Using a general and simple algebraic approach, some results on Krall-type orthogonal polynomials and some of their extensions are obtained.

We study the asymptotic behavior of $L_p\left(\sigma \right)$ extremal polynomials with respect to a measure of the form $\sigma =\alpha +\gamma$, where $\alpha$ is a measure concentrated on a rectifiable Jordan curve in the complex plane and $\gamma$ is a discrete measure concentrated on an infinite number of mass points.

A freak wave is a wave of very considerable height, ahead of which there is a deep trough. A case study examines some basic properties developed by performing wavelet analysis on a freak wave. We demonstrate several applications of wavelets and discrete and continuous wavelet transforms on the study of a freak wave. A modeling setting for freak waves will also be mentioned.

In nonparametric methods, if the number of observations is relatively small as compared to the sum of number of inputs and outputs, many units are evaluated as efficient. Several methods for prioritizing these efficient units are reported in literature. Andersen et al. and Mehrabian et al. proposed two methods for ranking efficient units, but both methods break down in some cases. This paper describes a new DEA ranking approach that uses $L_2$-norm.

We consider the problem of projecting a point onto a region defined by a linear equality or inequality constraint and two-sided bounds on the variables. Such problems are interesting because they arise in various practical problems and as subproblems of gradient-type methods for constrained optimization. Polynomial algorithms are proposed for solving these problems and their convergence is proved. Some examples and results of numerical experiments are presented.

An exact solution is constructed to a nonlinear optimization problem in an integral dynamic model with delay. The problem involves the unknown duration of the delay and has important applications to the optimal replacement of capital equipment under technological change.