XB-70 flight test data comparisons with simulation predictions of inlet unstart and buzz

XB-70 flight test data comparison with simulated predictions of inlet unstart and buz

On optimal truncation of divergent series solutions of nonlinear differential systems; Berry smoothing

We prove that for divergent series solutions of nonlinear (or linear) differential systems near a generic irregular singularity, the common prescription of summation to the least term is, if properly interpreted, meaningful and correct, and we extend this method to transseries solutions. In every direction in the complex plane at the singularity (Stokes directions {\em not} excepted) there exists a nonempty set of solutions whose difference from the ``optimally'' (i.e., near the least term) truncated asymptotic series is of the same (exponentially small) order of magnitude as the least term of the series. There is a family of generalized Borel summation formulas $\mathcal{B}$ which commute with the usual algebraic and analytic operations (addition, multiplication, differentiation, etc). We show that there is exactly one of them, $\mathcal{B}_0$, such that for any formal series solution $\tilde{f}$, $\mathcal{B}_0(\tilde{f})$ differs from the optimal truncation of $\tilde{f}$ by at most the order of the least term of $\tilde{f}$. We show in addition that the Berry (1989) smoothing phenomenon is universal within this class of differential systems. Whenever the terms ``beyond all orders'' {\em change} in crossing a Stokes line, these terms vary smoothly on the Berry scale $\arg(x)\sim |x|^{-1/2}$ and the transition is always given by the error function; under the same conditions we show that Dingle's rule of signs for Stokes transitions holds

Structural ambiguity of the Chinese version of the hospital anxiety and depression scale in patients with coronary heart disease

Background The Hospital Anxiety and Depression Scale (HADS) is a widely used screening tool designed as a case detector for clinically relevant anxiety and depression. Recent studies of the HADS in coronary heart disease (CHD) patients in European countries suggest it comprises three, rather than two, underlying sub-scale dimensions. The factor structure of the Chinese version of the HADS was evaluated in patients with CHD in mainland China. Methods Confirmatory factor analysis (CFA) was conducted on self-report HADS forms from 154 Chinese CHD patients. Results Little difference was observed in model fit between best performing three-factor and two-factor models. Conclusion The current observations are inconsistent with recent studies highlighting a dominant underlying tri-dimensional structure to the HADS in CHD patients. The Chinese version of the HADS may perform differently to European language versions of the instrument in patients with CHD

Phase-locked loop with sideband rejecting properties Patent

Phase locked loop with sideband rejecting properties in continuous wave tracking rada

Capillary Waves at Liquid/Vapor Interfaces: A Molecular Dynamics Simulation

Evidence for capillary waves at a liquid/vapor interface are presented from extensive molecular dynamics simulations of a system containing up to 1.24 million Lennard-Jones particles. Careful measurements show that the total interfacial width depends logarithmically on $L_\parallel$, the length of the simulation cell parallel to the interface, as predicted theoretically. The strength of the divergence of the interfacial width on $L_\parallel$ depends inversely on the surface tension $\gamma$. This allows us to measure $\gamma$ two ways since $\gamma$ can also be obtained from the difference in the pressure parallel and perpendicular to the interface. These two independent measures of $\gamma$ agree provided that the interfacial order parameter profile is fit to an error function and not a hyperbolic tangent, as often assumed. We explore why these two common fitting functions give different results for $\gamma$

Welding of commercial base plates is investigated

Investigation of aluminum alloy welds reveals that the combinations of metallic elements with hydrogen are not capable of producing weld porosity themselves, rather they tend to increase the amount of porosity only in the presence of arc contamination by water vapor

The fate of cannibalized fundamental-plane ellipticals

Evolution and disruption of galaxies orbiting in the gravitational field of a larger cluster galaxy are driven by three coupled mechanisms: 1) the heating due to its time dependent motion in the primary; 2) mass loss due to the tidal strain field; and 3) orbital decay. Previous work demonstrated that tidal heating is effective well inside the impulse approximation limit. Not only does the overall energy increase over previous predictions, but the work is done deep inside the secondary galaxy, e.g. at or inside the half mass radius in most cases. Here, these ideas applied to cannibalization of elliptical galaxies with fundamental-plane parameters. In summary, satellites which can fall to the center of a cluster giant by dynamical friction are evaporated by internal heating by the time they reach the center. This suggests that true merger-produced multiple nuclei giants should be rare. Specifically, secondaries with mass ratios as small as 1\% on any initial orbit evaporate and those on eccentric orbits with mass ratios as small as 0.1\% evolve significantly and nearly evaporate in a galaxian age. Captured satellites with mass ratios smaller than roughly 1\% have insufficient time to decay to the center. After many accretion events, the model predicts that the merged system has a profile similar to that of the original primary with a weak increase in concentration.Comment: 19 pages, 10 Postscript figures, uses aaspp4.sty. Submitted to Astrophysical Journa