Euclidean remainders for generalized polynomials

Generalized numerical ranges of matrix polynomials

In this paper, we introduce the notions of C-numerical range and C-spectrum of matrix polynomials. Some algebraic and geometrical properties are investigated. We also study the relationship between the C-numerical range of a matrix polynomial and the joint C-numerical range of its coefficients.

Nonhomogeneity of Remainders, Ii

We present an example of a separable metrizable topological group G having the property that no remainder of it is (topologically) homogeneous. 1. Introduction. All topological spaces under discussion are Tychonoff. A space X is homogeneous if for any two points x, y ∈ X there is a homeomorphism h from X onto itself such that h(x) = y. If bX is a com-pactification of a space X, then bX \ X is c...

Evolving Generalized Euclidean Distances for Training RBNN

In Radial Basis Neural Networks (RBNN), the activation of each neuron depends on the Euclidean distance between a pattern and the neuron center. Such a symmetrical activation assumes that all attributes are equally relevant, which might not be true. Non-symmetrical distances like Mahalanobis can be used. However, this distance is computed directly from the data covariance matrix and therefore t...

An Integral Formula for Generalized Gegenbauer Polynomials and Jacobi Polynomials

Polynomials Related to Generalized Chebyshev Polynomials

We study several classes of polynomials, which are related to the Chebyshev, Morgan-Voyce, Horadam and Jacobsthal polynomials. Thus, we unify some of well-known results.