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“中国粮、中国菜和中国肉都主要用上了中国种”,中国农业科学院院长、中国科学院院士黄三文委员自豪地说;

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Another decision to make is where to put the infrastructure code for “Independent Ventilation Scheduler” (see the diagram above). The default choice would be to use the MIM pattern and put it into the Infrastructure-Module of the “H&V Controller” module (i.e. “H&V Controller.Infra”), just as we did with H&V Scheduler’s infra code. But anticipating that it could also be reused, or maybe just to show how flexible the design process is, I will also extract it as a standalone “infrastructure-only” module.。PDF资料对此有专业解读

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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;

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