This paper describes the application of a combined orthogonal array design and overlapping resolution mapping to the optimization of miceller electrokinetic chromatography for the separation of 10 substituted benzenes. The most important factors were first determined according to an OA16(2(15)) through 16 pre-designed experiments; a second set of experiments was carried out according to a trian...

1. Introduction Generators for the groups SL(l; q), Sp(2m; q), U(l; q) and Sz(q) have been available in computer algebra systems for some time 1, 4, 12]. Until recently it has only been practical to work with these groups for small dimensions and small elds. This covered small orthogonal groups (but not in their natural representation) because the orthogonal groups up to dimension 6 are isomorp...

We give a lower bound for the essential dimension of a split simple algebraic group of “adjoint” type over a field of characteristic 2. We also compute the essential dimension of orthogonal and special orthogonal groups in characteristic 2.

In this paper we give the definitions and calculate the orders of some subgroups of GL(m,Zn) similar to the classical linear subgroups of the general linear group over any field. Specifically, the special modular linear group SL(m,Zn), the orthogonal modular group O(m,Zn), the special orthogonal modular group SO(m,Zn) and finally the symplectic modular group Sp(2m,Zn). The technique used consis...

The little Grothendieck problem consists of maximizing Σ ij Cijxixj for a positive semidef-inite matrix C, over binary variables xi ∈ {±1}. In this paper we focus on a natural generalization of this problem, the little Grothendieck problem over the orthogonal group. Given C ∈ ℝ dn × dn a positive semidefinite matrix, the objective is to maximize [Formula: see text] restricting Oi to take values...