Rational numbers with purely periodic β\beta-expansion

We study real numbers $\beta$ with the curious property that the $\beta$-expansion of all sufficiently small positive rational numbers is purely periodic. It is known that such real numbers have to be Pisot numbers which are units of the number field they generate. We complete known results due to Akiyama to characterize algebraic numbers of degree 3 that enjoy this property. This extends results previously obtained in the case of degree 2 by Schmidt, Hama and Imahashi. Let $\gamma(\beta)$ denote the supremum of the real numbers $c$ in $(0,1)$ such that all positive rational numbers less than $c$ have a purely periodic $\beta$-expansion. We prove that $\gamma(\beta)$ is irrational for a class of cubic Pisot units that contains the smallest Pisot number $\eta$. This result is motivated by the observation of Akiyama and Scheicher that $\gamma(\eta)=0.666 666 666 086 ...$ is surprisingly close to 2/3

Impact of female age and nulligravidity on fecundity in an older reproductive age cohort

To provide female age-related estimates of fecundity and incidence of infertility by history of prior pregnancy among women 30 to 44 years of age

Return and volatility reactions to monthly announcements of business cycle forecasts : an event study based on high-frequency data

This article contributes to the literature on macroeconomic announcements and their impact on asset prices by investigating how the 15-second Xetra DAX returns reflect the monthly announcements of the two best known business cycle forecasts for Germany, i.e. the ifo Business Climate Index and the ZEW Indicator of Economic Sentiment. From the methodological point of view, the main innovation lies in disentangling "good" macroeconomics news from "bad" news, and, simultaneously, considering time intervals with and without confounding announcements from other sources. Releases from both institutes lead to an immediate response of returns occurring 15 seconds after the announcements, i.e. within the first possible time interval. Announcements of both institutes are also clearly and immediately reflected in the volatility, which remains at a significantly higher level for approximately two minutes slightly elevated for approximately 15 minutes. Combining returns and volatility in a GARCH(1,1)-model, the paper reveals that significant increases in volatility only show up in the presence of simultaneous news released by other sources, whereas return reactions can be observed irrespective of whether confounding announcements are published or not

The Effects of Competition among Fertility Centers on Outcomes in In Vitro Fertilization

Context To successfully compete for future patients, fertility specialists strive to achieve high pregnancy rates. If the specialist transfers multiple embryos during an in vitro fertilization (IVF) procedure to obtain high pregnancy rates, the percentage of high order multiples (HOM) may inadvertently rise. ~-- Objective To measure the effect of competition among fertility centers on outcomes in in vitro fertilization. Design and Setting Retrospective cohort of 408 fertility clinics registered with the Society for Assisted Reproduction as providing IVF services in 2000. Competition is defined as number of clinics in a statistical area. Demand for services is based on the population of reproductive aged women. Subjects 381 fertility clinics reporting clinical outcomes Main outcome measures: The clinic high order multiple gestation rate (percentage of pregnancies that were high order multiples) and age adjusted pregnancy rate Results The number of clinics in an area of competition ranged from 1-22. HOM rate per clinic ranged from 0% to 50%. As demand increased, competition increased. As competition increased the number of high order multiples per clinic decreased. In areas of low competition (1-2 clinics) the clinic rate was 8.46%, in areas of intermediate competition (3-7 clinics) 8.39%, and in areas of high competition (8-22 clinics) 8.24%. In areas with intermediate demand, high levels of competition resulted in fewer high order multiples than intermediate competition (RR 0.56, 95% confidence interval 0.36,0.89) or low levels of competition (RR 0.57, 95% confidence interval 0.35, 0.94). Age adjusted pregnancy rates did not differ by level of competition. Conclusions Based on this data, the risk of high order multiple gestation decreases with increasing competition between clinics; however, pregnancy rates are unaffected.Master of Public Healt