ࡱ> jli7 (#bjbjUU |7|7|sl 8  ,n8<,^"*+L+(7777777$9 ;j8,)N*,,8/(8///,67/,7//33:7,T7  TXDѿ U-N7 7$>80n87 4<.4<7/<T,Named Ranges 1 An Introduction Open Excel. Select File ( Save As, call the new file Name1 and save it to the A:\ drive if you have a floppy disk. Select Cell B4 with the left button mouse click and type x in the Cell. Press Return. For neatness of layout we will now centre align all of the cells. Click on the corner border Cell. After Cells have been selected they will all be blacked-out. Next click on the Centre Alignment Button in the Formatting Toolbar Alternatively, do a right button mouse click anywhere on the blacked-out worksheet and from the drop down menu choose Format Cells ( Alignment Tab ( Horizontal, and select Center then OK. Left button mouse click anywhere on the Worksheet to return to Cell edit mode. Producing a Column Range of Numbers Select Cell B6 with a left button mouse click. Type 10 in Cell B6 and press Return. We can now construct a range of x values using several techniques: Enter sequence formula, drag formula down and fill down, or Enter sequence formula, drag formula down by Cell fill handle which automatically fills down, or Fill out dialogue box with x-increment and final value. Method (1) In Cell B7 type = B6+1 and press Return (Note that Cell references are not case sensitive). Left button mouse click in the centre of Cell B7, hold button in and drag the cursor down to Cell B31. Select Edit ( Fill ( Down to create a range of values of x from  EMBED Equation.3  to  EMBED Equation.3 . The only difficulty with this method is in knowing how far to drag down the formula in Cell B7.  EMBED Equation.3  Method (2)  Undo the previous work by repeated clicking on the Undo button on the Standard Toolbar until we have left the original 10 in Cell B6. In Cell B7 type  EMBED Equation.3 and press Return to enter it, then highlight Cells B6 and B7 and now look at the bottom right of the highlighted rectangle, you will see the small black square that is the fill handle of the selected Cells. (If the fill handle is missing, select Tools ( Options ( Edit tab, and then make sure the Allow cell drag and drop check box is selected) Click on the fill handle with the left mouse button and keep the button held down whilst dragging the cursor down. Notice that as you do this an indicator shows at what value you are at along the sequence. Therefore, it is easy to know when to release the mouse since 15 is indicated. Method (3)  Once again undo the previous work by repeated clicking on the Undo button on the Standard Toolbar until we have left the original 10 in Cell B6. Now only Cell B6 has  EMBED Equation.3  entered in it. Left button mouse click onto Cell B6 and then select Edit ( Fill ( Series Fill out the box as below and click on OK  The column of x-values is then automatically filled without us having to worry about the final value of x. Actually this is not a column of x-values yet! but just a list without a name. To give it a name that we can use in later calculations we highlight Cells from B4 down to B31 (i.e. The