Números Complexos: um estudo histórico sobre sua abordagem na coleção Matemática 2º ciclo

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On the Milnor fibre and L numbers of semi-weighted homogeneous arrangements

Inthispaperwestudygermsofpolynomialsformedbytheproductofsemi-weighted homogeneous polynomials of the same type, which we call semi-weighted homogeneous arrangements. It is shown how the L numbers of such polynomials are computed using only their weights and degree of homogeneity. A key point of the main theorem is to find the number called polar ratio of this polynomial class. An important consequence is the description of the Euler characteristic of the Milnor fibre of such arrangements only depending on their weights and degree of homogeneity. The constancy of the L numbers in families formed by such arrangements is shown, with the deformed terms having weighted degree greater than the weighted degree of the initial germ. Moreover, using the results of Massey applied to families of function germs, we obtain the constancy of the homology of the Milnor fibre in this family of semi-weighted homogeneous arrangements.

Previous Percutaneous Coronary Intervention as Risk Factor for Coronary Artery Bypass Grafting

Background: Percutaneous coronary intervention (PCI) has increased as the initial revascularization strategy in chronic coronary artery disease. Consequently, more patients undergoing coronary artery bypass grafting (CABG) have history of coronary stent. Objective: Evaluate the impact of previous PCI on in-hospital mortality after CABG in patients with multivessel coronary artery disease. Methods: Between May/2007 and June/2009, 1099 consecutive patients underwent CABG on cardiopulmonary bypass. Patients with no PCI (n=938, 85.3%) were compared with patients with previous PCI (n=161, 14.6%). Logistic regression models and propensity score matching analysis were used to assess the risk-adjusted impact of previous PCI on in-hospital mortality. Results: Both groups were similar, except for the fact that patients with previous PCI were more likely to have unstable angina (16.1% x 9.9%, p=0.019). In-hospital mortality after CABG was higher in patients with previous PCI (9.3% x 5.1%, p=0.034) and it was comparable with EuroSCORE and 2000 Bernstein-Parsonnet risk score. Using multivariate logistic regression analysis, previous PCI emerged as an independent predictor of postoperative in-hospital mortality (odds ratio 1.94, 95% CI 1.02-3.68, p=0.044) as strong as diabetes (odds ratio 1.86, 95% CI 1.07-3.24, p=0.028). After computed propensity score matching based on preoperative risk factors, in-hospital mortality remained higher among patients with previous PCI (odds ratio 3.46, 95% CI 1.10-10.93, p=0.034). Conclusions: Previous PCI in patients with multivessel coronary artery disease is an independent risk factor for in-hospital mortality after CABG. This fact must be considered when PCI is indicated as initial alternative in patients with more severe coronary artery disease. (Arq Bras Cardiol 2012;99(1):586-595)

The discriminants associated to isotropy representations of symmetric spaces

We consider a generalized discriminant associated to a symmetric space which generalizes the discriminant of real symmetric matrices, and note that it can be written as a sum of squares of real polynomials. A method to estimate the minimum number of squares required to represent the discrimininant is developed and applied in examples.

Mutual Information Rate and Bounds for It

The amount of information exchanged per unit of time between two nodes in a dynamical network or between two data sets is a powerful concept for analysing complex systems. This quantity, known as the mutual information rate (MIR), is calculated from the mutual information, which is rigorously defined only for random systems. Moreover, the definition of mutual information is based on probabilities of significant events. This work offers a simple alternative way to calculate the MIR in dynamical (deterministic) networks or between two time series (not fully deterministic), and to calculate its upper and lower bounds without having to calculate probabilities, but rather in terms of well known and well defined quantities in dynamical systems. As possible applications of our bounds, we study the relationship between synchronisation and the exchange of information in a system of two coupled maps and in experimental networks of coupled oscillators.

Definite integrals and operational methods

An operational method, already employed to formulate a generalization of the Ramanujan master theorem, is applied to the evaluation of integrals of various types. This technique provides a very flexible and powerful tool yielding new results encompassing different aspects of the special function theory. Crown Copyright (C) 2012 Published by Elsevier Inc. All rights reserved.

