Spectral geometry is the field of mathematics which concerns relationships between geometric structures of manifolds and the spectra of canonical differential operators. Inverse Spectral Geometry in particular concerns the geometric information that can be recovered from the knowledge of such spectra. A deep link between inverse spectral geometry and sampling theory has recently been proposed. Specifically, it has been shown that the very shape of a Riemannian manifold can be discretely sampled and then reconstructed up to a cutoff scale. In the context of Quantum Gravity, this means that, in the presence of a physically motivated ultraviolet cuttoff, spacetime could be regarded as simultaneously continuous and discrete, in the sense that information can. In this thesis, we look into the properties of the Laplace-Beltrami operator on a compact Riemannian manifold with no boundary. We discuss the behaviour of its spectrum regarding a perturbation of the Riemannian structure. Specifically, we concern ourselves with infinitesimal inverse spectral geometry, the inverse spectral problem of locally determining the shape of a Riemannian manifold. We discuss the recenSpectral geometry is the field of mathematics which concerns relationships between geometric structures of manifolds and the spectra of canonical differential operators. Inverse Spectral Geometry in particular concerns the geometric information that can be recovered from the knowledge of such spectra. A deep link between inverse spectral geometry and sampling theory has recently been proposed. Specifically, it has been shown that the very shape of a Riemannian manifold can be discretely sampled and then reconstructed up to a cutoff scale. In the context of Quantum Gravity, this means that, in the presence of a physically motivated ultraviolet cuttoff, spacetime could be regarded as simultaneously continuous and discrete, in the sense that information can. In this thesis, we look into the properties of the Laplace-Beltrami operator on a compact Riemannian manifold with no boundary. We discuss the behaviour of its spectrum regarding a perturbation of the Riemannian structure. Specifically, we concern ourselves with infinitesimal inverse spectral geometry, the inverse spectral problem of locally determining the shape of a Riemannian manifold. We discuss the recently presented idea that, in the presence of a cutoff, a perturbation of a Riemannian manifold could be uniquely determined by the knowledge of the spectra of natural differential operators. We apply this idea to the specific problem of determining perturbations of the two dimensional flat torus through the knowledge of the spectrum of the Laplace-Beltrami operator.tly presented idea that, in the presence of a cutoff, a perturbation of a Riemannian manifold could be uniquely determined by the knowledge of the spectra of natural differential operators. We apply this idea to the specific problem of determining perturbations of the two dimensional flat torus through the knowledge of the spectrum of the Laplace-Beltrami operator.

Bibliography: leaves 103-105. / xii, 105 leaves ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Pure Mathematics, 1997

This study investigated the use of UV-visible spectral imaging for the location and enhancement of substances of forensic interest using targeted approaches based on the spectrum of the substance. Spectral enhancement procedures were developed for blood with and without chemical enhancement, and for latent fingermarks after chemical enhancement. Focus was on substances whose spectrum exhibited a steep change in absorbance or fluorescence over a small wavelength range. Substances with such spectral features were able to be enhanced using arithmetic combinations of two or three spectral images taken at wavelengths near the steep spectral feature. Some enhancement reagents do not react to produce a product with a steep spectral feature suitable for photographic enhancement. In such cases reagents that compliment spectral imaging can be developed. A tridentate ligand for iron(II), BBIDMAPP, which forms a complex with a narrow intense charge-transfer band, was synthesised and was used to visualise muddy shoemarks. UV-visible spectral imaging systems based on a liquid crystal filter or a filter wheel were constructed to facilitate the acquisition of the spectral images and to perform the enhancement operations. A thorough characterisation of the imaging systems determined their limitations and sources of artefacts which could lead to complications in interpreting the enhanced images. The spectral imaging procedure used to visualise blood was incorporated into a near-real-time, hand-held imaging system for the location of blood staining. This prototype imaging system is capable of acquiring two spectral images simultaneously, perform the enhancement procedure, and display the enhanced image within 5 s, which would make it suitable as a non-chemical presumptive screening test for blood at crime scenes.

