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0 $begingroup$ For a manifold $M$ , let $f in C^{k}(M), k>0$ , be a level set (i.e. $rank(df)=1$ ). I understand that this trivially implies that ${{k.df: k in C^{k}(M)}}$ forms an integrable regular Pfaffian system, and that the level sets of $f$ form the integral manifolds of such a Pfaffian system. The converse, I know, is not true. The best one has is the following: Given a Pfaffian system generated by a one-form $alpha$ that is integrable, there exists an open nbd. $U$ for every $m in M$ on which there exists $f, g in C^k(U)$ s.t. $g.alpha |_U=df$ where $g$ is nowhere zero, and $f^{-1}(t_0)$ corresponds to the integral manifolds restricted to $U$ . Yet I still see physics references talking about a global level set prescription for such a manifold $M$ . Does someone know any simple example wher...

21 2 I ran into a weird problem when trying to move to C++17. The problem is that something (and I'm not sure what) changed in C++17 that made list-initialization work differently in the case of a default constructor. I tried to search https://en.cppreference.com/w/cpp/language/list_initialization for more info, but I didn't find anything that looks relevant. Does someone know the reason the code below compiles in C++14 but not in C++17 when calling B{} instead of B() ? (I tried it in both gcc 8.2 and 7.3 and icc 19) struct A{ protected: A() {} }; struct B : public A {}; B f(){ return B(); //compilation OK //return B{}; //compilation error } c++ c++17 list-initialization ...