We present a nonstandard hull construction for locally uniform groups in a spirit similar to Luxembourg’s construction of the nonstandard hull of a uniform space. Our nonstandard hull is a local group rather than a global group. We investigate how this construction varies as one changes the family of pseudometrics used to construct the hull. We use the nonstandard hull construction to give a no...

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...

This paper presents a new O(nlog(n)) algorithm for computing the convex hull of a set of 3 dimensional points. The algorithm first sorts the point in (x,y,z) then incrementally adds sorted points to the convex hull using the constraint that each new point added to the hull can 'see' at least one facet touching the last point added. The reduces the search time for adding new points. The algorith...

We consider an inverse source problem in the stationary radiating transport through a two dimensional absorbing and scattering medium. Of specific interest, exiting radiation is measured on arc. The attenuation properties of medium are assumed known. For kernels finite Fourier content angular variable, we show how to quantitatively recover part isotropic sources restricted convex hull measureme...

In the present study, the overall economic impact of hull fouling on a mid-sized naval surface ship (Arleigh Burke-class destroyer DDG-51) has been analyzed. A range of costs associated with hull fouling was examined, including expenditures for fuel, hull coatings, hull coating application and removal, and hull cleaning. The results indicate that the primary cost associated with fouling is due ...

As in the previous chapter, let us denote points in R by p = (x, y, z) and points in R by u = (u, v). An edge is then defined as the convex hull of (or, equivalently, the line segment between) two distinct points and a triangle as the convex hull of three non-collinear points. We will denote edges and triangles in R with capital letters and those in R with small letters, for example, e = [u1,u2...

We show that for every integer k ≥ 2 and every k graphs G1, G2, . . . , Gk, there exists a hull graph with k hull vertices v1, v2, . . . , vk such that link L(vi) = Gi for 1 ≤ i ≤ k. Moreover, every pair a, b of integers with 2 ≤ a ≤ b is realizable as the hull number and geodetic number (or upper geodetic number) of a hull graph. We also show that every pair a, b of integers with a ≥ 2 and b ≥...

We provide an explicit description of the convex hull of the set of matrices of bounded rank, restricted to balls for the spectral norm. As applications, we deduce two relaxed forms of the rank function restricted to balls for the spectral norm: one is the quasiconvex hull of this rank function, another one is the convex hull of the rank function, thus retrieving Fazel's theorem (2002). Key-wor...