Дисертації з теми "Quadratic polynomial"
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Boljunčić, Jadranka. "Quadratic programming : quantitative analysis and polynomial running time algorithms." Thesis, University of British Columbia, 1987. http://hdl.handle.net/2429/27532.
Повний текст джерелаz̅ - x̅
∞≤n∆(A) where n is the number of variables and ∆(A) is the largest absolute sub-determinant of the integer constraint matrix A . We have further shown that for any feasible solution z, which is not optimal for the separable quadratic integer programming problem, there exists a feasible solution z̅ having greater objective function value and with
z - z̅
∞≤n∆(A). Under some additional assumptions the distance between a pair of optimal solutions to the integer quadratic programming problem with right hand side vectors b and b', respectively, depends linearly on
b — b'
₁. The extension to the mixed-integer nonseparable quadratic case is also given. Some sensitivity analysis results for nonlinear integer programming problems are given. We assume that the nonlinear 0 — 1 problem was solved by implicit enumeration and that some small changes have been made in the right hand side or objective function coefficients. We then established what additional information to keep in the implicit enumeration tree, when solving the original problem, in order to provide us with bounds on the optimal value of a perturbed problem. Also, suppose that after solving the original problem to optimality the problem was enlarged by introducing a new 0 — 1 variable, say xn+1. We determined a lower bound on the added objective function coefficients for which the new integer variable xn+1 remains at zero level in the optimal solution for the modified integer nonlinear program. We discuss the extensions to the mixed-integer case as well as to the case when integer variables are not restricted to be 0 or 1. The computational results for an example with quadratic objective function, linear constraints and 0—1 variables are provided. Finally, we have shown how to replace the objective function of a quadratic program with 0—1 variables ( by an integer objective function whose size is polynomially bounded by the number of variables) without changing the set of optimal solutions. This was done by making use of the algorithm given by Frank and Tardos (1985) which in turn uses the simultaneous approximation algorithm of Lenstra, Lenstra and Lovász (1982).
Business, Sauder School of
Graduate
Tuncbilek, Cihan H. "Polynomial and indefinite quadratic programming problems: algorithms and applications." Diss., Virginia Tech, 1994. http://hdl.handle.net/10919/39040.
Повний текст джерелаPoirier, Schmitz Alfredo. "Invariant measures on polynomial quadratic Julia sets with no interior." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/96022.
Повний текст джерелаEn este artículo caracterizamos medidas invariantes sobre conjuntos de Julia sin interior asociados con polinomios cuadráticos. Probamos que más allá de la medida armónica —la única par e invariante—, el resto son generadas por su parte impar.
Ferragut, i. Amengual Antoni. "Polynomial inverse integrating factors of quadratic differential systems and other results." Doctoral thesis, Universitat Autònoma de Barcelona, 2006. http://hdl.handle.net/10803/3093.
Повний текст джерелаLa primera part
En l'estudi dels sistemes diferencials plans el coneixement d'una integral primera és molt important. Els seus conjunts de nivell estan formats per òrbites i ens permeten dibuixar el retrat de fase del sistema, objectiu principal de la teoria qualitativa de les equacions diferencials al pla. Com ja se sap, existeix una bijecció entre l'estudi de les integrals primeres i l'estudi dels inversos de factor integrant. De fet, és més senzill l'estudi dels inversos de factor integrant que el de les integrals primeres. Una classe és dels sistemes quadràtics àmpliament estudiada dins els sistemes diferencials al pla és la dels sistemes quadràtics. Hi ha més d'un miler d'articles publicats sobre aquest tipus de sistemes, però encara som lluny de conèixer quins d'aquests sistemes són integrables, és a dir, si tenen una integral primera.
En aquest treball, estudiam els sistemes quadràtics que tenen un invers de factor integrant polinomial V = V(x, y), i per tant també tenen una integral primera, definida allà on no s'anul·la. Aquesta classe de sistemes diferencials és important per diferents motius:
1. La integral primera és sempre Darboux.
2. Conté la classe dels sistemes quàdratics homogenis, àmpliament estudiada (Date, Sibirskii, Vulpe...).
3. Conté la classe dels sistemes quàdratics amb un centre, també estudiada (Dulac, Kapteyn, Bautin,...).
4. Conté la classe dels sistemes quàdratics Hamiltonians (Artés, Llibre, Vulpe).
5. Conté la classe dels sistemes quàdratics amb una integral primera polinomial (Chavarriga, García, Llibre, Pérez de Rio, Rodríguez).
6. Conté la classe dels sistemes quàdratics amb una integral primera racional de grau dos (Cairó, Llibre).
La segona part
Presentam els següents tres articles:
1. A. Ferragut, J. Llibre and A. Mahdi, Polynomial inverse integrating factors for polynomial vector ?elds, to appear in Discrete and Continuous Dynamical Systems.
2. A. Ferragut, J. Llibre and M.A. Teixeira, Periodic orbits for a class of C(1) three-dimensional systems, submitted.
3. A. Ferragut, J. Llibre and M.A. Teixeira, Hyperbolic periodic orbits coming from the bifurcation of a 4-dimensional non-linear center, to appear in Int. J. Of Bifurcation and Chaos.
En el primer article donam tres resultats principals. Primer provam que un camp vectorial polinomial que té una integral primera polinomial té un invers de factor integrant polinomial. El segon resultat és un exemple d'un camp vectorial polinomial que té una integral primera racional i no té ni una integral primera polinomial ni un invers de factor integrant polinomial. Era un problema obert el fet de sebre si existien camps vectorials polinomials veri?cant aquestes condicions. El tercer resultat és un exemple d'un camp vectorial polinomial que té un centre i no té invers de factor integrant polinomial. Un exemple d'aquest tipus era esperat però desconegut en la literatura.
