<p>We prove maximum norm regularity properties of L-stable finite difference</p><p>methods for linear-second order parabolic equations with coefficients</p><p>independent of time, valid for large time steps. These results are almost</p><p>sharp; the regularity property for first differences of the numerical solution</p><p>is of the same form as that of the continuous problem, and the regularity</p><p>property for second differences is the same as the continuous problem except for</p><p>logarithmic factors. </p><p>This generalizes a result proved by Beale valid for the constant-coefficient</p><p>diffusion equation, and is in the spirit of work by Aronson, Widlund and</p><p>Thome&eacute.</p><p>To prove maximum norm regularity properties for the homogeneous problem, </p><p> we introduce a semi-discrete problem (discrete in space, continuous in time).</p><p>We estimate the semi-discrete evolution operator and its spatial differences on</p><p>a sector of the complex plan by constructing a fundamental solution.</p><p>The semi-discrete fundamental solution is obtained from the fundamental solution to the frozen coefficient problem by adding a correction term found through an iterative process.</p><p>From the bounds obtained on the evolution operator and its spatial differences,</p><p>we find bounds</p><p>on the resolvent of the discrete elliptic operator and its differences through</p><p>the Laplace transform</p><p>representation of the resolvent. Using the resolvent estimates and the</p><p>assumed stability properties of the time-stepping method in the Cauchy integral</p><p>representation of the fully discrete solution operator</p><p>yields the homogeneous regularity result.</p><p>Maximum norm regularity results for the inhomogeneous</p><p>problem follow from the homogeneous results using Duhamel's principle. The results for the inhomogeneous</p><p>problem</p><p>imply that when the time step is taken proportional to the grid width, the rate of convergence of the numerical solution and its first</p><p>differences is second-order in space, and the rate of convergence for second</p><p>differences</p><p>is second-order except for logarithmic factors .</p><p>As an application of the theory, we prove almost sharp maximum norm resolvent estimates for divergence</p><p>form elliptic operators on spatially periodic grid functions. Such operators are invertible, with inverses and their first differences bounded in maximum norm, uniformly in the grid width. Second differences of the inverse operator are bounded except for logarithmic factors.</p> / Dissertation

The Kuroshio, one of the most important western boundary currents of world, controls modern hydrology conditions of the East China Sea (ECS) and carries warm and saline water to high latitudes. Previous researches mentioned that the Kuroshio might change its flow path and volume in the ECS by East Asia monsoon (EAM), Equatorial climate conditions, or global sea level change during glacials. However, shifting or not of the Kuroshio out of the Okinawa Trough during Last Glacial Maximum (LGM) is still in debate. In this study, records derived from multi-proxies, include of Mg/Ca-based paleotemperatures and stable isotopes and foraminiferal census data, of core GH08-2004 was conducted for comparing with records derived from core MD012404 to understand the possible changes of the Kuroshio in the ESC since 26 ka. Our comparing results reveal that the surface hydrological environments have no obvious difference between eastern and western sides of the Ryukyu Arc and imply that the Kuroshio might not shifted outside of the OT during LGM. Otherwise, our reconstructed temperatures, oxygen isotopes and foraminiferal assemblages infer that the flowing volume of the Kuroshio was gradually increased since 19 ka associated with rising sea level. Thus we believe that emerged terrain caused by shallow sea level may be an important factor controlling the flowing path of the Kuroshio. In this study, differences of paleotemperatures and oxygen isotopes between G. ruber and N. dutertrei, surface and subsurface dweller, were decreased at the Holocene, whereas the delta values of carbon isotopes were larger meanwhile. This descrapncy implies that the East Asian winter and summer monsoons were enhanced synchronously.

