Sumario de las muchas, y grandes indulgencias, concedidas por los sumos pontífices a la cofradia de la Cinta de N. P. S. Agustín con la invocación de Nuestra Señora la Virgen María de la Consolación y ahora nuevamente declaradas por N. Smo. P. Clemente X en su breve.

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Géométrie nodale et valeurs propres de l’opérateur de Laplace et du p-laplacien

La présente thèse porte sur différentes questions émanant de la géométrie spectrale. Ce domaine des mathématiques fondamentales a pour objet d'établir des liens entre la géométrie et le spectre d'une variété riemannienne. Le spectre d'une variété compacte fermée M munie d'une métrique riemannienne $g$ associée à l'opérateur de Laplace-Beltrami est une suite de nombres non négatifs croissante qui tend vers l’infini. La racine carrée de ces derniers représente une fréquence de vibration de la variété. Cette thèse présente quatre articles touchant divers aspects de la géométrie spectrale. Le premier article, présenté au Chapitre 1 et intitulé « Superlevel sets and nodal extrema of Laplace eigenfunctions », porte sur la géométrie nodale d'opérateurs elliptiques. L’objectif de mes travaux a été de généraliser un résultat de L. Polterovich et de M. Sodin qui établit une borne sur la distribution des extrema nodaux sur une surface riemannienne pour une assez vaste classe de fonctions, incluant, entre autres, les fonctions propres associées à l'opérateur de Laplace-Beltrami. La preuve fournie par ces auteurs n'étant valable que pour les surfaces riemanniennes, je prouve dans ce chapitre une approche indépendante pour les fonctions propres de l’opérateur de Laplace-Beltrami dans le cas des variétés riemanniennes de dimension arbitraire. Les deuxième et troisième articles traitent d'un autre opérateur elliptique, le p-laplacien. Sa particularité réside dans le fait qu'il est non linéaire. Au Chapitre 2, l'article « Principal frequency of the p-laplacian and the inradius of Euclidean domains » se penche sur l'étude de bornes inférieures sur la première valeur propre du problème de Dirichlet du p-laplacien en termes du rayon inscrit d’un domaine euclidien. Plus particulièrement, je prouve que, si p est supérieur à la dimension du domaine, il est possible d'établir une borne inférieure sans aucune hypothèse sur la topologie de ce dernier. L'étude de telles bornes a fait l'objet de nombreux articles par des chercheurs connus, tels que W. K. Haymann, E. Lieb, R. Banuelos et T. Carroll, principalement pour le cas de l'opérateur de Laplace. L'adaptation de ce type de bornes au cas du p-laplacien est abordée dans mon troisième article, « Bounds on the Principal Frequency of the p-Laplacian », présenté au Chapitre 3 de cet ouvrage. Mon quatrième article, « Wolf-Keller theorem for Neumann Eigenvalues », est le fruit d'une collaboration avec Guillaume Roy-Fortin. Le thème central de ce travail gravite autour de l'optimisation de formes dans le contexte du problème aux valeurs limites de Neumann. Le résultat principal de cet article est que les valeurs propres de Neumann ne sont pas toujours maximisées par l'union disjointe de disques arbitraires pour les domaines planaires d'aire fixée. Le tout est présenté au Chapitre 4 de cette thèse.

The problem of noncharacteristic quasimolecular X-rays in heavy ion collision

Quasi-molecular X-rays observed in heavy ion collisions are interpreted within a relativistic calculation of correlation diagrams using the Dirac-Slater model. A semiquantitative description of noncharacteristic M X rays is given for the system Au-I.

