The <Emphasis Type="Italic">su</Emphasis>(1,1) Dynamical Algebra for the Generalized MICZ-Kepler Problem from the Schrödinger Factorization

We apply the Schrödinger factorization to construct the generators of the dynamical algebra su(1,1) for the radial equation of the generalized MICZ-Kepler problem.     

Pair creation in QED-strong pulsed laser fields interacting with electron beams

QED effects are known to occur in a strong laser pulse interaction with a counterpropagating electron beam, among these effects being electron-positron pair creation. We discuss the range of laser pulse intensities of J≥5×10(22) W/cm2 combined with electron beam energies of tens of GeV. In this regime multiple pairs may be generated from a single beam electron, some of the newborn particles being capable of further pair production. Radiation backreaction prevents avalanche development and limits pair creation. The system of integro-differential kinetic equations for electrons, positrons and γ photons is derived and solved numerically.     

Compositional and structural medium energy ion scattering study of the temperature mediated diffusion determination at the Co/V interface in Co/V/MgO(100)

The impact of annealing at 300 °C on the elemental composition and the atomic structure of the Co/V interface in the 2.5 Å Co/70 Å V/MgO (100) system has been investigated by medium energy ion scattering (MEIS) using 100 keV He⁺ ions. By combining the experimental MEIS results with simulations we show that, while the Co/V interface is abrupt for the system kept at room temperature, annealing at 300 °C induces a strong interdiffusion leading to a Co_0.5V_0.5 surface bcc alloy with a high degree of disorder. Additionally, the MEIS data suggest that the surface of the annealed system is slightly rumpled by ~ 0.2 Å.     

Fractional quantum conductance values in Au nanoelectrodes due to hydrogen adsorption

Hydrogen adsorption in gold nanocontact electrodes in electrochemical solution is experimentally discerned. This is performed with gold nanocontact conductance histograms in an electrochemical environment in which both the electrochemical potential and the electrolyte type are varied. Different salts, acids, and hydrogen peroxide electrolytes are studied. Salts and acids exhibit at negative electrochemical potentials different fractional quantum conductance histograms peaks associated to extra stable structures due to H adsorption while these peaks do not appear for H₂O₂ where electron transfer between solution and electrodes occurs without hydrogen formation or hydrogen adsorption on the gold electrode.     

A general limit lifting theorem for 2-dimensional monad theory

We give a definition of weak morphism of T-algebras, for a 2-monad T, with respect to an arbitrary family Ω of 2-cells of the base 2-category. By considering particular choices of Ω, we recover the concepts of lax, pseudo and strict morphisms of T-algebras. We give a general notion of weak limit, and define what it means for such a limit to be compatible with another family of 2-cells. These concepts allow us to prove a limit lifting theorem which unifies and generalizes three different previously known results of 2-dimensional monad theory. Explicitly, by considering the three choices of Ω above our theorem has as corollaries the lifting of oplax (resp. σ, which generalizes lax and pseudo, resp. strict) limits to the 2-categories of lax (resp. pseudo, resp. strict) morphisms of T-algebras.     

Real Interpolation of Compact Bilinear Operators

We establish an analog for bilinear operators of the compactness interpolation result for bounded linear operators proved by Cwikel and Cobos, Kühn and Schonbek. We work with the assumption that \(T:(A_0+A_1) \times (B_0+B_1) \longrightarrow E_0+E_1\) is bounded, but we also study the case when this does not hold. Applications are given to compactness of convolution operators and compactness of commutators of bilinear Calderón–Zygmund operators.     

On the Weak Order Ideal Associated to Linear Codes

In this work we study a weak order ideal associated with the coset leaders of a non-binary linear code. This set allows the incrementally computation of the coset leaders and the definitions of the set of leader codewords. This set of codewords has some nice properties related to the monotonicity of the weight compatible order on the generalized support of a vector in \(\mathbb {F}_q^n\) which allows to describe a test set, a trial set and the set of zero neighbours of a linear code in terms of the leader codewords.     

Monotone and Accretive Vector Fields on Riemannian Manifolds

The relationship between monotonicity and accretivity on Riemannian manifolds is studied in this paper and both concepts are proved to be equivalent in Hadamard manifolds. As a consequence an iterative method is obtained for approximating singularities of Lipschitz continuous, strongly monotone mappings. We also establish the equivalence between the strong convexity of functions and the strong monotonicity of its subdifferentials on Riemannian manifolds. These results are then applied to solve the minimization of convex functions on Riemannian manifolds.     

Second-order negative-curvature methods for box-constrained and general constrained optimization

A Nonlinear Programming algorithm that converges to second-order stationary points is introduced in this paper. The main tool is a second-order negative-curvature method for box-constrained minimization of a certain class of functions that do not possess continuous second derivatives. This method is used to define an Augmented Lagrangian algorithm of PHR (Powell-Hestenes-Rockafellar) type. Convergence proofs under weak constraint qualifications are given. Numerical examples showing that the new method converges to second-order stationary points in situations in which first-order methods fail are exhibited.