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Tropical varieties with polynomial weights and corner loci of piecewise polynomials
Tropical varieties polynomial weights corner loci of piecewise polynomials
2011/2/28
Counting Euler characteristics of the discriminant of the quadratic equation in terms of
Newton polytopes in two different ways, G. Gusev ([Gus]) found an unexpected relation for
mixed volumes of tw...
Modular absolute decomposition of equidimensional polynomial ideals
Modular absolute decomposition equidimensional polynomial ideals
2011/2/25
In this paper, we present a modular strategy which describes key properties of the absolute
primary decomposition of an equidimensional polynomial ideal defined by polynomials with rational coefficie...
Non-linear Group Actions with Polynomial Invariant Rings and a Structure Theorem for Modular Galois Extensions
Non-linear Group Polynomial Invariant Rings
2010/11/24
Let $G$ be a finite $p$-group and $k$ a field of characteristic $p>0$. We show that $G$ has a \emph{non-linear} faithful action on a polynomial ring $U$ of dimension $n=\mathrm{log}_p(|G|)$ such that...
Limit cycle's uniqueness for second order O.D.E.'s polynomial in $\dot x$
Limit cycle's uniqueness O.D.E.'s polynomial
2010/11/12
We prove a uniqueness result for limit cycles of the second order ODE $\ddot x + \sum_{j=1}^{J}f_{j}(x)\dot x^{j} + g(x) = 0$. We extend a uniqueness result proved in \cite{CRV}. The main tool applied...
Euler characteristic of the bifurcation set for a polynomial of degree 2 or 3
Euler characteristic the bifurcation set polynomial
2010/11/11
Assume that the coefficients of a polynomial in a complex variable are Laurent polynomials in some complex parameters. The parameter space (a complex torus) splits into strata corresponding to differ...
This work gives the construction of an "activity matrix" whose determinant gives Tutte's activity words associated with spanning trees of the signed Tait graph coming from a pretzel knot diagram. Eva...
Vertex subsets with minimal width and dual width in $Q$-polynomial distance-regular graphs
Vertex subsets $Q$-polynomial distance-regular graphs
2010/11/15
We study $Q$-polynomial distance-regular graphs from the point of view of what we call descendents, that is to say, those vertex subsets with the property that the width $w$ and dual width $w^*$ sati...
Roots of any Polynomial with Complex Integer Coefficients using Replacement Sequences, Ruler and Compass
Roots Polynomial Complex Integer Coefficients Replacement Sequences
2010/11/1
The roots of any polynomial of degree m with complex integer coefficients can be computed by manipulation of sequences made from distinct symbols and counting the different symbols in the sequences. T...