The Region of Western Pacific Warm Pool (WPWP) is closely related to Global climate system. Previous studies indicate that the region of WPWP is affected by Walker circulation (WC) and Hadley cell (HC). WPWP expands when WC becomes stronger or when HC becomes weaker, and contracts when WC becomes weaker or when HC becomes stronger. In this study, records derived from core ODP1115B, including stable oxygen and carbon isotopes are used to reconstruct the long-term hydrological variations of WPWP over the past 2.2 Ma. We compared two species of foraminifera: Neogloboquadrina dutertrei and Globigerinoides sacculifer, for the reconstruction of differences between surface water and oceanic subsurface water. We try to find out the relationships between the thermocline depth in southern WPWP, the region of WPWP, HC and WC. However, our records indicate that the depth of thermocline in southern WPWP may be effected by the region of WPWP and the hydrology of southern WPWP. According to the Paleothermometry records of ODP806, ODP847, ODP1115 and MD063018, we can explain the relationship between WC, HC and the region of WPWP. Before 1.8 Ma, southern WPWP may not be affected by weak WC. During 1.8~1.2 Ma, WC becomes stronger and effect the region of WPWP. At the period of 1.2~0.9 Ma, southward migration of WPWP enhanced the influence of WC on the region of south WPWP and the depth of thermocline, then weakened HC in the southern hemisphere. After 0.9 Ma, the variation of hydrology in southern WPWP may be affected by stronge WC, not HC. We suggest that the influence of HC in southern WPWP is resulted in the southern region of WPWP.

The medieval period of Denmark (11th-16th centuries) witnessed two of the worst demographic, health, and dietary catastrophes in history: the Late Medieval Agrarian Crisis (LMAC) and the Black Death plague epidemic. Historians have argued that these events resulted in a change in subsistence from a cereal grain to a more pastorallyfocused diet, and that the population decimation resulted in improved living conditions. This dissertation bioarchaeologically examines the impact of these historically described events on the diet and health of the population from Jutland, Denmark. I examine the stable isotopic ratios of carbon and nitrogen, dental caries, cribra orbitalia, porotic hyperostosis, periosteal reactions, and femur length to examine the samples for dietary and health differences due to sex, time period, site and social status. The results suggest that there are few chronological differences in diet or health in these samples. There are greater disparities among the sites, as peasants from the rural site had a more terrestrially-based diet and poorer health than the urban sites. While there is little difference in diet by sex, there is a disparity in health between the sexes. However, the direction of difference varies by site, suggesting that the relative treatment of the sexes was not universal in Denmark. While the results indicate there is little difference in health by status, there are dietary differences, as elites had a more marinebased diet than peasants. This research indicates the importance of bioarchaeological analysis in the interpretation of historical events. The recording of history is dependent on the viewpoint of the recorder and may not accurately reflect the importance of events on the the population itself. Bioarchaeological techniques examine skeletal material from the individuals in question and may provide a better understanding of the consequences of historic events on the population, such as the effects of the LMAC and Black Death on the population of Denmark. This research reveals that, contrary to historical expectation, these events did not have a measurable impact on Danish diet or health. Thus, the use of historical documentation and bioarchaeological analyses provides a richer understanding of these historical events.

The green turtle, Chelonia mydas, is a circumglobal species that exhibits several important developmental or ontogenetic shifts throughout its life history. The first major shift occurs when juvenile turtles migrate from pelagic habitat, where they forage as omnivores, to coastal neritic habitat, where they become primarily herbivores, foraging on algae and seagrass. Anecdotal evidence and gut-content analyses suggest that juvenile green turtles in south Texas bays, such as the lower Laguna Madre and Aransas Bay, undergo an additional ontogenetic shift during this important life history stage. Evidence from stable isotope analysis (SIA) of scute tissues of green turtles from Texas' lower Laguna Madre and Aransas Bay supports an intermediate stage between this species' shift from pelagic waters to seagrass beds in neritic waters; this additional shift comprises an initial recruitment of post-pelagic juveniles to jetty habitat located on the channel passes Gulf-ward of adjacent bays before subsequently recruiting to seagrass beds in these bays. Examination of stable carbon ([delta]¹³C) and nitrogen ([delta]¹⁵N) isotopes in microlayers of scute tissue from several size classes of green turtles from the lower Laguna Madre and Aransas Bay was used to confirm the occurrence of two ontogenetic shifts. Smaller green turtles (< 35 cm SCL) exhibited more depleted [delta]¹³C signatures and more enriched [delta]¹⁵N signatures, consistent with jetty habitat, compared to those of larger counterparts (> 45 cm SCL) that displayed enriched [delta]¹³C signatures and depleted ¹⁵N signatures, consistent with seagrass habitat. Changes in the isotopic composition between these size classes indicate distinct shifts in diet. Post-pelagic juveniles first recruit to jetty habitat and forage primarily on algae, before subsequently shifting to seagrass beds and foraging primarily on seagrass. These findings indicate the use of a characteristic sequence of distinct habitats by multiple life history stages of green turtles in Texas bays, a conclusion with broad management implications for this endangered species.