2D-3D Rigid-Body Registration of X-Ray Fluoroscopy and CT Images

The registration of pre-operative volumetric datasets to intra- operative two-dimensional images provides an improved way of verifying patient position and medical instrument loca- tion. In applications from orthopedics to neurosurgery, it has a great value in maintaining up-to-date information about changes due to intervention. We propose a mutual information- based registration algorithm to establish the proper align- ment. For optimization purposes, we compare the perfor- mance of the non-gradient Powell method and two slightly di erent versions of a stochastic gradient ascent strategy: one using a sparsely sampled histogramming approach and the other Parzen windowing to carry out probability density approximation. Our main contribution lies in adopting the stochastic ap- proximation scheme successfully applied in 3D-3D registra- tion problems to the 2D-3D scenario, which obviates the need for the generation of full DRRs at each iteration of pose op- timization. This facilitates a considerable savings in compu- tation expense. We also introduce a new probability density estimator for image intensities via sparse histogramming, de- rive gradient estimates for the density measures required by the maximization procedure and introduce the framework for a multiresolution strategy to the problem. Registration results are presented on uoroscopy and CT datasets of a plastic pelvis and a real skull, and on a high-resolution CT- derived simulated dataset of a real skull, a plastic skull, a plastic pelvis and a plastic lumbar spine segment.

A survey addressing the fundamental matrix estimation problem

Epipolar geometry is a key point in computer vision and the fundamental matrix estimation is the only way to compute it. This article surveys several methods of fundamental matrix estimation which have been classified into linear methods, iterative methods and robust methods. All of these methods have been programmed and their accuracy analysed using real images. A summary, accompanied with experimental results, is given

Aproximaci?? a la problem??tica de l'atur juvenir a Ciutadella. 'Aproximaci??n a la problem??tica del paro juvenil en Ciutadella'

Este trabajo gan?? el primer premio Joan Mercadal sobre la juventud en Menorca

The relevance of the Laplacian of intracule and extracule density distributions for analyzing electron-electron interactions in molecules

A topological analysis of intracule and extracule densities and their Laplacians computed within the Hartree-Fock approximation is presented. The analysis of the density distributions reveals that among all possible electron-electron interactions in atoms and between atoms in molecules only very few are located rigorously as local maxima. In contrast, they are clearly identified as local minima in the topology of Laplacian maps. The conceptually different interpretation of intracule and extracule maps is also discussed in detail. An application example to the C2H2, C2H4, and C2H6 series of molecules is presented

On the system of rational difference equations x(n) = A+(1)over-bar y(n-p), y(n) = A+(gamma(n-1))over-bar x(n-r)y(n-5)

In this paper, we study the behavior of the positive solutions of the system of two difference equations [GRAPHICS] where p >= 1, r >= 1, s >= 1, A >= 0, and x(1-r), x(2-r),..., x(0), y(1-max) {p.s},..., y(0) are positive real numbers. (c) 2005 Elsevier Inc. All rights reserved.

The surface geometries of the medium and high coverage carbon monoxide structures c(2 × 4)–(2CO) and p(root7- x root7)R19°–(4CO) structure

The surface geometries of the p (root7- x root7)R19degrees-(4CO) and c(2 x 4)-(2CO) layers on Ni {111} and the clean Ni {111} surface were determined by low energy electron diffraction structure analysis. For the clean surface small but significant contractions of d(12) and d(23) (both 2.02 Angstrom) were found with respect to the bulk interlayer distance (2.03 Angstrom). In the c(2 x 4)-(2CO) structure these distances are expanded, with values of d(12) = 2.08 Angstrom and d(23) = 2.06 Angstrom and buckling of 0.08 and 0.02 Angstrom, respectively, in the first and second layer. CO resides near hcp and fcc hollow sites with relatively large lateral shifts away from the ideal positions leading to unequal C-Ni bond lengths between 1.76 and 1.99 Angstrom. For the p(root7- x root7-)R19'-(4CO) layer two best fit geometries were found, which agree in most of their atomic positions, except for one out of four CO molecules, which is either near atop or between bridge and atop. The remaining three molecules reside near hcp and fcc sites, again with large lateral deviations from their ideal positions. The average C Ni bond length for these molecules is, however, the same as for CO on hollow sites at low coverage. The average CNi bond length at hollow sites, the interlayer distances, and buckling in the first Ni layer are similar to the c(2 x 4)(2CO) geometry, only the buckling in the second layer (0.08 Angstrom) is significantly larger. Lateral and vertical shifts of the Ni atoms in the first layer lead to unsymmetric environments for the CO molecules, which can be regarded as an imprint of the chiral p(root7- x root7-)R19degrees lattice geometry onto the substrate.

