M. K. LAURENSON*†, R. A. NORMAN‡, L. GILBERT§, H. W. REID¶ and P. J. HUDSON†§ * CTVM, University of Edinburgh, Easter Bush, Roslin, Midlothian, EH25 9RG, UK; † The Game Conservancy Trust, Upland Research Group, Crubenmore Lodge, Newtonmore, PH20 1BE, UK; ‡ Department of Computing Science and Mathematics, University of Stirling, Stirling, FK9 4LA, UK; § Institute of Biology, University of Stirli...

Abstract A new family of p -Bernoulli numbers and polynomials was introduced by Rahmani (J. Number Theory 157:350–366, 2015) with the help Gauss hypergeometric function. Motivated that paper in light recent interests finding degenerate versions, we construct generalized Bernoulli means In addition, type Eulerian as a version numbers. For numbers, express them terms Stirling second kind, -Stirli...

This paper describes a new approach to modeling and designing free-piston Stirling engines with the goal of building a working prototype. The Stirling cycle is recast as a dynamic system where control design tools and techniques can be applied to determine optimal manufacturable parameters for the engine. A simplified state-space analysis exhibits the merits of this perspective by revealing a l...

Measurements were performed to characterize the performance of a Free Piston Stirling Cooler over a wide range of temperatures and heat lifts. The temperature range investigated was from –120°C to +5°C on the cold head side and from 30 to 60°C at the warm head, while heat lifts from 10 to 100W were evaluated. The publication discusses aspects of the experimental part of the investigation, inclu...

In this paper we provide an explicit formula for calculating the boolean number of a Ferrers graph. By previous work of the last two authors, this determines the homotopy type of the boolean complex of the graph. Specializing to staircase shapes, we show that the boolean numbers of the associated Ferrers graphs are the Genocchi numbers of the second kind, and obtain a relation between the Legen...

and that the Bernoulli numbers of the second kind bn for n > 0 may be generated by x ln(1+x) = ∑ ∞ n=0 bnx . In combinatorics, the signed Stirling number of the first kind s(n, k) may be defined such that the number of permutations of n elements which contain exactly k permutation cycles is the nonnegative number |s(n, k)| = (−1)s(n, k). The Bernoulli numbers of the second kind bn are also call...

M. K. LAURENSON*†‡, R. A. NORMAN§, L. GILBERT†, H. W. REID¶ and P. J. HUDSON†‡ * CTVM, University of Edinburgh, Easter Bush, Roslin, Midlothian, EH25 9RG, UK, † Institute of Biology, University of Stirling, Stirling FK9 4LA, UK, ‡ The Game Conservancy Trust, Upland Research Group, Crubenmore Lodge, Newtonmore, PH20 1BE, UK, § Department of Computing Science and Mathematics, University of Stirli...

A modified approach via differential operator is given to derive a generalization of Stirling numbers of the first kind. This approach combines the two techniques given by Cakic [3] and Blasiak [2]. Some new combinatorial identities and many relations between different types of Stirling numbers are found. Furthermore, some interesting special cases of the generalized Stirling numbers of the fir...

This paper considers the generalized Stirling numbers of the first and second kinds. First, we show that the sequences of the above generalized Stirling numbers are both log-concave under some mild conditions. Then, we show that some polynomials related to the above generalized Stirling numbers are q-log-concave or q-log-convex under suitable conditions. We further discuss the log-convexity of ...