. SP ] 5 F eb 2 00 4 IF THEY ARE LIMIT PERIODIC ?

ar X iv : m at h / 05 02 06 9 v 1 [ m at h . SP ] 3 F eb 2 00 5 Triviality of the Peripheral Point Spectrum

If T t = e Zt is a positive one-parameter contraction semigroup acting on l p (X) where X is a countable set and 1 ≤ p < ∞, then the peripheral point spectrum P of Z cannot contain any non-zero elements. The same holds for Feller semigroups acting on L p (X) if X is locally compact.

. SP ] 2 F eb 2 00 1 SEMICLASSICAL ASYMPTOTICS AND GAPS IN THE SPECTRA OF MAGNETIC SCHRÖDINGER OPERATORS

In this paper, we study an L version of the semiclassical approximation of magnetic Schrödinger operators with invariant Morse type potentials on covering spaces of compact manifolds. In particular, we are able to establish the existence of an arbitrary large number of gaps in the spectrum of these operators, in the semiclassical limit as the coupling constant μ goes to zero.

ar X iv : m at h / 04 11 43 2 v 4 [ m at h . A G ] 7 F eb 2 00 5 Hypersurface Singularities and the Swing ∗ Lê

Suppose that f defines a singular, complex affine hypersurface. If the critical locus of f is onedimensional, we obtain new general bounds on the ranks of the homology groups of the Milnor fiber of f . This result has an interesting implication on the structure of the vanishing cycles in the category of perverse sheaves.

X iv : h ep - p h / 07 02 01 5 v 1 1 F eb 2 00 7 Pion form factor at very large Q 2

The pion form factor at very large Q2 is obtained by using a new pion wave function. It shows that when Q2 >> (1.8GeV )2 the pion form factor reaches the asymptotic limit αs(Q) Q .

- ex / 0 40 20 06 v 1 5 F eb 2 00 4 1 Photoproduction of the doubly - strange Ξ Hyperons