Indigenous and institutional profile: Limpopo River Basin

River basins / Water resource management / History / Institutions / Social aspects / Legal aspects

Homotopy types of stabilizers and orbits of Morse functions on surfaces

Let $M$ be a smooth compact surface, orientable or not, with boundary or without it, $P$ either the real line $R^1$ or the circle $S^1$, and $Diff(M)$ the group of diffeomorphisms of $M$ acting on $C^{\infty}(M,P)$ by the rule $h\cdot f\mapsto f \circ h^{-1}$, where $h\in Diff(M)$ and $f \in C^{\infty}(M,P)$. Let $f:M \to P$ be a Morse function and $O(f)$ be the orbit of $f$ under this action. We prove that $\pi_k O(f)=\pi_k M$ for $k\geq 3$, and $\pi_2 O(f)=0$ except for few cases. In particular, $O(f)$ is aspherical, provided so is $M$. Moreover, $\pi_1 O(f)$ is an extension of a finitely generated free abelian group with a (finite) subgroup of the group of automorphisms of the Reeb graph of $f$. We also give a complete proof of the fact that the orbit $O(f)$ is tame Frechet submanifold of $C^{\infty}(M,P)$ of finite codimension, and that the projection $Diff(M) \to O(f)$ is a principal locally trivial $S(f)$-fibration.Comment: 49 pages, 8 figures. This version includes the proof of the fact that the orbits of a finite codimension of tame action of tame Lie group on tame Frechet manifold is a tame Frechet manifold itsel

Propulsion Study for Small Transport Aircraft Technology (STAT)

Propulsion requirements were determined for 0.5 and 0.7 Mach aircraft. Sensitivity studies were conducted on both these aircraft to determine parametrically the influence of propulsion characteristics on aircraft size and direct operating cost (DOC). Candidate technology elements and design features were identified and parametric studies conducted to select the STAT advanced engine cycle. Trade off studies were conducted to determine those advanced technologies and design features that would offer a reduction in DOC for operation of the STAT engines. These features were incorporated in the two STAT engines. A benefit assessment was conducted comparing the STAT engines to current technology engines of the same power and to 1985 derivatives of the current technology engines. Research and development programs were recommended as part of an overall technology development plan to ensure that full commercial development of the STAT engines could be initiated in 1988

Graz vom Schloßberg.

Blick vom Schloßberg gegen Süden mit drei Brücke