Effective bounds for very ample line bundles

Let be an ample line bundle on a non singular projective -fold . It is first shown that is very ample for . The proof develops an original idea of Y.T. Siu and is based on a combination of the Riemann-Roch theorem together with an improved Noetherian induction technique for the Nadel multiplier ideal sheaves. In the second part, an effective version of the big Matsusaka theorem is obtained, refining an earlier version of Y.T. Siu: there is an explicit polynomial bound of degree in the arguments, such that is very ample for . The refinement is obtained through a new sharp upper bound for the dualizing sheaves of algebraic varieties embedded in projective space. Oblatum 30-I-1995 & 18-V-1995     

Stochastic Lyapunov method

This paper is devoted to stability properties of solutions to stochastic differential equations obtained by a stochastic Lyapunov method.     

A two parameter mixed interior-exterior penalty algorithm

In this paper, we analyze the mixed penalty methods introduced in the classic book of Fiacco and McCormick usingtwo distinct penalty parametersr, t. The two penalty coefficients induce a two-parameter differentiable trajectory. We analyze the numerical behaviour of an extrapolation strategy that follows the path of the two-parameter trajectory. We show also how to remove the ill-conditioning by suitable transformations of the equations. In the resulting theory, we show that function values as well as distances to the optimum are both governed by the same behaviour as interior methods (two-step superlinearly convergent, with limiting exponent 4/3).Research partially supported by NSERC grant OGP0036512.Research partially supported by NSERC grant OGP0005491.     

How to deal with potentially huge dimensional state space: The meta-dynamics approach—application to a model of the co-evolution of bacterio-phage populations

In many problems coming from the “complexity sciences”, the presence of high-dimensional state spaces and non-linear equations renders traditional mathematical objects useless. To deal with these issues, several approaches have recently been studied, most of them presenting the particularity of splitting the dynamical events in two categories; an upper level in which the events describe how the structure of the system changes (the meta-dynamics) and a lower level with the events describing the evolution of the elements in the structure (the dynamics). The state space is then not defined in extenso but unfolds or contracts during the evolution of the system. In term of simulation, this view allows us to deal with only a small part of the state space at each step avoiding the time and memory limitations.     

On the Brownian motion of a massive sphere suspended in a hard-sphere fluid. I. Multiple-time-scale analysis and microscopic expression for the friction coefficient

The Fokker-Planck equation governing the evolution of the distribution function of a massive Brownian hard sphere suspended in a fluid of much lighter spheres is derived from the exact hierarchy of kinetic equations for the total system via a multiple-time-scale analysis akin to a uniform expansion in powers of the square root of the mass ratio. The derivation leads to an exact expression for the friction coefficient which naturally splits into an Enskog contribution and a dynamical correction. The latter, which accounts for correlated collisions events, reduces to the integral of a time-displaced correlation function of dynamical variables linked to the collisional transfer of momentum between the infinitively heavy (i.e., immobile) Brownian sphere and the fluid particles.     

Impulse capture basins of sets under impulse control systems

Given a target contained in a constrained set and an impulse control system governing the evolutions of runs or executions, that are hybrids of continuous and discrete evolutions, this paper studies and provides several characterizations of the capture basin of the target viable in the constrained set. It is the subset of initial runs from which start at least one run viable in the constrained set until it reaches the target in finite time. It also provides algorithms and regulation rules governing the runs that reach the targets while obeying state constraints.     

H2-broadening coefficients in the ν3 band of CH3D at low temperatures

Using a diode-laser spectrometer, we have measured H₂-broadening coefficients of CH₃D at low temperatures (153.5, 183.5, and 223.5 K) for four lines in the ν₃ band. The collisional widths are obtained by fitting each absorption line with three lineshape models: the Voigt, Rautian, and Galatry profiles. The broadening coefficients are also calculated on the basis of a semiclassical model of interacting linear molecules by considering an atom-atom Lennard-Jones potential in addition to electrostatic contributions. By comparing the broadening coefficients at room and low temperatures the temperature dependence of these broadenings has been determined both experimentally and theoretically.     

Synthesis of modified Weinreb amides: N-tert-butoxy-N-methylamides as effective acylating agents

An efficient preparation of N-methyl-O-tert-butylhydroxylamine hydrochloride has been settled, which allowed the synthesis of modified Weinreb amides. Nucleophilic addition of organolithium and Grignard reagents on these N-tert-butoxy-N-methylamides afforded efficiently the corresponding ketones and reduction with DIBAL furnished the corresponding aldehydes in good yields up to 97%.     

Selectivity among two lectins: probing the effect of topology, multivalency and flexibility of "clicked" multivalent glycoclusters

The design of multivalent glycoconjugates has been developed over the past decades to obtain high-affinity ligands for lectin receptors. While multivalency frequently increases the affinity of a ligand for its lectin through the so-called "glycoside cluster effect", the binding profiles towards different lectins have been much less investigated. We have designed a series of multivalent galactosylated glycoconjugates and studied their binding properties towards two lectins, from plant and bacterial origins, to determine their potential selectivity. The synthesis was achieved through copper(I)-catalysed azide-alkyne cycloaddition (CuAAC) under microwave activation between propargylated multivalent scaffolds and an azido-functionalised carbohydrate derivative. The interactions of two galactose-binding lectins from Pseudomonas aeruginosa (PA-IL) and Erythrina cristagalli (ECA) with the synthesized glycoclusters were studied by hemagglutination inhibition assays (HIA), surface plasmon resonance (SPR) and isothermal titration microcalorimetry (ITC). The results obtained illustrate the influence of the scaffold's geometry on the affinity towards the lectin and also on the relative potency in comparison with a monovalent galactoside reference probe.