En el segon article estudiam camps vectorials polinomials reversibles de grau quatre en R(3) que tenen, sota certes condicions genèriques, un nombre arbitrari d'-orbitesperi-odiques hiperb-oliques. Sense aquestes condicions, tenen un nombre arbitrari d'òrbites periòdiques hiperbòliques. Sense aquestes condicions, tenen un nombre arbitrari d'òrbites periòdiques.
Finalment, en el tercer article, estudiam la pertorbació d'un centre de R(4) que prove d'un problema de la física. Mitjançant la teoria dels termes mitjans de primer ordre dins els camps vectorials polinomials de grau quatre, el sistema pertorbat pot tenir fins a setze òrbites periòdiques hiperbòliques bifurcant de les òrbites peròdiques del centre.
This thesis is divided into two different parts. In the first one, we study the quadratic systems (polynomial systems of degree two) having a polynomial inverse integrating factor. In the second one, we study three different problems related to polynomial differential systems.
The ?rst part.
It is very important, for planar differential systems, the knowledge of a ?rst integral. Its level sets are formed by orbits and they let us draw the phase portrait of the system, which is the main objective of the qualitative theory of planar differential equations.
As it is known, there is a bijection between the study of the ?rst integrals and the study of inverse integrating factors. In fact, it is easier to study the inverse integrating factors than the ?rst integrals.
A widely studied class of planar differential systems is the quadratic one. There are more than a thousand published articles about this subject of differential systems, but we are far away of knowing which quadratic systems are integrable, that is, if they have a ?rst integral.
In this work, we study the quadratic systems having a polynomial inverse integrating factor V = V (x, y), so they also have a ?rst integral, de?ned where V does not vanish. This class of quadratic systems is important for several reasons:
1. The ?rst integral is always Darboux.
2. It contains the class of homogeneous quadratic system, widely studied (Date, Sibirskii, Vulpe,...).
3. It contains the class of quadratic systems having a center, also studied (Dulac, Kapteyn, Bautin,...).
4. It contains the class of Hamiltonian quadratic systems (Artés, Llibre, Vulpe).
5. It contains the class of quadratic systems having a polynomial ?rst integral (Chavarriga, García, Llibre, Pérez de Rio, Rodríguez).
6. It contains the class of quadratic systems having a rational ?rst integral of de gree two (Cairó, Llibre).
The classi?cation of the quadratic systems having a polynomial inverse integrating factor is not completely ?nished. There remain near a 5% of the cases to study. We leave their study for an immediate future.
The second part.
We present the following three articles:
1. A. Ferragut, J. Llibre and A. Mahdi, Polynomial inverse integrating factors for polynomial vector ?elds, to appear in Discrete and Continuous Dynamical Systems.
2. A. Ferragut, J. Llibre and M.A. Teixeira, Periodic orbits for a class of C(1) three-dimensional systems, submitted.
3. A. Ferragut, J. Llibre and M.A. Teixeira, Hyperbolic periodic orbits coming from the bifurcation of a 4-dimensional non-linear center, to appear in Int. J. Of Bifurcation and Chaos.
In the first article we give three main results. First we prove that a polynomial vector field having a polynomial must have a polynomial inverse integrating factor. The second one is an example of a polynomial vector ?eld having a rational ?rst integral and having neither polynomial ?rst integral nor polynomial inverse integrating factor. It was an open problem to know if there exist polynomial vector ?elds verifying these conditions. The third one is an example of a polynomial vector ?eld having a center and not having a polynomial inverse integrating factor. An example of this type was expected but unknown in the literature.
In the second article we study reversible polynomial vector ?elds of degree four in R(3) which have, under certain generic conditions, an arbitrary number of hyperbolic periodic orbits. Without these conditions, they have an arbitrary number of periodic orbits.
Finally, in the third article, we study the perturbation of a center in R(4) which comes from a problem of physics. By the ?rst order averaging theory and perturbing inside the polynomial vector ?elds of degree four, the perturbed system may have at most sixteen hyperbolic periodic orbits bifurcating from the periodic orbits of the center.
Riggs, Laurie Jan. "Polynomial equations and solvability: A historical perspective." CSUSB ScholarWorks, 1996. https://scholarworks.lib.csusb.edu/etd-project/1186.
Повний текст джерелаLiu, Dunxue Carleton University Dissertation Mathematics. "Dihedral polynomial congruences and binary quadratic forms: a class field theory approach." Ottawa, 1992.
Знайти повний текст джерелаLahnovych, Carrie. "Analysis and computation of a quadratic matrix polynomial with Schur-products and applications to the Barboy-Tenne model /." Online version of thesis, 2010. http://ritdml.rit.edu/handle/1850/12207.
Повний текст джерелаBegum, Monzu Ara. "Bifurcation in complex quadratic polynomial and some fold theorems involving the geometry of bulbs of the Mandelbrot set." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/MQ64045.pdf.
Повний текст джерелаRyu, Jong Hoon. "Permutation polynomial based interleavers for turbo codes over integer rings theory and applications /." Columbus, Ohio : Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1181139404.
Повний текст джерелаAli, Ali Hasan. "Modifying Some Iterative Methods for Solving Quadratic Eigenvalue Problems." Wright State University / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=wright1515029541712239.
Повний текст джерелаLazare, Arnaud. "Global optimization of polynomial programs with mixed-integer variables." Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLY011.
