We consider the sub-Riemannian length optimization problem on the group of
motions of hyperbolic plane i.e. the special hyperbolic group SH(2). The system
comprises of left invariant vector fields with 2 dimensional linear control
input and energy cost functional. We prove the global controllability of
control distribution and use Pontryagin Maximum Principle to obtain the
extremal control input and sub-Riemannian geodesics. The abnormal and normal
extremal trajectories of the system are analyzed qualitatively and investigated
for strict abnormality. A change of coordinates transforms the vertical
subssystem of the normal Hamiltonian system into mathematical pendulum. In
suitable elliptic coordinates the vertical and horizontal subsystems are
integrated such that the resulting extremal trajectories are parametrized by
Jacobi elliptic functions.
We present results of simulations on the influence of photon propagation and
The Cherenkov effect on the time resolution of LSO:Ce scintillators. The
Influence of the scintillator length on the coincidence time resolution is
Shown. Furthermore, the impact of the depth of interaction on the time
Our study shows that for most community-dwelling adolescents, depressive symptoms decrease over time. A possible interaction effect of time and SERT genotype will require confirmation in larger studies....
We study a subset of the movie collaboration network, imdb.com, where only
Adult movies are included. We show that there are many benefits in using such a
Network, which can serve as a prototype for studying social interactions. We
Find that the strength of links, i.e., how many times two actors hav...
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