Modelo de risco controlado por resseguro e desigualdades para a probabilidade de ruína

In the work reported here we present theoretical and numerical results about a Risk Model with Interest Rate and Proportional Reinsurance based on the article Inequalities for the ruin probability in a controlled discrete-time risk process by Ros ario Romera and Maikol Diasparra (see [5]). Recursive and integral equations as well as upper bounds for the Ruin Probability are given considering three di erent approaches, namely, classical Lundberg inequality, Inductive approach and Martingale approach. Density estimation techniques (non-parametrics) are used to derive upper bounds for the Ruin Probability and the algorithms used in the simulation are presented

Unicidade e discretização para problemas de valor inicial

This paper has two objectives: (i) conducting a literature search on the criteria of uniqueness of solution for initial value problems of ordinary differential equations. (ii) a modification of the method of Euler that seems to be able to converge to a solution of the problem, if the solution is not unique

Parâmetro de regularização em problemas inversos: estudo numérico com a transformada de Radon

In general, an inverse problem corresponds to find a value of an element x in a suitable vector space, given a vector y measuring it, in some sense. When we discretize the problem, it usually boils down to solve an equation system f(x) = y, where f : U Rm ! Rn represents the step function in any domain U of the appropriate Rm. As a general rule, we arrive to an ill-posed problem. The resolution of inverse problems has been widely researched along the last decades, because many problems in science and industry consist in determining unknowns that we try to know, by observing its effects under certain indirect measures. Our general subject of this dissertation is the choice of Tykhonov´s regulaziration parameter of a poorly conditioned linear problem, as we are going to discuss on chapter 1 of this dissertation, focusing on the three most popular methods in nowadays literature of the area. Our more specific focus in this dissertation consists in the simulations reported on chapter 2, aiming to compare the performance of the three methods in the recuperation of images measured with the Radon transform, perturbed by the addition of gaussian i.i.d. noise. We choosed a difference operator as regularizer of the problem. The contribution we try to make, in this dissertation, mainly consists on the discussion of numerical simulations we execute, as is exposed in Chapter 2. We understand that the meaning of this dissertation lays much more on the questions which it raises than on saying something definitive about the subject. Partly, for beeing based on numerical experiments with no new mathematical results associated to it, partly for being about numerical experiments made with a single operator. On the other hand, we got some observations which seemed to us interesting on the simulations performed, considered the literature of the area. In special, we highlight observations we resume, at the conclusion of this work, about the different vocations of methods like GCV and L-curve and, also, about the optimal parameters tendency observed in the L-curve method of grouping themselves in a small gap, strongly correlated with the behavior of the generalized singular value decomposition curve of the involved operators, under reasonably broad regularity conditions in the images to be recovered

Modelo de risco com dependência entre os valores das indenizações e seus intervalos entre ocorrências

We present a dependent risk model to describe the surplus of an insurance portfolio, based on the article "A ruin model with dependence between claim sizes and claim intervals"(Albrecher and Boxma [1]). An exact expression for the Laplace transform of the survival function of the surplus is derived. The results obtained are illustrated by several numerical examples and the case when we ignore the dependence structure present in the model is investigated. For the phase type claim sizes, we study by the survival probability, considering this is a class of distributions computationally tractable and more general

Ergodicidade em cadeias de Markov não-homogêneas e cadeias de Markov com transições raras

The central objective of a study Non-Homogeneous Markov Chains is the concept of weak and strong ergodicity. A chain is weak ergodic if the dependence on the initial distribution vanishes with time, and it is strong ergodic if it is weak ergodic and converges in distribution. Most theoretical results on strong ergodicity assume some knowledge of the limit behavior of the stationary distributions. In this work, we collect some general results on weak and strong ergodicity for chains with space enumerable states, and also study the asymptotic behavior of the stationary distributions of a particular type of Markov Chains with finite state space, called Markov Chains with Rare Transitions

A distribuição F generalizada para selecionar modelos de sobrevivência com fração de cura

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

NI-GMRES precondicionado

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Desempenho de uma lagoa de infiltração na absorção de cheias e na recarga de aquífero

A type of macro drainage solution widely used in urban areas with predomi-nance of closed catchments (basins without outlet) is the implementation of detention and infiltration reservoirs (DIR). This type of solution has the main function of storing surface runoff and to promote soil infiltration and, consequently, aquifer recharge. The practice is to avoid floods in the drainage basin low-lying areas. The catchment waterproofing reduces the distributed groundwater recharge in urban areas, as is the case of Natal city, RN. However, the advantage of DIR is to concentrate the runoff and to promote aquifer recharge to an amount that can surpass the distributed natu-ral recharge. In this paper, we proposed studying a small urban drainage catchment, named Experimental Mirassol Watershed (EMW) in Natal, RN, whose outlet is a DIR. The rainfall-runoff transformation processes, water accumulation in DIR and the pro-cess of infiltration and percolation in the soil profile until the free aquifer were mod-eled and, from rainfall event observations, water levels in DIR and free aquifer water level measurements, and also, parameter values determination, it is was enabled to calibrate and modeling these combined processes. The mathematical modeling was carried out from two numerical models. We used the rainfall-runoff model developed by RIGHETTO (2014), and besides, we developed a one-dimensional model to simu-late the soil infiltration, percolation, redistribution soil water and groundwater in a combined system to the reservoir water balance. Continuous simulation was run over a period of eighteen months in time intervals of one minute. The drainage basin was discretized in blocks units as well as street reaches and the soil profile in vertical cells of 2 cm deep to a total depth of 30 m. The generated hydrographs were transformed into inlet volumes to the DIR and then, it was carried out water balance in these time intervals, considering infiltration and percolation of water in the soil profile. As a re-sult, we get to evaluate the storage water process in DIR as well as the infiltration of water, redistribution into the soil and the groundwater aquifer recharge, in continuous temporal simulation. We found that the DIR has good performance to storage excess water drainage and to contribute to the local aquifer recharge process (Aquifer Dunas / Barreiras).

