In this paper we develop a technique for constructing self-concordant barriers for convex cones. We start from a simple proof for a variant of standard result [1] on transformation of a ν-self-concordant barrier for a set into a self-concordant barrier for its conic hull with parameter (3.08 √ ν + 3.57)2. Further, we develop a convenient composition theorem for constructing barriers directly fo...

The projective hull X̂ of a compact set X ⊂ P is an analogue of the classical polynomial hull of a set in C. In the special case that X ⊂ C ⊂ P, the affine part X̂ ∩C can be defined as the set of points x ∈ C for which there exists a constant Mx so that |p(x)| ≤ M x sup X |p| for all polynomials p of degree ≤ d, and any d ≥ 1. Let X̂(M) be the set of points x where Mx can be chosen ≤ M . Using an ...

Inspired by a question of Lovász, we introduce a hierarchy of nested semidefinite relaxations of the convex hull of real solutions to an arbitrary polynomial ideal, called theta bodies of the ideal. For the stable set problem in a graph, the first theta body in this hierarchy is exactly Lovász’s theta body of the graph. We prove that theta bodies are, up to closure, a version of Lasserre’s rela...

Based on a recent duality theory for linear differential inclusions (LDIs), the condition for stability of an LDI in terms of one Lyapunov function can be easily derived from that in terms of its conjugate function. This paper uses a particular pair of conjugate functions, the convex hull of quadratics and the maximum of quadratics, for the purpose of estimating the domain of attraction for sys...

Understanding the interactions between a hull and a propeller is a common problem naval architects have to solve to provide efficient powering solutions. The world of elite sport is becoming increasingly scientific in a similar drive for increased performance. To allow a kayak’s hull and paddle to be optimised, their interactions have to be considered to provide a realistic race scenario. It is...

In this paper we propose a computationally efficient implementation of general one factor short rate models with a trinomial tree. We improve the Hull–White’s procedure to calibrate the tree to bond prices by circumventing the forward rate induction and numerical root search algorithms. Our calibration procedure is based on forward measure changes and is as general as the Hull–White procedure, ...

Two different cartesian-grid methods are used to simulate the flow around the DDG 5415. The first technique uses a “coupled level-set and volume-of-fluid” (CLS) technique to model the free-surface interface. The noflux boundary condition on the hull is imposed using a finite-volume technique. The second technique uses a level-set technique (LS) to model the free-surface interface. A body-force ...

a class of new methods based on a septic non-polynomial spline function for the numerical solution of problems in calculus of variations is presented. the local truncation errors and the methods of order 2th, 4th, 6th, 8th, 10th, and 12th, are obtained. the inverse of some band matrixes are obtained which are required in proving the convergence analysis of the presented method. convergence anal...

in this paper, numerical simulation of frp composite cylinder tubes progressive crushing processes is conducted using ls-dyna. details on the numerical modeling strategy are given and discussed. it is found that triggers introduced in the numerical simulation can effectively model the bevel trigger at the end of the tubular specimens. it is also found that two-layer finite element model based o...

In this paper a numerical method for solving forth order fuzzy dierentialequations under generalized differentiability is proposed. This method is basedon the interpolating a solution by piecewise polynomial of degree 8 in the rangeof solution . We investigate the existence and uniqueness of solutions. Finally anumerical example is presented to illustrate the accuracy of the new technique.