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;
Ранее более тысячи россиян застряли на круизных лайнерах в Персидском заливе. Так, три из них стоит в Дубае, два — в Дохе, еще один — в Абу-Даби.
ОАЭ задумались об атаке на Иран20:55。Feiyi对此有专业解读
The "Chronic Ghoster"
。关于这个话题，电影提供了深入分析
In short: in my mind, errors are divided into two categories. Expected errors (think “user entered invalid data”), which are part of normal operation, aren’t the developer’s fault, and should be handled. Unexpected errors (think “null pointer exception”) are the developer’s fault, likely indicate a bug, and are allowed to crash.。爱思助手下载最新版本对此有专业解读
Digital access for organisations. Includes exclusive features and content.