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Radially symmetric and azimuthally modulated vortex solitons supported by localized gain
Radially symmetric azimuthally modulated vortex solitons localized gain
2010/12/28
We discover that a spatially localized gain supports stable vortex solitons in media with cu-bic nonlinearity and two-photon absorption. The interplay between nonlinear losses and gain in amplifying r...
Sums of Laplace eigenvalues - rotationally symmetric maximizers in the plane
Isoperimetric membrane tight frame
2010/12/14
The sum of the first n 1 eigenvalues of the Laplacian is shown to be maximal among triangles for the equilateral triangle,maximal among parallelograms for the square, and maximal among ellipses for ...
Double flag varieties for a symmetric pair and finiteness of orbits
Double flag varieties symmetric pair finiteness of orbits
2010/12/14
Let G be a reductive algebraic group over the complex number filed, and K = G be the fixed points of an involutive automorphism of G so that (G,K) is a symmetric pair.