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3 Jul 2008: For the first time, the asymptotics of type (1.2) were established by Soffer and Weinstein[24, 25] (see also [20]) for nonlinear U(1)-invariant Schrödinger equation with small initial ... c(ν)(t s)1/2(‖η(s)‖2Lβ ρ‖η(s)‖Lβ. ), 0 < t s < ν.

29 Jan 2008: B. PerrinLaboratoire Pierre Aigrain, UMR 8551, CNRS, Ecole Normale Supérieure,Département de Physique, 24 rue Lhomond, 75231 Paris Cedex 05, France. ... Combining Eqs. 21, 24, and 25 leads to the nonlin-ear diffusion equation satisfied by the local

18 Mar 2008: eA00fA D 0; (24)eA10fA D 0: (25). Anti-self-dual conformal structures in neutral signature 123. ... 4Other terminology includes neutral hyper-Kähler [28] and hyper-para-Kähler [24]. Anti-self-dual conformal structures in neutral signature 127.

30 Sep 2008: with width 1/σ (See figure (13)) We will now evaluate the resulting wave-function bysubstituting (24) for A in (23),. ... ψ|2U. 0x0(t). Figure 24: Initial state of wavepacket. x. |ψ|2U. 0.

13 Jun 2008: On the basis of 24 successful projects over the initial three years of NaTII, the estimated budget is £7 million.

23 Sep 2008: f• -. •'(y, z) (24). and the mean meridional and vertical velocities •,fv satisfy a zonally symmetric mass-conservation equation of the form. ... A more accurate 92 - version of (26), based on a more accurate version of (24), is presented by P.

25 Sep 2008: For = (ts t) 1 it follows from (3) and (23)that the dimensional blowing velocity has magnitudev̂b = O(U Re12 74 ) : (24)This blowing velocity causes a perturbation to the inviscid ... the continuity equation it follows thatthe perturbation velocity in

24 Apr 2008: d4x Tr (δAµ δAµ) = 2Sinst ρ2 (1.24). Note that, unlike the others, this component of the metric depends on the collective. ... in 5 1 dimensions is a sigma-model on a hyperKähler target space [24] which, for.

6 May 2008: L. (3.24). By taking logarithms of both sides of expression (3.23), we find the inequality.

3 Jul 2008: as2@cam.ac.uk. eived 9 March 2007epted 24 July 2007 2753 This journal is q 2007 The Royal Society.