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Abstract: We study the word length entropy of automorphisms of residually nilpotent groups, and how the entropy of such group automorphisms relates to the entropy of induced automorphisms on various n...
Abstract: Suppose that $n$ statistical units are observed, each following the model $Y(x_j)=m(x_j)+ \epsilon(x_j),\, j=1,...,N,$ where $m$ is a regression function, $0 \leq x_1 <...
A new approach for solving the Bethe ansatz (Gaudin-Richardson) equations of the standard pairing problem is established based on the Heine-Stieltjes correspondence.
Abstract: We consider a sign--determined Reidemeister torsion with multivariables for three manifolds with boundary. This invariant is often called the twisted Alexander polynomial when we consider li...
Abstract: The paper builds upon a recent approach to find the approximate bounds of a real function using Polynomial Chaos expansions. Given a function of random variables with compact support probabi...
Abstract: In this paper, we consider a control synthesis problem for a class of polynomial dynamical systems subject to bounded disturbances and with input constraints. More precisely, we aim at synth...
Squares in Polynomial Product Sequences     Squarefull numbers  Polynomial Product Sequences  Number Theory       font style='font-size:12px;'> 2011/8/31
Abstract: Let F(n) be a polynomial of degree at least 2 with integer coefficients. We consider the products N_x=\prod_{1 \le n \le x} F(n) and show that N_x should only rarely be a perfect power. In p...
Abstract: We provide polynomial upper bounds on the size of a shortest solution for quadratic equations in a free group. A similar bound is given for parametric solutions in the description of solutio...
Abstract: We construct a state model for the two-variable Kauffman polynomial using planar trivalent graphs. We also use this model to obtain a polynomial invariant for trivalent graphs embedded in th...
Abstract: We consider the problem of classifying the dynamics of complex polynomials $f: \mathbb{C} \to \mathbb{C}$ restricted to their basins of infinity. We synthesize existing combinatorial tools -...
Abstract: We study classes $P_{g,T}(\alpha;\beta)$ on the moduli space of stable, genus g curves with rational tails defined by pushing forward the virtual fundamental classes of spaces of relative st...
Abstract: In this paper we calculate the Ehrhart's polynomial associated with a 2-dimensional regular polytope (i.e. equilateral triangles) in $\mathbb Z^3$. The polynomial takes a relatively simple f...
On the degree-chromatic polynomial of a tree     Chromatic polynomial  graph coloring  tree       font style='font-size:12px;'> 2011/8/22
Abstract: The degree chromatic polynomial $Pm(G,k)$ of a graph $G$ counts the number of $k$-colorings in which no vertex has $m$ adjacent vertices of its same color. We prove Humpert and Martin's conj...
Abstract: A new approach for solving the Bethe ansatz (Gaudin-Richardson) equations of the standard pairing problem is established based on the Heine-Stieltjes correspondence. For $k$ pairs of valence...
Abstract: We study Heun's differential equation in the case that one of the singularities is apparent. In particular we conjecture a relationship with generalized hypergeometric differential equation ...

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