The generalized nonlinear Schrödinger (GNLS) equation is solved numerically by a split-step Fourier method. The first, second and fourth-order versions of the method are presented. A classical problem concerning the motion of a single solitary wave is used to compare the first, second and fourth-order schemes in terms of the accuracy and the computational cost. This numerical experiment shows t...

A simple method for estimation of parameters in first order systems with time delays is presented in this paper. The parameter estimation approach is based on a step response for the open loop system. It is shown that the estimation method does not require a complete step response, only a part of the response and the steady state value of the system before the step is applied. Further, for calc...

The Colin de Verdière parameters, μ and ν, are defined to be the maximum nullity of certain real symmetric matrices associated with a given graph. In this work, both of these parameters are calculated for all chordal graphs. For ν the calculation is based solely on maximal cliques, while for μ the calculation depends on split subgraphs. For the case of μ our work extends some recent work on com...

The Colin de Verdière parameters, μ and ν, are defined to be the maximum nullity of certain real symmetric matrices associated with a given graph. In this work, both of these parameters are calculated for all chordal graphs. For ν the calculation is based solely on maximal cliques, while for μ the calculation depends on split subgraphs. For the case of μ our work extends some recent work on com...

Split-plot experiments are appropriate when some factors are more difficult and/or expensive to change than others. They require two levels of randomization resulting in a non-independent error structure. The design of such experiments has garnered much recent attention, including work on exact D-optimal split-plot designs. However, many of these procedures rely on the a priori assumption that ...

We implement a robust, globally convergent root search method for transcendental equations guaranteed to locate all complex roots within a specified search domain, based on Cauchy’s residue theorem. Although several implementations of the argument principle already exist, ours has several advantages: it allows singularities within the search domain and branch points are not fatal to the method....

Proportional-integral-derivative (PID) controllers are widely used in industrial control systems because of the reduced number of parameters to be tuned. The most popular design technique is the Ziegler–Nichols method, which relies solely on parameters obtained from the plant step response. However, besides being suitable only for systems with monotonic step response, the compensated systems wh...

Chromatic dispersion and fiber attenuation pose a great problem in the detection of optical signals. Dispersion causes pulse broadening which limits the information carrying capacity of the fiber while attenuation limits the maximum transmission distance along the fiber. An approximate Gaussian pulse propagation model is obtained from the solution of Nonlinear Schrödinger Equation to represent ...

We present a new method for the synthesis of fuzzy-logic controllers (flcs) for amplitude-sensitive nonlin-ear plants based on sinusoidal-input describing-function (sidf) methods plus step-response optimization. This method involves a two-step process wherein an initial controller is obtained via the direct generation of the membership functions and output levels based on the \frequency respons...