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14 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.

14 Dec 2005: 5?/2 g à )9 $DtÄyª g à 93x?ÄVg à ;9 $D»Äª B B Ã Ä G. ... Bg à ;9 D<Ä G. ÆIg à )9 D,<?Äyª B B à 9Ä.

21 May 2005: BA. B. B. B. A A D. A. DCC. AA A A. ... 4, 5, 6} }. B B. AA. 2. 1. 2. 1. 3 4. 65. defines a simplicial complex that is a pseudo 2-manifold but not a 2-manifold.

28 Feb 2005: The reverse is not true, e.g. (fn a => fn b => b) (fn x => x x). ... is untypeable even though. fn b => b. is typeable. Pathologies of typechecking.

24 Apr 2005: G=<{D8;E &b c C 4 V x 2. G=< e H! ... BEDxKFIiWTGZXpbX AfDXRg! KPB"G N IP2eKPMT]OZXB b R 4 $4 GFw]TXRMTDPBHX BHWTX?

25 Oct 2005: A – B = A – B – (Ap B) – (B p A)must be also accepted, because. ... a ::= n |X |a a | aa |aa ;b ::= true | false | a a | b | b b ;c ::= skip | X := a | X := χ| c; c | if b then c else c | c or

17 Feb 2005: mf (b, b). xkymk. ei(bκ1aκ2) mf (b, a). xkymk+ ei(aκ1aκ2). mf (a, a). ... s 1, k = 1, 2, 3, 4,. wherev1 = (b, b), v2 = (b, a), v3 = (a, a), v4 = (a, b).

9 Aug 2005: For example: News in “Lisa Stark, A. B. C. News, Washington” (normally A. ... B. C. news) the President (normally the president apart from the President of U.

15 Sep 2005: successively larger instructions. LPn 3 n 16 B := A; A := P!nLP b B := A; A := P!bLPH h B := A; A := P!hLPW w B := A; A := P!w. ... instructions. The other cases use successively larger instructions. LG b B := A; A := G!bLG1 b B := A; A := G!(b 256)LGH h

21 May 2005: A B = {a b : a A, b B}, AB = {ab : a A, b B}. ... It shouldbe clear that. b. af > 0, and you should explain why this is so.

2 Sep 2005: 16+;: H$+?18-0K8<8/'j?/2147.<>B[B BG<?3$BTHVR<LB[BHAO$<. )! ... S O#;B09,Rj$@ <HAO49NAO# j8/2147L<LB[BG<LBWKH.=8<H f BC-GH.-9 7Ag«?LTÉ#0ªD80ªvF&iH$+?3kH3SU$+HR9 7aØWÑLvªETÉ#>ªr80ªvF&$. 9 'j8/2147.<>B[B

9 Aug 2005: £ð5M-ERDMNSéø3v s d d ( Nd û|uü | ø. T%B%V% T(! ... ERDMZSMZà EH<ZîZ["Û<-QHMZ=?SLT Û["ë3MNSLT?ÛdMZS#<ZûNûZðWÅ;[SsERD=?B fã.

29 Jan 2005: an R2n2. Proposition 6 The following is true:. B>B C>C = I, (4.3). ... a>p aq = [ b>p c. >p ]. [. bqcq. ]. = (b>p bq c>p cq) = (B. >B C>C)p,q = δp,q.

25 Jan 2005: iii) A standard notation for the size, i.e. number of elements, of a finite set Bis |B|. ... a) Explain why |A B| = |A| |B| |A B|, for finite sets A and B.

24 Apr 2005: 7 @?A% B DGF H J /! 78+#/! ; & 5$ ),H ; 3 £? V BN 8% $! ; ' ... N ¥ A "p ), ( " N ¥ A = & Q' 5 B u p 2@A u.

21 May 2005: 6. If A and B are subsets of Rn, we write A B for the set {a b : a A,b B}. ... Show that if Aand B are both closed and one of them is bounded, then A B is closed.

20 Sep 2005: r). A B, B A(r). (A B) (B A)(r). Lawrence C. ... Part of a Distributive Law. AA, BB, CA, B. B CA, B(l).

9 Aug 2005: E 9v?"(9Q"$ /Q58 Qv?"-! B!"1l Q Q } 8r? " vV( v! ... b v;X 2t ; ' v( Q?" rv! 8?": v( 3R?3Rvv v 2t < H8.

19 Jan 2005: by solving. (A B)x(k1) = Bx(k) b, k = 0, 1, 2,. ... If the real symmetric matrices A and A B B> areboth positive definite, then the spectral radius ofH = (A B)1B is strictly less than one.

21 May 2005: 6. If A and B are subsets of Rn, we write A B for the set {a b : a A, b B}. ... Show that if Aand B are both closed and one of them is bounded, then A B is closed.