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 series of inequalities involving Stirling numbers of the first and second kinds with adjacent indices are obtained. Some of them show log-concavity of Stirling numbers in three different directions. The inequalities are used to prove unimodality or strong unimodality of all the subfamilies of Stirling probability functions. Some additional applications are also presented.

We develop polynomials in z ∈ C for which some generalized harmonic numbers are special cases at z= 0. By using the Riordan array method, we explore interesting relationships between these polynomials, the generalized Stirling polynomials, the Bernoulli polynomials, the Cauchy polynomials and the Nörlund polynomials. © 2007 Elsevier B.V. All rights reserved.

The Jacobi-Stirling numbers of the first and second kinds were introduced in the spectral theory and are polynomial refinements of the Legendre-Stirling numbers. Andrews and Littlejohn have recently given a combinatorial interpretation for the second kind of the latter numbers. Noticing that these numbers are very similar to the classical central factorial numbers, we give combinatorial interpr...

Abstract In this paper, we discuss the properties of associated Stirling numbers. By means of the method of coefficients, we establish a series of identities involving associated Stirling numbers, Bernoulli numbers, harmonic numbers, and the Cauchy numbers of the first kind. In addition, we give the asymptotic expansion of certain sums involving 2-associated Stirling numbers of the second kind ...

Liquids can work in heat engine cycles that employ regeneration. Four such cycles are discussed: Stirling, Malone, Stirling-Malone, and Brayton. Both regeneration and the role of the second thermodynamic medium are treated, and the principles are verified by quantitative measurements with propylene in a Stirling-Malone cycle.

Stirling numbers of second kind S(n,k) denotes the number ways partitioning a set n elements into k nonempty sets. There are many types stirling which studied up to now. In this study, we use extended defined for arbitrary reals. First, define relation between and q-B-splines by using property that divided differences have representation with q-B-splines. addition, derive identities on q-integr...

1 Department of Computing Science and Mathematics, University of Stirling, Stirling, United Kingdom, 2 Department of Philosophy, University of Stirling, Stirling, United Kingdom, 3 Institute for Advanced Studies in the Humanities, University of Edinburgh, Edinburgh, United Kingdom, 4 School of Philosophy, Psychology and Language Sciences, University of Edinburgh, Edinburgh, United Kingdom, 5 De...