GENERALIZED FINITE ELEMENT METHOD ON NONCONVENTIONAL HYBRID-MIXED FORMULATION

The generalized finite element method (GFEM) is applied to a nonconventional hybrid-mixed stress formulation (HMSF) for plane analysis. In the HMSF, three approximation fields are involved: stresses and displacements in the domain and displacement fields on the static boundary. The GFEM-HMSF shape functions are then generated by the product of a partition of unity associated to each field and the polynomials enrichment functions. In principle, the enrichment can be conducted independently over each of the HMSF approximation fields. However, stability and convergence features of the resulting numerical method can be affected mainly by spurious modes generated when enrichment is arbitrarily applied to the displacement fields. With the aim to efficiently explore the enrichment possibilities, an extension to GFEM-HMSF of the conventional Zienkiewicz-Patch-Test is proposed as a necessary condition to ensure numerical stability. Finally, once the extended Patch-Test is satisfied, some numerical analyses focusing on the selective enrichment over distorted meshes formed by bilinear quadrilateral finite elements are presented, thus showing the performance of the GFEM-HMSF combination.

Bayesian analysis of random regression models using B-splines to model test-day milk yield of Holstein cattle in Brazil

The objective of this paper is to model variations in test-day milk yields of first lactations of Holstein cows by RR using B-spline functions and Bayesian inference in order to fit adequate and parsimonious models for the estimation of genetic parameters. They used 152,145 test day milk yield records from 7317 first lactations of Holstein cows. The model established in this study was additive, permanent environmental and residual random effects. In addition, contemporary group and linear and quadratic effects of the age of cow at calving were included as fixed effects. Authors modeled the average lactation curve of the population with a fourth-order orthogonal Legendre polynomial. They concluded that a cubic B-spline with seven random regression coefficients for both the additive genetic and permanent environment effects was to be the best according to residual mean square and residual variance estimates. Moreover they urged a lower order model (quadratic B-spline with seven random regression coefficients for both random effects) could be adopted because it yielded practically the same genetic parameter estimates with parsimony. (C) 2012 Elsevier B.V. All rights reserved.

Random regression analyses using B-spline functions to model growth of Nellore cattle

The objective of this study was to estimate (co)variance components using random regression on B-spline functions to weight records obtained from birth to adulthood. A total of 82 064 weight records of 8145 females obtained from the data bank of the Nellore Breeding Program (PMGRN/Nellore Brazil) which started in 1987, were used. The models included direct additive and maternal genetic effects and animal and maternal permanent environmental effects as random. Contemporary group and dam age at calving (linear and quadratic effect) were included as fixed effects, and orthogonal Legendre polynomials of age (cubic regression) were considered as random covariate. The random effects were modeled using B-spline functions considering linear, quadratic and cubic polynomials for each individual segment. Residual variances were grouped in five age classes. Direct additive genetic and animal permanent environmental effects were modeled using up to seven knots (six segments). A single segment with two knots at the end points of the curve was used for the estimation of maternal genetic and maternal permanent environmental effects. A total of 15 models were studied, with the number of parameters ranging from 17 to 81. The models that used B-splines were compared with multi-trait analyses with nine weight traits and to a random regression model that used orthogonal Legendre polynomials. A model fitting quadratic B-splines, with four knots or three segments for direct additive genetic effect and animal permanent environmental effect and two knots for maternal additive genetic effect and maternal permanent environmental effect, was the most appropriate and parsimonious model to describe the covariance structure of the data. Selection for higher weight, such as at young ages, should be performed taking into account an increase in mature cow weight. Particularly, this is important in most of Nellore beef cattle production systems, where the cow herd is maintained on range conditions. There is limited modification of the growth curve of Nellore cattle with respect to the aim of selecting them for rapid growth at young ages while maintaining constant adult weight.

Intervenção Coronariana Percutânea prévia como fator de risco para Revascularização Miocárdica

