One of the most efficient methods of reducing drag on planing craft is the use of transverse step on the bottom of a hull. Applying steps on the hull reduces the contact area with water and as a result, it reduces drag of the craft. Planing craft are able to have one or two transverse steps. In this paper, numerical hydrodynamic performance of the stepped planing craft and its step height effec...

Solving the direct kinematics of parallel spherical mechanisms with l legs boils down to solving systems of l 1 second-order multinomials. This paper presents a recurrent expression for the control points of these multinomials when expressed in Bernstein form. This result allows us to propose a technique for solving the direct kinematics of these mechanisms that takes advantage of the subdivisi...

Let X be a complex manifold and γ a simple closed curve inX . We address the question: What conditions on γ insure the existence of a 1-dimension complex variety Σ with boundary γ in X . When X = C, an answer to this question involves the polynomial hull of gamma. When X = P, complex projective space, the projective hull γ̂ of γ, a generalization of polynomial hull, comes into play. One always h...

Consider a system of linear algebraic equations with a nonsingular n by n matrix A. When solving this system with GMRES, the relative residual norm at the step k is bounded from above by the so called ideal GMRES approximation. This bound is sharp (it is attainable by the relative GMRES residual norm) in case of a normal matrix A, but it need not characterize the worstcase GMRES behavior if A i...

We introduce the notion of a projective hull for subsets of complex projective varieties parallel to the idea of a polynomial hull in affine varieties. With this concept, a generalization of J. Wermer’s classical theorem on the hull of a curve in Cn is established in the projective setting. The projective hull is shown to have interesting properties and is related to various extremal functions ...

In this article, Ritz approximation have been employed to obtain the numerical solutions of a class of the fractional optimal control problems based on the Caputo fractional derivative. Using polynomial basis functions, we obtain a system of nonlinear algebraic equations. This nonlinear system of equation is solved and the coefficients of basis polynomial are derived. The convergence of the num...

in this paper, we introduce the notions of c-numerical range and c-spectrum of matrix polynomials. some algebraic and geometrical properties are investigated. we also study the relationship between the c-numerical range of a matrix polynomial and the joint c-numerical range of its coefficients.

 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...