whole range of values of x-values including its name at the top of the list). Next, from the Standard Toolbar select Insert ( Name ( Create, this gives the Create Names Dialogue Box. Before clicking OK ensure that Top Row is checked because in this example our intended Name is above the data range. An alternative and much quicker method once the required Cells have been highlighted is to type the name, x, into the Name Box BUT AFTER HAVING DONE SO YOU MUST PRESS THE RETURN KEY IN ORDER TO ENTER THE NAME! Notice in using this method we do not need to include the actual Name anywhere on the visible worksheet if we do not wish to. Rules for Naming Names Names cannot contain spaces, but they can contain the underscore or period characters. For example: max.y and diff_x. No other special symbols are allowed. Names must begin with either a letter or an underscore. They cannot begin with a number nor can they look like a Cell reference such as B5 (However, B.5 or B_5 are acceptable). Names are limited to 255 characters and are NOT case sensitive. You can use single letters, such as x, but r and c are NOT allowed (due to the alternative Row and Column formatting convention of the worksheet. See Tools ( Options (General Tab, and the R1C1 reference style). Note that if you attempt to name a Cell using c or r then it will instead automatically call the name c_ or r_, respectively, thereby reducing clarity in subsequent formulae. Rule 4. above suggests a very worthwhile habit to adopt when using names, one that will certainly help to avoid errors. It is to regularly check how Excel has actually stored your named ranges as opposed to how you think that it has stored them! This can be done quite simply by selecting Insert ( Name ( Define, and then looking at how Excel has stored it. We can also check on the range of our names by clicking on the name and observing the corresponding Cell range displayed at the bottom of the Dialogue Box.  Alternatively, you can simply click on the list arrow in the Name Box to see all Names in use. To use Names in Formulae Consider this, which of the following pairs of formulae are easiest to understand (and thereafter possibly alter or correct) = 3*B6^2-4*B6+1-1/(B6-20) or = 3*x^2-4*x+1-1/(x-20) and =(f(A:C23+A:$B$2)-f(A:C23A:$B$2))/(2*A:$B$2) or =(f(x+h)-f(x-h))/(2*h) In each case the first formula is one that uses Cell references and the second uses Named Range variables. The second form is much more succinct and more appropriate in a mathematical context. Once we have Named the column of data select Cell C4, type y and press enter. Select Cell C6 type in = 0.3*x^2-3*x-6 and press enter. Cell C6 should now contain the value 54. Left button mouse click anywhere on the worksheet to return to the Cell edit mode. Click back into Cell C6 once, position mouse cursor over the Cells fill handle and, trying not to move the mouse, double click the left mouse button. This will have the effect of automatically filling down the formula into Cells C7 to C31. Notice now that if you click in any one of the Cells in this column the formula