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Modular curves and Ne19 eron models of generalized Jacobians
https://www.dpmms.cam.ac.uk/~ajs1005/preprints/neronfinal.pdf10 Feb 2023: Ṽ = AtC, Ẽ = B.6. • The endpoints of an edge b B are φ(b) A and ψ(b) C.The graph Γ̃Y is bipartite, and therefore has a canonical structure ... Then f inducesmaps A′ A, B′ B, C′ C which we also denote by f. -
vt06final.dvi
https://www.dpmms.cam.ac.uk/~ik355/PAPERS/vt.pdf5 Jun 2020: Theorem 2.2:Let Φ = {Φi : i 0} be anarbitraryMarkov chain with values onX, let B B be fixedmeasurable set, and letF1,F2,. ... n 1)H(γ‖γ1 P), (32). where γ is a bivariate probability measure on(X X,B B), whose marginalsγ1 andγ2 satisfy,. -
Riemannian metrics define ordinary metrics Recall that if g ...
https://www.dpmms.cam.ac.uk/~jar60/GeometryHandout1.pdf11 Feb 2014: Now let γ : [a,b] B(p) be a smooth path. If Lg(γ) and L(γ) are the lengthsof γ with respect to g and the Euclidean metric, then. ... theorem implies theremust be some point t [a,b] with d(γ(t)) = /2. -
Quasirandomness, Counting and Regularity for 3-Uniform Hypergraphs W. …
https://www.dpmms.cam.ac.uk/~wtg10/belapaper.pdf14 Mar 2005: Proof. Define B [N]2 to be the set of all (x,y) such that xy A. ... labelling vertices of a cube (as they would if a, b and c denoted three orthogonal vectors. -
Part III: Differential geometry (Michaelmas 2004) Alexei Kovalev…
https://www.dpmms.cam.ac.uk/~agk22/vb.pdf11 Nov 2019: Define an equivalencerelation between elements (b,h) UαG, (b′,h′) UβG, so that (b,h) (b′,h′) preciselyif b′ = b and h′ = ψβα(b)h. ... point b B is determined by the value s(b) at that point. -
LINEAR ANALYSIS – EXAMPLES 4 The “*” questions are ...
https://www.dpmms.cam.ac.uk/study/II/LinearAnalysis/2020-2021/EX-LinAn-4.pdf19 Jan 2021: 11. Let T B(B) compact and λ 6 (σp(T) {0}). Show that T λ is bounded below. ... 15. Given T B(B) define r1(T) := supλσ(T) |λ|. Show that the limit r2(T) :=limn |||Tn|||. -
� � � � � � � � � ...
https://www.dpmms.cam.ac.uk/~ajs1005/ega-index.pdf29 Jan 2010: x a u w t b w , - U k T V U 4 Q ( 8 g _ x ] ] w b _ b c e g h O - 0 4 6 1 k V ... c g h i j k@ A B @ B C B B B B D B E F G D H @ B C I J C @ BB B B D K -
A Dialectica-style Interpretation of Type Theory - Symposium in…
https://www.dpmms.cam.ac.uk/~jmeh1/Research/Slides/venice13.pdf27 Oct 2014: Concretely we have. Objects Over b B: x E(b′) with u : b′ b.Maps From y with v : c′ c to x with u : b′ b :. c′v. - c. y ... Bf. - A. '. a A, b B.IdA(f (b), a). -. B. wwwwwwwwwwwwwwwwwwwwwwwwf. -. -. A. wwwwwwwwwwwwwwwwwwwwwwww. The Sceptics -
neessnmeiwseis.dvi
https://www.dpmms.cam.ac.uk/~md384/neessnmeiwseis.pdf27 Nov 2012: Let (M,g) be a Riemannian manifold. A curve γ : (a,b) Mis said to be a geodesic if it locally minimises arc length, i.e. ... integral curve of V with γ(0) =, then T a < b T+ andγ|(a,b) = γ̃. -
Homotopy Theory, Examples 4 Oscar Randal-Williams Lent 2021 All ...
