We show that there exist a finite number of Cartan subgroups up to conjugacy in SL2(Qp) and we describe all of them. We show that the Cartan subgroup consisting of all diagonal matrices is generous and it is the only one up to conjugacy.

The ratio of pulmonary to systemic vascular resistance (Rp/Rs) largely determines the amount of left-to-right shunting and pulmonary to systemic flow rat (Qp/Qs) in the presence of a large isolated ventricular septal defect. The possibility that pharmacologic reduction of systemic vascular resistance with alpha-adrenergic receptor blockade or beta-adrenergic receptor stimulation would increase ...

We describe a branch-and-bound algorithm for the quadratic assignment problem (QAP) that uses a convex quadratic programming (QP) relaxation to obtain a bound at each node. The QP subproblems are approximately solved using the Frank-Wolfe algorithm, which in this case requires the solution of a linear assignment problem on each iteration. Our branching strategy makes extensive use of dual infor...

Introduction Let P = p1, . . . , pn be a simple polygon (all polygons are assumed convex throughout this paper). A fundamental problem in geometric optimization is to compute a minimum-area or a minimum-perimeter convex k-gon (denoted QA or Qp, resp.) that encloses P . While efficient algorithms for finding QA are known for more than 20 years [8, 1, 2], the problem of finding Qp has remained op...

We consider the set σP of the power non-negative polynomials of several variables.By QP we denote the class of the polynomials from σ1 which can be represented as a sum of squares.It is shown in the classic work by D.Hilbert[3] that QP does not coincide with σP .Step by step a number of polynomials belonging to σP but not belonging to QP was constructed(see[4]-[6]).It is interesting to note tha...

A poor bolus injection results in an unsatisfactory quantitative radionuclide angiocardiogram in as many as 20% of children with possible, left-to-right (L-R) cardiac shunts. Deconvolution analysis was applied to similar studies in experimental animals to determine whether dependence on the input bolus could be minimized. Repeated good-bolus, prolonged (greater than 2.5 sec), or multiple-peak i...

So far, we have used Integer Programs and their relaxation to Linear Programs, in order to obtain approximation algorithms for NP Complete problems. We will demonstrate how we can use Quadratic Integer Programs (QIP) for the same purpose, producing approximation algorithms for NP Complete problems, with better bounds than the previously devised algorithms. The general form of a QIP is the follo...