1,070 research outputs found
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
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.
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
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
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
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
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
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