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30 Aug 2019: kaakb = κkb. evaluated on the horizon, where ka is the time translation Killing vector.

30 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.

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

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

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.

30 Aug 2019: ka and the final state is a fernionic particle of 4-momentum qa and a scalar with 4-.

30 Aug 2019: spacelike) Killing vector. ka. xa=. z. and that the d-dimensional background metric is of the form.

30 Aug 2019: S = 12. (. F F kA F F). (1). where F is a four-form and A a three-form such that F = dA, and k is a constant.