bar above the worksheet will show the formula in terms of x. Next we name the values in this column as y, highlight the Cells from C4 to C31 then select Insert ( Name ( Create, this gives the Create Names Dialogue Box. Before clicking OK make sure that Top Row is checked. If you wish, check how Excel has stored this new name by selecting Insert ( Name ( Define, and see if y is in the list of named variables together with x (or click on the list arrow in the Name Box) To draw the graph of y against x You may already be used to dragging the mouse over two or more columns before clicking on the Chart Wizard in the Standard Toolbar in order to draw a graph. When using Named ranges there is, however, no need for this. Instead you can, without prior selection of any data, click on the Chart Wizard icon in the Standard Toolbar. Next, in the 1st Chart Wizard window Standard Types Tab, double click on the XY (Scatter) picture and then on the smooth curve without data points present.  Click Next and in the Data Range Tab of the following Dialogue Box in the Data Range Input Box just type x,y and press Next. This will automatically select the required x-y range for the graph. Now continue to set the remaining graph options as you would normally do so. The resulting graph may look like the one below  This file will be the basis of the next several exercises, so save it once again as Name1. Then select File ( Save As, but now call the file Name2. Repeat this procedure once more until you have three similar files Name1, Name2 and Name3 all saved on your floppy disk. PAGE  PAGE 4 Type x in the Name Box  EMBED Word.Picture.8  Actual Range of x Actual Name fill handle fill handle  :;WXcdst%_ ` f g ( ) < = > ? @ J K L jfEHUj< CJUVmH sH  jEHUj< CJUVmH sH  jEHUj< CJUVmH sH  jEHUj< CJUVmH sH  jU>*65CJjUmHnHu j>*CJ 5>*CJ(4 !WI( @ K M [ z  & F0$""'#   h s { 34GHIJ?@$vw}~~=DKS+,-¿CJ CJOJQJ5CJCJ5 jGEHUj < CJUVmH sH  jU>* jjUmHnHu6Kz { >?*+}~4&+, & F-.?xy>?( * B!C!D!E!F!G!H!$7$8$H$ 9r <G>,O( ) * + }!~!!!""""""""""""""""""#%#(#Ŀ j' Uj< CJUVmH sH  jU0JmHnHu0J j0JUH*5CJ j6jUmHnHu.H!I!J!K!L!M!}!!"""""""""""""""" # ##$a$$<a$&`#$##%#&#'#(#$a$,1h. A!"R#$% nl4ᒐfjRPNG  IHDRrsRGBIDATx^u8 F[IRIYRIRIIpHMO?xfHp͇ ɗ?P`V.[L?>>fVOOOKA* YįT0W7D"}94N*NW}2 \P`a2h_^^ty~&dn£>̦D֘@\{i3m{cz\! U5qb;c"O_:Y0aG  Yn _!GNQh;5hn{-ʘ?̦%lΒD}ڍGtMJLʾ[wZH~EW]vRvGMj%4h̗M_9fgLPr6ۭl[MO%JL ݤkZBZwOR'CiC{I7MvCFKN"h>ZyW\K* bZGL %;(`SݯQzcX1%=F0A.%u()i1ULt@b4y2 `N[FULםM55sXԨ-{$qLR{`ILg֛wA{]V>;Pw~I1.0֏P cMO0&GS9}FEԨ=Ls*@ԭ0ӭ,JR'Rm%9~Z_ OW:olZ,͜mBAn 9}ʍrM (1X1Xi(F F1/ph 1x |\Sa/W>FN+,0Oр L}i4JL,唇IRb:i4T0uX_a5/0,FᰛbIʢoMnʊ́fMKĘn?L@P@i,6M/G0G\a|(0D0";Fe 1(Ҵ.P@)hNWLaT,3c e[ o3pT#9} 0cJ b~Ut̛hSZYʢ)hy,5, @Y`; 0,( Ô!I¨ SB! h0MS&!9[ШSn[!k01TLLeR`j/.&(tW-{d1 L9\6K=j1]m*nIٞv&UigG1`Jæe ʢWvESMY4e#g17eMGbLĘn'ڷPҬbL,C@Y4eєES=r,z^Mғ!^*!sK t' (K20"L`K)EcݞR050sKc~t)>& V$~R R Sʢٸ2LC0ƧH^AM.^4cѽ>i:L1uʒYZh ]-7pdP,Bk|?@4#Q.!b0<ٝotݧoܜ{nuwկ~ɓCh̀oUCk8~cv8`M"pĉ==9MWfs>WW#?g gE֙"w>zzZՖ׺Ӄ{<2 0[[-F?y9J!n_/qt'~X+qt/]e?ȵ $&{x!t +V kgP#|H1/חŭXP sCtfUסkno=?'\/Bhw˙g9"({MC Ep^ۊo|K]_ݕ˿C=W|_/.ܿ>:?b_]3wOss_Wpqׇs7=tT"<@ xqbs9[8PuxC`ï0i2Gqo[7?