The Private space / install when needed apps
The new MacBook Pros will be available in 14- and 16-inch sizes. The M5 Pro variants will start at $2,199 and $2,699, respectively, with discounts of up to $200 for education shoppers who buy direct. They come with 1TB of base storage. Apple recommends them "for users running complex workflows, like coders optimizing algorithms and photographers processing massive image libraries," according to a company press release.
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Неожиданное прекращение ударов «Томагавками» по Ирану объяснилиВХ: США практически прекратили бить по Ирану «Томагавками»
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 \(\|v\|_g = \sqrt{\sum_{i,j} g_{ij}(p)\, v^i v^j}\).
Let’s describe our imaginary application: