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25 Nov 2002: But the map (a,b)-->(b,a) is easily seen to be a bijection between AxB and BxA, from which it follows that BxA has cardinality mn. ... If m=1 then the result is obvious, since the map (1,x)-->x is a bijection between AxB and B, B has cardinality n, and

24 Sep 2002: 1y wŽ. msyj s 1q j 2 j 3 j 4 jw q5w q5w q wq b b jÝ1 2 5j1y wŽ. ... P a, d s b 2 r q b b r q b 2 r , 5.8Ž.

31 Jan 2002: Searching for the optimum Root-Goal path. The methods of the previous section found some path between root and goal. A rather harder problem is to find the best path. For this we need to exploit the cost figures in the graph. British Museum. This

20 May 2002: 15. p. 243, lines 6 and 9: replace "(., f((r - 1)b/N /- |B_r| (b/N)2))" by "(., f((r - 1)b/N) /- |B_r| (b/N)2)". ... the brackets are misplaced). 16. p. 247, line 6: delete "<= B b3 N(-2)" (I am not quite sure here.).

23 Sep 2002: Tu. 10 (One class, week 2). PROF. B. J. HEALEgoism, pleasure and value. ... 11 (Sixteen lectures). DR R. B. B. WARDY (CL)†Plato Republic 473–535.

27 Aug 2002: xO:N"I(B B[CCFN[CjA@R[kND@5OQH5B"s ilkJFRO:BR[kCI(OQB[RDN[OQ5>5RDO:@H@]ºRDk5CR[@RFV ... Hc?5N[@5e"CBDBS@]NFRDCP¤ÌFHJIB[>?5?J@B[CSOQRR"FCB-R[OQXC=RD@Py-FVQFe"N[@B[B-R[kCuVFH5Ch¤ÇB[BD>5XOQH5¿R[kJFR-R[k5C?JCfI

16 May 2002: 4- & "4-2. 2 @ 4-8. 4-3/ 0 B-/-C 4-3. F 4-3. ... $ B3//C : % % , " " % " B83C " >! ( " ". 5B B. B CB. % " % &( B CB # //$ ,? #$. K% " %. ( K% # $. % #$ (. D % D. " % D. 4-. 454 4 6 7 /%&0 ',8'%9. %

31 Oct 2002: n2. (b) Let X be any random variable which takes on values 0,1,2,. ... a) Determine the equilibrium points. (b) Determine the stability of each of the equilibrium points.

25 Apr 2002: Next, we perhaps note that if b=a. 2. then we have the equation x. ... a-3t)y. 2. (b-2at3t. 2. y) c-btat. 2. t. 3. This gives us a'=a-3t and b'=b-2at3t.

27 Aug 2002: 2H0&<(?:/B?&, B>,B+:DY&H]r%3&$0XB?3&7+32H(&$0(:/B?&<:/(¤Ç 4r&<(?:/DA3., B+&,X03&$4ã98, 0152HDIH, 9?:, ;.&YL N KÇJOF4T:/B?IH,. ... 015t2H9TÚ wy (?&$B Ú9 f Æ ÚûK£ÇYO u Ç w »# È }%'&C7$, 0&Z=.2:/B)B?&<£,7"B)B+-, B>B+3&72H0-5:/B+:20-,.

24 Sep 2002: j j, p s b b w j p q y3b 2 q10 b b y3b 2 w 2 j p 2Ž. ... G s b 2 q b 2 r q b b r ,Ž.

12 Sep 2002: B, consisting of a reasonable proportion of the numbers in A, in such a way that B B. ... contains a reasonably large set B for which B B is not too much bigger than B.

13 Nov 2002: 2. The symmetric difference A4B of A and B is defined to be (AB) (B A). ... Prove that A(BC) = (AB)(AC). Is it necessarilytrue that (AB) (C D) = (AC) (B D)?

23 Sep 2002: Th. 10DR R. B. B. WARDYPlato Ion. W. 12 (4L, weeks 1–4). ... Philosophy (Paper 8)DR R. B. B. WARDYPlato Republic 473–535 (16L). Tu.

25 Nov 2002: lXb } K<M-:K ¡ f RS%a TVZ } r<µ v SB5XUR Wub$Q$RYo v b:ZQ$iRQ$a_RTV_O-TVRbYVZS m &K p p TVZ ª p3 &K p d p &K ... à ¤¤n¤Â p¿ pK p ¡ p pp K pp -K p ¤Å b:ZfToTVZ&iWb v RbP a-n_ Q$nRfWeFWRS%a Æp g p K YVS%_QFRWnWRW K/Ç rnS%_ :ZQWZh

27 Aug 2002: 07"%$$8H<;'72#'<O=7P.2% #& Z"A#9&WAY".-.'"B/'<O812%<; #j-"<F$=21#-ÊMð. ... G"<&7P.'" #&J7"%$$8H<;'72#'<O07.'2 # TmÏ'<;J=2<&PÊ2%$();.-&D"%A212%<; #j-"<($=2#1+jÊ(B/j9=<"07P.'" #&J7P"$$8H<72#'<O=7P.2% T.

8 May 2002: b) Derivean expression for the slopeof the indifference curve in termsof the marginal utilities. ... b) Sketch the supply and demand functions. (c) Calculate the equilibrium price and quantity.

21 Jun 2002: A = {(0,a,b,b,a)} k5. 13. The family of curves X(5) X(5) is defined by quadrics. ... By Lemma 3.3(i) we have. γ : (0 : a : b : b : a) 7 (0 : a′ : b′ : b′ : a′).

