Effect of Delta Operator on Umbral Composition in Finite Operator calculus

Towards psi-extension of Rota`s Finite Operator Calculus

ψ-extension of Gian-Carlo Rota's finite operator calculus due to Viskov [1, 2] is further developed. The extension relies on the notion of ∂ ψ-shift invariance and ∂ ψ-delta operators. Main statements of Rota's finite operator calculus are given their ψ-counterparts. This includes Sheffer ψ-polynomials properties and Rodrigues formula-among others. Such ψ-extended calculus delivers an elementar...

Pattern Avoiding Ballot Paths and Finite Operator Calculus

Counting pattern avoiding ballot paths begins with a careful analysis of the pattern. Not the length, but the characteristics of the pattern are responsible for the difficulties in finding explicit solutions. Certain features, like overlap and difference in number of → and ↑ steps determine the solution of the recursion formula. If the recursion can be solved by a polynomial sequence, we apply ...

Finite Operator Calculus With Applications to Linear Recursions

Entropy operator for continuous dynamical systems of finite topological entropy

In this paper we introduce the concept of entropy operator for continuous systems of finite topological entropy. It is shown that it generates the Kolmogorov entropy as a special case. If $phi$ is invertible then the entropy operator is bounded with the topological entropy of $phi$ as its norm.

Optimization of Body Composition Analyzer Facility, Considering Operator Dosimetry

Background: Changes in body composition may be used for monitoring progression/ regression of a disease. Prompt γ-rays in vivo neutron activation analysis (IVNAA) has been widely used for the measurement of body composition in recent years.Objective: In this paper, we tried to improve the safety of IVNAA operator.Methods: The most important factor for reducing the operator receiving dose is th...