Submitted by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-09-01T16:28:42Z No. of bitstreams: 1 arquivototal.pdf: 706603 bytes, checksum: 4bcd99d1191e9b1e81f9c94952955989 (MD5) / Approved for entry into archive by Fernando Souza (fernandoafsou@gmail.com) on 2017-09-04T10:55:58Z (GMT) No. of bitstreams: 1 arquivototal.pdf: 706603 bytes, checksum: 4bcd99d1191e9b1e81f9c94952955989 (MD5) / Made available in DSpace on 2017-09-04T10:55:58Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 706603 bytes, checksum: 4bcd99d1191e9b1e81f9c94952955989 (MD5) Previous issue date: 2015-02-27 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work, we will study inequalities between real numbers. In special, we will study the inequalities between means, Bernoulli’s inequality, the Cauchy-Schwarz inequality and Chebishev’s inequality and some applications. / Neste trabalho estudaremos algumas desigualdades entre números reais. De maneira especial, estudaremos as desigualdades das médias, as desigualdades de Bernoulli, Cauchy-Schwarz e de Chebishev, assim como algunas aplicações.

Neste trabalho, procuramos resolver o problema direto da equação da viga de Euler- Bernoulli bi-engastada com condições iniciais nulas. Estudamos o problema inverso da viga, que consiste em identificar a fonte de vibração, modelada como um elemento em L2, usando como dado a velocidade de um ponto arbitrário da viga, durante um intervalo de tempo arbitrariamente pequeno. A relevância deste trabalho na Engenharia encontra-se, por exemplo, na identificação de danos estruturais em vigas. / In this work, we try to solve the direct problem of the clamped-clamped Euler- Bernoulli beam equation, with zero initial conditions. We study the inverse problem of the beam, consisting in the identification of the source of vibration, shaped as an element in L2, using as data the speed from an arbitrary point of the beam, during a time interval arbitrarily small. The relevance of this work in Engineering, for example, is in the identification of structural damage in beams.

O problema de n?corpos é um dos problemas mais importantes em Sistemas Dinâmicos. Nós estudamos o modelo do problema dos três corpos restrito introduzido por Sitnikov. Nesse modelo os corpos primários tem a mesma massa e o terceiro corpo é de massa muito pequena com respeito aos corpos primários. Usando os métodos de Alekseev, nós mostramos a existência de uma ?ferradura de Smale?como um subsistema da dinâmica do terceiro corpo e concluímos ricas conseqüências probabilísticas. Nós também estudamos o problema pelo método de Melnikov / The n?body problem is one of the most important problems in dynamical systems. We study the model introduced by Sitnikov of restricted three body problem. In this model the primaries are of equal mass and the third body is very small with respect to the primaries. Using methods of Alekseev, we show the existence of ?Smale horseshoe?as a subsystem of the dynamic of the third body and conclude rich probabilistic consequences. We also study the same problem by Melnikov?s method

We give conditions which, given two Bernoulli trial measures, determine whether there exists a homeomorphism of Cantor space which sends one measure to the other, answering a question of Oxtoby. We then provide examples, relating these results to the notions of good and refinable measures on Cantor space.

