Proefschrift--Nederlandsche Economische Hoogeschool, Rotterdam. / "Stellingen": [4] p. inserted.

Thesis (M.S.)--West Virginia University, 2002. / Title from document title page. Document formatted into pages; contains xi, 87 p. : ill. Includes abstract. Includes bibliographical references (p. 84-87).

Thesis (Ph.D)--Aerospace Engineering, Georgia Institute of Technology, 2009. / Committee Chair: Mavris, Dimitri; Committee Member: Alley, Nicholas; Committee Member: Lakshmi, Sankar; Committee Member: Sriram, Rallabhandi; Committee Member: Stephen, Ruffin. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Thesis (Ph. D.)--Drexel University, 2005. / Includes abstract and vita. Includes bibliographical references (leaves 192-204).

Thesis (Ph. D.)--University of Texas at Austin, 2005. / Supervisor: Fernando Rodriguez-Villegas. Vita. Includes bibliographical references.

We develop several continuous method models for convex quadratic programming (CQP) problems with di.erent types of constraints. The essence of the continuous method is to construct one ordinary di.erential equation (ODE) system such that its limiting equilibrium point corresponds to an optimal solution of the underlying optimization problem. All our continuous method models share the main feature of the interior point methods, i.e., starting from any interior point, all the solution trajectories remain in the interior of the feasible regions. First, we present an a.ne scaling continuous method model for nonnegativity constrained CQP. Under the boundedness assumption of the optimal set, a thorough study on the properties of the ordinary di.erential equation is provided, strong con­vergence of the continuous trajectory of the ODE system is proved. Following the features of this ODE system, a new ODE system for solving box constrained CQP is also presented. Without projection, the whole trajectory will stay inside the box region, and it will converge to an optimal solution. Preliminary simulation results illustrate that our continuous method models are very encouraging in obtaining the optimal solutions of the underlying optimization problems. For CQP in the standard form, the convergence of the iterative .rst-order a.ne scaling algorithm is still open. Under boundedness assumption of the optimal set and nondegeneracy assumption of the constrained region, we discuss the properties of the ODE system induced by the .rst-order a.ne scaling direction. The strong convergence of the continuous trajectory of the ODE system is also proved. Finally, a simple iterative scheme induced from our ODE is presented for find­ing an optimal solution of nonnegativity constrained CQP. The numerical results illustrate the good performance of our continuous method model with this iterative scheme. Keywords: ODE; Continuous method; Quadratic programming; Interior point method; A.ne scaling.

Orientador: Antonio Jose Engler / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-06T01:37:33Z (GMT). No. of bitstreams: 1 OliveiraJunior_MauroRibeirode_M.pdf: 283417 bytes, checksum: ed6ca467b6f01b1fd631b10cca398846 (MD5) Previous issue date: 2006 / Resumo: Neste trabalho seguimos, nos quatro primeiros capítulos, para a construção efetiva de extensões quaterniônicas, a partir do acúmulo de informações obtidas nos capítulos iniciais 1 e 2, sobre a estrutura dos subcorpos intermediários a uma extensão deste tipo, conhecimentos quais são obtidos pela atuação forte da Teoria de Galois, uma vez que é muito bem conhecida a estrutura de subgrupos do grupos dos Quatérnios. Finalmente, em posse dos resultados e caracterizações dos capítulos precedentes, juntamente aos resultados que relacionam formas quadráticas e álgebras quaterniônicas, no capítulo 6 demonstramos o Critério de Witt, que acerta sobre a imersão de extensões biquadráticas em quaterniônicas. Deste critério obtemos um importante resultado de interesse da Teoria dos Números, uma nova caracterização dos números racionais que são somas de três quadrados / Mestrado / Algebra / Mestre em Matemática

Condition monitoring of epicyclic gearboxes through vibration signature analysis, with particular focus on time domain methods and the use of adaptive filtering techniques for the purpose of signal enhancement, is the central theme of this work. Time domain filtering methods for the purpose of removal of random noise components from periodic, but not necessarily stationary or cyclostationary, signals are developed. Damage identification is accomplished through vibration signature analysis by nonstationary timefrequency methods, belonging to Cohen’s general class of time-frequency distributions, strictly based in the time domain. Although a powerful and commonly used noise reduction technique, synchronous averaging requires alternate sensors in addition to the vibration pickup. For this reason the use of time domain techniques that employ only the vibration data is investigated. Adaptive filters may be used to remove random noise from the nonstationary signals considered. The well-known Least Mean Squares algorithm is employed in an adaptive line enhancer configuration. To counter the much discussed convergence difficulties that are often experienced when the least mean squares algorithm is applied, a new unconditionally convergent algorithm based on the spherical quadratic steepest descent method is presented. The spherical quadratic steepest descent method has been shown to be unconditionally convergent when applied to a quadratic objective function. Time-frequency methods are succinctly employed to analyse the vibration signals simultaneously in the time and frequency domains. Transients covering a wide frequency range are a clear and definite indication of impacting events as gear teeth mate, and observation of such events on a timefrequency distribution are used to indicate damage to the transmission. The pseudo Wigner-Ville distribution and the Spectrogram, both belonging to Cohen’s general class of time-frequency distributions are comparatively used to the end of damage identification. It is shown that an unconditionally convergent adaptive filtering technique used in conjunction with time-frequency methods can indicate a damaged condition in an epicyclic gearbox, where the non-adaptively filtered data did not present clear indications of damage. / Dissertation (MEng (Mechanical Engineering))--University of Pretoria, 2007. / Mechanical and Aeronautical Engineering / MEng / MEng / unrestricted

In this thesis, we present a detailed exposition of Koszul algebras and Koszul duality. We begin with an overview of the required concepts of graded algebras and homological algebra. We then give a precise treatment of Koszul and quadratic algebras, together with their dualities. We fill in some arguments that are omitted in the literature and work out a number of examples in full detail to illustrate the abstract concepts.

Associated to a split, semisimple linear algebraic group G is a group of invariant quadratic forms, which we denote Q(G). Namely, Q(G) is the group of quadratic forms in characters of a maximal torus which are fixed with respect to the action of the Weyl group of G. We compute Q(G) for various examples of products of the special linear, special orthogonal, and symplectic groups as well as for quotients of those examples by central subgroups. Homomorphisms between these linear algebraic groups induce homomorphisms between their groups of invariant quadratic forms. Since the linear algebraic groups are semisimple, Q(G) is isomorphic to Z^n for some n, and so the induced maps can be described by a set of integers called Rost multipliers. We consider various cases of the Kronecker tensor product map between copies of the special linear, special orthogonal, and symplectic groups. We compute the Rost multipliers of the induced map in these examples, ultimately concluding that the Rost multipliers depend only on the dimensions of the underlying vector spaces.