Повний текст джерелаIn this thesis, we are interested in the study of polynomial programs, that is optimization problems for which the objective function and/or the constraints are expressed by multivariate polynomials. These problems have many practical applications and are currently actively studied. Different methods can be used to find either a global or a heuristic solution, using for instance, positive semi-definite relaxations as in the "Moment/Sum of squares" method. But these problems remain very difficult and only small instances are addressed. In the quadratic case, an effective exact solution approach was initially proposed in the QCR method. It is based on a quadratic convex reformulation, which is optimal in terms of continuous relaxation bound.One of the motivations of this thesis is to generalize this approach to the case of polynomial programs. In most of this manuscript, we study optimization problems with binary variables. We propose two families of convex reformulations for these problems: "direct" reformulations and quadratic ones.For direct reformulations, we first focus on linearizations. We introduce the concept of q-linearization, that is a linearization using q additional variables, and we compare the bounds obtained by continuous relaxation for different values of q. Then, we apply convex reformulation to the polynomial problem, by adding additional terms to the objective function, but without adding additional variables or constraints.The second family of convex reformulations aims at extending quadratic convex reformulation to the polynomial case. We propose several new alternative reformulations that we compare to existing methods on instances of the literature. In particular we present the algorithm PQCR to solve unconstrained binary polynomial problems. The PQCR method is able to solve several unsolved instances. In addition to numerical experiments, we also propose a theoretical study to compare the different quadratic reformulations of the literature and then apply a convex reformulation to them.Finally, we consider more general problems and we propose a method to compute convex relaxations for continuous problems
Takam, Soh Patrice. "Estimation de la loi de la durée de séjour en présence d'une censure post-évènement d'intérêt. : Application à la croissance des fruits du cacaoyer et modélisation du risque d'attaque par la pourriture brune au Cameroun." Thesis, Montpellier 2, 2011. http://www.theses.fr/2011MON20163/document.
Повний текст джерелаWe are interested in this study in estimating the lifetime distribution by taking into consideration individuals on which the interest event and the censorship can occur in the same intervaland both events were then observed. We proposed two nonparametric approaches based on an asymptotic approximation when the lengthbetween two consecutive observation days tends to 0. The first one was based on an integral relationship and the second one on a lifetime restoration. We used theses approaches to build a fruitgrowth model depending on climatic variables. We also estimated the susceptibility (success probability of attack by a spore on a fruit) of the fruit depending of its developmental stage and theinfectious potential of the disease over time.This infectious potential could help to build a model of infectious potential depending on infected fruits. The knowledge of the infectious potential depending on infected fruits, the estimation of the susceptibility of the fruit and the model of growth will allow to built a dynamic model of infectious potential to predict the evolution risk of disease progression
Mogilka, Marcelo. "O uso da planilha eletrônica no estudo das funções e equações polinomiais." Universidade Federal da Paraíba, 2016. http://tede.biblioteca.ufpb.br:8080/handle/tede/9465.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
The use of technologies as teaching tool is a reality experienced by a significant portion of the student body in Brazil. However, there is still considerable demand for educational projects involving the teaching of mathematics with the technologies offered by computer programs. This work will address - through the Delta Project the usage of electronic spreadsheets as a tool for analysis and resolution of func- tional and polynomial equations, establishing links between the mathematical and computational knowledge.
A utilização das tecnologias como ferramentas didaticas ja é uma realidade vivida por uma parte significativa do alunado no Brasil. No entanto, o ritmo vertiginoso do avanço dessas tecnologias não é acompanhado pela devida adaptação e aplicação a realidade das escolas e, sobretudo, a realidade dos alunos. Diante deste descom- passo faz-se necessário ampliar as ofertas de trabalhos acadêmicos que utilizem as tecnologias oferecidas na forma de aplicativos, softwares ou programas específicos da area de educação, para auxiliar o professor na difícil tarefa de ensinar a matema- tica. Essa dissertação pretende contribuir exatamente nesse sentido. Através de um projeto didatico aplicado em sala de aula - o Projeto Delta - que tem como prin- cipal objetivo ampliar e aprofundar os conceitos de função quadratica, resolução de equações polinomiais, divisão de polinômios e cálculo de áreas e volumes de sólidos geométricos utilizando para tanto a planilha eletrônica como ferramenta didática e link entre os saberes das áreas de matemática e programação. Por meio de exemplos práticos da utilização da planilha eletrônica na criação de programas pelos alunos que participaram do Projeto Delta, e da devida fundamentação teórica, esse tra- balho acadêmico pretende mostrar que no processo de criar programas na planilha eletrônica para auxiliar a resolução de problemas matemáticos o aluno tem como subproduto positivo um aprofundamento do entendimento desses saberes matema- ticos e, mais ainda, uma postura analítica e protagonista diante dos conhecimentos dessa matéria em oposição a postura passiva e pouco reflexiva que, infelizmente, ainda é assumida por grande parte dos nossos alunos.
Ruan, Ning. "Global optimization for nonconvex optimization problems." Thesis, Curtin University, 2012. http://hdl.handle.net/20.500.11937/1936.
Повний текст джерелаFreiberger, Marianne. "Matings between Hecke groups and polynomials." Thesis, Queen Mary, University of London, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.368907.
Повний текст джерелаLeahy, Jennifer C. "The permutations of periodic points in quadratic polynominials /." Connect to online version, 2005. http://ada.mtholyoke.edu/setr/websrc/pdfs/www/2005/103.pdf.
Повний текст джерелаBaker, Audrey. "An algorithm for the strong freeness of quadratic lie polynomials /." Thesis, McGill University, 2006. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=100761.
