A problem from a class of unsteady plane potential flows with free boundary is considered. The entire occupied by the liquid free, and zero pressure maintained. There are neither external nor capillary forces. motion driven inertia. parameters prescribed at initial time velocity field domain fluid. task to determine these subsequent instants. solution sought in form power series, which then sum...

A novel non-paraxial Time-Domain technique based on Pade approximant for modeling ultra short optical pulses has been formulated and tested. The new method is an extension to the parabolic Time-Domain Beam Propagation Method (TDBPM) that solves the time domain wave equation along one direction that allows the time window to follow the evolution of the pulse. In this work the technique was appli...

In relation to Fourier-Pade approximation, Ed Sa¤ observed that Taylor and Lagrange interpolation projections satisfy the following property: P (f) P (g) 2 n =) P (f g) = P (f) P (g). We classify all projections that satisfy this property, thus answering a question of Sa¤. Some error formulas for approximation with the above mentioned projections are also produced. AMS Subject Classi…cation: 41...

We propose a modification of the famous step-by-step process of solving the Nevanlinna-Pick problems for Nevanlinna functions. The process in question gives rise to three-term recurrence relations with coefficients depending on the spectral parameter. These relations can be rewritten in the matrix form by means of two Jacobi matrices. As a result of the considered approach, we prove a convergen...

Let [Sn] n=0 be such that Sn tS+ j=1 aj* n j as n , with 1>|*1 |> |*2 |> } } } , such that limj *j=0. A well-known result by Wynn states that when the Shanks transformation or its equivalent =-algorithm is applied to [Sn] n=0 , then = (n) 2k &Stak+1[> k i=1 (*k+1&*i) (1&*i)] 2 *k+1 as n . In the present work we extend this result (i) by allowing some of the *j to have the same modulus and (ii) ...

Radio frequency (RF) power amplifier (PA) design using Gallium Nitride (GaN) transistor technology requires accurate device models in order to maximise performance and reduce development time. The current state-of-the-art frequency-domain behavioural focus on linear quadratic approximations the polyharmonic distortion (PHD) formalism. However, approximation suffers from poor accuracy under load...