tadqiqot metodlari sifatida adabiyotlar tahlili, qiyosiy tahlil va amaliy tatbiq misollarini o'rganish usullari qo'llanildi. Tadqiqot natijalari shuni ko'rsatadiki, BB84 protokoli va kvant kalitlarini taqsimlash (QKD) texnologiyalari klassik kriptografiyadan mutlaq xavfsizlik, tinglashni darhol aniqlash va kvant kompyuterlariga chidamlilik jihatidan ustun turadi. Xulosa sifatida kvant kriptografiyasi kelajakdagi axborot xavfsizligining asosiy poydevori bo'lib, bank tizimlari, davlat axborot tarmoqlari va korporativ infratuzilmalarda keng joriy etilishi zarur ekanligi aniqlandi.
GEOMETRIC PROPERTIES OF IDEMPOTENT PROBABILITY MEASURE SPACES: CATEGORICAL, METRIC AND DYNAMICAL ASPECTS
This paper presents an extended investigation I(X) of the geometric and categorical properties of the space of idempotent probability measures. Building upon earlier results, we prove the following new theorems: 1) the monad structure of the functor I(X) and its relationship with the hyperspace monad; 2) completeness degree and Lipschitz continuity of I(X) under the Hausdorff metric; 3) the strict contraction property of the idempotent Bellman operator and existence of its unique fixed idempotent measure; 4) local convex structure and cross-sectional properties of I(X). The main new result states: if X is a compact metric space and T:C(X)--C(X) is an idempotent Bellman operator, then there exists a unique fixed idempotent measure in I(X) for T.
idempotent measure, Maslov measure, Bellman operator, contraction, monad, Hausdorff metric, local convexity, cross-sections, fixed point.
MPLS TEXNOLOGIYASI ASOSIDA KORPORATIV TARMOQLARNI OPTIMALLASHTIRISH
Hozirgi korporativ tarmoqlar yuqori tezlik, ishonchlilik va xavfsizlik talablariga javob berishi zarur. Ushbu maqola MPLS (Multi-Protocol Label Switching) texnologiyasining korporativ tarmoqlarni optimallashtirishdagi rolini tahlil qiladi. MPLS yordamida trafikni samarali boshqarish, xizmat sifatini (QoS) oshirish va tarmoq resurslaridan oqilona foydalanish imkoniyatlari kengayadi. Tadqiqot natijalari MPLS implementatsiyasi orqali tarmoq unumdorligini oshirish, operatsion xarajatlarni kamaytirish va kengaytiriluvchanlikni ta'minlash mumkinligini ko'rsatadi.
NFV (Network Functions Virtualization) texnologiyasini joriy etishning samaradorligi
Ushbu maqola zamonaviy telekommunikatsiya infratuzilmasida NFV (Network Functions Virtualization) texnologiyasini joriy etishning samaradorligini tahlil qiladi. NFV an'anaviy tarmoq funksiyalarini virtualizatsiya qilish orqali operatsion xarajatlarni kamaytirish, tarmoqni boshqarishda moslashuvchanlikni oshirish va yangi xizmatlarni tezroq ishga tushirish imkoniyatini beradi. Tadqiqot NFVni muvaffaqiyatli tatbiq etishning asosiy omillarini, jumladan texnik va iqtisodiy jihatlarni ko'rib chiqadi. Maqola NFVning afzalliklari va potentsial qiyinchiliklarini baholash orqali kelajakdagi tarmoq rivojlanishi uchun muhim tavsiyalar beradi.
5G TEXNOLOGIYASINING SANOAT TARMOQLARIGA INTEGRATSIYASI VA IQTISODIY SAMARASI
Ushbu maqola 5G texnologiyasining sanoat tarmoqlariga integratsiyasi jarayonlarini va uning iqtisodiy samaradorligini chuqur tahlil qiladi. 5G ning yuqori tezlik, past kechikish va keng qamrov imkoniyatlari ishlab chiqarish, logistika va energetika kabi sohalarda raqamli transformatsiyani jadallashtirishda muhim rol o'ynaydi. Texnologiyaning joriy etilishi avtomatlashtirish darajasini oshirish, real vaqt rejimida ma'lumotlarni qayta ishlashni ta'minlash va operatsion xarajatlarni kamaytirish orqali korxonalarning samaradorligini sezilarli darajada oshiradi. Natijada, ushbu integratsiya yangi innovatsion xizmatlar va mahsulotlarni yaratishga zamin yaratib, milliy iqtisodiyotning raqobatbardoshligini mustahkamlaydi
Ikki o‘lchamli issiqlik o‘tkazuvchanlik tenglamasining matematik modeli va sonli yechish usullari
Mazkur maqolada issiqlik almashinuvi jarayonlari, issiqlik uzatish mexanizmlari va ikki oʻlchamli issiqlik oʻtkazuvchanlik tenglamasining matematik modeli ilmiy asosda tahlil qilingan. Furye qonuni asosida tenglamaning hosil qilinishi, boshlangʻich va chegaraviy shartlar hamda sonli yechish usullari, xususan chekli ayrimlar usuli koʻrib chiqilgan. Tadqiqot natijalari, sanoat, energetika, qurilish va mikroelektronika sohalarida issiqlik jarayonlarini samarali modellashtirish uchun muhim nazariy asos yaratadi.
Social media as a factor in the formation of communicative competence
This article examines the role of social media in the development of communicative competence. Based on a review of recent studies, the mechanisms through which virtual communication enhances verbal and non-verbal skills, critical thinking, and empathy are identified. An empirical study was conducted involving surveys and interviews with students who actively use social networks. The results indicate that participation in discussions, content creation, and engagement in thematic groups contribute to the development of adaptability, intercultural competence, and emotional sensitivity. The study highlights the significance of social media as a tool for fostering communicative competence and provides recommendations for its effective use in educational and professional contexts.
social media, communicative competence, digital communication, intercultural communication, empathy, education
Buzilgan ikkinchi tartibli oddiy differensial tenglamalar uchun boshlangʻich masalalar
Ushbu oddiy differensial tenglamalar bessel tenglamasiga keltirib ishlanadi
Bessel funksiyasi, differensial tenglama, ikkinchi tartibli tenglama, boshlang‘ich shart