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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 ...
The uppercase form of sigma (Σ) was re-borrowed into the Latin alphabet—more precisely, the International African Alphabet—to serve as the uppercase of modern esh (lowercase: ʃ). In phonology, σ is used to represent syllables. In linguistics, Σ represents the set of symbols that form an alphabet (see also computer science).
The form of the Kelvin equation here is not the form in which it appeared in Lord Kelvin's article of 1871. The derivation of the form that appears in this article from Kelvin's original equation was presented by Robert von Helmholtz (son of German physicist Hermann von Helmholtz) in his dissertation of 1885. [2]
This equation and the usual value of a = 3.5 only applies to main-sequence stars with masses 2M ⊙ < M < 55M ⊙ and does not apply to red giants or white dwarfs. As a star approaches the Eddington luminosity then a = 1. In summary, the relations for stars with different ranges of mass are, to a good approximation, as the following: [2] [4] [5]
[4] The approach of electron localization, in the form of atoms in molecules (AIM), was pioneered by Richard Bader . [ 5 ] Bader's analysis partitions the charge density in a molecule to "atoms" according to zero-flux surfaces (surfaces across which no electron flow is taking place). [ 6 ]
A Perrin microcosm: the escape time algorithm is applied to the Newton map of the entire Perrin function F(z) around critical point z = 1.225432 with viewport width 0.05320. The basins of attraction emanating from the centre correspond to the infinite number of real (left) and complex roots (right) F(z) = 0.
More generally, for weakly nonlinear and slowly modulated waves propagating in one space dimension and including higher-order dispersion effects – not neglecting the time and space derivatives and of the amplitude (,) when taking derivatives, where is a small modulation parameter – the averaged Lagrangian density is of the form: [22 ...