University of Macau / Faculty of Science and Technology / Department of Computer and Information Science

University of Macau / Faculty of Science and Technology / Department of Mathematics

The purpose of this thesis is to determine the spectrum of a type of integral operator called "Convolution Operator" acting on LP(0, °°) . In the special case p = 2 , we have a tool called the Mellin transform, this enables us to analyze the spectrum in more detail. A number of papers have dealt with special cases of our result, the reader is referred to the bibliography of a paper by D. W. Boyd; (to appear). Spectra of Convolution Operators. / Science, Faculty of / Mathematics, Department of / Graduate

This thesis concerns the absolute convergence of the Fourier series of functions belonging to certain Lipschitz classes on totally disconnected groups. The technique used is one of interpolating between certain endpoint results which are proven directly. These results are shown to be best possible and a counterexample in interpolation theory is given. / Science, Faculty of / Mathematics, Department of / Graduate

Chapter II of this thesis describes the operation of a Fourier Transform Ion Cyclotron Resonance Spectrometer. Included is a detailed discussion of software which was developed to run the spectrometer and analyze the data. An automatic data acquisition system for kinetic experiments is also described. Chapter III contains a short discussion of discrete versus continuous methods of data acquisition and problems with the FT-ICR method which utilizes discrete sampling. Two techniques are discussed which have been found to solve problems associated with a digital system, acquisition by "mixing" and zero-filling. Also, mass calibrations done on the FT-ICR spectrometer are presented. The reactions of some negative ions with esters in the gas phase have been studied by FT-ICR and are discussed in Chapter IV. The reactions of ¹⁸0 labelled methoxide with methyl trifluoroacetate, methyl benzoate, dimethyl carbonate, diethyl carbonate and dipropyl carbonate have been studied. It was found that there is incorporation of ¹⁸0 in product ions of the form RCOO⁻ showing that methoxide attacks esters in the gas phase partially at carbonyl carbon. Product distributions are found to be consistent with two competing mechanisms, B[sub AC]2 and S[sub N]2. Thus it was found that CH₃•0⁻ reacts with C₆H₅COOCH₃- 92% by a B[sub AC]2 type mechanism and 8% by an S[sub N]2 type mechanism. The amount of ¹⁸0 incorporation in product ions was seen to decrease with the presence of β hydrogens, due to the presence of an elimination channel. The reaction of ethoxide with the above named esters was studied and the products are also interpreted in terms of three competing mechanisms, B[sub AC]2, S[sub N]2 and elimination. / Science, Faculty of / Chemistry, Department of / Graduate

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In recent years there has been an extensive development of finite difference techniques for solution of the transient heat conduction equation due to the availability of high-speed digital computers. It is the purpose of this paper to investigate and compare several implicit methods for the solution of the Fourier equation with regards to truncation error, round-off error and computer time which probably are among the most important factors to be considered in choosing a method.

Yes / Two fractional Fourier transforms are used to define bi-fractional displacement operators, which interpolate between displacement operators and parity operators. They are used to define bi-fractional coherent states. They are also used to define the bi-fractional Wigner function, which is a two-parameter family of functions that interpolates between the Wigner function and the Weyl function. Links to the extended phase space formalism are also discussed.

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