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ANALYSIS I EXAMPLES 2 G.P. Paternain Lent 2011 Comments ...
https://www.dpmms.cam.ac.uk/~gpp24/aI-2.pdf3 Feb 2011: Show that f (x) = 0 for allx. 8. Let f : [a, b] R be bounded. ... 13. Let f : R R be a function which has the intermediate value property: If f (a) < c < f (b),then f (x) = c for some x between a and b. -
ANALYSIS I EXAMPLES 2 G.P. Paternain Lent 2011 Comments ...
https://www.dpmms.cam.ac.uk/study/IA/AnalysisI/2010-2011/aI-2.pdf15 Feb 2011: Show that f (x) = 0 for allx. 8. Let f : [a, b] R be bounded. ... 13. Let f : R R be a function which has the intermediate value property: If f (a) < c < f (b),then f (x) = c for some x between a and b. -
COMPLEX ANALYSIS EXAMPLES 2 Lent 2011 J. M. E. ...
https://www.dpmms.cam.ac.uk/~jmeh1/Teaching/complex11-2.pdf20 Feb 2011: 5. Let f be an entire function such that for some a C and r > 0, f takes no values in the discD(a, r). ... Show that |f (z)| as |z| ,and deduce that |f (z)| takes a minimum at some a C. -
ANALYSIS II (Michaelmas 2011): EXAMPLES 3 The questions are ...
https://www.dpmms.cam.ac.uk/~ajs1005/analysis_II/anII_ex_2011_s3.pdf13 Nov 2011: Explain geometrically why this is thecase. 5. (i) Suppose that f : R2 R is such that f/x is continuous in some open ball around (a,b),and f/y exists ... 11. Show that there is a continuous square-root function on some neighbourhood of I in Mn;that is, -
STATISTICS Part IB Example Sheet 1 (of 3) RJS/Lent ...
https://www.dpmms.cam.ac.uk/study/IB/Statistics/2010-2011/Example1.pdf1 Feb 2011: 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 minimal sufficient statistic T , and. -
PART II REPRESENTATION THEORYSHEET 1 Unless otherwise stated, all ...
https://www.dpmms.cam.ac.uk/study/II/RepresentationTheory/2010-2011/repex1.pdf10 Jan 2011: δ is abelian.(c) Assume that δ(g) = 1 for some g G. ... b) Find an example of a representation of some finite group over some field of charac-teristic p, which is not completely reducible. -
Numbers and Sets (2011–12) Example Sheet 1 of 4 ...
https://www.dpmms.cam.ac.uk/study/IA/Numbers%2BSets/2011-2012/examples-NS-11-1.pdf12 Oct 2011: about. (ii) m n a b (n m) [(a = 1) (b = 1) (ab 6= n)] ,. 5. The sum of some (not necessarily distinct) natural numbers is 100. ... 10. Let A = {1, 2, 3} and B = {1, 2, 3, 4, 5}? -
Example Sheet 1. Lectures 1–6, Galois Theory Michaelmas 2011 ...
https://www.dpmms.cam.ac.uk/study/II/Galois/2011-2012/2011_Galois_Ex1.pdf12 Oct 2011: Show that L = K(α) = {a bα |a, b K} for some α F with α2 K. ... ii) Show that if L/K is a finite extension with Q K, for which there exist only finitelymany intermediate subfields K K′ L, then L = K(α) for some α -
Numbers and Sets (2011–12) Example Sheet 2 of 4 ...
https://www.dpmms.cam.ac.uk/study/IA/Numbers%2BSets/2011-2012/examples-NS-11-2.pdf2 Nov 2011: 2. Find the convergents to the fraction 5744. Prove that if x and y are integers such that 57x 44y = 1 , then x = 17 44k and y = 57k 22 for some ... 3. Which of these are true for all natural numbers a , b and c? -
Example Sheet 2. Galois Theory Michaelmas 2011 Note. You ...
https://www.dpmms.cam.ac.uk/study/II/Galois/2011-2012/2011_Galois_Ex2.pdf24 Oct 2011: Show that they have the samesplitting field if and only if b = cnar for some c K and r N with gcd(r, n) = 1. ... for some divisor d > 1 of n. -
Topics in Analysis: Example Sheet 4 Michaelmas 2011-12 N. ...