Повний текст джерелаDiene, Adama. "Structure of Permutation Polynomials." University of Cincinnati / OhioLINK, 2005. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1123788311.
Повний текст джерелаSaygi, Elif. "Results On Lcz Sequences And Quadratic Forms." Phd thesis, METU, 2009. http://etd.lib.metu.edu.tr/upload/12611243/index.pdf.
Повний текст джерелаKettner, Michael. "Algorithmic and topological aspects of semi-algebraic sets defined by quadratic polynomials." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/19704.
Повний текст джерелаCommittee Chair: Basu, Saugata; Committee Member: Etnyre, John; Committee Member: Ghomi, Mohammad; Committee Member: Gonzalez-Vega, Laureano; Committee Member: Powers, Victoria.
Alves, Jesmmer da Silveira. "Definitividade de formas quadráticas – uma abordagem polinomial." Universidade Federal de Goiás, 2016. http://repositorio.bc.ufg.br/tede/handle/tede/6586.
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Fundação de Amparo à Pesquisa do Estado de Goiás - FAPEG
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
Quadratic forms are algebraic expressions that have important role in different areas of computer science, mathematics, physics, statistics and others. We deal with rational quadratic forms and integral quadratic forms, with rational and integer coefficients respectively. Existing methods for recognition of rational quadratic forms have exponential time complexity or use approximation that weaken the result reliability. We develop a polinomial algorithm that improves the best-case of rational quadratic forms recognition in constant time. In addition, new strategies were used to guarantee the results reliability, by representing rational numbers as a fraction of integers, and to identify linear combinations that are linearly independent, using Gauss reduction. About the recognition of integral quadratic forms, we identified that the existing algorithms have exponential time complexity for weakly nonnegative type and are polynomial for weakly positive type, however the degree of the polynomial depends on the algebra dimension and can be very large. We have introduced a polynomial algorithm for the recognition of weakly nonnegative quadratic forms. The related algorithm identify hypercritical restrictions testing every subgraph of 9 vertices of the quadratic form associated graph. By adding Depth First Search approach, a similar strategy was used in the recognition of weakly positive type. We have also shown that the recognition of integral quadratic forms can be done by mutations in the related exchange matrix.
Formas quadráticas são expressões algébricas que têm papel importante em diferentes áreas da ciência da computação, matemática, física, estatística e outras. Abordamos nesta tese formas quadráticas racionais e formas inteiras, com coeficientes racionais e inteiros respectivamente. Os métodos existentes para reconhecimento de formas quadráticas racionais têm complexidade de tempo exponencial ou usam aproximações que deixam o resultado menos confiável. Apresentamos um algoritmo polinomial que aprimora o melhorcaso do reconhecimento de formas quadráticas para tempo constante. Ainda mais, novas estratégias foram usadas para garantir a confiabilidade dos resultados, representando nú- meros racionais como frações de inteiros, e para identificar combinações lineares que são linearmente independentes, usando a redução de Gauss. Sobre o reconhecimento de formas inteiras, identificamos que os algoritmos existentes têm complexidade de tempo exponencial para o tipo fracamente não-negativa e polinomial para o tipo fracamente positiva. No entanto, o grau do polinômio depende da dimensão da álgebra e pode ser muito grande. Apresentamos um algoritmo polinomial para o reconhecimento de formas inteiras fracamente positivas. Este algoritmo identifica restrições hipercríticas avaliando todo subgrafo com 9 vértices do grafo associado à forma inteira. Através da busca em profundidade, uma estratégia similar pôde ser usada no reconhecimento do tipo fracamente positiva. Por fim, mostramos que o reconhecimento de formas inteiras pode ser feito através de mutações na matriz de troca relacionada.
Penrose, Christopher S. "On quotients of the shift associated with dendrite Julia sets of quadratic polynomials." Thesis, University of Warwick, 1990. http://wrap.warwick.ac.uk/106722/.
Повний текст джерелаManai, Arij. "Some contributions to backward stochastic differential equations and applications." Thesis, Le Mans, 2019. http://www.theses.fr/2019LEMA1022.
Повний текст джерелаThis thesis is dedicated to the study of backward stochastic differential equations (BSDEs) and their applications. In chapter 1, we study the problem of maximizing the utility from terminal wealth where the stock price may jump and there are investment constraints on the agent 's strategies. We focus on the BSDE whose solution represents the maximal utility, which allows transferring results on quadratic BSDEs, in particular the stability results, to the problem of utility maximisation. In chapter 2, we consider the problem of pricing American options from theoretical and numerical sides based upon an alternative representation of the value of the option in the form of a viscosity solution of a parabolic equation with a nonlinear reaction term. We extend the viscosity solution characterization proved in [Benth, Karlsen and Reikvam 2003] for call/put American option prices to the case of a general payoff function in a multi-dimensional setting. We address two new numerical schemes inspired by the branching processes. Our numerical experiments show that approximating the discontinuous driver of the associated reaction/diffusion PDE by local polynomials is not efficient, while a simple randomization procedure provides very good results. In chapter 3, we prove existence and uniqueness results for a general class of coupled mean-field forward-backward SDEs with jumps under weak monotonicity conditions and without the non-degeneracy assumption on the forward equation and we give an application in the field of storage in smart grids in the case where the production of electricity is unpredictable
Beyronneau, Robert Lewis. "The solvability of polynomials by radicals: A search for unsolvable and solvable quintic examples." CSUSB ScholarWorks, 2005. https://scholarworks.lib.csusb.edu/etd-project/2700.
Повний текст джерелаBarkat, Braham. "Design, estimation and performance of time-frequency distributions." Thesis, Queensland University of Technology, 2000.
