Operator algebras and a theorem of Dieudonne

LetA be aC*-algebra with second dualA″. Let (φ _n)(n=1,...) be a sequence in the dual ofA such that limφ _n(a) exists for eacha εA. In general, this does not imply that limφ _n(x) exists for eachx εA″. But if limφ _n(p) exists whenever p is the range projection of a positive self-adjoint element of the unit ball ofA, then it is shown that limφ _n(x) does exist for eachx inA″. This is a non-commutative generalisation of a celebrated theorem of Dieudonné. A new proof of Dieudonné’s theorem, for positive measures, is given here. The proof of the main result makes use of Dieudonné’s original theorem.     

Experimental and theoretical investigation of NMR 2JHH coupling constant on six-membered ring systems containing oxygen or sulfur atoms

Theoretical and experimental 2JHH coupling constants for six-membered rings containing oxygen or sulfur atoms were studied to investigate whether the 2JHH coupling constant can be used for stereoelectronic studies in heterocyclohexanes, instead of 1JCH, because it is well known that experimental measurements of 2JHH coupling constants at low temperature are much easier to determine than the corresponding 1JCH couplings. For all compounds studied here, the 2JHH coupling constants are affected by sigma*C-H antibonding occupancy together with bond angle effects. For cyclohexane and oxygen-containing compounds, the influence on the geminal coupling for Hax-C2-Heq and for X1-C2-X3 (X=O and C), bond angles are more pronounced than for the sulfur derivatives.     

Radial oscillations of neutron stars in strong magnetic fields

The eigen frequencies of radial pulsations of neutron stars are calculated in a strong magnetic field. At low densities we use the magnetic BPS equation of state (EOS) similar to that obtained by Lai and Shapiro while at high densities the EOS obtained from the relativistic nuclear mean field theory is taken and extended to include strong magnetic field. It is found that magnetized neutron stars support higher maximum mass whereas the effect of magnetic field on radial stability for observed neutron star masses is minimal.     

Stereoelectronic interaction and their effects on conformational preference for 2-substituted methylenecyclohexane: an experimental and theoretical investigation

Conformational preferences for 2-substituted methylenecyclohexanes were determined using (3) J H 2 H 3 spin-spin coupling constants, while stereoelectronic interactions were obtained by means of theoretical calculations and NBO analysis. The conformational equilibrium of compounds studied can be represented by their axial and equatorial conformers, the axial conformers being the most stable form in polar and nonpolar solvents. These conformational preferences were attributed to the hyperconjugative interactions between the pi C-C-->sigma* C-Xax. and sigma C-H-->sigma* C-Xax. orbitals, and the repulsive steric interaction observed between sigma C-H-->n Xeq..     

Total synthesis of (+)-crocacin D

[structure: see text] The total synthesis of (+)-crocacin D is described. The convergent asymmetric synthesis relies on the use of a Stille cross-coupling between an (E)-vinyl stannane with an (E)-vinyl iodide to establish the (E,E)-dienamide moiety followed by a mild and efficient copper-catalyzed coupling between (+)-crocacin C and a (Z)-vinyl iodide to establish the challenging (Z)-enamide function.     

Experimental, SOPPA(CCSD), and DFT analysis of substitutent effects on NMR 1JCF coupling constants in fluorobenzene derivatives

Interesting insight into the electronic molecular structure changes associated with substituent effects on the Fermi contact (FC) and paramagnetic spin-orbit (PSO) terms of (1)J(CF) NMR coupling constants (SSCCs) in o-X-, m-X-, and p-X-fluorobenzenes (X = NH(2); NO(2)) is presented. The formulation of this approach is based on the influence of different conjugative and hyperconjugative interactions on a second-order property, which can be qualitatively predicted if it is known how they affect the main virtual excitations entering into that second-order property. A set of consistent approximations are introduced in order to analyze the behavior of occupied and virtual orbitals, which define some experimental trends for (1)J(CF) spin-spin coupling constants. In addition, DFT hybrid functionals were used, and a similar degree of confidence to compute the (1)J(CF) with those observed for the SOPPA(CCSD) method was obtained. The (1)J(CF) SSCCs for ezetimibe, a commercially fluorinated drug used to reduce cholesterol levels, were measured and DFT-calculated, and the qualitative approach quoted above was applied. As a byproduct, a possible method to determine experimentally a significant PSO contribution to (1)J(CF) SSCCs is discussed.