It is well known that the zeros of a polynomial p are equal to the eigenvalues of the associated companion matrix A. In this paper we take a geometric view of the conditioning of these two problems and of the stability of algorithms for polynomial zerofinding. The -pseudozero setZ (p) is the set of zeros of all polynomials p̂ obtained by coefficientwise perturbations of p of size ≤ ; this is a s...

We present eecient and accurate algorithms to compute solutions of zero-dimensional multivariate polynomial equations in a given domain. The total number of solutions correspond to the Bezout bound for dense polynomial systems or the Bernstein bound for sparse systems. In most applications the actual number of solutions in the domain of interest is much lower than the Bezout or Bernstein bound....

In this paper, a simple technique is proposed for face recognition among many human faces. It is based on the polynomial coefficients, covariance matrix and algorithm on common eigenvalues. The main advantage of the proposed approach is that the identification of similarity between human faces is carried out without computing actual eigenvalues and eigenvectors. A symmetric matrix is calculated...

Cluster algebras are a recent topic of study and have been shown to be a useful tool to characterize structures in several knowledge fields. An important problem is to establish whether or not a given cluster algebra is of finite type. Using the standard definition, the problem is infeasible since it uses mutations that can lead to an infinite process. Barot, Geiss and Zelevinsky (2006) present...

SUMMARY Our RNA-As-Graph-Pools (RagPools) web server offers a theoretical companion tool for RNA in vitro selection and related problems. Specifically, it suggests how to construct RNA sequence/structure pools with user-specified properties and assists in analyzing resulting distributions. This utility follows our recently developed approach for engineering sequence pools that links RNA sequenc...

The correspondence principle is important in quantum theory on both the fundamental and practical levels: it is needed to connect theory to experiment, and for calculations in the technologically important domain lying between the atomic and classical regimes. Moreover, a correspondenceprinciple part of the S-matrix is normally separated out in quantum electrodynamics in order to obtain a remai...

When a function f(x) is holomorphic on an interval x ∈ [a, b], its roots on the interval can be computed by the following three-step procedure. First, approximate f(x) on [a, b] by a polynomial fN (x) using adaptive Chebyshev interpolation. Second, form the Chebyshev– Frobenius companion matrix whose elements are trivial functions of the Chebyshev coefficients of the interpolant fN (x). Third, ...

The phloem is a complex tissue composed of highly specialized cells with unique subcellular structures and a compact organization that is challenging to study in vivo at cellular resolution. We used confocal scanning laser microscopy and subcellular fluorescent markers in companion cells and sieve elements, for live imaging of the phloem in Arabidopsis leaves. This approach provided a simple fr...

This paper describes a learning companion system called Integration-Kid in the domain of learning indefinite integration. A learning companion system is an intelligent tutoring system of a new breed. Apart from the teacher, a learning companion models after an additional agent, called the learning companion. The learning companion acts as a companion for the human student in learning. Thus the ...

In mystical ethics, some virtues have a foundational role in relation to other virtues; that is, other virtues are in some ways dependent on, conditional to, or rooted in them. This is a gradational concept, and therefore one can speak of foundational and more foundational among foundational virtues in mysticism. Honesty is the most foundational virtue in mystical ethics, and other virtues are ...