Search
Search Funnelback University
201 -
250 of
712
search results for `some B B` |u:www.dpmms.cam.ac.uk
Fully-matching results
-
RN (nickl@maths.cam.ac.uk) Michaelmas 2022 Probability and Measure 1…
www.dpmms.cam.ac.uk/study/II/Probability%2BMeasure/2022-2023/ex1.pdf5 Oct 2022: algebra. 1.2. Show that the following sets of subsets of R all generate the same σ-algebra:(a) {(a,b) : a < b}, (b) {(a,b] : a < b}, (c) {(,b] : b ... 1.9. Let (E,E,µ) be a measure space. Call a subset N E null if N B for some B E withµ(B) = 0. -
Geometry of universal local lifting rings and some deformation…
https://www.dpmms.cam.ac.uk/~jcsl5/automorphylifting/7-Guillem.pdf18 Mar 2021: 1 Unramified up to twist: τ = (ψ ψ, 0) for some characterψ : IK C. ... 4 Irreducible: τ = (r0, 0) where r0 is the restriction of some irreducibleWeil-Deligne representation. -
Mich. 2021 ANALYSIS AND TOPOLOGY – EXAMPLES 1 AZ ...
www.dpmms.cam.ac.uk/study/IB/AnalysisandTopology/2021-2022/sheet1.pdf7 Oct 2021: ii) M R n N x S |fn(x)| 6 M. (b) In this case assume that S is a metric space. ... Prove that there is some subinterval [a,b] of [0, 1] with a < b on which f isbounded. -
GEOMETRY AND GROUPS – Example Sheet 2TKC Michaelmas 2012 ...
https://www.dpmms.cam.ac.uk/~tkc10/GeometryandGroups/Exercise2.pdf23 Oct 2012: J : z 7 az bcz d. for some complex numbers a, b, c, d with ad bc = 1. ... For which choices of a, b, c, d is this map J aninvolution, that is J 2 = I? -
Handout: The Cauchy-Kovalevskaya Theorem Part III: Analysis of…
https://www.dpmms.cam.ac.uk/~cmw50/resources/PartIIIPDE/PDECauchyKov.pdf15 Oct 2021: Bj,γ,δ. zγxδ, j = 1,. ,n1,. andc(z,x′) =. γ,δ. cγ,δzγxδ,. where these power series converge if |z| |x′| < s for some small s > 0. ... cγ,δzγxδ,. 4. with these power series converging for |x| |x′| < s for some (possibly smaller) s. -
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, -
GEOMETRY AND GROUPS – Example Sheet 1TKC Michaelmas 2012 ...
https://www.dpmms.cam.ac.uk/~tkc10/GeometryandGroups/Exercise1.pdf13 Oct 2012: Let u =(. ac. ), v =. (bd. )for some integers a, b, c, d with ad bc = 1. ... Show that every vector. w Z Z can be written as mu nv for some integers m and n. -
Riemann Surfaces, Examples 2 Michaelmas 2020 Please send any ...
www.dpmms.cam.ac.uk/study/II/Riemann/2020-2021/RS%20Sheet%202.pdf5 Oct 2020: 4. If the map f of Question 3 is a conformal equivalence, show that F(z) = λz µfor some λ C. ... 5. Show that complex tori C/⟨1,τ1⟩ and C/⟨1,τ2⟩ are analytically isomorphic ifand only if τ2 = (aτ1 b)/(cτ1 d), for some matrix ( a bc d ) SL2 -
Number Fields IID, Lent 2021: Example Sheet 3 of ...
www.dpmms.cam.ac.uk/study/II/NumberFields/2020-2021/ex-sheet3.pdf15 Jan 2021: some a,b 0. Hence prove that the class group of K is cyclic and find itsorder. -
Michaelmas Term 2003 J. M. E. Hyland Linear Algebra: ...
www.dpmms.cam.ac.uk/study/IB/LinearAlgebra/2ndla03.pdf21 May 2005: vary in difficulty but cover some instructive points. 1. For what values of a and b does the system of simultaneous linear equations. ... only if it is nilpotent, that is, αk = 0 for some natural number k. -
STATISTICS Part IB Example Sheet 1 (of 3) RJS/Lent ...
