Construções geométricas por dobradura (ORIGAMI): aplicações ao ensino básico

A presente dissertação tem o objetivo de mostrar a arte Origami sob um contexto matemático, apresentando um pequeno resumo dos aspectos história e o desenvolvimento do Origami ao longo do tempo e dando maior destaque às suas aplicações na matemática, com o emprego dos axiomas de Huzita e a proposta de ampliação deste conjunto de axiomas com a inclusão da circunferência no papel Origami. Com o uso das técnicas de dobraduras, este trabalho mostra várias aplicações do Origami na matemática, tais como: a solução de alguns problemas clássicos, a construção de polígonos, a demonstração da soma dos ângulos internos de um triângulo, cálculo de algumas áreas, a solução de alguns problemas de máximos e mínimos, seguidos dos conceitos matemático envolvidos em cada um deles. E a inclusão da circunferência no plano Origami permitiu ainda, o estudo das construções das cônicas por dobraduras.

José Carlos Rodrigues: um interlocutor privilegiado nos bastidores do poder (1867-1915)

A presente tese examina a história de vida do homem de negócios e jornalista fluminense José Carlos Rodrigues (1844 1923), detendo-se, em particular, no lapso de tempo compreendido entre os anos de 1867 e 1915. A primeira data corresponde ao início da temporada de José Carlos nos Estados Unidos da América e a segunda, ao seu afastamento do Jornal do Commercio, órgão da imprensa carioca, do qual foi proprietário entre 1890 e 1915. A pesquisa empreendida analisa as amizades pessoais, além dos vínculos profissionais estabelecidos por Rodrigues, a partir de sua inserção nos campos da imprensa, da política, dos negócios e das letras, no Rio de Janeiro, em Nova York e em Londres, cidades em que viveu no período abordado. Evidencia, também, que essa ampla rede de sociabilidade foi sendo tecida, progressivamente, não apenas pelo conhecido caráter empreendedor do publicista, mas, sobretudo, graças a arranjos sociais e políticos, através do acesso a informações privilegiadas. Mais do que bibliófilo e filantropo, José Carlos Rodrigues atuou nos círculos políticos, interferindo ora de forma clara, ora nos bastidores do poder.

Palinologia e taxonomia de espécies de Praxelis Cass. (subtribo Praxelinae, Eupatorieae-Asteraceae) ocorrentes no Brasil

Asteraceae é a segunda maior família de angiospermas com ca. 25.000 espécies distribuídas por todo mundo. Praxelis é o segundo maior gênero em número de espécies da subtribo Praxelinae, se caracteriza principalmente por apresentar capítulos cilíndricos/campanulados, receptáculo cônico e glabro, cipselas com carpopódio assimétrico e pápus com cerdas numerosas e barbeladas. No Brasil, as espécies predominam no Cerrado. O objetivo do presente trabalho foi analisar a palinologia e a taxonomia das espécies de Praxelis Cass. ocorrentes no Brasil. O material botânico utilizado foi obtido através de exsicatas depositadas nos herbários brasileiros. Os grãos de pólen foram acetolisados, medidos, descritos e ilustrados sob ML. Para observar detalhes da superfície e abertura, grãos de pólen não acetolisados foram analisados em MEV e, posteriormente, eletromicrografados. As peças florais foram colocadas sobre os mesmos suportes metálicos cobertos com fita dupla-face de carbono, previamente numerados. Para análise em MET, os grãos de pólen foram corados em cacodilato tamponado 0,125% OsO4, concentrados em pastilhas de ágar, e foram embebecidos em resina Epon-Araldite. As folhas, a capitulescência, o indumento do pedúnculo e o número de brácteas involucrais foram atributos relevantes para caracterizar as espécies, sobretudo o tamanho do invólucro e sua consistência. Foram caracterizados os grãos de pólen quanto à forma, ao tamanho, ao tipo de abertura, à polaridade e à constituição da exina. Foram descritos como: pequenos a médios, isopolares, oblato-esferoidais a subprolatos, 3(4)-colporados, com margem ornamentada, endoabertura com ou sem constricção, com presença de cávea, a sexina é espinhosa e sempre maior do que a nexina. Portanto, as análises palinológica e taxonômica foram utilizadas para segregar as espécies de Praxelis, porém apenas os atributos morfológicos externos foram mais informativos para diferenciar as espécies desse gênero.

