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25 Nov 2005: Show that f and g havethe same splitting field if and only if b = cmar for some c K and r N with gcd(r, m) = 1. ... Deduce that every finite abelian groupis the Galois group of some Galois extension K/Q.

3 Dec 2005: 35. A B. C D. E F. Fig. 7. Some best-fit results of deformable template matching. ... Some figures arerotated for plotting. (A) A fully laid egg in perfect condition.

8 Dec 2005: Suppose F is an ultrafilter and A, Ac 6 F. Then we must have B Fwith B A = (for otherwise F ′ = {C N : C A B for some B F}is ... 26. Proof. The first statement says that inside (A, M )(ω) there is some (B, L)(ω).

28 Oct 2005: Appendix A. List of Standards. Appendix B. Synthetic Photometry. Hi Mike Here are some comments on your WFCAM-2MASS colour equations, based on an analysis of the synthetic colours. ... Some of these colours seem quite odd e.g. A stars with negative Z-Y

25 Aug 2005: Some Caution:. This optimisation needs care: can’t reach strong conclusions. on the basis of a single algorithm. ... optimise the detector for PFA. Prioritised PFA list. The A-List (in some order of priority).

21 May 2005: Is ittrue that for some c in [a,b] we have. 1. ... i) Suppose that λ > 0. Show that there is some interval [c,d] in [a,b] with the property that.

21 May 2005: χ(z w) χ(z) χ(w). Remark for readers of Ahlfors or Jones & Singerman: their σ and ζ are not quite the same asψ and χ here, but for some ... f(z) =a(z z0) bc(z z0) d. ,. for some a,b,c,d,z0 C.

22 Nov 2005: only if U = Y V for some V open in (X,dX).(ii Show that A is closed in (Y,dY ) if and only if A = Y B for some B ... dy. dx= 2xy , with y = 1 when x = 0 ,. has a unique solution in some interval containing 0. In what interval can the differential

21 May 2005: only if U = Y V for some V open in (X,dX).(ii Show that A is closed in (Y,dY ) if and only if A = Y B for some B ... dy. dx= 2xy , with y = 1 when x = 0 ,. has a unique solution in some interval containing 0. In what interval can the differential

21 May 2005: for some x,y Z with (x,y) = 1, then there exist a,b Z such that p = a2 b2. ... subgroup of Q/Q2 generated by a,b. Determine whether the field Q(.