Isometries of the Dirichlet space among the composition operators

We show that every composition operator which is an isometry of the Dirichlet space is induced by a univalent full map of the disk into itself that fixes the origin. This is an analogue of the Hardy space result for inner functions due to Nordgren. The proof relies on the Stone-Weierstrass theorem and the Riesz representation theorem.

     

Remote stereocontrol by the sulfinyl group: Mukaiyama aldol reactions of (S)-2-[2-(p-tolylsulfinyl)phenyl]acetaldehyde in the asymmetric synthesis of β-hydroxyacids and 1,3-diols

(S)-2-[2-(p-Tolylsulfinyl)phenyl]acetaldehyde reacts with different O-silylated ketenethioacetals in the presence of Yb(OTf)₃ yielding β-hydroxythioesters in high yields and diastereoselectivities. The obtained compounds were readily transformed into β-hydroxyacids and their corresponding diols. These Mukaiyama aldol reactions are a direct evidence of the ability of the sulfinyl group to control 1,5- and 1,6-asymmetric induction processes.     

Maximizing a Linear Fractional Function on a Pareto Efficient Frontier

We consider the problem of maximizing a linear fractional function on the Pareto efficient frontier of two other linear fractional functions. We present a finite pivoting-type algorithm that solves the maximization problem while computing simultaneously the efficient frontier. Application to multistage efficiency analysis is discussed. An example demonstrating the computational procedure is included.     

Angular dependent rayleigh scattering of Mössbauer radiation on proteins

RSMR experiments with⁵⁷Fe radiation were performed on myoglobin. An areasensitive detector was employed for simultaneous angular dependent collection of the scattered quanta up to a maximum angle 2θ of 17‡. Experimental data of polycrystalline and lyophilized myoglobin are compared with computer calculations of the scattering which are based on the atomic coordinates determined by X-ray structure analysis. Special attention has been paid to the influence of coherence effects from collectively moving parts of the protein. A simple model is introduced in order to take into account these segmental motions. Our first results indicate that the sizes of collectively moving segments are comparable with spheres of about 6 å in diameter in dry myoglobin. In myoglobin crystals, where the molecules are surrounded by large hydration shells, the movements appear to be correlated in segments with sizes comparable to helices.

     

Modified gravity on the brane and dark energy

We analyze the dynamics of an AdS₅ braneworld with matter fields when gravity is allowed to deviate from the Einstein form on the brane. We consider exact five-dimensional warped solutions which are associated with conformal bulk fields of weight –4 and describe on the brane the following three dynamics: those of inhomogeneous dust, of generalized dark radiation, and of homogeneous polytropic dark energy. We show that, with modified gravity on the brane, the existence of such dynamical geometries requires the presence of non-conformal matter fields confined to the brane.     

Purification and some properties of squalene-2,3-epoxide: lanosterol cyclase from rat liver

Squalene-2,3-epoxide: lanosterol cyclase was purified from rat liver in five steps as a soluble and homogeneous protein. The purified enzyme showed a single band on SDS-polyacrylamide gel electrophoresis with a molecular weight of 75 kD. In its native state it behaved as a homo-dimer. The isoelectric point of 5.5 and the apparent Km value for (3S)-squalene-epoxide of 55 microM were estimated for the cyclase.     

Observation of the neutron radiative decay

The aim of this work is the experimental observation of and research into a rare neutron mode, the radiative beta decay, where a new particle, the radiative gamma quantum, is formed along with the expected decay products: a beta electron, a recoil proton, and an antineutrino. The discovery of this rare neutron decay mode was conducted through identification of triple-coincidence events: simultaneous registration of a beta electron, a proton, and a radiative gamma quantum. The ordinary neutron decay was registered by double coincidences of a beta electron and a recoil proton. The statistics collected allow one to deduce the branching ratio (BR) BR = (3.2 ± 1.6) × 10⁻³ (90% C.L.) in the gamma energy region greater than 35 keV. This value of BR is consistent with standard electroweak theory. The text was submitted by the authors in English. An erratum to this article is available at .     

Negative molecular ions of azafullerenes and their hydrogenated derivatives

The formation and decay of negative molecular ions of azafullerenes and their hydrogenated derivatives are investigated by mass spectrometry. The mechanisms of resonant electron capture and the lifetimes of negative molecular ions with respect to the electron autodetachment in azafullerene molecules are discussed. A comparative analysis of the data obtained for azafullerenes and hydrogenated fullerene derivatives is carried out.