The normal ordering formulae for powers of the boson number operator n̂ are extended to deformed bosons. It is found that for the “M-type” deformed bosons, which satisfy aa− qaa = 1, the extension involves a set of deformed Stirling numbers which replace the Stirling numbers occurring in the conventional case. On the other hand, the deformed Stirling numbers which have to be introduced in the ca...

Multirestricted Stirling numbers of the second kind count the number of partitions of a given set into a given number of parts, each part being restricted to at most a fixed number of elements. Multirestricted numbers of the first kind are then defined as elements of the matrix inverse to the matrix of corresponding multirestricted numbers of the second kind. The anomalous sign behavior of thes...

School of Psychology, University of Stirling, Stirling, FK9 4LA, UK School of Psychology, University of Aberdeen, Aberdeen, AB24 2UB, UK Dept of Zoology, University of Oxford, Oxford, OX1 3PS, UK School of Computer Science, University of St Andrews, St Andrews, KY16 9SX, UK Dept of Psychology, McMaster University, Ontario, L8S 4L8, Canada School of Psychology, University of St Andrews, St Andre...

Investigating the impact of deploying commercial Bombus terrestris for crop pollination on pathogen dynamics in wild bumble bees Penelope R Whitehorn, Matthew C Tinsley, Mark J F Brown and Dave Goulson Biological & Environmental Sciences, University of Stirling, Stirling, FK9 4LA, UK. School of Biological Sciences, Royal Holloway, University of London, Egham, Surrey TW20 0EX, UK. Current addres...

Application of finite element method and heat conductivity transfer model for calculation of temperature distribution in receiver for dish-Stirling concentrating solar system is described. The method yields discretized equations that are entirely local to the elements and provides complete geometric flexibility. A computer program solving the finite element method problem is created and great n...

We introduce a generalization of the Stirling numbers called the V-Stirling numbers which are inspired by the symmetric function form of the p, q-binomial coefficients. A number of properties are derived, including recurrence relations, generating functions, orthogonality relations and convolution formulas. The results are used to derive properties of some special cases and provide alternative ...

1 Plant & Invertebrate Ecology Department, and 2 Biomathematics & Bioinformatics Department, Rothamsted Research, Harpenden, Herts AL5 2JQ, UK; 3 School of Biological & Environmental Sciences, University of Stirling, Stirling FK9 4LA, UK; 4 School of Biological Sciences, University of Plymouth, Drake Circus, Plymouth PL4 8AA, UK; 5 Bio-protection & Ecology Division, PO Box 84, Lincoln Universit...

Bona [6] studied the distribution of ascents, plateaux and descents in the class of Stirling permutations, introduced by Gessel and Stanley [14]. Recently, Janson [18] showed the connection between Stirling permutations and plane recursive trees and proved a joint normal law for the parameters considered by Bona. Here we will consider generalized Stirling permutations extending the earlier resu...

This paper focuses on the design of a Stirling engine for distributed solar thermal applications. In particular, we design for the low temperature differential that is attainable with distributed solar collectors and the low cost that is required to be competitive in this space. We will describe how these considerations drive the core design, the methodology for improving the design, and summar...

The features of classical thermodynamic cycle of Stirling engine considering the periodic reciprocal motion of working body through the regenerator have been analyzed in this work. The possibility of satisfactory functioning of modified engine without regenerator with unidirectional pulsating motion of the working body in reсuperative heater and cooler has also been proved. The characteristic f...