On the computational efficiency index and some iterative methods for solving systems of nonlinear equations

In this paper two new iterative methods are built up and analyzed. A generalization of the efficiency index used in the scalar case to several variables in iterative methods for solving systems of nonlinear equations is revisited. Analytic proofs of the local order of convergence based on developments of multilineal functions and numerical concepts that will be used to illustrate the analytic results are given. An approximation of the computational order of convergence is computed independently of the knowledge of the root and the necessary time to get one correct decimal is studied in our examples.     

Large Deviations for Stochastic Volterra Equations in the Plane

We prove a Large Deviation Principle for the family of solutions of Volterra equations in the plane obtained by perturbation of the driving white noise. One of the motivations for the study of such class of equations is provided by non-linear hyperbolic stochastic partial differential equations appearing in the construction of some path-valued processes on manifolds. The proof uses the method developped by Azencott for diffusion processes. The main ingredients are exponential inequalities for different classes of two-parameter stochastic integrals; these integrals are related to the representation of the stochastic term in the differential equation as a representable semimatringale.     

Etude dans la série des pyrrolidinones. IV. Formation de quelques dérivés de l'acide L méthylène bis N-(oxo-5 pyrrolidine carboxylique-2)

Starting from the readily available 5-oxo-2-carboxypyrrolidine, methylene-bis-(N-5-oxo-2-carboxypyrrolidine) was prepared and transformed into a diamine, then into two isomeric diols, which cyclised into one ether. The meso configuration has been assigned for this ether. The reduction of both diols and ether was complete and gave rise to methylene-bis-N-pyrrolidine.     

Kähler tubes of constant radial holomorphic sectional curvature

We determine (up to holomorphic isometries) the family of Kähler tubes, around totally geodesic complex submanifolds, of constant radial holomorphic sectional curvature when the centreP of the tube is either simply connected or a complex hypersurface withH ¹ (P, R)=0. In the last case, these tubes have the topology of tubular neighbourhoods of the zero section of the complex lines bundles over symplectic manifolds (when they are Kähler) of the Kostant-Souriau prequantization.     

The Reactivity Of singlet carbenes. An ab initio study

The energy barriers for the addition to ethylene of a series of carbenes have been calculated at an ab initio level. using the STO-3G and 3-21G basis sets. It is shown that the usual extrapolation of experiment results, which predicts that the reactivity of carbenes decreases when increasing its nucleophilic character, is not valid.     

Gaussian mean curvature flow

In the Euclidean Space \mathbb Rⁿ⁺¹{\mathbb {R}^{n+1}} with a density e^{e\frac12 n m2 |x|2}, (e = ±1){e^{\varepsilon \frac12 n \mu^2 |x|^2},} {(\varepsilon =\pm1}), we consider the flow of a hypersurface driven by its mean curvature associated to this density. We give a detailed account of the evolution of a convex hypersurface under this flow. In particular, when e = -1{ \varepsilon=-1} (Gaussian density), the hypersurface can expand to infinity or contract to a convex hypersurface (not necessarily a sphere) depending on the relation between the bound of its principal curvatures and μ.     

On the Convolution of the Generalized Finite Legendre Transform

The translation operator and the convolution for the finite Legendre transformation are investigated in the space ??(?1,1) of testing-functions and its dual through an approach that emphasizes the close similarity existing between this transform and the infinite Mehler - Fock transformation. The theory developed is used in solving some distributional boundary-value problems.