Let G be a compact connected Lie group with trivial center. Using the action of G on its Lie algebra, we define an operator norm | |G which induces a bi-invariant metric dG(x, y) = |Ad(yx−1)|G on G. We prove the existence of a constant β ≈ .23 (independent of G) such that for any closed subgroup H ( G, the diameter of the quotient G/H (in the induced metric) is ≥ β.

Electrospinning was applied to nitrocellulose (NC) solutions  in DMF, DMSO  and  Ethyl  methyl  keton  to  obtain  NC  nanofibers. Electrospraying  process  was  observed  when  DMF  was  used  as solvent.  In  comparison  to NC/DMF, NC/DMSO  solution  resulted  in the  formation  of  a  coating  film  as  indicate  by  SEM.  Two  different electrospun  nanofibers,  smooth  nanofibers  wit...

This paper is devoted to the fast and exact diameter computation in graphs with n vertices and m edges, if the diameter is a large fraction of n. We give an optimal O(m+n) time algorithm for diameters above n/2. The problem changes its structure at diameter value n/2, as large cycles may be present. We propose a randomized O(m + n logn) time algorithm for diameters above (1/3 + )n for constant ...