In this paper, we present a hardware realization of a simplified Krawtchouk transform. The transform is realized on a Xilinx Field-programmable gate arrays chip. The hardware is stand-alone and… (More)

Fock spaces over zeons are introduced. Trace identities and a noncommutative “integration-by-parts” formula are developed. As an application, we find a new criterion, without involving powers of the… (More)

An alternative to Lagrange inversion for solving analytic systems is our technique of dual vector fields. We implement this approach using matrix multiplication that provides a fast algorithm for… (More)

A proof of the Generalized Road Coloring Problem, independent of the recent work by Beal and Perrin, is presented, using both semigroup methods and Trakhtman’s algorithm. Algebraic properties of… (More)

We investigate the structure of the Schrödinger algebra and its representations in a Fock space realized in terms of canonical Appell systems. Generalized coherent states are used in the construction… (More)

A vertex|matching-partition (V |M) of a simple graph G is a spanning collection of vertices and independent edges of G. Let vertex v ∈ V have weight wv and edge e ∈ M have weight we. Then the weight… (More)

We examine the Schrödinger algebra in the framework of Berezin quantization. First, the Heisenberg-Weyl and sl(2) algebras are studied. Then the Berezin representation of the Schrödinger algebra is… (More)

Consider a semigroup generated by matrices associated with an edge-coloring of a strongly connected, aperiodic digraph. We call the semigroup Lie-solvable if the Lie algebra generated by its elements… (More)

Let G be a strongly connected, aperiodic, two-out digraph with adjacency matrix A. Suppose A = R + B are coloring matrices: that is, matrices that represent the functions induced by an edge-coloring… (More)