Στόχος λοιπόν της διπλωματικής εργασίας είναι να δούμε πως μπορούμε να αναγνωρίσουμε ένα μη γραμμικό σύστημα ομοιόμορφα παρατηρήσιμο χρησιμοποιώντας την κανονική μορφή παρατηρησιμότητας και τα πολυώνυμα Laguerre. / The Objective of therefore diplomatic work is to see how we can identify a non linear system, uniformly observable using the observable canonical form and the polynomials Laguerre.

Made available in DSpace on 2014-06-11T19:30:27Z (GMT). No. of bitstreams: 0 Previous issue date: 2012-07-20Bitstream added on 2014-06-13T20:00:38Z : No. of bitstreams: 1 mello_mv_dr_sjrp_parcial.pdf: 191324 bytes, checksum: 834d46b5c37971622ceb90534e435e2c (MD5) Bitstreams deleted on 2014-08-22T14:57:09Z: mello_mv_dr_sjrp_parcial.pdf,Bitstream added on 2014-08-22T15:02:10Z : No. of bitstreams: 1 000697077.pdf: 803410 bytes, checksum: da262ae1b32f853d9d5b7460be7943f5 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Neste trabalho, estudamos propriedades dos zeros de polinômi os ortogonais do tipo Sobolev . Provam os resultados sobre entrelaçamento, monotonicidade e assintótica. Fornecemos, também , condições s necessárias e/ou suficientes para os zeros dos polinômios {Sn}n≥0, gerados pela fórmula Sn(x) = Pn(x) + an−1Pn−1(x), ou Sn(x) −bn−1Sn−1(x) = Pn(x), on d e {Pn}n≥0 é um a sequência de polinômios ortogonais, ser em todos reais / We study various properti s of the zeros of Sobolev typ e orthogonal polynomials. Results on interacing, monotonicity and asymptotic are proved . We also provide general necessary and/or sufficient con ditions in order to the zeros of the polynomials {Sn}n≥0, generated by the formulae Sn(x) = Pn(x) + an−1Pn−1(x), or Sn(x) −bn−1Sn−1(x) = Pn(x), where {Pn}n≥0 is a sequence of orthogon al polynomials, are all real

The Kazhdan-Lusztig polynomial of a matroid M, denoted P_M( t ), was recently defined by Elias, Proudfoot, and Wakefield. These polynomials are analogous to the classical Kazhdan-Lusztig polynomials associated with Coxeter groups. For example, in both cases there is a purely combinatorial recursive definition. Furthermore, in the classical setting, if the Coxeter group is a Weyl group then the Kazhdan-Lusztig polynomial is a Poincare polynomial for the intersection cohomology of a particular variety; in the matroid setting, if M is a realizable matroid then the Kazhdan-Lusztig polynomial is also the intersection cohomology Poincare polynomial of a variety corresponding to M. (Though there are several analogies between the two types of polynomials, the theory is quite different.) Here we compute the Kazhdan-Lusztig polynomials of several graphical matroids, including thagomizer graphs, the complete bipartite graph K_{2,n}, and (conjecturally) fan graphs. Additionally, we investigate a conjecture by the author, Proudfoot, and Young on the real-rootedness for Kazhdan-Lusztig polynomials of these matroids as well as a conjecture on the interlacing behavior of these roots. We also show that the Kazhdan-Lusztig polynomials of uniform matroids of rank n − 1 on n elements are real-rooted. This dissertation includes both previously published and unpublished co-authored material.

