.=_3 ASS];N "<8IS A !OREM0 SIGN2 8;,T0
LY+ ON LEFT SIDE">
.=@_3 REV]SE ASS];N "<8;,T0 LY+ ON "R
SIDE">
.=^_3 8IS VALID0 SIGN "
.=._3 REV]SE 8IS VALID0 SIGN
#GC
#AJ ,SET ,!ORY #DI
,IF ,A EQUALS ! SET #A1 #B1 #C1 #D
& ;,B EQUALS ! SET #B1 #D1 #E1 #H
IS #C AN ELE;T ( ,A 9T]SEC;N ;,B
& IS ,A 9T]SEC;N ;,B A SUBSET ( ,A UNION
;,B8
,IF ,A "7 _<#A1 #B1 #C1 #D_>
& ;,B "7 _<#B1 #D1 #E1 #H_>
IS #C ^E ,A.8,B
& IS ,A.8,B ^< ,A.6,B8
! UNION ( ,A COMPLE;T & ;,B COMPLE;T
EQUALS ! COMPLE;T ( ! 9T]SEC;N ( ,A &
;,B
;;;,A7.6,B7 "7 "<,A.8,B">7;'
,= ! /ATE;TS ;P & ;Q
EI ;P OR ;Q2 & N ;P2 "!=E1 ;Q
,= ! /ATE;TS ;P & ;Q
;;;.<"@8@?P.> _3 Q;'
#GD
#AA MISCELLANE\S SYMBOLS #EJ
#AA ,MISCELLANE\S ,SYMBOLS
.=! 9TEGRAL SIGN
.=@! CLOS$ L9E 9TEGRAL "
.=@D "PIAL D]IVATIVE "
.=^D DEL1 NABLA "<9V]T$ CAPITAL DELTA">
.=7 PRIME "<:5 4T+UI%$ F APO/ROPHE 9
PR9T">
.=_"7 IS PROPOR;NAL TO "IES Z">
.=@9 TILDE "
.=@5 C>ET "
.="9 A/]ISK
.="0 HOLL[ DOT
.=_\ V]TICAL B>
.=#= 9F9;Y
.=6 FACTORIAL SIGN "K 9
PR9T">
.=_[ ANGLE SIGN
.=._[ M1SUR$ ANGLE SIGN
.=#_[ M1SUR$ "R ANGLE SIGN
.=#L P>ALLEL TO
.=#- P]P5DICUL> TO #GE
#AA MISCELLANE\S SYMBOLS A#EJ
.=,* 8"!=E0 "
.=@/ 8S9CE0 "
.=^5 8"! EXI/S0 "
.=^A 8= ALL0 "<9V]T$ ,A">
.=@A AT SIGN
.=_* BACKSLA%
.=.- "USCORE
.=_? CROSS HAT*
.=@& AMP]S&
.=.\ BROK5 V]TICAL B>
-------------------------------------#EA
.=? F/ TRANSCRIB]-DEF9$ PR9T SYMBOL
.=#? SECOND TRANSCRIB]-DEF9$ PR9T SYMBOL
.=@#? ?IRD TRANSCRIB]-DEF9$ PR9T SYMBOL
.=^#? F\R? TRANSCRIB]-DEF9$ PR9T SYMBOL
.=_#? FIF? TRANSCRIB]-DEF9$ PR9T SYMBOL
.="#? SIX? TRANSCRIB]-DEF9$ PR9T SYMBOL
.=.#? SEV5? TRANSCRIB]-DEF9$ PR9T SYMBOL
#AA4A ,SPAC+
,9 G5]AL1 ! SPAC+ ( SYMBOLS C FOLL[
PR9T4 ,H["E IF A SYMBOL IS CLE>LY 2+ US$
Z A SIGN ( OP]A;N OR COMP>ISON1 #GF
#AA MISCELLANE\S SYMBOLS A#EA
FOLL[ ! GUIDEL9ES 9 ,SEC;N #A4A4
#AA4B ,UNUSUAL ,PR9T SYMBOLS
,IF A PR9T SYMBOL IS N DEF9$ 9 ,,UEB1
X C 2 REPRES5T$ EI US+ "O ( ! SEV5
TRANSCRIB]-DEF9$ PR9T SYMBOLS ABV1 OR BY
US+ ! TRANSCRIB]-DEF9$ %APE SYMBOLS 9
,SEC;N #AD4 "<,SEE EXAMPLE #AA4E4G 2L">
