992 resultados para Size-Ramsey numbers


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"UIUCDCS-R-81-1050"--Cover.

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In 1983, Chvatal, Trotter and the two senior authors proved that for any Delta there exists a constant B such that, for any n, any 2-colouring of the edges of the complete graph K(N) with N >= Bn vertices yields a monochromatic copy of any graph H that has n vertices and maximum degree Delta. We prove that the complete graph may be replaced by a sparser graph G that has N vertices and O(N(2-1/Delta)log(1/Delta)N) edges, with N = [B`n] for some constant B` that depends only on Delta. Consequently, the so-called size-Ramsey number of any H with n vertices and maximum degree Delta is O(n(2-1/Delta)log(1/Delta)n) Our approach is based on random graphs; in fact, we show that the classical Erdos-Renyi random graph with the numerical parameters above satisfies a stronger partition property with high probability, namely, that any 2-colouring of its edges contains a monochromatic universal graph for the class of graphs on n vertices and maximum degree Delta. The main tool in our proof is the regularity method, adapted to a suitable sparse setting. The novel ingredient developed here is an embedding strategy that allows one to embed bounded degree graphs of linear order in certain pseudorandom graphs. Crucial to our proof is the fact that regularity is typically inherited at a scale that is much finer than the scale at which it is assumed. (C) 2011 Elsevier Inc. All rights reserved.

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This thesis focuses mainly on linear algebraic aspects of combinatorics. Let N_t(H) be an incidence matrix with edges versus all subhypergraphs of a complete hypergraph that are isomorphic to H. Richard M. Wilson and the author find the general formula for the Smith normal form or diagonal form of N_t(H) for all simple graphs H and for a very general class of t-uniform hypergraphs H.

As a continuation, the author determines the formula for diagonal forms of integer matrices obtained from other combinatorial structures, including incidence matrices for subgraphs of a complete bipartite graph and inclusion matrices for multisets.

One major application of diagonal forms is in zero-sum Ramsey theory. For instance, Caro's results in zero-sum Ramsey numbers for graphs and Caro and Yuster's results in zero-sum bipartite Ramsey numbers can be reproduced. These results are further generalized to t-uniform hypergraphs. Other applications include signed bipartite graph designs.

Research results on some other problems are also included in this thesis, such as a Ramsey-type problem on equipartitions, Hartman's conjecture on large sets of designs and a matroid theory problem proposed by Welsh.

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This paper derives optimal life histories for fishes or other animals in relation to the size spectrum of the ecological community in which they are both predators and prey. Assuming log-linear size-spectra and well known scaling laws for feeding and mortality, we first construct the energetics of the individual. From these we find, using dynamic programming, the optimal allocation of energy between growth and reproduction as well as the trade-off between offspring size and numbers. Optimal strategies were found to be strongly dependent on size spectrum slope. For steep size spectra (numbers declining rapidly with size), determinate growth was optimal and allocation to somatic growth increased rapidly with increasing slope. However, restricting reproduction to a fixed mating season changed optimal allocations to give indeterminate growth approximating a von Bertalanffy trajectory. The optimal offspring size was as small as possible given other restrictions such as newborn starvation mortality. For shallow size spectra, finite optimal maturity size required a decline in fitness for large size or age. All the results are compared with observed size spectra of fish communities to show their consistency and relevance.

