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27 Apr 2021: Years later i found the complete scripts in an op shop, and yes, the ad lib.

23 May 2024: For the first part of the lemma, assume that Op has uniformiser t. ... intersection of setsΣi,p B(Op) for all primes p (finite and infinite).

23 Nov 2018: Prove the following: (i) if A L(Rn; Rm) then ‖A‖op =supxRn{0}. ... then 1n. (nj=1. mi=1 A. 2ij. )1/2‖A‖op. (nj=1. mi=1 A. 2ij.

18 Mar 2013: Theorem 6.1. P is a smooth point of V iff mP OP is a principal ideal. ... So in OP we have. xj = hj(x1,. ,xn) (x21,x1x2,. ,x2n) = m2P , (2 j n).

27 Oct 2014: We can identify that with. Σ(Sets2 Sets)op ,. the result of freely adding sums to the opposite of Setsindexed over Sets. ... Pol(PolF) = Σ(ΣFop)op = ΣΠF. and so one can find it inside the iterated polynomialmodel.

5 Jun 2020: FEFF005500740069006c0069006300650020006500730074006100200063006f006e0066006900670075007200610063006900f3006e0020007000610072006100200063007200650061007200200064006f00630075006d0065006e0074006f0073002000640065002000410064006f00620065002000500044004600

22 Oct 2020: Byconstruction j1OP(E1)(1) = OY (H2). Moreover, if ζ denotes the class of OP(E1)(1) inPic(P(E1)), then it is easy to compute. ... 32 = 0 on Y. So Y is indeed a. quadric surface fibration, cut out by a section of OP(E1)(2) O(2H1) on P(E1).

29 Jul 2011: op. Since I I is a central isogeny, UI U and UopI U. ... op. are isomorphisms.Step 4. The maps log and exp provide inverse isomorphisms of va-.

13 May 2006: Suppose given Ap SLn(Op) for all p S and let ε > 0. ... Suppose given Ap Matn(Op) with det(Ap) = δ for all p S and letε > 0.

28 Feb 2018: OP , where O denotes the origin. 3. Show the stereographic projection map π : S {N} C, where N denotes the northpole, defines a chart.

28 Feb 2022: Henry Reed. I learnt a new word the other day, from a copy (which i found in an op shop in Gisborne) of Mauve Gloves and Madmen, Clutter and Vine by

31 Jan 2006: "$#&%')(,.-0/214356,8793:<;='>:(?4@ ,.ACBED>79FG?4@IHKJ+@@LNM. O QPSRUTV2WYXZX W0 [ ])_ab>cW0d efhgjiZkml+ZnNbXopqb]KXr W srtXu]Wv [w ]kPSRqRxT>lZnyzXro{e|d efYrt ][w }Xr W sRqCgji kt ][w >kml+ZnNzXro{uowuaRxus4e|Yd efYKX WY rc [

18 Mar 2013: It is not hard to show that P is just the module of differentials OP /k.). ... Proof. Obviously OP dπP P. Let f = f(P) πP g OP = k mP.

4 Apr 2018: P : Mon(V)op Mon(V) Comon(V) (30)is called the Sweedler hom in [4]. ... The functor P (, ) : Mon(V)op Mon(V) Comon(V) is continuousin each variable.

10 Feb 2006: Ïf]WZp[Ñ<&&cfeEpOCWZooÇe;]lY[[XCf[;][Y[;O)£zËEszW¡Ô+[;<f{ Ð []fe»[;:p_[6a?ooacfÑÑda[Ipf?phËEsÕtÖ}:oZoCX{McÑÑ)[Op<fMpuË;i¤yy;yËEsz&l[Ce;]lY[[nl1up}ØÙ{Ã[;]. ... Ñ)][]p<Wo :c]eEpW]æhCW¡eCWoZo

14 Jun 2021: more widely known.The locus classicus for C20 Nonstandard Analysis is of course AbrahamRobinson op cit, but nowadays there are are other approaches to infinitesi-mals that have become available.