Estudo da permeação em membranas quitosana

This study proposes to do a study on the mathematical modeling of permeation of films based on chitosan. To conduct the study were obtained membranes with various compositions: a virtually pure membrane-based chitosan; one of chitosan associated with poly (ethylene oxide (PEO). The membranes of pure chitosan were treated with plasma in atmospheres of oxygen, argon and methane. The various types of films were characterized as to its permeation regarding sufamerazina sodium. In the process of mathematical modeling were compared the standard method of obtaining the coefficient of permeation recital straight down the slope of the plot obtained by extinction / time with a the integration process of numerical permeability rate will be calculated from the spectroscopy UV

Síntese de pigmento cerâmico ferrita de cobalto utilizando planejamento experimental

Synthetic inorganic pigments are the most widely used in ceramic applications because they have excellent chemical and thermal stability and also, in general, a lower toxicity to man and to the environment. In the present work, the ceramic black pigment CoFe2O4 was synthesized by the polymerization Complex method (MPC) in order to form a material with good chemical homogeneity. Aiming to optimize the process of getting the pigment through the MPC was used a fractional factorial design 2(5-2), with resolution III. The factors studied in mathematical models were: citric acid concentration, the pyrolysis time, temperature, time and rate of calcination. The response surfaces using the software statistica 7.0. The powders were characterized by thermal analysis (TG/DSC), x-ray diffraction (XRD), scanning electron microscopy (SEM) and spectroscopy in the UV-visible. Based on the results, there was the formation of phase cobalt ferrite (CoFe2O4) with spinel structure. The color of the pigments obtained showed dark shades, from black to gray. The model chosen was appropriate since proved to be adjusted and predictive. Planning also showed that all factors were significant, with a confidence level of 95%

Modelo Estocástico para bloqueio de poros e redução de permeabilidade

Modeling transport of particulate suspensions in porous media is essential for understanding various processes of industrial and scientific interest. During these processes, particles are retained due to mechanisms like size exclusion (straining), adsorption, sedimentation and diffusion. In this thesis, a mathematical model is proposed and analytical solutions are obtained. The obtained analytic solutions for the proposed model, which takes pore and particle size distributions into account, were applied to predict the particle retention, pore blocking and permeability reduction during dead-end microfiltration in membranes. Various scenarios, considering different particle and pore size distributions were studied. The obtained results showed that pore blocking and permeability reduction are highly influenced by the initial pore and particle size distributions. This feature was observed even when different initial pore and particle size distributions with the same average pore size and injected particle size were considered. Finally, a mathematical model for predicting equivalent permeability in porous media during particle retention (and pore blocking) is proposed and the obtained solutions were applied to study permeability decline in different scenarios

Modelagem e controle de um microveículo aéreo: uma aplicação de estabilidade robusta com a técnica backstepping em uma estrutura hexarrotor

In this Thesis, the development of the dynamic model of multirotor unmanned aerial vehicle with vertical takeoff and landing characteristics, considering input nonlinearities and a full state robust backstepping controller are presented. The dynamic model is expressed using the Newton-Euler laws, aiming to obtain a better mathematical representation of the mechanical system for system analysis and control design, not only when it is hovering, but also when it is taking-off, or landing, or flying to perform a task. The input nonlinearities are the deadzone and saturation, where the gravitational effect and the inherent physical constrains of the rotors are related and addressed. The experimental multirotor aerial vehicle is equipped with an inertial measurement unit and a sonar sensor, which appropriately provides measurements of attitude and altitude. A real-time attitude estimation scheme based on the extended Kalman filter using quaternions was developed. Then, for robustness analysis, sensors were modeled as the ideal value with addition of an unknown bias and unknown white noise. The bounded robust attitude/altitude controller were derived based on globally uniformly practically asymptotically stable for real systems, that remains globally uniformly asymptotically stable if and only if their solutions are globally uniformly bounded, dealing with convergence and stability into a ball of the state space with non-null radius, under some assumptions. The Lyapunov analysis technique was used to prove the stability of the closed-loop system, compute bounds on control gains and guaranteeing desired bounds on attitude dynamics tracking errors in the presence of measurement disturbances. The controller laws were tested in numerical simulations and in an experimental hexarotor, developed at the UFRN Robotics Laboratory