Quantifying seascape structure: extending terrestrial spatial pattern metrics to the marine realm

Spatial pattern metrics have routinely been applied to characterize and quantify structural features of terrestrial landscapes and have demonstrated great utility in landscape ecology and conservation planning. The important role of spatial structure in ecology and management is now commonly recognized, and recent advances in marine remote sensing technology have facilitated the application of spatial pattern metrics to the marine environment. However, it is not yet clear whether concepts, metrics, and statistical techniques developed for terrestrial ecosystems are relevant for marine species and seascapes. To address this gap in our knowledge, we reviewed, synthesized, and evaluated the utility and application of spatial pattern metrics in the marine science literature over the past 30 yr (1980 to 2010). In total, 23 studies characterized seascape structure, of which 17 quantified spatial patterns using a 2-dimensional patch-mosaic model and 5 used a continuously varying 3-dimensional surface model. Most seascape studies followed terrestrial-based studies in their search for ecological patterns and applied or modified existing metrics. Only 1 truly unique metric was found (hydrodynamic aperture applied to Pacific atolls). While there are still relatively few studies using spatial pattern metrics in the marine environment, they have suffered from similar misuse as reported for terrestrial studies, such as the lack of a priori considerations or the problem of collinearity between metrics. Spatial pattern metrics offer great potential for ecological research and environmental management in marine systems, and future studies should focus on (1) the dynamic boundary between the land and sea; (2) quantifying 3-dimensional spatial patterns; and (3) assessing and monitoring seascape change.

Gaussian etched single transverse mode vertical-cavity surface-emitting laser

A continuous Gaussian profile matched to the fundamental mode was etched onto the aperture of a vertical cavity surface emitting laser (VCSEL). Single Gaussian spot emission was achieved over the entire operating current range.

Reconstruction of surfaces of revolution from single uncalibrated views

This paper addresses the problem of recovering the 3D shape of a surface of revolution from a single uncalibrated perspective view. The algorithm introduced here makes use of the invariant properties of a surface of revolution and its silhouette to locate the image of the revolution axis, and to calibrate the focal length of the camera. The image is then normalized and rectified such that the resulting silhouette exhibits bilateral symmetry. Such a rectification leads to a simpler differential analysis of the silhouette, and yields a simple equation for depth recovery. It is shown that under a general camera configuration, there will be a 2-parameter family of solutions for the reconstruction. The first parameter corresponds to an unknown scale, whereas the second one corresponds to an unknown attitude of the object. By identifying the image of a latitude circle, the ambiguity due to the unknown attitude can be resolved. Experimental results on real images are presented, which demonstrate the quality of the reconstruction. © 2004 Elsevier B.V. All rights reserved.

Monitoring tunnel deformation induced by close-proximity bored tunneling using distributed optical fiber strain measurements

The paper describes the use of optical fiber Brillouin Optical Time Domain Reflectometry (BOTDR) to monitor the strain distribution in an existing tunnel while a twin tunnel was bored at close-proximity. The twin circular bored tunnels between Serangoon and Bartley stations on the new Circle Line Stage 3 subway in Singapore were constructed at close-proximity to avoid underpinning the foundations of adjacent buildings. The minimum clear separation of the two tunnels is 2.3m (0.4 times the tunnel diameter). The Outer Tunnel was constructed first, followed by the Inner Tunnel, with the earth-pressure balance tunnel boring machines maintained at a minimum of 100m apart. In this trial application of BOTDR, the strain distribution along the Outer Tunnel was measured, in order to monitor its deformation due to the boring of the Inner Tunnel at close-proximity. The aim of the trial application was to determine the practicality of this monitoring method for future use in 'live' tunnels. This paper compares the measurements obtained from optical fiber BOTDR with conventional methods of tunnel monitoring and describes preliminary installation and workmanship guidelines derived from lessons learnt during this trial. © 2007 ASCE.

Some new bounds on eigenvalues of the Hadamard product and the Fan product of matrices

Let A and B be nonsingular M-matrices. A lower bound on the minimum eigenvalue q(B circle A(-1)) for the Hadamard product of A(-1) and B, and a lower bound on the minimum eigenvalue q(A star B) for the Fan product of A and B are given. In addition, an upper bound on the spectral radius rho(A circle B) of nonnegative matrices A and B is also obtained. These bounds improve several existing results in some cases and the estimating formulas are easier to calculate for they are only depending on the entries of matrices A and B. (C) 2009 Elsevier Inc. All rights reserved.

Effects of constraint curvature on structural instability: tensile buckling and multiple bifurcations

Bifurcation of an elastic structure crucially depends on the curvature of the constraints against which the ends of the structure are prescribed to move, an effect which deserves more attention than it has received so far. In fact, we show theoretically and we provide definitive experimental verification that an appropriate curvature of the constraint over which the end of a structure has to slide strongly affects buckling loads and can induce: (i.) tensile buckling; (ii.) decreasing- (softening), increasing- (hardening), or constant-load (null stiffness) postcritical behaviour; (iii.) multiple bifurcations, determining for instance two bifurcation loads (one tensile and one compressive) in a single-degree-of-freedom elastic system. We show how to design a constraint profile to obtain a desired postcritical behaviour and we provide the solution for the elastica constrained to slide along a circle on one end, representing the first example of an inflexional elastica developed from a buckling in tension. These results have important practical implications in the design of compliant mechanisms and may find applications in devices operating in quasi-static or dynamic conditions.

