It is shown that the Stirling numbers of the first kind can be expressed in the form [n k ] = ∑n−1 j1<j2<···<jk−1 (n−1)! αQ[j1,j2,...,jk−1] , where Q is a product of k − 1 linear factors in the indices j1, j2, . . . , jk−1 and α is a normalization coefficient determined by the condition [ k k ] = 1. Several types of Q’s are shown to yield Stirling numbers (“be Stirling”), and some more are conj...

The Jacobi-Stirling numbers of the first and second kind were introduced in 2007 by Everitt et al. In this article we find new explicit formulas for Jacobi Stirling numbers. Furthermore, derive study class so-called generalized Some special cases such as Legendre-Stirling are given. interesting combinatorial identities obtained.

Savi Maharaj is a researcher near the beginning of her career as a lecturer at the University of Stirling. She has had extensive training in theoretical computer science as well as in software engineering. She has a general interest in the use of Formal Methods to produce reliable software systems and a particular interest in the development and use of tools to support this endeavour. She is sp...

A new family of generalized Stirling and Bell numbers is introduced by considering powers (V U)n of the noncommuting variables U, V satisfying UV = V U +hV s. The case s = 0 (and h = 1) corresponds to the conventional Stirling numbers of second kind and Bell numbers. For these generalized Stirling numbers, the recursion relation is given and explicit expressions are derived. Furthermore, they a...

Abstract. Inversion formulas have been found, converting between Stirling, tanh and Lah numbers. Tanh and Lah polynomials, analogous to the Stirling polynomials, have been defined and their basic properties established. New identities for Stirling and tangent numbers and polynomials have been derived from the general inverse relations. In the second part of the paper, it has been shown that if ...

-KW Stirling engine based on a testing -constant, and electrical heating was ctive efficiency was about 25.4%. Copyright © 2012 Universitas Ahmad Dahlan. All rights reserved. -V and T-S diagrams for Stirling engine

In recent years, using new methods in utilization of energy resources has become necessary due to environmental pollution and restriction of energy resources. The hybrid system presented in this article produced power with SOFC and Stirling engine. The purpose is to analyze a 50 kW Solid Oxide Fuel Cell that could produce enough thermal energy for a 10 kW Stirling engine working in the hybrid s...

A hierarchy is a distribution of elements on levels. For a given number of elements a certain hierarchy can be arrangend in a finite number of ways. We provide a counting formula for certain types of hierarchies. Mainly, this formula is a sum over the integer partitions of the number of elements. Furthermore, several basic combinatorical numbers like the Stirling numbers of the second kind, the...

In this article combinatorial aspects of normal ordering annihilation and creation operators of a multi-mode boson system are discussed. The modes are assumed to be coupled since otherwise the problem of normal ordering is reduced to the corresponding problem of the single-mode case. To describe the normal ordering in the multi-mode case for each mode a colour is introduced and coloured contrac...

This article describes a simple model obtained from a commercial Stirling engine and used for heating a caravan. The Stirling engine has been tested in the lab under different electrical load conditions, and the operating points obtained are presented. As an application of the model, a series of transient simulations was performed using TRNSYS. During these simulations, the caravan is traveling...