Dissertation (PhD)--University of Stellenbosch, 2002 / ENGLISH ABSTRACT: Singular spectrum analysis (SSA) originated in the field of Physics. The technique is non-parametric by nature and inter alia finds application in atmospheric sciences, signal processing and recently in financial markets. The technique can handle a very broad class of time series that can contain combinations of complex periodicities, polynomial or exponential trend. Forecasting techniques are reviewed in this study, and a new coordinate free joint-horizon k-period-ahead forecasting formulation is derived. The study also considers model selection in SSA, from which it become apparent that forward validation results in more stable model selection. The roots of SSA are outlined and distributional assumptions of signal senes are considered ab initio. Pitfalls that arise in the multivariate statistical theory are identified. Different approaches of recurrent one-period-ahead forecasting are then reviewed. The forecasting approaches are all supplied in algorithmic form to ensure effortless adaptation to computer programs. Theoretical considerations, underlying the forecasting algorithms, are also considered. A new coordinate free joint-horizon kperiod- ahead forecasting formulation is derived and also adapted for the multichannel SSA case. Different model selection techniques are then considered. The use of scree-diagrams, phase space portraits, percentage variation explained by eigenvectors, cross and forward validation are considered in detail. The non-parametric nature of SSA essentially results in the use of non-parametric model selection techniques. Finally, the study also considers a commercial software package that is available and compares it with Fortran code, which was developed as part of the study. / AFRIKAANSE OPSOMMING: Singulier spektraalanalise (SSA) het sy oorsprong in die Fisika. Die tegniek is nieparametries van aard en vind toepassing in velde soos atmosferiese wetenskappe, seinprossesering en onlangs in finansiële markte. Die tegniek kan 'n wye verskeidenheid tydreekse hanteer wat kombinasies van komplekse periodisiteite, polinomiese- en eksponensiële tendense insluit. Vooruitskattingstegnieke word ook in hierdie studie beskou, en 'n nuwe koërdinaatvrye gesamentlike horison k-periodevooruitskattingformulering word afgelei. Die studie beskou ook model seleksie in SSA, waaruit duidelik blyk dat voorwaartse validasie meer stabiele model seleksie tot gevolg het. Die agtergrond van SSA word ab initio geskets en verdelingsaannames van seinreekse beskou. Probleemgevalle wat voorkom in die meervoudige statistiese teorie word duidelik geïdentifiseer. Verskeie tegnieke van herhalende toepassing van een-periode-vooruitskatting word daarna beskou. Die benaderings tot vooruitskatting word in algororitmiese formaat verskaf wat die aanpassing na rekenaarprogrammering vergemaklik. Teoretiese vraagstukke, onderliggend aan die vooruitskattings-algortimes, word ook beskou. 'n Nuwe koërdinaatvrye gesamentlike horison k-periode-vooruitskattingsformulering word afgelei en aangepas vir die multikanaal SSA geval. Verskillende model seleksie tegnieke is ook beskou. Die gebruik van "scree"- diagramme, fase ruimte diagramme, persentasie variasie verklaar deur eievektore, kruis- en voorwaartse validasie word ook aangespreek. Die nie-parametriese aard van SSA noop die gebruik van nie-parametriese model seleksie tegnieke. Die studie vergelyk laastens 'n kommersiële sagtewarepakket met die Fortran bronkode wat as deel van hierdie studie ontwikkel is.

Thesis (PhD)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: See full text. / AFRIKAANSE OPSOMMING: Sien volteks.

A Thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg for the Degree of Doctor of Philosophy. Johannesburg, 1979

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1982. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE / Includes bibliographical references. / by Ilan Vardi. / Ph.D.

No description available.

Let X, Y be locally compact Hausdorff spaces. A linear operator T from C0(X,E) to C0(Y,F) is called disjointness preserving if coz(Tf)¡äcoz(Tg) = whenever coz(f)¡äcoz(g) = ∅. We discuss some cases on these compact disjointness preserving operators T and prove that if £f0 is a nonzero point of £m(T), then £f0 is an eigenvalue of T and we find a projection ∏: C0(X,E) ¡÷C0(X,E), such that for Y1 = ∏C0(X;E) and Y2 = (1-∏)C0(X;E), the operator T|Y1 -£f0 is a nilpotent and £f0-T|Y2 is invertible.

We extend the classical Ambarzumyan's theorem for the Sturm-Liouville equation, which is concerned only with the Neumann boundary conditions, to the general boundary conditions, by imposing an additional condition on the potential function. Our result supplements Poschel-Trubowitz's inverse spectral theory. We also have parallel results for the vectorial Sturm-Liouville system.

Thesis (Ph. D.)--University of Missouri-Columbia, 2000. / Typescript. Vita. Includes bibliographical references (leaves 71-78). Also available on the Internet.

Thesis (M.S.)--Florida State University, 2004. / Advisor: Dr. Xiuwen Liu, Florida State University, College of Arts and Sciences, Dept. of Computer Science. Title and description from dissertation home page (viewed June 17, 2004). Includes bibliographical references.

Thesis (Ph. D.)--University of Missouri-Columbia, 2000. / Typescript. Vita. Includes bibliographical references (leaves 71-78). Also available on the Internet.