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17 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).

30 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

30 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

7 Jul 2023: You may assume that thetransforms are well-defined.]. (c) Express the inverse transforms of cos ka and sin ka in terms of the δ-function,where a is a positive constant.

30 Aug 2019: where ka is the Killing vector associated with time translations. Briefly describe why thisintegral should be proportional to the mass.

12 Jul 2023: i) Assuming r = r+ is a Killing horizon of. ka =. (. v. )a,. determine the Hawking temperature TH of the Schwarzschild-AdS black hole.

30 Aug 2019: MATHEMATICAL TRIPOS Part III. Friday 6 June 2008 9.00 to 12.00. PAPER 65. APPLICATIONS OF DIFFERENTIAL GEOMETRY TO PHYSICS. Attempt FOUR questions. There are SEVEN questions in total. The questions carry equal weight. STATIONERY REQUIREMENTSCover

30 Aug 2019: EITHER : The Herbrand quotient and its role in norm index calculations for L/Ka cyclic extension of p-adic fields.

12 Jul 2023: iii) State Killing’s equation. Show that if Ka is a Killing vector, then Ja = TabKb.

20 Jul 2021: vector ka. END OF PAPER. Part III, Paper 309.