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2 Jun 2015: Some of the potential applications are described in[1], [3], [8], [13], [19]. ... To find some interesting examples over Q(T), we seta = b = 27j/(4(j 1728)) to obtain a model for Z(9), fibred over the j-line.

11 Sep 2015: for some a,b K. The discriminant condition is 2b(a2 4b) 6= 0. ... for some ξ3 K.Let L = K(. b/ξ1) and write f(l,m) = κ(l εm)(l εm) where κ K and.

22 Sep 2015: a. (1 exp(at). )exp at. = B exp at Ca. for some constant B. ... for some constant B. 106. If h(t) = C exp at for all t,.

7 Aug 2015: blow-ups.By Lemma 3.4(b), there exists some a > 0 such that πaτOY τ](OX) τOY.Applying Γ(X ,) produces inclusions πaO(Y) O(X) O(Y) inside ... X). Bysymmetry, we also obtain πbO(Y) O(X ′) O(Y) for some b > 0.

20 May 2015: i) = 0 for some λi F not all zero.Suppose that λk 6= 0 and let B be the matrix with ith column ei for i 6= k and. ... vector spaces. Definition. We say matrices A and B are similar (or conjugate) if B = P1APfor some invertible matrix P.

2 Dec 2015: tmin T distinct such that t0 =. mi=1 λiti for some λi F. ... LINEAR ALGEBRA 15. Suppose first thatki=1 λifi = 0 for some λi F.

10 Dec 2015: We now give some indications on the proof, concentrating for definiteness on the more difficult case,n = 8. ... are regular algebraic up to twist(and which is solved in some cases in 6).

10 Mar 2015: c(m) = c(a1)c(a2)c(a3). c(aN1)c(aN ) B. This is then transmitted via some channel to the receiver who needs to decode it to recover the ... Lecture 7 24. A code is said to be perfect if it is e-error correcting for some e and the balls B(c(a),e 1)