FUNDAMENTO: A Intervenção Coronariana Percutânea (ICP) vem aumentando na doença arterial coronariana crônica. Consequentemente, cada vez mais pacientes submetidos a Cirurgia de Revascularização Miocárdica (CRM) apresentam stent coronariano. OBJETIVO: Avaliar a influência do antecedente de stent coronariano na mortalidade hospitalar após CRM. MÉTODOS: Análise prospectiva com 1.099 pacientes consecutivos submetidos a CRM com circulação extracorpórea, entre maio/2007 e junho/2009. Pacientes sem ICP prévia (n = 938; 85,3%) foram comparados com pacientes com ICP prévia (n = 161; 14,6%), utilizando modelos de regressão logística e análise de pareamento de amostras. RESULTADOS: Ambos os grupos apresentavam semelhança em relação aos fatores de risco, exceto pela maior presença de pacientes com angina instável no grupo com ICP prévia (16,1% vs. 9,9%; p = 0,019). A mortalidade hospitalar após CRM foi maior entre os pacientes com ICP prévia (9,3% vs. 5,1%, p = 0,034), e foi semelhante à esperada em relação ao EuroSCORE e ao 2000 Bernstein-Parsonnet score. Na análise com regressão logística multivariada a ICP prévia emergiu como fator de risco independente para mortalidade hospitalar pós-operatória (odds ratio 1,94; IC 95% 1,02-3,68; p = 0,044) tão forte quanto diabetes (odds ratio 1,86; IC 95% 1,07-3,24; p = 0,028). Após o pareamento dos grupos, a mortalidade hospitalar continuou sendo maior entre os pacientes com ICP prévia, com odds ratio 3,46 ; IC 95% 1,10-10,93; p = 0,034. CONCLUSÃO: A ICP prévia em pacientes com doença coronariana multiarterial é fator de risco independente para mortalidade hospitalar após CRM. Tal fato deve ser considerado quando a ICP for indicada como alternativa inicial em pacientes com doença arterial coronariana mais avançada. (Arq Bras Cardiol. 2012; [online].ahead print, PP.0-0)

Cirurgia de revascularização miocárdica na fase aguda do infarto: análise dos fatores preditores de mortalidade intra-hospitalar

OBJETIVO: A cirurgia de revascularização miocárdica (CRM) na fase aguda do infarto do miocárdio (IAM) está associada a aumento do risco operatório. O objetivo do estudo foi determinar fatores preditores de mortalidade intra-hospitalar nos pacientes submetidos a CRM no IAM. MÉTODOS: Durante três anos, todos os pacientes submetidos a CRM no IAM foram analisados retrospectivamente, utilizando o banco de dados institucional. Sessenta variáveis por paciente foram avaliadas: 49 variáveis pré-operatórias provenientes dos escores 2000 Bernstein-Parsonnet e EuroSCORE; 4 variáveis pré-operatórias não consideradas por esses escores (tempo entre o IAM e a CRM, valor máximo de CKMB, valor máximo de troponina e supradesnivelamento do segmento ST) e 7 variáveis intraoperatórias [uso de circulação extracorpórea (CEC), tempo de CEC, tipo de cardioplegia, endarterectomia, número de enxertos, uso da artéria torácica interna e revascularização completa]. Análise univariada e multivariada para o desfecho mortalidade intra-hospitalar foram realizadas. RESULTADOS: O tempo médio entre o IAM e a CRM foi de 3,8 ± 3 dias. A mortalidade global foi 19%. Na análise multivariada: idade > 65 anos [OR 16,5 (IC 1,8-152), P=0,013]~ CEC >108 minutos [OR 40 (IC 2,7-578), P=0,007], creatinina > 2 mg/dl [OR 35,5 (IC 1,7-740), P=0,021] e pressão pulmonar sistólica > 60 mmHg [OR 31(IC 1,6-591), P=0,022] foram preditores de mortalidade intra-hospitalar. CONCLUSÃO: Variáveis pré-operatórias clássicas como idade > 65 anos, creatinina > 2 mg/dl e pressão pulmonar sistólica > 60 mmHg foram preditoras de mortalidade intra-hospitalar nos pacientes operados de revascularização miocárdica na fase aguda do infarto.

