Search

16 Jan 2008: Show that for any vector x,Ax may be written as! x for some suitable! ... σij = 2µ(eij 13 δij ekk) pδijfor some scalar µ known as the coefficient of viscosity.

25 Feb 2008: iv) F = φ for some function φ(x). In such a case, φ. ... dx = dφ, so BA. F. dx = B. A. dφ = φ(B) φ(A).

17 Jan 2008: Given that the particle’s trajectoryis r = a sin θ for some constant a, deduce that (up to an arbitrary additive constant)V r4. ... ithou. t per. mis. sion. 10 If µ(r) = |f (r)| for some function f , show that B.

17 Nov 2008: Therefore the integral curves of (3.1) are geodesics of some projective structure (anequivalence class of torsion-free connections sharing the same unparametrized geodesics). ... 3a3 ka c. where b and c are some constants. The pure dust case considered

26 Feb 2008: for some a, b, c, d, e, f R. By rotating the axes and shifting the origin (using ideas from the Part IBcourse Linear Algebra) we can always transform such an ... However, it. also works if the force is proportional to u3, or some linear combination of u2

8 Apr 2008: 7. 1.5 Application to Laplace’s equation. Suppose we wish to solve 2Ψ = 0 in some region B C , with Ψ(x,y) = Ψ0 on aboundary B with a complicated ... parameterising z z0 = ρeiθ with a ρ b). 11. Some Remarks.

11 Jul 2008: 10. Some time ago Grossman & Larson (1989) identified theButcher group,the algebraic struc-ture underlying B-series, with aHopf algebra. ... Mielnik, B. & Plebánski, J. (1970), ‘Combinatorial approach to Baker–Campbell–Haussdorfexponents’,Ann.

3 Jun 2008: Ampereequation, but not between solutions as some integral surfaces may have dx dy = 0. ... How can you tell whether these curves are the geodesics of some metric?

5 Dec 2008: ed w. ithou. t per. mis. sion. 2 Some Simple Flow Fields. ... 2.1 Poiseuille and Couette Flow. There are some flows which are rectilinear and this leads to considerable simplifications.

3 Jul 2008: Demoulini, D.M.A. Stuart. for some τi j L p2 W 1,p. ... 2 S2(which has an extension to a non constant harmonic map S2 S2.)Proof It is immediate from Lemma 15 that if |φν|L (B(y,r)) L < for some