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18 Jan 2007: G. Worster. (a). (b). (c). 12 cm. (b). (b). (a)(d). (c). ... dz= kl. d2T. dz2 b(T T). (2.3). 72 S. S. L.

25 Oct 2007: b) Let R([0, 1]. )denote the vector space of all integrable functions on [0, 1]. ... An interval is a set taking one of the forms (, ), (, b), (, b], [a, ), (a, ), [a, b], [a, b), (a, b]or (a, b) for some a, b R with a b.

5 Oct 2007: b) Use (a) to show that every finitely presented group is the fundamental groupof some space. ... Suppose that the maps A A′, B B′, D D′, and E E′ are isomorphisms.Show that the middle map γ : C C′ must be an isomorphism, as follows.

31 Jul 2007: e-. e+. H0. Z0Z0. b. b. q. q. Higgs couples to mass –so need to produce it from a massive particle decays tothe most massive particles allowed. ... e-. e+. H0. Z0Z0. b. b. q. q. Made on 30-A.

3 Jun 2007: 2. Let T : z 7 (az b)/(cz d) be a Möbius transformation.24. ... s s2 1 and s. s2 1. where. s =|a|2 |b|2 |c|2 |d|2.

26 Oct 2007: 3. Two players A and B play a best of 5 set tennis match. ... Hint: Recall that H(A,B) = H(A|B) H(B).]. (b) Show that. H(I|Y,X) = 0.

5 Oct 2007: Hn1(K) Hn(A B). Hn1(f ). y yHn(f )Hn1(K′). Hn(A′ B′). (b) Show that if the maps Hi(AB) Hi(A′B′), HiA HiA′, and HiB ... is not a 2-manifold.(b) Let K be an n-dimensional pseudomanifold. Show that Hn(K) is isomorphic.

30 Jul 2007: B. B throws a heavy balltowards A. B exerts forceon ball – ball exerts an equal and opposite force on B (N3) and B recoils (N2). ... A. B. A. B. B emits ball and A absorbs it.

3 Jun 2007: Find a continuousfunction B : R which is harmonic on and has B| = b. ... Note that the function B need no longer be uniquely determined by b.

25 Jan 2007: We can now define a further Lorentz scalarFµν G. µν = 4 E.B. ... D. j.E dV 1. µ0. D. E. curl B B.