Recently, Dawson and Feinstein showed that a Banach algebra integral extension B of a commutative Banach algebra A of topological stable rank one is again of topological stable rank one. In this thesis, we provide a partial converse to this statement: If an Arens-Hoffman extension A&#x00AE; of a commutative C*-algebra A has topological stable rank one then A has topological stable rank one.

The carbon and oxygen isotopes of planktonic foraminifera, and faunal assemblages of towing samples, £_13C of dissolved inorganic carbon, and £_18O of seawater collected from northern South China Sea (SCS) were analyzed in this study. Plankton tows were collected between December 2002 and December 2005 at water depth of 100m. In addition, fauna and sea water samples were sampled at different depths ranging between 50 and 300m at some stations. Generally, the faunal assemblages are dominated by Globigerinoides ruber, Globigerinoides sacculifer, Globigerinoides aequilateralis, Pulleniatina obliquiloculata, Neogloboquadrina dutertrei, and Globorotalia menardii. G. aequilateralis and G. menardii are dominated in warm months while G. ruber, G. sacculifer, and P. obliquiloculata are dominated in cold months. The relative abundances of G. sacculifer and G. aequilateralis obtained from towing samples in this study are significantly higher than those shown in underlying sediment traps and surface sediments, suggesting that the tests of these two taxa are prone to dissolution. In addition, the abundance of P. obliquiloculata which serves as an index taxon for the Kuroshio Current in Paleoceanography, is more abundant in the northern part than in the southern part of the SCS basin. Nevertheless, the £_13C and £_18O of G. sacculifer and P. obliquiloculata are significantly lighter than that in sediment traps and surface sediments, indicating some potential effects caused by the differential dissolution. Possible dwelling depths of P. obliquiloculata is estimated between 50 and 90m, whereas N. dutertrei is estimated between 20 and 80m according to Kim and O¡¦Neil (1997). The latter changes to 40~160m when the equation of Bouvier-Soumagnac and Duplessy (1985) is applied. Oxygen isotope compositions of G. sacculifer and G. ruber display a significant correlation with temperature (T) in the surface mixed layer. The slopes of £_18O/ T for these two species are similar to each other. The differences of £_18O (£G£_18O) between G. sacculifer and N. dutertrei, G. sacculifer and P. obliquiloculata, G. ruber and P. obliquiloculata are proved to be a good proxy indicator for reconstructing the upper water column based on the statistic relationship between £G£_18O and £GT (difference between mixed layer and 100m) in this study.

The main advantage of wavelet transform relative to its Fourier analysis counterpart is its suitability to deal with transient signals. Furthermore, wavelet packet transform has very good frequency analytic ability with the result that it is developing in very fast speed and widespread researched and used in industry and academia. We study the characteristics of fiber optic sensors by applying wavelet transform. Hence, in this paper, the traditional Fourier analysis is taken as a basis, and the wavelet packet analysis is taken as a comparison. The major objects include: (1) calibration of hydrophones; (2) vibration measurement. In calibration of hydrophones, the experimental results show a 2.72 dB re V/£gPa inaccuracies and a 5.3 dB re V/£gPa standard deviation by Fourier analysis, but 0.5 dB inaccuracies and 1.6 dB re V/£gPa standard deviation by wavelet packet analysis. It shows that the wavelet packet analysis has better analytic ability than that of traditional Fourier analysis. In vibration measurement, we utilize FBG interferometers to measure stable vibration. The experimental results denote that wavelet packet analysis has excellent frequency analytic ability as Fourier analysis. Besides, in obtaining transient characteristic signals induced by falling stones, the results appear that wavelet packet analysis has better resolution and identification capability relative to Fourier analysis.

