On the Homeomorphism Groups of Cantor's Discontinuum and the Spaces of Rational and Irrational Numbers

The paper shows that the homeomorphism groups of, respectively,Cantor's discontinuum, the rationals and the irrationals haveuncountable cofinality. It is well known that the homeomorphismgroup of Cantor's discontinuum is isomorphic to the automorphismgroup Aut B of the countable, atomless boolean algebra B. Soalso Aut B has uncountable cofinality, which answers a questionposed earlier by the first author and H. D. Macpherson. Thecofinality of a group G is the cardinality of the length ofa shortest chain of proper subgroups terminating at G. 2000Mathematics Subject Classification 20B22, 20E15.     

Experimental evidence for a light and broad scalar resonance in D(+) --> pi(-)pi(+)pi(+) decay

From a sample of 1172 +/- 61 D(+)-->pi(-)pi(+)pi(+) decays, we find gamma(D(+)-->pi(-)pi(+)pi(+))/gamma(D(+)-->K-pi(+)pi(+)) = 0.0311 +/- 0.0018(+0.0016)(-0.0026). Using a coherent amplitude analysis to fit the Dalitz plot of these decays, we find strong evidence that a scalar resonance of mass 478(+24)(-23) +/- 17 MeV/c(2) and width 324(+42)(-40) +/- 21 MeV/c(2) accounts for approximately half of all decays.     

Characterizing Automorphism Groups of Ordered Abelian Groups

A proof is given of the following theorem, which characterizesfull automorphism groups of ordered abelian groups: a groupH is the automorphism group of some ordered abelian group ifand only if H is right-orderable. 2000 Mathematics Subject Classification20K15, 20K20, 20F60, 20K30 (primary); 03E05 (secondary).     

Observation of color-transparency in diffractive dissociation of pions

We have studied the diffractive dissociation into dijets of 500 GeV/c pions scattering coherently from carbon and platinum targets. Extrapolating to asymptotically high energies (where t(min)-->0), we find that when the per-nucleus cross section for this process is parametrized as sigma = sigma0Aalpha, alpha has values near 1.6, the exact result depending on jet transverse momentum. These values are in agreement with those predicted by theoretical calculations of color-transparency.     

Direct measurement of the pion valence-quark momentum distribution, the pion light-cone wave function squared

We present the first direct measurements of the pion valence-quark momentum distribution which is related to the square of the pion light-cone wave function. The measurements were carried out using data on diffractive dissociation of 500 GeV/c pi(-) into dijets from a platinum target at Fermilab experiment E791. The results show that the /q&q> light-cone asymptotic wave function describes the data well for Q2 approximately 10 (GeV/c)(2) or more. We also measured the transverse momentum distribution of the diffractive dijets.     

Axially chiral amidinium ions as inducers of enantioselectivity in Diels-Alder reactions

[reaction: see text] Enantioselective catalysis of Diels-Alder reactions is mostly achieved by coordinating the dienophile to relatively strong chiral Lewis acids. Here we report on a novel approach employing the hydrogen-bond-mediated association of dienophiles to chiral host molecules. In a reaction forming the steroid skeleton of norgestrel, chiral amidinium ions induce 5:ent-5 ratios of up to 2.5:1. Improved and simplified amidinium catalysts may become interesting candidates to perform stereoselective transformations.     

ON TORSION-FREE CRAWLEY GROUPS

The notion of a Crawley p-group is well known in Abelian grouptheory. In this present work, a corresponding concept is introducedfor torsion-free groups. The principal result, which uses theset-theoretic notions of the diamond and Martin’s axiom,establishes an independence result for ₁-free Crawley groups.