Effects on the Structure of the Universe of an Accelerating Expansion

Recent experimental results from supernovae Ia observations have been interpreted to show that the rate of expansion of the universe is increasing. Other recent experimental results find strong indications that the universe is flat. In this paper, I investigate some solutions of Einstein's field equations which go smoothly between Schwarzschild's relativistic gravitational solution near a mass concentration to the Friedmann-Lemaître expanding universe solution. In particular, the static, curved-space extension of the Lemaître-Schwarzschild solution in vacuum is given. Uniqueness conditions are discussed. One of these metrics preserves the cosmological equation. We find that when the rate of expansion of the universe is increasing, space is broken up into domains of attraction. Outside a domain of attraction, the expansion of the universe is strong enough to accelerate a test particle away from the domain boundary. I give a domain-size–mass relationship. This relationship may very well be important to our understanding of the large scale structure of the universe.     

A chiral rhodium complex for rapid asymmetric transfer hydrogenation of imines with high enantioselectivity

[formula: see text] A chiral rhodium complex, (R)-Cp*RhCl[(1S,2S)-p-TsNCH(C6H5)CH(C6H5)NH2] (1a, (S,S)-Cp*RhClTsDPEN), generated from [Cp*RhCl2]2 and (1S,2S)-N-p-toluenesulfonyl-1,2-diphenylethylenediamine [(S,S)-TsDPEN], and its enantiomer 1b were found to provide superior catalysts for the rapid, high-yielding, asymmetric transfer hydrogenation of some heterocyclic imines, using an HCO2H-Et3N azeotrope as the hydrogen source.     

EOM/Propagator ionization potentials: Extension of the excitation operator manifold

The excitation operator manifold required for the calculation of vertical IPs in the EOM/propagator formalism is extended to include products of five spin orbital field operators (refered to as the h₅ basis). Spin symmetry adaptation is used for all the operators of this manifold. Using a direct diagonalization technique introduced previously the effect of inclusion of the h₅ basis on calculated IPs is illustrated for various levels of approximation to the electron density by numerical applications to ethylene and water. The fourth-order terms thus introduced are shown to have greater magnitude than previously included third-order terms, in agreement with earlier work.     

Energy analyzers: A study of their ultimate capabilities

A treatment and equation are developed whereby the maximum attainable resolution and transmission of an energy analyzer may be obtained without regard for specific electrode configuration employed to achieve focussing.     

Detailed Ge(Li)-Ge(Li) coincidence studies of levels in152Sm and152Gd

The decay of 12.4 y¹⁵²Eu to¹⁵²Sm and¹⁵²Gd was studied in a high resolution singles measurement and two 4096×2048 Ge(Li)-Ge(Li) coincidence studies. Forty-five gates were analyzed in order to confirm or establish the placement of the γ rays as well as to accurately determine the intensities of the 12 doublets, which included several not previously reported. A new γ-β interband transition, 4 _γ ⁺ →2 _β ⁺ (561.4 keV), a possible 3 _γ ⁺ →2 _β ⁺ (423.7 keV) transition, and a new 330.9 keV transition between the 4 _γ ⁺ level and theI ^π K=3^?0 octupole level were established from coincidence data. Levels at 1757.0 keV in¹⁵²Sm and 1282.5, 1318.7, and 1692.2 keV in¹⁵²Gd are now established on the basis of coincidence data. These data also establish for the first time the population in the¹⁵²Eu decay levels at 1680.0 and 1047.9 keV in¹⁵²Sm and¹⁵²Gd, respectively, as well as a new level at 1700.8 keV in¹⁵²Sm.