HETEROCYCLIC CATIONS WITH DELOCALISED PI-SYSTEMS AND SHORT INTRAMOLECULAR SULFUR… SULFUR CONTACTS: THE STRUCTURES OF TWO DERIVATIVES OF THE 2-(1,3-DITHIOL-2-YLIDENEMETHYL)-1,3-DITHIOLIUM CATION

Abstract

The effective size of bonded divalent sulfur in S…S contacts is a function of the orientation of the groups, with the shortest contacts occurring when the groups are coplanar. A lower limit for the loner is indicated by the structures of the 2-(1,3-benzodithiol-2-ylidenemethyl)-1,3-benzodithiolium and 2-(1,3-dithiolan-2-ylidenemethyl)-1,3-dithiolanium cations, 2 and 3. These show almost mm symmetry with all four sulfur atoms involved in stabilisation of the positive charge. Short intramolecular sulfur… sulfur contact distances, 0.5–0.7 Å within the sum of traditional van der Waals radii, and maximised by in-plane angular distortions, indicate a lower limit to the effective size of the bonded divalent sulfur atom of ca. 1.45 Å.     

Tracking accuracy of a semi‐Lagrangian method for advection–dispersion modelling in rivers

There is an increasing need to improve the computational efficiency of river water quality models because: (1) Monte‐Carlo‐type multi‐simulation methods, that return solutions with statistical distributions or confidence intervals, are becoming the norm, and (2) the systems modelled are increasingly large and complex. So far, most models are based on Eulerian numerical schemes for advection, but these do not meet the requirement of efficiency, being restricted to Courant numbers below unity. The alternative of using semi‐Lagrangian methods, consisting of modelling advection by the method of characteristics, is free from any inherent Courant number restriction. However, it is subject to errors of tracking that result in potential phase errors in the solutions. The aim of this article is primarily to understand and estimate these tracking errors, assuming the use of a cell‐based backward method of characteristics, and considering conditions that would prevail in practical applications in rivers. This is achieved separately for non‐uniform flows and unsteady flows, either via theoretical considerations or using numerical experiments. The main conclusion is that, tracking errors are expected to be negligible in practical applications in both unsteady flows and non‐uniform flows. Also, a very significant computational time saving compared to Eulerian schemes is achievable. Copyright © 2006 John Wiley & Sons, Ltd.     

Squares,clique graphs,and chordality

We study the squares and the clique graphs of chordal graphs and various special classes of chordal graphs. Chordality conditions for squares and clique graphs are given. Several theorems concering chordal graphs are generalized. © 1996 John Wiley & Sons, Inc.     

An in depth study of the formation of new tetrathiafulvalene derivatives from 1,8-diketones

A detailed study of the reactions of phosphorus pentasulfide and Lawesson's reagent with a series of 4,5-bis(RCOCH₂S)-1,3-dithiole-2-thiones (R=Ph, 4-MeOC₆H₄, 4-Br C₆H₄, Me) has been carried out. These reactions lead to fusion of either an unsaturated 1,4-dithiin ring or a thiophene to the dithiole; the former in higher yield, while the latter is a significant product in the reactions with Lawesson's reagent; as well as small amounts of minor products. A mechanistic rationalization of these products is discussed in some detail. The new fused dithioles have been converted to novel series of fused TTF derivatives.     

Rotational predissociation of extremely weakly bound atom-molecule complexes produced by Feshbach resonance association

We study the rotational predissociation of atom-molecule complexes with very small binding energy. Such complexes can be produced by Feshbach resonance association of ultracold molecules with ultracold atoms. Numerical calculations of the predissociation lifetimes based on the computation of the energy dependence of the scattering matrix elements become inaccurate when the binding energy is smaller than the energy width of the predissociating state. We derive expressions that represent accurately the predissociation lifetimes in terms of the real and imaginary parts of the scattering length and effective range for molecules in an excited rotational state. Our results show that the predissociation lifetimes are the longest when the binding energy is positive, i.e., when the predissociating state is just above the excited state threshold.     

On integer matrices obeying certain matrix equations

We discuss integer matrices B of odd order ν which satisfy

B^T = ± B, BB^T = vI − J, BJ = 0

Equivalence of Hadamard matrices

Supposem is a square-free odd integer, andA andB are any two Hadamard matrices of order 4m. We will show thatA andB are equivalent over the integers (that is,B can be obtained fromA using elementary row and column operations which involve only integers).     

The measurement of fetal liver T(*)(2) in utero before and after maternal oxygen breathing: progress towards a non-invasive measurement of fetal oxygenation and placental function

Utero-placental insufficiency is thought to be a major cause of growth retardation in utero and an important risk factor in the perinatal period. The purpose of this study was to investigate whether MRI could detect changes of fetal oxygenation, based on the blood oxygenation level dependence (BOLD) of the MRI tissue signal. Nine third trimester women (34-38 weeks) with normal pregnancies underwent abdominal MRI examinations. Following localization of the fetal liver using T(2)-weighted single-shot HASTE scans, up to 7 breath-held transaxial single-slice gradient-echo image sets were obtained through the fetal liver. The mother then commenced oxygen breathing with the imaging procedure repeated after 20 minutes of O(2) breathing. For each image set, T(*)(2) values are calculated using linear regression of log (signal) versus TE for a region of interest within the fetal liver selected by the attending radiologist. Fetal liver T(*)(2) values were calculated before and after O(2) breathing for each multi-echo image acquisition set. A signed rank test was used to test for a significant change in fetal liver T(*)(2) between the pre-O(2) and post-O(2) image sets. A significant increase in T*(2) (alpha < 0.05) was seen in 5 of the 9 fetal livers, a smaller increase (of borderline statistical significance, alpha = 0.057) in 2 livers, and no significant change (alpha > 0.05) in 2 livers. Our study indicates that T(*)(2) measurement of the fetal liver may detect alteration in fetal oxygen level following maternal oxygenation using the BOLD effect. This technique may potentially be applied to the identification and understanding of placental dysfunction in intra-uterine growth retardation.