Thesis--Universiteit van Amsterdam. / Published without thesis statement. Includes bibliographical references (p. [101]).

Report (M.S. Ed.)--Virginia Polytechnic Institute and State University, 1994. / Includes bibliographical references (leaf 22). Also available via the Internet.

No description available.

This thesis is concerned with the Galois groups of the root fields of the equations x[superscript]P - a = 0, (x[superscript]p - a)•(x[superscript]q - b) = 0 and (x[superscript]q - b) [superscript]p - a = 0, where p and q are distinct primes, and a and b are rationals. The correspondence of subflelds and subgroups is studied for each of the three cases. The field [formula omitted] formed by adjoining to the rational field F the elements [formula omitted and ⍺, a primitive pth root of unity, is shown to be the root field of x[superscript]p - a = 0, normal over F of degree p(p-l). The Galois group of [formula omitted] over F Is found to be the metacyclic group constructed from generators s and t subject to relations s[superscript]p = 1, t[superscript]p ⁻¹ = 1 and st = ts[superscript]r, where r is a primitive root modulo p, and where s is the automorphism which maps [formula omitted] onto [formula omitted] while t is the automorphism which maps ⍺. onto ⍺ [superscript]r. Various subgroups and corresponding subflelds are studied and nine theorems proven on their correspondences, illustrated with a partial lattice diagram. The field [formula omitted]where β is a primitive qth root of unity is shown to be the root field of (x[superscript]p - a)-(x[superscript]q - b) = 0 and the Galois group is proven to be the direct product of two of the type for the field [formula omitted]. The field [formula omitted] for i = 1, 2, 3 ... p, which is the root field of the equation (x[superscript]q - b) [superscript]p - a = 0 is studied and shown to have degree pq[superscript]p-(p-1)•(q-1). The Galois group is found to be generated by four independent generators: s, t, u, v subject to eleven defining relations. Here the elements s, t, u, v are the automorphisms which respectively map [formula omitted] onto [formular omitted], ⍺ onto ⍺[superscript r, [formula omitted] onto [formula omitted] β onto β [superscript]where w is a primitive root modulo q. A partial lattice diagram illustrates the correspondence of subgroups and subflelds. The thesis was carried out under the supervision of Dr. D. C. Murdoch. / Science, Faculty of / Mathematics, Department of / Graduate

No description available.

Lightning electric field (E) and electric field derivative (dE/dt) signals have been recorded using sensors with 40 ns and 10 ns response times, respectively. Field propagation between the source and the recording antennas was entirely over salt water, so that distortions due to ground wave propagation were minimal below about 20 MHz. The fast-varying, initial portions of return stroke E fields have 10% to 90% risetimes which average 90 ± 40 ns. Peak dE/dt values range from 7 to 71 V/m/μs, with a mean and standard deviation of 33 ± 14 V/m/μs, when normalized to 100 km using an inverse distance dependence. The shapes of first and subsequent stroke fields are similar, but peak subsequent stroke dE/dts are larger than peak first stroke dE/dts in some flashes. The temporal structure of the fast varying fields produced by leader steps near the ground are very similar to return stroke fields. The mean maximum leader dE/dt, at 100 km, is 27 ± 9 V/m/μs. Large amplitude radiation fields produced by cloud discharge processes tend to be bipolar, with either positive or negative initial polarity and usually have several, fast, unipolar pulses superimposed on the initial half cycle. Cloud discharge fields with positive initial polarity usually precede cloud-to-ground flashes and produce a mean maximum dE/dt of 16 ± 8 V/m/μs. The field derivatives for all processes tend to be large when the amplitude of the associated fast field change is large. Estimates of lightning current derivatives, made using range normalized dE/dt measurements, average 155 ± 70 kA/μs, 135 ± 45 kA/μs, and 80 ± 40 kA/μs, for return strokes, leader steps, and cloud discharges, respectively, and a current wavefront velocity of 1 x 10⁸ m/s. These values are about 10 times larger than the maximum dI/dt recorded in strikes to instrumented towers. Lightning field amplitude spectra have been derived by Fourier analyzing dE/dt waveforms, and the spectral amplitudes decrease as 1/f² or faster with increasing frequency in the interval from about 6 to 20 MHz.

