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15 Aug 2012: In advanceof stating this theorem, we present some further notation. Let C1,C2,. ... πD be a collection of site-disjoint green paths of Γ1, each joining some.

15 Aug 2012: for some functions a and b which are slowly varying as p pc. ... Potts, R. B. (1952). Some generalized order-disorder transformations. Proceedings of the Cam-.

15 Aug 2012: Theprobability that this construction ultimately includes some vertex of B dependstherefore only on the marginal probabilities. ... If Un Vn in D(n), we may pick an oriented path π of D(n) joining some.

26 Oct 2012: or(b)is of not less than five years’ standing from admission to his or her first degree of some other university and has been admitted (i) to some office in ... case the Degree Committee have allowed a candidate to submit material in some other language

28 Feb 2012: where α = 12(1. 71). Find an element of OK with norm 2a 3b 5 for some. ... Hint: Use that some power of a is principal.]. The following extra questions are on cyclotomic fields.

5 Nov 2012: 3.17. (i) Let f K(X). Show that K(X) = K(f) if and only if f = (aX b)/(cX d)for some a, b, c, d K with ad ... Deduce that every finite abelian group is the Galois group of some Galois extension K/Q.[It is a long-standing unsolved problem (inverse Galois

11 Apr 2012: More generally, for A, B Zdwe write A B (and similarly for the other relations) if a b for some a A and b B. ... directed edge from some x to x ed liesin no more than one of πa,b , πu,v.

6 Jun 2012: large number of individual members each interacting with their environment in some way. ... sequence of interactions.). In this course we consider mostly approach (A), but include some of approach (B).

24 Jul 2012: exp(iNαj) λj| < ǫ. for each 1 j M. Our construction requires some preliminary results. ... 14. 5 Some simple geometry of numbers. We need the following extension of Theorem 35.

8 Nov 2012: X R which satisfies (for some positivenumbers‖B‖, γ):. • ... whereP is any strictly positive polynomial (i.e.P (x) θ > 0 for some realθ.

13 Mar 2012: The event was attended by some of Europe’s leading businesses and academic institutions. ... Key challengesTogether with presentations drawn from current research at. the EITIM universities, the comparison of practices at these leading companies

2 Sep 2012: Despitethis complex form, the PDFs exhibit self-similarity undera diffusive scaling. Some physical considerations that maybe important in a theory of these results are suggested.Microscopy of Chlamydomonas suspensions was carried. ... There is some out-of

18 Oct 2012: Some peopledon’t require v(K) 6= {0} (so allow the “trivial valuation”).Examples. ... p 1}. for some N. In either case, vp(x) = min{n | an 6= 0}.

26 Oct 2012: Such a candidate shall offer the papers currently listed in Regulation 24(b). ... Paper A3 may include questions on literary, cultural, linguistic, or historical topics, some of which may be based on more extensive material in the foreign language, as

20 Apr 2012: such that Pa,b(Xm = a0,Ym = b0) > 0 for some m 0. ... To obtainthe necessary bounds on the exit times from the region B we now make precise some of theheuristics given above.

8 May 2012: 2I[y](φ) 0φ V0. Lemma 5.0.3 (Sufficient conditions) Assume y V is such that DI[y](φ) = 0φ V0 andthe second variation satisfies, for some c > 0,. ... One. explicit approach to determining whether (5.2) holds for some c > 0 is to calculate the

28 Nov 2012: F maps some neighbourhood U of x dif-feomorphically onto a neighbourhood V of (y,T(x)). ... for some function τ(s). (Note that 〈b, ḃ〉 = 0 since b has unit norm.).

28 Mar 2012: So called Automated Identification systems promise to address some of the limitations of these approaches by providing automated, ubiquitous, item level product identity information at any point in the supply chain. ... Yet the movement of an item can be

23 Jul 2012: There is some interest in the limit as q 0; see Section 1.5. ... If the temperatureis sufficiently low, the iron retains some residual magnetization, otherwise it doesnot.

2 Sep 2012: p2DtC. This experiment raises some interesting questions con-cerning the physics of an array of self-propelling objectsand their interactions with passive particles. ... In gen-eral one may write y2rmsy. 20 aRb , where a is some.