14,250 research outputs found
On the speed of convergence to the asymptotic cone for non-singular nilpotent groups
We study the speed of convergence to the asymptotic cone for Cayley graphs of
nilpotent groups. Burago showed that converges to and
its speed is in the sense of Gromov-Hausdorff distance. Later
Breuillard and Le Donne gave estimates for non-abelian cases, and constructed
an example whose speed of convergence is slower than .
For -step nilpotent groups, we show that if the Mal'cev completion is
non-singular, then the speed of convergence is for any choice
of generating set. In terms of subFinsler geometry, this condition is also
equivalent to the absence of abnormal geodesics on the asymptotic cone.Comment: 18pages,11 figure
Electron impact excitations of S2 molecules
Low-energy electron impact excitations of S_2 molecules are studied using the
fixed-bond R-matrix method based on state-averaged complete active space SCF
orbitals. Integral cross sections are calculated for elastic electron collision
as well as impact excitation of the 7 lowest excited electronic states. Also,
differential cross sections are obtained for elastic collision and excitation
of the a^1 Delta_g, b^1 Sigma_g^+ and B^3 Sigma_u^- states. The integrated
cross section of optically allowed excitation of the B^3 Sigma_u^- state agrees
reasonably well with the available theoretical result.Comment: 12 pages, 3 figures. Chemical Physics Letters, in pres
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