This study investigated the use of UV-visible spectral imaging for the location and enhancement of substances of forensic interest using targeted approaches based on the spectrum of the substance. Spectral enhancement procedures were developed for blood with and without chemical enhancement, and for latent fingermarks after chemical enhancement. Focus was on substances whose spectrum exhibited a steep change in absorbance or fluorescence over a small wavelength range. Substances with such spectral features were able to be enhanced using arithmetic combinations of two or three spectral images taken at wavelengths near the steep spectral feature. Some enhancement reagents do not react to produce a product with a steep spectral feature suitable for photographic enhancement. In such cases reagents that compliment spectral imaging can be developed. A tridentate ligand for iron(II), BBIDMAPP, which forms a complex with a narrow intense charge-transfer band, was synthesised and was used to visualise muddy shoemarks. UV-visible spectral imaging systems based on a liquid crystal filter or a filter wheel were constructed to facilitate the acquisition of the spectral images and to perform the enhancement operations. A thorough characterisation of the imaging systems determined their limitations and sources of artefacts which could lead to complications in interpreting the enhanced images. The spectral imaging procedure used to visualise blood was incorporated into a near-real-time, hand-held imaging system for the location of blood staining. This prototype imaging system is capable of acquiring two spectral images simultaneously, perform the enhancement procedure, and display the enhanced image within 5 s, which would make it suitable as a non-chemical presumptive screening test for blood at crime scenes.

This study investigated the use of UV-visible spectral imaging for the location and enhancement of substances of forensic interest using targeted approaches based on the spectrum of the substance. Spectral enhancement procedures were developed for blood with and without chemical enhancement, and for latent fingermarks after chemical enhancement. Focus was on substances whose spectrum exhibited a steep change in absorbance or fluorescence over a small wavelength range. Substances with such spectral features were able to be enhanced using arithmetic combinations of two or three spectral images taken at wavelengths near the steep spectral feature. Some enhancement reagents do not react to produce a product with a steep spectral feature suitable for photographic enhancement. In such cases reagents that compliment spectral imaging can be developed. A tridentate ligand for iron(II), BBIDMAPP, which forms a complex with a narrow intense charge-transfer band, was synthesised and was used to visualise muddy shoemarks. UV-visible spectral imaging systems based on a liquid crystal filter or a filter wheel were constructed to facilitate the acquisition of the spectral images and to perform the enhancement operations. A thorough characterisation of the imaging systems determined their limitations and sources of artefacts which could lead to complications in interpreting the enhanced images. The spectral imaging procedure used to visualise blood was incorporated into a near-real-time, hand-held imaging system for the location of blood staining. This prototype imaging system is capable of acquiring two spectral images simultaneously, perform the enhancement procedure, and display the enhanced image within 5 s, which would make it suitable as a non-chemical presumptive screening test for blood at crime scenes.

This study investigated the use of UV-visible spectral imaging for the location and enhancement of substances of forensic interest using targeted approaches based on the spectrum of the substance. Spectral enhancement procedures were developed for blood with and without chemical enhancement, and for latent fingermarks after chemical enhancement. Focus was on substances whose spectrum exhibited a steep change in absorbance or fluorescence over a small wavelength range. Substances with such spectral features were able to be enhanced using arithmetic combinations of two or three spectral images taken at wavelengths near the steep spectral feature. Some enhancement reagents do not react to produce a product with a steep spectral feature suitable for photographic enhancement. In such cases reagents that compliment spectral imaging can be developed. A tridentate ligand for iron(II), BBIDMAPP, which forms a complex with a narrow intense charge-transfer band, was synthesised and was used to visualise muddy shoemarks. UV-visible spectral imaging systems based on a liquid crystal filter or a filter wheel were constructed to facilitate the acquisition of the spectral images and to perform the enhancement operations. A thorough characterisation of the imaging systems determined their limitations and sources of artefacts which could lead to complications in interpreting the enhanced images. The spectral imaging procedure used to visualise blood was incorporated into a near-real-time, hand-held imaging system for the location of blood staining. This prototype imaging system is capable of acquiring two spectral images simultaneously, perform the enhancement procedure, and display the enhanced image within 5 s, which would make it suitable as a non-chemical presumptive screening test for blood at crime scenes.

Thesis (M.A.)--Edith Cowan University, 2006. / Submitted to the Faculty of Education and Arts, Western Australian Academy of Performing Arts. Includes bibliographical references.

Thesis (doctoral)--Technische Universiteit Delft, 1997. / Also published in the series: Communications on hydraulic and geotechnical engineering ; no. 97-4. Vita. Includes bibliographical references (p. [127]-136).

Thèse (M.Sc.)--Université Laval, 2007. / Bibliogr.: f. [72]. Publié aussi en version électronique dans la Collection Mémoires et thèses électroniques.

Thesis (Ph.D.)--Flinders University, School of Informatics and Engineering. / Typescript bound. Includes bibliographical references: (leaves 174-180) and index. Also available online.