Considering the problem of the minimal triangulation for a given polyhedra (dividing polyhedra into tetrahedra) it is known that the cone triangulation provides the number of tetrahedra which is the smallest, or the closest to it. It is also shown that when we want to know whether the cone triangulation is the minimal one, it is necessary to find the order of all vertices, as well as the order ...

Epidemiologic studies have revealed that minimal acute-phase changes predict poor prognoses in many conditions and predict disability and mortality in the elderly. These findings have usually been interpreted to indicate that inflammatory processes of some kind play a role in these situations. In fact, a minimal acute-phase response does not necessarily establish the existence of an inflammator...

We introduce, for block size 3, the problem of minimal enclosings of GDDs with u groups of size g into GDDs with u groups of size g + 1. We prove the necessary conditions are sufficient for the embedding of any GDD with group size 1, i.e., a BIBD(v, 3, λ), into a GDD with v groups of size 2. Minimal faithful enclosings of GDDs are given for group size 2 with any index into GDDs with group size ...

We consider the model theoretic notion of convex orderability, which fits strictly between the notions of VC-minimality and dp-minimality. In some classes of algebraic theories, however, we show that convex orderability and VC-minimality are equivalent, and use this to give a complete classification of VC-minimal theories of ordered groups and abelian groups. Consequences for fields are also co...

50.50 IRB duties. 50.51 Clinical investigations not involving greater than minimal risk. 50.52 Clinical investigations involving greater than minimal risk but presenting the prospect of direct benefit to individual subjects. 50.53 Clinical investigations involving greater than minimal risk and no prospect of direct benefit to individual subjects, but likely to yield generalizable knowledge abou...

We calculate the minimal surface bounded by four-sided figures whose projection on a plane is a rectangle, starting with the bilinear interpolation and using, for smoothness, the Chebyshev polynomial expansion in our discretized numerical algorithm to get closer to satisfying the zero mean curvature condition. We report values for both the bilinear and improved areas, suggesting a quantitative ...

We give a necessary and sufficient condition for an n-dimensional Riemannian manifold to be isometrically immersed in Sn×R or Hn×R in terms of its first and second fundamental forms and of the projection of the vertical vector field on its tangent plane. We deduce the existence of a one-parameter family of isometric minimal deformations of a given minimal surface in S ×R or H × R, obtained by r...

The concept of a closure operator ∇ in an ADL R was introduced. If ∇R is the set of all ∇−invariant elements of R, then the concepts of ∇R−ideal, ∇R−prime ideal are introduced. The interrelations between ∇R−prime ideal and minimal prime ideal of R are derived. If B is the Birkhoff centre of R, then a sufficient condition is derived for a B−ideal to be a minimal prime ideal of R. Mathematics Sub...

We give a necessary and sufficient condition for an n-dimensional Riemannian manifold to be isometrically immersed in Sn×R or Hn×R in terms of its first and second fundamental forms and of the projection of the vertical vector field on its tangent plane. We deduce the existence of a one-parameter family of isometric minimal deformations of a given minimal surface in S2 ×R or H2 × R, obtained by...