Thesis (Ph. D.)--University of Wisconsin--Madison, 1982. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaf 116).

Thesis--Wisconsin. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Chicago, 1922. / Biography. "A Dissertation, submitted to the Faculty of the Ogden Graduate School of Science in candidacy for the Degree of Doctor of Philosophy, Department of Mathematics. "Private edition, distributed by the University of Chicago Libraries, Chicago, Illinois." "Reprinted from Transactions American mathematical society, vol. XXIV, no. 2, September, 1922." Includes bibliographical references.

Thesis (Ph. D.)--University of Chicago, 1920. / Vita. "Private edition, distributed by the University of Chicago libraries." Also available on the Internet. Also issued online.

Thesis (Ph. D.)--Lehigh University, 2000. / Includes vita. Includes bibliographical references (leaves 140-143).

Th. doct.-ing.--Nancy, I.N.P.L., 1980.

In this thesis numerical integration in one and two dimensions is considered. In chapter two transformation methods are considered primarily for singular integrals and methods of computing the transformations themselves are derived. The well-known transformation based on the IMT rule and error function are extended to non-standard functions. The implementation of these rules and their performances are demonstrated. These transformations are then extended to two-dimensions and are used to develop accurate rules for integrating singular integrals. In addition to this, a polynomial transformation with the aim of the reduction in the number of function evaluations is also considered and the resultant product rule is applied to two-dimensional non-singular integrals. Finally, the use of monomials in the construction of integration rules for non-singular two-dimensional integrals is considered and some rules developed. In all these situations the rules developed are tested and compared with existing methods. The results show that the new rules compare favourably with existing ones.

Made available in DSpace on 2014-06-11T19:25:32Z (GMT). No. of bitstreams: 0 Previous issue date: 2006-10-26Bitstream added on 2014-06-13T20:14:07Z : No. of bitstreams: 1 salomao_lr_me_rcla.pdf: 917808 bytes, checksum: d44faa6f545a9927fe555baaacdcc99c (MD5) / Este trabalho pode ser separado em duas partes. Na primeira apresentamos, de forma resumida, a natureza fractal das séries de precipitação de chuvas, a estimativa do expoente de Hurst (H), a transformada wavelet, o seu uso na estimativa de H e a comprovação, por meio de testes com séries de movimento browniano fracionário geradas com H estabelecido a priori, que temos um bom método para estimar H com a transformada wavelet. Na segunda parte é feita uma análise das séries temporais de precipitação de chuvas (séries de chuva). As séries de chuvas foram obtidas junto ao Departamento de Águas e Energia Elétrica (DAEE) do estado de São Paulo e são constituídas de medições diárias, em milímetros, da quantidade de chuva em postos meteorológicos distribuídos em todo o estado. Algumas séries apresentam ausências de medições que acabam transformando uma série longa em duas ou mais séries menores. Em função disso foi estabelecido um procedimento que permite aproveitar essas séries com ausências (dias sem medições) para estimar o expoente de Hurst. A partir de considerações climáticas o estado foi dividido em nove regiões. Foram selecionadas séries com 20 anos de registros de chuva (de janeiro de 1978 a dezembro de 1997). Dos valores de H encontrados foi feita uma média para cada região climática do estado de São Paulo. / This work can be separated into two parts. In the first part is briefly presented the fractal nature of the rain precipitation series, the estimate of the Hurst exponent (H), the wavelet transform, its use in the estimate of H and the evidence, by tests with generated series of fractional brownian motion with H established a priori, that we have a good method to estimate H with wavelet transform. In the second part an analysis of rain precipitation series is made. The rain series had been obtained from the Departmento de Águas e Energia Elétrica (DAEE) of the state of São Paulo and contain daily measurements, in milimeters, of the amount of rain in distributed meteorological stations all over the state. Some series present absences of measurements, transforming a long series into two or more lesser series. A procedure was established, allowing to use these series with absences (days with no measurements) to estimate the Hurst exponent. From climatic considerations the state was divided into nine regions. The regions with rain data over a period of 20 years have been selected as rain series (from january 1978 to december 1997). From the several values of H, we computed an averaged value of H for each climatic regions of the state of São Paulo.

In this thesis two problems concerning linear transformations on Mn, the algebra of n-square matrices over the complex numbers, are considered. The first is the determination of the structure of those transformations which map non-singular matrices to non-singular matrices; the second is the determination of the structure of those transformations which, for some positive integer r, preserve the sum of the r x r principal subdeterminants of each matrix. In what follows, we use E to denote this sum, and the phrase "direct product" to refer to transformations of the form T(A) = cUAV for all A in Mn or T(A) = cUA'V for all A in Mn where U, V are fixed members of Mn and c is a complex number. The main result of the thesis is that both non-singularity preservers and Er-preservers, if r ≥ 4, are direct products. The cases r=1,2,3 are discussed separately. If r=1, it is shown that E₁ preservers have no significant structure. If r=2, it is shown that there are two types of linear transformations which preserve E₂, and which are not direct products. Finally, it is shown that these counter examples do not generalize to the case r=3. These results and their proofs will also be found in a forthcoming paper by M. Marcus and JR. Purves in the Canadian Journal of Mathematics, entitled Linear Transformations of Algebras of Matrices: Invariance of the Elementary Symmetric Functions. / Science, Faculty of / Mathematics, Department of / Graduate

The objective of this thesis is to determine the linear transformations of a Grassmann product space which sends the set of nonzero Grassmann product vectors (also called pure vectors) into itself. Let U be an n-dimensional vector space over a field F and let r be an integer such that 0 ≤ r≤ n. The r-th Grassmann product space will be denoted by Ar(U). Subspaces of Ar(U) consisting entirely of pure vectors are called pure subspaces. With each non-zero pure vector of Ar(U) we associate an r-dimensional subspace of U. By studying the set of subspaces of U corresponding to a basis set of a pure subspace of Ar(U) we are able to deduce the form of this pure subspace. In this way we are able to classify the pure subspaces of Ar(U), arriving at only two essentially distinct types. We next study the maximal pure subspaces, i. e. the pure subspaces which are not contained in larger pure subspaces. They are of importance because the assumptions on the linear transformations under consideration imply that a maximal pure subspace is mapped into another maximal pure subspace. The form of the transformation is now almost completely determined by examining the incidence relations between pairs of maximal pure subspaces before and after the transformation is applied. Some algebraic manipulations are then needed in order to display the form of the transformation completely. With the suitable assumptions, our results state that the transformations under consideration are induced by linear transformations of the vector space U, except possibly when 2r = n. When 2r = n two types of transformations are possible. This arises from the fact that the two types of maximal pure subspaces have the same dimensions, (unlike the situation when 2r ≠ n). One type of transformation (those induced by linear maps of U)does not alter the type of pure subspaces, while the other interchanges the two types. / Science, Faculty of / Mathematics, Department of / Graduate