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.     

The inelastic hard dimer gas: a nonspherical model for granular matter

We study a two-dimensional gas of inelastic smooth hard dimers. Since the collisions between dimers are dissipative, being characterized by a coefficient of restitution alpha<1, and no external driving force is present, the energy of the system decreases in time and no stationary state is achieved. However, the resulting nonequilibrium state of the system displays several interesting properties in close analogy with systems of inelastic hard spheres, whose relaxational dynamics has been thoroughly explored. We generalize to inelastic systems a recently method introduced [G. Ciccotti and G. Kalibaeva, J. Stat. Phys. 115, 701 (2004)] to study the dynamics of rigid elastic bodies made up of different spheres held together by rigid bonds. Each dimer consists of two hard disks of diameter d, whose centers are separated by a fixed distance a. By describing the rigid bonds by means of holonomic constraints and deriving the appropriate collision rules between dimers, we reduce the dynamics to a set of equations which can be solved by means of event-driven simulation. After deriving the algorithm we study the decay of the total kinetic energy, and of the ratio between the rotational and the translational kinetic energy of inelastic dimers. We show numerically that the celebrated Haff's homogeneous cooling law t(-2), describing how the kinetic energy of an inelastic hard-sphere system with a constant coefficient of restitution decreases in time, holds even in the case of these nonspherical particles. We fully characterize this homogeneous decay process in terms of appropriate decay constants and confirm numerically the scaling behavior of the velocity distributions.     

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.     

On the finiteness of optimal partitions

We prove that, under appropriate assumptions on the domain Ω and on the datumg, any optimal partition of Ω (minimizing the sum of the total perimeter and the approximation term is finite. Finiteness result for the problem of image segmentation in Artificial Vision can be deduced.

---

Sunto Dimostriamo che, in opportune ipotesi sul dominio Ω e sul datog, ogni partizione ottimale di Ω (minimizzante il perimetro totale in Ω più il termine di approssimazione è finita. Se ne deducono risultati di finitezza per il problema della segmentazione di immagini in Visione Artificiale.

     

(+)- 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.     

Reactions of 1,4-diaza-3-methylbutadien-2-ylpalladium(II) derivatives with chloro-bridged rhodium(I) complexes

The reactions of the organometallic 1,4-diazabutadienes, RN=C(R′)C(Me)=NR″ [R = R″ = p-C₆H₄OMe, R′ = trans-PdCl(PPh₃)₂ (DAB); R = p-C₆H₄OMe, R″ = Me, R′ = trans-PdCl(PPh₃)₂ (DAB^I; R = R″ = p-C₆H₄OMe, R′ = Pd(dmtc)-(PPh₃), dmtc = dimethyldithiocarbamate (DAB^II); R = R″ = p-C₆H₄OMe, R′ = PdCl(diphos), diphos = 1,2-bis(diphenylphosphino)ethane (DAB^III)] with [RhCl(COD)]₂ (COD = 1,5-cyclooctadiene, Pd/Rh ratio = $\text{1}\text{2}$) depend on the nature of the ancillary ligands at the Pd atom in group R′. In the reactions with DAB and DAB^I transfer of one PPh₃ ligand from Pd to Rh occurs yielding [RhCl(COD)(PPh₃)] and the new binuclear complexes [Rh(COD) {RN=C(R?)-C(Me)=NR″}], in which the diazabutadiene moiety acts as a chelating bidentate ligand. Exchange of ligands between the two different metallic centers also occurs in the reaction with DAB^II. In this case, the migration of the bidentate dmtc anion yields [Rh(COD)Pdmtc] and [Rh(COD) {RN=C(R?)C(Me)=NR″}]. In contrast, the reaction with DAB^III leads to the ionic product [Rh(COD)- (DAB^III)][RhCl₂(COD)], with no transfer of ligands. The cationic complex [Rh(COD)(DAB^III)]⁺ can be isolated as the perchlorate salt from the same reaction (Pd/Rh ratio = 1/1) in the presence of an excess of NaClO₄. In all the binuclear complexes the coordinated 1,5-cyclooctadiene can be readily displaced by carbon monoxide to give the corresponding dicarbonyl derivatives. The reaction of [RhCl(CO)₂]₂ with DAB and/or DAB^I yields trinuclear complexes of the type [RhCl(CO)₂]₂(DAB), in which the diazabutadiene group acts as a bridging bidentate ligand. Some reactions of the organic diazabutadiene RN=C(Me)C(Me)=NR (R = p-C₆H₄OMe) are also reported for comparison.