This paper deals with symmetric and non-symmetric polynomial perturbations of symmetric quasi-de nite bilinear functionals. We establish a relation between the Hessenberg matrices associated with the initial and the perturbed functionals using LU and QR factorizations. Moreover we give an explicit algebraic relation between the sequences of orthogonal polynomials associated with both functionals.

An essential requirement for providing secure services in wireless sensor networks is the ability to establish pairwise keys among sensors. Due to resource constraints on the sensors, the key establishment scheme should not create significant overhead. To date, several key establishment schemes have been proposed. Some of these have appropriate connectivity and resistance against key exposure, ...

Recently, Stanley [21] has defined a symmetric function generalization of the chromatic polynomial of a graph. Independently, Chung and Graham [4] have defined a digraph polynomial called the cover polynomial which is closely related to the chromatic polynomial of a graph (in fact, as we shall see, the cover polynomial of a certain digraph associated to a poset P coincides with the chromatic po...

Let S(n, k) be the classical Stirling numbers of the second kind, d > 1 be an integer, and P,Q,R ∈ Q[X1, . . . , Xm] be nonconstant polynomials such that P does not divide Q and R is not a dth power. We prove that if k1, . . . , km are any sufficiently large distinct positive integers then, setting Si = S(n, ki), Q(S1,...,Sm) P (S1,...,Sm) ∈ Z for only finitely many n ∈ N and R(S1, . . . , Sm) ...

Let R and S be two irreducible root systems spanning the same vector space and having the same Weyl group W , such that S (but not necessarily R) is reduced. For each such pair (R, S) we construct a family of W -invariant orthogonal polynomials in several variables, whose coefficients are rational functions of parameters q, t1, t2, . . . , tr, where r (= 1, 2 or 3) is the number of W -orbits in...

The A-polynomial of a knot in S defines a complex plane curve associated to the set of representations of the fundamental group of the knot exterior into SL2C . Here, we show that a non-trivial knot in S 3 has a non-trivial A-polynomial. We deduce this from the gauge-theoretic work of Kronheimer and Mrowka on SU2 -representations of Dehn surgeries on knots in S . As a corollary, we show that if...

Abstract. In this paper we study the orthogonality conditions satisfied by Jacobi polynomials P (α,β) n when the parameters α and β are not necessarily > −1. We establish orthogonality on a generic closed contour on a Riemann surface. Depending on the parameters, this leads to either full orthogonality conditions on a single contour in the plane, or to multiple orthogonality conditions on a num...

The Kronecker product of two homogeneous symmetric polynomials P1 and P2 is defined by means of the Frobenius map by the formula P1 ⊗ P2 = F (F−1P1)(F−1P2). When P1 and P2 are Schur functions sλ and sμ respectively, then the resulting product sλ ⊗ sμ is the Frobenius characteristic of the tensor product of the irreducible representations of the symmetric group corresponding to the diagrams λ an...

In this paper we introduce three new classes of nonnegative forms (or equivalently, symmetric tensors) and their extensions. The newly identified nonnegative symmetric tensors constitute distinctive convex cones in the space of general symmetric tensors (order 6 or above). For the special case of quartic forms, they collapse into the set of convex quartic homogeneous polynomial functions. We di...

In this paper, we examine the FFT of sequences x„ = xN + „ with period N that satisfy certain symmetric relations. It is known that one can take advantage of these relations in order to reduce the computing time required by the FFT. For example, the time required for the FFT of a real sequence is about half that required for the FFT of a complex sequence. Also, the time required for the FFT of ...