Construction of nonanuclear supramolecular structures from simple modular units

A porphyrazine based supramolecule with a nonanuclear structure has been prepared by the ready coordination of pyridine donor sites in octakis(4-pyridoxyethylthio)porphyrazinatomagnesium with vanadyl bis(acetylacetonate) and characterized by EPR spectroscopy.     

L'intégration graphique des équations différentielles ordinaires

In the period which precedes the appearance of computers, needs in calculation of the scientists and engineers led to an important development of graphic methods of integration. To contribute to the study of this little known phenomenon, the article presents techniques and instruments used for the graphic integration of ordinary differential equations, and looks for their historic origins by going back to the beginning of calculus: processes of geometric calculation by the polygonal method or the method of radius of curvature, use of tractional motion for the conception of integraphs, reduction to graphic quadratures in finite or infinite number.     

Dihydropyridine-based MCRs. New reaction pathways in the interaction with ethyl glyoxalate and non-aromatic amines

The Lewis acid-catalyzed interaction of dihydropyridines with ethyl glyoxalate and primary aliphatic amines yields, depending on the reaction conditions, bicyclic aminals or rearranged tetrahydropyridines in one-pot multicomponent reactions.     

Functional Quantization and Small Ball Probabilities for Gaussian Processes

Quantization consists in studying the L ^r -error induced by the approximation of a random vector X by a vector (quantized version) taking a finite number n of values. We investigate this problem for Gaussian random vectors in an infinite dimensional Banach space and in particular, for Gaussian processes. A precise link proved by Fehringer⁽⁴⁾ and Dereich et al. ⁽³⁾ relates lower and upper bounds for small ball probabilities with upper and lower bounds for the quantization error, respectively. We establish a complete relationship by showing that the same holds for the direction from the quantization error to small ball probabilities. This allows us to compute the exact rate of convergence to zero of the minimal L ^r -quantization error from logarithmic small ball asymptotics and vice versa.     

Asymptotic behaviour of the least squares estimator of the mean of AR(1) models

The aim of the paper is to investigate the limit behaviour of the least squares estimator of the shift parameter of nearly unstable, nearly stable, and nearly explosive AR(1) models. Both zero start and stationary cases are treated. Connection with the maximum likelihood estimator of the shift parameter of continuous time AR(1) processes is also discussed.     

Contractibility of Efficient Frontier of Simply Shaded Sets

In finite dimensional Euclidean space, we prove the contractibility of the efficient frontier of simply shaded sets. This work extends the result of Peleg [7], which confirms the contractibility of the efficient frontier in the convex case.     

Fracture strength of class II slot cavities restored with polymerizable restorative materials

This study compared the fracture strength of Class II slot cavities restored with polymerizable restorative materials. Sixty, caries-free, posterior teeth were divided into five groups of 12 teeth. The Class II slot cavities were prepared. The teeth were restored with two packable composites (Filtek P60, Surefil), a microhybrid composite (Filtek Z250)and two ormocer (Definite, Admira). The restorations were then subjected to fracture resistance tests. The marginal ridges of the restorations were loaded at an angle of 13.5° to the long axis of the tooth in an Universal Testing Machine until failure. Analysis of mean forces indicated that, Filtek P60, Surefil and Filtek Z250 exhibited better performance than Definite and Admira. The tested resin composites differed in their mechanical properties. This study suggested that fracture behavior were highly influenced by the filler system. Overall, Filtek P60, Surefil, Filtek Z250, demonstrated good fracture resistance. Copyright © 2003 John Wiley & Sons, Ltd.     

Quasi-free divisors and duality

We prove a duality theorem for some logarithmic $\text{D}$-modules associated with a class of divisors. We also give some results for the locally quasi-homogeneous case. To cite this article: F.J. Castro-Jiménez, J.M. Ucha-Enr??quez, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

The interlace polynomial of a graph

Motivated by circle graphs, and the enumeration of Euler circuits, we define a one-variable “interlace polynomial” for any graph. The polynomial satisfies a beautiful and unexpected reduction relation, quite different from the cut and fuse reduction characterizing the Tutte polynomial.It emerges that the interlace graph polynomial may be viewed as a special case of the Martin polynomial of an isotropic system, which underlies its connections with the circuit partition polynomial and the Kauffman brackets of a link diagram. The graph polynomial, in addition to being perhaps more broadly accessible than the Martin polynomial for isotropic systems, also has a two-variable generalization that is unknown for the Martin polynomial. We consider extremal properties of the interlace polynomial, its values for various special graphs, and evaluations which relate to basic graph properties such as the component and independence numbers.