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19 May 2007: Bipartite graphs of approximate rank 1. W. T. Gowers. 1. Introduction. Quasirandomness is a central concept in graph theory, and has played an important. part in arithmetic combinatorics as well. Roughly speaking, a notion of quasirandomness. for a

18 Sep 2007: 24. Q 10.4. (i) Write out the standard properties of powers xα when x and αare real and x > 0. ... In case (iv) you may find it useful to consider the effect of a translationfollowed by the map z 7 1/z.]Q 10.24.

18 Sep 2007: 24. and (sin z)2 (cos z)2 = 1 for all z, w C.(iv) sin(z) = sin z, cos(z) = cos z for all z C.(v) sin and cos

20 Apr 2007: 24. Definition 7.19. Suppose G is a group acting on a non-empty set X.

28 May 2007: 5, 3/5)2, then removing the middle 1/25th of each of the remaining 24 squares,and so on.

3 Jun 2007: 2. Let T : z 7 (az b)/(cz d) be a Möbius transformation.24.

26 Nov 2007: Methods for 4-descent and8-descent have been developed in the PhD theses of Siksek [18], Wom-ack [24] and Stamminger [20]. ... The generalisations to 3-coverings and 4-coverings aredescribed in [6] and [24].

5 Apr 2007: 24. Another celebrated Corollary of Theorem 5.3 is the so-called Closed graphtheorem.

8 Nov 2007: 232.1.4 The Einstein-Vlasov system. 24. 2.2 The initial value problem. 252.2.1 The constraint equations. ... Tµνvµvν 0. 24. Finally we have. Definition 2.12. Let (M,g) be a spacetime and f : P R a non-negativefunction.

2 Mar 2007: consider, the former was undergoing substantial development largely stimulated. by Lawvere (see [24,25,26,27]). ... on to characterise the category Set [24], a line of work which eventually led to the.