Further results on integral generalized inverses of integral matrices

This paper further investigates integral generalized inverses of integral matrices.     

Konversion der 238,6 keV-γ-Linie des ThB und Vergleich mit den Tabellen von Sliv und von Rose

The conversion ratiosK/L _I andK/L _II of the 238.6 keVγ transition of ThB have been measured with the new Heidelbergπ/2 √13Β-ray spectrometer. For this transition there are great discrepancies between the values as given bySliv andBand, and byRose. The experimental resultsK/L _I=5.96±0.26 andK/L _II=60.3±7.1 are in excellent agreement with the values ofSliv andBand.     

Electrons magnetic fields and background radio emission in the galaxy

Extensive data now available on the non-thermal background radio emission from different celestial directions, and recent measurements on the energy spectrum of cosmic ray electrons in the vicinity of the earth permit one to deduce information on the mean magnetic fields and cosmic electron spectra needed to exist in different regions of the Galaxy. It is found that in order to explain quantitatively the background radio brightness distributions from the Galaxy one needs (i) the same or nearly same electron spectrum that exists in the near interstellar space, to exist in almost all regions of Galactic space, (ii) a mean magnetic field close to 6×10^?6 Gauss in the Disc in the direction of the Anti-centre, (iii) a mean magnetic field close to 2·5×10^?6 Gauss in the radio Halo and (iv) a mean magnetic field probably close to 9·5×10^?6 Gauss towards the Galactic Ridge in the direction of the Centre. Some inferences are also drawn on the confinement of cosmic rays in the Galaxy.     

Gauge internal symmetry in extended supergravity

Extended supergravity theories with global O(2) and SO(3) internal symmetry have recently been constructed, and a mechanism which implements local O(2) and SO(3) gauge invariance is given here. The introduction of a minimal gauge coupling automatically leads to a $\text{spin}\text{-}\text{3}\text{2}$ mass and a cosmological term in order to preserve local supersymmetry. Local internal symmetry for a $\text{spin}\text{-}\text{3}\text{2}$ field is related to spontaneous breakdown of global supersymmetry. Perturbation theory results which confirm the physical consistency of the system are given.     

Mechanism of amine catalyzed isomerization of itaconic anhydride to citraconic anhydride: Citraconamic acid formation

The amine catalyzed isomerization of itaconic to citraconic anhydride has been investigated. Studies show that the rate of isomerization is dependent on the base strength and solvent media. Triethylamine causes complete isomerization within 5 min at room temperature in acetone or chloroform solvent, whereas aromatic tertiary amines such as pyridine and N,N-dimethylaniline require time perods as long as 23h at room temperature for almost complete isomerization. In the presence of aniline no isomerization occures even under acetone reflux conditions over a 24 h period. For the preparation of citraconamic acids from itaconic anhydrides and aliphatic diamines nuclear magnetic resonance and infrared spectroscopic evidence is presented to support the reaction path of initial isomerization of itaconic anhydride to citraconic anhydride followed by amine attack on the anhydride to form the corresponding cis-citraconamic acids. The mechanism of isomerization of itaconic to citraconic acids is proposed.     

1,3-Diyl trapping reactions. Fundamental investigations with application to the synthesis of linearly fused tricyclopentanoids

A comparison of the inter- and intramolecular diyl trapping routes to linearly fused tricyclopentanoids is presented. In addition, several of the factors which are responsible for the stereoselectivity which is associated with the intramolecular process are examined and it is concluded that conformational rather than electronic (secondary orbital) factors play the dominant role. It is shown that gem methyl groups located on the acyclic chain which joins the diyl and diylophile (in reference to 32 and 35, but not to 47) have no practical effect upon the outcome of the trapping reaction. The intramolecular process is stereospecific with respect to diylophile geometry, and highly stereoselective with respect to the ring junction stereochemistry. Finally, an abortive attempt to synthesize the marine natural product Δ⁹⁽¹²)-capnellene (19) as well as a successful synthesis of the mold metabolite d,l- hirsutene (18) is presented.