The application is based on the idea that if \ pi is a Hilbert-space representation of, say, a connected real semisimple linear Lie group " G ", then it has two natural actions : the complexification \ mathfrak { g } and the connected maximal compact subgroup " K ".
42.
"' Reverse stratigraphy "'( sometimes known as "'inverted stratigraphy "') is the result of a process whereby one sediment is unearthed by human or natural actions and moved elsewhere, whereby the latest material will be deposited on the bottom of the new sediment, and progressively earlier material will be deposited higher and higher in the stratigraphy.
43.
The JSKA emphasizes the development of effective techniques utilising the low and long stances introduced by Yoshitaka Funakoshi and passed on through Nakayama to Abe, and although they are a general feature of the Shotokan style, the self-defense / budo element is continually stressed where the significance of natural actions, utilising good posture and biomechanics, ensures the execution of a powerful and effective technique.
44.
Subsequent testing has shown that the V-22, and the tiltrotor in general, is less susceptible to VRS, the conditions are easily recognized by the pilots; recovery from VRS requires a more natural action by the pilot than recovery in helicopters, the altitude loss is significantly less than for helicopters, and, with sufficient altitude ( or more ), VRS recovery is relatively easy.
45.
Conversely, any depth two extension A | B has a Galois theory based on the natural action of \ mbox { End } \, { } _ BA _ B on A : denoting this endomorphism ring by S, one shows S is a left bialgebroid over the centralizer R ( those a in A commuting with all b in B ) with a Galois theory similar to that of Hopf-Galois theory.
46.
His more general consideration of light as a primary agent of physical causation appears in his " On Lines, Angles, and Figures " where he asserts that " a natural agent propagates its power from itself to the recipient " and in " On the Nature of Places " where he notes that " every natural action is varied in strength and weakness through variation of lines, angles and figures ."
47.
The classification of orbits can lead to interesting questions with relations to other mathematical areas, for example the Oppenheim conjecture ( proved by Margulis ) and the Littlewood conjecture ( partially proved by Lindenstrauss ) are dealing with the question whether every bounded orbit of some natural action on the homogeneous space SL _ { 2 } ( \ mathbb { R } ) \ backslash SL _ { 2 } ( \ mathbb { Z } ) is indeed periodic one, this observation is due to Raghunathan and in different language due to Cassels and Swinnerton-Dyer.
48.
They said also, in regard to the " natural actions ", that it was necessary to know wherefore and in what manner we receive the air into our lungs, and why we afterward expire it; why food is taken into the body, how it is there prepared, and then distributed through every part of it; why the arteries are subject to pulsation; what is the cause of sleep, wakefulness, etc .; and they maintained that people could not cure diseases relating to these many functions unless they were able to explain these phenomena.
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