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Publications | Department of Pure Mathematics and Mathematical…
www.dpmms.cam.ac.uk/publications?page=12523 Jul 2024: Mutual information, synergy and some curious phenomena for simple channels. I Kontoyiannis, B Lucena. – ... 2005,. 1651. (doi: 10.1109/isit.2005.1523625). Filtering: The case for "Noisier" data. B Lucena, I Kontoyiannis. – -
Mathematical Tripos: Part IB DJS/Lent 2015 Statistics: Example Sheet…
www.dpmms.cam.ac.uk/study/IB/Statistics/2014-2015/ex1.pdf22 Jan 2015: Xn be independent Poisson random variables, with Xi having meaniθ, for some θ > 0. ... b) For some n > 2, let X1,. ,Xn be iid with Xi Exponential(θ). -
Mapping class groupsProblem sheet 2 Lent 2021 1. What ...
www.dpmms.cam.ac.uk/study/III/MappingClassGroups/2020-2021/MCGs%20Sheet%202.pdf19 Jan 2021: a) Show that there is a surjection π1Sg G, for some g.(b) Show that G is a subgroup of Mod(Sh), for some h. ... a) Prove that TαTβ(α) = β. (b) Prove the braid relation: TαTβTα = TβTαTβ. -
slide 0 Modular formsand motivesA J Scholl slide 1 ...
https://www.dpmms.cam.ac.uk/~ajs1005/preprints/banff.pdf29 Jan 2010: slide 12. Lemma j = isomn on HM(;)(") Z[ 12k!].(each component of complement is xedby some with "( ) = 1.)[D]ix(pr0#D [ [prk#D)(") 7!y2 2Hk1M (Uky ;k 1)(")'Hk1M ... E fyg)k;k 1)(")Eisenstein symbol (B)ny = 0, some n > 1[n]y 2 Hk1M ((E 0)k;k 1)(")?yoHk1M -
Mapping class groupsProblem sheet 2 Michaelmas 2019 1. What ...
www.dpmms.cam.ac.uk/study/III/MappingClassGroups/2019-2020/MCGs%20Sheet%202.pdf12 Nov 2019: 1. 5. Let G be any finite group. (a) Show that there is a surjection π1Sg G, for some g.(b) Show that G is a subgroup of Mod(Sh), for -
Mich. 2012 ANALYSIS II—EXAMPLES 4 PAR 1. Use the ...
www.dpmms.cam.ac.uk/study/IB/AnalysisII/2012-2013/12sheet4.pdf26 Nov 2012: a) Suppose that D1f exists and is continuous in some open ball around (a, b), and that. ... b) Suppose instead that D1f exists and is bounded on some open ball around (a, b), and. -
Mich. 2013 ANALYSIS II—EXAMPLES 4 PAR 1. (a) Let ...
www.dpmms.cam.ac.uk/study/IB/AnalysisII/2013-2014/13sheet4.pdf29 Nov 2013: 7. Let f: R2 R and (a,b) R2.(a) Suppose that D1f exists and is continuous in some open ball around (a,b), and that. ... b) Suppose instead that D1f exists and is bounded on some open ball around (a,b), and. -
Mich. 2013 ANALYSIS II—EXAMPLES 1 PAR 1. Which of ...
www.dpmms.cam.ac.uk/study/IB/AnalysisII/2013-2014/13sheet1.pdf23 Oct 2013: 4. Let (fn) be a sequence of real-valued continuous functions on a closed, bounded interval [a,b], and. ... f. Prove that there is some subinterval [a,b] of [0, 1] with a < b on which f is bounded. -
DIFFERENTIAL GEOMETRY (PART III) MICHAELMAS 2021 EXAMPLE SHEET 2 ...
www.dpmms.cam.ac.uk/files/study/III/DifferentialGeometry/2021-2022/DGSheet2.pdf1 Nov 2021: Show that M M is trivial.(b) Show that for all n we have TSn R = Rn1 over Sn. ... 4.† Let α be a nowhere-zero 1-form on a manifold X, and let β be a p-form.(a) Show that if β = α γ for some (p -
Mich. 2012 ANALYSIS II—EXAMPLES 2 PAR 1. Let f ...
www.dpmms.cam.ac.uk/study/IB/AnalysisII/2012-2013/12sheet2.pdf29 Oct 2012: a sequence of points in [a, b] with xm x then fn(xn) f (x). ... f. Prove that there is some subinterval [a, b] of [0, 1] with a < b on which f is bounded.
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