Lokal bo`lmagan potensiyalga ega model operator uchun Faddeyev va Vaynberk tenglamalari
Ushbu bitiruv malakaviy ishida
Ushbu bitiruv malakaviy ishida
Ushbu dissertatsiya ishida turli chegaralanmagan sohalarda kichik hosilali singulyar koeffitsiyentli aralash tipdagi tenglamalar uchun lokal va nollokal chegaraviy masalalarni yechishga bag'ishlangan. Tadqiqotda yangi chegaraviy masalalar qo'yilgan va ularning yechimlari topilgan. Tadqiqot natijalari sambalii amaliy masalalarni yechishda foydali bo'lishi mumkin.
Ushbu dissertatsiya tadqiqoti matematik fizikada nomilol klassik tenglamalar bilan bog'liq masalalar, xususan, nol lokal chegara va teskari masalalarini o'rganishga bag'ishlangan. Tadqiqotda ko'p o'lchovli tenglamalar uchun birinchi va ikkinchi turdagi aralash tipdagi tenglamalarning noyob yechimi, mavjudligi va silliqligi o'rganilgan. Ushbu tadqiqot natijalari ko'p o'lchovli differensial tenglamalar nazariyasini rivojlantirishga hissa qo'shadi va ushbu sohadagi tadqiqotlar uchun muhim manba bo'lib xizmat qiladi.
Ushbu avtoreferat, fizika-matematika fanlari nomzodi ilmiy darajasini olish uchun taqdim etilgan dissertatsiyaning qisqacha mazmunidir. Dissertatsiya o'lchovli operatorlar algebralarida lokal differensiallash masalalariga bag'ishlangan. Unda, xususan, chekli fon Neyman algebralari va aniq normal yarim chekli iz bilan bog'langan nokommutativ Arens algebralaridagi lokal differensiallashlar tavsiflangan. Shuningdek, ayrim operatorlar uchun differensiallash bo'lish shartlari keltirilgan va kommunativ holda lokal differensiallashlar mavjudligi uchun zarur va yetarli shartlar aniqlangan. Ishda, shuningdek, I tipdagi fon Neyman algebralari uchun o'lchovli operatorlar algebralarida lokal differensiallashlar masalalari ham ko'rib chiqilgan.
Ushbu avtoreferat, O'zbekiston Milliy Universitetida Nurjanov Berdax Orinbayevich tomonidan taqdim etilgan "O'lchovli operatorlar algebralaridagi lokal differensiallashlar" mavzusidagi dissertatsiyaning qisqacha bayonidir. Unda differensiallash nazariyasi, lokal differensiallashlar va ularning operator algebralardagi xususiyatlari o'rganiladi. Ishning maqsadi o'lchovli operatorlar algebralarida lokal differensiallashlarni tavsiflashdan iborat. Tadqiqot metodlari funksional analiz va operatorlar algebrasi nazariyasiga asoslangan.
Ushbu dissertatsiya ishi uchinchi tartibli yklangan psevdoparabolik tenglamalar uchun no-lokal boshlang'ich-chegaraviy masalalarini tadqiq qilishga bag'ishlangan. Tadqiqotda ushbu turdagi tenglamalar uchun yangi no-lokal masalalar qo'yilib, ularning yechimlarini mavjudligi va yagonaligi isbotlangan. Shuningdek, ushbu masalalarning integrallashgan usullar yordamida yechimlari topilgan. Tadqiqot natijalari fizika, mexanika va tabiyotshunoslikning turli jabhalaridagi masalalarni modellashtirishda qo'llanilishi mumkin.
Ushbu doktorlik dissertatsiyasi
Ushbu doktorlik dissertatsiyasi avtoreferati singulyar koeffitsiyentli elliptik-giperbolik va elliptik-parabolik tipdagi differensial tenglamalar uchun no-lokal masalalarni qo'yish va o'rganishga bag'ishlangan. Tadqiqotda Frankl, Bitsadze-Samarskiy va siljish shartlari kabi no-lokal shartlar bilan chekli va spektral masalalar ko'rib chiqilgan. Ishda ushbu masalalarning mavjudligi va yagonaligi isbotlangan, shuningdek, masalalarning yechimlari uchun xos qiymatlar va xos funksiyalar topilgan. Tadqiqot natijalari matematik fizika va differensial tenglamalar nazariyasini rivojlantirishga hissa qo'shadi.
The journal "Problems of Modern Science and Education" No. 6 (126) in 2018 covers a wide range of scientific research, including physics and mathematics, biology, technical sciences, historical sciences, economic sciences, geographical sciences, pedagogical sciences, philological sciences, medical sciences, and philosophy. The journal features articles on solving non-local problems for hyperbolic equations, the ecological basis for predicting the number of green apple aphid, the regulation of the electrical activity of ureters with histamine, experimental equipment for investigating innovative methods of tube drawing, the features of calculation schemes in the choice of parameters of suspension systems of transport and technological machines, the study of temperature sensor circuits for radiation resistance, the calculation of the coefficient of technological efficiency of printed circuit boards, the problems of accounting for small businesses, the use of cash flow indicators in assessing the efficiency of financial strategies, the perspectives of international scientific and technological cooperation of Russia in the field of civil aviation, the development of an assessment method for master's programs, the study of precedent phenomena and phraseological expressions, the naming of orographic objects based on natural-geographical signs and features, the housing and economic conditions in the postwar period in the hero-city of Novorossiysk, the analysis of the relationship between the development of the Russian economy and small enterprises, the problem of social and communicative development of children of preschool age, aesthetic education of junior pupils by means of art, the fate of N.Ya. Danilevsky's heritage in the XXI century, questions of applied ethics in the light of N. Berdyaev's personalism, the recognition of voice binding dysfunction under laryngospasm in children, the evaluation of the effectiveness of some approaches in emergency medical assistance in diffunction of voice bindings in children, the features of electronic microscopy of kidney nephrons and weights of rat bodies in long-term food deprivation at highlands, and the formalization of positioning of stable isotopes.
Ushbu kitobda singulyar koeffitsientli elliptik, giperbolik va aralash tipdagi differentsial tenglamalar uchun chegaralangan va chegaralanmagan sohalarda noo'rin qo'yilgan masalalar o'rganilgan. Masalalarning yechimlari yagonaligi va mavjudligi isbotlangan.