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Search Results: 1 - 10 of 721261 matches for " Mário M. Gra a "
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Acceleration of nonhyperbolic sequences of Mann
Mário M. Gra a
International Journal of Mathematics and Mathematical Sciences , 2002, DOI: 10.1155/s0161171202013340
Abstract: Mann's sequences are difficult to accelerate in the presence of a nonhyperbolic fixed point. New accelerators are constructed for Mann's sequences which are useful even for other sets of very slowly convergent sequences.
Maps for global separation of roots
Mário M. Graa
Mathematics , 2015,
Abstract: Two simple predicates are adopted and certain real-valued piecewise continuous functions are constructed from them. This type of maps will be called quasi-step maps and aim to separate the fixed points of an iteration map in an interval. The main properties of these maps are studied. Several worked examples are given where appropriate quasi-step maps for Newton and Halley iteration maps illustrate the main features of quasi-step maps as tools for global separation of roots.
A Simple Derivation of Newton-Cotes Formulas with Realistic Errors
Mário M. Graa
Mathematics , 2012,
Abstract: In order to approximate the integral $I(f)=\int_a^b f(x) dx$, where $f$ is a sufficiently smooth function, models for quadrature rules are developed using a given {\it panel} of $n (n\geq 2)$ equally spaced points. These models arise from the undetermined coefficients method, using a Newton's basis for polynomials. Although part of the final product is algebraically equivalent to the well known closed Newton-Cotes rules, the algorithms obtained are not the classical ones. In the basic model the most simple quadrature rule $Q_n$ is adopted (the so-called left rectangle rule) and a correction $\tilde E_n$ is constructed, so that the final rule $S_n=Q_n+\tilde E_n$ is interpolatory. The correction $\tilde E_n$, depending on the divided differences of the data, might be considered a {\em realistic correction} for $Q_n$, in the sense that $\tilde E_n$ should be close to the magnitude of the true error of $Q_n$, having also the correct sign. The analysis of the theoretical error of the rule $S_n$ as well as some classical properties for divided differences suggest the inclusion of one or two new points in the given panel. When $n$ is even it is included one point and two points otherwise. In both cases this approach enables the computation of a {\em realistic error} $\bar E_{S_n}$ for the {\it extended or corrected} rule $S_n$. The respective output $(Q_n,\tilde E_n, S_n, \bar E_{S_n})$ contains reliable information on the quality of the approximations $Q_n$ and $S_n$, provided certain conditions involving ratios for the derivatives of the function $f$ are fulfilled. These simple rules are easily converted into {\it composite} ones. Numerical examples are presented showing that these quadrature rules are useful as a computational alternative to the classical Newton-Cotes formulas.
Recursive families of higher order iterative maps
Mário M. Graa
Mathematics , 2014,
Abstract: To approximate a simple root of an equation we construct families of iterative maps of higher order of convergence. These maps are based on model functions which can be written as an inner product. The main family of maps discussed is defined recursively and is called {\it Newton-barycentric}. We illustrate the application of Newton-barycentric maps in two worked examples, one dealing with a typical least squares problem and the other showing how to locate simultaneously a great number of extrema of the Ackley's function.
Higher-order root distillers
Mário M. Graa
Mathematics , 2015,
Abstract: Recursive maps of high order of convergence $m$ (say $m=2^{10}$ or $m=2^{20}$) induce certain monotone step functions from which one can filter relevant information needed to globally separate and compute the real roots of a function on a given interval $[a,b]$. The process is here called a root distiller. A suitable root distiller has a powerful preconditioning effect enabling the computation, on the whole interval, of accurate roots of an high degree polynomial. Taking as model high-degree inexact Chebyshev polynomials and using the {\sl Mathematica} system, worked numerical examples are given detailing our distiller algorithm.
Quadrature as a least-squares and minimax problem
Mário M. Graa
Mathematics , 2012,
Abstract: The vector of weights of an interpolatory quadrature rule with $n$ preassigned nodes is shown to be the least-squares solution $\omega$ of an overdetermined linear system here called {\em the fundamental system} of the rule. It is established the relation between $\omega$ and the minimax solution $\stackrel{\ast}{z}$ of the fundamental system, and shown the constancy of the $\infty$-norms of the respective residual vectors which are equal to the {\em principal moment} of the rule. Associated to $\omega$ and $\stackrel{\ast}{z}$ we define several parameters, such as the angle of a rule, in order to assess the main properties of a rule or to compare distinct rules. These parameters are tested for some Newton-Cotes, Fej\'er, Clenshaw-Curtis and Gauss-Legendre rules.
A unified framework for the computation of polynomial quadrature weights and errors
Mário M. Graa,M. Esmeralda Sousa-Dias
Mathematics , 2012,
Abstract: For the class of polynomial quadrature rules we show that conveniently chosen bases allow to compute both the weights and the theoretical error expression of a $n$-point rule via the undetermined coefficients method. As an illustration, the framework is applied to some classical rules such as Newton-Cotes, Adams-Bashforth, Adams-Moulton and Gaussian rules.
