Let $gamma(G)$ be the domination number of a graph $G$. For any permutation $pi$ of the vertex set of a graph $G$, the prism of $G$ with respect to $pi$ is the graph $pi G$ obtained from two copies $G_{1}$ and $G_{2}$ of $G$ by joining $uin V(G_{1})$ and $vin V(G_{2})$ iff $v=pi(u)$. We prove that $$gamma(pi C_{n})geq cases{frac{ n}{ 2}, &if $n = 4k ,$ cr leftlceilfrac{n+1}{2} ight ceil, &if $n eq 4k$,} mbox{and } gamma(pi C_{n}) leq leftlceil frac{2n-1}{3} ight ceil mbox{for all }pi.$$ We also find a permutation $pi_{t}$ such that $gamma(pi_{t} C_{n})=k$, where $k$ between the lower bound and the upper bound of $gamma(pi C_{n})$ in above. Finally, we prove that if $pi_{b}C_{n}$ is a bipartite graph, then $$gamma(pi_{b}C_{n})geq cases{frac{n}{2}, &if $n = 4k ,$cr leftlceilfrac{n+1}{2} ight ceil, &if $n = 4k+2$,} mbox{and } gamma(pi_{b}C_{n})leq leftlfloor frac{5n+2}{8} ight floor.$$

When wearing prism goggles that displace vision laterally, the initial pointing errors are rapidly corrected. When the goggles are removed after a sufficient period of prism adaptation (PA), there is an aftereffect in spatial responding in the opposite direction of the original displacement. In this study 24 participants were tested using a computerized PA procedure to explore the effects of displacement direction (left/right), type of feedback during adaptation (hand/indirect), and type of target (fixed/non-fixed) on pointing error during 180 PA trials and the time-course of the aftereffect when measured in two ways: Subjective Straight Ahead (SSA) pointing (proprioceptive guidance towards perceived straight-ahead) and Visual Open Loop (VOL) pointing (visual and proprioceptive performance when pointing toward a straight-ahead target). During the initial stage of adaptation, all groups adjusted pointing in the opposite direction of prismatic displacement. Pointing error was similar for left and right goggle groups, but was more accurate and faster to stabilize with hand than indirect feedback. After pointing stabilized, the left-goggle/hand feedback group reached beyond targets (‘over-corrected’ pointing error), while other conditions failed to fully adjust pointing and remained ‘under-corrected’. In all groups, SSA aftereffects were weak or absent, while VOL aftereffects endured for at least 40-minutes. VOL aftereffects were larger following hand-feedback at all post-PA latencies, and for left-goggle groups at early post-PA latencies. Target-type affected performance during the stabilized-phase of adaptation, but did not influence SSA or VOL aftereffects. These results suggest that computerized PA had induced changes in vision but not proprioception, and provide novel evidence that the technology induced reliable aftereffects following both hand and indirect feedback PA. The results, when considered together with the study’s strengths and weaknesses, provide insight into how future studies might assess computerized-PA can be used to explore more complex attention and space representation process in healthy-normal and patients suffering from unilateral neglect.

As ecosystem modeling becomes increasingly integrated with Geographic Information Systems (GIS) there is a rise in demand for spatially and temporally continuous meteorological data. But in order to justify management decisions or to provide robust scientific insights, the accuracy of meteorological data used as model input must be thoroughly quantified. Current methods to create spatially continuous climate data from discrete weather station data include inverse distance weighting, geostatistical techniques such as kriging and splines, local regression models such as Parameter-Elevation Regression on Independent Slope Model (PRISM) and Daymet, and regional regression models. For the conterminous United States, PRISM and Daymet are perhaps the most commonly used interpolated datasets. Both use similar inputs but apply different interpolation methods. To date, no comprehensive comparison of their respective accuracies exists. Here I show that for a wide range of conditions, PRISM is the preferred interpolation. I reached this conclusion by comparing the accuracy of predictions of annual and monthly minimum (Tmin) and maximum (Tmax) by PRISM and Daymet for the conterminous United States from 1980-2003. My goals were: (1) to determine which interpolation was more robust at predicting temperature values; and (2) to assess whether the performance of each method varies, either temporally (annual or seasonal), spatially, or by elevation. To evaluate comparative performance, I analyzed PRISM and Daymet temperature predictions of ground station temperatures by calculating the logs odds ratio (LOR), mean absolute error (MAE), and bias. In all the comparative performance analyses, PRISM was the better model. The monthly results followed the same trend as the annual average results. I found a spatial performance difference across the entirety of the conterminous United States with the largest difference on the coasts and in the mountainous western regions. Stratifying data by elevation demonstrated that as elevation increases, uncertainty from both PRISM and Daymet increased. Unless the daily resolution provided by Daymet is required, PRISM appears to be a more robust predictor of continuous temperature data over the conterminous United States from 1980-2003.