7 Aug 2008: Let us now consider algebraic operations op : (RR)I (RR)O of arity. ... op′X> (T ′X)O. Conversely, if op, op′ are algebraic operations such that the above diagram com-mutes then op′ can be obtained from op by the above process,

31 Jan 2007: "!$#&%')(,.-0/214356,8793:<;='>:(?4@ ,.ACBED>79FG?4@IHKJ+@@LNM. O QPSRUTV2WYXZX W0" [ ])_ab>cW0d efhgjiZkml+ZnNbXopqb]KXr W srtX"u]Wv" [w ]kPSRqRxT>lZnyzXro{e|d" "efYrt ][w }Xr W sRqCgjikt ][w >kml+ZnNzXro{uowuaRxus4e|Yd efYKX WY rc" [

14 Feb 2007: "!$#&%')(,.-0/214356,8793:<;='>:(?4@ ,.ACBED>79FG?4@IHKJ+@@LNM. OPQP RSUT">RQVWRXKYZ[U 0] Y_a[bcdRSe"fKRSWgh[ P RSi P RXY_]RQejRQk_RSml. n op deWUdKWqi bkb[UYZrjsturvj]wxW0 ... u P __z]w9rIRX0U ]_UR|wdzw" 08 n WdfWdRSwzRXKR P i.]_UWghRXK[RS[KWU]W n) z]Uk

12 Mar 2019: Part IB GEOMETRY (Lent 2019): Example Sheet 3. (jb128@dpmms.cam.ac.uk). 1. Let V be the open subset {0 < u < π, 0 < v < 2π}, and σ : V S2 be given by. σ(u, v) = (sin u cos v, sin u sin v, cos u). Prove that σ defines a smooth parametrization of

15 Oct 2021: We clearly have that for any non-zero x Rn:. ||Ax|| ||A||op. ... x||. holds for any x and thus||An||op. ||A||. nop. Definition 29.

13 Feb 2006: "$#&%')(,.-0/214356,8793:<;='>:(?4@ ,.ACBED>79FG?4@IHKJ+@@LNM. OPQP RSUT>RQVWRXKYZ[U 0] Y_a[bcdRSefKRSWgh[ P RSi P RXY_]RQejRQk_RSmln op deWUdKWqi bkb[UYZrjsturvj]wxW0 RSUTKr0sdyrvjRXz ... nK h j[RS}RQRSR>op deWU]KW0R P i_ P z>w VRXkb P RQgrh}RQeb

21 Nov 2016: 10. Let f : Rn Rn be a C1 map. Suppose that there is some constant µ < 1 such that‖Df|x I‖op µ for all x Rn.

21 May 2005: OP , where O denotes the origin. (2) Let V be the open subset {0 < u < π, 0 < v < 2π}, and σ : V S2 be given by.

1 Mar 2018: OP , where O denotes the origin. 3. Show the stereographic projection map π : S {N} C, where N denotes the northpole, defines a chart.

26 Oct 2013: We can identify that with. Σ(Sets2 Sets)op ,. the result of freely adding sums to the opposite of Setsindexed over Sets. ... Pol(PolF) = Σ(ΣFop)op = ΣΠF. one can find the Dialectica model inside the iteratedpolynomial model.

21 Feb 2011: vector OP , where O denotes the origin.

17 Feb 2010: Part IB GEOMETRY, Examples sheet 3 (Lent 2010, Burt Totaro). (1) Show that the tangent space to S2 at a point P = (x, y, z) S2 is the plane. normal to the vectorOP , where O denotes the origin. (2) Let V be the open subset {0 < u < π, 0 < v < 2π}

2 Mar 2017: OP , where O denotes the origin. 3. Show the stereographic projection map π : S {N} C, where N denotes the northpole, defines a chart.

7 Feb 2006: OP , where O denotes the origin. (2) Let V be the open subset {0 < u < π, 0 < v < 2π}, and σ : V S2 be given by.

6 Mar 2008: OP , where O denotes the origin. (2) Let V be the open subset {0 < u < π, 0 < v < 2π}, and σ : V S2 be given by.