Com ou sem CEC?: impacto dos escores de risco na cirurgia de revascularização miocárdica

OBJETIVO: Permanecem as controvérsias sobre a utilização de circulação extracorpórea (CEC) na cirurgia de revascularização miocárdica (CRM). O objetivo deste estudo foi avaliar o impacto do 2000 Bernstein Parsonnet (2000BP) e EuroSCORE (EU) para escolha de CEC na CRM. MÉTODOS: Foram submetidos à CRM 1.551 pacientes consecutivos. CEC foi utilizada em 1.121 (72,3%) pacientes. O desempenho do 2000BP e EU para a amostra foi avaliado mediante testes de calibração, discriminação e correlação. Para ambos os escores de risco, o aumento do valor do escore e a presença de CEC tiveram relação direta com maior chance de óbito (P<0,05). Portanto, com essas duas variáveis foi construído um modelo de regressão logística para cada escore de risco, com a finalidade de determinar em que valor do escore a presença de CEC aumenta significativamente a chance de óbito. RESULTADOS: A calibração, ao igual que a área abaixo da curva ROC para o grupo com CEC [2000BP=0,80; EU=0,78] e sem CEC [2000BP=0,81; EU=0,85] foram adequadas. A correlação de Spearman para os grupos com e sem CEC foi de 0,66 (P<0,001) e 0,62 (P<0,001), respectivamente. No 2000BP, para um valor>17,75, a presença de CEC aumentou a chance de óbito para 7,4 [IC95% (4,4-12,3), P<0,0001]. No EU, para um valor>4,5, a presença de CEC aumentou a chance de óbito para 5,4 [IC95% (3,3-9), P<0,0001]. CONCLUSÃO: Na tomada de decisões, o 2000BP>17,75 ou o EU>4,5 orientam a identificar pacientes que quando submetidos a CRM com CEC têm chance de óbito aumentada significativamente.

A prática pedagógica e a criação de um contexto favorável para a aprendizagem de ciências no Ensino Fundamental

Este artigo tem como objetivo identificar, com base em registros de observações de aulas de ciências no Ensino Fundamental II, em uma escola da rede pública estadual do município de Valinhos, SP, se a prática pedagógica pode criar condições que potencializem ou limitem a exigência conceitual no tratamento do conhecimento. As análises foram feitas por meio da comparação com outros estudos sobre práticas favoráveis à aproximação ao conhecimento científico, desenvolvidos sob a mesma perspectiva teórica a teoria de Basil Bernstein, e, nesse sentido, ficou evidente o quanto a prática pedagógica analisada se distancia do que vem sendo apontado como uma configuração mais adequada, especialmente por não permitir a intervenção dos alunos na determinação dos tempos envolvidos na aprendizagem, e por preservar rigidamente as fronteiras entre os conteúdos científicos, o que acaba criando condições favoráveis à redução do nível de exigência conceitual nas aulas.

Topics in geometry, analysis and inverse problems

The thesis consists of three independent parts. Part I: Polynomial amoebas We study the amoeba of a polynomial, as de ned by Gelfand, Kapranov and Zelevinsky. A central role in the treatment is played by a certain convex function which is linear in each complement component of the amoeba, which we call the Ronkin function. This function is used in two di erent ways. First, we use it to construct a polyhedral complex, which we call a spine, approximating the amoeba. Second, the Monge-Ampere measure of the Ronkin function has interesting properties which we explore. This measure can be used to derive an upper bound on the area of an amoeba in two dimensions. We also obtain results on the number of complement components of an amoeba, and consider possible extensions of the theory to varieties of codimension higher than 1. Part II: Differential equations in the complex plane We consider polynomials in one complex variable arising as eigenfunctions of certain differential operators, and obtain results on the distribution of their zeros. We show that in the limit when the degree of the polynomial approaches innity, its zeros are distributed according to a certain probability measure. This measure has its support on the union of nitely many curve segments, and can be characterized by a simple condition on its Cauchy transform. Part III: Radon transforms and tomography This part is concerned with different weighted Radon transforms in two dimensions, in particular the problem of inverting such transforms. We obtain stability results of this inverse problem for rather general classes of weights, including weights of attenuation type with data acquisition limited to a 180 degrees range of angles. We also derive an inversion formula for the exponential Radon transform, with the same restriction on the angle.

Construction of polynomial spline spaces over quadtree and octree T-meshes

[EN]We present a new strategy for constructing tensor product spline spaces over quadtree and octree T-meshes. The proposed technique includes some simple rules for inferring local knot vectors to define spline blending functions. These rules allow to obtain for a given T-mesh a set of cubic spline functions that span a space with nice properties: it can reproduce cubic polynomials, the functions are C2-continuous, linearly independent, and spaces spanned by nested T-meshes are also nested. In order to span spaces with these properties applying the proposed rules, the T-mesh should fulfill the only requirement of being a 0-balanced quadtree or octree. ..