www.dpmms.cam.ac.uk/study/IB/Statistics/2017-2018/Example1.pdf12 Feb 2018: 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. -
Mich. 2021 ANALYSIS AND TOPOLOGY – EXAMPLES 2 AZ ...
https://www.dpmms.cam.ac.uk/~az10000/2021-mich-partib-aandt-sheet2.pdf26 Oct 2021: Some more questions. 13. (a) A topological space is said to be second countable if there is a countable family Bof open sets such that every open set is a union ... of some members of B. -
RN (nickl@maths.cam.ac.uk) Michaelmas 2021 Probability and Measure 1…
www.dpmms.cam.ac.uk/study/II/Probability%2BMeasure/2021-2022/ex1.pdf7 Oct 2021: algebra. 1.2. Show that the following sets of subsets of R all generate the same σ-algebra:(a) {(a,b) : a < b}, (b) {(a,b] : a < b}, (c) {(,b] : b ... 1.9. Let (E,E,µ) be a measure space. Call a subset N E null if N B for some B E withµ(B) = 0. -
ANALYSIS I EXAMPLES 2 G.P. Paternain Lent 2010 Comments ...
www.dpmms.cam.ac.uk/study/IA/AnalysisI/2009-2010/aI2.pdf2 Feb 2010: 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. -
MATHEMATICAL TRIPOS: PART IA Lent 2017 PROBABILITY JRNExample Sheet…
www.dpmms.cam.ac.uk/study/IA/Probability/2016-2017/pex1.pdf14 Feb 2017: 6. Let (An : n N) be a sequence of events in some probability space (,F,P). ... Set. A = {ω : ω An infinitely often}, B = {ω : ω An for all sufficiently large n}. -
Mich. 2020 ANALYSIS AND TOPOLOGY – EXAMPLES 1 AZ ...
www.dpmms.cam.ac.uk/study/IB/AnalysisandTopology/2020-2021/sheet1.pdf19 Oct 2020: ii) M R n N x S |fn(x)| 6 M. (b) In this case assume that S is a metric space. ... Prove that there is some subinterval [a,b] of [0, 1] with a < b on which f isbounded. -
Analysis I: Example Sheet 1 AFB, Michaelmas 2004 Please ...
www.dpmms.cam.ac.uk/study/IA/AnalysisI/2004ex1-4.pdf21 May 2005: Is ittrue that for some c in [a,b] we have. 1. ... i) Suppose that λ > 0. Show that there is some interval [c,d] in [a,b] with the property that. -
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. -
The Eisenstein quotient
https://www.dpmms.cam.ac.uk/~jcsl5/mazur/8.TheEisensteinquotient.pdf18 Jan 2021: Proof. Let f : J0(N) A be the quotient map. There exists a mapg : A J0(N) such that fg = [n] for some n > 0. ... and for a given f, it’s possible that some Vf,p are of the form (trivial) (cyclotomic) while others aren’t. -
Lent Term 2016 O. Randal-Williams IB Groups, Rings, and ...
https://www.dpmms.cam.ac.uk/~or257/teaching/IBGRM/Sheet3.pdf15 Feb 2016: 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. -
A NOTE ON THE FAMILY SIGNATURE THEOREM OSCAR RANDAL-WILLIAMS ...
https://www.dpmms.cam.ac.uk/~or257/FamilySignature.pdf23 Jan 2019: As described above, by a theorem of Borel[Bor74] the maps (3.1) are isomorphisms, so ch4kd(ξH) is equal to some poly-nomial p(σ1,σ2,. , ... Hi(B; Q) 0.Now s(τc)|E = 0 so (τc)|E = u (E)x for some x H|c|d(B; Q). -
Riemann Surfaces, Examples 1 Michaelmas 2020 Please send any ...
