Variation-norm and fluctuation estimates for ergodic bilinear averages

For any dynamical system, we show that higher variation-norms for the sequence of ergodic bilinear averages of two functions satisfy a large range of bilinear Lp estimates. It follows that, with probability one, the number of fluctuations along this sequence may grow at most polynomially with respect to (the growth of) the underlying scale. These results strengthen previous works of Lacey and Bourgain where almost surely convergence of the sequence was proved (which is equivalent to the qualitative statement that the number of fluctuations is finite at each scale). Via transference, the proof reduces to establishing new bilinear Lp bounds for variation-norms of truncated bilinear operators on R, and the main ingredient of the proof of these bounds is a variation-norm extension of maximal Bessel inequalities of Lacey and Demeter--Tao--Thiele.Comment: 37 pages, new version fixed some references not displaying correctl

Investigation of the transient fuel preburner manifold and combustor

A computational fluid dynamics (CFD) model with finite rate reactions, FDNS, was developed to study the start transient of the Space Shuttle Main Engine (SSME) fuel preburner (FPB). FDNS is a time accurate, pressure based CFD code. An upwind scheme was employed for spatial discretization. The upwind scheme was based on second and fourth order central differencing with adaptive artificial dissipation. A state of the art two-equation k-epsilon (T) turbulence model was employed for the turbulence calculation. A Pade' Rational Solution (PARASOL) chemistry algorithm was coupled with the point implicit procedure. FDNS was benchmarked with three well documented experiments: a confined swirling coaxial jet, a non-reactive ramjet dump combustor, and a reactive ramjet dump combustor. Excellent comparisons were obtained for the benchmark cases. The code was then used to study the start transient of an axisymmetric SSME fuel preburner. Predicted transient operation of the preburner agrees well with experiment. Furthermore, it was also found that an appreciable amount of unburned oxygen entered the turbine stages

The z < 1.2 optical luminosity function from a sample of ∼410,000 galaxies in Boötes

Using a sample of ~410,000 galaxies to a depth of IAB=24 over 8.26 deg2 in the Boötes field (~10 times larger than the z~1 luminosity function (LF) studies in the prior literature), we have accurately measured the evolving B-band LF of red galaxies at z&lt;1.2 and blue galaxies at z&lt;1.0 In addition to the large sample size, we utilize photometry that accounts for the varying angular sizes of galaxies, photometric redshifts verified with spectroscopy, and absolute magnitudes that should have very small random and systematic errors. Our results are consistent with the migration of galaxies from the blue cloud to the red sequence as they cease to form stars and with downsizing in which more massive and luminous blue galaxies cease star formation earlier than fainter less massive ones. Comparing the observed fading of red galaxies with that expected from passive evolution alone, we find that the stellar mass contained within the red galaxy population has increased by a factor of ~3.6 from z~1.1 to z~0.1 The bright end of the red galaxy LF fades with decreasing redshift, with the rate of fading increasing from ~0.2 mag per unit redshift at z = 1.0 to ~0.8 at z = 0.2. The overall decrease in luminosity implies that the stellar mass in individual highly luminous red galaxies increased by a factor of ~2.2 from z = 1.1 to z = 0.1

Microsphere coated substrate containing reactive aldehyde groups

A synthetic organic resin is coated with a continuous layer of contiguous, tangential, individual microspheres having a uniform diameter preferably between 100 Angstroms and 2000 Angstroms. The microspheres are an addition polymerized polymer of an unsaturated aldehyde containing 4 to 20 carbon atoms and are covalently bonded to the substrate by means of high energy radiation grafting. The microspheres contain reactive aldehyde groups and can form conjugates with proteins such as enzymes or other aldehyde reactive materials