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.     

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.     

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.     

(+)- and (-)-2-aminocyclobutane-1-carboxylic acids and their incorporation into highly rigid beta-peptides: stereoselective synthesis and a structural study

[Chemical reaction: See text] Several derivatives of (+)- and (-)-2-aminocyclobutane-1-carboxylic acid, 1, have been prepared through enantiodivergent synthetic sequences. The stereoselective synthesis of free amino acid (+)-1 has been achieved, and this product has been fully characterized for the first time. Stereocontrolled alternative synthetic methodologies have been developed for the preparation of bis(cyclobutane) beta-dipeptides in high yields. Among them, enantio and diastereomers have been synthesized. beta,beta- and beta,delta-Dimers resulting from the coupling of a cyclobutane residue and a linear amino acid have also been prepared. The ability of the cyclobutane ring as a structure-promoting unit both in the monomers and in the dimers has been manifested. The NMR structural study and DFT theoretical calculations evidence the formation of strong intramolecular hydrogen bonds giving rise to cis-fused [4.2.0]octane structural units that confer high rigidity on these molecules both in solution and in the gas phase. The contribution of a cis-trans conformational equilibrium derived from the rotation around the carbamate N-C(O) bond has also been observed, the trans form being the major conformer. In the solid state, this equilibrium does not exist, and moreover, intermolecular hydrogen bonds are present.     

DFT description of the magnetic properties and electron localization in dinuclear di-mu-oxo-bridged manganese complexes

Density functional theory (DFT) was applied to describe the magnetic and electron-transfer properties of dinuclear systems containing the [MnO2Mn]n+ core, with n=0,1,2,3,4. The calculation of the potential energy surfaces (PESs) of the mixed-valence species (n=1,3) allowed the classification of these systems according to the extent of valence localization as Class II compounds, in the Robin-Day classification scheme. The fundamental frequencies corresponding to the asymmetric breathing vibration were also computed.     

Structural changes in the monomeric despentapeptide (B30-B26) insulin crystal

Insulin modified by the removal of its 5 B chain C terminal residues is monomeric but remains substantially potent. The crystal structures of the beef and insulin (dpi) with two molecules in the asymmetric unit has been determined by x-ray analysis. The 3-dimensional structure ofdpi proves to be generally similar to that of native molecule in 2Zn insulin. More detailed comparison reveals that the slight differences in the two independent molecules of beefdpi are distributed uniformly throughout the structure in contrast to insulin in 2Zn insulin, where the structural changes are concentrated in specific regions. The loss of symmetry in thedpi crystal appears to be the inability of the A9 serine to pack effectively in the C2 cell. The efficient packing of the sheepdpi molecule whose crystal structure has also been determined and where A9 is glycine supports this conclusion.     

Synthesis of novel 1,4‐dihydropyrido[3′,2′:5,6]thiopyrano[4,3‐c]‐pyrazoles and 5H‐pyrido[3′,2′:5,6]thiopyrano[4,3‐d]pyrimidines as potential antiproliferative agents

The synthesis of new planar derivatives characterized by the presence of a pyridothiopyranopyrazole or pyridothiopyranopyrimidine nucleus, carrying a substituted aryl group, is reported. The novel 1,4‐dihydropyrido[3′,2′:5,6]thiopyrano[4,3‐c]pyrazole derivatives were obtained by condensation of 2,3‐dihydro‐3‐hydroxymethylenethiopyrano[2,3‐b]pyridin‐4(4H)‐ones with appropriate hydrazines. The preparation of 2‐substituted pyrido[3′,2′:5,6]thiopyrano[4,3‐d]pyrimidines was accomplished from the intermediate 2,3‐dihy‐dro‐3‐dimethylaminomethylenethiopyrano[2,3‐b]pyridin‐4(4H)‐ones by reaction with the appropriate binucleophile amidines. The antiproliferative activity of some new products was tested by an in vitro assay on human tumour cell lines (HL‐60 and HeLa), but none of them showed any significant effects in the tests performed. Accordingly, linear flow dichroism measurements indicated their inability to form a molecular complex with DNA.     

Relative stability of the2 A 1g and2 E g states of the C2H 6 + ion

Anab initio study of the relative stability for the states² A _1g and² E _g of C₂H ₆ ⁺ has been carried out. The results of the Open Shell Restricted Hartree-Fock calculations lead to assign the² A _{1 g} as the ground state of the molecule in agreement with previous SCF calculations.The correlation energy associated to both states has been calculated within the correlation hole model and the results, contrary to those obtained from Configuration Interaction calculations, do not alter qualitatively the conclusions from SCF.