Ω-results for Beurling's zeta function and lower bounds for the generalised Dirichlet divisor problem

In this paper we study generalised prime systems for which the integer counting function NP(x) is asymptotically well behaved, in the sense that NP(x)=ρx+O(xβ), where ρ is a positive constant and . For such systems, the associated zeta function ζP(s) is holomorphic for . We prove that for , for any ε>0, and also for ε=0 for all such σ except possibly one value. The Dirichlet divisor problem for generalised integers concerns the size of the error term in NkP(x)−Ress=1(ζPk(s)xs/s), which is O(xθ) for some θ<1. Letting αk denote the infimum of such θ, we show that .

Stepwise construction of [Os6(CO)18(μ6-P)]-, a hexanuclear osmium cluster monoanion with trigonal-prismatic co-ordination for phosphorus: X-ray crystal structures of [Os6(μ-H)2(CO)20(MeCN)(μ3-PH)] and [PPh3Me][Os6(CO)18(μ6-P)]

Treatment of the labile cluster [Os3(CO)11(MeCN)] with PH3 affords the substituted product [Os3(CO)11(PH3)](1) in high yield. Subsequent reaction of (1) with Na2CO3 in MeOH, followed by acidification, gives the hydrido phosphido cluster [Os3(µ-H)(CO)10(µ-PH2)](2). When (2) is heated to 45–60 °C in the presence of [Os3(CO)11(MeCN)] a hexanuclear complex with the formulation [Os6(µ-H)2(CO)21(µ3-PH)](3) is obtained. If this reaction is repeated using [Os3(CO)10(MeCN)2] instead of [Os3(CO)11(MeCN)], an acetonitrile-containing product, [Os6(µ-H)2(CO)20(MeCN)(µ3-PH)](4), is obtained. An X-ray analysis of (4) shows that two Os3 triangular units are linked by a µ3-phosphinidene ligand, which symmetrically bridges an Os–Os edge of one triangle and is terminally co-ordinated to one Os atom of the second triangle. When (3) is treated with a weak base, such as [N(PPh3)2]Cl or [PPh3Me] Br, deprotonation to the corresponding cluster monoanion [Os6(µ-H)(CO)21(µ3-PH)]–(5) occurs. Treatment of (5) with a weak acid regenerates (3) in quantitative yield. Thermolysis of (3) leads to a closing up of the metal framework, affording the cluster [Os6(µ-H)(CO)18(µ6-P)], which readily deprotonates to give the anion [Os6(CO)18(µ6-P)]–(7) in the presence of [N(PPh3)2] Cl or [PPh3Me]Br. The same anion (7) may also be obtained by direct thermolysis of (5). An X-ray analysis of the [PPh3Me]+ salt of (7) confirms that the phosphorus occupies an interstitial site in a trigonal-prismatic hexaosmium framework, and co-ordinates to all six metal atoms with an average Os–P distance of 2.31 (1)Å. Proton and 31P n.m.r. data on all the new clusters are presented, and the position of the phosphorus resonance in the 31P n.m.r. spectrum is related to the changes in the environment of the phosphorus atom.

Preventing carbon contamination of optical devices for X-rays: the effect of oxygen on photon-induced dissociation of CO on platinum

Platinum is one of the most common coatings used to optimize mirror reflectivity in soft X-ray beamlines. Normal operation results in optics contamination by carbon-based molecules present in the residual vacuum of the beamlines. The reflectivity reduction induced by a carbon layer at the mirror surface is a major problem in synchrotron radiation sources. A time-dependent photoelectron spectroscopy study of the chemical reactions which take place at the Pt(111) surface under operating conditions is presented. It is shown that the carbon contamination layer growth can be stopped and reversed by low partial pressures of oxygen for optics operated in intense photon beams at liquidnitrogen temperature. For mirrors operated at room temperature the carbon contamination observed for equivalent partial pressures of CO is reduced and the effects of oxygen are observed on a long time scale.

An optimization problem concerning multiplicative functions

In this paper we study the problem of maximizing a quadratic form 〈Ax,x〉 subject to ‖x‖q=1, where A has matrix entries View the MathML source with i,j|k and q≥1. We investigate when the optimum is achieved at a ‘multiplicative’ point; i.e. where x1xmn=xmxn. This turns out to depend on both f and q, with a marked difference appearing as q varies between 1 and 2. We prove some partial results and conjecture that for f multiplicative such that 0