Serving both as an introduction to the subject and as a reference, this book presents the
theory in elegant form and with modern concepts and notation. It covers the general theory …

This study proposes a detection method that incorporates the extension theory with
fractional-order chaotic self-synchronization of dynamic errors in order to analyze ball …

Multivariate orthogonal polynomials in D real dimensions are considered from the
perspective of the Cholesky factorization of a moment matrix. The approach allows for the …

The paper contains a generalization of known properties of Chebyshev polynomials of the
second kind in one variable to polynomials of n variables based on the root lattices of …

Lie groups with two different root lengths allow two 'mixed sign'homomorphisms on their
corresponding Weyl groups, which in turn give rise to two families of hybrid Weyl group orbit …

The paper develops applications of symmetric orbit functions, known from irreducible
representations of simple Lie groups, in numerical analysis. It is shown that these functions …

Ten types of discrete Fourier transforms of Weyl orbit functions are developed. Generalizing
one-dimensional cosine, sine, and exponential, each type of the Weyl orbit function …

Four types of discrete transforms of Weyl orbit functions on finite point sets are developed.
The point sets are formed by intersections of dual-root lattices with fundamental domains of …

Discrete transforms of Weyl orbit functions on finite fragments of shifted dual root lattices are
established. The congruence classes of the dual weight lattices intersected with the …

Tight-binding models of electron propagation in single-layer triangular graphene quantum
dots with armchair and zigzag edges are developed. The electron hoppings to the nearest …