Space curves have a variety of uses within mathematics, and much attention has been paid to calculating quantities related to such objects. The quantities of curvature and energy are of particular interest to us. While the notion of curvature is well-known, the Mobius energy is a much newer concept, having been first defined by Jun O'Hara in the early 1990s. Foundational work on this energy was completed by Freedman, He, and Wang in 1994, with their most important result being the proof of the energy's conformal invariance. While a variety of results have built those of Freedman, He, and Wang, two topics remain largely unexplored: the interaction of curvature and Mobius energy and the generalization of the Mobius energy to curves with a varying thickness. In this thesis, we investigate both of these subjects. We show two fundamental results related to curvature and energy. First, we show that any simple, closed, twice-differentiable curve can be transformed in an energy-preserving and length-preserving way that allows us to make the pointwise curvature arbitrarily large at a point. Next, we prove that the total absolute curvature of a twice-differentiable curve is uniformly bounded with respect to conformal transformations. This is accomplished mainly via an analytic investigation of the effect of inversions on total absolute curvature. In the second half of the thesis, we define a generalization of the Mobius energy for simple curves of varying thickness that we call the "nonuniform energy." We call such curves "weighted knots," and they are defined as the pairing of a curve parametrization and positive, continuous weight function on the same domain. We then calculate the first variation formulas for several different variations of the nonuniform energy. Variations preserving the curve shape and total weight are shown to have no minimizers. Variations that "slide" the weight along the curve are shown to preserve energy is special cases.

The major purpose of this investigation was to study the structure, attributes , and supplemental aspects of equivalence classifying of words and pictures made by sixth graders, freshmen college students and junior and senior college students . A particular point of interest was whether or not increasing or decreasing the size of the groups results in different types of equivalence classifying. Other minor goals were to determine the effects of direction of grouping, type of stimuli, and class level on unique reasons produced and recall of stimuli. The results of the study support the thesis that there is a cognitive developmental progression which supports the works of Piaget, Bruner, Vinacke and others. Children, compared to college levels, use a less efficient grouping structure, lower level simple association and concrete and perceptual grouping attributes, lower quality responses, and more specific reasons for grouping. College levels, compared to six grade, use more representational grouping attributes, have higher quality responses, and have a more general level of specificity. In addition, decreasing grouping structure results in a high level of cognitive performance in all aspects of grouping. There were no main effect differences between the words and pictures. However, there were significant interaction effects involving directions, stimuli, and class levels. There were more stimuli recalled and unique reasons produced by the college students. More pictures than words were recalled by all groups. One implication of the results is that decreasing the size of groupings apparently results in a higher level of cognitive functioning. One reason ventured for this result is that decreasing group size results in more divergent thinking and allows the individual to contemplate more possibilities for his groupings. Increasing group size is related to convergent thinking in which the subject is hindered by a previous set. Another implication is that there is a cognitive development a l progression which results in an increasingly more sophisticated ability to deal with the complex stimuli of the environment. Also, there is some evidence that different grade levels handle pictures differently than they do words. More study is needed to clarify the role of different forms of stimuli in classifying. From this study it is clear that there are no main effect differences between words and pictures. However, there certainly appear to be some interaction effects, and these need further clarification.

Spectral methods have been used for many applications in digital logic design, digital signal processing and telecommunications. In digital logic design they are implemented for testing of logical networks, multiplexer-based logic synthesis, signal processing, image processing and pattern analysis. New developments of more efficient algorithms for spectral transformations (Rademacher-Walsh, Generalized Reed-Muller, Adding, Arithmetic, multiple-valued Walsh and multiple-valued Generalized Reed- Muller) their implementation and applications will be described.