2-Amino-6-[(2,6-dichlorophenyl)imino]-3-oxocyclohexa-1,4-dienecarbaldehyde
Cláudia M. B. Neves,José A. Fernandes,Mário M. Q. Simões,M. Graça P. M. S. Neves
Acta Crystallographica Section E , 2011, DOI: 10.1107/s1600536811042619
Abstract: The title compound, C13H8Cl2N2O2, was obtained by the oxidation of diclofenac {systematic name: 2-[2-(2,6-dichlorophenylamino)phenyl]acetic acid}, an anti-inflammatory drug, with hydrogen peroxide catalysed by chlorido[5,10,15,20-tetrakis(2,6-dichlorophenyl)porphyrinato]manganese(III), using ammonium acetate as co-catalyst. The asymmetric unit contains two crystallographically independent molecules of the title compound (Z′ = 2). The close packing of individual molecules is mediated by a series of strong and rather directional N—H...Cl and N—H...O hydrogen bonds, plus weak π–π [distance between the individual double bonds of symmetry-related iminoquinone rings = 3.7604 (13) ] and Cl...O interactions [3.0287 (18) ].
Attachment and Proliferation of Osteoblasts on Lithium-Hydroxyapatite Composites
Ana Paula M. Shainberg,Patrícia Valério,Alessandra Zonari,Faik N. Oktar,Lutfiye S. Ozyegin,Manuel Pedro F. Graa,Maria F. Leite,Alfredo M. Goes
Advances in Materials Science and Engineering , 2012, DOI: 10.1155/2012/650574
Abstract: The biocompatibility and bioactivity properties of hydroxyapatites (HAs) modified through lithium addition were investigated. Hydroxyapatites obtained from bovine bone were mixed with lithium carbonate (Li), in the proportions of 0.25, 0.50, 1.00, and 2.00%?wt, and sintered at 900°, 1000°, 1100°, 1200°, and 1300°C, creating LiHA samples. The osteoblast culture behavior was assessed in the presence of these LiHA compositions. The cellular interactions were analyzed by evaluating the viability and cellular proliferation, ALP production and collagen secretion. The cytotoxic potential was investigated through measurement of apoptosis and necrosis induction. The process of cellular attachment in the presence of the product of dissolution of LiHA, was evaluated trough fluorescence analysis. The physical characteristics of these materials and their cellular interactions were examined with SEM and EDS. The results of this study indicate that the LiHA ceramics are biocompatible and have variable bioactivities, which can be tailored by different combinations of the concentration of lithium carbonate and the sintering temperature. Our findings suggest that LiHA 0.25%?wt, sintered at 1300°C, combines the necessary physical and structural qualities with favorable biocompatibility characteristics, achieving a bioactivity that seems to be adequate for use as a bone implant material. 1. Introduction Bones provide mechanical protection for internal organs and the blood-forming marrow, and they facilitate locomotion and serve as a reservoir for calcium, magnesium, and phosphate minerals [1]. Bones are formed by a series of complex events involving mineralization with calcium phosphate in the form of hydroxyapatite (HA) on extracellular matrix proteins primarily consisting of collagen type I. HA is one of the most attractive materials for human hard tissue implants because of its close resemblance to bones and teeth [2]. Bone fractures and related damages result in more than 1.3 million surgical procedures every year in the United States [3]. In many cases, such as with acute and chronic injuries or defects, a bone graft substitute is necessary. Current options include autografts, allografts, and an assortment of synthetic or biomimetic materials and devices. Each of these options has significant limitations, such as the need for a second site of surgery, a limited resource supply, an inadequate size and shape, and morbidity associated with the donor site. Thus there remains a need for new options [4]. Calcium phosphate (Ca-P) biomaterials are a good option for use as
Teste de desencadeamento aberto no diagnóstico de alergia à proteína do leite de vaca
Correa, Fernanda Ferreira;Vieira, Mário César;Yamamoto, Danielle Reis;Speridi?o, Patrícia da Graa Leite;Morais, Mauro Batista de;
Jornal de Pediatria , 2010, DOI: 10.2223/JPED.1967
Abstract: objectives: to report the results of open challenge tests performed in children fed with cow's milk-free diet. descriptions: cross-sectional study evaluating cow's milk open challenge performed under supervision in a hospital setting during 2.5 hours and ambulatory follow-up for 30 days when no immediate reaction occurred. one hundred and twenty-one patients were included, with ages between 4 and 95 months. cow's milk open challenge tests were positive in 28 patients (23.1%). a clinical manifestation of cow's milk allergy different from the one presented at diagnosis occurred in 12 (24.9%) patients with positive challenge. positive challenge was more frequent (p = 0.042) in patients fed with extensively hydrolyzed formulae or amino acid-based formulae (30.3%) when compared to those fed with other exclusion diets (14.5%). conclusion: open challenge allowed the interruption of exclusion diet in a significant proportion of the patients.
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