Elementos of geometry and trigonometry : from the works of A.M. Legendre, adapted to the course of mathematical instruction in the United State

UANL

Development of Shape Descriptors Based on Legendre Polynomials and Content-Based Retrieval of Scoliosis Images

The wealth of information available freely on the web and medical image databases poses a major problem for the end users: how to find the information needed? Content –Based Image Retrieval is the obvious solution.A standard called MPEG-7 was evolved to address the interoperability issues of content-based search.The work presented in this thesis mainly concentrates on developing new shape descriptors and a framework for content – based retrieval of scoliosis images.New region-based and contour based shape descriptor is developed based on orthogonal Legendre polymomials.A novel system for indexing and retrieval of digital spine radiographs with scoliosis is presented.

Performance Study of an Improved Legendre Moment Descriptor as Region-Based Shape Descriptor

This paper reports a novel region-based shape descriptor based on orthogonal Legendre moments. The preprocessing steps for invariance improvement of the proposed Improved Legendre Moment Descriptor (ILMD) are discussed. The performance of the ILMD is compared to the MPEG-7 approved region shape descriptor, angular radial transformation descriptor (ARTD), and the widely used Zernike moment descriptor (ZMD). Set B of the MPEG-7 CE-1 contour database and all the datasets of the MPEG-7 CE-2 region database were used for experimental validation. The average normalized modified retrieval rate (ANMRR) and precision- recall pair were employed for benchmarking the performance of the candidate descriptors. The ILMD has lower ANMRR values than ARTD for most of the datasets, and ARTD has a lower value compared to ZMD. This indicates that overall performance of the ILMD is better than that of ARTD and ZMD. This result is confirmed by the precision-recall test where ILMD was found to have better precision rates for most of the datasets tested. Besides retrieval accuracy, ILMD is more compact than ARTD and ZMD. The descriptor proposed is useful as a generic shape descriptor for content-based image retrieval (CBIR) applications

Transmissió : associació a Claire Voie. 'Transmisión : asociación a Claire Voie'.

Trata de la opinión que tiene Catherine Zarcate, actriz especializada en literatura oral, narradora, así como también escritora para el público infantil y juvenil, de cómo se puede transmitir las diferentes situaciones que se viven a través de los cuentos. En este sentido la tradición es una cuestión importante a tener en cuenta, ya que esta plantea de una forma aguda y crucial la cuestión de la transparencia. A lo largo de su discurso, se va centrando en puntos como son, el amor y la transmisión, la transmisión de la experiencia del acto escénico, la palabra como vehículo de transmisión y el transmisor entre otros.

Le Travail de l’enseignant en lve à l’ecole primaire éclaire par la didactique comparée

Cette communication vise à éclairer le travail du professeur lorsqu’il enseigne l’anglais langue vivante étrangère (LVE), en France à l’école primaire. Nous tentons de comparer les différentes pratiques d’enseignement de quatre professeurs. Notre hypothèse est qu’elles varient d’un enseignant à l’autre en fonction de leur utilisation plus ou moins important de la langue maternelle (LM) dans le cours de LVE et les choix divers réalisés pour transmettre le savoir enseigné. Ces variations résultent de transpositions didactiques différentes et variées de la parole des maîtres selon leur formation, leur maîtrise de la LVE, et les approches distinctes qu’ils ont du savoir enseigné, etc

Affine processes, arbitrage-Free Term structures of legendre polynomials,and option pricing

Multivariate Affine term structure models have been increasingly used for pricing derivatives in fixed income markets. In these models, uncertainty of the term structure is driven by a state vector, while the short rate is an affine function of this vector. The model is characterized by a specific form for the stochastic differential equation (SDE) for the evolution of the state vector. This SDE presents restrictions on its drift term which rule out arbitrages in the market. In this paper we solve the following inverse problem: Suppose the term structure of interest rates is modeled by a linear combination of Legendre polynomials with random coefficients. Is there any SDE for these coefficients which rules out arbitrages? This problem is of particular empirical interest because the Legendre model is an example of factor model with clear interpretation for each factor, in which regards movements of the term structure. Moreover, the Affine structure of the Legendre model implies knowledge of its conditional characteristic function. From the econometric perspective, we propose arbitrage-free Legendre models to describe the evolution of the term structure. From the pricing perspective, we follow Duffie et al. (2000) in exploring Legendre conditional characteristic functions to obtain a computational tractable method to price fixed income derivatives. Closing the article, the empirical section presents precise evidence on the reward of implementing arbitrage-free parametric term structure models: The ability of obtaining a good approximation for the state vector by simply using cross sectional data.

Adrien-Marie Legendre (1752-1833) e suas obras em Teoria dos Números

The present thesis is an analysis of Adrien-Marie Legendre s works on Number Theory, with a certain emphasis on his 1830 edition of Theory of Numbers. The role played by these works in their historical context and their influence on the development of Number Theory was investigated. A biographic study of Legendre (1752-1833) was undertaken, in which both his personal relations and his scientific productions were related to certain historical elements of the development of both his homeland, France, and the sciences in general, during the 18th and 19th centuries This study revealed notable characteristics of his personality, as well as his attitudes toward his mathematical contemporaries, especially with regard to his seemingly incessant quarrels with Gauss about the priority of various of their scientific discoveries. This is followed by a systematic study of Lagrange s work on Number Theory, including a comparative reading of certain topics, especially that of his renowned law of quadratic reciprocity, with texts of some of his contemporaries. In this way, the dynamics of the evolution of his thought in relation to his semantics, the organization of his demonstrations and his number theoretical discoveries was delimited. Finally, the impact of Legendre s work on Number Theory on the French mathematical community of the time was investigated. This investigation revealed that he not only made substantial contributions to this branch of Mathematics, but also inspired other mathematicians to advance this science even further. This indeed is a fitting legacy for his Theory of Numbers, the first modern text on Higher Arithmetic, on which he labored half his life, producing various editions. Nevertheless, Legendre also received many posthumous honors, including having his name perpetuated on the Trocadéro face of the Eiffel Tower, which contains a list of 72 eminent scientists, and having a street and an alley in Paris named after him

Random regression models using Legendre polynomials or linear splines for test-day milk yield of dairy Gyr (Bos indicus) cattle

Studies investigating the use of random regression models for genetic evaluation of milk production in Zebu cattle are scarce. In this study, 59,744 test-day milk yield records from 7,810 first lactations of purebred dairy Gyr (Bos indicus) and crossbred (dairy Gyr × Holstein) cows were used to compare random regression models in which additive genetic and permanent environmental effects were modeled using orthogonal Legendre polynomials or linear spline functions. Residual variances were modeled considering 1, 5, or 10 classes of days in milk. Five classes fitted the changes in residual variances over the lactation adequately and were used for model comparison. The model that fitted linear spline functions with 6 knots provided the lowest sum of residual variances across lactation. On the other hand, according to the deviance information criterion (DIC) and Bayesian information criterion (BIC), a model using third-order and fourth-order Legendre polynomials for additive genetic and permanent environmental effects, respectively, provided the best fit. However, the high rank correlation (0.998) between this model and that applying third-order Legendre polynomials for additive genetic and permanent environmental effects, indicates that, in practice, the same bulls would be selected by both models. The last model, which is less parameterized, is a parsimonious option for fitting dairy Gyr breed test-day milk yield records. © 2013 American Dairy Science Association.