https://www.dpmms.cam.ac.uk/~or257/teaching/IIIHtyThy2021/Sheet4.pdf16 Mar 2021: ii) Show that iA iB : H̃(A) H̃(B) H̃(M {}) is an isomorphism. ... by pulling backE F B B along the diagonal; relate Th(E F) to Th(E) and Th(F)]. -
MOD-p ISOGENY CLASSES ON SHIMURA VARIETIES WITH PARAHORIC LEVEL ...
https://www.dpmms.cam.ac.uk/~rz240/Mod-p_isog2.pdf22 Oct 2020: GOL = Gx = Gx for somex B(G,L) as above and also that G contains the scalars. ... We assume G isof the form Gx for some x B(G,Qp). -
Homotopy Theory, Examples 3 Oscar Randal-Williams Lent 2021 1.* ...
https://www.dpmms.cam.ac.uk/~or257/teaching/IIIHtyThy2021/Sheet3.pdf16 Mar 2021: F i //. Ep //. p. B. {b0} // B B. ... for some monic polynomial p(x) H(B; Z)[x]. Homotopy Theory Example sheet 3. -
Analysis II Michaelmas 2017 Example Sheet 2 1. Let ...
https://www.dpmms.cam.ac.uk/~jar60/AnalysisII_2017_Ex2.pdf22 Oct 2017: Hint: Bolzano-Weierstrass.). 3. If A and B are subsets of Rn, let A B = {a b |a A,b B}. ... a) f(x) = sin x2 (b) f(x) = inf{|xn2| |n Z} (c) (sin x3)/(x 1). -
RN (nickl@maths.cam.ac.uk) Michaelmas 2022 Probability and Measure 1…
https://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 ... 1.8. Let B be a Borel subset of the interval [0, 1]. -
INDEPENDENCE OF ` FOR FROBENIUS CONJUGACY CLASSES ATTACHED TO ...
https://www.dpmms.cam.ac.uk/~rz240/l-indep_v2.pdf23 Jan 2023: Suppose there exists a class [b] B(G,{µ}) such that ν[b] = µ(such a class is necessarily unique if it exists by the above remark). ... µ. ′. INDEPENDENCE OF FOR FROBENIUS CONJUGACY CLASSES 11. (2) Let [b] B(G,µ) and [b′] := [f(b)] B(G′,{µ′}) -
REMARKS ON GLUING PUNCTURED LOGARITHMIC MAPS MARK GROSS Abstract. ...
https://www.dpmms.cam.ac.uk/~mg475/gluing.pdf6 Mar 2023: 2.2) Σ(C) = Γ(G,). // Σ(X). Σ(W) = ω = QR // Σ(B). ... stacks. We remind the reader that allproducts in this square are taken over B. -
Easter Term 2022 Optimization - Examples Sheet 1 1. ...
https://www.dpmms.cam.ac.uk/study/IB/Optimization/2021-2022/ex1.pdf26 Apr 2022: an and b 0, consider the problem. minimizen. i=1. aixi subject ton. ... a) minimize cT x subject to Ax = b. (b) minimize cT x subject to Ax b. -
Stable moduli spaces of high dimensional manifolds Oscar…
https://www.dpmms.cam.ac.uk/~or257/StabilityIIOberwolfach.pdf22 Sep 2014: Secondly, let hAut(θ) denote the grouplike topological monoid of self-homotopy. equivalences of B over BO(2n), i.e. ... homotopy equivalences f : B B such that. θ f = θ. -
Part II Differential Geometry Example Sheet 2 Prof. M. ...
https://www.dpmms.cam.ac.uk/~md384/m16dgp2_examplesheet2.pdf23 Oct 2016: φ(s,v) = α(s) r(n(s) cos v b(s) sin v). where n = n(s) and b = b(s) are the normal and binormal vectors of α. ... 10. Consider a surface of revolution parametrized by φ : (0, 2π) (a,b) R3, where. -
Analysis II Example Sheet 2 Michaelmas 2006 MJW Corrections ...