#AA4C ,GRADE #A 9DICATORS
,IF ! BRL V].N ( A PR9T SYMBOL AL HAS
A GRADE #B M1N+1 & GRADE #A MODE IS N
ALR 9 =CE1 !N GRADE #A 9DICATORS W 2
NE$$4 ,SYMBOLS 9 ! LI/ ABV = : ? APPLIES
>E ! 9TEGRAL SIGN1 ! PRIME SIGN & ! "!=E
SIGN4
#AA4D ,SYMBOLS : H M ?AN "O M1N+ 9
PR9T
,"O ( ! "ULY+ DESIGN F1TURES ( ,,UEB
IS T EA* PR9T SYMBOL %D H "O & ONLY "O
BRL EQUIVAL5T4 ,= EXAMPLE ! V]TICAL B>
IS US$ 9 PR9T TO REPRES5T ABSOLUTE
VALUE1 3DI;NAL PROBABIL;Y & ! ^WS #GG
#AA MISCELLANE\S SYMBOLS B#EA
8S* T01 TO GIVE J ?REE EXAMPLES4 ,! SAME
BRL SYMBOL %D 2 US$ 9 ALL ^! CASES4
-------------------------------------#EB
#AA4E ,EXAMPLES
#AA4E4A
,IF ;Y "7 F" !N ! D]IVATIVE IS DY
OV] DX OR ;F DA% ;X & ! "PIAL D]IVATIVE
IS CURLY ;D ;Y OV] CURLY ;D ;X
,IF ;Y "7 F" !N ! D]IVATIVE IS
;;(DY./DX) OR ;;F7" & ! "PIAL
D]IVATIVE IS ;;(@DY./@DX)4
#GH
#AA MISCELLANE\S SYMBOLS A#EB
#AA4E4B
! 9TEGRAL F #B TO #C ( "<#BX PLUS #A">
DX
EQUALS .<;X SQU>$ PLUS ;X.> SUB #B SUP]
#C
EQUALS "<#C SQU>$ PLUS #C"> M9US "<#B
SQU>$ PLUS #B">
EQUALS #AB M9US #F EQUALS #F
;;;!5#B9#C"<#BX"6#A">DX
"7 .5#B9#C
"7 "<#C9#B"6#C">"-"<#B9#B"6#B">
"7 #AB"-#F "7 #F;'
,NOTE3 ! SPAC+ ( ! 9TEGRAL SIGN 9 PR9T
C 2 UNCLE> OR 9CONSI/5T4 ,9 BRL X IS BE/
TO H ! 9TEGRAL SIGN UNSPAC$ F ! FUNC;N &
TR1T XS LIMITS Z SUBSCRIPTS &
SUP]SCRIPTS4 ,! DX AT ! 5D M1NS
89TEGRATE ) RESPECT TO ;X01 & C AL 2
WRITT5 UNSPAC$4
#GI
#AA MISCELLANE\S SYMBOLS #EC
#AA4E4C
"G$ BRACKETS 5CLOS+ ;N AT ! TOP & ;R
AT ! BOTTOM
EQUALS FRAC;N ;N FACTORIAL OV] ;R
FACTORIAL "TS "<;N M9US ;R"> FACTORIAL
5D FRAC;N">
;;;9N,C5R "7 "
"7 (N6./R6"6);'
,NOTE3 ! B9OMIAL COE6ICI5T "WS BETT] Z
A %APE ?AN A VECTOR "[4
#AA4E4D
,A/]ISK IS 4TRIBUTIVE OV] HOLL[ DOT IF
A A/]ISK "<;B HOLL[ DOT ;C"> EQUALS " HOLL[ DOT "
"9 IS 4TRIBUTIVE OV] "0 IF
A"9" "7 ""0"
,NOTE3 ! HOLL[ DOT %D N 2 US$ TO #HJ
#AA MISCELLANE\S SYMBOLS A#EC
REPRES5T ! A2REVIA;N = DEGREES1 : IS
COV]$ 9 ,SEC;N #C4
-------------------------------------#ED
#AA4E4E
,IF ;F F ;,X TO ;,Y IS A FUNC;N !N !