Innovative fabrication of PZT pillar arrays by a colloidal approach

An innovative approach for fabricating pillar arrays for ultrasonic transducer applications is disclosed. It involves the preparation of concentrated piezoelectric lead zirconate titanate (PZT) suspensions in aqueous solutions of epoxy resin and its polymerization upon adding a polyamine based hardener. Zeta potential and rheological measurements revealed that 1wt.% dispersant, 20wt.% of epoxy resin and a hardener/epoxy resin ratio of 0.275mLg -1, were the optimized contents to obtain strong PZT samples with high green strength (35.21±0.39MPa). Excellent ellipsoidal and semi-circle shaped pillar arrays presenting lateral dimensions lower than 10μm and 100μm height were successfully achieved. The organics burning off was conducted at 500°C for 2h at a heating rate of 1°Cmin -1. Sintering was then carried out in the same heating cycle at 1200°C for 1h. The microstructures of the green and sintered ceramics were homogeneous and no large defects could be detected. © 2011 Elsevier Ltd.

Consensus on homogeneous manifolds

The present paper considers distributed consensus algorithms for agents evolving on a connected compact homogeneous (CCH) manifold. The agents track no external reference and communicate their relative state according to an interconnection graph. The paper first formalizes the consensus problem for synchronization (i.e. maximizing the consensus) and balancing (i.e. minimizing the consensus); it thereby introduces the induced arithmetic mean, an easily computable mean position on CCH manifolds. Then it proposes and analyzes various consensus algorithms on manifolds: natural gradient algorithms which reach local consensus equilibria; an adaptation using auxiliary variables for almost-global synchronization or balancing; and a stochastic gossip setting for global synchronization. It closes by investigating the dependence of synchronization properties on the attraction function between interacting agents on the circle. The theory is also illustrated on SO(n) and on the Grassmann manifolds. ©2009 IEEE.

Consensus optimization on manifolds

The present paper considers distributed consensus algorithms that involve N agents evolving on a connected compact homogeneous manifold. The agents track no external reference and communicate their relative state according to a communication graph. The consensus problem is formulated in terms of the extrema of a cost function. This leads to efficient gradient algorithms to synchronize (i.e., maximizing the consensus) or balance (i.e., minimizing the consensus) the agents; a convenient adaptation of the gradient algorithms is used when the communication graph is directed and time-varying. The cost function is linked to a specific centroid definition on manifolds, introduced here as the induced arithmetic mean, that is easily computable in closed form and may be of independent interest for a number of manifolds. The special orthogonal group SO (n) and the Grassmann manifold Grass (p, n) are treated as original examples. A link is also drawn with the many existing results on the circle. © 2009 Society for Industrial and Applied Mathematics.

Stabilization of planar collective motion with limited communication

This paper proposes a design methodology to stabilize relative equilibria in a model of identical, steered particles moving in the plane at unit speed. Relative equilibria either correspond to parallel motion of all particles with fixed relative spacing or to circular motion of all particles around the same circle. Particles exchange relative information according to a communication graph that can be undirected or directed and time-invariant or time-varying. The emphasis of this paper is to show how previous results assuming all-to-all communication can be extended to a general communication framework. © 2008 IEEE.

Synchronization and balancing on the N-torus

In this paper, we study the behavior of a network of N agents, each evolving on the circle. We propose a novel algorithm that achieves synchronization or balancing in phase models under mild connectedness assumptions on the (possibly time-varying and unidirectional) communication graphs. The global convergence analysis on the N-torus is a distinctive feature of the present work with respect to previous results that have focused on convergence in the Euclidean space. © 2006 Elsevier B.V. All rights reserved.

Oscillator models and collective motion: Splay state stabilization of self-propelled particles

This paper presents a Lyapunov design for the stabilization of collective motion in a planar kinematic model of N particles moving at constant speed. We derive a control law that achieves asymptotic stability of the splay state formation, characterized by uniform rotation of N evenly spaced particles on a circle. In designing the control law, the particle headings are treated as a system of coupled phase oscillators. The coupling function which exponentially stabilizes the splay state of particle phases is combined with a decentralized beacon control law that stabilizes circular motion of the particles. © 2005 IEEE.