Spatial design matrices and associated quadratic forms: structure and properties

The paper provides significant simplifications and extensions of results obtained by Gorsich, Genton, and Strang (J. Multivariate Anal. 80 (2002) 138) on the structure of spatial design matrices. These are the matrices implicitly defined by quadratic forms that arise naturally in modelling intrinsically stationary and isotropic spatial processes. We give concise structural formulae for these matrices, and simple generating functions for them. The generating functions provide formulae for the cumulants of the quadratic forms of interest when the process is Gaussian, second-order stationary and isotropic. We use these to study the statistical properties of the associated quadratic forms, in particular those of the classical variogram estimator, under several assumptions about the actual variogram.     

Evidence against the hopping mechanism as an important electron transfer pathway for conformationally constrained oligopeptides

The rate constant of intramolecular electron transfer through oligopeptides based on the alpha-aminoisobutyric acid residue was determined as a function of the peptide length and found to depend weakly on the donor-acceptor separation. By measuring the electron-transfer activation energy and estimating the energy gap between donor and bridge, we were able to discard the electron hopping mechanism.     

Dendrimeric Gd(III) complex of a monophosphinated DOTA analogue: optimizing relaxivity by reducing internal motion

A marked increase of relaxivity has been observed upon rigidifying the internal frame of Gd-containing PAMAM dendrimers: the effect has been attained by either protonation of the dendrimer or by forming supramolecular adducts with cationic polyaminoacids.     

Chemical waves and pattern formation in the 1,2-dipalmitoyl-sn-glycero-3-phosphocholine/water lamellar system

The present work deals with the spatially extended oscillatory Belousov Zhabotinsky reaction-diffusion system carried out in an anisotropic environment of phosphatidylcholines/water binary system, which presents layered aqueous domains separated by lipid bilayers. We report the occurrence of stable Turing patterns, spiral waves, and other exotic structures in phospholipids bilayers that are generally used as a models for cell plasma membranes.     

Unexpected 1,2,3-triazole formation in the reaction of diethylaluminum azide with α′-amino-α,β-unsaturated ketones

4-Acyl-1H-1,2,3-triazoles are formed from diethylaluminum azide and α′-(N,N-dibenzylamino)-α,β-unsaturated ketones by [3+2] cycloaddition of azide, followed by 1,5 hydride transfer to the β carbon of the triazoline side chain and fragmentation of the tertiary amino group promoted by coordination of the latter to the Lewis acid. The structure of a triazole product is confirmed by X-ray crystallography.     

Computer simulations of enantioselective ester hydrolyses catalyzed by Pseudomonas cepacia lipase

On the basis of the X-ray crystal structure of the lipase from Pseudomonas cepacia (PcL)-an enzyme representative for a whole family of Pseudomonas lipases (lipase PS, SAM-2, AK 10, and others with a high degree of homology with PcL)-a computational study was performed to rationalize both the enantioselectivity and substrate specificity (tolerance) displayed by this lipase in the enantioselective hydrolysis of racemic esters 1a-12a from various secondary aromatic alcohols. The major goal of this project was the development of a binding model for PcL which is able to rationalize the experimental findings to predict "a priori the enantioselective behavior of PcL toward a wider range of substrates. A two-step modeling procedure, namely, docking experiments followed by construction of tetrahedral intermediates, was used for the simulation of the involved enzyme-substrate recognition/hydrolysis processes. The study of the recognition process (docking experiments) led to unambiguous identification of the binding geometry for the two enantiomeric series of substrates, but did not suggest a definitive interpretation of the behavior of PcL. Taking into consideration the stereoelectronic requirements of the enzymatic hydrolysis reaction, both the enantioselectivity and tolerance of the enzyme were then explained through the study of the tetrahedral intermediates, in turn constructed from the calculated docking geometries of 1a-12a.     

Synthesis of fused purinoquinazolines. Three new heterocyclic ring systems

The Ullmann reaction of 8-aminotheophylline or 8-aminocaffeine with 2-chlorobenzoic acid and of 8-bromotheophylline with ethyl-2-aminobenzoate afforded derivatives of three new heterocyclic systems: purino[7,8-α]quinazoline-5,9,11(6H,8H,10H)-trione, purino[8,9-b]quinazoline-2,4,11(1H,3H,5H)-trione and purino[8,7-b]quinazoline-2,4,6(1H,3H,11H)-trione, respectively.     

Lines of curvature near umbilical points on surfaces immersed in R4

LetM be a compact orientable surface,I:M R⁴ an immersion of classC ^r and a normal unitary smooth vector field. We prove that in the space of pairs (I, ) the family of pairs all whose umbilical points are Darbouxian is generic.