We prove that for any k = 1, . . . , 2 the 2-adic order of the Stirling number S(2, k) of the second kind is exactly d(k) − 1, where d(k) denotes the number of 1’s among the binary digits of k. This confirms a conjecture of Lengyel.

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 ...

The reported discrepancy between theory and experiment for external combustion Stirling engines is explained by the addition of thermal resistance of the combustion gasses to the standard Carnot model. In these cases, the Stirling engine ideal efficiency is not as is normally reported equal to the Carnot cycle efficiency but is significantly lower. A new equation for ideal Stirling engine effic...

We develop techniques that can be applied to find solutions to the recurrence ∣∣n k ∣∣ = ( n+ k + )∣∣n−1 k ∣∣+ ( ′n+ ′k + ′)∣∣n−1 k−1∣∣+ [n = k = 0]. Many interesting combinatorial numbers, such as binomial coefficients, both kinds of Stirling and associated Stirling numbers, Lah numbers, Eulerian numbers, and second-order Eulerian numbers, satisfy special cases of this recurrence. Our techniqu...

Stirling et al. (2003) reported the discovery of a 2.3 year periodic variation in the structural position angle of the parsec-scale radio core in the blazar BL Lac. We searched for independent confirmation of this periodic behavior using 43 GHz images of the radio core during ten epochs overlapping those of Stirling et al. Our maps are consistent with several periodicities, including one near t...

We present a new proof of result Knuth and Buckholtz concerning the period the number alternating congruences modulo an odd prime. The is based on properties special functions, specifically polylogarithm, Dirichlet eta beta Stirling numbers second kind.

The Dish Stirling systems have demonstrated the highest efficiency of any solar power generation system by converting nearly 31.25% [1] of direct normal incident solar radiation into electricity after accounting for parasitic power losses. Therefore, the Dish Stirling technology is anticipated to surpass parabolic troughs by producing power at more economical rates and higher efficiencies. Beca...