We present a short and self-contained proof of Jin’s theorem about the piecewise syndeticity of difference sets which is entirely elementary, in the sense that no use is made of nonstandard analysis, ergodic theory, measure theory, ultrafilters, or other advanced tools. An explicit bound to the number of shifts that are needed to cover a thick set is provided. Precisely, we prove the following:...

Heterostructured photocatalysts were prepared to have nanostructured (ns) TiO2 shells surrounding microcrystalline (mc) cores of (Ba,Sr)TiO3. The as-prepared heterostructures were annealed between 400°C and 600°C to improve crystallinity and core-shell interfacial bonding. X-ray diffraction, electron microscopy, and gas adsorption measurements demonstrated that 50 nm thick shells composed of na...

196 LLE Review, Volume 88 Introduction Polyimide is being developed as an ablator material for inertial confinement fusion (ICF) targets because of its superior mechanical and thermal properties.1 A typical target design for the OMEGA laser system consists of a spherical shell, 1 mm in diameter and 1 μm in wall thickness, with a 100-μm-thick layer of solid deuterium and tritium (DT) uniformly d...

Electron transfer (ET) dynamics from the 1Se electron state in quasi-type II CdSe/CdS core/shell quantum dots (QDs) to adsorbed methyl viologen (MV(2+)) were measured using femtosecond transient absorption spectroscopy. The intrinsic ET rate kET was determined from the measured average number of ET-active MV(2+) per QD, which permits reliable comparisons of variant shell thickness and different...

While the importance of dusty asymptotic giant branch (AGB) stars to galactic chemical enrichment is widely recognized, a sophisticated understanding of the dust formation and wind-driving mechanisms has proven elusive due in part to the difficulty in spatially resolving the dust-formation regions themselves. We have observed 20 dust-enshrouded AGB stars as part of the Keck Aperture Masking Exp...

in this paper, a thermoelasticity solution for steady state response of thick cylinders which are subjected to pressure and external heat flux in inner surface is presented. displacement field obeys the kinematics of the first order shear deformation theory (fsdt). it is assumed that the temperature varies both along the length and the thickness. the variation of the temperature occurs linearly...