We present a symbolic algorithm to solve for the zeros of a polynomial vector eld equivariant with respect to a nite subgroup of O(n). We prove that the module of equivariant polynomial maps for a nite matrix group is Cohen-Macaulay and give an algorithm to compute a fundamental basis. Equivariant normal forms are easily computed from this basis. We use this basis to transform the problem of nd...

The notions of input and output decoupling zeros are extended to a linear periodic discretetime system. The ordered sets of structural indices are also analyzed for these notions and for the notions of invariant zero, transmission zero, eigenvalue and pole of such a system. For any non-zero zero, eigenvalue and pole, the corresponding ordered set of structural indices is timeinvariant. The inpu...

We propose a new algorithm for the classical and still practically important problem of approximating the zeros z j of an n-th degree polynomial p(x) within the error bound 2 ?b max j jz j j. The algorithm uses O((n 2 log n) log(bn)) arithmetic operations and comparisons for approximating all the n zeros and O((kn log n) log(bn)) for approximating the k zeros lying in a xed domain (disc or squa...

Let D denote the open unit disk and let f(z) = P∞ n=0 anz n be analytic on D with positive monotone decreasing coefficients an. We answer several questions posed by J. Cima on the location of the zeros of polynomial approximants which he originally posed about outer functions. In particular, we show that the zeros of Cesàro approximants to f are well-behaved in the following sense: (1) if an an...

This correspondence introduces a new class of infinite impulse response (IIR) digital filters that unifies the classical digital Butterworth filter and the well-known maximally flat FIR filter. New closedform expressions are provided, and a straightforward design technique is described. The new IIR digital filters have more zeros than poles (away from the origin), and their (monotonic) square m...

This paper presents a formula-based method for the design of IIR filters having more zeros than (nontrivial) poles. The filters are designed so that their square magnitude frequency responses are maximally-flat at ! = 0 and at ! = and are thereby generalizations of classical digital Butterworth filters. A main result of the paper is that, for a specified half-magnitude frequency and a specified...

We give a new short proof of a theorem relating solutions of a system of polynomial equations to the eigenvalues of the multiplication operators on the quotient ring, in the case when the quotient ring is finite-dimensional. Everyone is familiar with the representation of a curve in the plane using an algebraic equation such as X + Y 2 = 1. Algebraic geometers have learned that it is more conve...

We have discussed predictions of Ue3 and JCP in the framework of the neutrino mass matrix with two zeros. The lower bound of Ue3 is 0.05, which depends on tan θ12 and tan θ23. We have investigated the stability of these predictions taking account of small corrections to zeros, which may come from radiative corrections or off-diagonal elements of the charged lepton mass matrix. We have found tha...

We prove several results about zeros of paraorthogonal polynomials using the theory of rank one perturbations of unitary operators. In particular, we obtain new details on the interlacing of zeros for successive POPUC. © 2006 Elsevier Inc. All rights reserved.

Isolated multiple zeros or clusters of zeros of analytic maps with several variables are known to be difficult to locate and approximate. This article is in the vein of the α-theory, initiated by M. Shub and S. Smale in the beginning of the eighties. This theory restricts to simple zeros, i.e., where the map has corank zero. In this article we deal with situations where the analytic map has cor...