A Geometric Characterization of Interpolation in $\hat{\E}^\prime(\R)$

We give a geometric description of the interpolating varieties for the algebra of Fourier transforms of distributions (or Beurling ultradistributions) with compact support on the real line.

Geometric characterization of red blood cells. Differentiation of normal and pathologic samples

Introduction. Fractal geometry measures the irregularity of abstract and natural objects with the fractal dimension. Fractal calculations have been applied to the structures of the human body and to quantifications in physiology from the theory of dynamic systems.Material and Methods. The fractal dimensions were calculated, the number of occupation spaces in the space border of box counting and the area of two red blood cells groups, 7 normal ones, group A, and 7 abnormal, group B, coming from patient and of bags for transfusion, were calculated using the method of box counting and a software developed for such effect. The obtained measures were compared, looking for differences between normal and abnormal red blood cells, with the purpose of differentiating samples.Results. The abnormality characterizes by a number of squares of occupation of the fractal space greater or equal to 180; values of areas between 25.117 and 33.548 correspond to normality. In case that the evaluation according to the number of pictures is of normality, must be confirmed with the value of the area applied to adjacent red blood cells within the sample, that in case of having values by outside established and/or the greater or equal spaces to 180, they suggest abnormality of the sample.Conclusions. The developed methodology is effective to differentiate the red globules alterations and probably useful in the analysis of bags of transfusion for clinical use 

A soft-tetramer model for diblock copolymer melts: structure formation and geometric characterization

The ability of block copolymers to spontaneously self-assemble into a variety of ordered nano-structures not only makes them a scientifically interesting system for the investigation of order-disorder phase transitions, but also offers a wide range of nano-technological applications. The architecture of a diblock is the most simple among the block copolymer systems, hence it is often used as a model system in both experiment and theory. We introduce a new soft-tetramer model for efficient computer simulations of diblock copolymer melts. The instantaneous non-spherical shape of polymer chains in molten state is incorporated by modeling each of the two blocks as two soft spheres. The interactions between the spheres are modeled in a way that the diblock melt tends to microphase separate with decreasing temperature. Using Monte Carlo simulations, we determine the equilibrium structures at variable values of the two relevant control parameters, the diblock composition and the incompatibility of unlike components. The simplicity of the model allows us to scan the control parameter space in a completeness that has not been reached in previous molecular simulations.The resulting phase diagram shows clear similarities with the phase diagram found in experiments. Moreover, we show that structural details of block copolymer chains can be reproduced by our simple model.We develop a novel method for the identification of the observed diblock copolymer mesophases that formalizes the usual approach of direct visual observation,using the characteristic geometry of the structures. A cluster analysis algorithm is used to determine clusters of each component of the diblock, and the number and shape of the clusters can be used to determine the mesophase.We also employ methods from integral geometry for the identification of mesophases and compare their usefulness to the cluster analysis approach.To probe the properties of our model in confinement, we perform molecular dynamics simulations of atomistic polyethylene melts confined between graphite surfaces. The results from these simulations are used as an input for an iterative coarse-graining procedure that yields a surface interaction potential for the soft-tetramer model. Using the interaction potential derived in that way, we perform an initial study on the behavior of the soft-tetramer model in confinement. Comparing with experimental studies, we find that our model can reflect basic features of confined diblock copolymer melts.

A geometric characterization of the upper bound for the span of the jones polynomial

Let D be a link diagram with n crossings, sA and sB be its extreme states and |sAD| (respectively, |sBD|) be the number of simple closed curves that appear when smoothing D according to sA (respectively, sB). We give a general formula for the sum |sAD| + |sBD| for a k-almost alternating diagram D, for any k, characterizing this sum as the number of faces in an appropriate triangulation of an appropriate surface with boundary. When D is dealternator connected, the triangulation is especially simple, yielding |sAD| + |sBD| = n + 2 - 2k. This gives a simple geometric proof of the upper bound of the span of the Jones polynomial for dealternator connected diagrams, a result first obtained by Zhu [On Kauffman brackets, J. Knot Theory Ramifications6(1) (1997) 125–148.]. Another upper bound of the span of the Jones polynomial for dealternator connected and dealternator reduced diagrams, discovered historically first by Adams et al. [Almost alternating links, Topology Appl.46(2) (1992) 151–165.], is obtained as a corollary. As a new application, we prove that the Turaev genus is equal to the number k of dealternator crossings for any dealternator connected diagram