The Okitsu mélange in the Shimanto accretionary complex, the onshore extension of the modern Nankai accretionary prism, consists of a kilometer-size duplex of oceanic basalt and trench-fill sedimentary rocks, and is thought to represent rocks underplated to the prism along the subduction plate-boundary at seismogenic depth. An internal, horsebounding thrust of the duplex, referred to as the Suzume fault, juxtaposes basalt in the hanging wall and sedimentary rocks in the footwall. Structure and fabric of the fault was characterized at the mesoscale to investigate the processes and structural evolution along a plate-boundary décollement. The fault zone in the hanging wall consists of decimeterthick ultracataclasite bounded by a several m thick zone of fractured basalt, and likely records 2+ km displacement along the thrust. The footwall consists of decimeter-thick ultracataclasite bounded by a 20-m-thick zone of ductile shear in flattened sedimentary host rock, and likely records 30+ km of displacement. The asymmetric structure across the Suzume fault, as well as inferred displacement fields and timing relations, are consistent with a tectonic model in which the footwall records early ductile, compactive deformation of poorly consolidated sediments during underthrusting at the prism toe region, followed by extremely localized cataclasis at the underplating depth. In contrast, the hanging wall is deformed by intense cataclasis, and only during underplating. Deformation style and strain state in the footwall of the Suzume fault is qualitatively similar to the modern Costa Rica underthrust section at the toe region. Similarity in the structure and fabric of the hanging wall between the Suzume fault and modern décollement zones sampled through scientific drilling suggests that intense cataclasis under horizontal contraction likely is a common feature for the hanging wall of the décollement zone throughout the toe to underplating regions. Structures in the Suzume fault that are not in common with the modern décollements imply progressive consolidation during underthrusting from the toe to underplating depths may be responsible for the localization of shear in the footwall. At several kilometers depth, displacement along the plate boundary is likely accommodated within an extremely narrow zone as recorded in the ultracataclasite of the Suzume fault.

No description available.

No description available.

Analyzer crystal based imaging techniques such as diffraction enhanced imaging (DEI) and multiple imaging radiography (MIR) utilize the Bragg peak of perfect crystal diffraction to convert angular changes into intensity changes. These X-ray techniques extend the capability of conventional radiography, which derives image contrast from absorption, by providing a large change in intensity for a small angle change introduced by the X-ray beam traversing the sample. Objects that have very little absorption contrast may have considerable refraction and ultra small angle X-ray scattering (USAXS) contrast thus improving visualization and extending the utility of X-ray imaging. To improve on the current DEI technique this body of work describes the design of an X-ray prism (XRP) included in the imaging system which allows the analyzer crystal to be aligned anywhere on the rocking curve without moving the analyzer from the Bragg angle. By using the XRP to set the rocking curve alignment rather than moving the analyzer crystal physically the needed angle sensitivity is changed from ìradians for direct mechanical movement of the analyzer crystal to milliradian control for movement the XRP angle. In addition to using an XRP for the traditional DEI acquisition method of two scans on opposite sides of the rocking curve preliminary tests will be presented showing the potential of using an XRP to scan quickly through the entire rocking curve. This has the benefit of collecting all the required data for image reconstruction in a single fast measurement thus removing the occurrence of motion artifacts for each point or line used during a scan. The XRP design is also intended to be compatible with combined imaging systems where more than one technique is used to investigate a sample. Candidates for complimentary techniques are investigated and measurements from a combined X-ray imaging system are presented.