In this research the Bring-Jerrard quintic polynomial equation is investigated for a formula. Firstly, an explanation given as to why finding a formula and the equation being unsolvable by radicals may appear contradictory when read out of context. Secondly, the reason why some mathematical software programs may fail to render a conclusive test of the formula, and how that can be corrected is explained. As an application, this formula is used to determine another formula that expresses the gravitational constant in terms of other known physical constants. It is also explained why up to now it has been impossible to determine this expression using the current underlying theoretical basis. / M. Sc. (Applied Mathematics)

This mathematics thesis deals with combinatorial representation theory. Cells were introduced in a 1979 paper written by D. Kazhdan and G. Lusztig, and have intricate links with many areas of mathematics, including the representation theory of Coxeter groups, Iwahori–Hecke algebras, semisimple complex Lie algebras, reductive algebraic groups and Lie groups. One of the main problems in the theory of cells is their classification for all finite Coxeter groups. This thesis is a detailed study of cells in type Bn with respect to certain choices of parameters, and contributes to the classification by giving the first characterisation of left cells when b/a = n − 1. Other results include the introduction of a generalised version of the enhanced right descent set and exhibiting the asymptotic left cells of type Bn as left Vogan classes. Combinatorial results give rise to efficient algorithms so that cells can be determined with a computer; the methods involved in this work transfer to a new, faster way of calculating the cells with respect to the studied parameters. The appendix is a Python file containing code to make such calculations.

This paper examines idam's conjuecture and some of its generalizations. In terms of Adam's conjecture, we prove Alspach and Parson's results f or Zpq and ZP2. More generally, we prove Babai's characterization of the CI-property, Palfy's characterization of CI-groups, and Brand's result for Zpr for polynomial isomorphism's. We also prove for the first time a characterization of the CI-property for 1 SG, and prove that Zn is a CI-Pn-group where Pn is the group of permutation polynomials on Z,, and n is square free.

No description available.

This thesis is concerned with the qualitative and quantitative properties of solutions of certain classes of ordinary di erential equations (ODEs); in particular linear boundary value problems of second order ODE's and non-linear ODEs of order at most four. The Lyapunov's second method of special functions called Lyapunov functions are employed extensively in this thesis. We construct suitable complete Lyapunov functions to discuss the qualitative properties of solutions to certain classes of non-linear ordinary di erential equations considered. Though there is no unique way of constructing Lyapunov functions, We adopt Cartwright's method to construct complete Lyapunov functions that are required in this thesis. Su cient conditions were established to discuss the qualitative properties such as boundedness, convergence, periodicity and stability of the classes of equations of our focus. Another aspect of this thesis is on the quantitative properties of solutions. New scheme based on interpolation and collocation is derived for solving initial value problem of ODEs. This scheme is derived from the general method of deriving the spline functions. Also by exploiting the Trigonometric identity property of the Chebyshev polynomials, We develop a new scheme for approximating the solutions of two-point boundary value problems. These schemes are user-friendly, easy to develop algorithm (computer program) and execute. They compare favorably with known standard methods used in solving the classes of problems they were derived for