https://www.dpmms.cam.ac.uk/study/IB/AnalysisII/2006-2007/ex2.pdf27 Oct 2006: 0|f| a normed space? 3. Which of the following subsets of R2 are (a) open, (b) closed? ... Show that there exist disjoint closed subsets A, B of R (or R2 if you prefer) withd(A, B) = 0. -
ANALYSIS II (Michaelmas 2009): EXAMPLES 2 The questions are ...
https://www.dpmms.cam.ac.uk/~agk22/anII-09-2.pdf26 Oct 2009: B}. Show thatif A and B are both closed and one of them is bounded then A B is closed. ... b) Is the space R[0, 1] of integrable functions on [0, 1], equipped with the uniform norm, complete? -
RN Michaelmas 2020 Probability and Measure 1 1.1. Let ...
https://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 ... 1.8. Let B be a Borel subset of the interval [0, 1]. -
Rips Theory.dvi
https://www.dpmms.cam.ac.uk/~hjrw2/Notes/rips.pdf18 Sep 2014: Lemma 3.3 Let B = b I be a Möbius band in X. ... Then λ must intersectsome band B = b I in at least 5 vertical segments. -
Analysis of Functions Dr. Claude Warnick May 1, 2021 ...
https://www.dpmms.cam.ac.uk/~cmw50/AoF.pdf6 Aug 2021: c) If A and B are both bounded, then so is A B. ... e) If A and B are both compact, then so is A B. -
us_paper.dvi
https://www.dpmms.cam.ac.uk/~ik355/PAPERS/suhov1.pdf5 Jun 2020: ixs xs. Here B B denotes the algebra generated by B and B and xs xs. ... suces to check that. limN. ess sup supA BN. PA j B PA. -
Top.dvi
https://www.dpmms.cam.ac.uk/~twk10/Top.pdf6 Dec 2021: Exercise 2.4. Let X = {a, b, c} with a, b and c distinct. ... Then B(x, 1/j) isopen, but. j=1 B(x, 1/j) = {x} is not. -
REPRESENTATION THEORY SIMON WADSLEY Contents Lecture 1 21.…
https://www.dpmms.cam.ac.uk/~sjw47/2023Lectures.pdf29 Nov 2023: 10if (ii) holds then (i)(a) is equivalent to (i)(b).11(ii) gives that (x,x) R. ... a2 3b2 2c2). Thus we see quickly that b = 0, a 2c = 0 and a2 2c2 = 6. -
Compressions and Probably IntersectingFamilies Paul A. Russell ∗†…
https://www.dpmms.cam.ac.uk/~par31/preprints/probint.pdf16 Aug 2011: family B A, we form the family φ(B) byreplacing appropriately chosen B B by CijB. ... Then there existsan injection φ : I(A) I(C) such that |φ(B)| = |B| for all B I(A). -
Mich. 2022 ANALYSIS AND TOPOLOGY—EXAMPLES 4 PAR 1. Define ...
https://www.dpmms.cam.ac.uk/study/IB/AnalysisandTopology/2022-2023/22sheet4.pdf24 Nov 2022: D2f exists at (a, b). Show that f is differentiable at (a, b). ... b) Suppose instead that D1f exists and is bounded on some open ball around (a, b), and. -
K-THEORY JACK SMITH 1. Introduction 1.1. Preamble. These are ...
https://www.dpmms.cam.ac.uk/~jes98/K-TheoryWeb.pdf27 Oct 2019: b a ,. for all a and b, so a b = a b = ba. ... Definition 3.4. An principal G-bundle is a triple (E,B,π) where:. • E is a space carrying a (continuous) G-action.• π is a map E B.• B is -
Partial Solutions for Exercises inNaive Decision Making T. W. ...
https://www.dpmms.cam.ac.uk/~twk10/Naiverep.pdf30 Aug 2022: 47. A A B B C CB C C A A BC B A C B AD C D C B B. ... Table 3. Two-sided die thrown four times. A A A A B B B B C C C C D D D DA B C D A B C D -
numset42020.dvi
https://www.dpmms.cam.ac.uk/study/IA/Numbers%2BSets/2020-2021/numset42020.pdf23 Nov 2020: 3. The symmetric difference of sets A and B is A B = (A B) (B A). ... 8. Define a relation R on N by setting aRb if a divides b or b divides a. -
Algebraic Topology, Examples 4 Michaelmas 2020 Questions marked by ...
