41,887 research outputs found
Translation-finite sets, and weakly compact derivations from \lp{1}(\Z_+) to its dual
We characterize those derivations from the convolution algebra
to its dual which are weakly compact. In particular, we
provide examples which are weakly compact but not compact. The characterization
is combinatorial, in terms of "translation-finite" subsets of ,
and we investigate how this notion relates to other notions of "smallness" for
infinite subsets of . In particular, we show that a set of
strictly positive Banach density cannot be translation-finite; the proof has a
Ramsey-theoretic flavour.Comment: v1: 14 pages LaTeX (preliminary). v2: 13 pages LaTeX, submitted. Some
streamlining, renumbering and minor corrections. v3: appendix removed. v4:
Modified appendix reinstated; 14 pages LaTeX. To appear in Bull. London Math.
Soc
Plastic deformation and wear process at a surface during unlubricated sliding
The plastic deformation and wear of a 304 stainless steel surface sliding against an aluminum oxide rider with a spherical surface (the radius of curvature: 1.3 cm) were observed by using scanning electron and optical microscopes. Experiments were conducted in a vacuum of one million Pa and in an environment of fifty thousandth Pa of chlorine gas at 25 C. The load was 500 grams and the sliding velocity was 0.5 centimeter per second. The deformed surface layer which accumulates and develops successively is left behind the rider, and step shaped proturbances are developed even after single pass sliding under both environmental conditions. A fully developed surface layer is gradually torn off leaving a characteristic pattern. The mechanism for tearing away of the surface layer from the contact area and sliding track contour is explained assuming the simplified process of material removal based on the adhesion theory for the wear of materials
Propagation of hydrodynamic interactions between particles in a compressible fluid
Hydrodynamic interactions are transmitted by viscous diffusion and sound
propagation: the temporal evolution of hydrodynamic interactions by both
mechanisms is studied by direct numerical simulation in this paper. The
hydrodynamic interactions for a system of two particles in a fluid are
estimated by the velocity correlation of the particles. In an incompressible
fluid, hydrodynamic interactions propagate instantaneously at the infinite
speed of sound, followed by the temporal evolution of viscous diffusion. On the
other hand, in a compressible fluid, sound propagates at a finite speed, which
affects the temporal evolution of the hydrodynamic interactions by the order of
magnitude relation between the time scales of viscous diffusion and sound
propagation. The hydrodynamic interactions are characterized by introducing the
ratio of these time scales as an interactive compressibility factor.Comment: 12 pages, 8 figure
Plastic deformation at surface during unlubricated sliding
The plastic deformation and wear of 304 stainless-steel surface slid against an aluminum oxide rider were observed by using a scanning electron microscope and an optical microscope. Experiments were conducted in a vacuum of 0.000001 Pa and in an environment of 0.0005 Pa chlorine gas at 25 C. The load was 500 grams and the sliding velocity was 0.5 centimeter per second. The deformed surface layer which accumulates and develops successively is left behind the rider, and step-shaped protuberances are developed even after single pass sliding under both environmental conditions. A fully developed surface layer is gradually torn off leaving a characteristic pattern. These observations result from both adhesion and an adhesive wear mechanism
First-order quantum correction to the Larmor radiation from a moving charge in a spatially homogeneous time-dependent electric field
First-order quantum correction to the Larmor radiation is investigated on the
basis of the scalar QED on a homogeneous background of time-dependent electric
field, which is a generalization of a recent work by Higuchi and Walker so as
to be extended for an accelerated charged particle in a relativistic motion. We
obtain a simple approximate formula for the quantum correction in the limit of
the relativistic motion when the direction of the particle motion is parallel
to that of the electric field.Comment: 12 pages, 2 figures, accepted for publication in Physical Review
Dynamics of Quasi-ordered Structure in a Regio-regulated pi-Conjugated Polymer:Poly(4-methylthiazole-2,5-diyl)
Dynamics of regio-regulated Poly(4-methylthiazole-2,5-diyl) [HH-P4MeTz] was
inves tigated by solid-state 1H, 2D, 13C NMR spectroscopies, and differential
scanning calorimetry(DSC) measurements. DSC, 2D quadrupolar echo NMR, 13C
cross-polarization and magic-angle spinning(CPMAS) NMR, and 2D spin-echo(2DSE)
CPMAS NMR spectroscopy suggest existence of a quasi-ordered phase in which
backbone twists take place with weakened pi-stackings. Two-dimensional exchange
2D NMR(2DEX) detected slow dynamics with a rate of an order of 10^2Hz for the
CD_3 group in d_3-HH-P4MeTz at 288K. The frequency dependence of proton
longitudinal relaxation rate at 288K shows a omega^-1/2 dependence, which is
due to the one-dimensional diffusion-like motion of backbone conformational
modulation waves. The diffusion rate was estimated as 3+/-2 GHz, which was
approximately 10^7 times larger than that estimated by 2DEX NMR measurements.
These results suggest that there exists anomalous dispersion of modulation
waves in HH-P4MeTz. The one-dimensional group velocity of the wave packet is
responsible for the behavior of proton longitudinal relaxation time. On the
other hand, the 2DEX NMR is sensitive to phase velocity of the nutation of
methyl groups that is associated with backbone twists. From proton T_1 and T_2
measurements, the activation energy was estimated as 2.9 and 3.4 kcal/mol,
respectively. These were in agreement with 3.0 kcal/mol determined by
Moller-Plesset(MP2) molecular orbital(MO) calculation. We also performed
chemical shielding calculation of the methyl-carbon in order to understand
chemical shift tensor behavior, leading to the fact that a quasi-ordered phase
coexist with the crystalline phase.Comment: 14 pages, 11 figures, to appear in Phys.Rev.
Robust and Scalable Scheme to Generate Large-Scale Entanglement Webs
We propose a robust and scalable scheme to generate an -qubit state
among separated quantum nodes (cavity-QED systems) by using linear optics and
postselections. The present scheme inherits the robustness of the Barrett-Kok
scheme [Phys. Rev. A {\bf 71}, 060310(R) (2005)]. The scalability is also
ensured in the sense that an arbitrarily large -qubit state can be
generated with a quasi-polynomial overhead . The
process to breed the states, which we introduce to achieve the scalability,
is quite simple and efficient, and can be applied for other physical systems.Comment: 5 pages, 3 figure
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