Spectral problems with band-gap spectral structure arise in numerous applications, including the study of crystalline structure and the determination of transmitted frequencies in photonic waveguides. Numerical discretization of these problems can result in spurious results, a phenomenon known as spectral pollution. We present a method for calculating eigenvalues in the gaps of self-adjoint ope...

Given a set S of n points in the plane, an -strongly convex -hull of S is de0ned as a convex polygon P with the vertices taken from S such that no point of S lies farther than outside P and such that even if the vertices of P are perturbed by as much as , P remains convex. This paper presents the 0rst parallel robust method for this generalized convex hull problem (note that the convex hull of ...

we characterize compact composition operators on real banach spaces of complex-valued bounded lipschitz functions on metric spaces, not necessarily compact, with lipschitz involutions and determine their spectra.

A study was carried out to investigate methods and to determine the "optimum" hull form for monohull ships, based upon several weighted criteria. The main product of this study is a hull form optimization program. Propulsion power minimization is the primary focus of the program, although simplified. seakeeping and weight/cost issues can also be studied with the existing program. The program us...

Biofouling is detrimental to the hydrodynamic performance of ships. In spite of advances in hull coating technology, a ship must usually undergo underwater hull cleaning to remove biofouling during her in-service time. However, some cleaning practices may also lead to decreased lifetime of the fouling-control coating. Therefore, cleaning forces should be minimized, according to the adhesion str...

An optimal algorithm is presented for computing the smallest set of linear inequalities that define the integer hull of a possibly unbounded two-dimensional convex polygon R. Input to the algorithm is a set of linear inequalities defining R, and the integer hull computed is the convex hull of the integer points of R. It is proven that the integer hull has at most O(n logAmax) inequalities, wher...

The present study was envisaged to prepare dietary fiber rich chicken meat rolls and patties. The combination of two different sources of dietary fiber viz. black gram hull and psyllium husk has been used. They were added in three different levels viz. 5% black gram hull and 2% psyllium husk, 5% black gram hull and 4% psyllium husk and 5% black gram hull and 6% psyllium husk. The sensory charac...

We study a standard method of regularization by projections of the linear inverse problem Y = Af + ǫ, where ǫ is a white Gaussian noise, and A is a known compact operator with singular values converging to zero with polynomial decay. The unknown function f is recovered by a projection method using the singular value decomposition of A. The bandwidth choice of this projection regularization is g...

Consider an operator dQ(f) = d dxk (Q(x)f(x)) where Q(x) is some fixed polynomial of degree k. One can easily see that dQ has exactly one polynomial eigenfunction pn(x) in each degree n ≥ 0 and its eigenvalue λn,k equals (n+k)! n! . A more intriguing fact is that all zeros of pn(x) lie in the convex hull of the set of zeros to Q(x). In particular, if Q(x) has only real zeros then each pn(x) enj...

Let (M, g) be a compact smooth Riemannian manifold with smooth boundary and suppose that U is an open set in M such that g|U is Euclidean. Let Γ = U ∩ ∂M be connected and suppose that U is the convex hull of Γ. We will study the uniqueness of an unknown potential for the Schrödinger operator −4g + q from the associated Dirichlet to Neumann map, Λq. Indeed, we will prove that if the potential q ...