An accurate, intuitive and tractable transform as been identified and developed from which the spatial harmonics of reticle patterns defined in polar coordinates can be obtained. A description of reticles and generic methods for describing them mathematically are presented along with some background on general harmonic analysis. Focus then turns to candidate transforms for analysis of reticle patterns and the most promising are investigated in more detail. A fast linear algorithm is devised to overcome some problems with implementation of a fast transform and this is followed by analysis of the transform basis functions to assist with interpretation of the transform in azimuth and radius. A sampling guideline is presented so that aliasing can be avoided and, finally, the transforms of some representative reticle patterns are shown along with some insight into their interpretation. The transformations presented provide a first step toward raising the resolution and harmonic content required in simulation image scenes that will ultimately result in optimal use of computing resources for the simulation of reticle seekers. / thesis (MSc(AppliedPhysics))--University of South Australia, 2005.

Hox genes are regulatory genes encoding small proteins containing a highly conserved 61-amino acid motif, the homeodomain, that enables Hox proteins to bind to DNA at specifically recognised binding sites and transcriptionally activate their target genes. In mammalian species there are 39 Hox genes and they are structural and functional homologs of the Drosophila homeotic complex (Horn-C). During embryogenesis and early development the Hox genes are expressed in a spatiotemporal fashion, where they operate as master transcriptional regulators. Hox genes are further expressed in fully differentiated adult cells, potentially in a tissue-specific manner involving maintenance of the normal phenotype. In selected oncogenic transformations, dysregulated Hox gene expression has been observed, indicating an involvement of these transcriptional regulators in carcinogenesis and metastasis. Utilising quantitative real-time PCR assays, these studies investigated the expression patterns of 20 Hox genes and two wellcharacterised Hox cofactors (Pbx and Meis) in malignant and non-malignant human breast and skin cancer cells. Dysregulated Hox expression was observed for all malignancies tested, of which some misexpressed Hox genes seemed random, whereas other Hox transcripts showed altered levels potentially corresponding with the invasive capacity of the cells. Also, the Hox cofactors Pbx and Meis showed no marked changes in expression levels from the non-malignant to the malignant phenotypes, indicating that it is dysregulated Hox gene expression rather than dysregulated gene expression of Hox cofactors that potentially commit the cell to redifferentiate and undergo oncogenic transformation. Although the Hox proteins are known to be key transcriptional regulators of development, the mechanisms by which they gain their in vivo functional specificity is still largely unknown. They all show strikingly similar transcriptional specificity in vitro, yet show unique specificity in their in vivo environment. This paradox has been the subject of intense scrutiny, however very few direct Hox target genes have been identified, making it a difficult task to decipher the exact manner in which Hox proteins exert their functional potential. Therefore, the studies presented herein were aimed at identifying further Hox target genes in the human system. Utilising differential display approaches, several potential downstream target genes were isolated. Substantiated with real-time PCR assays, one of these potential targets was selected as a likely direct Hox gene target, and as such subjected to further studies. By the combination of bioinformatic analyses, transfection protocols and luciferase assays, a gene encoding the SR-related protein SRrpl3O was shown to be trans-activated in vitro by HOXD4 via a putative Hox binding element within its promoter region. This is the first reported link between Hox transcription factors and the SR and SR-related family of pre-mRNA splicing proteins, offering a new and exciting insight into the complex nature of Hox functional specificity. Finally, this thesis also puts forward new ideas regarding how the Hox proteins gain their transcriptional and functional specificity. Utilising bioinformatic tools in conjunction with performing an extensive review of the disparate catalogue of Hox-related research reports, work herein offers the first comprehensive analysis of the mammalian Hox gene targets in relation to their promoter structures, as well as with respect to the expanded Hox DNA-binding elements. This work reports that identified Hox targets generally contain TATA-less core promoters, many of which have several GC-box elements. The Hox binding elements show no apparent preference regarding their location relative to the transcription start site (TSS), as they are found both upstream and downstream of the TSS, as well as being located close to proximal core promoter elements for some genes and at more distant positions in other gene promoters. Finally, the core Hox binding element TAAT/ATTA contains only part of the necessary recognition sequence involved in Hox-DNA binding, and the notion that flanking base pairs dictate trans-regulatory potential is further explored with the hypothesis that the immediate 3' base pair dictates an activator/repressor-switch of the Hox trans-regulatory effect.

