Polyhedral approximations of strictly convex compacta

We consider polyhedral approximations of strictly convex compacta in finite dimensional Euclidean spaces (such compacta are also uniformly convex). We obtain the best possible estimates for errors of considered approximations in the Hausdorff metric. We also obtain new estimates of an approximate algorithm for finding the convex hulls

Uniformly convex subsets of the Hilbert space with modulus of convexity of the second order

We prove that in the Hilbert space every uniformly convex set with modulus of convexity of the second order at zero is an intersection of closed balls of fixed radius. We also obtain an estimate of this radius

Weakly convex sets and modulus of nonconvexity

We consider a definition of a weakly convex set which is a generalization of the notion of a weakly convex set in the sense of Vial and a proximally smooth set in the sense of Clarke, from the case of the Hilbert space to a class of Banach spaces with the modulus of convexity of the second order. Using the new definition of the weakly convex set with the given modulus of nonconvexity we prove a new retraction theorem and we obtain new results about continuity of the intersection of two continuous set-valued mappings (one of which has nonconvex images) and new affirmative solutions of the splitting problem for selections. We also investigate relationship between the new definition and the definition of a proximally smooth set and a smooth set

General expression for the dielectronic recombination cross section of polarized ions with polarized electrons

A general expression for the differential cross section of dielectronic recombination (DR) of polarized electrons and polarized ions is derived by using usual atomic theory methods and is represented in the form of multiple expansions over spherical tensors. The ways of the application of the general expressions suitable for the specific experimental conditions are outlined by deriving asymmetry parameters of angular distribution of DR radiation in the case of nonpolarized and polarized ions and electrons.Comment: 4 page

Present and Future Gamma-Ray Probes of the Cygnus OB2 Environment

The MAGIC Collaboration has provided new observational data pertaining to the TeV J2032+4130 gamma-ray source (within the Cygnus OB2 region), for energies E_gamma >400 GeV. It is then appropriate to update the impact of these data on gamma-ray production mechanisms in stellar associations. We consider two mechanisms of gamma-ray emission, pion production and decay (PION) and photo-excitation of high-energy nuclei followed by prompt photo-emission from the daughter nuclei (A*). We find that while the data can be accommodated with either scenario, the A* features a spectral bump, corresponding to the threshold for exciting the Giant Dipole Resonance, which can serve to discriminate between them. We comment on neutrino emission and detection from the region if the PION and/or A* processes are operative. We also touch on the implications for this analysis of future Fermi and Cerenkov Telescope Array data.Comment: 6 pp, 2 figs. Matching version publihed in Phys. Rev.

Inelastic scanning tunneling spectroscopy: magnetic excitations on the nanoscale

Inelastic scanning tunneling spectroscopy is used to study elementary excitations (magnons) in magnetic systems of various dimensions: from bulk to single magnetic atoms. The creation mechanism, the excitation probability, the spectrum and the lifetimes of magnons are investigated

Comments: Private Investment: Trojan-horse or Shining Knight for America\u27s Public Housing Stock

The numbers are staggering. The nation\u27s largest public housing authorities ( HA\u27s ) are in a state of crisis as a result of massive budget shortfalls. The Department of Housing and Urban Development (HUD) estimates it would take roughly $26 billion to remedy the problem. To put this in perspective, in 2014 the New York City Public Housing Authority had a$77 million deficit and $18 billion worth of unfunded capital improvements, - a euphemism for basic upgrades to building systems such as water, heat, air conditioning, and elevators. At present, many of these systems are woefully below acceptable livability standards. This financial inability to make repairs and renovations has consequences beyond a lack of curb appeal. Crime increases if safety features, such as cameras and lighting, do not work, and if you force people to live in dilapidated and ruinous conditions then they in turn lose pride in their community. The result is a self-perpetuating cycle of distrust and apathy that brings down the public housing system as a whole

Comments: Private Investment: Trojan-horse or Shining Knight for America\u27s Public Housing Stock

The numbers are staggering. The nation\u27s largest public housing authorities ( HA\u27s ) are in a state of crisis as a result of massive budget shortfalls. The Department of Housing and Urban Development (HUD) estimates it would take roughly $26 billion to remedy the problem. To put this in perspective, in 2014 the New York City Public Housing Authority had a$77 million deficit and $18 billion worth of unfunded capital improvements, - a euphemism for basic upgrades to building systems such as water, heat, air conditioning, and elevators. At present, many of these systems are woefully below acceptable livability standards. This financial inability to make repairs and renovations has consequences beyond a lack of curb appeal. Crime increases if safety features, such as cameras and lighting, do not work, and if you force people to live in dilapidated and ruinous conditions then they in turn lose pride in their community. The result is a self-perpetuating cycle of distrust and apathy that brings down the public housing system as a whole