Orientador: Hu Sheng / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Científica / Made available in DSpace on 2018-07-17T13:13:33Z (GMT). No. of bitstreams: 1 Polettini_AltairdeFatimaFurigo_M.pdf: 1495169 bytes, checksum: 6501e69a39bcdd0908553a63a1f22cd4 (MD5) Previous issue date: 1982 / Resumo: Não informado. / Abstract: Not informed. / Mestrado / Mestre em Matemática

A tese está dividida em duas partes. A primeira parte é dedicada a análise de quando certas aplicações definidas em uma classe de anéis não-associativos são aditivas. Esta questão foi estudada para anéis associativos por Martindale, [38], e outros, [35], [4], [22], [23], [37], [39], [36], [7] e [27]. Para anéis de Jordan, foi estudada por Ji Peisheng, [26], e para anéis alternativos por Ferreira e Guzzo, [12], [13] e [14]. Muito pouco se conhece ainda sobre esta questão com relação a anéis e álgebras não-associativas em geral. Assim, um propósito é o de tentar ampliar ou aprofundar esse conhecimento para outras classes de anéis não-associativos. Um teorema muito importante na teoria das álgebras associativas é o Teorema de Wedderburn. A segunda parte a ser investigada nesta tese procura provar um teorema do tipo Wedderburn para b-álgebras do tipo (, ). Muitos autores buscam provar um teorema do tipo de Wedderburn para algumas álgebras não-associativas, já temos isso feito para as álgebras alternativas e de Jordan. No caso das b-álgebras definimos: No capitulo 4, definimos bdecomposição de Wedderburn. Assim, outra linha es- tudada é ver se alguma b-álgebra possu uma b-decomposição de Wedderburn. / The thesis is divided into two parts. The first part is dedicated to analysis when certain applications defined in a class of non-associative rings are additive. This question was studied for associative rings by Martindale, [38], and others, [35], [4], [22], [23], [37] , [39], [36], [7] and [27]. For Jordans rings, it was studied by Ji Peisheng, [26], and for alternative rings, by Ferreira and Guzzo, [12], [13] and [14]. We know very few results with regard to nonassociative rings and algebras, in general. This way, a purpose is the one of try to extend or to deepen that knowledge to other classes of non-associative rings. A very important theorem in the theory of associative algebras is the Theorem of Wedderburn. The second part to be investigated try to prove a theorem of Wedderburn type to b-algebras (, ) type. Many authors seek to prove a theorem of Wedderburn for some type of non-associative algebras, we have done it for alternative algebras and Jordan. In the case of b-algebras defined: In chapter 4, we define bWedderburn decomposition. Thus, another line study is to see if some b-algebra possess a b-Wedderburn decomposition.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1949. / Typescript. Includes "Author's Note" (i.e., errata) and vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaf 71).

Computing the structure of a finite-dimensional algebra is a classical mathematical problem in symbolic computation with many applications such as polynomial factorization, computational group theory and differential factorization. We will investigate the computational complexity and exhibit new algorithms for this problem over the field \mathbb{F}_{q}(y), where \mathbb{F}_{q} is the finite field with q elements. In this thesis we will present new efficient probabilistic algorithms for Wedderburn decomposition and the computation of the radical.

Computing the structure of a finite-dimensional algebra is a classical mathematical problem in symbolic computation with many applications such as polynomial factorization, computational group theory and differential factorization. We will investigate the computational complexity and exhibit new algorithms for this problem over the field \mathbb{F}_{q}(y), where \mathbb{F}_{q} is the finite field with q elements. In this thesis we will present new efficient probabilistic algorithms for Wedderburn decomposition and the computation of the radical.

