ar X iv : c s . C C / 0 70 11 23 v 1 19 J an 2 00 7 Feasible Depth

ar X iv : 0 71 0 . 35 19 v 1 [ cs . C C ] 1 8 O ct 2 00 7 P - matrix recognition is co - NP - complete

This is a summary of the proof by G.E. Coxson [1] that P-matrix recognition is co-NP-complete. The result follows by a reduction from the MAX CUT problem using results of S. Poljak and J. Rohn [5].

ar X iv : 0 70 7 . 40 46 v 1 [ m at h . A G ] 2 7 Ju l 2 00 7 CLIFFORD ’ S THEOREM FOR COHERENT SYSTEMS

Let C be an algebraic curve of genus g ≥ 2. We prove an analogue of Clifford’s theorem for coherent systems on C and some refinements using results of Re and Mercat.

ar X iv : 0 70 7 . 14 19 v 1 [ he p - ph ] 1 0 Ju l 2 00 7 Unparticle as a field with continuously distributed mass

We point out that the notion of an unparticle, recently introduced by Georgi, can be interpreted as a particular case of a field with continuously distributed mass considered in ref.[11]. We also point out that the simplest renormalizable extension of the SU c (3)⊗SU L (2)⊗U (1) Standard Model is the extension with the replacement of the U (1) gauge propagator 1 k 2 → 1 k 2 + ∞ 0 ρ(t) −t+k 2 +i...

ar X iv : c s . C G / 0 70 30 23 v 1 6 M ar 2 00 7 Computing a Minimum - Dilation Spanning Tree is NP - hard ∗

In a geometric network G = (S,E), the graph distance between two vertices u, v ∈ S is the length of the shortest path in G connecting u to v. The dilation of G is the maximum factor by which the graph distance of a pair of vertices differs from their Euclidean distance. We show that given a set S of n points with integer coordinates in the plane and a rational dilation δ > 1, it is NP-hard to d...

ar X iv : 0 70 4 . 33 68 v 2 [ gr - q c ] 2 6 A pr 2 00 7 Search for gravitational waves from binary inspirals in S 3 and S 4 LIGO data