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14 Jun 2024: a and b, and writing for the group operation, we do not necessarily have ab=ba).

30 Aug 2019: a) Use suffix notation to prove that. a (b c) = c (a b). ... r (a b b c c a) = a (b c),.

22 Aug 2023: i) Order the vectors by magnitude. (ii) Use the scalar product to find the angles between the pairs of vectors (a) A and B, (b) B and C,leaving your answer ... iii) Find the lengths of the projections of the vectors (a) A onto B, (b) B onto A.

30 Aug 2019: a) Let G act on B B by g(B1,B2) = (gB1, gB2). ... B B | (B,F(B)) O(w)}. Show that X(w) can be identified with the variety L1(BwB)/B, for a rational Borelsubgroup B, and show that there exists a

30 Aug 2019: µ0ρ(B b b B),. b. t= B u u B. Consider solutions of the form u(s, φ, z, t) = ũ(s, z)eσtimφ, etc., where m is aninteger. ... Then verify that. B b b B = Jẑ b 12imJb,.

30 Aug 2019: ρ. t+ u ρ = ρ u ,. p. t+ u p = γp u ,. ρ. (ut. u u). = ρΦ p 1µ0. ( B) B ,. Bt. = (u B) , B = 0. STATIONERY REQUIREMENTS SPECIAL REQUIREMENTSCover sheet ... δρ = ξ ρ ρ ξ ,δp = ξ p γp ξ ,. δB = ξ B B ξ B( ξ) ,. ρ2ξ. t2= δΠ g δρ

30 Aug 2019: Now suppose given a frame homomorphism h : B A. We say two nuclei j andk on A are B-equivalent if j(h(b)) = k(h(b)) for all b B. ... By considering the nucleus{o(h(b)) c(j(h(b))) | b B} (where j is an arbitrary nucleus), show that each B-.

30 Aug 2019: Bt u B = B u α B η2B,. where α is a constant and where the simple shear flow u = T 1(y, 0, 0). ... 2 A model for an “α2” dynamo, analogous to the Parker wave model, is given bythe equations (where A = A(x, t), B = B(x, t)):.

30 Aug 2019: H(,B) are natural in B B. Part III, Paper 22. 3. ... B(KB′,B)B(ρ. B′,B). B(B′,B). is a bijection. (iii) ρB : B KB is an isomorphism in B.

30 Aug 2019: ρ. t+ uρ = ρu ,. p. t+ up = γpu ,. ρ. (u. t+ uu. )= ρΦ p 1. µ0( B) B ,. B. t= (u B) ,. B = 0 ,2Φ = 4 π Gρ. ... iωu = p̃ 1µ0ρ. (imJb 2Jêz b) ,. iωb = imJu ,. where p̃ is a modified pressure and ρ is the fluid density.