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.
Pregnancy-induced rhinitis (PIR) is often misclassified and under-diagnosed. There is currently no cure or opti- mum symptomatic treatment.
To summarize current knowledge of PIR and assess evidence supporting treatment options.
Structured literature se...
The purpose of this paper is to discuss a recently described modification of a standard photo slit lamp system for ocular transillumination, with special emphasis on the light transmission through the eye wall and the photographic technique. Transillumination photography was carried...
We conducted a systematic review and meta-analysis of published case-control studies. We identified 36 studies which reported on polymorphic variation in 19 genes and CLL risk. Out of the 23 polymorphic variants, significant associations (P <0.05) were seen in pooled analyses for only four variants:...
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