Ingeniero Civil / Los nuevos desafíos arquitectónicos, han ocasionado que los muros de hormigón armado nacionales, posean largos importantes, con secciones transversales no siempre rectangulares, por lo tanto, los modelos basados en la Hipótesis de Bernoulli y el cálculo del ancho efectivo, podrían no ser válidos para el diseño y detallamiento de estas nuevas configuraciones. Para estudiar estos supuestos, el trabajo comienza validando un modelo tipo shell no lineal para muros de hormigón armado, desarrollado en el framework de elementos finitos SAFE-TB [21]. Usando ensayos experimentales encontrados en la literatura, se obtuvieron resultados satisfactorios para el comportamiento global y el perfil de deformaciones. Modelando muros de hormigón armado con secciones transversales T, canal y compuesta, se verifica que el modelo bajo Hipótesis de Bernoulli, sobrestima la capacidad para muros chatos, en cambio, estima de buena forma la capacidad para muros esbeltos. Adicionalmente, es posible calibrar un modelo analítico para el perfil de deformación del ala traccionada en muros con sección T. Por otra parte, al incluir el efecto del corte en la modelación, ocurre una amplificación de la compresión máxima y una reducción de la tracción máxima en el alma, observadas principalmente en muros chatos. Para evaluar estos efectos, se emplean modelos analíticos calibrados por Ahumada [4] para muros rectangulares. Además de la variación de las deformaciones entre los modelos, el modelo a flexión genera una posición del eje neutro similar al modelo con corte, en efecto, a partir de compresiones superiores al 0.3%, la línea neutra permanece invariable y entre valores de resistencia similares. Finalmente, se calculan los anchos efectivos con la tensión promedio del ala traccionada, encontrando que estos dependen principalmente del largo del ala y de la deriva de techo. Luego de la primera fluencia del ala, el ancho efectivo crece rápidamente, concluyendo que independiente de la geometría y de la esbeltez, el ancho efectivo del ala traccionada equivale a la totalidad de la sección.

IntelliDrive systems, including inter-vehicle communication and vehicle infrastructure integration, aim to improve safety, mobility, and efficiency of transportation. They build on the wireless ad hoc network technologies, enabling vehicles to communicate with roadside infrastructure and with each other. The process of information propagation in a multi-hop network underlies the system design and efficiency. As of now, the research has been restricted to a single road of traffic. This work expands the study of information propagation to two parallel roads, a step further towards the discrete network case. This thesis presents two methodologies to model the process of information propagation. By identifying an approximate Bernoulli process, we are able to derive the expectation and variance of propagation distance. A road separation distance of square root of 3 over 2 times the transmission range distinguishes two cases for approximating the success probability in the Bernoulli process. In addition, our results take the single road as a special case. The numerical test shows that the developed approximation works well. This work further identities a Markov property for instantaneous information propagation along two parallel roads based on two types of transmission regions. Communication capable vehicles are assumed to follow two homogeneous Poisson processes on both roads. The Markov property enables us to derive exact expectation and variance of the propagation distance and further, obtain a recursive formula for the probability distribution of successful propagation distance. The developed formulas enable numerical calculation of the characteristics of propagation process. We hope this research will shed light on studies of vehicular ad hoc networks on more general discrete roadway networks.

New measuring methods continue to be developed in the field of wind anemometry for various environments subject to low-speed and high-speed flows, turbulent-present flows, and ideal and non-ideal flows. As a result, anemometry has taken different avenues for these environments from the traditional cup model to sonar, hot-wire, and recent developments with sphere anemometers. Several measurement methods have modeled the air drag force as a quadratic function of the corresponding wind speed. Furthermore, by incorporating non-drag fluid forces in addition to the main drag force, a dynamic set of equations of motion for the deflection and strain of a spherical anemometer's beam can be derived. By utilizing the equations of motion to develop a direct relationship to a measurable parameter, such as strain, an approximation for wind speed based on a measurement is available. These ODE's for the strain model can then be used to relate directly the fluid speed (wind) to the strain along the beam’s length. The spherical anemometer introduced by the German researcher Holling presents the opportunity to incorporate the theoretical cantilevered Euler-Bernoulli beam with a spherical mass tip to develop a deflection and wind relationship driven by cross-area of the spherical mass and constriction of the shaft or the beam's bending properties. The application of Hamilton's principle and separation of variables to the Lagrangian Mechanics of an Euler-Bernoulli beam results in the equations of motion for the deflection of the beam as a second order partial differential equation (PDE). The boundary conditions of our beam's motion are influenced by the applied fluid forces of a relative drag force and the added mass and buoyancy of the sphere. Strain gauges will provide measurements in a practical but non-intrusive method and thus the concept of a measuring strain gauge is simulated. Young's Modulus creates a relationship between deflection and strain of an Euler-Bernoulli system and thus a strain and wind relation can be modeled as an ODE. This theoretical sphere anemometer's second order ODE allows for analysis of the linear and non-linear accuracies of the motion of this dynamic system at conventional high speed conditions.

