Kneser-type oscillation criteria for self-adjoint two-term differential equations

It is proved that the even-order equationy ⁽²ⁿ⁾ +p(t)y=0 is (n,n) oscillatory at if

Nilpotency of Connes'' periodicity operator and the idempotent conjectures

For certain classes of discrete groups we verify the idempotent conjectures for various group algebras by the method of cyclic cohomology. In particular, the Banach ¹ (G) of a torsion free word hyperbolic groupG of Gromov contains no nontrivial idempotents. Moreover, the range of any tracial state onK ₀(¹(G)) is .Sponsored in part by a grant from the National Science Foundation.     

Level crossing resonance due to chlorine nuclei in a free radical

Muonium adds to allyl chloride, CH₂=CHCH₂Cl, to form two radicals: MuCH₂CHCH₂Cl (main product) and CH₂CHMuCH₂Cl (minor product). Both radicals were fully characterized bySR andLCR. In the main product, the LCR lines due to the³⁵Cl and³⁷Cl nuclei were observed. Also, the temperature dependence of various hyperfine coupling constants (hfc) indicates that both Mu and Cl eclipse the unpaired electronp ₂-orbital in the minimum energy conformation. For the fragment-CH₂Cl, the presence of Mu in the-position is found to affect significantly the hfc of Cl in the-position; an internal rotational barrier of 12 kJ mol^–1 was estimated using a simpleV ₂ torsional potential.     

Interior-point algorithm for quadratically constrained entropy minimization problems

In this paper, we develop an interior point algorithm for quadratically constrained entropy problems. The algorithm uses a variation of Newton's method to follow a central path trajectory in the interior of the feasible set. The primal-dual gap is made less than a given in at most steps, wheren is the dimension of the problem andm is the number of quadratic inequality constraints.