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

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

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.

Philosophical Roots of the Anthropic Principle

The relevance of this topic to the present meeting is partly due to the fact that almost two decades have elapsed since an astrophysicist, Brandon Carter, had first introduced the Anthropic Cosmological Principle. This has taken place here, in Cracow, at the special Symposium of the IAU devoted to the anniversary of Nicolas Copernicus (Carter 1974). In recent years the Anthropic Principle (AP) has became a matter hotly disputed in the physical, philosophical and theological literature. The constantly increasing interest of the humanities community in the AP may testify to the conjecture that this principle is no accident in the history of ideas. Besides immediate scientific prehistory it may have a substantive philosophical background

Research Notes : Varietal differences of soybeans sensitivity to low temperatures during germination

Developing of cold-tolerant soybean varieties is one of the new main trends in soybean breeding. Such studies were started in the USA (Veitenheimer et al., 1984; Unander and Orf, 1984; Harrison and Nickell, 1984; Hillsman et al., 1977; Hicks, 1978; Seddigh and Jolliff, 1984; Littlejohns and Tanner, 1976; Hume and Jackson, 1981; Voldeng et al., 1984; Sanbuichi, 1980; Goto and Yamamoto, 1972; Schmid and Keller, 1980; Szyrmer and Janicka, 1985; Gromova, 1975; Lunin, 1981; Malysh and Bobrikov, 1984; Sherepitko and Balashow, 1985). The experiments demonstrated that low temperatures reduced germination, field emergence, the rate of early growth and soybean yield

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

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

Microscopic Calculation of Total Ordinary Muon Capture Rates for Medium - Weight and Heavy Nuclei

Total Ordinary Muon Capture (OMC) rates are calculated on the basis of the Quasiparticle Random Phase Approximation for several spherical nuclei from 90^Zr to 208^Pb. It is shown that total OMC rates calculated with the free value of the axial-vector coupling constant g_A agree well with the experimental data for medium-size nuclei and exceed considerably the experimental rates for heavy nuclei. The sensitivity of theoretical OMC rates to the nuclear residual interactions is discussed.Comment: 27 pages and 3 figure