Efficient Finite Difference Solutions to the Time-Dependent Schrödinger Equation

The matrix elements of the exponential of a finite difference realization of the one-dimensional Laplacian are found exactly. This matrix is used to formulate an efficient algorithm for the numerical solution to the time-dependent quantum mechanical scattering of a single particle from a time-independent potential in one-space and one-time dimension. The method generalizes to higher spatial dimensions, as well as to multiparticle problems.     

Master-slave synchronization and the Lorenz equations

Since the seminal remark by Pecora and Carroll [Phys. Rev. Lett. 64, 821 (1990)] that one can synchronize chaotic systems, the main example in the related literature has been the Lorenz equations. Yet this literature contains a mixture of true and false, and of justified and unsubstantiated claims about the synchronization properties of the Lorenz equations. In this note we clarify some of the confusion. (c) 1997 American Institute of Physics.     

Molecular Structure of 1-Substituted Bicyclo[2.2.0]hexanes: A Combined X-Ray Structural and Ab Initio Study

The synthesis and X-ray crystal structure of the p-bromoanilide derivative of bicyclo[2.2.0]hexane-l-carboxylic acid (1), N-(4-bromophenyl)-bicyclo[2.2.0]hexane-l-carboxamide (2), is reported. N-(4-Bromophenyl)-bicyclo[2.2.0]hexane-l-carboxamide is synthesized in good yield via the DCC coupling of bicyclo[2.2.0]hexane-l-carboxylic acid (1) with p-bromoaniline. Low-temperature X-ray analysis of 2 reveals that the bonds of the bicyclo[2.2.0]hexane skeleton vicinal to the amide group show a slight lengthening due to conjugative interaction with the -accepting amide group. Ab initio calculations at the 6-31G* level of theory on bicyclo[2.2.0]hexane-l-carboxamide, a model for 2, and for other 1-substituted bicyclo[2.2.0]hexanes are also reported.     

Compact Laws of the Iterated Logarithm for B-Valued Random Variables with Two-Dimensional Indices

Let be a real separable Banach space and {X, X _{n, m}; (n, m) N ²} B-valued i.i.d. random variables. Set . In this paper, the compact law of the iterated logarithm, CLIL(D), for B-valued random variables with two-dimensional indices ranging over a subset D of N ² is studied. There is a gap between the moment conditions for CLIL(N ¹) and those for CLIL(N ²). The main result of this paper fills this gap by presenting necessary and sufficient conditions for the sequence to be almost surely conditionally compact in B, where, for 0, 1 r 2, N ^r (, ) = {(n, m) N ²; n m n exp{(log n) ^r–1 (n)}} and (·) is any positive, continuous, nondecreasing function such that (t)/(log log t) is eventually decreasing as t , for some > 0.     

Stoney’s Electron

George Johstone Stony, th man who maned the electron, was led to the concept of a fundamental unit of electic charge by combining electro-chemistry with the kinetic theory of gases. But his understanding was incomplete (so the discovery of the electron is associated wit JJ Thomsons determination of its charge to mass ratio in October 1897)     

Ultrahigh-sensitivity fiber-optic strain and temperature sensor

We report ultrahigh-sensitivity static strain sensing (noise equivalent strain 相似文献   

Investigation of alkali borosilicate glass durability using tritium tracing, β-autoradiography, scanning electron microscopy and ion beam analysis

A Li-Na-containing borosilicate glass was submitted to aqueous corrosion in static mode in tritiated solutions of various pH at room temperature and 90 °C. Tritium counting, β-autoradiography, scanning electron microscopy (SEM) and ion beam analysis (IBA) techniques have been used to investigate the composition variations of the leached glass surfaces. In an acidic medium, the glass surface is covered by a thick hydrated silica layer; mobile elements like Li, Na and B and transition elements like Fe and Mo are strongly depleted. Near pH 7, relative enrichments of aluminium and iron are shown together with strong Li, Na and B depletions. In a basic medium, the glass surface exhibits iron and molybdenum enrichments whereas mobile elements seem to be kept at their nominal concentration level at the glass surface. The tritium activity and distribution on the leached glass surface is shown to depend strongly on the pH of the tritiated solutions. These observations are correlated with the observed changes of the surface morphology and chemistry characterized by IBA and SEM analysis. Elemental solubility versus pH of various chemical species have been calculated for comparison purpose with the experimental observations.     

An efficient and straightforward access to sulfur substituted [2.2]paracyclophanes: application to stereoselective sulfenate salt alkylation

A straightforward and high-yielding access to various [2.2]paracyclophanes possessing a sulfur-based functional group is reported, the key step being a SEAr reaction mediated by a sulfonium salt. The versatility of the methodology was exemplified by an original application in sulfenate salt chemistry, from which a remarkable chirality transfer was observed.     

A formal synthesis of the callipeltoside aglycone

A synthesis of the macrocyclic core structure of callipeltoside A and a C9 epimer has been achieved by applications of chiral vinylzinc or Kishi-Nozaki-Hiyama (K-N-H) additions, Roskamp homologations, and acylketene or intramolecular K-N-H macrolactonizations as key bond-forming steps.     

Sintokamides A to E, chlorinated peptides from the sponge Dysidea sp. that inhibit transactivation of the N-terminus of the androgen receptor in prostate cancer cells

The new chlorinated peptides sintokamides A to E (1-5) have been isolated from specimens of the marine sponge Dysidea sp. collected in Indonesia. Their structures were elucidated by a combination of spectroscopic and single-crystal X-ray diffraction analyses. Sintokamide A (1) is an inhibitor of N-terminus transactivation of the androgen receptor in prostate cancer cells.