Атрофдаги оламни билиш - унинг моделларини яратишдан иборат. Улар ушбу олам объектлари билан бизнинг ўзаро таъсиримиз оқибатларини кўриш имконини беради. Моделларни яратиш инсон тафаккурининг ташкилий тузилишини такомиллаштириш жараёни ҳисобланади. Мазкур психологик ташкилий тузилиш мақсадга йўналган ҳаракатлар кўринишида моддийликка айланади, уларни инсон ўзида мавжуд моделлар асосида амалга оширади. Ушбу мақолада математик моделлаштиришнинг асосий масалалари ҳақида фикрлар ёритилган.

The teaching of speech acts in the English language, especially as a second or foreign language (ESL/EFL), must employ a manner that is thoroughly systematic, well-grounded theoretically and innovative if the situation is to guarantee the learners' effective acquisition of communicative competence. The aim was, among other objectives, to create didactic systems and to design instructional materials that might improve students' abilities, directly or indirectly, to know and then apply in practice these pragmatic rules. Drawing from Speech Act Theory, Politeness Theory, and Task-Based Language Teaching (TBLT), the present study's intent was to evaluate methods which could serve as interactive, authentic, and culture-sensitive resources for pedagogical implementation in support of pragmatic competence. Data sources comprised classroom observations, role-plays, case studies, and reflective analyses. From the study, it has been learned that the integration of multimedia resources, real-life scenarios, and collaborative tasks strongly enhanced learners' competences in enacting acts of conversational cooperation: invitations, refusals, and requests. The study concludes with practical suggestions on didactic designs meant to direct the course of learners with respect to pragmalinguistic fluency and socialversible creativity.

Ushbu maqolada fazoviy tasvirlarni tahlil qilish asosida inson yuzini aniqlash muammosi ko‘rib chiqiladi. Yuzni aniqlash — kompyuter ko‘rish (Computer Vision) va biometrik identifikatsiya sohalarining dolzarb yo‘nalishlaridan biri hisoblanadi. Ayniqsa, raqamli tasvirlarni chastota sohasida ifodalash orqali ularning asosiy xususiyatlarini ajratib olish va tahlil qilish, sun’iy intellektga asoslangan tizimlar uchun katta ahamiyatga ega. Fourier o‘zgarishlari raqamli tasvirlarni fazodan chastotaga o‘tkazishga imkon beradi, bu esa yuzni aniqlash vazifasini ancha soddalashtiradi. Maqolada DFT (Diskret Fourier o‘zgarishi) va uning ikki o‘lchamli (2D) ko‘rinishlari, tasvirni tahlil qilishda foydalaniladigan algoritmlar, tajriba natijalari, grafik tahlillar, sun’iy neyron tarmoqlari bilan integratsiya holatlari keng yoritilgan.

Ushbu maqolada tabiatsevar yozuvchi mengziyo safarov hayoti va ijodi tahlil qilinadi. Adibning asarlarining bosh gʻoyasi tabiat haqida boʻlib, unda tabiatni asrash, ekologiyaga zarar yetkazmaslik, hayvonlarni asrab avaylash toʻgʻrisida soʻz borgan. Mengziyo Safarov mohir qalamkash sifatida yoritayotgan mavzuning tub mohiyatiga katta ahamiyat bergan yozuvchidir.

Language acquisition is a fundamental aspect of human development and has been the subject of extensive study across multiple disciplines, including linguistics, cognitive science, psychology, and education. Understanding how individuals acquire language, whether their first language (L1) or a second/foreign language (L2), is crucial for the development of effective teaching methodologies and learning environments. This paper provides an in-depth examination of the primary theories that attempt to explain the process of language acquisition. The Behaviorist Theory, pioneered by B.F. Skinner, emphasizes imitation, reinforcement, and habit formation. In contrast, the Nativist Theory, led by Noam Chomsky, argues for an innate, biological capacity for language learning, proposing the existence of a “language acquisition device” (LAD). The Cognitive Theory, influenced by Jean Piaget, highlights the role of mental processes and developmental stages in language learning, while the Social Interactionist Theory, associated with Lev Vygotsky, stresses the importance of social context and interaction in the acquisition of language.