https://www.dpmms.cam.ac.uk/study/II/AlgebraicTopology/2020-2021/Sheet4.pdf23 Nov 2020: b) Use the Mayer–Vietoris sequence to compute the homology of Σg#Sn, andhence deduce that it is homeomorphic to Sn2g. ... Show that the linear map A : R2 R2 preserves the equivalence relation (a,b) (a′,b′) (aa′,b b′) Z2,and so induces a -
LINEAR ANALYSIS – EXAMPLES 4 H is a complex ...
https://www.dpmms.cam.ac.uk/study/II/LinearAnalysis/2022-2023/EX-LinAn-4.pdf28 Oct 2022: 11. Let T B(B) compact and λ 6 (σp(T) {0}). Show that T λ is bounded below. ... 14. Given T B(H), define W(T) := {〈Tx,x〉, ‖x‖ = 1} C. -
Optimisation send comments to m.tehranchi@statslab.cam.ac.ukExample…
https://www.dpmms.cam.ac.uk/study/IB/Optimization/2019-2020/example1.pdf14 May 2020: For b R let. ϕ(b) = inf{f(x) : g(x) b, x X}. ... Assuming that ϕ(b) > for all b R, show that ϕ is convex. -
Example sheet 1 Example sheet 1 Problem 1. Show ...
https://www.dpmms.cam.ac.uk/study/IB/Optimization/2020-2021/example1rev.pdf21 May 2021: an and b 0, consider the problem. minimizen. i=1. aixi. subject ton. ... a) minimize cT x subject to Ax = b. (b) minimize cT x subject to Ax b. -
Michaelmas Term 2022-23 Numbers and Sets: Examples Sheet 4 ...
https://www.dpmms.cam.ac.uk/study/IA/Numbers%2BSets/2022-2023/numset4_2022.pdf19 Nov 2022: 3. The symmetric difference of two sets A and B is A4B = (AB) (B A). ... 8. Define a relation R on N by setting aRb if a divides b or b divides a. -
ON THE CARTAN MAP FOR CROSSED PRODUCTS ANDHOPF-GALOIS EXTENSIONS ...
https://www.dpmms.cam.ac.uk/~sjw47/HopfGalois.pdf27 Feb 2008: If M is an A-module and N is a B-module, then. ... in A, the following conditions hold:• if A,C B then B B,• if B,C B then A B. -
GLOBAL SECTIONS OF EQUIVARIANT LINE BUNDLES ON THE p-ADIC ...
https://www.dpmms.cam.ac.uk/~sjw47/Drinfeld.pdf20 Dec 2023: LetB be a K-Banach algebra, let θ: A B is a K-Banach algebra homomorphismand b B. ... b) (i) b B,(ii) bθ(a) θ(a)b = θ(δ(a)) for all a A,. -
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https://www.dpmms.cam.ac.uk/study/IA/AnalysisI/2005-2006/sheet4.pdf27 Feb 2006: ngi{_bie|g?t}&X;phYXXq&ZY[X+]. u:/u&9qfYucwE9& :q&>j uc Efc;A :q&> uc 9&E U ... k&mnbi]n}ZY[X}&XlZ<X;h<{y_]nbi]pZZ<ggi¥&Zb?_]b?]b?eoZYXhY]nb?ZY_iXµt:gphY{eb?ZY_gi]vg?tZY[_wWt9bpEZA[nb?Z«}&gfXWqZY[_wWh<X+}& -
LINEAR ANALYSIS – EXAMPLES 4 H is a complex ...
https://www.dpmms.cam.ac.uk/study/II/LinearAnalysis/2021-2022/EX-LinAn-4.pdf29 Nov 2021: 11. Let T B(B) compact and λ 6 (σp(T) {0}). Show that T λ is bounded below. ... 14. Given T B(H), define W(T) := {〈Tx,x〉, ‖x‖ = 1} C. -
Pattern Matching and Lossy Data Compression on Random Fields ...
