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13 Jun 2008: It focuses on:.  visual and simple.  the fact that the first 20% of effort gets 80% of the result.

27 Jan 2008: 20. for sufficiently small t. We will prove this. Let (U,ϕ) be a chart containing p then, in thesecoordinates, τ will have the form.

3 Jul 2008: Now consider the integrated form of the first equation of (1.20) (i.e. ... and corresponding Sobolev norms ‖ ‖Hs on the space of sections defined as in [20].

1 Jul 2008: ρ0. z. (ρ0f. 20. N2. ψ′. z. )= q′ , (15).

1 Jul 2008: 4, 8, 14, 17, 19, 20] andsetting c = 0, b = 1 gives the dKP equation. ... Math. Phys. 273 357–78. [20] Pavlov M V 2003 Integrable hydrodynamic chains J.

30 Sep 2008: ψ(x, t) = χ(x) exp. (. iEt. ). (20). Substituting for (20) for ψ in the Schrödinger equation yields the time-independent. ... States of the special form (20) are known as stationary states.

3 Jun 2008: 20. with (x1,x2) = (x,y) yields a second order ODE of the form.

3 Jul 2008: 4π. jφp(x)d x = d.}. (20). Observe that V2 = V sinceu(φ) = K( jφ σ). ... because h φ W 1,20 (Br)). c θ. p2. 0. (s R)2.

26 Feb 2008: f (x1)f (x2). =f (αx1)f (αx2). 20. for any α. (If we changed our units of length from metres to centimetres, for instance, we would haveα = 100.).

8 Apr 2008: Mathematical Tripos Part IB 2007. COMPLEX METHODSSummary. 0. Introduction. Aims: to explain the application of complex-variable theory to. (i) Harmonic functions (and hence to Laplace’s equation in two dimensions).(ii) Real integration(iii)