RELA;N ;F SUP] M9US #A F ;,Y TO ;,X IS
XF A FUNC;N IF & ONLY IF = ALL ;Y 9 ;,Y
"! EXI/S ;X 9 ;,X S* T ;F ( ;X EQUALS ;Y
,IF ;;;F3 ,X \O ,Y;' IS A FUNC;N !N !
RELA;N ;;;F9<"-#A>3 ,Y \O ,X;' IS XF A
FUNC;N IF & ONLY IF
;;;^AY ^E ,Y ^5X ^E ,X;' S* T
;;;F" "7 Y;'
,NOTE3 SEE ,SEC;N #AC = ! REPRES5TA;N
( >R[S4
#AA4E4F
,! SET ( "<;X1 ;Y"> S* T ;X PLUS ;Y
EQUALS #F
;;;_<" _\ X"6Y "7 #F_>;'
#HA
#AA MISCELLANE\S SYMBOLS A#ED
#AA4E4G
,BABYLONIAN NUM]ALS USE TWO SYMBOLS1
;? M1NS #A & #? M1NS #AJ4
,NOTE3 ! TWO TRANSCRIB] DEF9$ SYMBOLS
WD 2 DEF9$ EI ON ! SPECIAL SYMBOLS PAGE
OR 9 A TRANSCRIB]'S NOTE4
-------------------------------------#EE
#AA4F ,EMBELLI%$ CAPITAL LRS
,EMBELLI%$ CAPITAL LRS >E (T5 US$ TO
"N COMMON SETS S* Z ! UNIV]SAL SET ;,E1
! SET ( R1L NUMB]S ;,R OR 9TEG]S ,I4 ,^!
V>Y 9 PR9T F BOOK TO BOOK B C 2
REPRES5T$ 9 BRL BY ! SCRIPT TYPE=M
9DICATORS4
,! SET ( R1L NUMB]S @2;,R
-------------------------------------#EF
#AA4G ,GREEK LRS
,GREEK LRS >E US$ H1VILY 9 ,MA!MATICS4
,! ALPHABET IS LI/$ 2L4 ,REF] AL TO !
,RULE ON ,LRS & _! MODIFI]S4
#HB
#AA MISCELLANE\S SYMBOLS A#EF
.=.A ,GREEK ALPHA
.=.B ,GREEK 2TA
.=.G ,GREEK GAMMA
.=.D ,GREEK DELTA
.=.E ,GREEK EPSILON
.=.Z ,GREEK ZETA
.=.: ,GREEK ETA
.=.? ,GREEK !TA
.=.I ,GREEK IOTA
.=.K ,GREEK KAPPA
.=.L ,GREEK LAMBDA
.=.M ,GREEK MU
.=.N ,GREEK NU
.=.X ,GREEK XI
.=.O ,GREEK OMICRON
.=.P ,GREEK PI
.=.R ,GREEK RHO
.=.S OR .S ,GREEK SIGMA
.=.T ,GREEK TAU
.=.U ,GREEK UPSILON
.=.F ,GREEK PHI
.=.& ,GREEK *I
.=.Y ,GREEK PSI
.=.W ,GREEK OMEGA #HC
#AA MISCELLANE\S SYMBOLS B#EF
.=,.A CAPITAL ,GREEK ALPHA
.=,.B CAPITAL ,GREEK 2TA
.=,.G CAPITAL ,GREEK GAMMA
.=,.D CAPITAL ,GREEK DELTA
.=,.E CAPITAL ,GREEK EPSILON
.=,.Z CAPITAL ,GREEK ZETA
.=,.: CAPITAL ,GREEK ETA
.=,.? CAPITAL ,GREEK !TA
.=,.I CAPITAL ,GREEK IOTA
.=,.K CAPITAL ,GREEK KAPPA
.=,.L CAPITAL ,GREEK LAMBDA
.=,.M CAPITAL ,GREEK MU
.=,.N CAPITAL ,GREEK NU
.=,.X CAPITAL ,GREEK XI
.=,.O CAPITAL ,GREEK OMICRON
.=,.P CAPITAL ,GREEK PI
.=,.R CAPITAL ,GREEK RHO
.=,.S CAPITAL ,GREEK SIGMA
.=,.T CAPITAL ,GREEK TAU
.=,.U CAPITAL ,GREEK UPSILON
.=,.F CAPITAL ,GREEK PHI