https://www.dpmms.cam.ac.uk/~ik355/PAPERS/RFS2.pdf5 Jun 2020: φ(k) = sup{|P(B|A) P(B)| : B σ(XU ), A σ(XV ), P(A) > 0|U| , |V | < , d(U,V ) k}. ... IEEE Trans. Inform. Theory, 39(3):877–886, 1993. [25] T. Wiegand and B. -
ANALYSIS II EXAMPLES 2 Michaelmas 2005 J. M. E. ...
https://www.dpmms.cam.ac.uk/~jmeh1/Teaching/an05-2.pdf19 Mar 2008: 4. Which of the following subsets of R2 are (a) open, (b) closed? ... 1. 2 ANALYSIS II EXAMPLES 2. 7. If A and B are subsets of Rn, we write A B for the set {a b : a A, b B}. -
C:\Documents and…
https://www.dpmms.cam.ac.uk/~ik355/PAPERS/balanced.pdf5 Jun 2020: The process of routing calls through the directlink is an M/M/B/B loss system (Poisson arrival, exponential service time,B servers—corresponding to the B direct links, up to ... Applying Erlang’s loss formula (e.g., [9]),. P1 =(λ/µ)B. B! (B. i=0. ( -
Michaelmas Term 2021-22 Numbers and Sets: Examples Sheet 4 ...
https://www.dpmms.cam.ac.uk/study/IA/Numbers%2BSets/2021-2022/numset4_2021.pdf23 Nov 2021: 3. The symmetric difference of two sets A and B is A4B = (AB) (B A). ... 8. Define a relation R on N by setting aRb if a divides b or b divides a. -
numset42019.dvi
https://www.dpmms.cam.ac.uk/study/IA/Numbers%2BSets/2019-2020/numset42019.pdf27 Nov 2019: 3. The symmetric difference of sets A and B is A B = (A B) (B A). ... 8. Define a relation R on N by setting aRb if a divides b or b divides a. -
Algebraic Topology, Examples 4 Michaelmas 2019 Questions marked by ...
https://www.dpmms.cam.ac.uk/study/II/AlgebraicTopology/2019-2020/Sheet4.pdf25 Nov 2019: b) Use the Mayer–Vietoris sequence to compute the homology of Σg#Sn, andhence deduce that it is homeomorphic to Sn2g. ... Show that the linear map A : R2 R2 preserves the equivalence relation (a,b) (a′,b′) (aa′,b b′) Z2,and so induces a -
GRAPH THEORY - EXAMPLE SHEET 4 Lent 2021 Julian ...
https://www.dpmms.cam.ac.uk/study/II/Graphs/2020-2021/example-sheets-4.pdf15 Mar 2021: 1. |B|vB. d(v) > (α ε)|A|. Show there is B′ B with |B′| > ε|B| so that d(v) > α|A|, for all v B′. ... Prove that A. contains an infinite set B such that no point of B is a convex combination of other points of B. -
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https://www.dpmms.cam.ac.uk/study/IA/Numbers%2BSets/2006-2007/numset32006.pdf8 Nov 2006: 4O:=<CKI@asgD6m{¡MO<>MK?b |7| IU6 J8;:U47L :@JMnMOD:@J¢{0:[ADIPM<=8;:ib |j b |g Sh,£?b | b |g SG[ADIPMub |7|; VT:iU6 J8;:U47L ... B64u<CKC º 1 jsgD6m{MO<>Mub |7|; U6 J8;:U47L :@I@G}<JDWWD:UMO:U47[tJD:nKMOIkCK[tKM@» t4O:=<ChJAD[aV :4ubvea¿>b b b d -
Families Intersecting on an Interval Paul A. Russell∗† October ...
https://www.dpmms.cam.ac.uk/~par31/preprints/intersections.pdf10 Oct 2006: n}.How large can we make a family A of subsets of [n] subject to thecondition that for all A, A′ A, there is some B B with B A A′? ... n}.How large can we make a family A of subsets of [n] subject to thecondition that for all A, A′ A, there is some
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