Знайти повний текст джерелаVeronese, Daniel Oliveira. "Propriedades e convergência de certas fórmulas de quadratura interpolatórias /." São José do Rio Preto : [s.n.], 2005. http://hdl.handle.net/11449/94285.
Повний текст джерелаBanca: Sandra Augusta Santos
Banca: Cleonice Fátima Bracciali
Resumo: Dentre as diversas fórmulas de quadratura interpolatórias estão aquelas que utilizam em sua construção as propriedades dos polinômios ortogonais Pn, ou ainda dos polinômios similares Bn. Consideramos, aqui, fþormulas de quadratura envolvendo polinôomios em x da forma .n(x, .) = Pn-1(.)Pn(x) - Pn(.)Pn-1(x), e da forma Gn(x, u) = Bn-1(u)Bn(x) - Bn(u)Bn-1(x). Abordamos ainda certas fþormulas de quadratura que visam aproximar a integral de um produto de duas funções k e f sendo k Lebesgue integrþavel e f Riemann integrþavel. O principal objetivo deste trabalho þe analisar propriedades das fþormulas de quadratura utilizando-se .n e obter propriedades anþalogas para o caso onde utiliza-se Gn, bem como estudar o erro e as propriedades de convergência das fórmulas envolvendo k e f. Propriedades dos pesos das fórmulas de quadratura nos diversos casos são analisadas, a convergência das fórmulas associadas a k e f são estudadas mediante determinadas escolhas de pontos.
Abstract: Among the many well known quadrature formulas one finds those interesting interpolatory quadrature formulas that take advantage of the properties of orthogonal polynomials Pn or similar polynomials Bn. Here, we consider the interpolatory quadrature rules based on the zeros of the polynomials øn(x, î) = Pn.1(î)Pn(x).Pn(î)Pn.1(x), and Gn(x, u) = Bn.1(u)Bn(x) . Bn(u)Bn.1(x) where î and u are arbitrary parameters. One of the objective of this dissertation is to study some of the known properties of quadrature rules based on øn(x, î) and consider the analogous properties of the quadrature rules based on Gn(x, u).We also look at the convergence properties of those quadrature rules that serve to approximate integrals of the product of functions k and f, where k is a Lebesgue integrable function and f needs to be a Riemann integrable function.
Mestre
Veronese, Daniel Oliveira [UNESP]. "Propriedades e convergência de certas fórmulas de quadratura interpolatórias." Universidade Estadual Paulista (UNESP), 2005. http://hdl.handle.net/11449/94285.
Повний текст джерелаCoordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
Dentre as diversas fórmulas de quadratura interpolatórias estão aquelas que utilizam em sua construção as propriedades dos polinômios ortogonais Pn, ou ainda dos polinômios similares Bn. Consideramos, aqui, fþormulas de quadratura envolvendo polinôomios em x da forma .n(x, .) = Pn-1(.)Pn(x) - Pn(.)Pn-1(x), e da forma Gn(x, u) = Bn-1(u)Bn(x) - Bn(u)Bn-1(x). Abordamos ainda certas fþormulas de quadratura que visam aproximar a integral de um produto de duas funções k e f sendo k Lebesgue integrþavel e f Riemann integrþavel. O principal objetivo deste trabalho þe analisar propriedades das fþormulas de quadratura utilizando-se .n e obter propriedades anþalogas para o caso onde utiliza-se Gn, bem como estudar o erro e as propriedades de convergência das fórmulas envolvendo k e f. Propriedades dos pesos das fórmulas de quadratura nos diversos casos são analisadas, a convergência das fórmulas associadas a k e f são estudadas mediante determinadas escolhas de pontos.
Among the many well known quadrature formulas one finds those interesting interpolatory quadrature formulas that take advantage of the properties of orthogonal polynomials Pn or similar polynomials Bn. Here, we consider the interpolatory quadrature rules based on the zeros of the polynomials øn(x, î) = Pn.1(î)Pn(x).Pn(î)Pn.1(x), and Gn(x, u) = Bn.1(u)Bn(x) . Bn(u)Bn.1(x) where î and u are arbitrary parameters. One of the objective of this dissertation is to study some of the known properties of quadrature rules based on øn(x, î) and consider the analogous properties of the quadrature rules based on Gn(x, u).We also look at the convergence properties of those quadrature rules that serve to approximate integrals of the product of functions k and f, where k is a Lebesgue integrable function and f needs to be a Riemann integrable function.
Burns, Jonathan. "Recursive Methods in Number Theory, Combinatorial Graph Theory, and Probability." Scholar Commons, 2014. https://scholarcommons.usf.edu/etd/5193.
Повний текст джерелаGoffard, Pierre-Olivier. "Approximations polynomiales de densités de probabilité et applications en assurance." Thesis, Aix-Marseille, 2015. http://www.theses.fr/2015AIXM4026/document.
Повний текст джерелаThis PhD thesis studies numerical methods to approximate the probability density function of random variables governed by compound distributions. These random variables are useful in actuarial science to model the risk of a portfolio of contracts. In ruin theory, the probability of ultimate ruin within the compound Poisson ruin model is the survival function of a geometric compound distribution. The proposed method consists in a projection of the probability density function onto an orthogonal polynomial system. These polynomials are orthogonal with respect to a probability measure that belongs to Natural Exponential Families with Quadratic Variance Function. The polynomiam approximation is compared to other numerical methods that recover the probability density function from the knowledge of the moments or the Laplace transform of the distribution. The polynomial method is then extended in a multidimensional setting, along with the probability density estimator derived from the approximation formula. An aggregation procedure adapted to life insurance portfolios is also described. The method aims at building a portfolio of model points in order to compute the best estimate liabilities in a timely manner and in a way that is compliant with the European directive Solvency II
AraÃjo, Adenildo Texeira de. "NÃmeros complexos: um estudo de aplicaÃÃes a trigonometria e as equaÃÃes algÃbricas." Universidade Federal do CearÃ, 2014. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=14006.
