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- ItemMétodos Do Tipo Newton Aplicados A Métodos De Restauração Inexata(Universidade Federal de São Paulo (UNIFESP), 2017-03-14) Herrera, Francis Lorena Larreal [UNIFESP]; Bueno, Luis Felipe Cesar Da Rocha [UNIFESP]; Universidade Federal de São Paulo (UNIFESP)
Mostrar mais In this dissertation, we study Brent’s method to solve systems of equations and their relation with Inexata Restoration methods. Brent’s method solves a non-linear system by dividing it into blocks and considering linearizations of these blocks in each iteration. We reconstruct a proof of a theorem in which are established the conditions so that the point sequence generated by Brent’s method has local quadratic convergence to the system solution. Inexact Restoration methods are developed to solved constrained optimization problems and the have the characteristic of dividing each iteration into two phases. In the first one, they seek to improve viability and, in the second, optimality. So, it is natural to think that Inexact Restoration methods look to solve the KKT system by dividing it into two blocks. For this reason, it seems evident the existence of a relation between Brent’s and Inexact Restoration methods. Considering this, we present a quadratic local convergence result for the point sequences generated by the Inexact Restoration methods, derived from adaptations in the convergence demonstration of Brent’s method. After that, we propose two iterative computational methods for optimization, introducing small modifications in the Inexact Restoration method. We show that these two methods also have quadratic convergence and we discuss possible advantages and disadvantages of each one of them. Finally we briefly comment some ideas about how these methods could be inserted into a scheme with global convergence.Mostrar mais - ItemCódigos Perfeitos Na Métrica De Lee E A Conjectura De Golomb-Welch(Universidade Federal de São Paulo (UNIFESP), 2017-03-23) Morais, George Absalao Pandino De [UNIFESP]; Jorge, Grasiele Cristiane [UNIFESP]; Universidade Federal de São Paulo (UNIFESP)
Mostrar mais The Aim Of This Work Is The Study Of The Golomb-Welch Conjecture And The Relations Between Perfect Codes In The Lee Metric In Zn And Znq , Q 2 N, Q 2, And Tilings In Rn. In This Study, We Stress Two Articles: \Perfect Codes In The Lee Metric And The Packing Of Polyominoes", Written By Solomon W. Golomb E Lloyd R. Welch, Which Presents The Conjecture And Some Facts About Tilings Of Zn By Lee Spheres And \A New Approach Towards The Golomb-Welch Conjecture", Written By Peter Horak E Otokar Grosek, Which Gives A Soloution For Some Cases Of The Conjecture Introducing A New Algebraic Invariant Related To Abelian Groups.Mostrar mais - ItemPrimos Em Corpos De Funções(Universidade Federal de São Paulo (UNIFESP), 2017-06-23) Moyano, Luis Santiago Eduardo Palacios [UNIFESP]; Silva, Robson Da [UNIFESP]; Universidade Federal de São Paulo (UNIFESP)
Mostrar mais In This Work, We Study The Bases Of The So-Called Number Theory In Function Fields. In This Context, The Monic Polynomials Play The Role Of The Positive Integers And The Irreducible Monics Polynomials, The Prime Numbers. We Also Investigate How Some Classical Results Of Number Theory Extend To This New Context Of Function Fields. Finally We Explore Results From Recent Articles, Which Extend To Function Fields The Problem, Not Yet Solved In The Integers, Of Finding Nontrivial Infinite Sets Of Primes P Such That If P Belongs To P Then R Belongs To P For All Prime R Dividing P - 1.Mostrar mais - ItemInvariantes E Equivariantes Relativos Para Grupos De Lie Compactos(Universidade Federal de São Paulo (UNIFESP), 2017-08-11) Sampaio, Cassia Ferreira [UNIFESP]; Antoneli, Fernando Martins [UNIFESP]; Universidade Federal de São Paulo (UNIFESP)
Mostrar mais A large variety of problems and models on bifurcation theory of dynamical systems have space symmetries and time reversing symmetries that are combined into a group of spacetime symmetries for the study of bifurcation theory of reversible-equivariant dynamical systems. One of the main methods of bifurcation theory is to reduce to the normal form that attempt to simplify a vector field through coordinate transformations that preserve their local dynamical properties. In bifurcation theory of dynamical systems with symetries this is done with the aid of the theory of the invariants associated with the action of the spacetime symmetries group in question. In this dissertation, we present a unified theory of invariants under linear actions of compact Lie groups which generalizes the classical theory, including the reversing-time symetries, based on description of the srtucture of relativeinvariant polinomials and the structure of the relative-equivariant mappings. Finally, we discuss some computational aspects that are naturally motivated by the main results of the theory.Mostrar mais - ItemUm Estudo Sobre O Problema De Empacotamento De Círculos(Universidade Federal de São Paulo (UNIFESP), 2018-06-15) Oliveira, Juliana Rodrigues Silva De [UNIFESP]; Senne, Thadeu Alves [UNIFESP]; Universidade Federal de São Paulo (UNIFESP)
