Abstract— In this paper, input impedance of a vertical rod under lightning stroke is first computed by applying the method of moments (MoM) on the Maxwell’s equations. The circuit model is then achieved through applying modified vector fitting (MVF) on the computed input impedance. After then the equivalent circuit is again extracted for a few values of soil conductivity and rod radius. Finally...

β1 ψ dx− ab+ α1β1. Young’s inequality [2, 1, 4] states that for every a ∈ [α1, α2] and b ∈ [β1, β2] (2) 0 ≤ F (a, b), where the equality holds iff φ(a) = b (or, equivalently, ψ(b) = a). Among the classical inequalities Young’s inequality is probably the most intuitive. Indeed, its meaning can be easily grasped once the integrals are regarded as areas below and on the left of the graph of φ (see...

by using euler-maclaurin's summation formula and the way of real analysis, a more accurate multiplehilbert-type inequality and the equivalent form are given. we also prove that the same constantfactor in the equivalent inequalities is the best possible.

We give a new Hilbert-type integral inequality with the best constant factor by estimating the weight function. And the equivalent form is considered.

The notion of linear finite transducer (LFT) plays a crucial role in a family of cryptosystems introduced in the 80’s and 90’s. However, as far as we know, no study was ever conducted to count and enumerate these transducers, which is essential to verify if the size of the key space, of the aforementioned systems, is large enough to prevent an exhaustive search attack. In this paper, we determi...