ar X iv : 1 10 6 . 33 18 v 2 [ m at h . L O ] 2 3 Ju n 20 11 EFFECTIVE VERSIONS OF LOCAL CONNECTIVITY PROPERTIES

ar X iv : 0 90 6 . 18 57 v 1 [ m at h . C O ] 1 0 Ju n 20 09 On the circumference , connectivity and dominating cycles

Every 4-connected graph with minimum degree δ and connectivity κ either has a cycle of length at least 4δ − 2κ or has a dominating cycle.

ar X iv : 0 70 7 . 33 03 v 1 [ m at h . O A ] 2 3 Ju l 2 00 7 OPERATOR - VALUED FRAMES

ar X iv : m at h / 06 06 33 9 v 1 [ m at h . SP ] 1 4 Ju n 20 06 Eigenfunction expansions associated with 1 d periodic differential operators of order 2 n

We prove an explicit formula for the spectral expansions in L(R) generated by selfadjoint differential operators (−1) d dx2n + n−1

ar X iv : n uc l - th / 0 11 20 08 v 2 1 5 Ju l 2 00 2 Theoretical Study of the 3 He ( μ − , ν μ ) 3 H Capture

ar X iv : 0 70 4 . 17 02 v 2 [ m at h . A G ] 2 6 Ju n 20 08 THE CANONICAL VOLUME OF 3 - FOLDS OF GENERAL TYPE WITH χ ≤ 0

We prove that the canonical volume K ≥ 1 30 for all 3-folds of general type with χ(O) ≤ 0. This bound is sharp.