Birth Order and BMI in Teenage Girls

The goal of this study was to investigate the relation of birth order to relative weight and prevalence of obesity in a group of 13–15 years old girls. In 1997, 1458 girls were examined. The height and weight measured by trained staff were recorded. Family size and birth order were obtained by a questionnaire. For the purpose of the present study, 776 and 250 girls coming from two- and three-child full families, respectively, were selected from the total sample on the basis of complete information. The Body Mass Index (kg/m2) was adjusted to reference US population (NCHS) by means of the LMS parameters. Prevalence of overweight and obesity was defined according to recommendation of the International Obesity Task Force. The effect of birth order on BMI was tested by one-way analysis of variance. Prevalence of obesity was tested by the means of Pearson chi-square. First and second born girls from two-sibling families did not show significant differences in average standardized BMI. Relative weight significantly differs among girls coming from three sibling families, decreasing along with the birth order. The first-born girls were 1.5 times at higher risk of obesity in comparison to later- born girls. Differences in the proportion of overweight girls among birth order groups showed a high significance within three sibling families

Dual Active Surface Heat Flux Gage Probe

A unique plug-type heat flux gage probe was tested in the NASA Ames Research Center 2x9 turbulent flow duct facility. The probe was fabricated by welding a miniature dual active surface heat flux gage body to the end of a hollow metal cylindrical bolt containing a metal inner tube. Cooling air flows through the inner tube, impinges onto the back of the gage body and then flows out through the annulus formed between the inner tube and the hollow bolt wall. Heat flux was generated in the duct facility with a Huels arc heater. The duct had a rectangular cross section and one wall was fabricated from 2.54 centimeter thick thermal insulation rigid surface material mounted onto an aluminum plate. To measure heat flux, the probe was inserted through the plate and insulating materials with the from of the gage located flush with the hot gas-side insulation surface. Absorbed heat fluxes measured with the probe were compared with absorbed heat fluxes measured with six water-cooled reference calorimeters. These calorimeters were located in a water-cooled metal duct wall which was located across from the probe position. Correspondence of transient and steady heat fluxes measured with the reference calorimeters and heat flux gage probe was generally within a satisfactory plus or minus 10 percent. This good correspondence was achieved even though the much cooler probe caused a large surface temperature disruption of 1000K between the metal gage and the insulation. However, this temperature disruption did not seriously effect the accuracy of the heat flux measurement. A current application for dual active surface heat flux gages is for transient and steady absorbed heat flux, surface temperature and heat transfer coefficient measurements on the surface of an oxidizer turbine inlet deflector operating in a space shuttle test bed engine

The frequency map for billiards inside ellipsoids

The billiard motion inside an ellipsoid Q \subset \Rset^{n+1} is completely integrable. Its phase space is a symplectic manifold of dimension $2n$, which is mostly foliated with Liouville tori of dimension $n$. The motion on each Liouville torus becomes just a parallel translation with some frequency $\omega$ that varies with the torus. Besides, any billiard trajectory inside $Q$ is tangent to $n$ caustics $Q_{\lambda_1},...,Q_{\lambda_n}$, so the caustic parameters $\lambda=(\lambda_1,...,\lambda_n)$ are integrals of the billiard map. The frequency map $\lambda \mapsto \omega$ is a key tool to understand the structure of periodic billiard trajectories. In principle, it is well-defined only for nonsingular values of the caustic parameters. We present four conjectures, fully supported by numerical experiments. The last one gives rise to some lower bounds on the periods. These bounds only depend on the type of the caustics. We describe the geometric meaning, domain, and range of $\omega$. The map $\omega$ can be continuously extended to singular values of the caustic parameters, although it becomes "exponentially sharp" at some of them. Finally, we study triaxial ellipsoids of \Rset^3. We compute numerically the bifurcation curves in the parameter space on which the Liouville tori with a fixed frequency disappear. We determine which ellipsoids have more periodic trajectories. We check that the previous lower bounds on the periods are optimal, by displaying periodic trajectories with periods four, five, and six whose caustics have the right types. We also give some new insights for ellipses of \Rset^2.Comment: 50 pages, 13 figure

The K\"ahler-Ricci flow on surfaces of positive Kodaira dimension

The existence of K\"ahler-Einstein metrics on a compact K\"ahler manifold has been the subject of intensive study over the last few decades, following Yau's solution to Calabi's conjecture. The Ricci flow, introduced by Richard Hamilton has become one of the most powerful tools in geometric analysis. We study the K\"ahler-Ricci flow on minimal surfaces of Kodaira dimension one and show that the flow collapses and converges to a unique canonical metric on its canonical model. Such a canonical is a generalized K\"ahler-Einstein metric. Combining the results of Cao, Tsuji, Tian and Zhang, we give a metric classification for K\"aher surfaces with a numerical effective canonical line bundle by the K\"ahler-Ricci flow. In general, we propose a program of finding canonical metrics on canonical models of projective varieties of positive Kodaira dimension

Aerothermal Performance Constraints for Small Radius Leading Edges Operating at Hypervelocity

Small radius leading edges and nosetips were used to minimize wave drag in early hypervelocity vehicle concepts until further analysis demonstrated that extreme aerothermodynamic heating blunted the available thermal protection system materials. Recent studies indicate that ultra-high temperature composite (UHTC) materials are shape stable at temperatures approaching 3033 K and will be available for use as sharp leading edge components in the near future. Steady-state aerothermal performance constraints for UHTC components are presented in this paper to identify their non-ablating operational capability at altitudes from sea level to 90 km. An integrated design tool was developed to estimate these constraints. The tool couples aerothermodynamic heating with material response using commercial finite element analysis software and is capable of both steady-state and transient analysis. Performance during entry is analyzed by transient thermal analysis along the trajectory. The thermal load condition from the transient thermal analysis is used to estimate thermal stress. Applying the tool to UHTC materials shows that steady-state, non-ablating operation of a HfB2/SiC(A-7) (A-7) component is possible at velocities approaching Earth's circular orbital velocity of 7.9 km/s at altitudes approaching 70 km

Hyperbolic outer billiards : a first example

We present the first example of a hyperbolic outer billiard. More precisely we construct a one parameter family of examples which in some sense correspond to the Bunimovich billiards.Comment: 11 pages, 8 figures, to appear in Nonlinearit

Polya's inequalities, global uniform integrability and the size of plurisubharmonic lemniscates

First we prove a new inequality comparing uniformly the relative volume of a Borel subset with respect to any given complex euclidean ball \B \sub \C^n with its relative logarithmic capacity in \C^n with respect to the same ball \B. An analoguous comparison inequality for Borel subsets of euclidean balls of any generic real subspace of \C^n is also proved. Then we give several interesting applications of these inequalities. First we obtain sharp uniform estimates on the relative size of \psh lemniscates associated to the Lelong class of \psh functions of logarithmic singularities at infinity on \C^n as well as the Cegrell class of \psh functions of bounded Monge-Amp\`ere mass on a hyperconvex domain \W \Sub \C^n. Then we also deduce new results on the global behaviour of both the Lelong class and the Cegrell class of \psh functions.Comment: 25 page