Mostrar mais The Packing Problems Consist In Arranging Some Subjects Within A Certain Region. In This Work, We Study A Particular Case Of This Problem: The Problem Of Packing Circular Items, In Which The Items That Has To Be Organized Inside Of A Certain Region Are Unitary Circles. We Considered That The Region That Have Those Items Has One Of These Forms: Circular, Square, Rectangular And Triangular Or Strip (That Is, A Rectangle That Has One Of Two Dimensions Fixed). The Goal Is To Minimize The Dimensions Of The Object So That There Is No Overlap Between Any Two Pairs Of Items And Each Item Is Prevented To Cross The Boundary Of The Object. The Knowledge Of This Class Of Problems Is Essential For The Understanding More About The Complex Problems, Such As Packing Molecules. So, The Study About This Subject Is Relevant. Here, We Solve The Problem Of Packing Circles Using Algencan, That Is A Software Based On The Augmented Lagrangian Method For Nonlinear Optimization Problems, And We Compared The Performance Of The OriginalMostrar mais - ItemEspaços De Lipschiz-Livres E Propriedades De Aproximação(Universidade Federal de São Paulo (UNIFESP), 2018-08-07) Romao, Joao Victor Bateli [UNIFESP]; Kaufmann, Pedro Levit [UNIFESP]; Universidade Federal de São Paulo (UNIFESP)
Mostrar mais This Work Consists Of Studying Approximation Properties In Lipschitz-Free Spaces, Which Involves: In-Depth Study Of Prerequisites Of Functional Analisys And Topology In Order To Comprehend The Engaged Concepts; Research And Analisys Of Existant Bibliography On The Subject; And The Detailed Study Of Specific Results In This Area, Prioritizing Recent Central Results Under The Development Of The Area.Mostrar mais - ItemImagens de polinômios multilineares sobre algumas subálgebras de matrizes(Universidade Federal de São Paulo (UNIFESP), 2019-01-18) Fagundes, Pedro Souza [UNIFESP]; Mello, Thiago Castilho De [UNIFESP]; Universidade Federal de São Paulo (UNIFESP)
Mostrar mais In this dissertation we will study the images of multilinear polynomials on matrix algebras. We will present results from Shoda, Albert and Muckenhoupt, Mesyan and Buzinski and Winstanley to study the cases where the multilinear polynomials have degree up to four. We will also describe the images of multilinear polynomials of degree up to four on the upper triangular matrix algebra as well as the images of multilinear polynomials of arbitrary degree on the strictly upper triangular matrix algebra. Moreover, we will study some results from Brešar and Klep about the relation between the linear span of the images of noncommutative polynomials on algebras and Lie ideals.Mostrar mais - ItemEstudo e implementação computacional de problemas de otimização topológica 3D(Universidade Federal de São Paulo (UNIFESP), 2019-02-18) Alvarez, Gustavo David Quintero [UNIFESP]; Senne, Thadeu Alves [UNIFESP]; Universidade Federal de São Paulo (UNIFESP)
Mostrar mais The topology optimization is a class of structural optimization problems to obtain a structure that is as rigid as possible, satisfying a constraint on the amount of material available inside a certain domain, and which is subjected to the application of external forces. In other words, the objective is to find the optimal distribution of the material that composing this structure, so that its average compliance is minimized (or, equivalently, its stiffness should be maximized). Initially, topology optimization problems are formulated in a continuous medium, so that at each point in the domain that contains the structure, it must be decide whether or not there will be material. In this case, we have an optimization problem with an infinite number of binary variables. In order to make the problem treatable from a numerical point of view, this continuous medium is replaced by a discrete medium through the application of the Finite Element Method. Thus, we obtain a nonlinear optimization problem with a finite number