Повний текст джерелаThe study of the complex numbers in the medium teaching is characterized, almost exclusively, for the algebraic approach leaving the geometric part and their applications without a due importance. This work presents a study on complex numbers as well as some of their applications so much of the algebraic part, applied to polynomials, as of the geometric part especially applied to the trigonometry. Of I begin did an approach of the historical facts of those numbers mentioning some mathematical that gave their contributions near of that complex group. Soon afterwards the part theoretical, algebraic and geometric is presented, as well as some applications the trigonometry. Finally we presented the theory of the quadratic and cubic algebraic equations and the interaction of those with the complex numbers.
Ghazo, Hanna Zeina. "Cycles combinatoires et géométriques." Thesis, Brest, 2020. http://www.theses.fr/2020BRES0006.
Повний текст джерелаThe work in this thesis concerns the combinatorial theory of graphs, algebraic combinatorics and discrete geometry. On one side, it is about enumerating Hamiltonian paths and cycles of a given type in a tournament; On the other side, it studies numerical sequences verifying a quadratic difference equation.Concerning the results of the first part, we find: an equality between the number of Hamiltonians paths (resp. cycles) of a given type, in a tournament and its complement; an expression of the number of Hamiltonian oriented paths of a given type in a transitive tournament in terms of a recursive function F called the « path-function »; and the construction of an algorithm to compute F.In the second part of the work, we study cyclic graphs altogether with a solution to a quadratic difference equation.A parameter of this equation distinguishes real and complex sequences. A correspondence between real solutions and a class of polynomials with positive integer coefficients is established. To complete the correspondence, 1-step Eulerian digraphs interfere. A complex solution determines a closed planar walk in the plane, for which at each step we turn either left or right by a constant angle (the turning angle). This time, cyclotomic polynomials play a major role. Characterizing polynomials that determine such a solution is a problem that we study to the end of finding geometric properties of such polygonal cycles.When the walk exploits the sides of a regular polygon with exterior angle 2 π/n, we find unexpected phenomena when n≥ 12
Duong, Chinh Cuong. "Exploration d'alternatives aux LMI non-quadratiques pour l'analyse des systèmes non linéaires représentés par des modèles Takagi-Sugeno." Thesis, Reims, 2013. http://www.theses.fr/2013REIMS012/document.
Повний текст джерелаThis thesis deals with the stability and stabilization of nonlinear systems represented by Takagi-Sugeno (T-S) models. The objective of this work is to explore and find out some alternatives to classical LMI conditions in order to reduce the conservatism. First, we focus on robust stabilisation of uncertain switched T-S models. Based on a switched Lyapunov function, the stabilisation conditions are obtained in terms of LMI. Then, a new approach for the stability analysis of polynomial T-S models is proposed. The goal is here to explore alternatives to LMI in the non-quadratic framework. Therefore, an extension of some preliminary result on the stability analysis of polynomial T-S models is proposed by the use of a multiple polynomial Lyapunov function which lead to less conservatism. The stability conditions are given in terms of Sum-of-Squares (SOS) polynomial optimization problem. Finally, classical T-S models being a particular case of polynomial ones, an attempt is done as an alternative to LMI in the non quadratic framework for the design of non-PDC controllers via SOS techniques. Within this framework, global stability may be guaranteed if there exists a solution to the SOS constraints. Moreover, it didn't require unknown parameters in advance like in LMI based non quadratic approaches. However, these SOS based controller design conditions are obtained through a restrictive modelling assumption, suggesting future prospects to this work
Rezende, Alex Carlucci. "A geometria de algumas famílias tridimensionais de sistemas diferenciais quadráticos no plano." Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-25112014-142038/.
Повний текст джерелаPlanar quadratic differential systems occur in many areas of applied mathematics. Although more than one thousand papers have been written on these systems, a complete understanding of this family is still missing. Classical problems, and in particular Hilberts 16th problem, are still open for this family. One of the goals of recent researchers is the topological classification of quadratic systems. As this attempt is not possible in the whole class due to the large number of parameters (twelve, but, after affine transformations and time rescaling, we arrive at families with five parameters, which is still a large number), many subclasses are considered and studied. Specific characteristics are taken into account and this implies a decrease in the number of parameters, which makes possible the study. In this thesis we mainly study two subfamilies of quadratic systems: the first one possessing a finite semielemental triple node and the second one possessing a finite semielemental saddlenode and an infinite semielemental saddlenode formed by the collision of an infinite saddle with an infinite node. The bifurcation diagram for both families are tridimensional. The family having the triple node yields 28 topologically distinct phase portraits, whereas the closure of the family having the saddlenodes within the bifurcation space of its normal form yields 417. Invariant polynomials are used to construct the bifurcation sets and the phase portraits are represented on the Poincaré disk. The bifurcation sets are the union of algebraic surfaces and surfaces whose presence was detected numerically. Moreover, we also present the analysis of a differential system known as SIS model (this kind of systems are easily found in applied mathematics) and the complete classification of quadratic systems possessing invariant hyperbolas.
Bhiri, Bassem. "Stabilité et stabilisation en temps fini des systèmes dynamiques." Thesis, Université de Lorraine, 2017. http://www.theses.fr/2017LORR0100/document.