Four separate but complimentary studies investigated the role of grain sorghum as a predator source for Southern Rolling Plains cotton in 2001 and 2002. Objectives were to: (1) determine the timing and magnitude of predator movement between crops, (2) test putative causes of movement by manipulating prey levels at different stages of crop phenology, (3) explore the feeding and reproductive behavior of a common predator colonizing cotton, and (4) examine the effects of grain sorghum and uncultivated areas on cotton predator abundance at an area-wide scale. Rubidium mark-recapture experiments indicated grain sorghum fields produced a net predator gain for adjacent cotton. Analysis suggested two coccinellids, Hippodamia convergens Guérin-Méneville and Scymnus loewii Mulsant, were responsible for the overall pattern of predator movement. Predator movement into cotton did not appear to be concentrated at specific stages of sorghum phenology. Manipulations of aphid levels in field cages were used to determine if prey abundance or phenology influenced the movement of H. convergens into cotton. In both years, more lady beetle adults were collected on cotton during the latest stages of sorghum phenology. In the second year, relatively low aphid densities (15 per plant) appeared to influence the movement of beetles onto caged cotton. Carbon isotope ratios of H. convergens were used to assess adult feeding behavior after colonizing cotton and to determine if prey consumed in sorghum contributed to egg production in cotton. Though aphids were absent 2001, H. convergens adults stayed in cotton, did not produce eggs and apparently consumed few prey. Cotton aphids were present in 2002 and H. convergens isotope ratios changed from prey consumed in cotton. The isotope ratios of egg masses collected in 2002 indicated prey consumed in grain sorghum contributed very little to egg production in cotton. An area-wide pattern analysis suggested the abundance of grain sorghum and uncultivated areas both positively influenced cotton predator levels. While these landscape effects were less important overall than prey levels and cotton planting dates, in some sampling periods landscape composition appeared to be the most important factor in determining cotton predator levels.

Recent wireless communication research faces the challenge of meeting a predicted 1000x increase in demand for wireless Internet data over the next decade. Among the key reasons for such explosive increase in demand include the evolution of Internet as a provider of high-definition video entertainment and two-way video communication, accessed via mobile wireless devices. One way to meet some of this demand is by using multiple antennae at the transmitter and receiver in a wireless device. For example, a system with 4 transmit and 4 receive antennae can provide up to a 4x increase in data throughput. Another key aspect of the overall solution would require sharing radio frequency spectral resources among users, causing severe amounts of interference to wireless systems. Consequently, wireless receivers with multiple antennae would be deployed in network environments that are rife with interference primarily due to wireless resource sharing among users. Other significant sources of interference include computational platform subsystems, signal leakage, and external electronics. Interference causes severe degradation in communication performance of wireless receivers. Having accurate statistical models of interference is a key requirement to designing, and analyzing the communication performance of, multi-antenna wireless receivers in the presence of interference. Prior work on statistical modeling of interference in multi-antenna receivers utilizes either the Gaussian distribution, or non-Gaussian distributions exhibiting either statistical independence or spherical isotropy. This dissertation proposes a framework, based on underlying statistical-physical mechanism of interference generation and propagation, for modeling multi-antenna interference in various network topologies. This framework can model interference which is spherically isotropic, or statistically independent, or somewhere on a continuum between these two extremes. The dissertation then utilizes the derived statistical models to analyze communication performance of multi-antenna receivers in interference-limited wireless networks. Accurate communication performance analysis can highlight the tradeoffs between communication performance and computational complexity of various multi-antenna receiver designs. Finally, using interference statistics, this dissertation proposes receiver algorithms that best mitigate the impact of interference on communication performance. The proposed algorithms include multi-antenna combining strategies, as well as, antenna selection algorithms for cooperative communications. / text