The Brjuno Functions and Their Regularity Properties

We show that various possible versions of the Brjuno function, based on different kinds of continued fraction developments, are all equivalent and we study their regularity (L ^p, BMO and H?lder) properties, through a systematic analysis of the functional equation which they fulfill. Received: 21 March 1995 / Accepted: 8 August 1996     

The cohomological equation for Roth-type interval exchange maps

We exhibit an explicit class of minimal interval exchange maps (i.e.m.'s) for which the cohomological equation

has a bounded solution provided that the datum belongs to a finite codimension subspace of the space of functions having on each interval a derivative of bounded variation. The proof is purely dynamical and is based on a renormalization argument and on Gottshalk-Hedlund's theorem. If the datum is more regular the loss of differentiability in solving the cohomological equation will be the same.

The class of interval exchange maps is characterized in terms of a diophantine condition of Roth type imposed to an acceleration of the Rauzy-Veech-Zorich continued fraction expansion associated to . More precisely one must impose a growth rate condition for the matrices appearing in the continued fraction algorithm together with a spectral gap condition (which guarantees unique ergodicity) and a coherence condition. We also prove that the set of Roth-type interval exchange maps has full measure.

In the appendices we construct concrete examples of Roth-type i.e.m.'s and we show how the growth rate condition alone does not imply unique ergodicity.

     

Binary,ternary and quaternary complexes invloved in the systems pyridoxamine-glycine-imidazole with some bivalent metal ions

Equilibrium-based computer models using MINIQUAD-75 program were utilized to determine the stoichiometry and formation constants involved in the systems pyridoxamine(Pm)-glycine (Gly)-imidazole (lmd) with CO(II), Ni(II), Cu(II), Zn(II) and Cd(II) metal ions. The data were obtained from potentiometric pH titration of the various binary and ternary quaternary systems under physiological-like conditions (0.15 M NaNO₃-37°C). Various composition ratios of metal and ligands were used. The ligand concentrations did not exceed 4 times the concentration of metal ion in the binary systems and 4 times of the metal ions in ternary systems. In case of the quaternary systems only imidazole concentrations were two or four times the concentrations of metal ions keeping those of other ligands equal to that of metal ions. The stability constants of the quaternary species are discussed in terms of binary and ternary constants as are the effect of ring size on the stability of mixed ligand species. In addition, electrostatic as well as statistical effects also are mentioned and the biological implications of these model equilibria are described.     

Autour de la condition d'engel dans les algèbres de bernstein

We know that, in general, an algebra satisfying an Engel's condition is a nilalgebra. But an Engel's condition don't implies necessarily the nilpotency of the algebra. In this paper we show that every Bernstein algebra satisfying the second or the third Engel's condition is genetic, that is, the kernel of his weight fonction is nilpotent. This is also the case for a Bernstein algebra satisfying the second weak Engel's condition.

On sait que, en général, toute algèbre vérifiant une condition d'Engel est une nilalgèbre. Cependant, une condition d'Engel n'entraîne pas nécessairement la nilpotence de l'algèbre. Nous montrons, dans ce papier, que taute algèbre de Bernstein vérifiant la deuxième ou la troisième condition d'Engel est génétique, c'est-à-dire, le noyau de sa pondération est nilpotent. C'est aussi le cas pour la deuxième condition faible d'Engel.     

Some variants of the classical Aubin–Lions Lemma

This paper explores two generalizations of the classical Aubin–Lions Lemma. First, we give a sufficient condition to commute weak limit and multiplication of two functions. We deduce from this criteria a compactness theorem for degenerate parabolic equations. Second, we state and prove a compactness theorem for noncylindrical domains, including the case of dual estimates involving only divergence-free test functions.     

Feasibility on a piezoresistive tactile normal force sensor array

The plasmon resonance of periodic and random arrays of Au-nanodiscs and nano-squares was investigated experimentally and numerically. By randomization, plasmon resonance spectra become broadened, however, the electro-magnetic field enhancement is augmented by a factor of 10–10 $^2$ times at some specific wavelength as shown by the finite-element time-domain calculations. The spatial localization takes place at a fewer hot-spots. The randomized structures are promising for the applications in opto-electronics, sensing and light harvesting.     

Palladium-catalysed direct arylation of a tris-cyclometallated Ir(III) complex bearing 2,2'-thienylpyridine ligands: a powerful tool for the tuning of luminescence properties

Palladium-catalysed direct 5-arylation of metallated thiophenes of fac-Ir(N^C(3')-thpy)(3) with aryl bromides via C-H bond functionalisation allows the synthesis of a variety of new Ir complexes in only one step (thpyH = 2,2'-thienylpyridine). The method offers simple modification of the nature of the ligand and hence of the photophysical properties of such complexes.     

Geodesic diameter of sets defined by few quadratic equations and inequalities

We prove a bound for the geodesic diameter of a subset of the unit ball in ${\mathbb{R}^n}$ described by a fixed number of quadratic equations and inequalities, which is polynomial in n, whereas the known bound for general degree is exponential in n. Our proof uses methods borrowed from D’Acunto and Kurdyka (to deal with the geodesic diameter) and from Barvinok (to take advantage of the quadratic nature).