Повний текст джерелаThis dissertation deals with the finite time stability and the finite time stabilization of dynamic systems. Indeed, it is often important to ensure that during the transient regime, the state trajectories do not exceed certain predefined limits in order to avoid saturations and excitations of the nonlinearities of the system. Hence the interest is to study the stability of the dynamic system in finite time. A dynamic system is said to be stable in finite time (FTS) if, for any initial state belonging to a predetermined bounded set, the state trajectory remains within another predetermined bounded set for a finite and fixed time. When the system is disturbed, it is called finite time boundedness (FTB). In this manuscript, the goal is to improve the results of finite time stability used in the literature. First, new sufficient conditions expressed in terms of LMIs for the synthesis of an FTB controller by dynamic output feedback have been developed via an original descriptor approach. An original method has been proposed which consists in using a particular congruence transformation. Second, new LMI conditions for the study of finite time stability and finite time stabilization have been proposed for disturbed and undisturbed nonlinear quadratic systems. Third, to obtain even less conservative conditions, new developments have been proposed using polynomial Lyapunov functions
Hou, Ya-Fang, and 侯雅芳. "An Improvement of The Multiple Polynomial Quadratic Sieve." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/9xjv59.
Повний текст джерела國立中山大學
資訊工程學系研究所
96
Large integer factoring problem is a difficult computing problem. The security of many public-key cryptograohy system depend on the large interger factoring problem. Dr. Guan implement 「The Multiple Polynomail Quadratic Sieve Algorithm」 and name the program 「GQS」. The program successfully factor RSA-130 interger in 2004. It can reduce the time of sieving that the MPQS algorithm retain the smooth number with one or two prime. But finally the size of factor basis is large. We use some of the prime retained by the MPQS algorithm to match with the smooth number and reduce the size of factor basis. And then we can reduce the time of factoring. In this paper, we implement our idea in a AIX server and the result of this paper can be a suggestion of the improvement of MPQS.
廖偉呈. "Constructing Psi-Series Solution for Quadratic Polynomial Systems." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/31900501163873546899.
Повний текст джерела國立清華大學
數學系
100
In this paper, we discuss how to build a local solution for a system of ordinary differentiable equations of quadratic forms by constructing a psi-series. We want to understand how the solution behaves around the singularities. There are a necessary and sufficient condition: Real leading coefficients ensure the occurrence of blow up in finite time, and real time singularity implies that the leading coefficients of one asymptotic series are real. The Psi-series of quadratic systems on the plane has been studied. The relationship between the behavior and integrability of the system is also illustrated.
Chih-Chiang, Chen, and 陳志強. "Computer Assisted Multi-segment Quadratic Polynomial Circuit Synthesizer." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/69489483405833909915.
Повний текст джерела中華大學
電機工程學系碩士班
102
Abstract The goal of this thesis is mainly to discuss the computer assisted design(CAD) of multi-stage combination of quadratic polynomial circuit synthesizer(CAD). Only need to know the value of the coefficients of quadratic polynomials, the multi-stage quadratic polynomial circuit can be produced. Or by use of second-order Taylor expansion to approximate the natural logarithm, exponential and other irregular functions, we can use computer assisted quadratic polynomial circuit synthesizer to complete them. For design of quadratic polynomial multistage combinational circuit in this thesis tools used HSPICE and MATLAB. Circuit layout used the TSMC 0.18μm CMOS simulation process which provided via CIC. The area of the chip is about 0.32 mm × 0.32mm, sigmoid function current input range -140 μA to 200 μA, the bandwidth of about 426.4MHz,sigmoid inverse function current input range -200 μA to 118 μA, the bandwidth is about 409.2MHz.
"A simple polynomial-time algorithm for convex quadratic programming." Laboratory for Information and Decision Systems, Massachusetts Institute of Technology], 1988. http://hdl.handle.net/1721.1/3092.
Повний текст джерелаCaption title.
Includes bibliographical references.
This research is partially supported by the U.S. Army Research Office (Center for Intelligent Control Systems), contract DAAL03-86-K-0171 This research is partially supported by the National Science Foundation grant NSF-ECS-8519058
Chen, Ya-Hui, and 陳雅蕙. "D-optimal designs for linear and quadratic polynomial models." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/21278758614042882999.
Повний текст джерела國立中山大學
應用數學系研究所
91
This paper discusses the approximate and the exact n-point D-optimal design problems for the common multivariate linear and quadratic polynomial regression on some convex design spaces. For the linear polynomial regression, the design space considered are q-simplex, q-ball and convex hull of a set of finite points. It is shown that the approximate and the exact n-point D-optimal designs are concentrated on the extreme points of the design space. The structure of the optimal designs on regular polygons or regular polyhedra is also discussed. For the quadratic polynomial regression, the design space considered is a q-ball. The configuration of the approximate and the exact n-point D-optimal designs for quadratic model in two variables on a disk are investigated.
Xiao, Fu-Yuan, and 蕭富源. "The parameter estimation of quadratic polynomial model with measurement errors." Thesis, 2004. http://ndltd.ncl.edu.tw/handle/53778850809137336090.
Повний текст джерела淡江大學
數學學系碩士班
94
Regression analysis is a statistic method for understanding the relationship between independent variable and dependent variable. When establishing the Regression Analysis, sometimes people will meet the problem that the independent variable in the data base cannot be measure exactly, and that is what people called measurement error model. The reason to determine the regression analysis of measurement error model is to explain when the variable becomes independent in measurement error and regression error, and the measurement error and regression error are bivariate normal, the parameter is unidentifiable. Therefore, in the measurement error model, the basic problem is what conditions can make the parameters to be identifiable. In this thesis, we suppose that the measurement error is normal distribution with mean zero and unknown variable, and discuss the identifiable qualifications of parameters in simple linear regression model and in quadratic polynomial model respectively. We also discuss the estimators of parameters which are consistency, and simulate the performance of mean square error.