Technologies for Anatomical and Geometric Characterization of the Corneal Structure and Anterior Segment: A Review

Corneal and anterior segment imaging techniques have become a crucial tool in the clinical practice of ophthalmology, with a great variety of applications, such as corneal curvature and pachymetric analysis, detection of ectatic corneal conditions, anatomical study of the anterior segment prior to phakic intraocular lens implantation, or densitometric analysis of the crystalline lens. From the Placido-based systems that allow only a characterization of the geometry of the anterior corneal surface to the Scheimpflug photography-based systems that provide a characterization of the cornea, anterior chamber, and crystalline lens, there is a great variety of devices with the capability of analyzing different anatomical parameters with very high precision. To date, Scheimpflug photography-based systems are the devices providing the more complete analysis of the anterior segment in a non-invasive way. More developments are required in anterior segment imaging technologies in order to improve the analysis of the crystalline lens structure as well as the ocular structures behind the iris in a non-invasive way when the pupil is not dilated.

Ensaios em pontes

Dissertação para a obtenção do grau de Mestre em Engenharia Civil na Área de Especialização em Estruturas

Equidistribution estimates for Fekete points on complex manifolds

We study the equidistribution of Fekete points in a compact complex manifold. These are extremal point configurations defined through sections of powers of a positive line bundle. Their equidistribution is a known result. The novelty of our approach is that we relate them to the problem of sampling and interpolation on line bundles, which allows us to estimate the equidistribution of the Fekete points quantitatively. In particular we estimate the Kantorovich-Wasserstein distance of the Fekete points to its limiting measure. The sampling and interpolation arrays on line bundles are a subject of independent interest, and we provide necessary density conditions through the classical approach of Landau, that in this context measures the local dimension of the space of sections of the line bundle. We obtain a complete geometric characterization of sampling and interpolation arrays in the case of compact manifolds of dimension one, and we prove that there are no arrays of both sampling and interpolation in the more general setting of semipositive line bundles.

An axiomatization of the nucleolus of the assignment game

[cat] En el domini dels jocs bilaterals d’assignació, es presenta una axiomàtica del nucleolus com l´unica solució que compleix les propietats de consistència respecte del joc derivat definit per Owen (1992) i monotonia de les queixes dels sectors respecte de la seva cardinalitat. Com a conseqüència obtenim una caracterització geomètrica del nucleolus mitjançant una propietat de bisecció més forta que la que satisfan els punts del kernel (Maschler et al, 1979).

An axiomatization of the nucleolus of the assignment game

[cat] En el domini dels jocs bilaterals d’assignació, es presenta una axiomàtica del nucleolus com l´unica solució que compleix les propietats de consistència respecte del joc derivat definit per Owen (1992) i monotonia de les queixes dels sectors respecte de la seva cardinalitat. Com a conseqüència obtenim una caracterització geomètrica del nucleolus mitjançant una propietat de bisecció més forta que la que satisfan els punts del kernel (Maschler et al, 1979).

Axiomatization of the nucl eolus of assignment games

On the domain of general assignment games (with possible reservation prices) the core is axiomatized as the unique solution satisfying two consistency principles: projection consistency and derived consistency. Also, an axiomatic characterization of the nucleolus is given as the unique solution that satisfies derived consistency and equal maximum complaint between groups. As a consequence, we obtain a geometric characterization of the nucleolus. Maschler et al. (1979) provide a geometrical characterization for the intersection of the kernel and the core of a coalitional game, showing that those allocations that lie in both sets are always the midpoint of certain bargaining range between each pair of players. In the case of the assignment game, this means that the kernel can be determined as those core allocations where the maximum amount, that can be transferred without getting outside the core, from one agent to his / her optimally matched partner equals the maximum amount that he / she can receive from this partner, also remaining inside the core. We now prove that the nucleolus of the assignment game can be characterized by requiring this bisection property be satisfied not only for optimally matched pairs but also for optimally matched coalitions. Key words: cooperative games, assignment game, core, nucleolus

