Трехстороннюю встречу по Украине отложили20:29
Often people write these metrics as \(ds^2 = \sum_{i,j} g_{ij}\,dx^i\,dx^j\), where each \(dx^i\) is a covector (1-form), i.e. an element of the dual space \(T_p^*M\). For finite dimensional vectorspaces there is a canonical isomorphism between them and their dual: given the coordinate basis \(\bigl\{\frac{\partial}{\partial x^1},\dots,\frac{\partial}{\partial x^n}\bigr\}\) of \(T_pM\), there is a unique dual basis \(\{dx^1,\dots,dx^n\}\) of \(T_p^*M\) defined by \[dx^i\!\left(\frac{\partial}{\partial x^j}\right) = \delta^i{}_j.\] This extends to isomorphisms \(T_pM \to T_p^*M\). Under this identification, the bilinear form \(g_p\) on \(T_pM \times T_pM\) is represented by the symmetric tensor \(\sum_{i,j} g_{ij}\,dx^i \otimes dx^j\) acting on pairs of tangent vectors via \[\left(\sum_{i,j} g_{ij}\,dx^i\otimes dx^j\right)\!\!\left(\frac{\partial}{\partial x^k},\frac{\partial}{\partial x^l}\right) = g_{kl},\] which recovers exactly the inner products \(g_p\!\left(\frac{\partial}{\partial x^k},\frac{\partial}{\partial x^l}\right)\) from before. So both descriptions carry identical information;
。新收录的资料对此有专业解读
Что думаешь? Оцени!，详情可参考新收录的资料
数十年来，人类对“我们是否在宇宙中孤独”的追问从未停歇，而围绕不明飞行物（UFO），即如今所称“未解异常现象”（UAP）的争论亦持续升温，衍生出大量阴谋论与影视作品。 2024 年，美国一名前国防部官员在国会作证时甚至声称，政府雇员曾在与外星人接触中受伤，但这一说法并未得到实质性证据支持。 更早之前，前情报官员、曾负责分析 UAP 的大卫·格鲁什（David Grusch）也宣称五角大楼长期秘密回收并试图“逆向工程”坠毁的不明飞行器，引发舆论广泛关注。。新收录的资料是该领域的重要参考