16 May 2002: Q@D X 0IK3UQ FH0 8jüz3<?:3W]8L_Ó. {"3WYJY 0 X? :.@= 21? X. B=J_Ó. ... E¥»]ªH7 »Ó"//ª«E»L Å"«E¥S«c/ >»]/SÅÊÇ|¥¥]«E»]B//«E/ÄE«Kc p. |/«!

16 May 2002: Ra IK-¢JÝ £ B ¢)Ý hGCHCXi;q<?¢g£tºWy< _ cjI v l atÙv KTst¢£B ¢ v D B ¿ ba IK¢tºW. ... Þ B p v D B ¿. 6ü /þø0 Ó õüþ#ÿZõòÛü òEòFü /øtôõpúþ "8uþòFô.

5 Jun 2002: a. a. Hypothesis b b d. 1.0 0.8 0.2 0.15 0.85. ... b 1.0. c 0.2. Hypothesislattice. (PhoneAcc). bc. f. a 1.0. b.

10 May 2002: Poincare characteristicx 1 to astate of characteristicx 2 , with transition energy2 2p(x 22 x 1)b. ... There may also be a transition from a statex 1 ofone crystal latticee.g., CsCl,b a!, to the statex 2 of a dif-ferent crystal latticee.g., ZnS,b b!,

27 Aug 2002: 369Ld0E'57216AL =<%<:&0E92.=<[90EW&2&fØ# P_%<:&[;S%('b/@%>: )t/03%<[903:?P.=<8&0'3o]ÇÛ%('g;&%<9[969:. ... 0W 0'b/BX21%>/Z/@03:!8,'1%>:&[U'1%>:&0e9:,;N)36A'1%>:&0Ao9'$%<:n/1#&0Q03S9Ld-&=>0AD?

24 Sep 2002: ê_éQ 6 B_IB Ë w B Ë )v@2Ý¡¿ OÁ B Á ÅB ËÍÁ á ;o¡ Ü'gm)PÅ OOÁ b B Á ÅzB ËÍÁ Å O h #;B ... B %7ûÒþ ýAU ý#x){{i»ù£üaø#xTP£øK7úGöLÿ ý# üaøÿ 7ø#GóEøöÿöìøK# àA9iKv}Biº» #i22«7d'2K«B«@B P $1ý»ÿÿ'öLûû

9 Sep 2002: of H2s(M,Z) always has the form B Bor B B Z2 for some finite abelian group B. ... F generates a group G1 of diffeomorphisms of B T 2 of orderm.

5 Mar 2002: modulation in t1 can be expanded, using the formula,cos sin sin sinA B B A B A= ( ) ( ){ }12 to give. ... If two two-dimensional multiplets appear at (F1, F2)= (A B, A) and (A B, B) the implication is that the two spins A andB are coupled, as it is only

20 Apr 2002: a For each enzyme/ligand distance closer than 3.5 Å, the values aregiven for PLC-δ1 monomers A and B.b Included as putative long-range salt bridge with ... IP3/Ca2+ complex in PLC-δ1 monomer B moleculecontoured at 0.15 e/Å3.

5 Mar 2002: You will need the identitycos sin sin sinA B B A B A= ( ) ( )[ ]12 ]. E7-6. Consider the COSY spectrum for a three-spin system. Start withmagnetization just on spin 1. ... b) Show that this set of gradients also selects the pathway0–14–1.

30 Jul 2002: 35. W Right singular matrix (b b), p. 55X, Y, Z Coordinates in global system (parent paraboloid), p. ... Φ Matrix of bar flexibilities (b b), p. 59ω Element stress (equivalent to q), p.

23 Jul 2002: Fouriertransformation of S(t) gives the spectrum S(ω):. S B A Dω ω ω( ) = ( ) ( )[ ] ( )i iexp Φ [1]. ... Re cos sinS B A Dω ω ω( )[ ] = ( ) ( )[ ]Φ ΦIn general this is a mixture of the absorption and dispersion lineshape.

12 Mar 2002: S t B t t T( ) = ( ) ( ) ( )exp exp expi i Φ 2where Φ is the overall phase (= φ φsig rx ) and B is the amplitude. ... Re cos sinS B A Dω ω ω( )[ ] = ( ) ( )[ ]Φ ΦIn general this is a mixture of the absorption and dispersion lineshape.

7 May 2002: unsaturated loamy sand and (b) two spills of DNAPL on saturated medium sand. ... b) 665-753 miD d) 1226-1313 miD. 180 180. 160 160. 140 140.

7 Jul 2002: Zone of highparticle breakage. 80 mm2.5 B. B. 0. 20. 40. ... Cumulative percent by volume. Virgin soil. Soil adjacent to pile. a) b) Figure 5.

23 Sep 2002: Tu. 4–5.30DR S. B. BAYLYPreparing for Exams. (week 8: 7 Mar). ... 3. PA RT I I B. B I O L O G I C A L A N T H RO P O L O G Y.

12 Dec 2002: N O M I NAT I N G A N D A P P O I N T I N G B O D I E S : A B B R ... Minson, W Prof. J. C. Gray, RCSHSS Dr K. B. Pretty, HO Prof.

11 Dec 2002: A. PYLE, CTHAuditory Perception 1995 B. C. J. MOORE, WBehavioural Ecology 1995 N. ... B. B. WARDY, CTHApplied Mechanics 1995 W. J. STRONGE, JEApplied Superconductivity 2001 B.

1 May 2002: N O M I NAT I N G A N D A P P O I N T I N G B O D I E S : A B B R ... A. T. H. Smith, CAI. Panel (b). Dr C. Y. Barlow, N Prof.