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MATHEMATICAL TRIPOS Part III Monday 13 June, 2005 9 ...
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2005/Paper62.pdf30 Aug 2019: kaakb = κkb. evaluated on the horizon, where ka is the time translation Killing vector. -
MATHEMATICAL TRIPOS Part II Friday 9 June 2006 9 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2006/PaperII_4.pdf17 Jun 2019: If Ka are the components of a contravariant vector field and gab the componentsof a metric tensor, let. ... In a particular co-ordinate system (x1,x2,x3,x4), it is given that Ka = (0, 0, 0, 1),Qab = 0. -
MATHEMATICAL TRIPOS Part III Tuesday 12 June 2001 9 ...
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2001/Paper76.pdf30 Aug 2019: MATHEMATICAL TRIPOS Part III. Tuesday 12 June 2001 9 to 12. PAPER 76. COMBINATORIAL NUMBER THEORY. Attempt any THREE questions. The questions carry equal weight. You may not start to read the questions. printed on the subsequent pages until. -
MATHEMATICAL TRIPOS Part IA Friday, 2 June, 2017 1:30 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2017/paperia_2_0.pdf17 Jun 2019: For all N, find integers ka(N) and kb(N)such that. kb(N). k=ka(N). -
MATHEMATICAL TRIPOS Part IB Friday 8 June 2001 1.30 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2001/PaperIB_4.pdf17 Jun 2019: cosh kx cosh ka),. where k is a constant such thatlk = 2 sinh ka. -
MATHEMATICAL TRIPOS Part II Alternative B Wednesday 2 June ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2004/PaperIIB_2.pdf17 Jun 2019: Let N(k) = aR′(a)/R(a). Show that. tan δ(k) =N(k) j(ka) kaj′(ka)N(k) n(ka) kan′(ka). -
MATHEMATICAL TRIPOS Part II Wednesday, 2 June, 2010 9:00 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2010/PaperII_2.pdf17 Jun 2019: tan(ka δ0). ka=. tan κa. κa,. where κ2 = k 2 γ 2. ... Part II, Paper 2 [TURN OVER. 22. 36B General Relativity. A vector field ka which satisfies. -
MATHEMATICAL TRIPOS Part III Monday 9 June 2003 1.30 ...
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2003/Paper25.pdf30 Aug 2019: iii) Deduce from Plünnecke’s inequality that if A is a subset of an Abelian group,|A A| 6 C|A| and k, l are positive integers, then |kA lA| 6 -
MATHEMATICAL TRIPOS Part III Monday 9 June 2003 1.30 ...
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2003/Paper56.pdf30 Aug 2019: MATHEMATICAL TRIPOS Part III. Monday 9 June 2003 1.30 to 4.30. PAPER 56. BLACK HOLES. Attempt THREE questions. There are four questions in total. The questions carry equal weight. You may not start to read the questions. printed on the subsequent -
MATHEMATICAL TRIPOS Part III Friday 9 June, 2006 9 ...
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2006/Paper63.pdf30 Aug 2019: where ka is the Killing vector associated with time translations. Briefly describe why thisintegral should be proportional to the mass.
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