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Arden's rule and some stuff like that
https://www.dpmms.cam.ac.uk/~tef10/cam_only/langs-and-automata/2-3.html13 Aug 2009: 2.3 Arden's rule and some stuff like that. B I G H O L E H E R E. -
Principal Ideal Domains and Factorization A principal ideal domain ...
https://www.dpmms.cam.ac.uk/~par31/notes/pid.pdf23 Mar 2009: As R is a PID we have (a, b) = d for some d R. ... So. i=1. (ai) = (b). 1. for some b R. So b (ak) for some k, and then. -
Analysis II (Michaelmas 2009) A.G. Kovalev@dpmms.cam.ac.uk Term by…
https://www.dpmms.cam.ac.uk/~agk22/uniform.pdf15 Oct 2009: k=1 uk(x0) converges at some point x0 [a, b] and. (ii) the series of derivatives. ... Then for x [a, b] we can write g(x) g(x0) = g′(ξ)(x x0) with some ξ [x0, x] [a, b] (or ξ [x, x0] [a, b]), using the -
GEOMETRY Keith Carne t.k.carne@dpmms.cam.ac.uk…
https://www.dpmms.cam.ac.uk/~tkc10/Geometry_2009/Overhead_1.pdf28 Jan 2009: Proposition 1.2 Isometries of E2. An orientation preserving isometry of E2 is:(a) The identity.(b) A translation.(c) A rotation about some point c E2. ... a) The identity.(b) A translation.(c) A rotation about some line. (d) A screw rotation, that is a -
Part II Riemann Surfaces, Michaelmas 2009 pmhw@dpmms.cam.ac.uk…
https://www.dpmms.cam.ac.uk/study/II/Riemann/2009-2010/RS09.2.pdf30 Nov 2009: 4) If the map f of Question 3 is a conformal equivalence, show that F(z) = λz µfor some λ C. ... 5) Show that complex tori C/〈1,τ1〉 and C/〈1,τ2〉 are analytically isomorphic if andonly if τ2 = (aτ1 b)/(cτ1 d), for some matrix. -
One-step refutations using bombs
https://www.dpmms.cam.ac.uk/~tef10/cam_only/langs-and-automata/1-4-1.html13 Aug 2009: some as followed by some bs and then some as again (and then some bs). ... We will show that will accept some strings that aren't palindromes, and therefore doesn't recognise {a. -
Euclidean Domains A Euclidean domain is an integral domain ...
https://www.dpmms.cam.ac.uk/~par31/notes/ed.pdf23 Mar 2009: a = qb r. for some q, r R with r = 0 or d(r) < d(b).For example. ... N by. N(a b. 2. )= a2 2b2. (=. a b22) (a, b Z). -
ANALYSIS II (Michaelmas 2009): EXAMPLES 4 The questions are ...
https://www.dpmms.cam.ac.uk/~agk22/anII-09-4.pdf7 Dec 2009: 5. (i) Suppose that f : R2 R is such that D1f = f/x is continuous in some open ball around(a,b), and D2f = f/y exists at (a,b). ... 11. Show that there is a continuous square-root function on some neighbourhood of I in Mn;that is, show that there is an -
STATISTICS Part IB Example Sheet 1 (of 3) RJS/Lent ...
https://www.dpmms.cam.ac.uk/study/IB/Statistics/2008-2009/Example1.pdf4 Mar 2009: Xn be independent Poisson random variables, with Xi having parameteriθ for some θ > 0. ... b) For some n > 2, let X1,. ,Xniid Exp(θ). Find a real-valued sufficient statistic T, and. -
The Thought-experiment
https://www.dpmms.cam.ac.uk/~tef10/cam_only/langs-and-automata/1-2.html13 Aug 2009: Let us try some examples. Let L be the set of strings over the alphabet {a, b} which have the same number of as as bs. ... a. n. b. n. : n } This is the language of strings consisting of any number of as followed by the same number of bs.
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