In this paper, a numerical solution for a system of linear Fredholm integro-differential equations by means of the sinc method is considered. This approximation reduces the system of integro-differential equations to an explicit system of algebraic equations. The exponential convergence rate $O(e^{-k sqrt{N}})$ of the method is proved. The analytical results are illustrated with numerical examp...

In this paper we consider the construction, analysis, implementation and application of exponential integrators. The focus will be on two types of stiff problems. The first one is characterized by a Jacobian that possesses eigenvalues with large negative real parts. Parabolic partial differential equations and their spatial discretization are typical examples. The second class consists of highl...

Abstract. In this paper, we propose to study a generalized form of the exponential power distribution which contains others in the literature as special cases. This unifying exponential power distribution is characterized by a parameter ω and a function h(ω) which regulates the tail behavior of the distribution, thus making it more flexible and suitable for modeling than the usual normal di...

Although the random sum distribution has been well-studied in probability theory, inference for the mean of such distribution is very limited in the literature. In this paper, two approaches are proposed to obtain inference for the mean of the Poisson-Exponential distribution. Both proposed approaches require the log-likelihood function of the Poisson-Exponential distribution, but the exact for...

where we in introduce the standard notation e(x) = exp(2πix). Question 1.1. What is the magnitude of | ∑ x∈S e(x)|? By the trivial bound, we find that | ∑ x∈S e(x)| ≤ N , with equality whenever the terms are all equal. One can of course make the sum much smaller–simply sum the Nth roots of unity. In between these two extremes–completely in phase and maximally out of phase–we should consider wha...

Using ultrafilter techniques we show that in any partition of N into 2 cells there is one cell containing infinitely many exponential triples, i.e. triples of the kind a, b, ab (with a, b > 1). Also, we will show that any multiplicative IP ∗ set is an “exponential IP set”, the analogue of an IP set with respect to exponentiation. Introduction A well-known theorem by Hindman states that given an...