A Computerized Demonstration of the Central Limit Theorem in Statistics

The Central Limit Theorem is one of the most important concepts in statistics. It provides a link between sample statistics and population parameters. It is a basic concept for understanding various hypothesis-testing techniques such as Student\u27s t-distribution, x2-distribution and F-distribution

Self-dual Vortices in the Generalized Abelian Higgs Model with Independent Chern-Simons Interaction

Self-dual vortex solutions are studied in detail in the generalized abelian Higgs model with independent Chern-Simons interaction. For special choices of couplings, it reduces to a Maxwell-Higgs model with two scalar fields, a Chern-Simons-Higgs model with two scalar fields, or other new models. We investigate the properties of the static solutions and perform detailed numerical analyses. For the Chern-Simons-Higgs model with two scalar fields in an asymmetric phase, we prove the existence of multisoliton solutions which can be viewed as hybrids of Chern-Simons vortices and $CP^1$ lumps. We also discuss solutions in a symmetric phase with the help of the corresponding exact solutions in its nonrelativistic limit. The model interpolating all three models---Maxwell-Higgs, Chern-Simons-Higgs, and $CP^1$ models--- is discussed briefly. Finally we study the possibility of vortex solutions with half-integer vorticity in the special case of the model. Numerical results are negative.Comment: 32 pages, LATEX, SNUTP 92-7

The incidence of enlarged chondrons in normal and osteoarthritic human cartilage and their relative matrix density

OBJECTIVE: To quantitate changes in the pericellular matrix in osteoarthritic (OA) articular cartilage. DESIGN: Chondrons were enzymatically isolated from normal and OA human cartilage. The cross-sectional area of the chondrons were measured. After immunolabeling for keratan sulfate, type VI collagen and type II collagen, the relative matrix density was determined for different size classes of chondrons with quantitative fluorescence microscopy. RESULTS: For individual chondrons, the average cross-sectional area (344+/-28 microm(2), mean+/-SE) for the normal specimens was significantly smaller than the average area (439+/-30 microm(2)) for the OA specimens. Using 496 microm(2) (mean+2 SD of the normal area) as the cut-off for enlarged chondrons, 33% of individual OA chondrons were enlarged compared to 16% for the normal. Chondrons under 300 microm(2) had a significantly higher density of keratan sulfate and type VI collagen than larger chondrons, while chondrons over 400 microm(2) had similar matrix densities. CONCLUSIONS: There is a higher incidence of enlarged chondrons in OA cartilage than in normal cartilage. The enlargement may initially be due to hydrodynamic swelling but further increases in size are due to increased matrix deposition

Poincar\'e Husimi representation of eigenstates in quantum billiards

For the representation of eigenstates on a Poincar\'e section at the boundary of a billiard different variants have been proposed. We compare these Poincar\'e Husimi functions, discuss their properties and based on this select one particularly suited definition. For the mean behaviour of these Poincar\'e Husimi functions an asymptotic expression is derived, including a uniform approximation. We establish the relation between the Poincar\'e Husimi functions and the Husimi function in phase space from which a direct physical interpretation follows. Using this, a quantum ergodicity theorem for the Poincar\'e Husimi functions in the case of ergodic systems is shown.Comment: 17 pages, 5 figures. Figs. 1,2,5 are included in low resolution only. For a version with better resolution see http://www.physik.tu-dresden.de/~baecker

Mucus Sugar Content Shapes the Bacterial Community Structure in Thermally Stressed Acropora muricata

