Necessary Conditions for Attaining a Crystalline Beam

Necessary Conditions for Attaining a Crystalline Beam

Molecular dynamics is employed to study the nature and magnitude of beam cooling that is required in order to achieve a crystalline beam. Analysis is presented of a number of cooling systems now in use, or whose use is contemplated, none of which has been shown to be able to achieve the crystalline state. However, for an adequately strong cooling system that produces on average a constant angul...

Some Results on Necessary Conditions for Tow Quasidifferentiable Optimization Problems

New Necessary Conditions for

In this paper, we obtain several nonexistence results for abelian Hadamard diier-ence sets. In particular, we prove that there are no Hadamard diierence sets in abelian groups G = Z 2 Z 2 P , where jPj = p 2 , is odd and p is a prime congruent to 1(mod 4). Also we give a detailed proof for a connection between certain reversible Hadamard diierence sets and projective three-weight codes which wa...

Necessary and Sucient Optimality Conditions for a Control Fuzzy Linear Problem

Necessary Conditions for Subdivision Surfaces

Subdivision surfaces are considered which consist of tri-or quadrilateral patches in a mostly regular arrangement with nitely many irregularities. A sharp estimate on the lowest possible degree of the patches is given. It depends on the smoothness and exibility of the underlying subdivision scheme.