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9 Jan 2009: Colle-ges geven op zichzelf niet een volledig begrip. 4 4. 4 4. ... volgen zoals deze tevoorschijn komen enniet door deze slechts blindelings op te schrij-ven.

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).

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.

13 Dec 2017: 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.

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.

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

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" [

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

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

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.