ar X iv : 0 80 7 . 12 85 v 1 [ nl in . A O ] 8 J ul 2 00 8 Collective Phase Sensitivity

ar X iv : 0 80 7 . 00 58 v 1 [ m at h . D G ] 1 J ul 2 00 8 EQUIVARIANT DIFFERENTIAL CHARACTERS AND SYMPLECTIC REDUCTION

We describe equivariant differential characters (classifying equi-variant circle bundles with connections), their prequantization, and reduction.

ar X iv : 0 80 5 . 09 92 v 2 [ m at h . C O ] 8 J ul 2 00 8 FIBONACCI IDENTITIES AND GRAPH COLORINGS

We generalize both the Fibonacci and Lucas numbers to the context of graph colorings, and prove some identities involving these numbers. As a corollary we obtain new proofs of some known identities involving Fibonacci numbers such as Fr+s+t = Fr+1Fs+1Ft+1 + FrFsFt − Fr−1Fs−1Ft−1.

ar X iv : 0 80 6 . 01 70 v 2 [ m at h . Q A ] 1 J ul 2 00 8 WEIGHT MULTIPLICITY POLYNOMIALS OF MULTI - VARIABLE WEYL MODULES

This paper is based on the observation that dimension of weight spaces of multi-variable Weyl modules depends polynomially on the highest weight (Conjecture 1). We support this conjecture by various explicit answers for up to three variable cases and discuss the underlying combinatorics.

ar X iv : 0 80 7 . 35 09 v 1 [ nl in . P S ] 2 2 Ju l 2 00 8 EXACT SOLITONS IN THE NONLOCAL GORDON EQUATION

We find exact monotonic solitons in the nonlocal Gordon equation utt = J ∗u−u−f(u), in the case J(x) = 1 2 e−|x|. To this end we come up with an inverse method, which gives a representation of the set of nonlinearities admitting such solutions. We also study u(iv) + λu′′ − sinu = 0, which arises from the above when we write it in traveling wave coordinates and pass to a certain limit. For this ...

ar X iv : h ep - p h / 03 07 03 8 v 1 2 J ul 2 00 3 1 Scalar meson exchange in Φ → P 0 P 0 γ decays ∗