As a follow-up to a recent paper considering two symmetric queues, the Shortest Queue First service discipline is presently analysed for two general asymmetric queues. Using the results previously established and assuming exponentially distributed service times, the bivariate Laplace transform of workloads in each queue is shown to depend on the solution M to a two-dimensional functional equati...

The classical action of a two dimensional N = 2 supersymmetric theory, characterized by a general Kähler potential, is written down on a non(anti)commutative superspace. The action has a power series expansion in terms of the determinant of the non(anti)commutativity parameter C αβ. The theory is explicitly shown to preserve half of the N = 2 supersymmetry, to all orders in (det C) n. The resul...

In this paper, we obtain new observability inequalities for the vibrating string. This work was motivated by a recent paper of Szijártó and Hegedűs in which the authors ask the question of determining the initial data by only knowing the position of the string at two distinct time instants. The choice of the observation instants is crucial and the estimations rely on the Fourier series expansio...

We show how to find series expansions for π of the form π = ∞ n=0 S(n) mn pn a n , where S(n) is some polynomial in n (depending on m, p, a). We prove that there exist such expansions for m = 8k, p = 4k, a = (−4) k , for any k, and give explicit examples for such expansions for small values of m, p and a.

We derive a beautiful series expansion for Spearman’s rho, ρ(θ) of the Ali-Mikhail-Haq (AMH) copula with paramater θ which is also called α or θ. Further, via experiments we determine the cutoffs to be used for practically fast and accurate computation of ρ(θ) for all θ ∈ [−1, 1].

We show how to find series expansions for π of the form π = ∞ n=0 S(n) mn pn a n , where S(n) is some polynomial in n (depending on m, p, a). We prove that there exist such expansions for m = 8k, p = 4k, a = (−4) k , for any k, and give explicit examples for such expansions for small values of m, p and a.

We prove that a two-variable p-adic lq-function has the series expansion lp,q s, t, χ 2 q/ 2 F ∑F a 1, p,a 1 −1 a χ a qa/〈a pt〉 ∑∞ m 0 −s m F/〈a pt〉 mE∗ m,qF which interpolates the values lp,q −n, t, χ E∗ n,χn,q pt − pχn p 2 q/ 2 qp E∗ n,χn,q t , whenever n is a nonpositive integer. The proof of this original construction is due to Kubota and Leopoldt in 1964, although the method given in this ...

The generalized Taylor expansion including a secret auxiliary parameter h which can control and adjust the convergence region of the series is the foundation of the homotopy analysis method proposed by Liao. The secret of h can’t be understood in the frame of the homotopy analysis method. This is a serious shortcoming of Liao’s method. We solve the problem. Through a detailed study of a simple ...

We consider some multivariate rational functions which have (or are conjectured to have) only positive coefficients in their series expansion. We consider an operator that preserves positivity of series coefficients, and apply the inverse of this operator to the rational functions. We obtain new rational functions which seem to have only positive coefficients, whose positivity would imply posit...

The projection conditions for the quotient gauge theory of the D-brane world volume theory are studied for C/Z3 × Z3.The series expansion solutions which satisfy these conditions are constructed and they are shown to be incompatible with the F-flatness conditions for the discrete torsion case.