Fix R = k[[x]]. Let Q_n be the category whose objects are ((M₁,...,M_n),(f₁,...,f_n-1)) where each M_i is a free R-module and f_i:M_i⟶M_i+1 for each i=1,...,n-1, and in which the morphisms are the obvious ones. Let β_n be the full subcategory of Ω_n in which each map f_i is a monomorphism whose cokernel is a torsion module. It is shown that there is a full dense functor Ω_n⟶β_n. If X is an object of β_n, we say that X <u>diagonalizes</u> if X is isomorphic to a direct sum of objects ((M₁,...,M_n),(f₁,...,f_n-1)) in which each M_i is of rank one. We establish an algorithm which diagonalizes any diagonalizable object X of β_n, and which fails only in case X is not diagonalizable. Let Λ be an artin algebra of finite type. We prove that for a fixed C in mod(Λ) there are only finitely many modules A in mod(Λ) (up to isomorphism) for which a short exact sequence of the form 0⟶A⟶B⟶C⟶0 is indecomposable. / Ph. D. / incomplete_metadata

Thesis (Ph. D.)--University of Missouri-Columbia, 2000. / Typescript. Vita. Includes bibliographical references (leaves 113-117). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2000. / Typescript. Vita. Includes bibliographical references (leaves 113-117). Also available on the Internet.

Thesis (M.S.)--Rochester Institute of Technology, 1993. / Typescript. Includes bibliographical references (leaf 96).

Thesis (M.S.)--Rochester Institute of Technology, 1993. / Typescript. Includes bibliographical references (leaf 101).

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Este trabalho apresenta a morfologia matemática multiescalar com quatro escalas aplicada no sinal de eletrocardiografia para a detecção do complexo QRS. Para o desenvolvimento deste trabalho pluridisciplinar de Engenharia Biomédica foram utilizados conhecimentos de Cardiologia, Eletrocardiografia, Bioestatística, Processamento Digital de Sinais Biomédicos, Teoria de Detecção de Sinais, Análise ROC e Índices de Desempenho de Classificadores, interagindo com áreas da edicina, da Estatística, da Matemática, da Engenharia da Computação e da Engenharia Elétrica. Testes foram realizados com o banco de sinais de ECG do MIT/BIH. O desempenho do método foi avaliado através da curva ROC e do índice DER. Os resultados foram comparados com a morfologia multiescalar de uma, duas e de três escalas. Nos resultados foi observado que o método de morfologia multiescalar com quatro escalas, aplicado nas condições estabelecidas, apresentou índices melhores de detecção do complexo QRS, confirmando seu potencial no processamento de sinais biomédicos, dando suporte na manipulação do complexo QRS e oferecendo melhorias na detecção. / This work presents the multiscale mathematical morphology with four scales applied in the ECG signal for detection of the QRS complex. To develop this Biomedical Engineering multidisciplinary work were used knowledge of Cardiology, Electrocardiography, Biostatistics, Biomedical Digital Signal Processing, Signal Detection Theory, ROC Analysis and Performance Classifiers Indexes, interacting with areas of Medicine, Statistics, Mathematics, Computer Engineering and Electrical Engineering. The tests were realized with MIT/BIH ECG signals database. The performance of the method was evaluated using ROC curves and the DER index. The results were compared with the multiscale mathematical morphology of one, two and three scales. In the results was observed that the multiscale mathematical morphology with four scales presented better indexes detection of the QRS complex, confirming its potential in biomedical signal processing, supporting the handling of the QRS complex and offering improvements in detection.