"We have our fair share of hoards in Norfolk, but this is so, so different - it is really, really special," he added.
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;
Facial expressions are controlled by several brain regions working together. Different areas encode facial gestures with different scales, from fast changing signals to slow, stable ones. This timing hierarchy may explain how facial expressions stay socially meaningful and well coordinated.。关于这个话题，新收录的资料提供了深入分析
В России допустили «второй Чернобыль» в Иране22:31
。新收录的资料对此有专业解读
% if you like, we could write it as using some infix notation as `Ps : sublist(Xs, Ys)`，推荐阅读新收录的资料获取更多信息
Политолог Александр Асафов и вовсе считает, что эпизод с задержанием украинских инкассаторов в Венгрии вряд ли будет иметь серьезные последствия для Зеленского.