Synthesis of new silylated sulfur-containing heterocycles through thionation of bis(acylsilanes)

The thionation of bis(acylsilanes) with spacers of variable size with hexamethyldisilathiane under cobalt(II) chloride or trimethylsilyl triflate catalysis affords 2,5-bis(trialkylsilyl)-thiophenes, 2,6-bis(trialkylsilyl)-4H-thiopyrans and 2,7-bis(trialkylsilyl)-4,5-dihydrothiepine generally along with a minor amount of the corresponding oxo analogue. The synthesis of both symmetrical and unsymmetrical bis(trialkylsilyl) derivatives was achieved.     

Passive control of the flow around a square cylinder using porous media

The passive control of bluff body flows using porous media is investigated by means of the penalization method. This method is used to create intermediate porous media between solid obstacles and the fluid in order to modify the boundary layer behaviour. The study covers a wide range of two‐dimensional flows from low transitional flow to fully established turbulence by direct numerical simulation of incompressible Navier–Stokes equations. A parametric study is performed to illustrate the effect of the porous layer permeability and thickness on the passive control. The numerical results reveal the ability of porous media to both regularize the flow and to reduce the drag forces up to 30%. Copyright © 2004 John Wiley & Sons, Ltd.     

Identifying phylogenetic trees

A central problem that arises in evolutionary biology is that of displaying partitions of subsets of a finite set X on a tree whose vertices are partially labelled with the elements of X. Such a tree is called an X-tree and, for a collection of partitions of subsets of X, characterisations for the existence and uniqueness of an X-tree that displays have been previously given in terms of chordal graphs. In this paper, we obtain two closely related characterisations also in terms of chordal graphs. The first describes when identifies an X-tree, and the second describes when a compatible subset of is of maximum size.     

Optimally Dense Packings of Hyperbolic Space

In previous work, a probabilistic approach to controlling difficulties of density in hyperbolic space led to a workable notion of optimal density for packings of bodies. In this paper we extend an ergodic theorem of Nevo to provide an appropriate definition of those packings to be considered optimally dense. Examples are given to illustrate various aspects of the density problem, in particular the shift in emphasis from the analysis of individual packings to spaces of packings.     

Exploring interactions in high-dimensional genomic data: an overview of Logic Regression, with applications

Logic Regression is an adaptive regression methodology mainly developed to explore high-order interactions in genomic data. Logic Regression is intended for situations where most of the covariates in the data to be analyzed are binary. The goal of Logic Regression is to find predictors that are Boolean (logical) combinations of the original predictors. In this article, we give an overview of the methodology and discuss some applications. We also describe the software for Logic Regression, which is available as an R and S-Plus package.     

Isospectral theory of Euler equations

Isospectral problem of both 2D and 3D Euler equations of inviscid fluids, is investigated. Connections with the Clay problem are described. Spectral theorem of the Lax pair is studied.     

Recognition of subgroups of direct products of hyperbolic groups

We give examples of direct products of three hyperbolic groups in which there cannot exist an algorithm to decide which finitely presented subgroups are isomorphic.

     

Microwave structural studies of organoselenium compounds 1. Microwave spectra, molecular structure, and methyl barrier to internal rotation of dimethyl diselenide

The rotational spectra of nine isotopomers of dimethyl diselenide, CH₃SeSeCH₃, have been measured with a molecular-beam Fourier transform microwave spectrometer. The spectra were complex due to the presence of many isotopomers in natural abundance and the splitting caused by the interactions with two methyl internal rotors. The spectra were assigned and fit to experimental precision to an effective rotational Hamiltonian for molecules with two periodic internal motions. The spectra of the symmetric isotopomers are consistent with a C₂ equilibrium structure. The rotational constants were used to determine the r_s structure of the C-Se-Se-C frame with the results r(SeSe)=2.306(3) Å, r(SeC)=1.954(6) Å, ?(CSeSe)=99.8(2)°, ?(CSeSeC)=85.2(1)°. A barrier to internal rotation of the methyl groups of 395 ± 2 cm⁻¹ was derived from the internal rotation splittings.