A característica de Euler

Pós-graduação em Matemática em Rede Nacional - IBILCE

Geometria e topologia das superfícies através de recorte e colagem

Pós-graduação em Matemática Universitária - IGCE

Robust fitting of Zernike polynomials to noisy point clouds defined over connected domains of arbitrary shape

A new method for fitting a series of Zernike polynomials to point clouds defined over connected domains of arbitrary shape defined within the unit circle is presented in this work. The method is based on the application of machine learning fitting techniques by constructing an extended training set in order to ensure the smooth variation of local curvature over the whole domain. Therefore this technique is best suited for fitting points corresponding to ophthalmic lenses surfaces, particularly progressive power ones, in non-regular domains. We have tested our method by fitting numerical and real surfaces reaching an accuracy of 1 micron in elevation and 0.1 D in local curvature in agreement with the customary tolerances in the ophthalmic manufacturing industry.

A NEW PROOF OF OKAJI'S THEOREM FOR A CLASS OF SUM OF SQUARES OPERATORS

Let P be a linear partial differential operator with analytic coefficients. We assume that P is of the form ""sum of squares"", satisfying Hormander's bracket condition. Let q be a characteristic point; for P. We assume that q lies on a symplectic Poisson stratum of codimension two. General results of Okaji Show that P is analytic hypoelliptic at q. Hence Okaji has established the validity of Treves' conjecture in the codimension two case. Our goal here is to give a simple, self-contained proof of this fact.

The sum-of-the-parts method: An international application

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Finance from the NOVA – School of Business and Economics

Intersection Pairing and intersection motive of surfaces

We construct the Chow motive modelling intersection co-homology of a proper surface. We then study its functoriality properties. Using Murre's decompositions of the motive of a desingularization into KÄunneth components [Mr1], we show that such decompositions exist also for the intersection motive.

Réhabilitation accélérée multimodate postcésarienne, la somme de toutes les astuces [Fast-track multimodal rehabilitation after cesarean, the sum of all tricks].

Fast-track multimodal rehabilitation after cesarean, the sum of all tricks Fast-track multimodal rehabilitation after caesarean is an interdisciplinary concept allowing an accelerated return to normal physiology. Fast-track rehabilitation combines minimising surgical trauma, regional anaesthesia and active management of pain control, minimally invasive postoperative care while promoting return to autonomy.

Receipt (copy) for the amount received from Burton and Bro. for the sum of $944.00 paid in full

Receipt (copy) for the amount received from Burton and Bro. for the sum of $944.00 paid in full for stumpage on berths 192 and 198. It is signed by S.D. Woodruff, May 24, 1878.

Molecular tectonics : supramolecular 2D nanopatterning of surfaces by self-assembly

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal

On the maximal connected component of hypercube with faulty vertices

In evaluating an interconnection network, it is indispensable to estimate the size of the maximal connected components of the underlying graph when the network begins to lose processors. Hypercube is one of the most popular interconnection networks. This article addresses the maximal connected components of an n -dimensional cube with faulty processors. We first prove that an n -cube with a set F of at most 2n - 3 failing processors has a component of size greater than or equal to2(n) - \F\ - 1. We then prove that an n -cube with a set F of at most 3n - 6 missing processors has a component of size greater than or equal to2(n) - \F\ - 2.