.=,.& CAPITAL ,GREEK *I
.=,.Y CAPITAL ,GREEK PSI
.=,.W CAPITAL ,GREEK OMEGA #HD
#AB ,B>S & DOTS OV] & "U #EG
#AB ,B>S & DOTS ETC4 OV] & "U
.=: B> OV] PREVI\S ITEM
.=,: B> "U PREVI\S ITEM
.=@: L9E "? PREVI\S ITEM "
.=^: SIMPLE "R PO9T+ >R[ OV] PREVI\S
ITEM
.=,^: SIMPLE "R PO9T+ >R[ "U PREVI\S
ITEM
.=^4 DOT OV] PREVI\S ITEM
.=,^4 DOT "U PREVI\S ITEM
.=_: TILDE OV] PREVI\S ITEM
.=,_: TILDE "U PREVI\S ITEM
.=": HAT OV] PREVI\S ITEM
.=,": HAT "U PREVI\S ITEM
.=._: >C OV] PREVI\S ITEM
#AB4A ,! DEF9I;N ( AN ITEM
,! DEF9I;N ( AN ITEM 2L IS ! SAME Z T
GIV5 = SUP]SCRIPTS & SUBSCRIPTS 9 ,SEC;N
#G4A4
#HE
#AB ,B>S & DOTS OV] & "U A#EG
,Z 9 ,SEC;N #G1 AN ITEM IS DEF9$ Z ANY
( ! FOLL[+ GR\P+S3
#A4 ,AN 5TIRE NUMB]1 I4E4 ! 9ITIAT+
NUM]IC SYMBOL & ALL SU3E$+ SYMBOLS )9
! NUM]IC MODE ?US E/ABLI%$ "<: WD
9CLUDE ANY 9T]IOR DECIMAL PO9TS1
COMMAS1 SEP>ATOR SPACES1 OR SIMPLE
NUM]IC FRAC;N L9ES">4
#B4 ,AN 5TIRE G5]AL FRAC;N1 5CLOS$ 9
FRAC;N 9DICATORS "4
#C4 ,AN 5TIRE RADICAL EXPRES.N1 5CLOS$ 9
RADICAL 9DICATORS "4
#D4 ,AN >R[ "4
#E4 ,AN >BITR>Y %APE "4
#F4 ,ANY EXPRES.N 5CLOS$ 9 MAT*+ PAIRS (
R.D P>5!SES1 SQU>E BRACKETS OR CURLY
BRACES "4
#G4 ,ANY EXPRES.N 5CLOS$ 9 ! BRL GR\P+
9DICATORS4
#H4 ,IF N"O ( ! =EGO+ APPLY1 ! ITEM IS
SIMPLY ! PREVI\S 9DIVIDUAL SYMBOL4
#HF
#AB ,B>S & DOTS OV] & "U #EH
,EXAMPLES3
;X B> EQUALS #AJ PLUS #AA PLUS #AB ALL
OV] #C ": ;X B> IS ! >I?METIC M1N4
;;;X: "7 (#AJ"6#AA"6#AB./#C);' ": X;: IS
! >I?METIC M1N4
,NOTE3 ! SECOND O3UR;E ( ;X B> NE$S A
GRADE #A SYMBOL 9DICATOR 2C X IS )9 A
GRADE #B PASSAGE4
;X PLUS ;Y ALL ) A B> "U
22,:
EQUALS SIGN ) A L9E "? X "
"7@:
#J4C ) A DOT OV] ! #C,-! RECURR+ DECIMAL
#J4CCCCC444
#J4<#C>^4
,NOTE3 BRL GR\P+ SIGNS >E NE$$ "H
O!RWISE ! DOT WD REF] TO ! 5TIRE NUMB]4
#HG
#AB ,B>S & DOTS OV] & "U A#EH
,! RECURR+ DECIMAL #J4EFABCABCABC 444
#J4EF<#A>^4#B<#C>^4
,2C ! DIGITS #ABC >E 2+ IMPLICITLY GR\P$
9 PR9T ? C AL 2 WRITT5 Z3
#J4EF<#ABC>^4
D]IVATIVES ;X DOT & ;X D\BLE DOT
D]IVATIVES X^4 & ;;X.9<44>
,ANGLE ,,ABC ) A HAT OR C>ET OV] ! ;,B
,ANGLE ;;,A,B":,C
-------------------------------------#EI
#AB4B ,TWO 9DICATORS APPLI$ TO !
