Asymptotic behavior of iterative M-estimartors for location

In this paper, we study the Huber M-estimator for location when they are computed by a class of numerical iterative procedures. This class includes the usual method of Newton-Raphson, iterated weighted least squares and iterated winsorization. We show that under mild conditions, the numerical iterative procedures converge and the resulting estimators are consistent and asymptotically normal.     

Finiteness of the number of solutions of Plateau’s problem for polygonal boundary curves II

In this article, the author proves that a simple closed polygon can bound only finitely many immersed minimal surfaces of disc-type if it meets the following two requirements: firstly it has to bound only minimal surfaces without boundary branch points, and secondly its total curvature, i.e. the sum of the exterior angles at its N + 3 vertices, has to be smaller than 6π.      

Schottky Uniformizations of Genus 3 and 4 Reflecting S4

Schottky uniformizations are provided of every closed Riemannsurface S of genus g {3,4} admitting the symmetric group S₄as group of conformal automorphisms. These Schottky uniformizationsreflect the group S₄ and permit concrete representations ofS₄ to be obtained in the respective symplectic group Sp_g(Z).Their corresponding fixed points, in the Siegel space, giveprincipally polarized Abelian varieties of dimension g. Forg = 3 and for some cases of g = 4 they turn out to be holomorphicallyequivalent to the product of elliptic curves.     

Mechanism for room-temperature single-atom lateral manipulations on semiconductors using dynamic force microscopy

Vacancy-mediated lateral manipulations of intrinsic adatoms of the Si(111)-(7x7) surface at room temperature are reported. The topographic signal during the manipulation combined with force spectroscopy measurements reveals that these manipulations can be ascribed to the so-called pulling mode, and that the Si adatoms were manipulated in the attractive tip-surface interaction regime at the relatively low short-range force value associated to the manipulation set point. First-principles calculations reveal that the presence of the tip induces structural relaxations that weaken the adatom surface bonds and manifests in a considerable local reduction of the natural diffusion barriers to adjacent adsorption positions. Close to the short-range forces measured in the experiments, these barriers are lowered near the limit that enables a thermally activated hopping at room temperature.     

A bonding evolution theory study on the catalytic Noyori hydrogenation reaction

ABSTRACT

The electronic rearrangements involved in Noyori hydrogenation reactions with double bonds (ethene and formaldehyde) are analysed using the bonding evolution theory. The study and analysis of the changes on the electron localisation function topology along a given reaction path reveals fluxes of electron density, allowing to unambiguously identify the main chemical events happening along the chemical reactions. This analysis shows that the first hydrogen transfer (with hydride character) occurs before the transition state (TS), while the second hydrogen transfer (with proton character) takes places after having reached the TS. The lower energy barrier found for formaldehyde over ethene is explained by two reasons. First, the hydride transfer is favoured for the C?=?O bond over C?=?C due to the electrophilic character of the carbon atom. Second, a negatively charged CH₃–X (X?=?CH₂, O) hidden intermediate is formed in the proximities of the TS region. The oxygen atom is able to stabilise this negatively charged species more effectively than the CH₂ group due to its higher electronegativity and the presence of V(O) lone pairs. The obtained analysis explains and rationalises catalyst chemoselectivity (C?=?O vs. C?=?C). Finally, a curly arrow representation diagram accounting for the electronic rearrangements is proposed on the basis of BET results.     

Linear stability analysis of the natural convection in inclined rotating parallel plates

The linear stability analysis of the natural convection in a rectangular tilted infinite cavity filled with a Boussinesq fluid subject to Coriolis force is presented. The bottom and top surfaces have fixed temperatures. Both unstable and stable thermal conditions are studied (heated from below and heated from above respectively). The rotation axis passes through the center and it is orthogonal to the hot and cold surfaces. The stability equations were solved using the Tau–Chebyshev spectral method. The critical Rayleigh number and critical wave number were obtained for several rotation rates and different orientation of convective oblique rolls in a range of inclination of the cavity from 0 to 120 degrees. The stability analysis show that rotation rate affects the basic velocity profile, onset of convection, wave number and critical orientation of convective rolls.     

Electronic and magnetic properties of double perovskites (, Ca)

We have studied the magnetic and electronic properties of double perovskites A₂FeReO₆ with A=Ba and Ca using ab initio methods based on density functional theory. It has been shown that when changing Ba by Ca the system undergoes a metal–insulator transition coincidentally to a structural phase transition, even if conduction band fillings are not significantly changed. Our results suggest that only considering a quite large correlation term on the Re site could explain an insulating character for Ca₂FeReO₆. Instead, we found that small correlations could induce a bad metallic behavior as suggested in more recent experiments.