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The Gosper island is a well-known fractal belonging to a family of self-similar “root 7” curves constructed from a simple iterative algorithm [1]. One begins with a regular hexagon (the initiator, corresponding to iteration n = 0) with sides of reference length l0, and then breaks each of these straight-edge elements into three equal segments of length ln = l0 (1/71/2)n where n = 1, 2,3,… (the generator...
We present the first detailed account of kaleidoscope laser modes where the equivalent Fresnel number Neq and magnification M may assume arbitrary values. Properties of these linear fractal eigenmodes are explored through extensive numerical computations. Considerations are extended to demonstration and analyses of new contexts for spontaneous nonlinear optical fractals.
For a simply supported beam with a quadratic-like index containning the first order partial differential operator, the algebraic operator Riccati equation is derived and the exact solution of which is obtained for a class of operators. The result is applied to the bean vibration feedback control problems.
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