A relation between a.c. spectrum of ergodic Jacobi matrices and the spectra of periodic approximants

We study ergodic Jacobi matrices onl ²(Z), and prove a general theorem relating their a.c. spectrum to the spectra of periodic Jacobi matrices, that are obtained by cutting finite pieces from the ergodic potential and then repeating them. We apply this theorem to the almost Mathieu operator: (H _{, ,} u)(n)=u(n+1)+u(n–1)+ cos(2n+)u(n), and prove the existence of a.c. spectrum for sufficiently small , all irrational 's, and a.e. . Moreover, for 0<2 and (Lebesgue) a.e. pair , , we prove the explicit equality of measures: |_ac|=||=4 –2.Work partially supported by the US-Israel BSF     

Effects of Added Urea and Alkylureas on Gel to Liquid-Crystal Transitions in Doab Vesicles

The gel to liquid-crystal transition for vesicles in aqueous solution formed by dimethyldi-n-octadecylammonium bromide (DOAB) occurs at 44.7°C. Moreover, the shapes of the scans recorded by a sensitive DSC microcalorimeter are very similar when the vesicular solutions are prepared starting with solid DOAB and comparable amounts of either solid urea or solid alkylureas. Therefore, the DOAB vesicles in aqueous solution accommodate this class of solutes without marked changes in the melting temperature and the enthalpy of the transition. The contrast with effects of added surfactants and simple organic solutes such as THF and ethanol is particularly significant. This revised version was published online in August 2006 with corrections to the Cover Date.     

The Nevai Condition

We study Nevai’s condition that for orthogonal polynomials on the real line, $K_{n}(x,x_{0})^{2}K_{n}(x_{0},x_{0})^{-1}\,d\rho(x)\to\delta_{x_{0}}We study Nevai’s condition that for orthogonal polynomials on the real line, K_n(x,x₀)²K_n(x₀,x₀)^-1 dr(x)?d_x0K_{n}(x,x_{0})^{2}K_{n}(x_{0},x_{0})^{-1}\,d\rho(x)\to\delta_{x_{0}} , where K _n is the Christoffel–Darboux kernel. We prove that it holds for the Nevai class of a finite gap set uniformly on the spectrum, and we provide an example of a regular measure on [−2,2] where it fails on an interval.     

High-spin structure of yrast-band in 78Kr

Lifetime of levels up to 22⁺, have been measured in ⁷⁸Kr and an oblate shape is assigned to the ground state using the CSM and the configuration dependent shell correction calculations. Calculations further show that ⁷⁸Kr is highly γ-soft nucleus. The experimental Q _t values coupled with theoretical calculations indicate an oblate shape for ⁷⁸Kr at low spins and triaxial shape at higher spins