Showing papers on "Distribution (differential geometry) published in 1970"
Patent•
04 Feb 1970
TL;DR: In this article, a distribution system for fluid, oil, gas or water from a bulk supply thereof to multiple outlets 12 at a distance from the supply involves an underground pipe 6 extending from a supply either directly to or adjacent to an accessible manifold 8 situated near the outlets 12.
Abstract: 1,180,573. Water supplies. ESSO RESEARCH & ENG. CO. 17 Jan., 1968 [9 Feb., 1967], No. 6316/67. Heading E1X. [Also in Division F4] A distribution system for fluid, oil, gas or water from a bulk supply thereof to multiple outlets 12 at a distance from the supply involves an underground pipe 6 extending from the supply either directly to or adjacent to an accessible manifold 8 situated near the outlets 12. When the pipe 6 extends only to adjacent the manifold then it is connected to the manifold by a feeder pipe 7. The outlets 12 are connected to the manifold by further underground pipes 11. All pipes are fitted adjacent the manifold with control valves and meters are provided in each of the pipes 11 adjacent the manifold, which is located in an underground inspection pit 9.
2 citations
01 Mar 1970
TL;DR: In this article, the authors define the parameter of distribution and the line of striction in relation to the enveloping space and show that they have the usual properties in the hyperbolic case.
Abstract: Bonnet's theorem on ruled surfaces [2, p. 449] deals solely with intrinsic properties if an intrinsic definition of the line of striction is adopted. Contrasting this, our aim is to define the parameter of distribution and the line of striction in relation to the enveloping space and to show that they have the usual properties. Attention will be called occasionally to the changes required to treat the hyperbolic case. The two theorems hold in hyperbolic space with minor variations and follow by formally analogous proofs. In fact, in the first one K S -1 must be assumed and in the second the hyperbolic tangent of the distance has to be used. Notation and terminology will largely be taken from [1]. Let "D be the standard connection on the Euclidean 4-space such that "DvW= (VWi)ei where ei, i= 1, 2, 3, 4 constitutes the natural frame field. Our elliptic 3-space is represented by the unit hypersphere (x, x) = 1, so the position vector x serves as unit normal and we have IDvx = V. If now 'D stands for the induced connection on the elliptic space we find for vectors tangent to it