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The Radarsat-1 Antarctic Mapping Project (RAMP) compiled a mosaic of Antarctica and the adjacent ocean zone from more than 3000 high-resolution Synthetic Aperture Radar (SAR) images acquired in September and October 1997. The mosaic with a pixel size of 100 m was used to determine iceberg size distributions around Antarctica, combining an automated detection with a visual control of all icebergs larger than 5 km**2 and correction of recognized false detections. For icebergs below 5 km**2 in size, the numbers of false detections and accuracies of size retrievals were analyzed for three test sites. Nearly 7000 icebergs with horizontal areas between 0.3 and 4717.7 km**2 were identified in a near-coastal zone of varying width between 20 and 300 km. The spatial distributions of icebergs around Antarctica were calculated for zonal segments of 20° angular width and related to the types of the calving fronts in the respective section. Results reveal that regional variations of the size distributions cannot be neglected. The highest ice mass accumulations were found at positions of giant icebergs (> 18.5 km) but also in front of ice shelves from which larger numbers of smaller icebergs calve almost continuously. Although the coastal oceanic zone covered by RAMP is too narrow compared to the spatial coverage needed for oceanographic research, this study nevertheless demonstrates the usefulness of SAR images for iceberg research and the need for repeated data acquisitions extending ocean-wards over distances of 500 km and more from the coast to monitor iceberg melt and disintegration and the related freshwater input into the ocean.

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Void breaking and formation in a packed bed are important phenomena in stabilising and optimising the performance of reactors such as the blast furnace, spouted bed and catalytic regenerator. These phenomena have been studied using a mathematical model. The model is based on a previously published force balance approach to predict the cavity size. Limited numbers of experiments, at room temperature, have been carried out in order to compare the experimental results with theory. A good agreement has been found between the experimental and theoretical results. In addition, the predictions have been compared with published data, which give reasonable agreement. The role of various forces (friction, pressure and bed weight) on void initiation and breaking has been investigated. The effect of bed height, particle diameter and density, void fraction, as well as gas flow rate on void formation and breaking has also been studied.

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Air can be trapped on the crevices of specially textured hydrophobic surfaces immersed in water. This heterogenous state of wetting in which the water is in contact with both the solid surface and the entrapped air is not stable. Diffusion of air into the surrounding water leads to gradual reduction in the size and numbers of the air bubbles. The sustainability of the entrapped air on such surfaces is important for many underwater applications in which the surfaces have to remain submersed for longer time periods. In this paper we explore the suitability of different classes of surface textures towards the drag reduction application by evaluating the time required for the disappearance of the air bubbles under hydrostatic conditions. Different repetitive textures consisting of holes, pillars and ridges of different sizes have been generated in silicon, aluminium and brass by isotropic etching, wire EDM and chemical etching respectively. These surfaces were rendered hydrophobic with self-assembled layer of fluorooctyl trichlorosilane for silicon and aluminium surfaces and 1-dodecanethiol for brass surfaces. Using total internal reflection the air bubbles are visualized with the help of a microscope and time lapse photography. Irrespective of the texture, both the size and the number of air pockets were found to decrease with time gradually and eventually disappear. In an attempt to reverse the diffusion we explore the possibility of using electrolysis to generate gases at the textured surfaces. The gas bubbles are nucleated everywhere on the surface and as they grow they coalesce with each other and get pinned at the texture edges.

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In this paper we study the effective electron mass (EEM) in Nano wires (NWs) of nonlinear optical materials on the basis of newly formulated electron dispersion relation by considering all types of anisotropies of the energy band constants within the framework of k . p formalism. The results for NWs of III-V, ternary and quaternary semiconductors form special cases of our generalized analysis. We have also investigated the EEM in NWs of Bi, IV-VI, stressed Kane type materials, Ge, GaSb and Bi2Te3 by formulating the appropriate 1D dispersion law in each case by considering the influence of energy band constants in the respective cases. It has been found that the 1D EEM in nonlinear optical materials depend on the size quantum numbers and Fermi energy due to the anisotropic spin orbit splitting constant and the crystal field splitting respectively. The 1D EEM is Bi, IV-VI, stressed Kane type semiconductors and Ge also depends on both the Fermi energy and the size quantum numbers which are the characteristic features of such NWs. The EEM increases with increase in concentration and decreasing film thickness and for ternary and quaternary compounds the EEM increases with increase in alloy composition. Under certain special conditions all the results for all the materials get simplified into the well known parabolic energy bands and thus confirming the compatibility test.

