Let $\Omega \subset {ℂ}^n$ be a domain with smooth boundary and $p\in \partial \Omega$. A holomorphic function $f$ on $\Omega$ is called a $C^k$ ($k=0,1,2,\cdots$) peak function at $p$ if $f\in C^k\left(\overline{\Omega }\right)$, $f\left(p\right)=1$, and $\left|f\right(q\left)\right|<1$ for all $q\in \overline{\Omega }\setminus \left\{p\right\}$. If $\Omega$ is strongly pseudoconvex, then $C^{\infty }$ peak functions exist. On the other hand, J. E. Fornaess constructed an example in ${ℂ}^2$ to show that this result fails, even for $C^1$ functions, on a weakly pseudoconvex domain [Math. Ann. 227, 173-175 (1977; Zbl 0346.32026)]. Subsequently, E. Bedford and J. E. Fornaess showed that there is always a continuous peak function on a...

[For the entire collection see Zbl 0699.00032.] It was previously known that for every principal fibre bundle P there is some corresponding transitive Lie algebroid A(P) - a vector bundle equipped with some structure like the structure of a Lie algebra in the module of sections. The author of this article shows that the Chern-Weil homomorphism of P is a notion of the Lie algebroid of P, i.e. knowing only A(P) of P one can uniquely reproduce the ring of invariant polynomials ${\left(V{g}^{*}\right)}_I$ and the Chern-Weil...

[For the entire collection see Zbl 0699.00032.] In this interesting paper the authors show that all natural operators transforming every projectable vector field on a fibered manifold Y into a vector field on its r-th prolongation $J^{r}Y$ are the constant multiples of the flow operator. Then they deduce an analogous result for the natural operators transforming every vector field on a manifold M into a vector field on any bundle of contact elements over M.