Existence of Wave Operators with Time-Dependent Modifiers for the Schrödinger Equations with Long-Range Potentials on Scattering Manifolds

We construct time-dependent wave operators for Schrödinger equations with long-range potentials on a manifold M with asymptotically conic structure. We use the two space scattering theory formalism, and a reference operator on a space of the form ${\mathbb{R} \times \partial M}$ , where ${\partial M}$ is the boundary of M at infinity. We construct exact solutions to the Hamilton–Jacobi equation on the reference system ${\mathbb{R} \times \partial M}$ and prove the existence of the modified wave operators.     

Epitaxial growth of Bi thin films on Ge(1 1 1)

We investigated Bi thin film growth on Ge(1 1 1) by using low-energy electron diffraction (LEED) and scanning tunneling microscopy (STM). In the submonolayer regime, adsorbed Bi atoms form patches of the (2×1) structure. However, the structure does not grow to a long-range order. Following the formation of a (1×1) monolayer (ML) film, two-dimensional (1 1 0)-orientated Bi islands grow. The film orientation changes from (1 1 0) to (1 1 1) at 6-10 ML. The (1 1 0)-oriented Bi film shows a six-domain LEED pattern with missing spots, associated with a glide-line symmetry. The hexagonal (1 1 1) film at 14 ML has a lattice constant 2% smaller than bulk Bi(1 1 1).     

Identification of a regulatory element for yeast tryptophan permease Tat2 ubiquitination using high hydrostatic pressure

ABSTRACT

Tryptophan uptake in the yeast Saccharomyces cerevisiae is extremely sensitive to high pressure; therefore, the growth of tryptophan auxotrophic strains is impaired. Degradation of tryptophan permease Tat2 is enhanced at 25?MPa, depending on Rsp5 ubiquitin ligase. Any defect in Tat2 ubiquitination confers high pressure growth capacity, which is a luminous phenotype of the yeast used to explore the mechanism by which Rsp5 mediates Tat2 ubiquitination. Here we show that the N-terminal four (K17, K20, K29, and K31) among five lysines are required for efficient Tat2 degradation under high pressure. We found that a domain spanning D70 to S76 is also critical for Tat2 degradation at 25?MPa probably because of the recognition by Bul1, an adaptor protein of Rsp5. Defects in Tat2 ubiquitination do not produce any remarkable mutant phenotype at 0.1?MPa. Therefore, we suggest that high pressure is a unique and advanced tool to explore ubiquitination-dependent Tat2 regulation.     

Numerical analysis of radiation by a relativistic electron beampropagating parallel to a reflection grating

Two-dimensional radiation by a relativistic sheet electron beam propagating parallel to a reflection grating composed of a sinusoidally corrugated conducting surface is studied rigorously using the mode-matching method. Accurate dispersion curves for the eigenmodes that govern the Smith-Purcell radiation and the instability of the electromagnetic surface wave are presented. The imaginary parts of the eigenwavenumber and eigenfrequency give the leakage coefficient of space-charge waves and the growth rate of electromagnetic surface waves. Their dependences on the dimensions of the radiating structure are discussed. Optimum parameters for achieving the maximum leakage coefficient and the growth rate are determined. The method is general and can be applied to any two-dimensional system of electron beam coupled to an open periodic structure of arbitrary profile     

Ebulliometric determination and prediction of (vapor + liquid) equilibria for binary and ternary mixtures containing alcohols (C1–C4) and dimethyl carbonate

(Vapor + liquid) equilibrium (VLE) data for a ternary mixture, namely {methanol + propan-1-ol + dimethyl carbonate (DMC)}, and four binary mixtures, namely an {alcohol (C₃ or C₄) + DMC}, containing the binary constituent mixtures of the ternary mixture, were measured at p = (40.00 to 93.32) kPa using a modified Swietoslawski-type ebulliometer. The experimental data for the binary systems were correlated using the Wilson model. The Wilson model was also applied to the ternary system to predict the VLE behavior using parameters from the binary mixtures. The modified UNIFAC (Dortmund) model was also tested for the predictions of the VLE behavior of the binary and ternary mixtures. In addition, the experimental VLE data for the ternary and constituent binary mixtures were correlated using the extended Redlich–Kister (ERK) model, which can completely represent the azeotropic points. For the ternary system, a comparison of the experimental and the predicted or correlated boiling points obtained using the Wilson and ERK models showed that the ERK model is more accurate. The valley line, i.e., the curve which divides the patterns of vapor–liquid tie lines, was found in the (methanol + propan-1-ol + DMC) system. This valley line could be represented by the ERK model. Finally, the composition profile for simple distillation of this ternary mixture was obtained by analysis of the residue curves from the estimated Wilson parameters of the constituent binary mixtures.     

Trinuclear copper(II) complex showing high selectivity for the hydrolysis of 2'-5' over 3'-5' for UpU and 3'-5' over 2'-5' for ApA ribonucleotides

The cooperative action of multiple Cu(II) nuclear centers is shown to be effective and selective in the hydrolysis of 2'-5' and 3'-5' ribonucleotides. Reported herein is the specific catalysis by two trinuclear Cu(II) complexes of L3A and L3B. Pseudo first-order kinetic studies reveal that the L3A trinuclear Cu(II) complex effects hydrolysis of Up(2'-5')U with a rate constant of 28 x 10(-)(4) min(-)(1) and Up(3'-5')U with a rate constant of 0.5 x 10(-)(4) min(-)(1). The hydrolyses of Ap(3'-5')A and Ap(2'-5')A proceed with rate constants of 24 x 10(-)(4) min(-)(1) and 0.5 x 10(-)(4) min(-)(1) respectively. The L3A trinuclear Cu(II) complex demonstrates high specificity for Up(2'-5')U and Ap(3'-5')A. Similar studies with the more rigid L3B trinuclear Cu(II) complex shows no selectivity and yields lower rate constants for hydrolysis. The selectivity observed with the L3A ligand is attributed to the geometry of the ligand-bound diribonucleotide which ultimately dictates the proximity of the attacking hydroxyl and the phosphoester to a Cu(II) center for activation and subsequent hydrolysis.