Supercavitation technology can greatly improve the speed of underwater vehicles by reducing drag. However, time-delay characteristic a supercavitating vehicle presents control challenge. In this paper, linear parameter-varying (LPV) model for is established analysing characteristics planing force. Moreover, considering that cavitation radius easily perturbed external disturbances, LPV delay dep...

We build facets of the quadratic 0-1 knapsack polytope following two different approaches. The quadratic 0-1 knapsack polytope is included in the Boolean quadric polytope introduced by Padberg [12] for unconstrained 0-1 quadratic problem. So in a first approach, we ask the question which are the facets of the Boolean quadric polytope that are still facets of the quadratic 0-1 knapsack polytope....

A polytope is integral if all of its vertices are lattice points. The constant term of the Ehrhart polynomial of an integral polytope is known to be 1. In previous work, we showed that the coefficients of the Ehrhart polynomial of a lattice-face polytope are volumes of projections of the polytope. We generalize both results by introducing a notion of k-integral polytopes, where 0-integral is eq...

The convexity theorem of Atiyah and Guillemin-Sternberg says that any connected compact manifold with Hamiltonian torus action has a moment map whose image is the convex hull of the image of the fixed point set. Sjamaar-Lerman proved that the Marsden-Weinstein reduction of a connected Hamitonian G-manifold is a stratified symplectic space. Suppose 1 → A → G → T → 1 is an exact sequence of compa...

2 Convex Polyhedron 3 2.1 What is convex polytope/polyhedron? . . . . . . . . . . . . . . . . . . . . . . 3 2.2 What are the faces of a convex polytope/polyhedron? . . . . . . . . . . . . . . 3 2.3 What is the face lattice of a convex polytope . . . . . . . . . . . . . . . . . . . 4 2.4 What is a dual of a convex polytope? . . . . . . . . . . . . . . . . . . . . . . . 4 2.5 What is simplex? . ....