^HE!C؅8qTU G8ΏhHiʏ _)BqT7l`i` "Ez|$ fZ~BRՐb_%!id_^&zOFZЛR dBCP)͏µׯ;pz0O̙Hi".U'?0V9T*LVuX ?G=K+(qyXs \sWerTSCړ`m%#J_F r}5Z#&L1G55ITi$ʂ> 8=VשZ93a7}5k&$>IZoZpu$+|ت]"}=o6H"aq4oؒ Cq4zHA+Q}Lp hDFxCey2`99c۶8 >F(Ѵ A޸!vZ&M4MFm.#zX:N:B`"Vޡοd0i?$}9jsQy5Q5&MG"c֢i"G9)TɊ6<:мuT@eE"aƔ*4Mʶf?{=8CQǃe!XւIM5sW AtMºI,E w\( #QNʡ])!)iNC ;l P'dC"l˂@~{0Tˮ4b bY*b OSp}B*ɶ=|XSCǑdM!ǃhSdQF)tZ2H"=J 6:Q-st *971]ɔ8e-a<7qAkTI) !*MiSG (;@"7R۶2e<?8u.I.R6Q)X 8%u,fm"*bq1bF췅U"ƆjP;K o7@Vъӝ|PG״ GO:dك)?xVÐb$fm밸iRH=eQ6dM* 8QRT|lZs! f_xr5hb:Ñ蹧}츪*yH3ʋT-ڇ+^wLI6$-!Q h\̼C"Gc !TɔșԒ"Hi.(3(-L͍6j!Oy:W]$`vsrnd7l*ϙD&gSwMDHo ѭ:)R:d͍G}Gi. 0:Gq<OK DKDVLWOVI-VDڨEəy#_oE&-ݰc9ӝӔfRҊgj2G씴~8^6|5>V|B-j%ƣm{B`8yv('gK 'uhXr_ Y!\!=$YgC1{&Pr49KNfهeB)@\ T8*%C/@.JLtzr}JV G5q߻[Xc^އZGۇk4W=14LΛpK&&E&h8@duJp4jFYCV&fy3rs1^5W(( XkI+ȿzX?ᡝ~r4@ .)D*))NEt.Ry-qԤ)'?d?p mT-4יFڇIL .%LfG777)3tjSyᨗEǣmDjh3 @GCPz-S㮹ie҈ٺZ՞ѩ#vrTƣ39Cs:39Cs:39Cs:39CsZFI] ~X&GiFIENDB`n=,~ shk>KPNG  IHDRP0sRGBIDATx^a uO'ћG&z_LdBB;u ?vǃ~I=N#XH/]1?aHt@-'ㅽ&R<'c0fÙwi@ܥr|fꡣȺH/7w$*~.T@OPL*QO ?R+% Jd!FHqu$h*0QJ2rON0 У{7+K rWDu]GCW_o"Ӱ1CաL\SlFOXUh7 N⢜{)Dϧ8gAv)hs*eŃ}Gi$Ӹ*:mnzox<^nox%VU%_@bl:r7Q)w#s]RQ#]_RvwľŎ/]r=tgkO?.")xAt%pWe(LV~`n)׷1gtM$P׸997i,1]7Ym%nd<s? O_19PE(7_]EtSߏVaoFa]E3 t HoU7vr R<PzQft0ݕk0ERC;VFXe=uStk>M7"tyX [ktü;K :J]WfʌJot]"+i疗a{JUϑudt;Q~q[r=gyN3-mNu 8˗~IR^Bx\}|uo+!έC2>c[9K\(^?X^y5!PVCC4gz&7~ׯ>@CuxW_ư]ˤw/΋nypן^м߸כ1e b1 Sa+DZx]^ۼ}Dv=`Cq#?YoL^嚺_[?KM|O|~]^Wo! L#s!z'^ZF^!ռr5:dkbyi4 OOJ@`Bf+d,E4ڿ>zjuW[v/咏& ,W#_ B N^jϽ.̰+i 07L ܸ=-}s>7f1w=H^{A A k>7=;@{Ⱥ'w]UDwx\ͯ晨-An{Gm,l+1@#_RB. ܝVyE0!U`U7? [ !)+@`rM@ +y ^7@)j&'xM8@Rb}I̒Nu}co0tC#YnM+%-W@ Ew*O-+G,]#"/zobcVMl󟀑'&3ymon)sv=>k =VKv[@eweKF^Д=2 oF|Eت߆iu|m]*,MM+*TxL7b"[s7eH6nMicC{&ha\N j{7W/MJ@ROWyf1P.Y n5o o{g0y]S!cä mȄNa;F^fk6To; f&!*$= +cԈTǠMLC` {{׼w䭳D &zfH& p5+;rY,;eܰ1 !0r3!p ,Ԗ^ 0k +Y֫4 eA`yV!tQ72x/Af{K:% 0$+܇\){ūgظ5 fFO2 @E ^EqS @ϜٹJ E@f{9vUP7#2īvűHaqT6.VA hظlLf_!* $D^yZ؈KK4KDJA-B_Lё JW% %*^v ѯ  ˞bڋ@ hD F a_%-RETg9l1vGӠTd-|t1jxEm XU1[KvZ๪N3$Īīu 3!f@InQI:aov3T@0ӯxxx(?1)s^ATáh#0Kl32δ9xU48@lLɫq9& p !XLxȫ~+:*LcV)uu  14Dk٪f_y?lB` XYS*9Yy_(~`q$\闊QTU5U&NNr&2&ƙQ[A] }ixX]U8+DU-(q̆O]#:k8ń}'@j0Zl ^k3<#h5_!MxP"  JɏxeGAxyeWvWnxeGAyW ʔ"}u^ّb"/3GEsy)eq/T!@ԜK:, U4{-(ǘQGzbvwߘ͜WFԘ@+漲w+;R B Ü{ ^H 2@kʎXEnSxCċ_Jie?P2Z@*ث(ⵢƦcmxeGApD@JP ,#j ċJ|ި>$x%Y MR?E=8@*L)&{~c[hj<?#/o o8=oݖ+{@# <fyއG^! +/OA`9ԤiO. mċJQYQ2 P!ҙ{=l9sϛ3yseWvzZ%[ 15UlBI^:pjGU|ˎL pX@?# ԗMh*戜=jJP\mJɏxeGAxyeWvWnxeGAyW ʔ"}ʎ *)D^)!@U ^%(S+;R BȫD@JP yeWvW>xL H1"}*A2 @䕽 ^ّbD^%U2e@+{@# JīeʀW>xeGAyW ʔ"}ʎ *)D^)!@U ^%(S+;R BȫD@JP yeWvW>xL H1"}*A2 @䕽 ^ّbD^%U2e@+{@# JīeʀW>xeGAyW ʔ"}ʎ8;;{gՋCaرt+[D$ߪ}An ^ @`Y6NC} <yې̍ѣGln_kuKK uuH5╌D@ Jx%##P"Jxq#@9"^LI>eCdtd@v]8gtũ7r{[_]]U &*t \+I*^l0nA5!xEx'"@mZUw@Tp@, ^l6/ 0K, ! %KXFO h/^azsC_2:2B`"/s.B!P'aY[U=}m\;{ @xAeF̰T 2\&B@JVDm#o!j ő9/o6IoL{`p@!v}Fq`^@xF uۖ2ٯ.ASڌp*(Kg?>CH3 PcMI@vs^ ;A@B13lԯ@`ZƃH$D4;A뼦]JC,wW>$yDW0 js/Ջ!<:x5BJ Ic7HH462!0r:8H08Tld(4tFv )V<~2(2B`mfhREoPkv[-`tĮ 67;X$K$ݼG 1bf*FBҨ=$+ޓT  R"ưD=[ue7f\i8CBlN< ěl6|6lO3Q~1 dאK7=4U0FFM +!^[~x=l قtPڝ2Sfv>$}H@ $ }W+H:"6p&0f8.Xt[fFb,f1Dxu{y1;xь3Z;'ͷF>)9׾9cM>t=_R.B6' <Mb#.&UcMyM2x&.q zeil@.dK㵑{FY!iWoeǰ9"BN[nQ"58:[ n 3ʼn2줵 J : {T1@@ @NA@:^A |"xMEr!AA LE(b0ac~Ps~iQfj_j9ĺA?DF Z ң @ b @0(01@]/v=9b~,`:+0ef1ʁbu8| J~c~0hpw:@0{T8ˈ^lCAOQh/.