Finitely convergent deterministic and stochastic iterative methods for solving convex feasibility problems

We propose finitely convergent methods for solving convex feasibility problems defined over a possibly infinite pool of constraints. Following other works in this area, we assume that the interior of the solution set is nonempty and that certain overrelaxation parameters form a divergent series. We combine our methods with a very general class of deterministic control sequences where, roughly speaking, we require that sooner or later we encounter a violated constraint if one exists. This requirement is satisfied, in particular, by the cyclic, repetitive and remotest set controls. Moreover, it is almost surely satisfied for random controls.

     

A Particle-Mesh Method for the Shallow Water Equations Near Geostrophic Balance

In this paper we outline a new particle-mesh method for rapidly rotating shallow water flows based on a set of regularized equations of motion. The time-stepping method uses an operator splitting of the equations into an Eulerian gravity wave part and a Lagrangian advection part. An essential ingredient is the advection of absolute vorticity by means of translated radial basis functions. We show that this implies exact conservation of enstrophy. The method is tested on two model problems based on the qualitative features of the solutions obtained (i.e., dispersion or smoothness of potential vorticity contours) as well as on the increase in mean divergence level.     

Collective and two-quasiparticle states in 158Gd observed through study of radiative neutron capture in 157Gd

The level structure of ¹⁵⁸Gd has been studied using the prompt γ-rays and conversion electrons emitted following neutron capture in ¹⁵⁷Gd. The γ-ray energy and intensity measurements were made using both Ge(Li) detectors and a curved-crystal spectrometer. Conversion-electron energy and intensity measurements were made using two separate magnetic spectrometers: one to measure the primary electron spectrum and the other to measure the lower energy secondary electron spectrum. Some γ-γ coincidence measurements were also made among the secondary γ-rays. From these data, a neutron separation energy of 7937.1 ± 0.5 keV has been determined for ¹⁵⁸Gd. A level scheme containing 59 excited states with energies < 2.25 MeV, for which de-excitation modes have been identified, is proposed for ¹⁵⁸Gd. Many of these states have been grouped into rotational bands. A total of thirteen excited rotational bands with band-head energies below 2.0 MeV are contained in the level scheme. Features of the proposed level scheme include: the K^π = 0^?, 1^? and 2^? octupole-vibrational bands with band-head energies of 1263, 977 and 1793 keV, respectively; the γ-vibrational band at 1187 keV; three excited K^π = 0⁺ bands with band-head energies of 1196, 1452 and 1743 keV; several two-quasiparticle bands with band-head energies in keV (and K^π assignments) of 1380 (4⁺), 1636 (4^?), 1847 (1⁺), 1856 (1^?), 1920 (4⁺) and 1930 (1⁺). An analysis of (d, p) reaction data is presented which permits definite two-quasiparticle configuration assignments to be made to most of these latter bands. Evidence is presented which suggests strong mixing of some two-neutron and two-proton bands. A phenomenological four-band mixing analysis is made of the energy and E2 transition-probability data for the ground-state band and the three lowest-lying excited collective positive-parity bands. Good agreement with experiment is obtained. A Coriolis-mixing analysis of the octupole bands has been carried out and good agreement with the data on level energies and E1 transition probabilities to the ground-state band has been achieved. Values of Z, the ratio of the E1 transition matrix element with ΔK = 1 to that with ΔK = 0, involving the octupole bands and the first four 0⁺ bands are derived. For three of these 0⁺ bands, absolute values of these matrix elements are deduced. An interesting alternation in the sign of Z is observed for these four 0⁺ bands.     

Raman spectroscopy on single- and multi-walled nanotubes under high pressure

The pressure dependence of the high-energy Raman modes in single- and multi-walled carbon nanotubes was measured in the range 0–10 GPa. We found the pressure coefficient to be linear in both materials but 25% smaller in MWNT. Given that the curvature effects on vibrational properties of the rolled-up graphene sheets are small, we can explain this difference simply with elasticity theory. Received: 17 May 1999 / Accepted 18 May 1999 / Published online: 4 August 1999     

Structure and mobility of lipid membranes on a thermoplastic substrate

Supported lipid membranes constitute one of the most important model systems for cell membranes. The properties of lipid membranes supported by the hydrophobic solid polymer cyclic olefin copolymer (COC) were investigated. Lipid layers consisting of varying amounts of 1,2-dioleoyl-3-trimethylammonium propane (DOTAP, cationic) and 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC, neutral) prepared by vesicle fusion and solvent exchange were compared. All lipid mixtures coated the COC surface homogeneously forming a fluid membrane as verified by fluorescence microscopy and fluorescence recovery after photobleaching (FRAP). The exact structure of the supported membranes was determined by synchrotron reflectivity experiments using a microfluidic chamber. The X-ray data are in agreement with a compressed (head-to-head distance = 29 angstroms) and less densely packed bilayer.