Stable polynomial

About: Stable polynomial is a research topic. Over the lifetime, 2466 publications have been published within this topic receiving 39429 citations.

Hypergeometric Orthogonal Polynomials and Their q-Analogues

Abstract: Definitions and Miscellaneous Formulas- Classical orthogonal polynomials- Orthogonal Polynomial Solutions of Differential Equations- Orthogonal Polynomial Solutions of Real Difference Equations- Orthogonal Polynomial Solutions of Complex Difference Equations- Orthogonal Polynomial Solutions in x(x+u) of Real Difference Equations- Orthogonal Polynomial Solutions in z(z+u) of Complex Difference Equations- Hypergeometric Orthogonal Polynomials- Polynomial Solutions of Eigenvalue Problems- Classical q-orthogonal polynomials- Orthogonal Polynomial Solutions of q-Difference Equations- Orthogonal Polynomial Solutions in q?x of q-Difference Equations- Orthogonal Polynomial Solutions in q?x+uqx of Real

Solving systems of polynomial equations

Abstract: Polynomials in one variable Grobner bases of zero-dimensional ideals Bernstein's theorem and fewnomials Resultants Primary decomposition Polynomial systems in economics Sums of squares Polynomial systems in statistics Tropical algebraic geometry Linear partial differential equations with constant coefficients Bibliography Index.

On the Structure of Polynomial Time Reducibility

Abstract: Two notions of polynomml time reduclbihty, denoted here by ~ T e and <.~P, were defined by Cook and Karp, respectively The abstract propertms of these two relatmns on the domain of computable sets are investigated. Both relations prove to be dense and to have minimal pairs. Further , there is a strictly ascending sequence with a minimal pair of upper bounds to the sequence. Our method of showing density ymlds the result that if P ~ NP then there are members of NP -P that are not polynomml complete

On the convergence of generalized polynomial chaos expansions

Abstract: A number of approaches for discretizing partial differential equations with random data are based on generalized polynomial chaos expansions of random variables. These constitute generalizations of the polynomial chaos expansions introduced by Norbert Wiener to expansions in polynomials orthogonal with respect to non-Gaussian probability measures. We present conditions on such measures which imply mean-square convergence of generalized polynomial chaos expansions to the correct limit and complement these with illustrative examples.

Polynomial identities and asymptotic methods

Abstract: Polynomial identities and PI-algebras $S_n$-representations Group gradings and group actions Codimension and colength growth Matrix invariants and central polynomials The PI-exponent of an algebra Polynomial growth and low PI-exponent Classifying minimal varieties Computing the exponent of a polynomial $G$-identities and $G\wr S_n$-action Superalgebras, *-algebras and codimension growth Lie algebras and nonassociative algebras The generalized-six-square theorem Bibliography Index.