New uniqueness theorems for trigonometric series

A uniqueness theorem is proved for trigonometric series and another one is proved for multiple trigonometric series. A corollary of the second theorem asserts that there are two subsets of the -dimensional torus, the first having a countable number of points and the second having points such that whenever a multiple trigonometric series ``converges' to zero at each point of the former set and also converges absolutely at each point of the latter set, then that series must have every coefficient equal to zero. This result remains true if ``converges' is interpreted as any of the usual modes of convergence, for example as ``square converges' or as ``spherically converges.'

     

Progress in direct-drive inertial confinement fusion research at the laboratory for laser energetics

Direct-drive inertial confinement fusion (ICF) is expected to demonstrate high gain on the National Ignition Facility (NIF) in the next decade and is a leading candidate for inertial fusion energy production. The demonstration of high areal densities in hydrodynamically scaled cryogenic DT or D₂ implosions with neutron yields that are a significant fraction of the “clean” 1-D predictions will validate the ignition-equivalent direct-drive target performance on the OMEGA laser at the Laboratory for Laser Energetics (LLE). This paper highlights the recent experimental and theoretical progress leading toward achieving this validation in the next few years. The NIF will initially be configured for X-ray drive and with no beams placed at the target equator to provide a symmetric irradiation of a direct-drive capsule. LLE is developing the “polar-direct-drive” (PDD) approach that repoints beams toward the target equator. Initial 2-D simulations have shown ignition. A unique “Saturn-like” plastic ring around the equator refracts the laser light incident near the equator toward the target, improving the drive uniformity. LLE is currently constructing the multibeam, 2.6-kJ/beam, petawatt laser system OMEGA EP. Integrated fast-ignition experiments, combining the OMEGA EP and OMEGA Laser Systems, will begin in FY08.     

Atmospheric chemistry of isopropyl formate and tert‐butyl formate

Formates are produced in the atmosphere as a result of the oxidation of a number of species, notably dialkyl ethers and vinyl ethers. This work describes experiments to define the oxidation mechanisms of isopropyl formate, HC(O)OCH(CH₃)₂, and tert‐butyl formate, HC(O)OC(CH₃)₃. Product distributions are reported from both Cl‐ and OH‐initiated oxidation, and reaction mechanisms are proposed to account for the observed products. The proposed mechanisms include examples of the α‐ester rearrangement reaction, novel isomerization pathways, and chemically activated intermediates. The atmospheric oxidation of isopropyl formate by OH radicals gives the following products (molar yields): acetic formic anhydride (43%), acetone (43%), and HCOOH (15–20%). The OH radical initiated oxidation of tert‐butyl formate gives acetone, formaldehyde, and CO₂ as major products. IR absorption cross sections were derived for two acylperoxy nitrates derived from the title compounds. Rate coefficients are derived for the kinetics of the reactions of isopropyl formate with OH (2.4 ± 0.6) × 10^?12, and with Cl (1.75 ± 0.35) × 10^?11, and for tert‐butyl formate with Cl (1.45 ± 0.30) × 10^?11 cm³ molecule^?1 s^?1. Simple group additivity rules fail to explain the observed distribution of sites of H‐atom abstraction for simple formates. © 2010 Wiley Periodicals, Inc. Int J Chem Kinet 42: 479–498, 2010     

A unique geometry of the active site of angiotensin-converting enzyme consistent with structure-activity studies

Summary Previous structure-activity studies of captopril and related active angiotensin-converting enzyme (ACE) inhibitors have led to the conclusion that the basic structural requirements for inhibition of ACE involve (a) a terminal carboxyl group; (b) an amido carbonyl group; and (c) different types of effective zinc (Zn) ligand functional groups. Such structural requirements common to a set of compounds acting at the same receptor have been used to define a pharmacophoric pattern of atoms or groups of atoms mutually oriented in space that is necessary for ACE inhibition from a stereochemical point of view. A unique pharmacophore model (within the resolution of approximately 0.15 Å) was observed using a method for systematic search of the conformational hyperspace available to the 28 structurally different molecules under study. The method does not assume a common molecular framework, and, therefore, allows comparison of different compounds that is independent of their absolute orientation.Consequently, by placing the carboxyl binding group, the binding site for amido carbonyl, and the Zn atom site in positions determined by ideal binding geometry with the inhibitors' functional groups, it was possible to clearly specify a geometry for the active site of ACE.