Influência dos modelos digitais de terreno na modelagem de circulação hidrodinâmica 2DH: um estudo de caso

Digital Elevation Models (DEM) are numerical representations of a portion of the earth surface. Among several factors which affect the quality of a DEM, it should be emphasized the attention on the input data and the choice of the interpolating algorithm. On the other hand, several numerical models are used nowadays to characterize nearshore hydrodynamics and morphological changes in coastal areas, whose validation is based on field data collection. Independent on the complexity of the physical processes which are modeled, little attention has been given to the intrinsic bathymetric interpolation built within the numerical models of the specific application. Therefore, this study aims to investigate and to quantify the influence of the bathymetry, as obtained by a DEM, on the hydrodynamic circulation model at a coastal stretch, off the coast of the State of Rio Grande do Norte, Northeast Brazil. This coastal region is characterized by strong hydrodynamic and littoral processes, resulting in a very dynamic morphology with shallow coastal bathymetry. Important economic activities, such as oil exploitation and production, fisheries, salt ponds, shrimp farms and tourism, also bring impacts upon the local ecosystems and influence themselves the local hydrodynamics. This fact makes the region one of the most important for the development of the State, but also enhances the possibility of serious environmental accidents. As a hydrodynamic model, SisBaHiA® - Environmental Hydrodynamics System ( Sistema Básico de Hidrodinâmica Ambiental ) was chosen, for it has been successfully employed at several locations along the Brazilian coast. This model was developed at the Coastal and Oceanographical Engineering Group of the Ocean Engineering Program at the Federal University of Rio de Janeiro. Several interpolating methods were tested for the construction of the DEM, namely Natural Neighbor, Kriging, Triangulation with Linear Interpolation, Inverse Distance to a Power, Nearest Neighbor, and Minimum Curvature, all implemented within the software Surfer®. The bathymetry which was used as reference for the DEM was obtained from nautical charts provided by the Brazilian Hydrographic Service of the Brazilian Navy and from a field survey conducted in 2005. Changes in flow velocity and free surface elevation were evaluated under three aspects: a spatial vision along three profiles perpendicular to the coast and one profile longitudinal to the coast as shown; a temporal vision from three central nodes of the grid during 30 days; a hodograph analysis of components of speed in U and V, by different tidal cycles. Small, but negligible, variations in sea surface elevation were identified. However, the differences in flow and direction of velocities were significant, depending on the DEM

Dificuldades de aprendizagem em estequiometria: uma proposta de ensino apoiada na modelagem

In order to learn/teach chemistry some themes are relevant, like the stoichiometry, which consists in the study of the weight ratios in the combination of elements and compounds between themselves. This is an underlying subject in the understanding/representation/forethought of chemical reactions. Considering these aspects, our study presents a modeling-based proposal to develop the content of stoichiometry with prospective chemistry teachers. With this aim, we have made a review of literature, which we considered when tried to identify the learning difficulties using both quizzes and pedagogical tests, and then, from those difficulties we could propose a teaching unit for this concept and, consequently the evaluation of our proposal. The participants were chemistry undergraduates at the Universidade Federal do Rio Grande do Norte (UFRN) from assorted levels. As a methodological framework, we rely on the discursive textual analysis to characterize the speech of participants. As main results we observed ideas of appearance or disappearance of matter during chemical transformations, disregard of stoichiometric proportions when using drawings to represent the microscopic level of a reaction and confusion between the magnitude amount of matter and other magnitudes such as mass and volume. The final product is a sequence of instruction, based on the modeling previous research literature , with the goal of improving students ability to articulate the macroscopic and submicroscopic levels of representation of the matter

Modelagem multiescala de fenômenos eletrocinéticos em meios porosos carregados eletricamente: aplicação a meios porosos argilosos

In this master thesis, we propose a multiscale mathematical and computational model for electrokinetic phenomena in porous media electrically charged. We consider a porous medium rigid and incompressible saturated by an electrolyte solution containing four monovalent ionic solutes completely diluted in the aqueous solvent. Initially we developed the modeling electrical double layer how objective to compute the electrical potential, surface density of electrical charges and considering two chemical reactions, we propose a 2-pK model for calculating the chemical adsorption occurring in the domain of electrical double layer. Having the nanoscopic model, we deduce a model in the microscale, where the electrochemical adsorption of ions, protonation/ deprotonation reactions and zeta potential obtained in the nanoscale, are incorporated through the conditions of interface uid/solid of the Stokes problem and transportation of ions, modeled by equations of Nernst-Planck. Using the homogenization technique of periodic structures, we develop a model in macroscopic scale with respective cells problems for the e ective macroscopic parameters of equations. Finally, we propose several numerical simulations of the multiscale model for uid ow and transport of reactive ionic solute in a saturated aqueous solution of kaolinite. Using nanoscopic model we propose some numerical simulations of electrochemical adsorption phenomena in the electrical double layer. Making use of the nite element method discretize the macroscopic model and propose some numerical simulations in basic and acid system aiming to quantify the transport of ionic solutes in porous media electrically charged.