Radiation effect studies in single crystal of Trifluoroacetyl-α-Aminoisobutyric acid

In this study, electron paramagnetic resonance of γ-irradiated single crystals of N-Trifluoroacetyl-α-amino isobutyric acid (F₃Ac-Aib-OH) was investigated at room temperature and analyzed for different orientations of the crystal in the magnetic field. The paramagnetic species in N-Trifluoroacetyl-α-aminoisobutyric acid was attributed to the ?F₂-R radical (R= CONHC(CH₃)COOH). Hyperfine coupling constants and g value were also determined. In addition, the single crystal of F₃Ac-Aib-OH was UV-irradiated and paramagnetic species formed was studied at room temperature. The effects of gamma irradiation on fluoroamino acid and stability were discussed.     

Toward reactant encapsulation for substrate-selectivity

A synthetic tris-(bis-(aminomethyl)pyridine) receptor was prepared in excellent yields via reversible imine condensation strategy. Catalytic activity in Henry reactions of the corresponding copper(II) complex was studied. Capitalizing on previous works by Anslyn with related receptors, the dramatic increase in basicity induced by this type of complex on diketo-derivatives was used to perform a nucleophilic addition of a deprotonated substrate onto an electrophile within the cavity. Hence, a Lewis acid stabilized nitronate was reacted with various aldehydes. A notable preference for small reactants easily accommodated in the cavity over encumbered ones was observed, thus representing an example of substrate-selectivity.     

A value on ′AN

We prove here the existence of a value (of norm 1) on the spaces N A and even A N, the closure in the variation distance of the linear space spanned by all games f, where is a non-atomic, non-negative finitely additive measure of mass 1 and f a real-valued function on [0,1] which satisfies a much weaker continuity at zero and one. 1991 Mathematics Subject Classification. 90A08, 90A07This research was in part supported by the Belgian Programme on Interuniversity Poles of Attraction, initiated by the Prime Ministers Science Policy Office.     

On Non-Continuous Dirichlet Processes

We introduce here some Itô calculus for non-continuous Dirichlet processes. Such calculus extends what was known for continuous Dirichlet processes or for semimartingales. In particular we prove that non-continuous Dirichlet processes are stable under C ¹ transformation.     

Characterization of Trimmed NURBS Surface Boundaries Using Topological Criteria

This paper presents an approach based on topology for the determination of characteristics and properties of curves used in the trimming of NURBS surfaces. Through discrete subdivision and topological criteria, a method is presented to determine characteristics of the boundary; such as whether the set of trimming curves forms a set of closed loops, whether trimming curves contain singularities or self intersections, and whether the boundary is simply connected. A surface mesh partitionning the parameter space is used, formed of isoparametric lines in both parametric directions. Topological properties of the cells of this mesh and their intersections with the trimming curves allow to localize the boundary. Topological treatment of this localization allows to define the interior and exterior of the face, and to refine the boundary localization. Singularities and self intersections of the boundary as well as voids in the face are investigated through the study of topological properties of neighbors. As an application, an algorithm for point localization is presented that very rapidly allows to determine whether a given point in parameter space lies inside, on the boundary or outside of the trimmed surface.     

Sur les équations de Lane–Emden avec opérateurs non linéaires

In this Note we consider nonnegative solutions for the nonlinear equation

$\text{M}{}^{\mathrm{+}}{}_{\mathrm{\lambda ,\Lambda }}\text{D}{}^2\text{u}\text{+|x|}{}^{\mathrm{\alpha }}\text{u}{}^{\mathrm{p}}\text{=0}$

in $\text{R}{}^{\mathrm{N}}$, where $\text{M}{}^{\mathrm{+}}{}_{\mathrm{\lambda ,\Lambda }}\text{(D}{}^2\text{u)}$ is the so called Pucci operator

$\text{M}{}^{\mathrm{+}}{}_{\mathrm{\lambda ,\Lambda }}\text{(M)=λ}\text{∑}\text{e}{}_{\mathrm{i}}\text{<0}\text{e}{}_{\mathrm{i}}\text{+Λ}\text{∑}\text{e}{}_{\mathrm{i}}\text{>0}\text{e}{}_{\mathrm{i}}\text{,}$

and the e_i are the eigenvalues of M et Λ?λ>0. We prove that if u satisfies the decreasing estimate

$\text{lim}\text{|x|→+∞}\text{|x|}{}^{\mathrm{\beta ?1}}\text{u(x)=0}$

for some β satisfying (β?1)(p?1)>2+α then u is radial. In a second time we prove that if $\text{p<}\text{N+2α+2}\text{N?2}$ and u is a nonnegative radial solution of (1), u(x)=g(r), such that g″ changes sign at most once, then u is zero. To cite this article: I. Birindelli, F. Demengel, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Analysis of a Poisson system with boundary conditions

We consider a class of problems originating from a Raman laser amplification model, for which the equations can be written as a Poisson system with boundary conditions. Once reformulated, this system becomes an integro-differential equation that we study here in some detail. In particular, we show the existence of a smooth solution under general assumptions, and prove its uniqueness for boundary values that are not too far apart. Eventually, we completely solve the question of uniqueness for systems of dimensions one and two. To cite this article: F. Castella et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Des équations de Dirac et de Schrödinger pour la transformation de Fourier

Dyson has associated with the Fredholm determinants of the even (resp. odd) Dirichlet kernels a Schrödinger equation on the half-axis and has used, in tandem, the Gel'fand–Levitan and Marchenko methods of inverse scattering theory to study the asymptotics of these determinants. We have proposed following our unearthing of the conductor operator to seek to realize the Fourier transform itself as a scattering, and we obtain here to this end two Dirac systems on the entire real axis which are intrinsically associated, respectively, to the cosine and to the sine transforms. To cite this article: J.-F. Burnol, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Curvature Conditions for Immersions of Submanifolds and Applications

Some curvature conditions about the geodesics emanating from a submanifold are obtained. These conditions are used to to study the topological and geometric properties of the ambient spaces which admit some minimal submanifolds.