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1 - 10 of 45 search results for `some B B` |u:www.dpmms.cam.ac.uk

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  2. Mich. 2023 ANALYSIS AND TOPOLOGY—EXAMPLES 4 PAR 1. Let ...

    https://www.dpmms.cam.ac.uk/~par31/at/4.pdf
    21 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.

  3. Recent papers and preprints

    https://www.dpmms.cam.ac.uk/~ik355/pubs.html
    17 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

  4. Lent 2024 Number Fields – Example Sheet 3 P.P. ...

    https://www.dpmms.cam.ac.uk/~pv270/example3.pdf
    8 Mar 2024: 2(1. 71). Find an element of OK with norm 2a 3b 5 for some. ... a,b 0. Hence prove that the class group of K is cyclic and find its order.

  5. Lent 2024 LOGIC AND SET THEORY – EXAMPLES 4 ...

    https://www.dpmms.cam.ac.uk/study/II/Logic/2023-2024/sheet4.pdf
    3 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

  6. Mich. 2023 ANALYSIS AND TOPOLOGY—EXAMPLES 1 PAR 1. Let ...

    https://www.dpmms.cam.ac.uk/~par31/at/1.pdf
    12 Oct 2023: a, b], and suppose that fn converges pointwise to a continuous function f. ... Show that there is some subinterval [a, b] of [0, 1] with a < b on which (fn) is uniformly.

  7. Mich. 2023 ANALYSIS AND TOPOLOGY—EXAMPLES 4 PAR 1. Let ...

    https://www.dpmms.cam.ac.uk/study/IB/AnalysisandTopology/2023-2024/4.pdf
    24 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.

  8. Michaelmas Term 2023 T.A. Fisher Galois Theory: Example Sheet ...

    https://www.dpmms.cam.ac.uk/~taf1000/galois_theory-23-4.pdf
    21 Nov 2023: 4. Let K be a field containing a primitive mth root of unity for some m > 1. ... Showthat f and g have the same splitting field if and only if b = cmar for some c Kand r N with gcd(r,m) = 1.

  9. Lent 2024 Number Fields – Example Sheet 3 P.P. ...

    https://www.dpmms.cam.ac.uk/study/II/NumberFields/2023-2024/example3.pdf
    23 Feb 2024: 2(1. 71). Find an element of OK with norm 2a 3b 5 for some. ... a,b 0. Hence prove that the class group of K is cyclic and find its order.

  10. Lent 2024 LOGIC AND SET THEORY – EXAMPLES 4 ...

    https://www.dpmms.cam.ac.uk/~az10000/2024-lent-partii-logic-and-set-sheet4.pdf
    31 Mar 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

  11. Lent Term 2024 O. Randal-Williams IB Groups, Rings, and ...

    https://www.dpmms.cam.ac.uk/~or257/teaching/IBGRM/2024/Sheet3.pdf
    11 Jan 2024: Could there be some other Euclidean function φ making Z[3] into a Euclidean domain? ... iii) Show that if R is a PID, the gcd of elements a and b exists and can be written as rasbfor some r,s R.

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