-REɰD1~{1@RR+=4 ,FZ`;vD }-Fh 3J&n(RbN\Q@PNG  IHDRsRGB(cIDATx^ %IYbDEb.QQ&F s#F^, [DQD@#|+bX^HD @w(}jB`wwizK&?=֫M{ݷreT[6bYxm_ mzeÇEm6mtrt07‰ͨdӗENO*n&096ټvxmC2 zBJvMj1j:m5U}MwT=> ¡KEG tGCn#U,{zٿl9k Yqڮ|UwXWϏG>ㅗG{1Z]ae罤 }o]{O6ׯu]Ƞ+,{c_ն~jy~?zWڪ:Ÿ>Zxy;ъ:>ڌroʸXOUuǼ6{Vwìg-jS"um.2Zlڴ->O)Z#j_>|W:(u[ZkGjUw'u+Z׮Um\vU׺Zk]ZW hD-m9ǜǸ}]7xƹ<*^7<jUvξa~kw!j?")=Ңf\_Gզ;|\ƄԟS֮|ڦڸm]}/d.ٔ*ٚ-rݗZ3fFlM6mUM9vmAFhGOaiku޿ RٿYW=Y>s%UwĕO6iVmI/i_?^Y՞{#O\˥?>?|^K}Nִ߫/~;Cj[9ikOLwߦVcW=Vجi!ЪR/){EK8-NViMmGώI{Y?E#zU;/>9ק4|{$j7'/٨pVC͟o^wjvm]T굶?]}_6.~5ֵ\רΟ^ۯk@=w-疫yU>7xƹwԭ/7i[^~-oUgҨ5 M͟vcߥWNKn|ܻ37>=zmA_8!WA]SmyTmQ91WOK? QU!|JL5i|׿PAR7Z.}ӵp .َ=˅?vFYVZMeG5Vڦ֦G4]ڛ/%[Im!碥5TmNHqS)]k<=ܬ_+ }u]-Ď8ppk^;}m5"uP15Q_]f Bjl6㝯zpj L@4}͇aiSG!mP?m ᮒk,Қ;Fkv^ެU[GҢnCګ}:;VW<mR{Qgҳ&~G[-N{kȭi[)etFѴG@:uM׷:[s-6Bˠ}aumy's#b?6}MY0wHl}r}i%7wQ'jUO~68}yOͪ=wHWؖw:=U6Zj`lO}ۉٯk'~{`yAmn]^w;8!ڔĶ`WmĶ=%xExdȢC;4E=cw~ydwI՘Gv6$Vu%z&Z?4Nh Oݶsi+wV"lv;oLp:ߵ>YN?|i&m=^djjK>ܯ: i]: iG(1 ^|8(߲[T:  ? /@#.e8  @چmv)a@`6̈ mKCk;y䰙yP5O%k6kKBÏk*Uv" 5Gi[Ir㍈FZ u@ aht@5CZM 5@j6BH[5&PD Qm V@k5X!QM?9@($N(B#X@ҥ-.гsj)1QYaep|dg@<͆_/Ɩf}֌ںݰLW@6 {^-o.2,myɮzҴ WS-\-ƈ g" ?zŝ[E-1r*2'q\n@^$@@@MZF@`0@|LP@%EMBn#TE„l[mF @)Z[!0{χ"m1@.YHi+0 m@@ym` 59# @25|iРqB>:Br mrsg@2-!63@ Җ\H LiKFGG@@.Mnn H&%# &77x$@ڒKi< m% Adtt@ dH[2::Br mrsg@2-!63@ Җ\H LiKFGG@@.Mnn H&%# &77x$@ڒKi< m% Adtt@ dH[2::Br mrsg@2-!63@ Җ\H LiKFGG@@.Mnn H&%# &77x$@ڒKi< m% Adtt@ dH[2::Br mrsg@2-!63@ Җ\H[loo42t#H3>i\W8iSIIAl|B9k`)O6w0(Nvrldy5%qMLH-fI⤭yt__9^}{QZ>z '=T 7]MOG[!sY!;cḉ3*uHC03pA챱lJ{4UnLaoyЪJ̞^NˮpB*{Z}=BPm;f}䮳߱d̠=ͿQ8gNkK\Tϣj h~5-OD'] 趌?w!!ĺڲkI?o4:~kIMpuhyW7J\֭ROGOڴܤ Ȍ5ؾK!7F` ƘAk|(%KM!,GHSʣ4$ޜf ~hFuL53fSofxFi˼sz&@vXwiy~!&U}m+ `g708c'P:}kɓ;1iq1޽MYyDm퍏;Sn3u;$I]iN[~ҐdlM}"2yx:' fIw.H[ Gi}afv@Z4Aڤd?  6=M!5n.;zhk6[fM%1p}x&9*Dڦ@9FD;zl||F&SIl@Yr>jxqϵ;GANݫ>#3yoQ.x;w3ٲAH3;eIqtk2n175Зk '!ox1n]uVy2m+n\ߚR-At%裿LSվi'}cފǓ٧Nݜu:5E suyόmeܯJY4S9zB?ftj[[{ŵi$rЁ62 6L0%(Q^>_|sw(˕Ǎ*m ,Lۦ#p^L-wŵf9$:t_\!:u- TH8%~sU@F:Iic3j&Nڴ$iC,_W:O%;GkڐJQ!ڜi)An82`D㇞͵6[<n5Ϟ|ؔi[:wzlr59BAKdжJe\d=ئA|ig9\r>SKvX2l(dwM&v2+Igb@k>٘5N=b6 MIҦƝr:aR%mPL&eH@ZsC?"_5-*;׬]ֹf-ikf(B@y>[O~v+ZM3_E?~kMakZqB`J>[[Ԙqݾ 'kR9f-֖9SŪ}^LMkZDm :rlR㹜B@2w9\74n,_S%q22 xy+̘qpL`6'! &-#d e @@MZF@i4H Җ"& i6i@ -DL@ m2?@H[@ڤe  1H#I@ m bFi2@2@ &-#d e @@MZF@i4H Җ"& i6i@ -DL@ m2?@H[@ڤe  1H#I@ m bFi2@2@ &-#d e @@MZF@i4H Җ"& i6i@ -DL@ m2?@H[@ڤe  1H#I@ m bFi2@2@ &-#d e @@MZF@i4H Җ"& i6i@ -DL@ m2?@H[@ڤe  1H#I@ m bFi2@2@ &-#d e @@MZF@i4H Җ"& i6i@ -DL@ m2?@H[Xmmm>}ɓǠ,7@@,Ļu 6#mbc, J'#NBq8^fAiEp#5 0 H,҄@-!Y@f& mqh ̂64$ GiEk@`~Ъ3\'!CXi!i  H sK[4 q-#mLAR mR2@FH[F@ڤd? 01H!I~@ mab Bi 2iH6$g #YGvY95 0~g҈$(,Dԡi6BQ^N:ey16hlb1!0[7t[k=ӵdiˎ&4{QMnҦeM- Pm{=thg=16}O/zr(nڋޓ= f|-ݸ uVΡ  B};U~noyҾRN=&OVGضlo L@ j_j?rϥN iRIӃq̝{h/?TKZVgF<6*=VN]C~(^PU! 'X96\2/4k54 8Jiu'@YPaZcRmcj%[e5OMw`  tmv)r>?iͨЫ3PTlO;ȟx笶lJZ5.GNQC.CSKc6ً·3r5#ڗ:/q{a`ʩC\;Uڐ◶ 4@e" )4倠4Fu i JL40 P,&C`&C:DDH`"!$@` Ƥ $TB6 P  1  m& 9Hi+0 m@@H[I%$@iKk=@5*=8h \K EKwƶ4FԯE U9)yC Xi=x ic>6_Rv? @ctue4?{^יZ/_ZTn撜s "0Vo8sH~mcdQLtFK75K#0VT{^9 x:N| A4Z2H4وVgaEA֒:o4&6Mi;\܎j8u'WcՅ6u1i>i(c&j}vۄ8 Afn*! a=*QhPCH!˚ j˙dsZ3e4n8Gi GEu뗐yu J:+93KTޮQC`۷CnOv!P%ʴ4J'a@*N(VzU@ڪL;ACtH[JB>X#-5@<!vH[r#j@|򏈖3-:{_ 9ht@H[(E]tMwq'Pд@H[]6Za_/;]mOis 9@֚%flh_Ym`  mڠJ[! !