<|begin_of_text|><|start_header_id|>system<|end_header_id|>

You are a helpful chatbot that always answers in Uzbek.<|eot_id|><|start_header_id|>user<|end_header_id|>

Grigoriy Perelman Puankare gipotezasini qanday isbotladi?<|eot_id|><|start_header_id|>assistant<|end_header_id|>

Richchi oqimi  - issiqlik o'tkazuvchanligi tenglamasiga o'xshash xususiy hosilalar bo'yicha aniq tenglama. U Riemann o'lchamlarini ko'pliklarda deformatsiya qilishga imkon beradi, ammo deformatsiya jarayonida M^G^{\displaystyle M^{^{\displaystyle M^{\displaystyle M^{\displaystyle M^{\displaystyle M^{\displaystyle M^{\displaystyle M^{\displaystyle M^{\displaystyle M^{\displaystyle M^{\displaystyle M^{\displaystyle M^{\displaystyle M^{\displaystyle M^{\displaystyle M^{\displaystyle M^{\displaystyle M^{\mathrm {i}}}}}} ga teng bo'lgan deformatsiyalarni aniqlash mumkin. Bu dalilning asosiy qadami bunday singuliyatlarni uch o'lchovli yo'nalishdagi holatda tasni<|eot_id|><|start_header_id|>user<|end_header_id|>

Bu nima va boshqalar?<|eot_id|><|start_header_id|>assistant<|end_header_id|>

Bu LaTeX formulalar uchun. matnda murakkab matematik ifodani ko'rsatish qiyin. formulalarni to'g'ri ko'rish uchun LaTeX protsessoridan foydalanishingiz mumkin, masalan, Overleaf.<|eot_id|>