Characterization of supercommuting matrices

For a given n-by-n matrix A, we consider the set of matrices which commute with A and all of whose principal submatrices commute with the corresponding principal submatrices of A. The properties of this set are examined, with particular attention to its dimension.     

Space tilings and local isomorphism

We prove for a large class of tilings that, given a finite tile set, if it is possible to tile Euclideann-space with isometric copies of this set, then there is a tiling with the ‘local isomorphism property’. Research supported in part by NSF Grant No. DMS-9001475.     

The thermolysis of dicarbonylcyclopentadienyliron dimer: The formation of biferrocene

The thermolysis of dicarbonylcyclopentadienyliron dimer in a sealed tube at 300°C has been reported to produce ferrocene, carbon monoxide, carbon dioxide, cyclopentadiene and elemental iron. We observe in addition to these products the production of biferrocene and elemental carbon. Thermolysis of carbonylcyclopentadienyliron tetramer (produced from the dimer by thermolysis in refluxing xylene) produces ferrocene, iron and carbon monoxidre; no biferrocene, carbon dioxide or elemental carbon are produced. A scheme is proposed to account for these products.     

A convenient method for regioselective C-5 halogenation of 4(3H)-oxo-7H-pyrrolo[2,3-d]pyrimidines

N-7, O-Disilylation of 4(3H)-oxo-7H-pyrrolo[2,3-d]pyrimidines provides a convenient method for activation of these compounds toward regiospecific halogenation at C-5. The sequence is conveniently carried out without isolation of the silylated derivatives and desilylation is spontaneous upon addition of water to the reaction mixture.     

TGF-β1 induction of the adenine nucleotide translocator 1 in astrocytes occurs through Smads and Sp1 transcription factors

Background  

The adenine nucleotide translocator 1 (Ant1) is an inner mitochondrial membrane protein involved with energy mobilization during oxidative phosphorylation. We recently showed that rodent Ant1 is upregulated by transforming growth factor-beta (TGF-β) in reactive astrocytes following CNS injury. In the present study, we describe the molecular mechanisms by which TGF-β1 regulates Ant1 gene expression in cultured primary rodent astrocytes.     

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.