Loops of H-spaces with finitely generated cohomology rings

AbstractLet X be a simply connected ap-space. The mod p cohomology rings of Ω,X are studied. When these rings are finitely generated as algebras, Ω,X hasthe mod p homotopy type of a generalized Eilenberg-MacLane space. If X is just an H-space with H∗(Ω,X;Zp) finitely generated as an algebra, H∗(Ω,X;Zp) is still primitively generated free commutative

On the collapse of certain Eilenberg–Moore spectral sequences

AbstractLet Z be a path connected H-space with H∗(Z;Zp) concentrated in even degrees. Then the Eilenberg–Moore spectral sequences associated to the path loop fibrations ΩZ→PZ→Z,Ω2Z→PΩZ→ΩZ collapse at the E2 term

Evaluation of Formal posterior distributions via Markov chain arguments

We consider evaluation of proper posterior distributions obtained from improper prior distributions. Our context is estimating a bounded function $\phi$ of a parameter when the loss is quadratic. If the posterior mean of $\phi$ is admissible for all bounded $\phi$, the posterior is strongly admissible. We give sufficient conditions for strong admissibility. These conditions involve the recurrence of a Markov chain associated with the estimation problem. We develop general sufficient conditions for recurrence of general state space Markov chains that are also of independent interest. Our main example concerns the $p$-dimensional multivariate normal distribution with mean vector $\theta$ when the prior distribution has the form $g(\|\theta\|^2) d\theta$ on the parameter space $\mathbb{R}^p$. Conditions on $g$ for strong admissibility of the posterior are provided.Comment: Published in at http://dx.doi.org/10.1214/07-AOS542 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Measuring nonlinear stresses generated by defects in 3D colloidal crystals

The mechanical, structural and functional properties of crystals are determined by their defects and the distribution of stresses surrounding these defects has broad implications for the understanding of transport phenomena. When the defect density rises to levels routinely found in real-world materials, transport is governed by local stresses that are predominantly nonlinear. Such stress fields however, cannot be measured using conventional bulk and local measurement techniques. Here, we report direct and spatially resolved experimental measurements of the nonlinear stresses surrounding colloidal crystalline defect cores, and show that the stresses at vacancy cores generate attractive interactions between them. We also directly visualize the softening of crystalline regions surrounding dislocation cores, and find that stress fluctuations in quiescent polycrystals are uniformly distributed rather than localized at grain boundaries, as is the case in strained atomic polycrystals. Nonlinear stress measurements have important implications for strain hardening, yield, and fatigue.Comment: in Nature Materials (2016

Effect of operating conditions on gearbox noise

Low contact ratio spur gears were tested in the NASA gear noise rig to study the noise radiated from the top of the gearbox. The measured sound power from the gearbox top was obtained from a near field acoustic intensity scan taken at 63 nodes just above the surface. The sound power was measured at a matrix of 45 operating speeds and torque levels. Results are presented in the form of a spectral speed map and as a plot of sound power versus torque (at constant speed) and as sound power versus speed (at constant torque). Because of the presence of vibration modes, operating speed was found to have more impact on noise generation than torque level. A NASA gear dynamics code was used to compute the gear tooth dynamic overload at the same 45 operating conditions used for the experiment. Similar trends were found between the analytical results for dynamic tooth overload and experimental results for sound power. Dynamic analysis may be used to design high quality gears with profile relief optimized for minimum dynamic load and noise

Hard x-ray polarimetry with the Ramaty High Energy Solar Spectroscopic Imager (RHESSI)

Although designed primarily as a hard X-ray imager and spectrometer, the Ramaty High Energy Solar Spectroscopic Imager (RHESSI) is also capable of measuring the polarization of hard X-rays (20-100 keV) from solar flares. This capability arises from the inclusion of a small unobstructed Be scattering element that is strategically located within the cryostat that houses the array of nine germanium detectors. The Ge detectors are segmented, with both a front and rear active volume. Low energy photons (below about 100 keV) can reach a rear segment of a Ge detector only indirectly, by scattering. Low energy photons from the Sun have a direct path to the Be and have a high probability of Compton scattering into a rear segment of a Ge detector. The azimuthal distribution of these scattered photons carries with it a signature of the linear polarization of the incident flux. Sensitivity estimates, based on simulations and in-flight background measurements, indicate that a 20-100 keV polarization sensitivity of less than a few percent can be achieved for X-class flares

Comparison of analysis and experiment for dynamics of low-contact-ratio spur gears

Low-contact-ratio spur gears were tested in NASA gear-noise-rig to study gear dynamics including dynamic load, tooth bending stress, vibration, and noise. The experimental results were compared with a NASA gear dynamics code to validate the code as a design tool for predicting transmission vibration and noise. Analytical predictions and experimental data for gear-tooth dynamic loads and tooth-root bending stress were compared at 28 operating conditions. Strain gage data were used to compute the normal load between meshing teeth and the bending stress at the tooth root for direct comparison with the analysis. The computed and measured waveforms for dynamic load and stress were compared for several test conditions. These are very similar in shape, which means the analysis successfully simulates the physical behavior of the test gears. The predicted peak value of the dynamic load agrees with the measurement results within an average error of 4.9 percent except at low-torque, high-speed conditions. Predictions of peak dynamic root stress are generally within 10 to 15 percent of the measured values