www.dpmms.cam.ac.uk/study/II/Riemann/2020-2021/RS%20Sheet%201.pdf5 Oct 2020: az b, for some a C and b C. ... conformally equivalent). 9. Define an equivalence relation on C by z w iff z = 2sw for some s Z.Show that the quotient space R = C/ has the natural structure of -
problemsm3p18
https://www.dpmms.cam.ac.uk/~cmw50/resources/M3P18/FAproblems5.pdf15 Oct 2021: g2Zngv. Show that if 2 D(Rn) with supp K for some compact K Rn then. ... u[] =X. g2Agv[],. for some finite set A Zn which depends only on K. -
MATHEMATICAL TRIPOS, PART II, 2020/2021REPRESENTATION THEORY EXAMPLE…
www.dpmms.cam.ac.uk/study/II/RepresentationTheory/2020-2021/IIRT1.pdf14 Oct 2020: δ is abelian.(c) Assume that δ(g) = 1 for some g G. ... irreducible. 3 Find an example of a representation of some finite group over some field of charac-teristic p, which is not completely reducible. -
Number Fields IID, Lent 2020: Example Sheet 3 of ...
www.dpmms.cam.ac.uk/study/II/NumberFields/2019-2020/ex-sheet3.pdf9 Mar 2020: some a,b 0. Hence prove that the class group of K is cyclic and find itsorder. -
ALGEBRAIC TOPOLOGY MICHELMAS 2008 EXAMPLE SHEET 1 1. Let ...
www.dpmms.cam.ac.uk/study/II/AlgebraicTopology/2008-2009/Examples1.pdf14 Oct 2008: Show thatf(x) = x for some x S1. 3. Which of the letters A,B,. ... 1,1) π1(S1,f(1)) when. (a) f(eiθ) = ei(θπ/2). (b) f(eiθ) = einθ for some n Z. -
Analysis of Partial Differential Equations Example sheet II (Chapter…
https://www.dpmms.cam.ac.uk/~md384/example_sheet_PDE_2-v3.pdf11 Nov 2016: u(0,x) =1. 1 x2. 1. 5. (Cauchy-Kovalevskaya Theorem for systems of ODEs) Suppose b > 0 and F : u0 (b,b)d Rd bereal analytic in a neighbourhood of ... u′(t) = F(t,u(t)), u(0) = u0 Rd,. on (a,a) for some a > 0 with u((a,a)) u0 (b,b)d. -
RN Michaelmas 2020 Probability and Measure 1 1.1. Let ...
www.dpmms.cam.ac.uk/study/II/Probability%2BMeasure/2020-2021/ex1.pdf10 Oct 2020: algebra. 1.2. Show that the following sets of subsets of R all generate the same σ-algebra:(a) {(a,b) : a < b}, (b) {(a,b] : a < b}, (c) {(,b] : b ... 1.9. Let (E,E,µ) be a measure space. Call a subset N E null if N B for some B E withµ(B) = 0. -
Lent 2016 ANALYSIS I – EXAMPLES 2 AZ 1. ...
www.dpmms.cam.ac.uk/study/IA/AnalysisI/2015-2016/sheet2.pdf9 Feb 2016: 5. Let f be a function on a set A and let B A. ... some c (a,b) the vectors(f(b),g(b). )(f(a),g(a). )and. (f ′(c),g′(c). )in R2. -
filtersurprise.dvi
https://www.dpmms.cam.ac.uk/~ik355/PAPERS/filtering.pdf5 Jun 2020: This makes a direct comparison possible and enables us topresent some theoretical results. ... There exists some number K such that k(n) < K for all n. -
Homotopy Theory, Examples 3 Oscar Randal-Williams Lent 2015 1. ...
https://www.dpmms.cam.ac.uk/~or257/teaching/IIIHtyThy2015/Sheet3.pdf11 Feb 2015: Fi //. Ep //. p. B. {b0} // B B. and show using the naturality of the Serre spectral sequence that the compositions. ... for some monic polynomial p(x) with coefficients in H(B; Z). Homotopy Theory Example sheet 3. -
Symmetric sets and graph models of set and multiset ...
https://www.dpmms.cam.ac.uk/~tef10/dangthesis.pdf23 Dec 2010: Byuniqueness, we can call x = t(R). Lemma 20. Any x V is t(R) for some R B. ... B,b] to an SPG [Q,q]. 28. By Lemma 23, there is a bijection θ : Dom Q ι5“H for some H M. -
Mich. 2021 ANALYSIS AND TOPOLOGY – EXAMPLES 2 AZ ...
