Friedmanns Generalization

It is tempting to add that the second sheet represents Naan s anti-world, which lies on the opposite side of the projective double cover. 

Introduction of the cosmological term therefore results in an empty universe with a time-dependent metric exactly the opposite of Einstein s intention to produce a matter dominated static universe. 

The contradictions inherent in the schemes of Einstein and de Sitter were never resolved, despite what Capria (2005) calls a circuitous retmn [to] basic Newtonian concepts , eventually to be superseded by a more general formulation of the problem. 

By recalculating the line element (6.3), starting from a pseudo-Euchdean hypersurface with constant negative curvature 

The general solution of the field equations (6.4), by using the Robertson-Walker metric, was obtained by Aleksandr Friedmann on substituting (6.6) into (6.4). Details of the procedure are outlined by Narlikar (2002). By considering the matter distribution, as galaxies in space, to be like dust, the 

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Yee, J.K., Miyanohara, A., LaPorte, P., Bouic, K., Burns, J.C. and Friedmann, T. (1994) A general method for the generation of high-titer, pantropic retroviral vectors highly efficient infection of primary hepato-cytes. Proceedings of the National Academy of Sciences USA 91, 9564-9568. 

It is always risky to identify the origin of an idea. The basic idea of the Big Bang may be identified with the Russian mathematical physicist, Alexander A. Friedmann, who in 1922, armed with Einstein s general relativistic equations, developed the picture of the universe expanding from a point origin. The timing was wrong,... 

The time-evolution of H describes the evolution of the universe. Employing the Robertson-Walker metric in the Einstein equations of General Relativity (relating matter/energy content to geometry) leads to the Friedmann equation... 

For matter (non-relativistic matter often called dust ), p p, so that p/po = (ao/a)3. In contrast, for radiation (relativistic particles) p = pi3, so that p/po = (ao/a)4. Another interesting case is that of the energy density and pressure associated with the vacuum (the quantum mechanical vacuum is not empty ). In this case p = —p, so that p = po- This provides a term in the Friedmann equation entirely equivalent to Einstein s cosmological constant A. More generally, for p = wp, p/po = (ao/a)3(1+w Allowing for these three contributions to the total energy density, eq. 2.9 may be rewritten in a convenient dimensionless form... 

The Big Bang. In what is generally known as the standard family of Big Bang (Friedmann) models, 7Li is the only LiBeB nuclide synthesised in observable amounts. This Li in full or in part is seen in warm very metal-poor stars, as the Spite plateau. Nonstandard Big Bang models in a wide variety of forms have been proposed. Often, the consequences for the primordial nucleosynthesis are a focus of these proposals. 

This is not a requirement of general relativity, as often stated, but of the expanding Friedmann model, which is not covariant. 

To keep the record straight, what is generally known as standard cosmology refers to the model proposed by Einstein and de Sitter (1932). It consists of a Ftiedmann solution with A = 0, A = 0 and zero pressure, without reference to Friedmann or Lemaitre. The space-time is topologically like M and... 

Alexandr Alexandrovitch Friedmann (1888-1925), Russian mathematician and physicist, in his articie in Zeit. Phys., 10, 377 (1922), proved on the basis of Einstein s general theory of relativity that the curvature of the Universe must change, which became the basis of cosmological models of the expanding Universe. During World War I, Friedman was a pilot in the Russian army and made bombing raids over my beloved Przemysl. 

Although the positive evidence in support of the tricarboxylic acid cycle is thus incomplete in the case of some animal tissues, it may be said that the data on the whole favor the view that the cycle is operative in animal tissues generally. Such data as are available—on the occurrence of the enzymes and the effect of malonate—are in accordance with this view, and no positive evidence in support of major alternative pathways of the oxidation of acetate has so far come to light. A direct oxidation of acetate via glycollate, glyoxalate, and oxalate is, according to isotope experiments of Weinhouse and Friedmann, of no quantitative importance in the rat. 

The idea that the correlation functions and other statistical moments of the fluid mechanical fields must be recognized as the fundamental characteristics of turbulence was first stated by Keller and Friedmann ([81] see also [8], Sect. 2.2 [112], Chap. 2), who proposed a general method of obtaining the differential equations for the moments of arbitrary order for the description of turbulent flow. The determination of... 

In general, these reductions arc only partially, not completely, optically selective, though the formation of practically pure (- -)-/S-hydroxy-n-butyric acid by the action of fermenting yeast on the potassium salt of ethyl acetoacetate has been claimed by Friedmann (41). 

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