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26 Nov 2012: D2 det |I as a bilinear map. 9. Let f : R2 R and (a, b) R2. ... D2f exists at (a, b). Show that f is differentiable at (a, b).

28 Nov 2012: Forexample if a,b C and x,y,z V , then. (x,ay bz) =1. ... Then 〈Pa,Pb〉 = (a,b) for a,b V. So for each g G.

21 Nov 2012: 3. The symmetric difference of sets A and B is A B = (A B) (B A). ... 8. Define a relation R on N by setting aRb if a divides b or b divides a.

27 Jan 2012: likelihood estimate of θ is (2a b)/(b 2c). 5. (a) Let X1,. ... b) For some n > 2, let X1,. ,Xn be iid with Xi Exponential(θ).

15 Oct 2012: possible area is an arc of a circle passing through A and B. ... where n = n(s) and b = b(s) are the normal and binormal vectors of α.

26 Apr 2012: Then 〈Pa,Pb〉 = (a,b) for a,b V. So for each g G. ... P1gPa,P1gPb) = 〈gPa,gPb〉 = 〈Pa,Pb〉 = (a,b).Thus P1gP Un(C) for each g G as required.

27 Nov 2012: Let (M,g) be a Riemannian manifold. A curve γ : (a,b) Mis said to be a geodesic if it locally minimises arc length, i.e. ... integral curve of V with γ(0) =, then T a < b T+ andγ|(a,b) = γ̃.

8 Oct 2012: This basis B has the niceproperty that T C(B) B is wellfounded: the bad sets are declared in terms of eachother and wellfounded sets only. ... It sendsatoms to themselves, and if b B is a set of atoms in MB we want i(b) to beb if b is finite and b (A B)

14 May 2012: In section 7 we prove Theorem B, and in section 8 we proveTheorem D. ... a) is [54, Proposition 4.5] and (b) is [15, Theorem 3.9].

27 Nov 2012: Then b is a scalar multiple of a, say b = ta witht R. ... So b′ = b ka is also in Λ and has.

24 Feb 2012: Every set Hb occurs in the numbering exactly once. More precisely, all b B areindices of sets Hb occurring in the numbering F0,F1,F2,. ; ... The class {B : B m A} is calledthe many-one degree of A.