Trois thèmes ont été poursuivis dans la thèse : -On introduit les fonctions symétriques non commutatives dans le cadre des extensions de Ore. On généralise les résultats obtenus par Gelfand, Retakh et Wilson. Notre méthode est en outre plus naturelle et évite l’utilisation des quasi déterminants. -On montre que les factorisations des polynômes de Wedderburn sont en bijection avec des drapeaux complets d’espaces vectoriels provenant de noyaux d’applications polynomiales en des transformations pseudo-linéaires. D’autres résultats, motivés par la théorie des codes, concernent la factorisation dans des anneaux de Ore construits sur des corps finis. On y montre, en particulier, comment se ramener au cas d’un anneau de polynômes classique. -On caractérise l’existence de P.P.C.M. à gauche de polynômes linéaires dans des extensions de Ore sur des anneaux quelconques. Dans ce cadre, une étude détaillée des transformations pseudo-linéaires s’est révélée, une fois encore, un outil indispensable. / Three themes have been pursued in the thesis : We introduce the noncommutative symmetric functions in the frame of Ore extensions. We generalize the results obtained by Gelfand, Retakh and Wilson. Moreover our method is more natural and avoid the use of quasideterminants. We show that the factorizations of Wedderburn polynomials are in bijection with complete flags of vector spaces coming from kernels of polynomial maps in pseudo-linear transformations. Other results, motivated by coding theory, concern the factorizations in Ore extension over finite fields. In particular, we show how to translate factorisations in these rings into factorisations in the usual polynomial rings. We characterize the existence of L.L.C.M of linear polynomials in Ore extensions over general rings. In this frame, a detailed study of pseudo-linear transformations was necessary.

Tech. Universiẗat, Diss., 2003--Aachen.

The three-dimensional (3D) baroclinic response of Cayuga Lake to surface wind forcing was investigated using the fully nonhydrostatic MITgcm. The model was validated against observed temperature data using a hydrostatic 450 m (horizontal) grid and both qualitative and quantitative methods. The model correctly reproduces the basin-scale dynamics (e.g., seiche with horizontal mode-one period T1 = 80 h) with a basin-wide root-mean-square error of 1.9 C. Nonlinear internal surges were visualized to evolve due to (i) a wind-induced locally downwelled thermocline (wind duration Twind < T1/4), (ii) a basin-scale wind-induced upwelled thermocline (Twind > T1/4), (iii) internal hydraulic jumps (IHJs). Results from a 113 m grid and field observations were used to characterize the basin-scale internal wave field according to composite Froude number (G2), Wedderburn number (WN), and Lake number (LN). The typical Cayuga Lake response is a surge when ~ 1 < WN (LN) < ~ 2-12 and a surge with emergent nonlinear internal waves (NLIWs) when WN or LN < ~ 2, in agreement with published laboratory studies. An observed shock front was simulated to be an IHJ, occurring at mid-basin during strong winds when WN < 0.8. This is the first simulation of a mid-basin seiche-induced IHJ due to super critical conditions (G2 > 1) in a lake. The topographic-induced IHJs were also shown to form when the surges interact with a sill-contraction topographic feature. Both high-resolution hydrostatic and nonhydrostatic models were used to investigate the evolution, propagation and shoaling of NLIWs at medium lake-scale. A nonhydrostatic 22 m grid with lepticity λ ~ 1 ensures minimal numerical relative to physical dispersion, qualitatively reproducing observed dispersive NLIWs using ~ 2.3E+8 grid cells. Solitary waves evolve with almost unchanged wavelengths upon grid refinement from 40 m (λ ~ 2) to 22 m; suggesting model convergence to the correct solution. Corresponding hydrostatic grids were shown to produce a packet of narrower spurious solitary-like motions with different wavelengths, representing a balance between nonlinear steepening and numerical dispersion. Local gyre-like patterns and secondary transverse NLIW packets were visualized to result from wave-topography interaction, suggesting that NLIW propagation in long narrow lakes, where the bottom topography has irregularities is fundamentally 3D. / Thesis (Ph.D, Civil Engineering) -- Queen's University, 2012-12-14 12:45:21.727

Thesis (MA(N.T.))--University of Pretoria, 2006. / Includes bibliographical references (leaves 206-217) Available on the Internet via the World Wide Web.

In this thesis, we will explore the structure of Terwilliger algebras over several different types of finite groups. We will begin by discussing what a Schur ring is, as well as providing many different results and examples of them. Following our discussion on Schur rings, we will move onto discussing association schemes as well as their properties. In particular, we will show every Schur ring gives rise to an association scheme. We will then define a Terwilliger algebra for any finite set, as well as discuss basic properties that hold for all Terwilliger algebras. After specializing to the case of Terwilliger algebras resulting from the orbits of a group, we will explore bounds of the dimension of such a Terwilliger algebra. We will also discuss the Wedderburn decomposition of a Terwilliger algebra resulting from the conjugacy classes of a group for any finite abelian group and any dihedral group.