It has been proposed that the chemical composition of a coral’s mucus can influence the associated bacterial community. However, information on this topic is rare, and non-existent for corals that are under thermal stress. This study therefore compared the carbohydrate composition of mucus in the coral Acropora muricata when subjected to increasing thermal stress from 26°C to 31°C, and determined whether this composition correlated with any changes in the bacterial community. Results showed that, at lower temperatures, the main components of mucus were N-acetyl glucosamine and C6 sugars, but these constituted a significantly lower proportion of the mucus in thermally-stressed corals. The change in the mucus composition coincided with a shift from a γ-Proteobacteria- to a Verrucomicrobiae- and α-Proteobacteria-dominated community in the coral mucus. Bacteria in the class Cyanobacteria also started to become prominent in the mucus when the coral was thermally stressed. The increase in the relative abundance of the Verrucomicrobiae at higher temperature was strongly associated with a change in the proportion of fucose, glucose and mannose in the mucus. Increase in the relative abundance of α-Proteobacteria were associated with GalNAc and glucose, while the drop in relative abundance of γ-Proteobacteria at high temperature coincided with changes in fucose and mannose. Cyanobacteria were highly associated with arabinose and xylose. Changes in mucus composition and the bacterial community in the mucus layer occurred at 29°C, which were prior to visual signs of coral bleaching at 31°C. A compositional change in the coral mucus, induced by thermal stress could therefore be a key factor leading to a shift in the associated bacterial community. This, in turn, has the potential to impact the physiological function of the coral holobiont

Geometrical structure effect on localization length of carbon nanotubes

The localization length and density of states of carbon nanotubes are evaluated within the tight-binding approximation. By comparison with the corresponding results for the square lattice tubes, it is found that the hexagonal structure affects strongly the behaviors of the density of states and localization lengths of carbon nanotubes.Comment: 7 pages, 4 figures, revised version to appear in Chin. Phys. Lett. The title is changed. Some arguments are adde

Bogomol'nyi Equations of Maxwell-Chern-Simons vortices from a generalized Abelian Higgs Model

We consider a generalization of the abelian Higgs model with a Chern-Simons term by modifying two terms of the usual Lagrangian. We multiply a dielectric function with the Maxwell kinetic energy term and incorporate nonminimal interaction by considering generalized covariant derivative. We show that for a particular choice of the dielectric function this model admits both topological as well as nontopological charged vortices satisfying Bogomol'nyi bound for which the magnetic flux, charge and angular momentum are not quantized. However the energy for the topolgical vortices is quantized and in each sector these topological vortex solutions are infinitely degenerate. In the nonrelativistic limit, this model admits static self-dual soliton solutions with nonzero finite energy configuration. For the whole class of dielectric function for which the nontopological vortices exists in the relativistic theory, the charge density satisfies the same Liouville equation in the nonrelativistic limit.Comment: 30 pages(4 figures not included), RevTeX, IP/BBSR/93-6

Housing and Business Investment in Nebraska\u27s Non-metropolitan Communities and Declining Urban Neighborhoods

This study focuses on one subject area of the Urban Affairs Committee\u27s charge: housing and business investment in Nebraska\u27s declining urban neighborhoods and non-metropolitan communities. From its beginning the study has had two primary objectives: First, to ascertain the demand for housing and business investment funds in the declining urban neighborhoods of Nebraska\u27s two major metropolitan cities, Omaha and Lincoln, and in the State\u27s non-metropolitan communities; and the perceptions of homeowners, renters, landlords and businessmen in these communities and neighborhoods regarding the availability to them of such funds. Second, to identify factors which discourage or hamper housing and business investment in the declining urban neighborhoods of Omaha and Lincoln and in the State\u27s non-metropolitan communities, and to recommend legislation and other measures to eliminate such factors and to provide incentives for increased investment in these neighborhoods and communities

The Burrell-Optical-Kepler-Survey (BOKS). I. Survey Description and Initial Results

We present the initial results of a 40 night contiguous ground-based campaign of time series photometric observations of a 1.39 deg^2 field located within the NASA Kepler Mission field of view. The goal of this pre-launch survey was to search for transiting extrasolar planets and to provide independent variability information of stellar sources. We have gathered a data set containing light curves of 54,687 stars from which we have created a statistical sub-sample of 13,786 stars between 14 < r < 18.5 and have statistically examined each light curve to test for variability. We present a summary of our preliminary photometric findings including the overall level and content of stellar variability in this portion of the Kepler field and give some examples of unusual variable stars found within. We present a preliminary catalog of 2,457 candidate variable stars, of which 776 show signs of periodicity. We also present three potential exoplanet candidates, all of which should be observable by the Kepler mission