Approximation by Several Rationals

Following T. H. Chan, we consider the problem of approximation of a given rational fraction a/q by sums of several rational fractions a_1/q_1, ..., a_n/q_n with smaller denominators. We show that in the special cases of n=3 and n=4 and certain admissible ranges for the denominators q_1,..., q_n, one can improve a result of T. H. Chan by using a different approach

Chan-Paton Soliton Gauge States of Compatified Open String

We study the mechanism of enhanced gauge symmetry of bosonic open string compatified on torus by analyzing the zero-norm soliton (nonzero winding of wilson line) gauge states in the spectrum. Unlike the closed string case, we find that the soliton gauge state exists only at massive levels. These soliton gauge states correspond to the existence of enhanced massive gauge symmetries with transformation parameters containing both Einstein and Yang-Mills indices. In the T-dual picture, these symmetries exist only at some discrete values of compatified radii when N D-branes are coincident.Comment: 9 pages, update reference

Testing the Box-Cox Parameter for an Integrated Process

This paper analyses the constant elasticity of volatility (CEV) model suggested by Chan et al. (1992). The CEV model without mean reversion is shown to be the inverse Box-Cox transformation of integrated processes asymptotically. It is demonstrated that the maximum likelihood estimator of the power parameter has a nonstandard asymptotic distribution, which is expressed as an integral of Brownian motions, when the data generating process is not mean reverting. However, it is shown that the t-ratio follows a standard normal distribution asymptotically, so that the use of the conventional t-test in analyzing the power parameter of the CEV model is justified even if there is no mean reversion, as is often the case in empirical research. The model may applied to ultra high frequency data.Box-Cox transformation; Brownian Motion; Constant Elasticity of Volatility; Mean Reversion; Nonstandard distribution

The Glasgow Necropolis : theft, bribery and drunken gate keepers in a city of the dead

Wun Fung Chan is a geographer working at the University of Strathclyde. On visiting Glasgow City Archives he came across nine Necropolis Committee books containing some lively insights into Victorian landscapes of death

Preliminary Results of Initial Testing for Coronavirus (COVID-19) in the Emergency Department

Introduction: On March 10, 2020, the World Health Organization declared a global pandemic due to widespread infection of the novel coronavirus 2019 (COVID-19). We report the preliminary results of a targeted program of COVID-19 infection testing in the ED in the first 10 days of its initiation at our institution.Methods: We conducted a review of prospectively collected data on all ED patients who had targeted testing for acute COVID-19 infection at two EDs during the initial 10 days of testing (March 10-19, 2020). During this initial period with limited resources, testing was targeted toward high-risk patients per Centers for Disease Control and Prevention guidelines. Data collected from patients who were tested included demographics, clinical characteristics, and test qualifying criteria. We present the data overall and by test results with descriptive statistics.Results: During the 10-day study period, the combined census of the study EDs was 2157 patient encounters. A total of 283 tests were ordered in the ED. The majority of patients were 18-64 years of age, male, non-Hispanic white, had an Emergency Severity Index score of three, did not have a fever, and were discharged from the ED. A total of 29 (10.2%) tested positive. Symptoms-based criteria most associated with COVID-19 were the most common criteria identified for testing (90.6%). All other criteria were reported in 5.51–43.0% of persons being tested. Having contact with a person under investigation was significantly more common in those who tested positive compared to those who tested negative (63% vs 24.5%, respectively). The majority of patients in both results groups had at least two qualifying criteria for testing (75.2%).Conclusion: In this review of prospectively collected data on all ED patients who had targeted testing for acute COVID-19 infection at two EDs in the first 10 days of testing, we found that 10.2% of those tested were identified as positive. The continued monitoring of testing and results will help providers understand how COVID-19 is progressing in the community