A tridimensional optical display is described which is capable of producing real images with no optics between the observer and the image. This display, which is called the Visually Integrated Volumetric Image (VIVID), was developed as a laboratory system designed to be used in vision research. Three dimensional Lissajous patterns were produced, whose rotational position and axial depth could be precisely controlled by a general purpose digital minicomputer. By reversing the direction of rotation of the pattern in a known manner, and recording a subject's ability to perceive the true rotational direction for various amounts of axial image depth, the transition between the kinetic depth effect and true depth perception could be investigated. This transition forms the basis for defining a depth perception threshold for this type of a dynamic three dimensional image. Two experiments were performed using this approach. In the first experiment, ten undergraduate and graduate students (both male and female) observed the pattern during 24 one-minute trials. Eight different axial depth values were used, with three trials at each depth. The patterns were made to reverse rotation direction in a pseudo-random manner which was different for each trial presented to a given subject. The subject indicated the perceived direction of rotation by controlling a two position rotary switch, which was monitored by the computer. The total time during which the subject correctly tracked the rotation was integrated by the computer. The ratio of this correct tracking time to the total trial time was taken as a measure of the subject's ability to perceive the axial depth of the image. Plots of this ratio as a function of image depth are presented and discussed. The results averaged over all subjects produce a remarkably smooth curve, yielding a depth perception threshold of 2 mm for the subject population under the given experimental conditions. The characteristics of the stimulus were: (a) 2 cm high by 2 cm wide pattern; (b) Lissajous pattern frequency ratio of 6:1; (c) Axial distance from observer of 55 cm; (d) Wavelength of 533 nm (green); (e) Horizontal rotation axis; (f) Rotation period of 7 seconds; (g) Neutral background field illumination over a 40° come angle; (h) Image line width of 0.5 mm. The second experiment was a pilot experiment designed to investigate the effect of wavelength variations on this form of depth perception. A single subject was presented with a total of 192 one-minute trials at four wavelengths spanning the visible region (i.e., 6 one-minute trials for each of eight depth values at each wavelength). No significant wavelength dependence was observed in this pilot experiment.

An isogeny between elliptic curves is an algebraic morphism which is a group homomorphism. Many applications in cryptography require evaluating large degree isogenies between elliptic curves efficiently. For ordinary curves of the same endomorphism ring, the previous fastest algorithm known has a worst case running time which is exponential in the length of the input. In this thesis we solve this problem in subexponential time under reasonable heuristics. We give two versions of our algorithm, a slower version assuming GRH and a faster version assuming stronger heuristics. Our approach is based on factoring the ideal corresponding to the kernel of the isogeny, modulo principal ideals, into a product of smaller prime ideals for which the isogenies can be computed directly. Combined with previous work of Bostan et al., our algorithm yields equations for large degree isogenies in quasi-optimal time given only the starting curve and the kernel.

Generally urban drainage systems are built to protect urban property and control runoff. Moreover, these systems collect the runoff for storage purposes to serve society through sufficient water supply to meet the needs of demand, irrigation, and drainage. Urban environments are exposed to risks of extreme hydrological events. Therefore, urban water systems and their management are critical. Precipitation data are crucial, but may be prone to errors due to the lack of information e.g., short length of records. In this thesis, a Monte Carlo simulation and regional frequency analysis based on L-moments approach were utilized during the research in order to estimate the uncertainty in the Intensity Duration Frequency (IDF) curves by using historical precipitation data from Environment Canada (EC) weather stations and simulating a new series of data through a weather generator (WG) model. The simulations were then disaggregated from daily into hourly data for extraction of the annual maximum precipitation for different durations in hours (1, 2, 6, 10, 12, and 24). Regional frequency analysis was used to form the sites into groups based on homogeneity test results, and the quantile values were computed for various sites and durations with the return periods (T) in years (2, 10, 20, and 100). As a result, the regional frequency analysis was used to estimate the regional quantile values based on L-moment approach. Moreover, the box and whisker plots were utilized to display the results. When the return periods and durations increased, the uncertainty slightly increased. The historical IDF curves of London site falls within the regional simulated IDF curves. Furthermore, 1000 runs have been generated by using the weather generator.

No description available.

The primary topic of this thesis is the construction of explicit projective equations for the modular curves $X_0(N)$. The techniques may also be used to obtain equations for $X_0^+(p)$ and, more generally, $X_0(N) / W_n$. The thesis contains a number of tables of results. In particular, equations are given for all curves $X_0(N)$ having genus $2 le g le 5$. Equations are also given for all $X_0^+(p)$ having genus 2 or 3, and for the genus 4 and 5 curves $X_0^+(p)$ when $p le 251$. The most successful tool used to obtain these equations is the canonical embedding, combined with the fact that the differentials on a modular curve correspond to the weight 2 cusp forms. A second method, designed specifically for hyperelliptic curves, is given. A method for obtaining equations using weight 1 theta series is also described. Heights of modular curves are studied and a discussion is given of the size of coefficients occurring in equations for $X_0(N)$. Finally, the explicit equations are used to study the rational points on $X_0^+(p)$. Exceptional rational points on $X_0^+(p)$ are exhibited for $p = 73,103,137$ and 191.

Thesis (Ph. D.)--University of Hawaii at Manoa, 2004. / Includes bibliographical references. / Also available by subscription via World Wide Web / xxxiii, 335 leaves, bound ill. 29 cm

Thesis (M.S.)--Ohio University, March, 1999. / Title from PDF t.p.

Thesis (M.S.) -- Rochester Institute of Technology, 2008. / Typescript. Includes bibliographical references (leaves 57-60).

Thesis (Ph. D.)--University of Hong Kong, 2008. / Includes bibliographical references (p. 159-170) Also available in print.

Thesis (M.S.)--Ohio University, August, 1998. / Title from PDF t.p.