A Dixmier-Schaefer-Zhang theorem for operator algebras

Schaefer and Zhang have recently obtained an analogue, for sequentially order continuous functionals on , of a much earlier theorem of Dixmier. In this note it is shown that the Schaefer-Zhang Theorem has a natural generalisation to non-commutative -algebras. These results are obtained as consequences of our main theorem which is concerned with affine functions on compact convex sets.

     

(±)‐2,3‐dialkyl‐1,2,3,4‐tetrahydroquinoline‐3‐carboxylic esters by a tandem reduction‐reductive amination reaction

A series of 2‐methyl‐2‐(2‐nitrobenzyl)‐substituted β‐keto ester derivatives has been subjected to reductive cyclization under hydrogenation conditions to assess the importance of the ester group position on the diastereoselectivity of the process. Hydrogenation over 5% palladium‐on‐carbon at 4 atmospheres pressure resulted in formation of (±)‐2,3‐dialkyl‐1,2,3,4‐tetrahydroquinoline‐3‐carboxylic esters with a preference for the product isomer having the C2 alkyl cis to the C3 ester. The product ratios were synthetically useful (6‐16:1), but less than that observed in cyclizations to prepare (±)‐2‐alkyl‐1,2,3,4‐tetrahydroquinoline‐4‐carboxylic esters. The reduced selectivity in the current reactions has been rationalized in terms of the greater conformational mobility around the ester bearing carbon, which decreases the ability of the ester to sterically influence the addition of hydrogen to the final imine intermediate.     

Cross section and parity-violating spin asymmetries of W± boson production in polarized p + p collisions at sqrt[s] = 500 GeV

Large parity-violating longitudinal single-spin asymmetries A(L)(e+) = -0.86(-0.14) (+0.30) and A(L)(e-) = 0.88(-0.71) (+0.12) are observed for inclusive high transverse momentum electrons and positrons in polarized p+p collisions at a center-of-mass energy of sqrt[s] = 500 GeV with the PHENIX detector at RHIC. These e± come mainly from the decay of W± and Z0 bosons, and their asymmetries directly demonstrate parity violation in the couplings of the W± to the light quarks. The observed electron and positron yields were used to estimate W± boson production cross sections for the e± channels of σ(pp → W+ X) × BR(W+ → e+ ν(e)) = 144.1 ± 21.2(stat)(-10.3) (+3.4) (syst) ± 21.6(norm) pb, and σ(pp → W- X) × BR(W- → e- ν[over ˉ](e)) = 31.7 ± 12.1(stat)(-8.2) (+10.1) (syst) ± 4.8(norm) pb.     

Ethyl (1R∗,3aS∗,7aS∗)-Octahydro-7a-methyl-7-oxo-1H-indene-1-acetate Using Tandem Reactions

The title compound was prepared in 29.5% overall yield using a five-step sequence involving two tandem reactions. The current work supports the earlier finding that a strong thermodynamic preference exists for an all-cis relationship across the three contiguous stereocenters at C(1), C(3a), and C(7a).     

J/psi production in sqrt s_NN=200 GeV Cu+Cu collisions

Yields for J/psi production in Cu+Cu collisions at sqrt s_NN=200 GeV have been measured over the rapidity range |y|<2.2 and compared with results in p+p and Au+Au collisions at the same energy. The Cu+Cu data offer greatly improved precision over existing Au+Au data for J/psi production in collisions with small to intermediate numbers of participants, in the range where the quark-gluon plasma transition threshold is predicted to lie. Cold nuclear matter estimates based on ad hoc fits to d+Au data describe the Cu+Cu data up to N_part approximately 50, corresponding to a Bjorken energy density of at least 1.5 GeV/fm(3).