A clear dig, then, at Arsenal’s south of the river history from the Woolwich days and, as mentioned, very much a part of a rivalry where goading and baiting go hand in hand with the loathing. Arsenal had been similarly provocative before the derby against Spurs at the Emirates Stadium last November, lighting the pre-match scene with a tifo featuring images of various club greats. The most prominent at the top of it? Sol Campbell, of course.
Gemini for Home now uses updated models to improve the quality and accuracy of answers too and will more reliably play newly-released songs. Other key updates include better targeting for smart home devices by room, house and device, reduced instances of cutting off a speaker prematurely, better reliability for user-created automations by voice and more. Too see all those changes, check out Google Home's latest changelog,
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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;