Following the results of cite{Med}, regarding the Aluthge transform of polynomial matrices, the symbolic computation of the Duggal transform of a polynomial matrix $A$ is developed in this paper, using the polar decomposition and the singular value decomposition of $A$. Thereat, the polynomial singular value decomposition method is utilized, which is an iterative algorithm with numerical charac...

This paper addresses the problem of finding tight affine lower bound functions for multivariate polynomials, which may be employed when global optimisation problems involving polynomials are solved with a branch and bound method. These bound functions are constructed by using the expansion of the given polynomial into Bernstein polynomials. The coefficients of this expansion over a given box yi...

In this paper a reformulation technique is presented that takes a given linear zero-one programming problem, converts it into a zero-one polynomial programming problem, and then relinearizes it into an extended linear program. It is shown that the strength of the resulting reformulation depends on the degree of the terms used to produce the polynomial program at the intermediate step of this me...

A comparison between towing tank testing and full-scale CFD simulations is presented at three different target speeds. For the current self-propulsion simulation, point was obtained using polynomial interpolation. The studies of boundary layer thickness, a basic grid uncertainty assessment verification were performed to give some confidence application simulation. All are commercial software ST...

Recently there has been considerable research on simple mixed-integer sets, called mixing sets, and closely related sets arising in uncapacitated and constant capacity lot-sizing. This in turn has led to study of more general sets, called network-dual sets, for which it is possible to derive extended formulations whose projection gives the convex hull of the network-dual set. Unfortunately this...

let $p(lambda)$ be an $n$-square complex matrix polynomial, and $1 leq k leq n$ be a positive integer. in this paper, some algebraic and geometrical properties of the $k$-numerical range of $p(lambda)$ are investigated. in particular, the relationship between the $k$-numerical range of $p(lambda)$ and the $k$-numerical range of its companion linearization is stated. moreover, the $k$-numerical ...

in this paper, we develop two piecewise polynomial methods for the numerical evaluation of cauchy principal value integrals of oscillatory kind. the two piecewisepolynomial quadratures are compact, easy to implement, and are numerically stable. two numerical examples are presented to illustrate the two rules developed, the convergence of the two schemes is proved and some error bounds obtained,

This article describes a 3D CFD (computational fluid dynamics) simulation implementation of the stepped planning hull in calm water. The turbulent free surface flow around the stepped planing hull is computed with a RANSE method, using the solver ANSYS-CFX. The turbulence model used is standard k–ε. In order to simulate the disturbed free surface, VOF model is implemented. The CFD model has bee...