Available fragile site identification software packages (FSM and FSM3) assume that all chromosomal breaks occur independently. However, under a Mendelian model of inheritance, homozygosity at fragile loci implies pairwise correlation between homologous sites. We construct correlation models for chromosomal breakage data in situations where either partitioned break count totals (per-site single-break and doublebreak totals) are known or only overall break count totals are known. We derive a likelihood ratio test and Neyman’s C( α) test for correlation between homologs when partitioned break count totals are known and outline a likelihood ratio test for correlation using only break count totals. Our simulation studies indicate that the C( α) test using partitioned break count totals outperforms the other two tests for correlation in terms of both power and level. These studies further suggest that the power for detecting correlation is low when only break count totals are reported. Results of the C( α) test for correlation applied to chromosomal breakage data from 14 human subjects indicate that detection of correlation between homologous fragile sites is problematic due to sparseness of breakage data. Simulation studies of the FSM and FSM3 algorithms using parameter values typical for fragile site data demonstrate that neither algorithm is significantly affected by fragile site correlation. Comparison of simulated fragile site misclassification rates in the presence of zero-breakage data supports previous studies (Olmsted 1999) that suggested FSM has lower false-negative rates and FSM3 has lower false-positive rates.

Research is performed to assess the viability of applying the least squares model to one-dimensional heat transfer and Euler-Bernoulli Beam Theory problems. Least squares models were developed for both the full and mixed forms of the governing one-dimensional heat transfer equation along weak form Galerkin models. Both least squares and weak form Galerkin models were developed for the first order and second order versions of the Euler-Bernoulli beams. Several numerical examples were presented for the heat transfer and Euler- Bernoulli beam theory. The examples for heat transfer included: a differential equation having the same form as the governing equation, heat transfer in a fin, heat transfer in a bar and axisymmetric heat transfer in a long cylinder. These problems were solved using both least squares models, and the full form weak form Galerkin model. With all four examples the weak form Galerkin model and the full form least squares model produced accurate results for the primary variables. To obtain accurate results with the mixed form least squares model it is necessary to use at least a quadratic polynominal. The least squares models with the appropriate approximation functions yielde more accurate results for the secondary variables than the weak form Galerkin. The examples presented for the beam problem include: a cantilever beam with linearly varying distributed load along the beam and a point load at the end, a simply supported beam with a point load in the middle, and a beam fixed on both ends with a distributed load varying cubically. The first two examples were solved using the least squares model based on the second order equation and a weak form Galerkin model based on the full form of the equation. The third problem was solved with the least squares model based on the second order equation. Both the least squares model and the Galerkin model calculated accurate results for the primary variables, while the least squares model was more accurate on the secondary variables. In general, the least-squares finite element models yield more acurate results for gradients of the solution than the traditional weak form Galkerkin finite element models. Extension of the present assessment to multi-dimensional problems and nonlinear provelms is awaiting attention.

Quantum mechanics is a theory developed to explain both particle and wave-like properties of small matter such as light and electrons. The consequences of the theory can be counter-intuitive but lead to mathematical and physical theory rich in fascinating phenomena and challenging questions. This dissertation investigates the nature of quantum systems in Bernoulli distributed random potentials for systems on the one dimensional lattice {0, 1, ..., L, L+1} ⊂ Z in the large system limit L → ∞. For single particle systems, the behavior of the low energy states is shown to be approximated by systems where positive potential is replaced by infinite potential. The approximate shape of these states is described, the asymptotics of their eigenvalues are calculated in the large system limit L → ∞, and a Lifschitz tail estimate on the sparsity of low energy states is proven. For interacting multi-particle systems, a Lieb-Liniger model with Bernoulli distributed potential is studied in the Gross-Pitaevskii approximation. First, to investigate localization in these settings, a general inequality is proven to bound from below the support of the mean-field. The bound depends on the per particle energy, number of particles, and interaction strength. Then, the ground state for the one-dimensional lattice with Bernoulli potential is studied in the large system limit. Specifically, the case where the product of interaction strength and particle density is near zero is considered to investigate whether localization can be recovered.