Nonvacuum taub-type cosmological model

The Einstein universe is a simple model describing a static cosmological spacetime, having a constant radius and a constant curvature, and, as is well known, it does not describe our universe. We propose a model which is an extension of Einstein's. Our metric, havingR × S ³ topology, describes a nonisotropic homogeneous closed (finite) universe of Bianchi type IX. This metric is similar to that of Taub, but is simpler. Unlike the Taub solution (which is a cosmological extension of the NUT solution), however, the universe described by our metric contains matter. Like the Taub metric, our metric has two positive constants (, T). The gravitational red shift calculated from our metric is given. Similarly to the Schwarzschild metric, which has a singularity atr = 2m, this metric has the same kind of singularity att = 2. The maximal extension of the coordinates in our metric is fairly analogous to that of the Schwarzschild metric.     

Oxidative addition of water and aliphatic alcohols by IrCl(trialkylphosphine)(3)

Oxidative addition of aliphatic alcohols to (C(8)H(14))IrCl(PMe(3))(3) in benzene yields the cis-hydrido-alkoxo products mer-cis-HIr(OR)Cl(PMe(3))(3) (R = Me, Et, 1-pentyl, 2-propyl). The analogous hydroxo complex is prepared by oxidative addition of water in THF. The addition rate depends on the nature of the alcohol (methanol > 1-pentanol > 2-propanol and methanol > water). The reaction is retarded in polar media but accelerated by protic cosolvents. Anionic ligand redistribution involving chloride and alkoxide (or hydroxide) competes with the oxidative addition reaction. A detailed kinetic study suggests that the 16-electron IrCl(PMe(3))(3) is the species undergoing the oxidative addition, and mer-cis-HIr(OR)Cl(PMe(3))(3) is the kinetic product. The reaction proceeds by a single-step nucleophilic attack of the metal on the O-H proton. Pi-donation by chloride stabilizes the transition state and governs the stereochemical course of the reaction. Protic solvent aggregation in the transition state in an apolar medium is suggested. mer-cis-HIr(OH)Cl(PEt(3))(3), obtained by water addition to IrCl(PEt(3))(3), was crystallographically characterized, showing an unusual hydrophobic cage around the hydride ligand.     

Intramolecular van der Waals Interactions Challenge Anion Binding in perthio-Bambusurils

Bambusurils (BUs) are known to be rigid cavitands that feature an extended, jigger-like conformation, and the BU[6]s strongly bind anions within their hydrophobic cavity. These features are not necessarily shared by the family of perthio-BUs. This study reveals that perthio-BUs assume a compact conformation and perthio-BU[6]s are poor anion binders, crystallizing as anion-free species from solutions containing halide salts. Computational studies show that the equatorial sulfur atoms compete against guest anions for binding with the glycoluril methine groups via strong van der Waals (vdW) attractive interactions. These competitive contacts not only account for the diminished anion-binding of perthio-BUs, but also explain their compact conformation. The semithio- and perthio-BU[4]s form linear coordination polymers with Hg^II in the solid-state regardless of their intrinsic molecular conformation. The strong involvement of sulfur atoms in intramolecular interactions differentiates the equatorial from the axial (peripheral) heteroatoms, thus offering chemoselective and regioselective transformations.     

Switchable Cucurbituril–Bipyridine Beacons

4‐Aminobipyridine derivatives form strong inclusion complexes with cucurbit[6]uril, exhibiting remarkably large enhancements in fluorescence intensity and quantum yields. The remarkable complexation‐induced pK_a shift (ΔpK_a=3.3) highlights the strong charge–dipole interaction upon binding. The reversible binding phenomenon can be used for the design of switchable beacons that can be incorporated into cascades of binding networks. This concept is demonstrated herein by three different applications: 1) a switchable fluorescent beacon for chemical sensing of transition metals and other ligands; 2) direct measurement of binding constants between cucurbit[6]uril and various nonfluorescent guest molecules; and 3) quantitative monitoring of biocatalytic reactions and determination of their kinetic parameters. The latter application is illustrated by the hydrolysis of an amide catalyzed by penicillin G acylase and by the elimination reaction of a β‐cabamoyloxy ketone catalyzed by aldolase antibody 38C2.     

Some applications of Ball's extension theorem

We present two applications of Ball's extension theorem. First we observe that Ball's extension theorem, together with the recent solution of Ball's Markov type problem due to Naor, Peres, Schramm and Sheffield, imply a generalization, and an alternative proof of, the Johnson-Lindenstrauss extension theorem. Second, we prove that the distortion required to embed the integer lattice , equipped with the metric, in any -uniformly convex Banach space is of order .

     

Surface lattice solitons

We study theoretically nonlinear surface waves in optical lattices and show that solitons can exist at the heterointerface between two different semi-infinite 1D waveguide arrays, as well as at the boundaries of a 2D nonlinear lattice. The existence and properties of these surface soliton solutions are investigated in detail.     

Precise large deviation estimates for a one-dimensional random walk in a random environment

ω_x } (taking values in the interval [1/2, 1)), which serve as an environment. This environment defines a random walk {X _k } (called a RWRE) which, when at x, moves one step to the right with probability ω _x , and one step to the left with probability 1 −ωx. Solomon (1975) determined the almost-sure asymptotic speed (= rate of escape) of a RWRE, in a more general set-up. Dembo, Peres and Zeitouni (1996), following earlier work by Greven and den Hollander (1994) on the quenched case, have computed rough tail asymptotics for the empirical mean of the annealed RWRE. They conjectured the form of the rate function in a full LDP. We prove in this paper their conjecture. The proof is based on a “coarse graining scheme” together with comparison techniques. Received: 22 July 1997/Revised version: 15 June 1998     

Atomic volume dependence of the153Eu isomer shift in ScxY1−x

Mössbauer studies of dilute¹⁵³Eu in Sm_0.05Sc _x Y_0.95–x (0x0.95) reveal large changes in the isomer shift as a function ofx. The strong dependence of the isomer shift on alloy composition, is interpreted in terms of changes in the charge density at the Eu nucleus ((0)), which result from changes in atomic volume. The isomer shift was found to depend linearly on V/V (V/V changes between 0 and –0.3). A value of (–17.5±2.0)a ₀ ^–3 was obtained for d(0)/d lnV.This research was supported by a grant from the United States—Israel Binational Science Foundation (BSF), Jerusalem, Israel.