SAME ITEM
,IF TWO 9DICATORS APPLY TO ! SAME
ITEM1 !N BRL GR\P+ SYMBOLS M/ 2 US$ TO
%[ : APPLIES F/4
;X TO ! 8;Y B>0
;;X9
;X TO ! ;Y ) A B> OV] ! :OLE EXPRES.N
;;: #HH
#AC ,>R[S #FJ
#AC ,>R[S
#AC4A ,SIMPLE >R[S
.=\ >R[ 9DICATOR
.=^\ BOLD >R[ 9DICATOR
.=\O SIMPLE "R PO9T+ >R[ "
.=\[ SIMPLE LEFT PO9T+ >R[ "
.=\+ SIMPLE UP PO9T+ >R[ "
.=\% SIMPLE D[N PO9T+ >R[ "]
.=\S SIMPLE UP & "R PO9T+ >R[ "
.=\< SIMPLE D[N & "R PO9T+ >R[ "
.=\: SIMPLE UP & LEFT PO9T+ >R[
"
.=\> SIMPLE D[N & LEFT PO9T+ >R[
"
,A SIMPLE >R[ HAS A /&>D B>B$ TIP AT
"O 5D "4 ,! %AFT IS /RAIE N SIGNIFICANT4 ,^! >R[S >E
REPRES5T$ BY AN OP5+ >R[ 9DICATOR & !
APPROPRIATE CLOS+ >R[ 9DICATOR4 ,NOTICE
T ALL ^! T]M9AT+ SYMBOLS H ?REE #HI
#AC ,>R[S A#FJ
DOTS1 >RANG$ 9 A 3SI/5T PATT]N T BE/
DESCRIBES ! DIREC;N4
,NOTE T UN.S Y >E ALR 9 GRADE #A MODE1
! >R[ 9DICATOR W NE$ A GRADE #A SYMBOL
9DICATOR4 ,! BOLD >R[ 9DICATOR W N NE$
"O1 Z ? TWO CELL SYMBOL DOES N H A GRADE
#B M1N+4 ,BO? >R[ 9DICATORS SET >R[ MODE
S NO FUR!R GRADE #A 9DICATORS W 2 NE$$4
,>R[S >E SIGNS ( COMP>ISON S %D
USUALLY 2 SPAC$4 ,AN EXCEP;N IS :5 !Y >E
WRITT5 2L ! LIMIT FUNC;N "4
,D N USE >R[ 9DICATORS :5 A SIMPLE "R
PO9T+ >R[ IS ! ONLY MODIFI] ABV OR 2L AN
ITEM4 ,SEE 8>R[ OV] PREVI\S ITEM0 & 8>R[
2L PREVI\S ITEM0 9 ,SEC;N #AB4
-------------------------------------#FA
;N "R >R[ #J,-;N T5DS TO Z]O
;;;N \O #J;'
9PUT 8"R >R[0 PROCESS 8BOLD "R >R[0
\TPUT
9PUT ;\O PROCESS ^\O \TPUT #IJ
#AC ,>R[S A#FA
#AC4B ,>R[S ) UNUSUAL %AFTS & A /&>D
B>B$ TIP
,%AFT SYMBOLS3
.=3 %ORT S+LE /RAI
.=5 CURV$ OR B5T TO ! "R "
.=4 %>P TURN TO ! "R "<9 L9E ( DIREC;N">
.=0 %>P TURN TO ! LEFT "<9 L9E (
DIREC;N">
,ALL %AFT SYMBOLS C 2 EL;GAT$ BY
REPETI;N4 ,! %AFT SYMBOLS >E PLAC$ 2T !
OP5+ & CLOS+ >R[ 9DICATORS4 ,>R[ L5G?
