Kyle Kucharski/ZDNETApple's MacBooks are infamous for being difficult to repair. It has proprietary components, requires specialized tools, and some models feature soldered RAM and batteries. This is by design: Apple has monetized its repair business by keeping its users within its ecosystem and gatekeeping the process.
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;
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任何被证明拥有高利润的缝隙，一旦被大规模观察到，其背后的隐性知识有可能就会被 AI 或平台型应用迅速扫描、结构化并吞噬。，详情可参考51吃瓜
回溯法兰泰克近三年业绩情况不难看出，2023年、2024年、2025年前三季度，公司分别实现归母净利润1.63亿元、1.67亿元、1.71亿元，合计约5.01亿元；参考最近五年来公司Q4净利润在0.25亿元-0.45亿元区间内，完成5.1亿的三年总目标似乎轻而易举。