Innovative LIDAR 3D dynamic measurement system to estimate fruit-tree leaf area

In this work, a LIDAR-based 3D Dynamic Measurement System is presented and evaluated for the geometric characterization of tree crops. Using this measurement system, trees were scanned from two opposing sides to obtain two three-dimensional point clouds. After registration of the point clouds, a simple and easily obtainable parameter is the number of impacts received by the scanned vegetation. The work in this study is based on the hypothesis of the existence of a linear relationship between the number of impacts of the LIDAR sensor laser beam on the vegetation and the tree leaf area. Tests performed under laboratory conditions using an ornamental tree and, subsequently, in a pear tree orchard demonstrate the correct operation of the measurement system presented in this paper. The results from both the laboratory and field tests confirm the initial hypothesis and the 3D Dynamic Measurement System is validated in field operation. This opens the door to new lines of research centred on the geometric characterization of tree crops in the field of agriculture and, more specifically, in precision fruit growing.

Caracterização geométrica de um sistema fluvial, formação Ttaquaquecetuba, Terciário da Bacia de São Paulo

The objective of this study is the geometric characterization of a fluvial system, exemplified by the Itaquaquecetuba Formation. The studied area is a quarry located in Itaquaquecetuba, distant 35 km from the city of São Paulo, which is inserted in the context of São Paulo Basin. Fluvial systems are important hydrocarbon reservoirs, and this study may contribute with an analogue for ancient reservoirs. It was elaborated ten facies logs along a distance of 200 m (log spacing of 20 m), with a vertical column (thickness) of 40 m for each log. Eight facies cycles, and its lateral chrono-correlation allowed to map the potential reservoir and non-reservoir facies within each cycle. Regarding the depositional model for the studied section, it is assumed an alluvial fan system composed of meandering and ribbon-type fluvial channels.

Measuring the bending of asymmetric planar EAP structures

The geometric characterization of low-voltage dielectric electro-active polymer (EAP) structures, comprised of nanometer thickness but areas of square centimeters, for applications such as artificial sphincters requires methods with nanometer precision. Direct optical detection is usually restricted to sub-micrometer resolution because of the wavelength of the light applied. Therefore, we propose to take advantage of the cantilever bending system with optical readout revealing a sub-micrometer resolution at the deflection of the free end. It is demonstrated that this approach allows us to detect bending of rather conventional planar asymmetric, dielectric EAP-structures applying voltages well below 10 V. For this purpose, we built 100 μm-thin silicone films between 50 nm-thin silver layers on a 25 μm-thin polyetheretherketone (PEEK) substrate. The increase of the applied voltage in steps of 50 V until 1 kV resulted in a cantilever bending that exhibits only in restricted ranges the expected square dependence. The mean laser beam displacement on the detector corresponded to 6 nm per volt. The apparatus will therefore become a powerful mean to analyze and thereby improve low-voltage dielectric EAP-structures to realize nanometer-thin layers for stack actuators to be incorporated into artificial sphincter systems for treating severe urinary and fecal incontinence.

Caracterização geométrica e mecânica de macrofibras poliméricas.