ONLY NE$S TO 2 9DICAT$ 9 BRL :5 9 PR9T
>R[S ( DI6]5T L5G?S H DI6]5T M1N+S4
,^! EXAMPLES / H /&>D B>B$ TIPS4 #IA
#AC ,>R[S B#FA
D\BLE %AFT$ M$IUM L5G? "R PO9T+ >R[
;\77O
M$IUM >R[ PO9T+ UP ) A %>P TURN TO ! "R
;\44+
M$IUM L5G? "R PO9T+ >R[ B5D+ CLOCKWISE
;\55O
-------------------------------------#FB
L;G1 BROK5 LEFT PO9T+ >R[
;\111[
%ORT1 M$IUM & L;G D[N PO9T+ SIMPLE >R[S
;\3% ;\% ;\333%
#AC4C ,>R[S ) UNUSUAL TIPS
,B>B SYMBOLS3
.=R REGUL> B>B1 FULL1 9 L9E ( DIREC;N
.=W REGUL> B>B1 FULL1 C.T] TO L9E (
DIREC;N
.=@W REGUL> B>B1 UPP] HALF1 C.T]
.=,W REGUL> B>B1 L[] HALF1 C.T] #IB
#AC ,>R[S A#FB
.=@R REGUL> B>B1 UPP] HALF1 9 L9E
.=,R REGUL> B>B1 L[] HALF1 9 L9E
.=& CURV$1 FULL1 C.T]
.=Y CURV$1 FULL1 9 L9E
.=@& CURV$1 UPP] HALF1 C.T]
.=,& CURV$1 L[] HALF1 C.T]
.=@Y CURV$1 UPP] HALF1 9 L9E
.=,Y CURV$1 L[] HALF1 9 L9E
.=\ /RAI
.=@\ /RAI
.=,\ /RAI
,IF AN >R[ HAS UNUSUAL TIPS1 DECIDE :
IS ! H1D 2F Y *OOSE ! DIREC;N ( YR CLOS+
9DICATOR4 ,! COMPLETE RULES = DECID+ >R[
DIREC;N >E3
#A4 ,IF "! >E DIREC;NAL TIPS1 & ALL L1D
9 ! SAME DIREC;N1 ! H1D IS ! 5D T LIES
9 T DIREC;N4
#B4 ,IF "! >E NO DIREC;NAL TIPS1 B "O 5D
HAS A TIP & ! O!R DOES N1 ! 5D ) ! TIP
IS ! H1D4
#C4 ,9 ALL O!R CASES1 ! H1D ( ! #IC
#AC ,>R[S B#FB
>R[ IS DEEM$ TO 2 ! 5D AT ! "R1 OR 9 !
CASE ( /RICTLY V]TICAL >R[S1 AT ! TOP4
-------------------------------------#FC
,! TIP" & %AFT SEG;T" >E
TRANSCRIB$ 2T ! OP5+ & CLOS+ 9DICATORS4
,^! ITEMS >E EXPRESS$ 9 LOGICAL ORD]1 T
IS />T+ ) ! >R[ TAIL & PROGRESS+ T[>DS !
H1D1 EV5 IF T RUNS C.T] TO ! PHYSICAL
ORD] "R[">4
,C]TA9 ELE;TS >E OMITT$1 CORRESPOND+ TO
^! R1D] RULES3
#A4 ,IF NO TIP IS TRANSCRIB$1 X IS
"U/OOD T AN ORD9>Y FULL B>B$ TIP O3URS
AT ! >R[ H1D1 & "! IS NO O!R TIP4
#B4 ,IF NO %AFT IS TRANSCRIB$1 X IS
"U/OOD T ! %AFT IS A /RAI AL APPLIES2 IF
"O TIP IS TRANSCRIB$1 X IS AT ! H1D2
IF TWO TIPS >E TRANSCRIB$1 ! F/ IS AT
! TAIL & ! SECOND AT ! H1D4
#ID
#AC ,>R[S A#FC
O!RWISE ORD9>Y "R >R[1 ) CURV$ H1D
;\YO
COMMON HORIZONTAL BIDIREC;NAL >R[
;\WRO
HORIZONTAL BIDIREC;NAL >R[1 TILT$ F L[]
LEFT TO UPP] "R
;\WRS
O!RWISE ORD9>Y "R >R[1 ) TAIL & H1D TIPS
;\RRO
O!RWISE ORD9>Y "R >R[1 ) TWO H1D TIPS
;\33RRO
O!RWISE ORD9>Y LEFT >R[1 ) TAIL & H1D
TIPS
;\RR[
O!RWISE ORD9>Y LEFT >R[1 ) TWO H1D TIPS
;\33RR[
#IE