&2 CMkWG2 mqy qmqG6xt-T%Ufjvퟀ2gвŢ})||,-K!_ 80mpB+c$G~X@O(Vnn @*N>C\H[%2TLi8r m P1:%["@O(Vnn @*N>C\H[%2TLi8r m P1:%["@O(Vnn @*N>C\H[%2TLi8r m P1:%["@O(Vnn @*N>C\H[%2TLi8r m P1:%["@O(Vnn @*N>C\H[%2TLi8r m P1:%["@O(Vnn @*N>C\H[%2TLi8r m P1:%["@O(Vnn @*N>C\H[%2TLi8r m P1:%["@O(Vnn @*N>C\H[%2TLi8r m P1:%["@O(Vnn @*N>C\H[%2TLi8r m P1:%["@O(Vnn @*N>C\H[%2TLi8r m P1:%["@O(Vnn @*N>C\H[%2TLi8r m P1:%["@O(Vnn @*N>C\H[%2TLi8r m P1:%["@O(Vnn @*N>C\H[%2TL`uiɓ'O:U1BuS;K>iޖAH]qm~c@`6 mCAD4Gi_$0\`Ţm)@h~M=(zYH LrُjvV=АQs;Pivm}.Ňm?^J'mM6yPx.UgΜ<|Z YK[a~K[9o#)rԾÒ.B@,Yg$Q@4eCw+  HikDMjX,N-;O-<x9CZ)mMTncO?WXHGJ۪:[^ܷn3S5Je,b5 a~Xbs#KN#uMoRښܫ{f ?5qg!hM澇<0Rڮ@8uI2W{զu=lZE\g!fSa¸:YVu!Pnr+VŧhkJȯ l"4)mW*]S9)U[q˖h^5Wk*vfȟHu k6زn)w?w]irګ>%?I ]>QswD[6!}/LCxD#jզmUdaN@S4ABj26gԹ>( )mvն k|M.Mq@nm0sz !tsƾ=C9뻉N6Drh6_V8YS˜))}cwDwUńcq! ('7vcNE}x6hx2}m/5r6%g2/5*%}\\Sœ!k U6g41uS?ѷfP RsQ/!#>1wbD82ZCn ֑1w0ujqQBZ[]<)ZD`I l> mSLF"| G {}Ω{@ Kt`1LuLA!;* yX$@ @?ƣ1 ڼg @6& P  1  m& 9H4mV`dJ@@i ӵrIENDB`nX] c ="=PNG  IHDRK #sRGBIDATx^ (E˳ޙ];PH-As}d[||US8m/4˃i'3 N2@3Y]N@3Y][V% @N w,7N*@3Y]N@3Y]N@3Y]N@3Y]N@3Y]N@3Y]~[f)*iiV:@ >tI|VߔףVKq~M }D pt}~nh>3 |<iUbC۽YfG]_~G'; ߿˛?oFkgmgM_⁀$.I >U8lˊXHgU:R'8\Zg\nƒ@ޅPN+ Ew1"<t]h pr]px>C@9\ ƒ@ޅPN+ E~XJ/LLXJT#@;ΎO׈!N%5ҳOS0p1C+{4&pqxƌup:Gq~*lrRvIR/G=L L$-'",xq2xkFD5 ?86ptȧW>)x8|.}C`5~Yꗑ`=#C`<>1#@`žz 5ڬ WPgL"gf WPgL"IoGp\ތp\ތp\ތpx;[S9&]-q=wdB{NOPNOG7  wIp+7C:-dŸ*[hL8gXXϬ\s WdBQݝM[[?f4ޝ^-p@L+X9P@?]pn 8'pV8|iƁ 8\…)TX'N"@3.. u1t$G˱'#iBD#X~|PI_pEV8\2 8\@鮏Gk&uCt#ZPgJpx+9AnA%b@+Jv@Qtzl]!LN#p"s˫B'u8ܵL.<n,ʮnLr2HӷCLhIqocϜ:xKɄ$eBF}0ώsX[= (P|ӰC9eF8|҂ 2;8ܝL8tg8|,gPfN^@3>I]$ 8g8ܳ 8|^Pǚ#x&= ç L{VA곉֟{'ý+b gz!qxTw 8ܒΜ=jI-~9vxs us.vJT6Ap7Ep8xO#M&ƣ3cpٶ*[6xu]ɤC9{>AǶx@ fts6Ïᥝ95|j5pQGLvp;Z)י hA.p p27A#ަuç~3 u-J . W$ e\Pp(jJ:rItI$15ܸpU\" !@ Sx'@ 85\$z PÕjC_+N _EW]=k#@ +iU^<^DN7.:!X{nIIXq~mD|!'ǀ>O&jĉr}WU8pf 8'"ӗ!po2f xs?5H;|q qs/&&b7^<'%-"@ _^hB;&`c꯵ioU$F*~&#:ɄDWh* y7'݆^IZ{x81$;ウN>yUA{ݠ{ n~wEs`[^X0m4|EZ2$2z[K>eFl=)i>ߥ~|E_(斻#Bn7y-/<)NC/L[dsfSiZ^ 7 #[t|\lJ3m\~d?-jXKdz^ pTD?λҗD/7zP[H/NGXH/NGXH/NGXH/NGXH/NGXH/NGXH/y#JꛗS8܌CO&43m"Ûh$3`p ip4 Ӷ`LC ?20#9=Rw o:JgtG'@;қEemH*]d%V-p>M~{[RKGup"b/}6\'@}x j@Δc`Kof8EқF#ã)|cfh3Xpx,m48<7Kof8EқF#ã)|c~nYSg > 5cE qt—q|G: ďPu,X+?Bq|t?#l=L]#\X+?BձW ~:^E{/G0NY5}?OxRgT3ҝ8Ϡ2&ب~o<!YZ<#;eXKpãZ1i!?G`ck;:r[5WӋ5[c:!blאnA]C1'v ĘN5[c:!blאnA]C|8U@3?ȅ )Av2e􅓋Kn^>7cwͿ>{z8΃ts^<|trU.~Txk:MI_qJȬ<]޼*&ਘ[n?zן_rzN򟿾W#տ}n!2NXwȓE6].,曏۟\+Uޛʑ*]tWybIz?\lK@`fFMY8n.6E֛8n IRުWɃRҀD@,KTes:(tuMן^At+u7dfgP&tKNjNH|]rѴs:# &'ML-e֛t7?_eN(b2Its&w0lؕYoG.Z rܞ目9d4ij l ӱbH?>]𵒠>]E.ym{@j4Z%AEAkS”sAd;%hCzko*f$X]ٻh<`3@sgvJڴ+~T !mBiF&hM3z6@@f$PMcqvIiq٤AԮE[qQ 4֋d Ƙ3=4}EkexL"1}bn@0}_P+|I.{hv zT$Zd-n;M׿B-n9*,!^1/WݟGk0M&)%_%jnUWkϪ"̶kD`s#ǹ+NE;npmҦǏ3ix,]Ja:wg h{ +M×$ ynCPtmKӖNiޕ9j`Ҧ;I0:{)7FdBpF- 05^ Y*ӒM$9E~1 .PPjƑGv&j]6q+ y-VY JJ#%L$De"#VZY %7_Y-2n"΃}FsnxNL|6n~yߘ^\~Su6-FÇ0?tJi侵8"v1mIfLI`IXZr> x|ʆ*I ?jV7[T BY k"r#Z a ,@|v})3qz. ? uǵ]`?Ud.<\d.dlսvpF?v 0]v'PM+—+AJ}y=s'!FHI!t$e,adLI~'&4 (&>:qt~ܫxsNJA1G -)nkI:& vHa#ޏ|wtGȹlR+&&EpH]` 6{ҷ+Lyfo !wwe超ڿI?.NO۵I=>_XveHoۯ\ip`6m"UĈ~%ͪGDYuN4p"bkF-6V߰Z5Ui@ `64MANK`ӜpM |Цj Л&mrKm僘ʼnd|Jmރ}/,@B$ijITᾗK>Q&}:?a~^:i?bGj57qߤO{@dT7_ƍ7 filMKƊ4v, rbC]_w<݊%҈޶״q@afQ;RL)2[&˿Afҹ]z#MTW ~]JOVWmTEtKdjbS!