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 report an extremely sensitive and highly selective nanoporous gold/aptamer based surface enhanced resonance Raman scattering (SERRS) sensor. The optical sensor has an unprecedented detection sensitivity of 1 pM (0.2 ppt) for Hg2+ ions, the most sensitive Hg2+ optical sensor known so far. The sens...
We have used a 3D structure-from-motion (SFM) integrative task to characterize the neuronal underpinnings of 3D perception in WS and to probe whether gamma oscillatory patterns reflect changed holistic perception. Coherent faces were parametrically modulated in 3D depth (three different depth levels...
We investigate the relation between the bulk null
Energy condition (NEC) of the stress-energy tensor with the strong
Sub-additivity (SSA) property of entanglement entropy in the boundary theory.
In a background that interpolates between an AdS to an
AdS-Reissner-Nordstrom-type geometry, we find that...
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