Orientador: Walter Alexandre Carnielli / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciencias Humanas / Made available in DSpace on 2018-08-14T13:45:04Z (GMT). No. of bitstreams: 1 Carolino_PietroKreitlon_M.pdf: 612208 bytes, checksum: d9a9dde30e7c7ea6f5a420ad1dfde09c (MD5) Previous issue date: 2009 / Resumo: A obra de George Boole, pedra fundamental da lógica contemporânea, não separa métodos de análise matemática, de métodos lógicos propriamente ditos. Se, por um lado, a falta de fronteiras metodológicas nítidas tem-lhe valido azedas críticas, por outro lado fazem da obra de Boole uma verdadeira síntese do pensamento formal, herdada de Aristóteles, Leibniz, Newton e dos analistas a partir do século XVII, como Taylor, MacLaurin e Lagrange. O que foi chamado em [12] de polinomizar é precisamente a tentativa de reavaliar os métodos oriundos de Boole e Leibniz, que permitem representar a semântica e a sintaxe de diversos sistemas lógicos pela manipulação algébrica. Tirando partido de resultados combinatórios elementares, é possível tratar todas as lógicas multivalentes verofuncionais com base em manipulação polinomial; não somente estas, mas também lógicas não-verofuncionais, e ainda fragmentos da lógica de primeira ordem, que formalizam a teoria clássica de silogismos de Aristóteles. Este trabalho pretende esclarecer tais questões de forma mais abrangente, e investigar a possibilidade de estender o tratamento da polinomização a outras lógicas. São obtidos alguns resultados positivos, como novas demonstrações de teoremas conhecidos, mas também negativos, que mostram as limitações do método. Investiga-se também a relação da polinomização de lógicas com outros tratamentos conhecidos, como paraconsistentização, temporalização, algebrização etc. / Abstract: The work of George Boole, cornerstone of contemporary logic, does not draw a clear distinction between the methods of mathematical analysis, and those of logic proper. If, on the one hand, this lack of well-de ned borders has earned it harsh criticism, on the other hand it makes Boole's work a true synthesis of formal thought, inherited from Aristotle, Leibniz, Newton and the 17th-century analysts, such as Taylor, MacLaurin and Lagrange. What was called polynomizing in [12] is precisely the attempty to re-evaluate the methods originiating in Boole and Leibniz, which allow one to represent the semantics and syntax of varioius logical systems through algebraic manipulation. Using elementary combinatorial results, it is possible to treat all multivalent truth-functional logics by polynomial manipulation; not only these, but some non-truth-functional logics, and also fragments of first-order logic, which formalize Aristotle's classical theory of syllogisms. The present work intends to throw light upon such questions in a broader way, and to investigate the possibility of extending the method of polynomization to other logics. Some positive results are obtained, such as new proofs of known theorems, but also some negative ones, which show the inherent limitations of the method. We further investigate the relationship between polynomization of logics and other known treatments, such as paraconsistentization, temporalization, algebrization etc. / Mestrado / Filosofia / Mestre em Filosofia

Factorial design has played a prominent role in the field of experimental design because of its richness in both theory and application. It explores the factorial effects by allowing the arrangement of efficient and economic experimentation, among which orthogonal design, uniform design and some other factorial designs have been widely used in various scientific investigations. The main contribution of this thesis shows the recent advances in the classification and selection of orthogonal designs. Design isomorphism is essential to the classification, selection and construction of designs. It also covers various popular design criteria as necessary conditions, such connection has led to a rapid growth of research on the novel approaches for either detecting the non-isomorphism or identifying the isomorphism. But further classification of non-isomorphic designs has received little attention, and hence remains an open question. It motivates us to propose the degree of isomorphism, as a more general view of isomorphism, for classifying non-isomorphic subclasses in orthogonal designs, and develop the column-wise identification framework accordingly. Selecting designs in sequential experiments is another concern. As a well-recognized strategy for improving the initial design, fold-over techniques have been widely applied to construct combined designs with better property in a certain sense. While each fold-over method has been comprehensively studied, there is no discussion on the comparison of them. It is the motivation behind our survey on the existing fold-over methods in view of statistical performance and computational complexity. The thesis involves five chapters and it is organized as follows. In the beginning chapter, the underlying statistical models in factorial design are demonstrated. In particular, we introduce orthogonal design and uniform design associated with commonly-used criteria of aberration and uniformity. In Chapter 2, the motivation and previous work of design isomorphism are reviewed. It attempts to explain the evolution of strategies from identification methods to detection methods, especially when the superior efficiency of the latter has been gradually appreciated by the statistical community. In Chapter 3, the concepts including the degree of isomorphism and pairwise distance are proposed. It allows us to establish the hierarchical clustering of non-isomorphic orthogonal designs. By applying the average linkage method, we present a new classification of L 27 (3 13 ) with six different clusters. In Chapter 4, an efficient algorithm for measuring the degree of isomorphism is developed, and we further extend it to a general framework to accommodate different issues in design isomorphism, including the detection of non-isomorphic designs, identification of isomorphic designs and the determination of non-isomorphic subclass for unclassified designs. In Chapter 5, a comprehensive survey of the existing fold-over techniques is presented. It starts with the background of these methods, and then explores the connection between the initial designs and their combined designs in a general framework. The dictionary cross-entropy loss is introduced to simplify a class of criteria that follows the dictionary ordering from pattern into scalar, it allows the statistical performance to be compared in a more straightforward way with visualization