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We define Ptolemy coordinates for representations that are not necessarily boundary-unipotent. This gives rise to a new algorithm for computing the SL(2; C) Apolynomial, and more generally the ...
We investigate the use of polynomial matrices to give efficient presentations of nonnegative matrices exhibiting prescribed spectral and algebraic behavior.
It is well known that the real cohomology of a compact Riemannian manifold M is isomorphic to the algebra of its harmonic forms. When M is a fiat Riemannian manifold, i.e. a Euclidean manifold, a ...
Let K be an algebraically closed field of characteristic zero and let f ∈ K[x]. The m-th cyclic resultant of f is rm = Res(f, xm − 1). A generic monic polynomial is determined by its full sequen...
We consider nonlinear systems dx/dt=f(x(t)) where Df(x(t)) is known to lie in the convex hull of L n times n matrices A_1,ldots,A_L. For such systems, quadratic Lyapunov functions can be determined us...
In this paper, we present a method for computing the domain of attraction for non-linear dynamical systems. We propose a level-set method where sets are represented as sublevel sets of polynomials. Th...
In this paper we consider the problem of computing decentralized control policies in a discrete stochastic decision problem. For the problem we consider, computation of optimal decentralized policies ...
In this paper we consider the problem of determining optimal decentralized decision rules in discrete stochastic decision problems. Here we consider a static single-stage problem. It has been shown in...
In this paper we consider the problem of how to computationally test whether a matrix inequality is positive semidefinite on a semialgebraic set. We propose a family of sufficient conditions using the...
We present a methodology for analyzing robust independent-of-delay and delay-dependent stability of equilibria of systems described by nonlinear Delay Differential Equations by algorithmically constru...
oint Block Diagonalization (JBD) of a given Hermitian matrix set A=fAi g p i=0 is to nd a nonsingular matrixWsuch that W H AiWfor i = 0;1;:::;pare all block diagonal matrices with the same pr...
We consider a class of operators defined by taking averages along polynomial sequences in discrete nilpotent groups. As in the continuous case, one can consider discrete maximal Radon transforms...
We consider the problem of testing isomorphism of groups of order n given by Cayley tables. The trivial nlog n bound on the time complexity for the general case has not been improved over the past fou...
This paper proves that if points $Z_1,Z_2,...$ are chosen independently and identically using some measure $\mu$ from the unit circle in the complex plane, with $p_n(z) = (z-Z_1)(z-Z_2)...(z-Z_n)$, th...
We generalize the IP-polynomial Szemer\'edi theorem due to Bergelson and McCutcheon and the nilpotent Szemer\'edi theorem due to Leibman. Important tools in our proof include a generalization of Leibm...

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