No description available.

The purpose of this thesis is to study the concept of completeness in an ordered field. Several conditions which are necessary and sufficient for completeness in an ordered field are examined. In Chapter I the definitions of a field and an ordered field are presented and several properties of fields and ordered fields are noted. Chapter II defines an Archimedean field and presents several conditions equivalent to the Archimedean property. Definitions of a complete ordered field (in terms of a least upper bound) and the set of real numbers are also stated. Chapter III presents eight conditions which are equivalent to completeness in an ordered field. These conditions include the concepts of nested intervals, Dedekind cuts, bounded monotonic sequences, convergent subsequences, open coverings, cluster points, Cauchy sequences, and continuous functions.

Particle Image Velocimetry (PlY) is a technique for measuring instantaneous twodimensional fluid velocity fields from a chosen plane of interest within a flow field. This thesis presents new developments and applications of the technique which have been used to study both the non-reacting and reacting flow fields within cylindrical combustion chambers. Non-reacting, swirling laminar flow fields near the transitional flow regime have been investigated by both Computational Fluid Dynamics (CFD) modelling and PIV experiments. Direct comparisons between CFD, PlY and other published results are made and close agreements are found. Additionally, the PlY technique has been optimised by careful use of a thin laser illumination sheet and correct choice of laser pulse separation. This has enabled successful PlY measurements in the boundary layers of the flow field where high velocity gradients exist. The PlY technique has been applied to measure the flame development and propagation process within the chamber under both quiescent and swirling flow conditions. Representative sequences of PIV results at different flame propagation stages are obtained and the accuracy in the extraction of the flame location is discussed. They clearly reveal the instantaneous flame front position and the unburned gas velocity field simultaneously. These features provide further insight into the combustion process itself and also the interaction between the combustion and flow field. A new application of PIV, combined with a flame speed detection technique, has been proposed and developed to obtain direct measurements of the laminar burning velocity of combustible mixtures. The laminar burning velocity is determined as the difference between the flame speed and the unburned gas velocity immediately ahead of the flame front. PIV is used to measure the unburned gas velocity field and either a pair of ionisation probes or a laser beam refraction technique is used to measure the local flame speed simultaneously. The relative merits of each technique are compared. The laminar burning velocities of propane-air mixtures initially at atmospheric conditions for equivalence ratios ranging from 0.7 - 1.4 were measured. The measured values show close agreement with previously published results based on other techniques. The advantages and limitations of the PIV techniques used in this work are examined and the prospects of their improvement and further application are discussed.

Texture segmentation is an effortless process in scene analysis, yet its neural mechanisms are not sufficiently understood. A common assumption in most current approaches is that texture segmentation is a vision problem. However, considering that texture is basically a surface property, this assumption can at times be misleading. One interesting possibility is that texture may be more intimately related with touch than with vision. Recent neurophysiological findings showed that receptive fields (RFs) for touch resemble that of vision, albeit with some subtle differences. To leverage on this, here I propose three ways to investigate the tactile receptive fields in the context of texture processing: (1) performance, (2) development, and (3) analysis. For performance, I tested how such distinct properties in tactile receptive fields can affect texture segmentation performance, as compared to that of visual receptive fields. Preliminary results suggest that touch has an advantage over vision in texture segmentation. These results support the idea that texture is fundamentally a tactile (surface) property. The next question is what drives the two types of RFs, visual and tactile, to become different during cortical development? I investigated the possibility that tactile RF and visual RF emerge based on the same cortical learning process, where the only difference is in the input type, natural-scene-like vs. texture-like. The main result is that RFs trained on natural scenes develop RFs resembling visual RFs, while those trained on texture resemble tactile RFs. These results again suggest a tight link between texture and the tactile modality, from a developmental context. To investigate further the functional properties of these RFs in texture processing, the response of tactile RFs and visual RFs were analyzed with manifold learning and with statistical approaches. The results showed that touch-based manifold seems more suitable for texture processing and desirable properties found in visual RF response can carry over to those in the tactile domain. These results are expected to shed new light on the role of tactile perception of texture; help develop more powerful, biologically inspired texture segmentation algorithms; and further clarify the differences and similarities between touch and vision.