We show the classical q-Stirling numbers of the second kind can be expressed more compactly as a pair of statistics on a subset of restricted growth words. The resulting expressions are polynomials in q and 1+q. We extend this enumerative result via a decomposition of a new poset Π(n, k) which we call the Stirling poset of the second kind. Its rank generating function is the q-Stirling number S...

In this paper, we propose the another yet generalization of Stirling numbers of the rst kind for non-integer values of their arguments. We discuss the analytic representations of Stirling numbers through harmonic numbers, the generalized hypergeometric function and the logarithmic beta integral. We present then in nite series involving Stirling numbers and demonstrate how they are related to Eu...

The dish-Stirling technology for power generation, using a Stirling engine fed with a renewable energy such as solar, means a promising development regarding electricity generation. The dish-Stirling technology presents the highest efficiency, around 30%, in relation to other solar energy generation systems. However the technology status has not achieved enough advancement to be competitive wit...

Purely combinatorial methods are used to show that Stirling numbers, defined combinatorially, satisfy orthogonality relations. The proofs are extended to several generalizations of Stirling numbers.

In this paper we prove that some results concerned the generalized Stirling numbers are the consequence of the results of Toscano and Chak. The new explicit expressions for generalized Stirling numbers are also given.

The efficiency of the ideal stirling cycle assumes, that the cylinder volumes are isothermal and that the temperatures in the cylinder volumes are identical to the temperatures in the heat sink and the heat source. The efficiency is then identical to the efficiency of the Carnot cycle. However, in a real stirling machine the cylinder volumes are nearly adiabatic instead of isothermal, and the h...

This paper uses lumped parameter dynamic equations to model the mass flow, piston dynamics, and control volume behavior inside a free-piston Stirling engine. A new model for a Stirling engine thermal regenerator that incorporates a dynamically changing temperature gradient is presented. The use of graphite as a regenerator matrix material is justified despite its limited background by comparing...

Yathunanthan Sivarajah*, Eun-Jung Holden , Roberto Togneri, Mike Dentith 2 and Jeffrey Shragge 1 Centre for Exploration Targeting, University of Western Australia, 35 Stirling Hwy, Nedlands, WA 6009, Australia. 2 Centre for Petroleum Geoscience and CO2 Sequestration, University of Western Australia, 35 Stirling Hwy, Nedlands, WA 6009, Australia. 3 Electrical, Electronic and Computer Engineering...

In this note, we provide a combinatorial proof of a generalized recurrence formula satisfied by the Stirling numbers of the second kind. We obtain two extensions of this formula, one in terms of r-Whitney numbers and another in terms of q-Stirling numbers of Carlitz. Modifying our proof yields analogous formulas satisfied by the r-Stirling numbers of the first kind and by the r-Lah numbers.

A longitudinal study of policy effect (smoke-free legislation) on smoking norms: ITC Scotland/UK Authors: Abraham Brown, Crawford Moodie, Gerard Hastings. Authors affiliations: Abraham Brown MSc, Centre for Tobacco Control Research, Institute for Social Marketing, University of Stirling, UK. Crawford Moodie PhD, Centre for Tobacco Control Research, Institute for Social Marketing, University of ...