Uma grande diversidade de macrofibras poliméricas para reforço de concreto se encontram disponibilizadas hoje em dia. Por natureza estas fibras apresentam grande diversidade de características e propriedades. Estas variações afetam sua atuação como reforço no concreto. No entanto, não há normas brasileiras sobre o assunto e as metodologias de caracterização de normas estrangeiras apresentam divergências. Algumas normas definem que a caracterização do comportamento mecânico deva ser feita nos fios originais e outras que se devam utilizar métodos definidos para caracterização de materiais metálicos. A norma EN14889-2:2006 apresenta maior abrangência, mas deixa dúvidas quanto à adequação dos critérios de caracterização geométrica das fibras e não define um método de ensaio específico para sua caracterização mecânica. Assim, há a necessidade de estabelecimento de uma metodologia que permita a realização de um programa de controle de qualidade da fibra nas condições de emprego. Esta metodologia também proporcionaria uma forma de caracterização do material para estudos experimentais, o que permitiria maior fundamentação científica desses trabalhos que, frequentemente, fundamentam-se apenas em dados dos fabricantes. Assim, foi desenvolvido um estudo experimental focando a caracterização de duas macrofibras poliméricas disponíveis no mercado brasileiro. Focou-se o estudo na determinação dos parâmetros geométricos e na caracterização mecânica através da determinação da resistência à tração e avaliação do módulo de elasticidade. Na caracterização geométrica foi adotada como referência a norma europeia EN14889-2:2006. As medições do comprimento se efetuaram por dois métodos: o método do paquímetro e o método de análise de imagens digitais, empregando um software para processamento das imagens. Para a medição do diâmetro, além das metodologias mencionadas, foi usado o método da densidade. Conclui-se que o método do paquímetro, com o cuidado de esticar previamente as macrofibras, e o método das imagens digitais podem ser igualmente utilizados para medir o comprimento. Já parar determinar o diâmetro, recomenda-se o método da densidade. Quanto à caracterização mecânica, foi desenvolvida uma metodologia própria a partir de informações obtidas de outros ensaios. Assim, efetuaram-se ensaios de tração direta nas macrofibras coladas em molduras de tecido têxtil. Complementarmente, foi avaliado também o efeito do contato abrasivo das macrofibras com os agregados durante a mistura em betoneira no comportamento mecânico do material. Também se avaliou o efeito do método de determinação da área da seção transversal nos resultados medidos no ensaio de tração da fibra. Conclui-se que o método proposto para o ensaio de tração direta da fibra é viável, especialmente para a determinação da resistência à tração. O valor do módulo de elasticidade, por sua vez, acaba sendo subestimado. A determinação da área da seção da fibra através do método da densidade forneceu também os melhores resultados. Além disso, comprovou-se que o atrito das fibras com o agregado durante a mistura compromete o comportamento mecânico, reduzindo tanto a resistência quanto o módulo de elasticidade. Assim, pode-se afirmar que a metodologia proposta para o controle geométrico e mecânico das macrofibras poliméricas é adequada para a caracterização do material.

Análise computacional de imagens de lâminas delgadas na predição dos parâmetros hidráulicos porosidade e condutividade hidráulica do aquífero Barreiras-RN

The understanding of the occurrence and flow of groundwater in the subsurface is of fundamental importance in the exploitation of water, just like knowledge of all associated hydrogeological context. These factors are primarily controlled by geometry of a certain pore system, given the nature of sedimentary aquifers. Thus, the microstructural characterization, as the interconnectivity of the system, it is essential to know the macro properties porosity and permeability of reservoir rock, in which can be done on a statistical characterization by twodimensional analysis. The latter is being held on a computing platform, using image thin sections of reservoir rock, allowing the prediction of the properties effective porosity and hydraulic conductivity. For Barreiras Aquifer to obtain such parameters derived primarily from the interpretation of tests of aquifers, a practice that usually involves a fairly complex logistics in terms of equipment and personnel required in addition to high cost of operation. Thus, the analysis and digital image processing is presented as an alternative tool for the characterization of hydraulic parameters, showing up as a practical and inexpensive method. This methodology is based on a flowchart work involving sampling, preparation of thin sections and their respective images, segmentation and geometric characterization, three-dimensional reconstruction and flow simulation. In this research, computational image analysis of thin sections of rocks has shown that aquifer storage coefficients ranging from 0,035 to 0,12 with an average of 0,076, while its hydrogeological substrate (associated with the top of the carbonate sequence outcropping not region) presents effective porosities of the order of 2%. For the transport regime, it is evidenced that the methodology presents results below of those found in the bibliographic data relating to hydraulic conductivity, mean values of 1,04 x10-6 m/s, with fluctuations between 2,94 x10-6 m/s and 3,61x10-8 m/s, probably due to the larger scale study and the heterogeneity of the medium studied.