The analysis of Lie groups depends to a large extent on their maximal tori. For a compact connected topological group G, the subgroups analogous to the maximal tori are the maximal connected Abelian subgroups. As in Hofmann and Morris [7] we call them maximal protori. We sharpen some results of [7] by showing that each maximal protorus is in a natural way the projective limit of maximal tori Tα in the corresponding Gα, where G= projGα. This sharpened characterization together with some methods of Moskowitz [4], [10] will be used to show that a number of well‐known theorems concerning Lie groups extend in a natural way to all compact connected groups.
In other words, the speed is the product of a geometric quantity and the flow rate of the liquid. The speed can also be expressed as an explicit function of time, provided we can solve V (t) = φ(h) explicitly for h. More variants of this problem can be obtained by defining the revolving function differently, by computing the volume with a different technique, etc. One favorite function of mine is y = −1/ √ x because revolving that curve, e.g., for 0 < x ≤ 1, around the y-axis generates an infinite vessel of finite volume.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.