of variables, which represent the material density in each of the elements of the discretized domain. In this work, we performed a study on the formulation of topological optimization problems of three-dimensional structures (which have many applications in the automotive and aerospace industries), and implemented an optimization’s method denominated Sequential Linear Programming (SLP) to solve these problems. We perform several computational tests that prove the efficiency of this method in the resolution of topological optimization problems.Mostrar mais - ItemOtimização aplicada ao planejamento de dosagem radioterápica para o tratamento do câncer(Universidade Federal de São Paulo (UNIFESP), 2019-03-15) Vivas, Angelica Maria Narvaez [UNIFESP]; Senne, Thadeu Alves [UNIFESP]; Universidade Federal de São Paulo (UNIFESP)
Mostrar mais When a person is diagnosed with cancer and receives the prescription of treatment with radiotherapy, it is necessary to draw up a treatment plan. For this, the patient undergoes a 3D computed tomography scan, in order to delineate the organs affected by the tumor. Based on tomographic imaging, the oncologist is able to predict the distribution of radiation doses throughout the patient’s body. In the late 1990s, a radiotherapy technique called IMRT (Intensity Modulated Radiation Therapy) was developed, which aims to concentrate high doses of radiation only in the tumor regions, sparing as much as possible the adjacent healthy organs. The IMRT is based on linear accelerators and uses multiple beams of angular radiation and non-uniform intensities along with the use of mathematical optimization methods to determine the optimal distribution of radiation doses. Among the several variants of the IMRT technique, we adopted, in this work, the BAO (Beam Angle Optimization) variant. In the BAO, given an initial set of candidate radiation beams, the objective is to determine which of them are optimal, that is, those beams that will have a significant contribution to the treatment planning. To solve the associated optimization problem, we use a method called Adaptive ℓ2, 1-Minimization. We will make a comparative analysis between some treatment plans for prostate cancer obtained with this method, starting from several different sets of candidate radiation beams.Mostrar mais - ItemRecuperação ótima para funcionais lineares(Universidade Federal de São Paulo (UNIFESP), 2019-04-29) Marzo, Matheus Micadei [UNIFESP]; Ferraz, Vanessa Goncalves Paschoa [UNIFESP]; Universidade Federal de São Paulo (UNIFESP)
Mostrar mais The Optimal Recovery problems seek to construct and characterize the best method of approximation of a certain functional in different classes of functions, considering some data that are available. Several classical problems such as interpolation, uniform approximation and numerical integration can be approached in this context. The object of study is the general theory of optimal recovery which provides appropriate mathematical tools for the analysis and comparison of error of different methods.Mostrar mais - ItemRedução do número de graus de liberdade de sistemas Hamiltonianos: aplicações a problemas de Mecânica Celeste(Universidade Federal de São Paulo (UNIFESP), 2019-09-20) Ospina, Daniela Cortes [UNIFESP]; Moraes, Rodolpho Vilhena De [UNIFESP]; Universidade Federal de São Paulo (UNIFESP)
Mostrar mais Often, dynamical systems derived from Celestial Mechanics involving both translational and rotational motion - or both simultaneously - are treated using Hamiltonian formulation. In these problems, disturbances are considered by conservative forces. The differential equations involved are generally nonlinear, for which, except in some particular cases, it is not possible to obtain a closed analytical solution. In the present work, we will use classical theorems to study some of these systems, looking for first integrals that can reduce the number of degrees of freedom of the same. We will apply the studies done to the problem of the orbital motion of an artificial satellite around a central body. In this we will consider, besides the problem of two bodies, perturbations due to the non distribution of mass of the central body, as well as the gravitational attraction for a third body. At the end we present the construction of Adelphic integrals for Hamiltonian systems, whose Hamiltonian function is not explicitly time dependent and is expressed in trigonometric series.Mostrar mais - ItemRedes de sistemas dinâmicos acoplados com estrutura gradiente ou hamiltoniana(Universidade Federal de São Paulo (UNIFESP), 2020-03-03) Melo Junior, Antonio Edimar De [UNIFESP]; Antoneli Jr, Fernando Martins [UNIFESP]; Universidade Federal de São Paulo