Analyzer crystal based imaging techniques such as diffraction enhanced imaging (DEI) and multiple imaging radiography (MIR) utilize the Bragg peak of perfect crystal diffraction to convert angular changes into intensity changes. These X-ray techniques extend the capability of conventional radiography, which derives image contrast from absorption, by providing a large change in intensity for a small angle change introduced by the X-ray beam traversing the sample. Objects that have very little absorption contrast may have considerable refraction and ultra small angle X-ray scattering (USAXS) contrast thus improving visualization and extending the utility of X-ray imaging. To improve on the current DEI technique this body of work describes the design of an X-ray prism (XRP) included in the imaging system which allows the analyzer crystal to be aligned anywhere on the rocking curve without moving the analyzer from the Bragg angle. By using the XRP to set the rocking curve alignment rather than moving the analyzer crystal physically the needed angle sensitivity is changed from ìradians for direct mechanical movement of the analyzer crystal to milliradian control for movement the XRP angle. In addition to using an XRP for the traditional DEI acquisition method of two scans on opposite sides of the rocking curve preliminary tests will be presented showing the potential of using an XRP to scan quickly through the entire rocking curve. This has the benefit of collecting all the required data for image reconstruction in a single fast measurement thus removing the occurrence of motion artifacts for each point or line used during a scan. The XRP design is also intended to be compatible with combined imaging systems where more than one technique is used to investigate a sample. Candidates for complimentary techniques are investigated and measurements from a combined X-ray imaging system are presented.

<p> An investigation is reported on the kinetics of Ca0-β quartz solid state reaction on basal and prism planes of β-quartz at temperatures in the range between 1000 degrees Celsius and 1200 degrees Celsius. Excess lime present in all the samples ensured ensured the formation of c2s (dicalcium silicate) only. The thickness of the c2s product layer was measured on a Zeiss camera microscope Ultraphot II. The line scans for the distribution of Ca and Si across the reaction layer were obtained on the electron microprobe analyser. The kinetics of the reaction on basal and prism planes of a-quartz in wet and dry nitrogen atmospheres in the temperature range considered was studied by measuring the thickness of c2s as a function of time of reaction. </p> <p> The CaO-β quartz reaction was found to be anisotropic, the basal plane reaction being faster than the .Prism plane reaction. The reaction on both basal and prism planes in the temperature range between l000°C and 1200°C was found to be enhanced in the presence of moisture. The enhancement due to the presence of moisture was found to be more on the basal plane reaction than on the prism plane reaction. This appears to be due to the fact that different polymorphs of c2s with different sensitivities to the presence of moisture are produced on different crystallographic planes of a-quartz considered. The activation energies for the reaction on basal plane and prism plane were found to be about 53 kcal/mole and 63 kcal/mole respectively. They have good agreement with the activation energies of 55 kcal/mole and 65 kcal/mole for Ca diffusion in a-c2s and a-c2s respectively as reported by Lindner. </p> / Thesis / Master of Engineering (MEngr)

A description of several experiments carried out to investigate the behaviour of 3.2 cm. microwaves on passing through a dielectric prism is given in this thesis. Chapter I contains a description of the experimental apparatus used to generate electromagnetic radiation and to measure the field intensity in a plane perpendicular to the refracting edge of the prism. Particular emphasis is placed on a description of the receiver amplifier, and on the construction of the wax prism. In Chapter II are given the results of several preliminary investigations of the field close to, and polarized parallel to the retracting edge of the prism. Fresnel interference fringes were observed with the prism oriented as a biprism. Diffraction fringes of a 45˚ wedge, both dielectric and metallic, were observed incidentally. Evidence of the evanescent wave predicted for total internal reflection was obtained directly in this experiment where earlier evidence of such waves in the optical and microwave regions has been indirect. / Thesis / Master of Science (MSc)