We study the half-integral k-Directed Disjoint Paths Problem ( 2kDDPP) in highly strongly connected digraphs. The integral kDDPP is NP-complete even when restricted to instances where k = 2, and the input graph is L-strongly connected, for any L ≥ 1. We show that when the integrality condition is relaxed to allow each vertex to be used in two paths, the problem becomes efficiently solvable in h...

Let V be a real finite dimensional representation of a compact Lie group G. It is well-known that the algebra R[V ] of G-invariant polynomials on V is finitely generated, say by σ1, . . . , σp. Schwarz [38] proved that each G-invariant C-function f on V has the form f = F (σ1, . . . , σp) for a Cfunction F on R. We investigate this representation within the framework of Denjoy–Carleman classes....

The group PGL(2, q) has an embedding into PGL(3, q) such that it acts as the group fixing a nonsingular conic in PG(2, q). This action affords a coherent configuration R(q) on the set L(q) of non-tangent lines of the conic. We show that the relations can be described by using the cross-ratio. Our results imply that the restrictions R+(q) and R−(q) of R(q) to the set L+(q) of secant (hyperbolic)...

Hosik Lee,1 Young-Woo Son,1 Noejung Park,2 Seungwu Han,3 and Jaejun Yu1,* 1School of Physics and Center for Strongly Correlated Materials Research, Seoul National University, Seoul 151-747, Korea 2Department of Applied Physics, Dankook University, Seoul 140-714, Korea 3Department of Physics, Ewha Womans University, Seoul 120-750, Korea Received 23 May 2005; revised manuscript received 14 Septem...