On Symplectic Coverings of the Projective Plane

We prove that a resolution of singularities of any finite covering of the projective plane branched along a Hurwitz curve $\bar H$ and, maybe, along a line "at infinity" can be embedded as a symplectic submanifold into some projective algebraic manifold equipped with an integer K\"{a}hler symplectic form (assuming that if $\bar H$ has negative nodes, then the covering is non-singular over them). For cyclic coverings we can realize this embeddings into a rational algebraic 3--fold. Properties of the Alexander polynomial of $\bar{H}$ are investigated and applied to the calculation of the first Betti number $b_1(\bar X_n)$ of a resolution $\bar X_n$ of singularities of $n$-sheeted cyclic coverings of $\mathbb C\mathbb P^2$ branched along $\bar H$ and, maybe, along a line "at infinity". We prove that $b_1(\bar X_n)$ is even if $\bar H$ is an irreducible Hurwitz curve but, in contrast to the algebraic case, that it can take any non-negative value in the case when $\bar H$ consists of several irreducible components.Comment: 42 page

Models and phenomenology

It is evident that models of the knee should match the observational phenomenology. In this talk I discuss a few aspects of phenomenology, which are important not only for the understanding of the knee origin, but also for the general problem of the origin of cosmic rays. Among them are the shape of the energy spectrum, its irregularity, the sharpness of the knee and its fine structure. The classification of models is given and some examples of the most recent models are discussed. The most probable conclusion deduced from this examination is that the knee has an astrophysical origin and the so called 'source' models of the knee are most likely among them.Comment: 13 pages, 4 figures, overview talk at 19th European Cosmic Ray Symposium, Firenze, Italy, 30.08-4.09.2004 (to be published in the Int.J.Mod.Phys.A

Cosmic Rays from Gamma Ray Bursts in the Galaxy

The rate of terrestrial irradiation events by galactic gamma-ray bursts (GRBs) is estimated using recent standard-energy results. We assume that GRBs accelerate high-energy cosmic rays, and present results of three-dimensional simulations of cosmic rays moving in the Galactic magnetic field and diffusing through pitch-angle scattering. An on-axis GRB extinction event begins with a powerful prompt gamma-ray and neutron pulse, followed by a longer-lived phase from cosmic-ray protons and neutron-decay protons that diffuse towards Earth. Our results force a reinterpretation of reported ~ 10^{18} eV cosmic-ray anisotropies and offer a rigorous test of the model where high-energy cosmic rays originate from GRBs, which will soon be tested with the Auger Observatory.Comment: 9 pages, 4 figures, ApJ Letters, in press. Clarified limit of test-particle approximation, prediction that Auger will not confirm SUGAR source. (Data may not appear onscreen at low magnification.) Simulations at http://heseweb.nrl.navy.mil/gamma/~dermer/invest/sim/index.ht

The Sun in Time: Age, Rotation, and Magnetic Activity of the Sun and Solar-type Stars and Effects on Hosted Planets

Multi-wavelength studies of solar analogs (G0-5 V stars) with ages from ~50 Myr to 9 Gyr have been carried out as part of the "Sun in Time" program for nearly 20 yrs. From these studies it is inferred that the young (ZAMS) Sun was rotating more than 10x faster than today. As a consequence, young solar-type stars and the early Sun have vigorous magnetohydrodynamic (MHD) dynamos and correspondingly strong coronal X-ray and transition region / chromospheric FUV-UV emissions. To ensure continuity and homogeneity for this program, we use a restricted sample of G0-5 V stars with masses, radii, T(eff), and internal structure (i.e. outer convective zones) closely matching those of the Sun. From these analogs we have determined reliable rotation-age-activity relations and X-ray - UV (XUV) spectral irradiances for the Sun (or any solar-type star) over time. These XUV irradiance measures serve as input data for investigating the photo-ionization and photo-chemical effects of the young, active Sun on the paleo-planetary atmospheres and environments of solar system planets. These measures are also important to study the effects of these high energy emissions on the numerous exoplanets hosted by solar-type stars of different ages. Recently we have extended the study to include lower mass, main-sequence (dwarf) dK and dM stars to determine relationships among their rotation spin-down rates and coronal and chromospheric emissions as a function of mass and age. From rotation-age-activity relations we can determine reliable ages for main-sequence G, K, M field stars and, subsequently, their hosted planets. Also inferred are the present and the past XUV irradiance and plasma flux exposures that these planets have endured and the suitability of the hosted planets to develop and sustain life.Comment: 12 pages, 6 figures; to appear in the proceedings of IAU 258: The Ages of Star

Lateral distribution on charged particles in EAS

Lateral distribution of charged particles which allow for the finiteness of energy gamma-quanta, the inhomogeneity of the atmosphere and the experimental selection of EAS are needed to interpret experimental data. The effects of finiteness of energy of gamma-quanta which produce the partial electron-photon cascades were considered by substituting K R sub m instead of R sub m in NKG approximation where K was found to be 0.56 from comparison with the experimental data. New results on the lateral distribution of electrons in the partial cascades from gamma-quanta were obtained. It is shown that the coefficient K can be regarded as a constant. The last approximation of K was found to be most adequate when compared with the experimental data. The inhomogeneity of the atmosphere, muons and experimental selection are considered. The calculation of Ne are extended from 100,000 to 10 million for sea level and for Akeno level