In this paper, we define two natural (p, q)-analogues of the generalized Stirling numbers of the first and second kind S(α, β, r) and S(α, β, r) as introduced by Hsu and Shiue [17]. We show that in the case where β = 0 and α and r are nonnegative integers both of our (p, q)-analogues have natural interpretations in terms of rook theory and derive a number of generating functions for them. We al...

We present the superconformal gauge theory living on the world-volume of D3 branes probing the toric singularities with horizon the recently discovered Sasaki-Einstein manifolds L. Various checks of the identification are made by comparing the central charge and the R-charges of the chiral fields with the information that can be extracted from toric geometry. Fractional branes are also introduc...

This paper describes the application of the p-q power theory to the differential protection of power transformers. The information provided by the harmonic content of the differential active and reactive power components is used to detect winding insulation failures and to distinguish them from magnetizing inrush current transients. A variety of test cases is presented in the paper, demonstrati...

this paper presents a novel method to calculate the reference source current and the referencecompensating current for shunt active power filters (sapfs). this method first calculates theamplitude and phase of the fundamental load current from a recursive algebraic approach blockbefore calculating the displacement power factor. next, the amplitude of the reference mains currentis computed with ...

in the present article, we propose the $(p,q)$variant of genuine baskakov durrmeyer operators. we obtain moments and establish some directresults, which include weighted approximation and results in terms of modulus of continuity of second order.

This work is about symmetric numerical semigroups. The semigroups are very important in semigroup theory. They play an role especially algebraic geometry, coding theory and other areas of algebra. Here, we examine Arf closure $S_q$ semigroup, give some relations between such that $S_q=\langle p, p q+k\rangle$, where $p$ a prime number $q \geq 1, q \in \mathbb{Z}$ for $k=1,2$ $p-1$. Received: Ju...