It is shown that projectivized irreducible components of nilpotent cones of complex symmetric spaces are projective self-dual algebraic varieties. Other properties equivalent to their projective self-duality are found. 1. Let g be a semisimple complex Lie algebra, let G be the adjoint group of g, and let θ ∈ Aut g be an element of order 2. We set k := {x ∈ g | θ(x) = x}, p := {x ∈ g | θ(x) = −x...

The chemical evolution of the Milky Way is investigated using a dual-phase metal-enriched infall model in which primordial gas fuels the earliest epoch of star formation, followed by the ongoing formation of stars from newly accreted gas. The latest metallicity distribution of local K-dwarfs is reproduced by this model, which allows the Galactic thin disk to form from slightly metal-enriched ga...

let $g$ be a finite group and $pi_{e}(g)$ be the set of element orders of $g $. let $k in pi_{e}(g)$ and $s_{k}$ be the number of elements of order $k $ in $g$. set nse($g$):=${ s_{k} | k in pi_{e}(g)}$. in this paper, it is proved if $|g|=|$ pgl$_{2}(q)|$, where $q$ is odd prime power and nse$(g)= $nse$($pgl$_{2}(q))$, then $g cong $pgl$_

Introduction In a series of earlier papers, ([ST1-4]) we began a systematic study of locally analytic representations of a locally L-analytic group G, where L ⊆ C p is a finite extension of Q p. Such a representation is given by a continuous action of G on a locally convex topological vector space V over a spherically complete extension field K ⊆ C p of L, such that the orbit maps g → gv are lo...

Let K be a complete field with a discrete valuation v, ring of integers OK , and maximal ideal (πK). Let k := OK/(πK) be the residue field, assumed to be separably closed of characteristic p ≥ 0. Let A/K be any abelian variety of dimension g. Let A/OK denote its Néron model, with special fiber Ak/k and group of components ΦA,K . Let A′/K denote the dual abelian variety, with Néron model A/OK an...

In the last lecture a primal-dual analysis was used to show a 2-approximation for theVertex Cover problem. Here we extend these ideas to show a 2-approximation for the Steiner Forest problem using a primal-dual analysis. In the Steiner Forest problem there is a graph G = (V,E) where each edge e ∈ E has a cost ce ∈ R. We are given k pairs of terminals s1, t1, s2, t2, . . . sk, tk ∈ V . The goal ...

314 4. Smith, H. J., Nichol, K. A., Hoban, D. J. et al. (2002). Dual activity of fluoroquinolones against Streptococcus pneumoniae: the facts behind the claims. Journal of Antimicrobial Chemotherapy 49, 893–5. 5. Heaton, V. J., Ambler, J. E. & Fisher, L. M. (2000). Potent antipneumococcal activity of gemifloxacin is associated with dual targeting of gyrase and topoisomerase IV, and in vivo targ...