2 Mar 2007: OP , where O denotes the origin. (2) Let V be the open subset {0 < u < π, 0 < v < 2π}, and σ : V S2 be given by.

2 Mar 2007: together with a strict product preserving identity-on-objects functor from the op-. ... extend the monad for groups from Set to T op. That is reasonably straightforward,.

9 Mar 2016: OP , where O denotes the origin. 3. Show the stereographic projection map π : S {N} C, where N denotes the northpole, defines a chart.

5 Jun 2020: Chapter 5 it is shown to enjoy important op-timality properties.

17 Apr 2015: OP , where O denotes the origin. 2. Let V be the open subset {0 < u < π, 0 < v < 2π}, and σ : V S2 be given byσ(u,v) = (sin u cos

5 Jun 2020: The problem of op-timally choosing a distribution from M to describe our data in as few bits as possibleis exactly the topic of an area known as universal data compression

17 Oct 2016: non-stochastic), then AnXnd AX. iv) If Xnd X as n , then (Xn)n0 is bounded in probability, or Xn = OP (1), i.e.

13 Nov 2006: "#%$'&((). -,/.1032547698".;:=<>?@0A.CBD:FEHG%?HI'.KJL0A.M>IN?HG%>POQ:F>RTSVU1OWS=X-INYZ8[FNG%YZ]I'GF_BD:FEab2c476!deOWf'?H0Ngh<ZJL.MRi<.MEHRIjUMOj X7kml? n>Ro0NgZ.<Jp.MR<.MEHRoGFPS Uq S X

29 Sep 2003: Q|svGG|QduËO: pvy6zu+p{'}vzucp{ÖH6vJ|u_{vOp{HMO|d}VucOz{Hyzu_xu_9pu_}O È {v{HurtsvdH{Hsvzu_xMuM|{HosvGQ{oz{|'|svu:z{vz{v¡Op QsHuMud

19 Jan 2018: 10. Let f : Rn Rn be a C1 map. Suppose that there is some constant µ < 1 such that‖Df|x I‖op < µ for all x Rn.

17 May 2024: IBM T.J. WATSON RESEARCH CENTER (USA) June 1995 – Dec. 1995Research Co-op.

21 Oct 2015: subgroup of G is denoted Op(G) and the Fitting and second Fittingsubgroups are denoted by F(G) and F2(G) respectively.

7 Aug 2008: Superconvex spaces have, admittedly, a rather profligate collection of op-erations. However one can economise: they can all be defined in terms of onesuch operation, for example that where pn =

7 Jul 2007: and he wrote the op-eration on ordinals with a ‘U ’ not a ‘T ’.3 |[0, n]| is two types higherthan n.

5 Jun 2020: FEFF005500740069006c0069006300650020006500730074006100200063006f006e0066006900670075007200610063006900f3006e0020007000610072006100200063007200650061007200200064006f00630075006d0065006e0074006f0073002000640065002000410064006f00620065002000500044004600

29 Jan 2010: Let op be the localisation of oK at p. As in the proof of 4.5, we observe that bycondition (i), the dening equation (4.5.1) gives a nite morphism ... P1 op whosegeneric bre is j:X! P1K. Hence in the notation of 2.15 the morphism jZ :X!

5 Jun 2020: FEFF005500740069006c0069006300650020006500730074006100200063006f006e0066006900670075007200610063006900f3006e0020007000610072006100200063007200650061007200200064006f00630075006d0065006e0074006f0073002000640065002000410064006f00620065002000500044004600

11 Jan 2013: Let Op Kp be the valuation ring and Ip Gpthe inertia subgroup. ... Lemma 6.1. If λ Op with λ(λ 1)(λ3 8λ2 5λ 1) 6 0 (mod p) thenim δp = Op /(Op )7 and im δ′p = Hom(Gp/Ip,

5 Jun 2020: address the question of how close one can come to the optimumperformance theoretically achievable (OPTA) function, as op-posed to the rate-distortion function. ... of the form on. Taking to be the optimalreproduction distribution at distortion level, the