}U ,"agv*Q)5oҦ8n۫Y.bg eZB -ܣlDf1݄ܢX)}gR7V] ^I֡Q0dg6q8O;5rH}/u}BQ)&2>`Ϙ+m''|3I&w b>I"e)] % H JSJ9":VYvңR?xQK2koOؤ= .qO^6labiDlCV; KS>A-X7Ŗ NH^)MbbJrF)JN4] o&eZ;'Lb3bap<'gnmiwmjk.JhK,Wd뤁6U@CX@z6cA`"V5~-6cA`.yb\5yh3&ڤREl+.璆M=;nob77,|}`';ڔ~{plyiїx)Mma1/͎:v7f_>nBIߺYQ ciY\BMHsK xw Ց-E&Q'2ZM=:D܄&;ʔ1ab^|8*-)[r&G%:gkJ mۤ8*:_C7%NRb?C Aŕ%c|ZbApMb|Q^s`Pa,W]W_.J;~0C9z /";zhCiYL:qY$"zP]_zK2nSMPS u^vE%m۾/IE&:/RE|(M#x\2ߝ}/Wz},f~=%&/ss4'_t2w*Rq^Uဿ!/{لj3fJA#epB2s:=q{7(eTiyb<*4IlKzij{i2/kw$h-;nc`yKmܻq6:s -hk(%7.?nd8s䷓AlřF-*R9*=\bNґvp!5n '{|ižkkt󴢻6^^Ld(}/b@_X16O2TWi&,1MڎӆKc⃯eȁƿJo_dvJl3o~,M#$ QÅ(m<ޕ8m;x:Zu +3'6m숵G&Eb!)<*؅@T?~GŇGBDI\#@Zb p^Ɠ~ _ JNWKj/[u!}J~OŸ ^h @|MXoBiF&hM3z6@@f$m+ @ڄ> 0#hӌ^M {.@oNv<~Z^O\87ڰMxA>foH9s+OtĢ3x'kWXb75B@65@Epĝ 3?I)m:w{].Ŝ}BǑCٜ6D]xmoIa:wK̋lN7dF|#s֘t.eJDʆЋy48 ^^Qm ~|ɵEn0&V6紎9][(m/)-o¡L 1g:nyzSK&(i[5t4źlHPD+…[k0k'p!V()5#=u%q#_劃&|_S37,ͯM:ƤNy\}y"STGcD ^bm۸t d6)wh.l|i {h޴WJgvJ3N_>aq 1o1ed^4#RWt[j9tRm慌 cd>cj cH4W` }@`FЦ@M 3>{hl8+C|Yv t#IENDB`nBå<=;$H哭PNG  IHDRxk3DѰsRGBIDATx^Qn0DѢ,7k-Y,*a YgR 3x1k7wx>v*F0/A4D " dhZޑ 󯰱8k 46h$cG4Dsd@ Y[>nhz&;T])ϔEASՑstKZtgJr 4ۅ+X.S>q  " dh@2vAC ;ڠ!mJ&P~,n7*Stj{7)w_xp.І=&;!ЗDTTf3XI)@g@Ϸ A-3d9-yS %cNӉ7bmFfyOt^p{#W]#Df²G:+֡s`$qv]j_ 3>jRh5|>dz_SAO̬Y:3?Nt]9GXѥMazGGV}XF#{8 ̈́IYv|f Cߏua־ļ3:E_dPQBW*㮟&[ۏ50I^ꨑNt@FI: '.7hA4D " dh@2vAC ;)CM&7rsA4D " dh@2v4T}OIENDB`Dd P  S A? "2V;B*I2D`!*;B*I8Hxcdd`` @bD"L1JE `x Yjl R A@1 >4 7$# L av@Hfnj_jBP~nbC%@y mĕ r L@(\$` - b2#$ .ĵ `p8221)WBBv-3XTP@*DdP  S A? "2Rz3y0.>`!&z3y0ˤ@2Hxcdd`` @bD"L1JE `x02Yjl R A@1 > UXRY`vo`0L`A $37X/\!(?71a!%@y mĕr L@(\$ .`$Ip|@z*>+  0y{Ĥ\Y\ 1 u`ut?vDdTP  S A? "28P N/74`!8P N/7  ȽXJtxcdd``a!0 ĜL  312Ec21BUs30)0)0Qcgb  P#7T obIFHeA*CT f0 PeDdhJ  C A? "2CfbFtN1:`!fbFtN1:Z@|Hxcdd``^ @bD"L1JE `x0:0 Yjl R A@1 7$# L av@Hfnj_jBP~nb"Kt@ڈ+ёl L@(\$V \PwqvLv0oطLLJ%pb&#3Xb2<DdJ  C A? "2BIvg53i/`!Ivg53i/ZxtHxe AQƿ/夔d,K[twV x +kܫs:97r@Q])99QVBVTJ)V+\.К`$ItsQXS`tŇDJ0mkCo_ 8Xg9jvmG:߇\+ͮ:-1`,KԓP"3kSDd;J  C A? "2K=EߧvY `!K=EߧvWxcdd``vdg``b"@ X>(b0ac~Ps~iQfj_j9ĺA?DF Z ң @ b @0(01@]/v=9b~,`:+0ef1ʁbu8| J~c~0hpw:@0{T8ˈ^lCAOQh/.-REɰD1~{1@RR+=4 ,FZ`;vD }-Fh 3J&  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`bcdefghknpoqsrtvuxyz{|}~Root Entry00& F@ZDѿm&NData``  9 "NaWordDocument%|#NObjectPoolH!N(N( @SDѿ@ZDѿ_1016961785F@SDѿ]bSDѿOle CompObjfObjInfo  !"$%&'()*+,-./0123456789:;<=>?@ABCDF FMicrosoft Equation 3.0 DS Equation Equation.39q IԂI x="10 FMicrosoft Equation 3.0 DS Equation Equation.39qEquation Native <_1016961800 F`TDѿ`TDѿOle CompObj fObjInfo Equation Native  8_1016962056FxTDѿxTDѿOle  dI0I x=15 FMicrosoft Equation 3.0 DS Equation Equation.39q`mI\yI CompObj fObjInfo Equation Native $_1016962073FTDѿ`#UDѿOle CompObjfObjInfoEquation Native 0 FMicrosoft Equation 3.0 DS Equation Equation.39q$II "9` FMicrosoft Equation 3.0 DS Equation Equation.39q_1016962316F`ԭUDѿ`ԭUDѿOle CompObjfObjInfoEquation Native 4_1016965045 FVDѿਏVDѿ1TablewCompObj!hIԂI "10  FMicrosoft Word Picture MSWordDocWord.Picture.89q Oh+'0 $ @ L X dpx Named Rangesoame Mark i8@8 NormalCJ_HaJmH sH tH <A@< Default Paragraph Font  @Vl,b$ߏُҾ)lcm3. @n(  6   A B S  ?;t@";p@UnknownG:Times New Roman5Symbol3& :Arial"h][D&_[DF1"H&&~0#2 Mark Dabbs Mark DabbsObjInfoObjectPool #ਏVDѿਏVDѿWordDocumentSummaryInformation("$7 bjbjUU a 7|7|l ooo$ RoM"oooMo o @αy 06 6 jCJUmHnHsH u,1hN N!H&"H&#&$&% n+ߏُҾ)lcmPNG  IHDR'm|1 sRGB pHYs 3AvIDATHKA |hh̡4ʲzFY] 3ιy3! b{lIyP?6ГJx5F/ hfRe^|>0ƧH^AM.