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8 Dec 2005: Position relative to pile tip, 2h/B(b). Vol. umet. ric s. trai. ... 18. 200 2 4 6 8 10. Horizontal position relative to pile tip, 2x/B(b).

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.

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.

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.

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.

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.

9 Aug 2005: D /kb,"FiAF,"b.@b(D 5/ 5tEb?A,F,Bsk7 bBKb?4.'b. ... kD x?A,"Fb?4.'/ b?A5kB), 5cAb.D /A,8 DZt j,. 7n795j,8 bF.D /kDl/}x].'/48 b, B)b(D /}x]B,"bBEb?4.'b6.'F, /A5b68D9B9G5D

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.

24 Apr 2005: d( 6 Á j¤ : %'=:<> iÁ Á j¤ : %'=: 'Áª B # z zE C @EF Õ$# C! ... E. E. Õ E. Õ E. Õ. Õ. [E. [E. B #. B #. f«z Ñ / ¡ @zRDR@¤H Å zRzHzRp«$ ¢ª@HRHz ¡ ¡¡ zHªD « 4Gg2 S l %' #¤z¿ ( Á @?KJ B|DzR/ #

9 Aug 2005: $%! b%)(P3- % A "& 8$C(/$%B#."&TS %fN % B7 &N # )(.&B#.8 7G+ / %&&)(P%WPb%B&b%B!'&"#G6B&! & "# ... 7= # % &N (< %"! B7 <= # %. #b <b% 8. %BA -b%B!<'&B#.@(<b%B7bB! % 8 )($! %

21 May 2005: BA. B. B. B. A A D. A. DCC. AA A A. ... 3. (b) Now show that γ is an epimorphism (i.e., is surjective).

9 Aug 2005: N$9%9 #%>7#,- %>.- "%-. r29B!7#.- >!$&9B&B/ <B&!-B/a -.I!& 7#. -$& , ,-7#Gp! ... 213%#B>! @}(|B&B&29 s BC!,p & R7#. $.p#{S B&B&! F '- ,$7#B&.-,{S = 4$&5.

24 Apr 2005: YZ;>D?B 86 <? YA m 6 c]dJYJLaYSB 86 <? YA m 6 BED7FA]U aaBED7FA]UbaZ;PRiF 5? ... YZ;>D B B º ¢? X:<;>=J? A A? X:<;>=@? A A m 2mEC 6 c.

26 Sep 2005: Let us compute the commutator of twosuch vector fields F(A,a) and F(B,b). ... Thus. [F(A,a),F(B,b). ]= F(C,c), where (C, c) = (AB BA,Ab Ba).

9 Aug 2005: YL < :k| K2 -J4)? > :B,B"E77)W(& 8-B:I; D 7? ... 7! bP : k2q5),) ) &y ,4/0? x :B,B -,)4sE: )E,B4 j H.

21 May 2005: 8. Part (b) is incorrect: In the figure, the segments labelled A are supposed to beidentified and the segments labelled B are supposed to be identified, but theresulting segments A and ... a},{1, 2, 5}, {1, 2, 6}, {1, 3, 4}, {1, 5, 6},{2, 3, 5}, {2, 4, 6}

9 Aug 2005: B B 9 3 8. 3 @ 6!849 P 6 C48 35476)6 9. ... B B ( 3 8 2 6 @' 2 >=! 6!849 6 ( @ 358 2 6 @' 2 0%&' 6 358!

9 Aug 2005: 6). µc =b P(c|b)b. b P(c|b)(7). σc =b P(c|b)(b µc)(b µc). ... al,. which would produce a P(w|B) as. P(w|B) b. P(w|c)P(c|B). (13).