Oscilador harmônico amortecido e séries infinitas

Neste trabalho discute-se um arranjo experimental bastante simples e de baixo custo, cujo objetivo consiste em se exemplificar de forma concreta a aplicação de técnicas matemáticas envolvendo solução por séries infinitas destinadas ao estudo de determinado fenômeno físico. Esta prática desenvolvida e direcionada aos alunos de um curso de Graduação em Matemática, consiste basicamente de um estudo quantitativo relacionado ao comportamento oscilatório amortecido de um sistema constituído por uma massa acoplada a uma mola. Os resultados experimentais corroboraram muito bem a teoria fenomenológica e possibilitam a determinação numérica de uma constante física normalmente considerada desprezível, mencionada de passagem nos livros textos. Um fato de destaque deste trabalho referente ao fenômeno ondulatório estudado, ilimitado no tempo, mas limitado no espaço, é o de permitir uma boa discussão com os estudantes sobre o conceito de limite matemático.

A multidimensional version of the Carlson inequality

We give a multidimensional extension of a one-dimensional integral inequality due to F. Carlson. The extension presented here involves Lp spaces with mixed norms in a very natural way. © 1984.

Transient non-Darcy forced convective heat transfer from a flat plate embedded in a fluid-saturated porous medium

Transient non-Darcy forced convection on a flat plate embedded in a porous medium is investigated using the Forchheimer-extended Darcy law. A sudden uniform pressure gradient is applied along the flat plate, and at the same time, its wall temperature is suddenly raised to a high temperature. Both the momentum and energy equations are solved by retaining the unsteady terms. An exact velocity solution is obtained and substituted into the energy equation, which then is solved by means of a quasi-similarity transformation. The temperature field can be divided into the one-dimensional transient (downstream) region and the quasi-steady-state (upstream) region. Thus the transient local heat transfer coefficient can be described by connecting the quasi-steady-state solution and the one-dimensional transient solution. The non-Darcy porous inertia works to decrease the velocity level and the time required for reaching the steady-state velocity level. The porous-medium inertia delays covering of the plate by the steady-state thermal boundary layer. © 1990.

Coupled Bose-Einstein condensate: Collapse for attractive interaction

The collapse of trapped Boson-Einstein condensate (BEC) of atoms in states 1 and 2 was studied. When the interaction among the atoms in state i was attractive the component i of the condensate experienced collapse. When the interaction between an atom in state 1 and state 2 was attractive both components experienced collapse. The time-dependant Gross-Pitaevski (GP) equation was used to study the time evolution of the collapse. There was an alternate growth and decay in the number of particles experiencing collapse.

Otimização da distância de extração de madeira com forwarder

The activities and management operations of wood harvesting do not have good computational tools available to help the forest technicians with the task of cost reduction. In many cases, machines of high investment are used in wood harvesting without adequate operation planning; consequently, the cost per hour of these machines, which is high, could be reduced. Using technological resources such as the Geographic Information Systems (GIS) integrated with the Global Positioning System (GPS), which are the basis of precision harvesting. In this research, a technological tool capable of calculating and optimizing the average skidding distance of the forwarder was developed. It was used in stands of different sizes and formats through mathematical techniques and available functionalities in the Geographic Information System GRASS. The developed tool, called optimized model, divides the stand in small parts in relation to shorter skidding distances. The main variable considered was the alignment of plantation. The model was tested in eucalypt stands located in the State of São Paulo. Sixteen stands were randomly selected: eight with a rectangular polygon form, and eight with irregular polygon form. The main variables were collected in these stands. Results showed that the optimized model developed, is efficient and flexible. It was possible to divide the stands in small parts resulting in smaller skidding medium distances. The stands with irregular form had shorter skidding medium distances than the rectangular stands.

