Two questions in diophantine approximation

The first question is about a possible variation on Dirichlet's approximation theorem for linear forms x+y+z, wherex,y are restricted topositive integers. The second question, which turns out to be related to the first, is about approximation to elements in a power series fieldk((t ^–1)) by solutions of first order linear differential equationsx+y+z=0, wherex,y,z are polynomials int. Dedicated to Prof. Dr. E. Hlawka on the occasion of his 60th birthday     

Bending insensitivity of fiber Bragg gratings in suspended-core optical fibers

This Letter presents simulation and experimental results that explore bending insensitivity of fiber Bragg gratings in suspended-core optical fibers. The implementation of thin silica bridge in the fibers enhances index contrast of the fiber core and reduces bending-induced strain transfer to the fiber core. This fiber design lead to a reduction of over 7 times in strain-induced fiber Bragg grating resonant peak shifts in the suspended-core fiber compared with that in standard telecommunication fiber, and an 0.14 dB bending loss at a bending radius of 6.35 mm.