Here's a complete rundown of the new M5 MacBook Airs' spec sheets. Chip and storage aside, their only other upgrade is a connectivity bump to WiFi 7 and Bluetooth 6. Otherwise, they're basically the same laptops as the M4 MacBook Airs (which isn't necessarily a bad thing — we loved them).
Sony is pulling a U-turn on its multi-platform strategy, with Bloomberg’s Jason Schreier reporting that first-party PS5 games soon to become exclusive once again, at the expense of PC players.
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那么问题来了，一台能触控 MacBook，能带来什么样的价值？
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A Riemannian metric on a smooth manifold \(M\) is a family of inner products \[g_p : T_pM \times T_pM \;\longrightarrow\; \mathbb{R}, \qquad p \in M,\] varying smoothly in \(p\), such that each \(g_p\) is symmetric and positive-definite. In local coordinates the metric is completely determined by its values on basis tangent vectors: \[g_{ij}(p) \;:=\; g_p\!\left(\frac{\partial}{\partial x^i}\bigg|_p,\; \frac{\partial}{\partial x^j}\bigg|_p\right), \qquad g_{ij} = g_{ji},\] with the matrix \((g_{ij}(p))\) positive-definite at every point. The length of a tangent vector \(v = \sum_i v^i \frac{\partial}{\partial x^i}\in T_pM\) is then \(\|v\|_g = \sqrt{\sum_{i,j} g_{ij}(p)\, v^i v^j}\).
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