Synchronizing Brazilian Sign Language (LIBRAS) on videos for Open Digital TV with educational purposes

The TV is a potential midia of communication that affects all social classes and it is available in 98% of Brazilian homes. It has been used as a distributor of educational materials since the 1950s. By 2016 the Open Digital TV (ODTV) in Brazil might cover the entire national territory, replacing the TV with analog signals. Concerns about accessibility for People with Special Needs (PSN) in that media have become more intense since the 1990s worldwide. In Brazil, it is estimated 24.6 million of PSN, 23% of them having some type of hearing loss. Of these, 2.9% are reported as deafs. Brazilian Sign Language (LIBRAS) is considered the first literacy language for deaf people in Brazil. In this context, this paper presents a proposal to facilitate the generation of educational content for ODTV based on two components. One is called SynchrLIBRAS and allows subtitles synchronization in Portuguese and a LIBRAS translator window of videos downloaded from the Web. The second component allows the visualization of this content through the Brazilian System of Digital TV and IPTV - environments that implement the middleware Ginga-NCL. The main focus of this paper is the presentation of the first component: SynchrLIBRAS. This proposal has educational purposes, contributing to teach LIBRAS to people who may collaborate with social inclusion of the deaf people.

A class of hypergeometric polynomials with zeros on the unit circle: Extremal and orthogonal properties and quadrature formulas

The class of hypergeometric polynomials F12(-m,b;b+b̄;1-z) with respect to the parameter b=λ+iη, where λ>0, are known to have all their zeros simple and exactly on the unit circle |z|=1. In this note we look at some of the associated extremal and orthogonal properties on the unit circle and on the interval (-1,1). We also give the associated Gaussian type quadrature formulas. © 2012 IMACS.

Reduction of infinite dimensional systems to finite dimensions: Compact convergence approach

We consider parameter dependent semilinear evolution problems for which, at the limit value of the parameter, the problem is finite dimensional. We introduce an abstract functional analytic framework that applies to many problems in the existing literature for which the study of asymptotic dynamics can be reduced to finite dimensions via the invariant manifolds technique. Some practical models are considered to show wide applicability of the theory. © 2013 Society for Industrial and Applied Mathematics.

Perturbation of a nonautonomous problem in ℝn

In this paper, we prove a stability result about the asymptotic dynamics of a perturbed nonautonomous evolution equation in ℝn governed by a maximal monotone operator. Copyright © 2013 John Wiley & Sons, Ltd. Copyright © 2013 John Wiley & Sons, Ltd.

On computational aspects of discrete Sobolev inner products on the unit circle

In this paper, we show how to compute in O(n2) steps the Fourier coefficients associated with the Gelfand-Levitan approach for discrete Sobolev orthogonal polynomials on the unit circle when the support of the discrete component involving derivatives is located outside the closed unit disk. As a consequence, we deduce the outer relative asymptotics of these polynomials in terms of those associated with the original orthogonality measure. Moreover, we show how to recover the discrete part of our Sobolev inner product. © 2013 Elsevier Inc. All rights reserved.

Simulação de choques em modelo de crescimento com interdependência

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Ferramentas matemáticas para modelagem da temperatura com aplicação em graus-dias para otimização da produção agrícola

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

O método de pontos interiores no planejamento da radioterapia

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Otimização da distância de extração de madeira com forwarder

Pós-graduação em Agronomia (Energia na Agricultura) - FCA

Programação linear no planejamento do tratamento de câncer por radiocirurgia

Medical Physics has been reaching an important role among several lines in Science, providing means for the improvement of several theories and procedures. Currently, its main application is related with the use of ionizing radiations, specially, in treatment procedures such as Radiotherapy. Radiosurgery is a Radiotherapy technique which consists in administering a single tumoricidal dose of radiation exclusively to the tumorous lesion. It becomes then an interesting alternative to surgical treatment, mainly in cerebral metastases, which are the most frequent cerebral tumors in the central nervous system. The radio neurosurgical team works out a planning for the Radiosurgery treatment, aiming for obtaining an appropriate ideal treatment for each case. For the working out of this treatment planning, Computed Tomography images of the region to be treated are obtained, digitalized and later, fused with nuclear magnetic resonance images. Through these images, critical structures, organs at risk and lesions are localized. After this, calculations are made to determine three-dimensional positions of isocenters, isodose curves, prescribed dose, collimators sizes, position, numbers and respective weight of isocentric conformal fields, and others. The treatment planning is commonly based in desired levels of dose for specific types of tumors and organs at risk concerning the irradiated region. Theses levels of dose are chosen in a way that a high probability of cure may be achieved and meanwhile, that the probability of complications, in whichever organ at risk, may be minimal. Thus, many researches have been carried out, showing that mathematical techniques may help to obtain an optimal planning for the treatment of cerebral metastases. Among the methods of optimization in the study...(Complete abstract click electronic access below)