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Families Intersecting on an Interval
https://www.dpmms.cam.ac.uk/~par31/preprints/intersections-abs.html23 Mar 2007: Fix some subset B of [n]. How large a family A of subsets of [n] can we find such that the intersection of any two sets in A contains a cyclic ... Chung, Graham, Frankl and Shearer have proved that, in the case where B is a block of length t, we can do -
Part IID RIEMANN SURFACES (2007–2008): Example Sheet 2…
https://www.dpmms.cam.ac.uk/~agk22/rs2.pdf20 Oct 2007: f(z) =a(z z0) bc(z z0) d. ,. for some a,b,c,d,z0 C. ... 1 < |z| < 2}, {0 < |z| < 1}, {0 < |z| < }. 8. (i) Let R and S be some Riemann surfaces, f : R S a continuous map, and p a pointin R. -
MATHEMATICAL TRIPOS Part III Before Thursday 11th June, 2007 ...
https://www.dpmms.cam.ac.uk/~tkc10/complex_2007/MockExam2007.pdf3 Jun 2007: The questions carry equal weight. This is a Mock examination, intended to give you some idea of the sortof questions you will face in the proper Part III examination. ... The function f : DR C is analytic on some disc DR = {z C : |z| < R} withR > 1 and -
Mich. 2007 ANALYSIS II—EXAMPLES 4 PAR 1. At which ...
https://www.dpmms.cam.ac.uk/study/IB/AnalysisII/2007-2008/sheet4.pdf21 Nov 2007: a) Suppose that D1f exists and is continuous in some open ball around (a, b), and that D2f exists at (a, b). ... Show that f is differentiable at (a, b). (b) Suppose instead that D1f exists and is bounded on some open ball around (a, b), and that for -
Part IID RIEMANN SURFACES (2007–2008): Example Sheet 4…
https://www.dpmms.cam.ac.uk/~agk22/rs4.pdf21 Nov 2007: Questions 7–10 are more challenging than others and some parts certainly go beyond limitsof the examination. ... neous cubic polynomial in the generalized Weierstrass normal form XZ24Y 3AX2Y BX3,for some complex constants A, B, A3 27B2 6= 0. -
Part IID RIEMANN SURFACES (2007–2008): Example Sheet 2…
https://www.dpmms.cam.ac.uk/study/II/Riemann/2007-2008/rs2.pdf20 Oct 2007: f(z) =a(z z0) bc(z z0) d. ,. for some a,b,c,d,z0 C. ... 1 < |z| < 2}, {0 < |z| < 1}, {0 < |z| < }. 8. (i) Let R and S be some Riemann surfaces, f : R S a continuous map, and p a pointin R. -
Mich. 2007 ANALYSIS II—EXAMPLES 1 PAR 1. Which of ...
https://www.dpmms.cam.ac.uk/study/IB/AnalysisII/2007-2008/sheet1.pdf12 Oct 2007: Show that if fn f uniformly and (xm) isa sequence of points in [a, b] with xm x then fn(xn) f (x). ... Prove that there is some subinterval [a, b] of [0, 1] with a < b on which f is bounded. -
Examples sheet 2 for Part II Algebraic Topology Burt ...
https://www.dpmms.cam.ac.uk/study/II/AlgebraicTopology/2006-2007/toex2.pdf5 Oct 2007: b) Use (a) to show that every finitely presented group is the fundamental groupof some space. ... Freeness of a group action is as definedin lectures; some people call this property “free and properly discontinuous”.). -
MATHEMATICAL TRIPOS PART II (2006–07) Graph Theory - Example ...
https://www.dpmms.cam.ac.uk/study/II/Graphs/2006-2007/ex4.pdf9 Mar 2007: Riordan. Basic Examples: straightforward material on some of the main definitions and theorems. ... Let B̃ be the (n1)m matrix obtained by deleting some row of B. -
RIEMANN SURFACES AND DISCRETE GROUPS TKC Lent 2007 1. ...
https://www.dpmms.cam.ac.uk/~tkc10/complex_2007/Exercise_2007_1.pdf3 Jun 2007: u(z) = b log |z| Re a(z)for some b R and some analytic function a : A C. ... a) Show that Z(T) is a subgroup of Möb.(b) Find which groups (up to isomorphism) can arise as Z(T) for some Möbius transformation T.
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