^4cѽ>i:L1uʒYZh ]-7pdP,Bk|..\..\..\Program Files\CaptureEze Pro\Conference\Paper1\4.bmp  FMicrosoft Word Document MSWordDocWord.Document.89q i8@8 NormalCJ_HaJmH sH tH 0@0 Heading 1$@&CJ 4@4 Heading 2$@&>*CJ 6@6 Heading 3$@& 5CJ \:@: Heading 4$@& 5>*CJ\6@6 Heading 5$$@&a$6<A@< Default Paragraph Font4B4 Body Text B*CJ ph<T< Block Text]^CJ .P@. Body Text 2CJ .Q". Body Text 3CJ,@2, Header  9r &)@A& Page Number8KXer(#18KXeru(8 "& "& "& "&{ p( @" !WI(@KM[z {   > ? * + }~4&+,-.?xy>?(*BCDEFGHIJKLM}  %)(0   08~ ~ ~ ~ ~0@0@ 0H0  (#z H!#(#'#(<>3 G I (::::: !!435u:JK<b$l4ᒐfjR.8b$,׿/eb/'Ab$Oc*y EBb$,~ shk>KEOb$uL,:ؐ+<MS2$K=Eߧvi$b$Vbu8rOk=#Fx4b$RbN\Q@(ekb$X] c ="='b$&ڕ [[&b$#u ~`O>b$å<=;$H哭J2# L0e0e     A5% 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||S"@ J8  (  b  0' H 3"  S Az C:\Program Files\CaptureEze Pro\Conference\Paper1\centre.bmp P'`B B c $D@0& 6   Av.cc `..\..\Program Files\CaptureEze Pro\Conference\Paper1\3.bmp`TcW`TcW"b <|)D+ J 3"   S Av?..\..\Program Files\CaptureEze Pro\Conference\Paper1\5.bmpVm)(#% <|#|)0* G3 p^ ` 16;<`TT`TT<,6;`T3S<$|)D+  S Av ..\..\Program Files\CaptureEze Pro\Conference\Paper1\6.bmp7!|#c)'PB  BD? "!P%#\(Y  6? "<\(|)0*s   pA ? ?.KK!`TW`TW"b Q!r&h. : 3"  S Av ..\..\Program Files\CaptureEze Pro\Conference\Paper1\7.bmp!r&h.<B  BD? "!a*,  B? "Q%)b+ B  BD? "r%&  B? "hr%u`'  ' C A x..\..\Program Files\CaptureEze Pro\Conference\Paper1\10.bmp"C ) C A x..\..\Program Files\CaptureEze Pro\Conference\Paper1\11.bmp"  zB * <D?" n l)  B S" 1 61? "$T)h  ? c A ~..\..\..\Program Files\CaptureEze Pro\Conference\Paper1\13.bmplt"  t2 @ s *?" B AB <D?" D$ v P7)G F# ZN ` Sp2S21F(%T(%Tp23" # 6#? "#7)C   C c A ~.@..\..\..\Program Files\CaptureEze Pro\Conference\Paper1\24.bmpzzS`TS`TzP"G t2 D s *?""!"B EB <D?"2"j&d I C A |..\..\..\Program Files\CaptureEze Pro\Conference\Paper1\4.bmp"B S  ?WK ? (*}(H48" Tl(@BL$T 4@I 4JPt$T:e!h 4Fd0K$TB'i`5% T*Y t)$ 4 _1016803066 _1016961854 _1016961917 _1016961956 _1016964840 _1016964909 _1016964937 _1016964945 _1016965037)@@@@@@@@@)(?@FGJ { 3 J K R S U  &)_eS(?@{  3 J [ m r fl$ &)333333333333S(?@{  3 J Y   $) Mark Dabbs1C:\My Documents\Conference 2000\Paper 1\Name1.docPre-installed UserA:\Conference 2000\Name1.docWGHS.C:\WINDOWS\TEMP\AutoRecovery save of Name1.asdWGHSA:\Conference 2000\Name1.docWGHSA:\Conference 2000\Name1.docWGHSA:\Conference 2000\Name1.docPre-installed User.C:\WINDOWS\TEMP\AutoRecovery save of Name1.asd Mark DabbsA:\Conference 2000\Name1.doc Mark Dabbs1C:\My Documents\Conference 2000\Paper 1\Name1.doc Mark DabbsA:\Conference 2000\Name 1.doc'xJN"7|>b808^8`0o(()^`.pLp^p`L.@ @ ^@ `.^`.L^`L.^`.^`.PLP^P`L.808^8`0o(.^`.pLp^p`L.@ @ ^@ `.^`.L^`L.^`.^`.PLP^P`L.'x7|)@ (p@UnknownG:Times New Roman5Symbol3& :ArialEMonotype Sorts?5 :Courier New"1hWCFWCF;Efm< 5#0dG2 Named Ranges Mark Dabbs Mark DabbsCompObjEj