We use the matrices of transformations between Chebyshev and Bernstein basis and the matrices of degree elevation and reduction of Chebyshev polynomials to present a simple and efficient method for r times degree elevation and optimal r times degree reduction of Bézier curves with respect to the weighted L2-norm for the interval [0,1], using the weight function wðxÞ 1⁄4 1= ffiffiffiffiffiffiffi...

Sediment Bypass Tunnels (SBTs) are deviant channels that convey the current containing sediments from the upstream of the reservoir to the downstream of the dam. In this research, by applying submerged plates on the entrance of a 90-degree diversion channel for sediment transport, the effect of hydraulic parameters of flow and changes in the angle of plates on sediment transport and deviated fl...

Given a Bézier curve of degree n, the problem of optimal multi-degree reduction (degree reduction of more than one degree) by a Bézier curve of degreem (m< n−1) with constraints of endpoints continuity is investigated. With respect to L2 norm, this paper presents one approximate method (MDR by L2) that gives an explicit solution to deal with it. The method has good properties of endpoints inter...

Cooperation search algorithm (CSA) is a new metaheuristic inspired from the team cooperation behaviors in modern enterprises and characterized by fast convergence. However, for complex multimodal problems, it may get trapped into local optima suffer premature convergence shortcoming of population updating guided only leading individuals. In this paper, issue low efficiency accuracy CSA on probl...