Mostrar mais A recent generalization of the group-theoretic notion of symmetry replaces global symmetries by bijections between certain subsets of the digraph of a network, the “input sets”. A symmetry group becomes a groupoid and this formalism makes it possible to extend group theoretic methods to more general networks, and in particular it leads to a classification of patterns of synchrony in terms of the structure of the network. A network of dynamical systems is equipped with a canonical set of observables for the states of its individual nodes. Moreover, the form of the underlying ODE is constrained by the network topology and how those equations relate to each other. For the coupled systems associated with a network, there can be flow-invariant spaces (synchrony subspaces where some subsystems evolve synchronously), whose existence is independent of the systems equations and depends only on the network topology. Furthermore, any coupled system on the network, when restricted to such a synchrony subspace, determines a new coupled system associated with a smaller network (quotient). A regular network is a network with one kind of node and one kind of coupling. We show conditions for a codimension one bifurcation from a synchronous equilibrium in a regular network at linear level be isomorphic to a generalized eigenspace of the adjacency matrix of the network. We then focus on coupled cell systems in which individual cells are also gradient or Hamiltonian. In broad terms, we prove that only systems with bidirectionally coupled digraphs can be gradient or Hamiltonian. We characterize the conditions for the coupled systems property of being gradient or Hamiltonian to be preserved by the lift and quotient coupled systems. Aside from the topological criteria, we also study the linear theory of regular gradient (Hamiltonian) coupled cell systems. We then prove results on steady-state bifurcations and a version of the Equivariant Branching Lemma and the Equivariant Hopf Theorem. We illustrate a neural network given by two sets of neurons that are mutually coupled through either excitatory or inhibitory synapses, which is modelled by a coupled system exhibiting both gradient and Hamiltonian structures, and how periodic solutions from equilibrium appear in the Restricted Three Body Problem.Mostrar mais - ItemUm estudo sobre Proper Orthogonal Decomposition: fundamentação teórica(Universidade Federal de São Paulo (UNIFESP), 2020-07-28) Cunha, Daniel Ammirante Da [UNIFESP]; Mesquita, Claudia Aline Azevedo Dos Santos [UNIFESP]; Universidade Federal de São Paulo
Mostrar mais The main objective of this work is to study the mathematical foundations of the Proper Orthogonal Decomposition (POD) method, the essence of which is to provides an orthogonal basis for representing a given set of data in a certain least-squares optimal sense. This method can be used to create low-order models. Its foundation is based on results of functional analysis and spectral theory in Hilbert spaces. The main results related to POD are linked to the spectral representation of compact and self-adjoint operators. These theorems are used in the description of the POD method. At the end of the work, it is presented two illustrative examples as application of the method; the first in the wave equation, and the second in the undamped free vibration of a structure.Mostrar mais - ItemÓrbitas nas vizinhanças da inclinação crítica(Universidade Federal de São Paulo (UNIFESP), 2020-08-04) Rodriguez Castilla, Alberto Enrique [UNIFESP]; Moraes, Rodolpho Vilhena De [UNIFESP]; Universidade Federal de São Paulo
Mostrar mais This work consists of analyzing the stability of the orbits of space satellites orbiting satellites planetariums in the neighborhoods of critical inclinations. Such analysis mainly involves the study of the problem of the two bodies, of the Lagrange Planetary equations, of the gravitational potential of a planet, of the equations of motion in the Hamiltonian form and of the Lyapunov's stability. We will see some results on the behavior of orbits in the neighborhood of a critical inclination and the importance of the C₂₂ coecient when studying the Lyapunov stability of the solution of the system of equations of motion, in the Hamiltonian form, with specic initial conditions, when C₂₂=0 and when C₂₂≠0.Mostrar mais - ItemConstruções de reticulados via corpos de números(Universidade Federal de São Paulo (UNIFESP), 2020-08-10) Nogueira, Ana Flavia Cesario Machado Alckmin [UNIFESP]; Jorge, Grasiele Cristiane [UNIFESP]; Universidade Federal de São Paulo
