ar X iv : m at h / 03 02 33 9 v 1 [ m at h . A P ] 2 7 Fe b 20 03 NONLINEAR SCHRÖDINGER EQUATIONS WITH STARK POTENTIAL

ar X iv : h ep - p h / 03 02 18 5 v 1 2 0 Fe b 20 03 Nonlinear corrections to the DGLAP equations ; looking for the saturation limits ∗

The effects of the first nonlinear corrections to the DGLAP equations are studied in light of the HERA data. Saturation limits are determined in the DGLAP+GLRMQ approach for the free proton and for the Pb nucleus.

ar X iv : m at h / 03 02 12 9 v 1 [ m at h . A P ] 1 1 Fe b 20 03 Singular and regular solutions of a non - linear parabolic system

We study a dissipative nonlinear equation modelling certain features of the Navier-Stokes equations. We prove that the evolution of radially symmetric compactly supported initial data does not lead to singularities in dimensions n ≤ 4. For dimensions n > 4 we present strong numerical evidence supporting existence of blow-up solutions. Moreover, using the same techniques we numerically confirm a...

ar X iv : h ep - p h / 03 02 12 9 v 1 1 7 Fe b 20 03 Scalar σ meson effects in radiative ρ 0 - meson decays

ar X iv : m at h / 03 02 20 2 v 1 [ m at h . C O ] 1 8 Fe b 20 03 PERIODIC DE BRUIJN TRIANGLES : EXACT AND ASYMPTOTIC RESULTS

We study the distribution of the number of permutations with a given periodic up-down sequence w.r.t. the last entry, find exponential generating functions and prove asymptotic formulas for this distribution. §

ar X iv : m at h / 02 01 22 7 v 2 [ m at h . SP ] 1 3 Fe b 20 03 PROJECTION METHODS FOR DISCRETE SCHRÖDINGER OPERATORS

Let H be the discrete Schrödinger operator Hu(n) := u(n − 1) + u(n + 1) + v(n)u(n), u(0) = 0 acting on l(Z) where the potential v is real-valued and v(n) → 0 as n → ∞. Let P be the orthogonal projection onto a closed linear subspace L ⊂ l(Z). In a recent paper E.B. Davies defines the second order spectrum Spec2(H,L) of H relative to L as the set of z ∈ C such that the restriction to L of the op...