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Changes in the age structure and population size of white grunt, Haemulon plumieri, from North Carolina through the Florida Keys were examined using records of landings and size frequencies of fish from commercial, re~reational, and headboat fisheries from 1986-1998. Data were stratified into two geographical areas: North Carolina and South Carolina; and southeast Florida. Population size in numbers at age was estimated for each year and geographical area by applying an uncalibrated separable virtual population analysis (SVPA) to the landings in numbers at age. A calibrated virtual population analysis, FADAPT, was also run for data from North Carolina and South Carolina. SVPA and FADAPT were used to estimate annual, age-specific fishing mortality (F) for four levels of natural mortality (M = 0.20, 0.25, 0.30, and 0.35). The best estimate of M for white grunt is 0.30. Landings of white grunt in the Carolinas for the three fisheries have generally decreased in recent years, but have held fairly steady for the species in southeast Florida. Age at entry and age at full recruitment were age-1 and age-4 for the Carolinas, and age-l and age-3 for southeast Florida. With M = 0.30, levels of fishing mortality (F) on the fully-recruited ages were 0.23 for the Carolinas and 0.33 for southeast Florida. Spawning potential ratio (SPR) at M = 0.30 was 57% for the Carolinas and 61% for southeast Florida, which indicates that the species, by definition, has not been over-exploited by fishing. The results of this assessment of the white grunt population off the Carolinas agree with the recent F/FMSY analysis of white grunt (Anonymous, 1999). (PDF contaons 72 pages)

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Changes in the age structure and population size of vermilion snapper, Rhornboplites aurorubens, from North Carolina through the Florida Keys were examined using records of landings and size frequencies of fish from commercial, recreational, and headboat fisheries from 1986-1996. Population size in numbers at age was estimated for each year by applying separable virtual population analysis (SVPA) to the landings in numbers at age. SVPA was used to estimate annual, age-specific fishing mortality (F) for four levels of natural mortality (M = 0.20, 0.25, 0.30, and 0.35). Although landings of vermilion snapper for the three fisheries have declined, minimum fish size regulations have resulted in an increase in the mean size of fish landed. Age at entry and age at full recruitment were age-1 andage-3 fDr 1986-1991, compared with age-1 and age-4, respectively, for 1992-1996. Levels of mortality from fishing (F) ranged from 0.38 - 0.61 for the entire period. Current spawning potential ratio (SPR) is 21% or 27% depending on the natural mortality estimate. SPR could be raised to 30% or 40% with a reduction in F, or by increasing the age at entry to the fisheries. The latter could be enhanced now if fishermen, particularly recreational, comply with minimum size regulations. However, released fish mortality, modeled in the assessment at 27%, will continue to make the achievement of 30% and 40% SPR more difficult. (PDF contains 63 pages)

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Understanding the diet of crocodilians is important because diet affects condition, behavior, growth, and reproduction. By examining the diet of crocodilians, valuable knowledge is gained about predator-prey interactions and prey utilization among habitats. In this study, I examined the diet and condition of adult American alligators (Alligator mississippiensis) in three central Florida lakes, Griffin, Apopka, and Woodruff. Two hundred adult alligators were captured and lavaged from March through October 2001, from April through October 2002, and from April through August 2003. Alligators ate a variety of vertebrate and invertebrate prey, but vertebrates were more abundant and fish dominated alligator diets in the lakes. Species composition of fish varied among the lakes. The majority of the diet of alligators from Lakes Apopka and Woodruff was fish, 90% and 84% respectively. Lake Apopka alligators consumed a significantly (P = 0.006) higher proportion of fish in their diet. Fish were 54% of the diet of Lake Griffin alligators and the infrequent occurrence of reptiles, mammals, birds, and amphibians often resulted in a large biomass. Differences in alligator diets among lakes may be due to differences in sample size (higher numbers of samples from Lake Griffin), prey availability, habitat, prey vulnerability, or prey size. Alligator condition (Fulton’s Condition Factor, K) was significantly (P < 0.001) different among the lakes. Alligators from Lake Apopka had the highest condition, followed by those from Lake Griffin, and alligators from Lake Woodruff had the lowest condition. Composition of fish along with diversity and equitability of fish in alligator diets may have contributed to differences in condition among lakes. Condition was probably also due to factors other than diet such as alligator hunting behavior, alligator density, or year-round optimal temperature that prolongs feeding. The observed diet and condition differences probably reflect both habitat differences and prey availability in these three lakes.

