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PTOLEMY COORDINATES, DEHN INVARIANT AND THE A-POLYNOMIAL
A-POLYNOMIAL DEHN INVARIANT
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2015/12/17
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 ...
SMALL POLYNOMIAL MATRIX PRESENTATIONS OF NONNEGATIVE MATRICES
SMALL POLYNOMIAL MATRIX NONNEGATIVE MATRICES
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2015/9/29
We investigate the use of polynomial matrices to give efficient presentations of nonnegative matrices exhibiting prescribed spectral and algebraic behavior.
On the Polynomial Cohomology of Affine Manifolds
Affine Manifolds Polynomial Cohomology
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2015/9/29
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 ...
POLYNOMIAL RECURRENCES AND CYCLIC RESULTANTS
POLYNOMIAL RECURRENCES CYCLIC RESULTANTS
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2015/8/14
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...
A polynomial-time algorithm for determining quadratic Lyapunov functions for nonlinear systems
Nonlinear systems quadratic lyapunov function and convex programming function
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2015/8/12
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...
Polynomial level-set methods for nonlinear dynamical systems analysis
dynamical systems analysis level-set methods
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2015/6/19
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...
Decentralized Stochastic Decision Problems and Polynomial Optimization
Decision Problems Polynomial Optimization
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2015/6/19
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 ...
A Polynomial Eigenproblem Approach for General Joint Block Diagonalization
general joint block diagonalization polynomial eigenproblem
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2014/9/26
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...
AVERAGES ALONG POLYNOMIAL SEQUENCES IN DISCRETE NILPOTENT GROUPS: SINGULAR RADON TRANSFORMS
AVERAGES ALONG POLYNOMIAL SEQUENCES DISCRETE NILPOTENT GROUPS SINGULAR RADON TRANSFORMS
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2014/4/3
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...
Polynomial-time Isomorphism Test for Groups with Abelian Sylow Towers
polynomial-time algorithm, group isomorphism, solvable group
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2012/12/3
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...
On the Distribution of Critical Points of a Polynomial
Critical Points Polynomial Probability
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2012/7/11
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...
A nilpotent IP polynomial multiple recurrence theorem
ergodic Ramsey theory IP-sets nilpotent Hales-Jewett theorem nilpotent Szemeredi theorem
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2012/6/14
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...
On the algebraic K-theory of truncated polynomial algebras in several variables
algebraic K-theory truncated polynomial algebras several variables Algebraic Topology
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2012/6/14
We consider the algebraic K-theory of a truncated polynomial algebra in several commuting variables, K(k[x_1, ..., x_n]/(x_1^a_1, ..., x_n^a_n)). This naturally leads to a new generalization of the bi...
A quasi-tree expansion of the Krushkal polynomial
quasi-tree expansion Krushkal polynomial Combinatorics
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2012/5/24
We introduce a generalization of the Krushkal polynomial to nonorientable surfaces, and prove that this polynomial has a natural quasi-tree expansion. This generalized Krushkal polynomial contains the...
Symmetries of Julia sets of polynomial skew products on C^2
Complex dynamics skew product Green function
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2012/4/18
We consider the symmetries of Julia sets of polynomial skew products on C^2, which are birationally conjugate to rotational products. Our main results give the classification of the polynomial skew pr...