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7 Aug 2002: some consequence of (ii) and (iii) without really knowing where it was going. ... Earlier we promised to choose b at some point. Clearly it should be chosen to be a.

9 Sep 2002: This is described in more detail in Section 2.5. We close the introduction by describing some of the elements of the proofs ofTheorems A and B, and by describing a ... Moreover, every ZZ subgroup of π1(M) isconjugate into the fundamental group of some

6 Mar 2002: b in B (that is, some non-zero b (mod p)) such that the set of all bx. ... Hence, if we can find some b that does not belong to A, then we have constructed the desired injection.

12 Oct 2002: In some sense a flow is a collection of integral curves.Wenotebut shall notprove that the smoother thevectorfield the smoother. ... for some > 0 then the Fourier transform and Fourier inverse transform ofq is Cl.

21 Jun 2002: We suppose for a contradiction that S has positive degree.Then S(φ) = 0 for some φ = u(a,b) and R(φ) = f(a,b)S(φ) = 0. ... 26). Let φ 2V W be an elliptic normal quintic. Then φ = (gV ,gW )u(a,b)for some (gV ,gW ) SL(V ) SL(W ) and (a,b) A.

25 Apr 2002: Then, with some embarrassment, we note to ourselves that we can solve the equation when a = 0. ... 1. Is there a similar way to simplify a cubic so that some of the coefficients become zero?

9 Sep 2002: We would like to close this introduction by illustrating some of the ideas withspecific examples. ... of H2s(M,Z) always has the form B Bor B B Z2 for some finite abelian group B.

10 Sep 2002: It has complexity w. 2. if after the first move the game has complexity awb for some a,b. ... x. for some x in X, and the map x goes to t.

12 Sep 2002: 13. (ii) A theorem of A has a consequence in B, but it takes some work to prove it. ... rithms 1, 221-230. [K] B. S. Kashin, Sections of some finite dimensional sets and classes of smooth functions,.