On the separable quotient problem for Banach spaces

While the classic separable quotient problem remains open, we survey general results related to this problem and examine the existence of a particular infinitedimensional separable quotient in some Banach spaces of vector-valued functions, linear operators and vector measures. Most of the results presented are consequence of known facts, some of them relative to the presence of complemented copies of the classic sequence spaces c_0 and l_p, for 1 <= p <= \infty. Also recent results of Argyros - Dodos - Kanellopoulos, and Sliwa are provided. This makes our presentation supplementary to a previous survey (1997) due to Mujica

Structural, Vibrational and Thermodynamic Properties of AgnCu34-n Nanoparticles

We report results of a systematic study of structural, vibrational and thermodynamical properties of 34-atom bimetallic nanoparticles from the AgnCu34-n family using model interaction potentials as derived from the embedded atom method and in the harmonic approximation of lattice dynamics. Systematic trends in the bond length and dynamical properties can be explained largely on arguments based on local coordination and elemental environment. Thus increase in the number of silver atoms in a given neighborhood introduces a monotonic increase in bond length while increase of the copper content does the reverse. Moreover, based on bond lengths of the lowest coordinated (6 and 8) copper atoms with their nearest neighbors (Cu atoms), we find that the nanoparticles divide into two groups with average bond length either close to (~ 2.58 A) or smaller (~ 2.48 A) than that in bulk copper, accompanied by characteristic features in their vibrational density of states. For the entire set of nanoparticles, vibrational modes are found above the bulk bands of copper/silver. Furthermore, a blue shift in the high frequency end with increasing number of copper atoms in the nanoparticles is traced to a shrinkage of bond lengths from bulk values. The vibrational densities of states at the low frequency end of the spectrum scale linearly with frequency as for single element nanoparticles, however, the effect is more pronounced for these nanoalloys. The Debye temperature was found to be about one third of that of the bulk for pure copper and silver nanoparticles with a non-linear increase with increasing number of copper atoms in the nanoalloys.Comment: 37 pages, 12 figure

Vorticity cutoff in nonlinear photonic crystals

Using group theory arguments, we demonstrate that, unlike in homogeneous media, no symmetric vortices of arbitrary order can be generated in two-dimensional (2D) nonlinear systems possessing a discrete-point symmetry. The only condition needed is that the non-linearity term exclusively depends on the modulus of the field. In the particular case of 2D periodic systems, such as nonlinear photonic crystals or Bose-Einstein condensates in periodic potentials, it is shown that the realization of discrete symmetry forbids the existence of symmetric vortex solutions with vorticity higher than two.Comment: 4 pages, 5 figures; minor changes in address and reference

Positioning systems in Minkowski space-time: Bifurcation problem and observational data

In the framework of relativistic positioning systems in Minkowski space-time, the determination of the inertial coordinates of a user involves the {\em bifurcation problem} (which is the indeterminate location of a pair of different events receiving the same emission coordinates). To solve it, in addition to the user emission coordinates and the emitter positions in inertial coordinates, it may happen that the user needs to know {\em independently} the orientation of its emission coordinates. Assuming that the user may observe the relative positions of the four emitters on its celestial sphere, an observational rule to determine this orientation is presented. The bifurcation problem is thus solved by applying this observational rule, and consequently, {\em all} of the parameters in the general expression of the coordinate transformation from emission coordinates to inertial ones may be computed from the data received by the user of the relativistic positioning system.Comment: 10 pages, 7 figures. The version published in PRD contains a misprint in the caption of Figure 3, which is here amende

Cross section parameterizations for cosmic ray nuclei. 1: Single nucleon removal

Parameterizations of single nucleon removal from electromagnetic and strong interactions of cosmic rays with nuclei are presented. These parameterizations are based upon the most accurate theoretical calculations available to date. They should be very suitable for use in cosmic ray propagation through interstellar space, the Earth's atmosphere, lunar samples, meteorites, spacecraft walls and lunar and martian habitats

Propagation of cosmic-ray nucleons in the Galaxy

We describe a method for the numerical computation of the propagation of primary and secondary nucleons, primary electrons, and secondary positrons and electrons. Fragmentation and energy losses are computed using realistic distributions for the interstellar gas and radiation fields, and diffusive reacceleration is also incorporated. The models are adjusted to agree with the observed cosmic-ray B/C and 10Be/9Be ratios. Models with diffusion and convection do not account well for the observed energy dependence of B/C, while models with reacceleration reproduce this easily. The height of the halo propagation region is determined, using recent 10Be/9Be measurements, as >4 kpc for diffusion/convection models and 4-12 kpc for reacceleration models. For convection models we set an upper limit on the velocity gradient of dV/dz < 7 km/s/kpc. The radial distribution of cosmic-ray sources required is broader than current estimates of the SNR distribution for all halo sizes. Full details of the numerical method used to solve the cosmic-ray propagation equation are given.Comment: 15 pages including 23 ps-figures and 3 tables, latex2e, uses emulateapj.sty (ver. of 11 May 1998, enclosed), apjfonts.sty, timesfonts.sty. To be published in ApJ 1998, v.509 (December 10 issue). More details can be found at http://www.gamma.mpe-garching.mpg.de/~aws/aws.html Some references are correcte