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The Kemp’s ridley sea turtle, Lepidochelys kempi, was on the edge of extinction owing to a combination of intense egg harvesting and incidental capture in commercial fishing trawls. Results from a cooperative conservation strategy initiated in 1978 between Mexico and the United States to protect and restore the Kemp’s ridley turtle at the main nesting beach at Rancho Nuevo, Tamaulipas, Mexico are assessed. This strategy appears to be working as there are signs that the species is starting to make a recovery. Recovery indicators include: 1) increased numbers of nesting turtles, 2) increased numbers of 100+ turtle nesting aggregations (arribadas), 3) an expanding nesting season now extending from March to August, and 4) significant nighttime nesting since 2003. The population low point at Rancho Nuevo was in 1985 (706 nests) and the population began to significantly increase in 1997 (1,514 nests), growing to over 4,000 nests in 2004. The size and numbers of arribadas have increased each year since 1983 but have yet to exceed the 1,000+ mark; most arribadas are still 200–800+ turtles.

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Length frequency distributions of the sea bream collected during the period 1953 to 1958 have been analysed. The increase in average sizes of the sea bream with depth suggests a movement to deeper waters with increase in size. By numbers, the sea bream is more abundant between 21 and 30 fathoms than in deeper areas. The recruitment was continuous and regular. There is no sign of entry or progression of a dominant brood throughout the period under study. Length frequency distribution shows three distinct modes. The first mode occurs regularly but does not progress beyond 40cm, recruitment being balanced by natural and fishing mortality. The other two which are not regular are probably the result of fishing outside regular areas. Short sections of “growth” lines which fit into one another when extrapolated, are evident. The larger lines obtained by extrapolation are parallel to one another. These tentative "growth lines" indicate that this species which enters the fishing grounds, when 15 cm or larger in length are exploited by the trawl fishery for a period of three to four years. This species appears to be six months old when it enters the fishing grounds and increases in length by about 37.5 cm in the next 30 months. Later growth slows down. The average size of the specimens sampled continued to get smaller from 1953 till 1957. It is shown that this reduction in size is due to increased fishing effort.

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BACKGROUND: Primary angle-closure glaucoma (PACG) is a major cause of visual morbidity in East Asia. Dark-room provocative test (DRPT) has been used to determine which narrow angles have the risk to develop angle closure. However, the accuracy of DRPT might be altered because that after emerging from the dark room, the configuration of the angle is affected by the light of the slit-lamp and the appositionally closed angle reopens. The aim of this study was to examine the pupillary diameter in different light conditions and use it as a parameter to assess the accuracy of dark-room provocative test. METHODS: Patients with suspected primary angle-closure glaucoma undergoing DRPT were recruited. The anterior chamber angle was examined by anterior segment optical coherence tomography under the following conditions: (1) in standard room illumination; (2) after short-term dark-adaptation and (3) after DRPT. Mean values of pupil size and numbers of appositionally closed angle under different conditions were compared. RESULTS: A total of 47 eyes of 47 patients were analyzed. The pupil size after DRPT was smaller than that after short-term dark-adaptation (P < 0.001) and smaller than that in standard room illumination (P = 0.026). The numbers of appositionally closed angles after short-term dark-adaptation were significantly larger than those after DRPT (P < 0.001). There was no significant difference between the numbers of appositionally closed angles in standard room illumination and after DRPT (P = 0.157). CONCLUSIONS: Constriction of pupil size immediately after prolonged dark room provocative test may lead to change in the angle configuration, which may lead to false negative results. We suggest a modified protocol of recording intraocular pressure immediately after DRPT and performing gonioscopy following short-term dark adaptation to improve the accuracy of angle closure assessment.