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Holly Krieger — Cambridge
https://www.dpmms.cam.ac.uk/~hk439/research.html9 May 2023: Juul, N. Looper, M. Manes, B. Thompson, L. Walton), Research Directions in Number Theory, Association for Women in Mathematics Series, Vol. ... Some consequences of Schanuel's conjecture (with C. Cheng, B. Dietel, M. -
The Cauchy-Schwarz inequality
https://www.dpmms.cam.ac.uk/~wtg10/csineq.html4 Oct 2001: 1. /b. 1. rather than some other a. i. /b. i. , ... i. are equal. This still leaves a minor problem that some of the b. -
Recent papers and preprints
https://www.dpmms.cam.ac.uk/~ik355/pubs.html17 May 2024: pdf]. I. Kontoyiannis. "Some information-theoretic computations related to the distribution of prime numbers." In Festschrift in Honor of Jorma Rissanen, (P. ... Mutual information, synergy, and some curious phenomena for simple channels." 2005 IEEE -
Lent 2024 LOGIC AND SET THEORY – EXAMPLES 4 ...
https://www.dpmms.cam.ac.uk/study/II/Logic/2023-2024/sheet4.pdf3 Apr 2024: Show further that if f : X Y is a continuous function between Polish spacesand f is injective on a Borel set B X, then f(B) is Borel. ... 14. Prove that a set A (in some Polish space) is analytic if and only if there exist closedsets An1,.,nk (indexed by -
Henkin on ω-consistency and ω-completeness JSL 1954 and 1957: ...
https://www.dpmms.cam.ac.uk/~tef10/henkin.pdf8 Jan 2021: After allT might prove φ(a) for every a in Γ and yet prove φ(b) for some constant bnot in Γ. ... We need some definitions. DEFINITION 4. A theory T is Γn-complete iff whenever φ(x1,. -
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 -
DIFFERENTIAL GEOMETRY (PART III) MICHAELMAS 2021 EXAMPLE SHEET 2 ...
https://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 -
Publications | Department of Pure Mathematics and Mathematical…
https://www.dpmms.cam.ac.uk/publications?page=18718 Jul 2024: 753,. 442. Set colourings of graphs. B BOLLOBAS, A THOMASON. – Discrete Mathematics. ... SOME MISLEADING ARGUMENTS INVOLVING CONDITIONAL INDEPENDENCE. AP DAWID. – JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-METHODOLOGICAL. -
The existence of root two
https://www.dpmms.cam.ac.uk/~wtg10/roottwo.html20 Sep 2001: We know that some numbers are irrational, but we can still describe them, by means of their decimal expansions. ... 2. in some way, consistent with the principle that 0 < a < b implies that a. -
Mich. 2023 ANALYSIS AND TOPOLOGY—EXAMPLES 4 PAR 1. Let ...
https://www.dpmms.cam.ac.uk/study/IB/AnalysisandTopology/2023-2024/4.pdf24 Nov 2023: 10. 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.
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