Habilitationsschrift--Universität des Saarlandes, Saarbrücken. / At head of title: Mathematisches Institut der Universität Erlangen-Nürnberg. Includes bibliographical references (p. 99-102).

Thesis (Ph. D.)--University of Washington, 2006. / Vita. Includes bibliographical references (p. 99-103).

This thesis is the outcome of research conducted into the quantization of observables defined over a Riemannian configuration manifold, and is naturally divided into three chapters: The first chapter is essentially concerned with the development from physical bases, of the concepts of classical and quantum “global measurability”, which, when combined with the requirement that all quantizable momenta shall be either classically or quantum mechanically globally measurable, result in the exclusion form the class of quantizable momenta of all those observables which are not quantizable in accordance with G. W. Mackey's natural procedure. The refinement of exact global measurability is then introduced and the physically important class of “killing” momenta are found to be exactly classically and quantum mechanically globally measurable and moreover quantizable by means of Mackey's scheme. The second chapter seeks to analyse the algebraic structure of the Mackey-quantizable momenta, so as to compare and contrast his geometric scheme with the various algebraic schemes which have frequently been proposed. As an extension of this work, a natural geometric quantization is proposed for the more general class of observables “linear in momentum”, the set of quantizable such entities determines, and its algebraic properties discussed. It is concluded that, if Mackey's procedure is, as we argue, correct and exhaustive of the quantizable momenta, then algebraic rules of quantization do not, in general, obtain among the momenta defined over a Riemannian space, ‘though in the case of momenta, such as the Killing momenta, reflecting the symmetry of the configuration manifold, such laws not only exist but are moreover of great practical importance. The third chapter is concerned with the quantization of the observables “multilinear in momentum” and in particular with the delimitation of the possible operators of formal quantization as circumscribed by the requirement of operator symmetry, and the question of the essential self-adjointness of local observables associated with the multilinear momenta. Finally some possible means of determining and exact quantization are discussed and contrasted and a tentative selection made of a particular scheme which is then illustrated by concrete example on the real line with the usual metric. We conclude this preface with a brief indication of the layout of the thesis: Each chapter or associated group of appendices has been treated for the purpose of all textual numbering and referencing systems, as a separate unit, and is prefixed by a detailed list of contents, and concluded by the appropriate group of reference, so that all pointers of a chapter or group of appendices refer, unless otherwise indicated, to the text of that chapter or group of appendices. Finally note that a bibliography has been included which will serve as a collected list of references to papers and books employed.

The standard guideline for accounting for construction firms is AC109/IAS11: Construction Contracts, which recognises that contract start and end dates usually fall into different accounting periods. This creates the problem that forms the primary focus of this study: the allocation of contract revenue and costs to the accounting periods in which construction work is performed. Critical to the above allocation is the ability to determine percentage of completion of contract and cost to completion at the balance sheet date (reporting date). The important activities in this regard are to “measure” and “estimate” reliably. AC109/IAS11 contains detailed guidelines on what is to be done with regard to the above. Questions then arise as to who must do what is required, and how it must be done. It seemed apparent that the guidelines used for determining the stage of completion should correspond with the guidelines for on site cost control. South African literature on the subject is limited to textbooks with detailed guidelines to assist accounting students and qualified accountants. In this study an attempt was made to obtain clarification on key aspects from the experts on the subject, namely the registered auditors and accountants of contractors. The results of a survey indicated that they interpret AC109/IAS11 to require no other skills than general accounting abilities. It also showed that certain important terms and activities described in AC109/IAS11 were interpreted in a way that differed from how built environment professionals would interpret the same terms and use them in “on site cost control”. It appears from the study therefore, that problems in construction accounting could arise due to the fact that certain guidelines and terms in AC109/IAS11 are not consistently interpreted by all involved. / Dissertation (MSc (Construction Management))--University of Pretoria, 2008. / Construction Economics / unrestricted

The logarithmic Mahler measure of an n-variable Laurent polynomial, P(x1,...,xn) is defined by [expression]. Using experimental methods, David Boyd conjectured a large number of explicit relations between Mahler measures of polynomials and special values of different types of L-series. This thesis contains four papers which either prove or attempt to prove conjectures due to Boyd. The introductory chapter contains an overview of the contents of each manuscript. / Science, Faculty of / Mathematics, Department of / Graduate

In this paper we are concerned with the problem of finding 'limits' of inverse (or projective) systems of measure spaces (for a definition of these see e.g. Choksi: Inverse Limits of Measure, Spaces, Proc. London Math. Soc. 8, 1958). Our basic limit measure, ῦ, is placed on the Cartesian product of the spaces instead of on the inverse limit set, L. As a result we obtain an existence theorem for this measure with fewer conditions on the system than are usually needed. We also investigate the existence of a limit measure on L by restricting our measure ῦ to L. This enables us to generalize known results and to explain some of the difficulties encountered by the standard inverse limit measure. In particular we show that the product topology may be too fine to allow the limit measure to have good topological properties' (e.g. to be Radón). Another topology which is related to the product structure is introduced and we show that limit measures which are Radón w.r.t. this topology can be obtained for a wide class of inverse systems of measure spaces. / Science, Faculty of / Mathematics, Department of / Graduate

This thesis attempts to prove the Lebesgue measure is a concrete realization of measure.

No description available.

A measure of concordance, $\kappa$, is of polynomial type if and only if $\kappa (tA+(1-t)B)$ is a polynomial in $t$ where $A$ and $B$ are 2-copulas. The degree of such a type of measure of concordance is simply the highest degree of the polynomial associated with $\kappa$. In previous work [2], [3], properties of measures of concordance preserving convex sums (equivalently measures of concordance of polynomial type degree one) were established; however, a characterization was not made. Here a characterization is made using approximations involving doubly stochastic matrices. Other representations are provided from this characterization leading naturally to two interpretations of degree one measures of concordance. The existence of a family of measures of concordance of polynomial type having higher degree generated by a certain family of Borel measures on $(0,1)^{2n}$ is also shown. The representation of this family immediately leads to a probabilistic interpretation for all finite measures in $d_n$. Also, higher degree analogs of commonly known degree one measures of concordance are given as examples. For the degree 2 case in particular, we see there is no finite measure in $d_2$ generating Kendall's tau. Finally, another family of measures of concordance is given containing those generated by finite measures in $d_2$ as well as Kendall's tau.

No description available.