www.dpmms.cam.ac.uk/study/IB/AnalysisandTopology/2021-2022/sheet2.pdf28 Oct 2021: Some more questions. 13. (a) A topological space is said to be second countable if there is a countable family Bof open sets such that every open set is a union ... of some members of B. -
Example Sheet 3 Analysis of FunctionsClaude Warnick Lent 2020 ...
www.dpmms.cam.ac.uk/study/II/AnalysisofFunctions/2019-2020/ExamplesAoF3.pdf4 Mar 2020: Z. Rn. eix eiy2. ||2sd 6 Cn, |x y|2. b) Show that if s = n2 k for some k 2 Z>0, 0 < < 1, then. ... for some 2 R if and only if:. w(x) = Hk1(x1) Hkn(xn)e12 |x|. -
MATHEMATICAL TRIPOS: PART IA Lent 2022 PROBABILITY Dominic YeoExample …
www.dpmms.cam.ac.uk/study/IA/Probability/2021-2022/pex22_sheet1.pdf22 Jan 2022: 1. 6. Let (An : n N) be a sequence of events in some probability space (,F,P). ... Recall that (1 1/x)x e. as x. ]. Extensions. Some of the following questions have a more puzzle-like quality. -
ALGEBRAIC TOPOLOGY LENT 2010 EXAMPLE SHEET 1 1. Let ...
www.dpmms.cam.ac.uk/study/II/AlgebraicTopology/2009-2010/Examples1.pdf19 Jan 2010: Show thatf(x) = x for some x S1. 3. Which of the letters A,B,. ... 1,1) π1(S1,f(1)) when. (a) f(eiθ) = ei(θπ/2). (b) f(eiθ) = einθ for some n Z. -
Part IIB RIEMANN SURFACES (2003–2004): Example Sheet 2…
www.dpmms.cam.ac.uk/study/II/Riemann/2003-2004/rs2.pdf21 May 2005: χ(z w) χ(z) χ(w). Remark for readers of Ahlfors or Jones & Singerman: their σ and ζ are not quite the sameas ψ and χ, but for some constants ... 9. (i) Prove Schwartz lemma: if f : is holomorphic and f(0) = 0 then either|f(z)| < |z|, for every z , -
RIEMANN SURFACES EXAMPLES 2 H. Krieger Michaelmas 2018 Comments ...
www.dpmms.cam.ac.uk/study/II/Riemann/2018-2019/rs_ex2_18.pdf22 Oct 2018: C/Λ2 are conformally equivalent if and only if thelattices are related by Λ2 = λΛ1 for some λ C. ... 5. Show that complex tori C/〈1,τ1〉 and C/〈1,τ2〉 are analytically isomorphic if and only if τ2 =. (aτ1 b)/(cτ1 d), for some matrix(a bc d -
Mich. 2019 ANALYSIS AND TOPOLOGY – EXAMPLES 1 AZ ...
www.dpmms.cam.ac.uk/study/IB/AnalysisandTopology/2019-2020/sheet1.pdf22 Oct 2019: 8. Let fn, n N, and f be real-valued continuous functions on the closed bounded interval[a, b]. ... Prove that there is some subinterval [a, b] of [0, 1] with a < b on which f isbounded. -
Mich. 2019 ANALYSIS AND TOPOLOGY – EXAMPLES 2 AZ ...
www.dpmms.cam.ac.uk/study/IB/AnalysisandTopology/2019-2020/sheet2.pdf5 Nov 2019: Assume that for some K > 0 we have ‖ϕ(t, x) ϕ(t, y)‖ 6 K‖xy‖ forall t [a, b] and all x, y BR(y0). ... Assume further that. sup{‖ϕ(t, x)‖ : t [a, b], x BR(y0). -
ANALYSIS II EXAMPLES 4 Michaelmas 2005 J. M. E. ...
