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Let (N, G), where N is a normal subgroup of G<SL_n(C), be a pair of finite groups and V a finite-dimensional fundamental G-module. We study the G-invariants in the symmetric algebra S(V) by giving explicit formulas of the Poincar\'{e}…
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Let $D_n$ be the dihedral group with $2n$ elements, and suppose $n$ is greater than one. We call ring system a finite $D_n$-symmetric set of points in $\mathbb{R}^2$. Ring systems have been used as models for planets surrounded by rings,…
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Lyapunov's indirect method is an attractive method for analyzing stability of non-linear systems since only the stability of the corresponding linearized system needs to be determined. Unfortunately, the proof for finite-dimensional systems…
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