Cross section design of holey optical fibers with coating based on stress analysis in tension

In this paper, the mechanical behavior of newly developed holey optical fibers with and without coating was investigated by numerical analysis. Based on experimental work, the tensile failure characteristics were observed. The stress characteristics of some typical holey fibers with different section design were studied though the finite element method under tensile load. The optimum design of air hole arrangements and sizes were proposed according to the numerical results. The influence of the coating thickness on the axial stress of holey optical fiber was also investigated. The numerical results and conclusions will be useful for the cross section optimum design of holey optical fiber for increase its strength

Quasi-Whittaker modules for the Schr\"odinger algebra

In this paper, we construct a new class of modules for the Schr\"{o}dinger algebra \mS, called quasi-Whittaker module. Different from \cite{[ZC]}, the quasi-Whittaker module is not induced by the Borel subalgebra of the Schr\"{o}dinger algebra related with the triangular decomposition, but its Heisenberg subalgebra \mH. We prove that, for a simple \mS-module $V$, $V$ is a quasi-Whittaker module if and only if $V$ is a locally finite \mH-module; Furthermore, we classify the simple quasi-Whittaker modules by the elements with the action similar to the center elements in U(\mS) and their quasi-Whittaker vectors. Finally, we characterize arbitrary quasi-Whittaker modules.Comment: 17 page