Exact formulas for traces of singular moduli of higher level modular functions

Zagier proved that the traces of singular values of the classical j-invariant are the Fourier coefficients of a weight 3/2 modular form and Duke provided a new proof of the result by establishing an exact formula for the traces using Niebur's work on a certain class of non-holomorphic modular forms. In this short note, by utilizing Niebur's work again, we generalize Duke's result to exact formulas for traces of singular moduli of higher level modular functions.Comment: 8 page

Dependence of GCRs influx on the Solar North-South Asymmetry

We investigate the dependence of the amount of the observed galactic cosmic ray (GCR) influx on the solar North-South asymmetry using the neutron count rates obtained from four stations and sunspot data in archives spanning six solar cycles from 1953 to 2008. We find that the observed GCR influxes at Moscow, Kiel, Climax and Huancayo stations are more suppressed when the solar activity in the southern hemisphere is dominant compared with when the solar activity in the northern hemisphere is dominant. Its reduction rates at four stations are all larger than those of the suppression due to other factors including the solar polarity effect on the GCR influx. We perform the student's t-test to see how significant these suppressions are. It is found that suppressions due to the solar North-South asymmetry as well as the solar polarity are significant and yet the suppressions associated with the former are larger and more significant.Comment: 17 pages, 3figures, accepted to JAST

Long-Term X-Ray Variabilities of the Seyfert Galaxy MCG-2-58-22 : Secular Flux Decrease and Flares

We have studied the long-term X-ray light curve (2$-$10 keV) of the luminous Seyfert 1 galaxy MCG-2-58-22 by compiling data, from various X-ray satellites, which together cover more than 20 years. We have found two distinct types of time variations in the light curve. One is a gradual and secular decrease of the X-ray flux, and the other is the episodic increase of X-ray flux (or flare) by a factor of 2$-$4 compared with the level expected from the secular variation. We detected 3 such flares in total; a representative duration for the flares is $\sim$2 years, with intervening quiescent intervals lasting $\sim 6-8$ years. We discuss a few possible origins for these variabilities. Though a standard disk instability theory may explain the displayed time variability in the X-ray light curve, the subsequent accretions of stellar debris, from a tidal disruption event caused by a supermassive black hole in MCG-2-58-22, cannot be ruled out as an alternative explanation.Comment: 11 pages, 1 eps figure, accepted for publication in Journal of the Korean Astronomical Society(JKAS

Combinatorial growth of Si nanoribbons

Silicon nanoribbons (Si NRs) with a thickness of about 30 nm and a width up to a few micrometers were synthesized. Systematic observations indicate that Si NRs evolve via the following sequences: the growth of basal nanowires assisted with a Pt catalyst by a vapor-liquid-solid (VLS) mechanism, followed by the formation of saw-like edges on the basal nanowires and the planar filling of those edges by a vapor-solid (VS) mechanism. Si NRs have twins along the longitudinal < 110 > growth of the basal nanowires that also extend in < 112 > direction to edge of NRs. These twins appear to drive the lateral growth by a reentrant twin mechanism. These twins also create a mirror-like crystallographic configuration in the anisotropic surface energy state and appear to further drive lateral saw-like edge growth in the < 112 > direction. These outcomes indicate that the Si NRs are grown by a combination of the two mechanisms of a Pt-catalyst-assisted VLS mechanism for longitudinal growth and a twin-assisted VS mechanism for lateral growth

Staphylococcal enterotoxin sensitization in a community-based population : a potential role in adult-onset asthma

Background: Recent studies suggest that Staphylococcus aureus enterotoxin sensitization is a risk factor for asthma. However, there is a paucity of epidemiologic evidence on adult-onset asthma in community-based populations. Objective: We sought to evaluate the epidemiology and the clinical significance of staphylococcal enterotoxin sensitization in community-based adult populations. Methods: The present analyses were performed using the baseline data set of Korean adult population surveys, consisting of 1080 adults (mean age=60.2years) recruited from an urban and a rural community. Questionnaires, methacholine challenge tests, and allergen skin tests were performed for defining clinical phenotypes. Sera were analysed for total IgE and enterotoxin-specific IgE using ImmunoCAP. Results: Staphylococcal enterotoxin sensitization (0.35kU/L) had a prevalence of 27.0%. Risk factors were identified as male sex, current smoking, advanced age (61years), and inhalant allergen sensitization. Current asthma was mostly adult onset (18years old) and showed independent associations with high enterotoxin-specific IgE levels in multivariate logistic regression tests. In multivariate linear regressions, staphylococcal enterotoxin-specific IgE level was identified as the major determinant factor for total IgE level. Conclusions and Clinical Relevance: Staphylococcal enterotoxin sensitization was independently associated with adult-onset asthma in adult community populations. Strong correlations between the enterotoxin-specific IgE and total IgE levels support the clinical significance. The present findings warrant further studies for the precise roles of staphylococcal enterotoxin sensitization in the asthma pathogenesis