https://www.dpmms.cam.ac.uk/study/II/TopicsinAnalysis/2011-2012/11-12sheet4.pdf30 Nov 2011: limz. znf (z) = c,. prove that f (z0) = 0 for some z0 C. ... a) g(z) = z for some z S1. (b) g(z) = z for some z S1. -
Topics in Analysis: Example Sheet 1 Michaelmas 2011-12 N. ...
https://www.dpmms.cam.ac.uk/study/II/TopicsinAnalysis/2011-2012/11-12sheet1.pdf30 Oct 2011: Hint: argue by contradiction.). (6) Let f : B B be a continuous map from the open disc B = {(x, y) R2 : x2 y2 < 1} into it-self. ... 1. (11) Suppose f : R R has the intermediate value property that if a, b R, f (a) < c < f (b),then f (y) = c for some y -
ANALYSIS II (Michaelmas 2011): EXAMPLES 4 The questions are ...
https://www.dpmms.cam.ac.uk/~ajs1005/analysis_II/anII_ex_2011_s4.pdf2 Dec 2011: Find this solution to some reasonable accuracy using a pocket calculator or thecalculator on your computer (remember to work in radians!), and justify the claimed accuracy ofyour approximation. ... norm. Show, however, that T is a contraction under the -
Example Sheet 3. Galois Theory Michaelmas 2011 Finite fields ...
https://www.dpmms.cam.ac.uk/study/II/Galois/2011-2012/2011_Galois_Ex3.pdf12 Nov 2011: 3.17. (i) Let f K(X). Show that K(X) = K(f) if and only if f = (aX b)/(cX d)for some a, b, c, d K with ad ... Deduce that every finite abelian group is the Galois group of some Galois extension K/Q.[It is a long-standing unsolved problem (inverse Galois -
Compressions and Probably IntersectingFamilies Paul A. Russell ∗†…
https://www.dpmms.cam.ac.uk/~par31/preprints/probint.pdf16 Aug 2011: larger family Aand then randomly discard some of the sets in A to form a subfamily B. ... Then A = vf (W )Xfor some W U , X X W2 YW and W X B. -
60 APPENDIX: ADEQUATE SUBGROUPS ROBERT GURALNICK, FLORIAN HERZIG,…
https://www.dpmms.cam.ac.uk/~jat58/appendix.pdf29 Jul 2011: Then Lemma 5(applied to the image of ψ/Fl) gives the desired map log : U Lie U ad V ′. Step 6: Some properties of G0(Fl). The pair ... k1γ(T(Fl)/Z0)γ1k = k′(T(Fl)/Z0)k′1. for some k′ B(Fl). Then (kk′)1γ lies in H and we deduce that Γ -
3kat.dvi
https://www.dpmms.cam.ac.uk/~par31/preprints/notnested.pdf25 Aug 2011: n1. maximising the number of intersecting subfamilies of size s. Theorem 2tells us that A = [n](>3) B for some B [n](2). ... Let U = {A [n](t) : B A for some B U} be the upper shadow of Uin layer t. -
MINIMISATION AND REDUCTION OF 5-COVERINGS OFELLIPTIC CURVES TOM…
https://www.dpmms.cam.ac.uk/~taf1000/papers/minred5.pdf21 Dec 2011: So if we lift a1 to Z[X5] thena21c4 c6 = 2f for some f Z[X5]. ... Notice that if Φ′ = gΦfor some g = [A,B] with A,B GL5(K) then (Φ′) = (Φ) v(det g). -
ON FAMILIES OF n-CONGRUENT ELLIPTIC CURVES T.A. FISHER Abstract. ...
https://www.dpmms.cam.ac.uk/~taf1000/papers/highercongr.pdf9 May 2011: First we construct some covariant columns. Let x1 = (a,b,c,d,e)T. If γ. ... Let (a : b : c : d : e) be the K-point on X(11) corresponding to (E,φ) for some. -
ON THE AUTOMORPHY OF l-ADIC GALOISREPRESENTATIONS WITH SMALL RESIDUAL …
https://www.dpmms.cam.ac.uk/~jat58/bigness.pdf29 Jul 2011: In the firstsection we recall some results on the Galois representations associatedto automorphic forms. ... If π is ramified, then as above we have for some t > 0.
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