Liao, Shi-Yuan, and 廖士元. "Using Two-Segments Quadratic Polynomial Curve Approximation for Road Boundary Detection." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/16911200189346728386.
Повний текст джерела國立中正大學
電機工程所
97
In this thesis, we propose a new way to describe the road boundary more accurately. Originally, based on the 2nd–order polynomial equation, we can substitute the coordinates of the boundary points into the equation and minimize the sum of square errors to obtain the polynomial solution and hence the approximate curve. However, the quadratic polynomial curve cannot fit all road boundary curves well, especially when the road has abrupt turning point. In these cases, even though the higher order polynomial can be applied yet too complicated to solve. In this research, we try to find a boundary point which separates the whole curve into two segments, and the total sum of square errors of the two curve segments must be minimized. According to our experiments, the curves turned out are definitely more accurate, especially the road has sharper turning point. The time needed to spend for this is to be considered next.
Wu, Pei-Lun, and 吳培綸. "Design of CMOS Quadratic Polynomial Circuit Using Best Fit Method and Four-Segment Method." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/95497873543099295336.
Повний текст джерела中華大學
電機工程學系碩士班
100
In this thesis, we design CMOS quadratic polynomial circuit using best fit method and four-segment method. The propose of this thesis is based on CMOS current-mode quadratic function circuits, its W/L ratio and construction could be adjusted by the relative error that the users needed. First we explain how to implement CMOS current-mode quadratic circuits and design the proposed circuit in the way of multiple corrections. We use the best fit CMOS quadratic polynomial circuit to realization exponential function. The imitative result based on the range of -48μA~22μA, and the relative error within±3%. The output dynamic range of 14.1dB, and linearity error less than ±0.3dB. Four-segment CMOS quadratic polynomial circuit utilize Taylor to fitting sigmoid function. The circuit is designed by four sets of quadratic polynomial circuit and three sets of segmentation control circuit. The imitative result based on the range of -277μA~480μA, and the relative error within±3%. The PSRR are 34.3. The imitative tool is HSPICE and MATLAB. Circuit layout software used the CADANCE which provided with CIC and TSMC 0.35μm process.
Rauh, Nikolas Marcel. "Resultants and height bounds for zeros of homogeneous polynomial systems." 2013. http://hdl.handle.net/2152/20950.
Повний текст джерелаtext
Begum, Monzu Ara. "Bifurcation in complex quadratic polynomial and some folk theorems involving the geometry of bulbs of the mandelbrot set." Thesis, 2001. http://spectrum.library.concordia.ca/1443/1/MQ64045.pdf.
Повний текст джерелаShao-RongWang and 王勺融. "Correction of the Quadratic Light Source Dependence of the Aberration Polynomial based on the Characteristic Function of Hamilton." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/32525619105244978255.
Повний текст джерела國立成功大學
機械工程學系碩博士班
100
Nowadays the way of designing optical systems, most of people use optical design code to insert system model. For correcting aberration people set variables and what they want to optimize for, then optimize the system with the optimization tool of optical design code. It sets many system variables and spends a lot of execution time for design result. Although the design way is very complete and effective, the basis of optical feature is wake. This thesis takes based on optical aberration theory and discusses how to correct the quadratic light source dependence of the aberration polynomial which is based on the characteristic function of Hamilton. A connection between the mathematical model and the physical model due to the property of the aberration is built. Conditions of correcting the aberration in real physical system are found though the connection.
Mbuntcha, Wuntcha Calvin. "Optimisation quadratique en variables binaires : quelques résultats et techniques." Thèse, 2009. http://hdl.handle.net/1866/6625.
Повний текст джерелаChi, Fu-Chung, and 紀富中. "Evaluation of the Two-Stages Hough Transform to Detect Lines and Circles in Digital Images by Using Quadratic Polynomial Fitting." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/16031202306840683091.
Повний текст джерела國立交通大學
電機與控制工程系
90
A new two-stages Hough transform for detecting lines and circles in digital image is proposed here. The main feature of the new two-stages Hough transform is to evaluate the normal direction of the feature point by using quadratic polynomial fitting and decompose n dimension parameter array into n-1 dimension parameter array. The method is extended to detect lines in the digital image. In complicated images, the most curves are straight lines and circles and arcs. By using quadratic polynomial fitting, the normal direction and the curvature would be computed. By using the property of the different curvature between the lines and arcs, the non-straight lines are suppressed not to vote and only let the straight lines to vote in the two-stages Hough transform with quadratic polynomial fitting. The approach would get good performance in the experiment. The technique would be applied in CAD image and real pattern to get good results.
(10732485), Clinton W. Bradford. "Square Forms Factoring with Sieves." Thesis, 2021.
Знайти повний текст джерелаAckermann, Maria Helena. "Mixture models based on power means and generalised Q-fractions." Diss., 2011. http://hdl.handle.net/2263/27481.
Повний текст джерелаDissertation (MSc)--University of Pretoria, 2011.
Chemical Engineering
unrestricted
Massey, John Sirles. "Surface shape regions as manifestations of a socio-economic phenomenon : a solution to the choropleth mapping problem." Thesis, 2012. http://hdl.handle.net/2440/84536.
Повний текст джерелаThesis (M.Sc.(M&CS)) -- University of Adelaide, School of Mathematical Sciences, 2012