Let T be an infinite locally finite tree. We say that T has exactly one end, if in T any two one-way infinite paths have a common rest (infinite subpath). The paper describes the structure of such trees and tries to formalize it by algebraic means, namely by means of acyclic monounary algebras or tree semilattices. In these algebraic structures the homomorpisms and direct products are considere...

Infinite words over a finite special confluent rewriting system R are considered and endowed with natural algebraic and topological structures. Their geometric significance is explored in the context of Gromov hyperbolic spaces. Given an endomorphism φ of the monoid generated by R, existence and uniqueness of several types of extensions of φ to infinite words (endomorphism extensions, weak endo...

The paper is consisted of two parts. In the first part, we are presenting the smooth and impulsive solution space B of the system of algebraic and differential equations A (ρ)β (t) = 0, ρ := dt where A (ρ) ∈ R [ρ] (with detA (ρ) 6= 0) is given. The solution space is given in terms of the finite and infinite Jordan pairs of the polynomial matrix A (ρ), and therefore a necessary introduction is g...

In this paper, we propose Hermite collocation method for solving Thomas-Fermi equation that is nonlinear ordinary differential equation on semi-infinite interval. This method reduces the solution of this problem to the solution of a system of algebraic equations. We also present the comparison of this work with solution of other methods that shows the present solution is more accurate and faste...

In this phase of the attempt to advance finite dimensional algebraic function approximation technique in eigenvalue problems of lossless metallic guides filled with anisotropic and/or inhomogeneous media, to exact analysis in infinite dimensions, it is seen that the problem in infinite dimensions, can be reduced to finite dimensions, by virtue of a result in perturbation theory. Furthermore, it...

Bent functions as optimal combinatorial objects are difficult to characterize and construct. In the literature, bent idempotents are a special class of bent functions and few constructions have been presented, which are restricted by the degree of finite fields and have algebraic degree no more than 4. In this paper, several new infinite families of bent functions are obtained by adding the the...