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Luminosity functions are used to study the properties of large groups or classes of objects, such as the stars in clusters or the galaxies in the Local Group. Note that the term "function" is slightly misleading, and the luminosity function might better be described as a luminosity distribution. Given a luminosity as input, the luminosity ...
The Press–Schechter formalism predicts that the number of objects with mass between and + is: = (+) ¯ (+) / (() (+) /). where is the index of the power spectrum of the fluctuations in the early universe (), ¯ is the mean (baryonic and dark) matter density of the universe at the time the fluctuation from which the object was formed had gravitationally collapsed, and is a cut-off mass ...
Paul L. Schechter (born May 30, 1948) is an American astronomer and observational cosmologist. He is the William A. M. Burden Professor of Astrophysics, Emeritus, at MIT . Schechter received his bachelor's degree from Cornell in 1968, and his Ph.D. degree from Caltech in 1975.
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Eric Schechter (born August 1, 1950) is an American mathematician, retired from Vanderbilt University with the title of professor emeritus. His interests started primarily in analysis but moved into mathematical logic .
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Since the situation is symmetric, it seems obvious that there is no point in switching envelopes. On the other hand, a simple calculation using expected values suggests the opposite conclusion, that it is always beneficial to swap envelopes, since the person stands to gain twice as much money if they switch, while the only risk is halving what ...