We study the geometry of Gorenstein curve singularities genus two, and their stable limits. These come in two families, corresponding to either Weierstrass or conjugate points on a semistable tail. For every $1\leq m <n$, stability condition - using one markings as reference point, therefore not $\mathfrak S_n$-symmetric defines proper Deligne-Mumford stacks $\overline{\mathcal M}_{2,n}^{(m)}$ ...

We started our research with the intent on answering the following question: can we find a way to calculate all the subgroups of the symmetric group. This is easier said that done, as the number of subgroups for a symmetric group grows quickly with each successive symmetric group. This problem can actually be simplified to finding the subgroup conjugacy classes. So now we have the slightly diff...

—Conjugate symmetry is an entirely new approach to symmetric Boolean functions that can be used to extend existing methods for handling symmetric functions to a much wider class of functions. These are functions that currently appear to have no symmetries of any kind. Such symmetries occur widely in practice. In fact, we show that even the simplest circuits exhibit conjugate symmetry. To demons...

Consider y" (t) + A (t)y (t) + 0, y is a real n-dimensinal vector and A(t) is a real nxn matrix, continuous on some interval. Some positivity properties of solutions and conjugate points of y"(t) + A(t)y (t) = 0 appeared in literature. We prove similar results for focal points