https://www.dpmms.cam.ac.uk/~jmeh1/Teaching/an05-4.pdf19 Mar 2008: only if U = Y V for some V open in (X, dX ).(ii Show that A is closed in (Y, dY ) if and only if A = Y B for some B ... a contraction? Deduce that the differential equation. dy. dx= 2xy , with y = 1 when x = 0 ,. has a unique solution in some interval -
MATHEMATICAL TRIPOS: PART IA Lent 2022 PROBABILITY Dominic YeoExample …
www.dpmms.cam.ac.uk/study/IA/Probability/2021-2022/pex22_sheet4.pdf8 Mar 2022: Find the probability densityfunction of the radius of the circle. Have you seen this distribution before for some value of λ? ... TN aNbN. , for some aN,bN. (b) Let αN = bN/3c and βN = b2N/3c. -
Mich 2023 FUNCTIONAL ANALYSIS – EXAMPLES 4 AZ 1. ...
https://www.dpmms.cam.ac.uk/~az10000/2023-mich-partiii-func-anal-sheet4.pdf25 Nov 2023: Some more questions. 15. Show that the direct sum A B of C-algebras A and B is a C-algebra withcoordinate-wise operations and with ‖(x,y)‖ = max. ... norm ‖‖. Let ‖‖1 be some (possibly incomplete) algebra-normon A. Show that ‖f‖6 ‖f‖1 -
problemsaof
www.dpmms.cam.ac.uk/study/II/AnalysisofFunctions/2021-2022/ExamplesAoF4.pdf1 Feb 2022: Z. Rn. eix eiy2. ||2sd 6 Cn, |x y|2. b) Show that if s = n2 k for some k 2 Z>0, 0 < < 1, then. ... for some 2 R if and only if:. w(x) = cHk1(x1) Hkn(xn)e12 |x|. -
Part IID RIEMANN SURFACES (2007–2008): Example Sheet 2…
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. -
Lent 2016 ANALYSIS I – EXAMPLES 3 AZ 1. ...
www.dpmms.cam.ac.uk/study/IA/AnalysisI/2015-2016/sheet3.pdf18 Feb 2016: f(x) = limx. g(x) = 0. Assume that for some c > 0, we have g′(x) 6= 0 for all x > c and that f′(x)g′(x). ... Show thatif f ′(a) < y < f ′(b) for some a < b in I and y R, then there exists x I witha < x < b and f ′(x) = y. -
ANALYSIS I EXAMPLES 2 G.P. Paternain Lent 2012 Comments ...
www.dpmms.cam.ac.uk/study/IA/AnalysisI/2011-2012/aI_2.pdf7 Feb 2012: 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 ...
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. -
Proofs for some results inTopics in Analysis T. W. ...
www.dpmms.cam.ac.uk/study/II/TopicsinAnalysis/2023-2024/Caesar.pdf25 Oct 2023: Proofs for some results inTopics in Analysis. T. W. Körner. October 25, 2023. ... Now P(z) = 0 if and only if z = ajfor some 1 j m. -
STABILIZERS OF IRREDUCIBLE COMPONENTS OF AFFINEDELIGNE–LUSZTIG…
https://www.dpmms.cam.ac.uk/~rz240/stabilizer.pdf25 Aug 2021: We refer to [VW11], [HP17], and[LT20] for some special cases of this result. ... If α = αv′ for some v′ {v}, then we define d(α,v) = d(v′).
Refine your results
Date
- 83 2021
- 58 2020
- 48 Past year
- 40 2008
- 39 2023
- 36 2016
- 35 2019
- 35 2010
- 32 2015
- 32 2009
- 30 2012
- 30 2014
- 29 2007
- 28 2022
- 27 2018
- 27 2017
- 26 2024
- 24 2011
- 24 2013
- 23 2006
- 22 2005
- 21 Past 6 months
- 11 Past 3 months
- 9 2002
- 8 2003
- 7 2001
- 6 2004
- 3 Past fortnight
- 3 Past month
- 2 Past week
- 2 Yesterday
- 1 1998
- 1 2000
Search history
Recently clicked results
Recently clicked results
Your click history is empty.
Recent searches
Recent searches
Your search history is empty.