Under a non-degeneracy condition on the nonlinearities we show that sequences of approximate entropy solutions of mixed elliptic-hyperbolic equations are strongly precompact in the general case of a Caratheodory flux vector. The proofs are based on deriving localization principles for H-measures associated to sequences of measure-valued functions. This main result implies existence of solutions...

Nonlocal problems for hyperbolic equations of the first order describe the dynamic of population [1]–[3]. During the last thirty years the existence and uniqueness of the solution of nonlocal problems for the system of hyperbolic equations have been considered in a number of papers [4]–[8]. The authors assumed that the nonlinear functions satisfy the Lipschitz condition with respect to the unkn...

Ship hull form module is the main module in ship design. The problem of creating fair ship hull surface is of major importance in Computer Aided Ship Design environment. The fitness of these surfaces is generally considered a subjective notion depending on the judgment of the designers (eg. visually pleasing, devoid of unnecessary bumps or wiggles, satisfying certain continuity requirements). O...

There are different methods to reduce drag in high speed hulls. One of these methods is a change in the shape of the body by adding longitudinal side tunnels. In this paper it has been attempted to determine the influence of the tunnel height on hydrodynamic characteristics of the hull to achieving an optimum shape for the tunnel. To achieve this purpose, numerical simulation of the problem has...

Introduced in [1] by Jason Cantarella, Greg Kuperberg, Robert B. Kusner, and John M. Sullivan, the hull number is a complexity measure for links similar to the bridge number. By definition, it is the maximum integer n such that for any realization of the link there is a point c ∈ R such that any plane through c intersects the curves representing the link at least 2n times. Clearly, the hull num...

A coarse outer hull of a mesh is a good tool used in computer graphics to reduce algorithm complexity, especially, in applications such as collision detection or ray-tracing. It is often required that the hull has some very specific parameters concerning its shape and quality since these influence general flexibility and numerical stability of the algorithms. This paper overviews existing probl...

We prove a general Borg-type inverse spectral result for a reflectionless unitary CMV operator (CMV for Cantero, Moral, and Velázquez [13]) associated with matrix-valued Verblunsky coefficients. More precisely, we find an explicit formula for the Verblunsky coefficients of a reflectionless CMV matrix whose spectrum consists of a connected arc on the unit circle. This extends a recent result [39...

with a1, a2 > 0. (Indeed any rank 2 matrix can be written as RA with A as above, and R orthogonal. Hence any affine transformation can be written as h ◦ f with f as claimed and g a rigid motion.) Hence, by Caratheodory uniqueness theorem it is sufficient to show that λ2(ASu(α1, α2)) = |det(A)|λ2(Su(α1, α2)) for all u = (u1, u2) ∈ R, αi ∈ R+ (3) Su(α, β) ≡ { x = (x1, x2) ∈ R : x1 ∈ (u1, u1 + α1]...