Thesis (doctoral)--Universität Bonn, 1988. / Includes bibliographical references.

We consider the differential equation d²u/dz² - zⁿu = 0 (z, u complex variables; n a positive integer), which is the simplest second order ordinary differential equation with a turning point of order n. The solutions which we study, herein called Aռ functions, are generalizations of Airy functions. Most of their properties are then deduced from those of related Bessel functions of order [formula omitted], but in the discussion of the zeros in section 3, results are deduced directly from the differential equation. It is easy to see that the Aռ functions are special cases of functions studied by Turrittin [9]. The relation of the former to Bessel functions, however,, enables us to use methods not available in [9] to obtain uniform asymptotic representations for large z. We obtain new results on the distribution of the zeros which extend a property [6] of Airy functions, that is, of A₁functions,, to all positive integers n. A similar remark applies to bounds [8] for Airy functions and their reciprocals. / Science, Faculty of / Mathematics, Department of / Graduate

Light scattering by small particles is the physical phenomenon that produces the natural rainbow in the sky. The same phenomenon can be reproduced in laboratory with monochromatic light giving rise to non-intrusive laser based techniques for the measurement of size and refractive index of particles suspended in a medium possessing lower refractive index. These techniques are commonly called "Rainbow Thermometry" techniques and appear at the beginning of the nineties. The measurement of size and refractive index of the particles is obtained through the analysis of the interference fringe image generated in the far field by means of the interaction between the laser light and the particles themselves. The work presented in this thesis has as objective the improvement of the Rainbow Techniques both on the theoretical aspects and the application. In this thesis the Airy theory, which is used as theoretical model for the Standard Rainbow Thermometry, has been improved to minimize the discrepancies it was presenting respect to more complex and complete theories and it has been generalized to spherical particles presenting a spherically symmetric refractive index gradient. This generalized model has been used to evaluate the size and temperature of a n-octane burning droplet in standard atmosphere with good results. The generalization of the Standard Rainbow Thermometry to multiple particles, Global Rainbow Thermometry, is presented both theoretically and experimentally and the role of the particle asphericity in the light scattered intensity is evaluated. Two experimental application of the Global Rainbow Thermometry are reported. The first one concerns the measurement of size and refractive index of silicon oil droplets suspended in an aqueous bulk. This experiment allows the Global Rainbow Thermometry validation through the comparison with measurements simultaneously obtained with well known experimental techniques as Back-Light scattering and thermocouple measurement with satisfactory results. The second experiment concerns Global Rainbow Thermometry measurement performed on an evaporating flat-fan water spray. The results obtained, both for temperature and for size, are in satisfactory agreement with predictions already done by other authors and with numerical simulations performed by the engineering code CASIMIRE.

No description available.

Thesis (M.A.)--State University of New York at Binghamton, Department of English, General Literature and Rhetoric, 2005.

Zugl.: Bonn, University, Diss., 1988.

No description available.

No description available.

Thesis (Ph. D.)--University of Pennsylvania, 1929. / Bibliography: p. [153]-167.

Thesis (Ph. D.)--Ohio State University, 2003. / Title from first page of PDF file. Document formatted into pages; contains x, 227 p.; also includes graphics Includes bibliographical references (p. 224-227). Available online via OhioLINK's ETD Center