Mostrar mais In this work we study of the theoretical basis that grounding the theory of algebraic lattices and we present some constructions of the E8 lattice with emphasis on the construction presents in the paper A new number field construction of the lattice E8. For this purpose, it were studied concepts of algebraic number theory, Galois theory and lattice theory.Mostrar mais - ItemUma resolução livre para certas álgebras(Universidade Federal de São Paulo (UNIFESP), 2020-09-18) Araujo Junior, Hilario Fernandes De [UNIFESP]; Bianchi, Angelo Calil [UNIFESP]; Universidade Federal de São Paulo
Mostrar mais The notion of resolutions in homological algebra is generally used to define invariants that characterize an algebraic structure. The objective of this dissertation is to study a free resolution for associative algebras by David Anick. This free resolution is adequate to determine the homology of an algebra, that is the calculation of the Tor functor and the Poincaré series. We specialize Anick’s result in the context of the universal enveloping algebras for certain Lie algebras, with the support of Shirshov-Gröbner bases theory.Mostrar mais - ItemOperadores hipercíclicos em espaços de Banach(Universidade Federal de São Paulo, 2020-12-07) Salcedo, Anderson Jose Mercado [UNIFESP]; Cirilo, Patricia Romano [UNIFESP]; http://lattes.cnpq.br/8477080812857959; http://lattes.cnpq.br/5964284694957893
Mostrar mais Nesta dissertação tratamos da dinâmica de operadores lineares em espaços de Banach, sob o aspecto de hiperciclicidade. Estudamos em quais condições o fenômeno da hiperciclicidade se apresenta e relacionamos com outros fenômenos que ocorrem na dinâmica de operadores como transitividade topológica, topologicamente mixing, topologicamente weakly mixing e caoticidade (caos no sentido de Devaney). Estudamos a relação do Teorema da Transitividade de Birkhoff e a hiperciclicidade. Mostraremos o Critério de Hiperciclicidade como condição suficiente para determinar se um operador definido em um espaço de Banach é hipercíclico. Além disso apresentaremos alguns exemplos clássicos de operadores que são hipercíclicos e, ao final, o Teorema de Bès-Peris.Mostrar mais - ItemSuperálgebras de Lie de dimensão finita(Universidade Federal de São Paulo, 2021-02-19) Andrade, Aline Jaqueline de Oliveira [UNIFESP]; Macedo, Tiago Rodrigues [UNIFESP]; http://lattes.cnpq.br/6725002674545546; http://lattes.cnpq.br/0630867981252157
Mostrar mais Lie superalgebras are importante gadgets used in Particle Physics and Supersymmetry. In this dissertation, some basic concepts, such as vector superspaces, Lie superalgebras and representations, are presented. Furthemore, the classi cation of nite-dimensional Lie superalgebras over the eld of complex number is also presented.Mostrar mais - ItemContinuidade do conjunto de equilíbrios de um problema parabólico não linear com termos concentrados na fronteira(Universidade Federal de São Paulo, 2021-07-23) Morales Ramirez, Daniel Alberto [UNIFESP]; Aragão, Gleciane da Silva; Astudillo Rojas, María Rosario; http://lattes.cnpq.br/4748340839963994; http://lattes.cnpq.br/2376991776742062; http://lattes.cnpq.br/8350397063604657
Mostrar mais Neste trabalho, analisamos o comportamento das soluções de um problema parabólico não linear, quando alguns termos de reação estão concentrados em uma vizinhança da fronteira do domínio e esta vizinhança contrai-se a fronteira, quando um parâmetro tende a zero. Mais precisamente, provamos a continuidade do conjunto de equilíbrios do problema parabólico não linear. Os pontos de equilíbrios são as soluções de um problema elíptico não linear associado ao problema parabólico.Mostrar mais - ItemCaracterização de variedades não matriciais em álgebras associativas(Universidade Federal de São Paulo, 2022-02-24) Martins, Vinicius Capellari [UNIFESP]; Mello, Thiago Castilho de [UNIFESP]; http://lattes.cnpq.br/7963957338675273; http://lattes.cnpq.br/4929626636384396
Mostrar mais Uma variedade de álgebras associativas é dita uma variedade não matricial, se ela não contém a álgebra das matrizes 2x2 sobre o corpo base, K, já que isso implica que ela não contém nenhuma álgebra de matrizes. Nessa dissertação apresentaremos algumas caracterizações para variedades não matriciais, variedades não matriciais que não contém G (álgebra de Grassmann) e variedades não matriciais que não contém GxG.Mostrar mais