Thesis (Ph.D.)--University of Nebraska-Lincoln, 2007. / Title from title screen (site viewed Dec. 4, 2007). PDF text: xviii, 149 p. : ill. ; 7 Mb. UMI publication number: AAT 3271931. Includes bibliographical references. Also available in microfilm and microfiche formats.

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

Soit A un opérateur pseudo-différentiel elliptique auto-adjoint d'ordre 1 invariant à gauche sur un groupe de Lie G. Mon travail a consisté à approximer de e-itA par un OFI invariant à gauche. Puis, j'ai étudié les représentations unitaires irréductibles et la méthode des orbites de Kirillov. Enfin, j'ai fait la démonstration d'une formule asymptotique de Weyl pour pi(a) ou a est un élément formellement positif elliptique de U(g).

Les logiciels de simulation du comportement thermique jouent un rôle capital dans l'amélioration des performances énergétiques des bâtiments. Se pose cependant le problème du crédit à apporter aux résultats de simulations de ces logiciels, autrement dit, de l'aptitude de ces derniers et des modèles intégrés à représenter la réalité. Dans ces travaux, nous appliquons une méthodologie basée sur la vérification du logiciel et sur la validation expérimentale de modèles. Pour mener à bien la première phase, nous appliquons une procédure qui a fait ses preuves : la procédure de comparaison inter-logiciels BESTEST. La validation expérimentale nécessite d'une part, la recherche des sollicitations mal prises en compte par le modèle et d'autre part, l'identification des paramètres les plus influents de ce derniers. Nous proposons, pour la première étude, l'utilisation d'un outil d'analyse temps-fréquence : la transformée de Fourier à court-terme. En ce qui concerne la seconde, une méthode d'analyse de sensibilité paramétrique de modèles, basée sur les outils d'analyse spectrale, a été développée. Cette technique constituant le coeur de ces travaux, un chapitre entier est dédié à l'analyse de sensibilité.

The use of efficient basis functions to model and represent flows with internal sharp velocity gradients, such as shocks or eddy microfronts, are investigated. This is achieved by analysing artificial data, observed atmospheric turbulence data and by the use of a Burgers' equation based spectral model. The concept of an efficient decomposition of a function into a basis set is presented and alternative analysis methods are investigated. The development of a spectral model using a generalized basis for the Burgers' equation is presented and simulations are performed using a modified Walsh basis and compared with the Fourier (trigonometric) basis and finite difference techniques. The wavelet transform is shown to be superior to the Fourier transform or the windowed Fourier transform in terms of defining the predominant scales in time series of turbulent shear flows and in 'zooming in' on local coherent structures associated with sharp edges. Disadvantages are found to be its inability to provide clear information on the scale of periodicity of events. Artificial time series of varying amounts of noise added to structures of different scales are analyzed using different wavelets to show that the technique is robust and capable of detecting sharp edged coherent structures such as those found in shear driven turbulence. The Haar function is used as a wavelet to detect ubiquitous zones of concentrated shear in turbulent flows sometimes referred to as microfronts. The location and organization of these shear zones suggest that they may be edges of larger scale eddies. A wavelet variance of the wavelet phase plane is defined to detect and highlight events and obtain measures of predominant scales of coherent structures. Wavelet skewness is computed as an indicator of the systematic sign preference of the gradient of the transition zone. Inverse wavelet transforms computed at the dilation corresponding to the peak wavelet variance are computed and shown to contain a significant fraction of the total energy contained in the record. The analysis of data and the numerical simulation results are combined to propose that the sharp gradients normally found in shear induced turbulence significantly affect the nature of the turbulence and hence the choice of the basis set used for the simulation of turbulence. / Graduation date: 1991