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 the results of the mitochondrial DNA (mtDNA) sequence polymorphisms analyses to assess the genetic diversity and possible maternal origin of Bangladeshi indigenous chickens. A 648-bp fragment of mtDNA control region (D-loop) was analyzed in 96 samples from four different chicken population...
We perform plasmon-enhanced femtosecond laser ablation of silicon using gold nanorods to produce sub-diffraction limit features. While the observed hole shape seems inconsistent with calculated field distribution, we show that using a carrier diffusion-based model, both shape and depth of the nanoho...
We investigate the physical conditions that can
Theoretically explain the growth from interstellar dust to millimeter-sized
Grains in disks around brown dwarf. We modeled the evolution of dust particles
Under conditions of low-mass disks around brown dwarfs. We used coagulation,
Fragmentation and di...
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