#AC ,>R[S #FD
"R >R[ ) A /RAIR[ UP1 FOLL[$ BY ORD9>Y >R[ D[N
^\+\%
COMMON "R >R[ OV] COMMON LEFT >R[,-SEE
,SEC;N #AD4C4C REG>D+ V]TICAL
JUXTAPOSI;N
;\O]\[
HALF B>B$ LEFT >R[ OV] HALF B>B$ "R
>R[,-REV]SIBLE *EMICAL REAC;N
;\@R[]\,RO
,SEE ,SEC;N #AF = EQUILIBRIUM >R[S T
O3UR 9 ,*EMI/RY4
#IF
#AD ,%APE ,SYMBOLS #FE
#AD ,%APE ,SYMBOLS & ,COMPOSITE
,SYMBOLS
,LI/+ ( %APE 9DICATORS3
.=$ %APE 9DICATOR
.=_$ FILL$ " %APE 9DICATOR
.=.$ %AD$ %APE 9DICATOR
.=@$ TRANSCRIB]-ASSIGN$ %APE 9DICATOR
.=@_$ TRANSCRIB]-ASSIGN$ FILL$ "
%APE 9DICATOR
.=@.$ TRANSCRIB]-ASSIGN$ %AD$ %APE
9DICATOR
.=: %APE T]M9ATOR
,LI/+ ( SPECIFIC %APES3
.=$#C REGUL> " TRIANGLE
.=$#D SQU>E
.=$#E REGUL> P5TAGON
.=$#F REGUL> HEXAGON
.=$#G REGUL> HEPTAGON
.=$#H REGUL> OCTAGON "
POLYGONS">
.=$= CIRCLE #IG
#AD ,%APE ,SYMBOLS A#FE
.=$@#D P>ALLELOGRAM
,COMPOSITE ,SYMBOLS3
.=& SUP]POSI;N 9DICATOR
.== HORIZONTAL JUXTAPOSI;N 9DICATOR
.=] V]TICAL JUXTAPOSI;N 9DICATOR
.=[ PHYSICAL 5CLOSURE 9DICATOR
-------------------------------------#FF
#AD4A ,USE ( ! %APE T]M9A;N 9DICATOR
#AD4A4A ,IF A %APE IS FOLL[$ BY A
SPACE !N NO T]M9A;N SYMBOL IS NE$$4
TRIANGLE SYMBOL SPACE ,,ABC
;$#C ,,ABC
#AD4A4B ,IF ! %APE SYMBOL IS FOLL[$ BY
PUNCTUA;N1 OR UNSPAC$ F A FOLL[+ SYMBOL1
!N ! %APE T]M9ATOR M/ 2 US$4
TRIANGLE ,,ABC UNSPAC$
;$#C:,,ABC
#IH
#AD ,%APE ,SYMBOLS A#FF
,:AT IS ! NEXT %APE8
OP5 BRACE SQU>E1 %AD$ CIRCLE1 SOLID
TRIANGLE1 %AD$ SQU>E 444 CLOSE BRACE
,:AT IS ! NEXT %APE8
_<;$#D:1 .$=:1 _$#C:1 .$#D 444_>
,NOTE T UN.S Y >E ALR 9 GRADE #A MODE1
A GRADE #A SYMBOL 9DICATOR W 2 NE$$ 2F !
%APE 9DICATOR4 ,? DOES N H["E APPLY TO !
%AD$ & FILL$ %APE 9DICATORS 2C ^! TWO
CELL SYMBOLS D N H A GRADE #B M1N+4 ,ALL
! 9ITIAL %APE 9DICATORS 9ITIATE %APE
MODE S NO FUR!R GRADE #A 9DICATORS W 2
NE$$4
#AD4B ,TRANSCRIB] DEF9$ %APES
,! DESCRIP;N )9 TRANSCRIB] DEF9$ %APES
%D 2 A %ORT S]IES ( 9ITIALS OR A S+LE
GRADE #A ^W4 ,!Y %D N 2 US$ IF ! PR9T
SYMBOL IS ALR COV]$ ELSE": 9 ! CODE4 ,!
DEF9I;NS ( ALL %APE SYMBOLS %D 2
AVAILABLE TO ! R1D] 9 EI A TRANSCRIB]'S
NOTE OR ON A SPECIAL SYMBOLS PAGE4 #II
#AD ,%APE ,SYMBOLS B#FF
,= EXAMPLE1 A SMIL+ FACE US$ Z AN ICON
"?\T A BOOK CD 2 DEF9$ Z
@$SF OR @$SMILE
R ?AN
@$
: IS TOO L;G & REQUIRES BRL GR\P+
SYMBOLS TO /OP ! SPACE T]M9AT+ ! %APE4
-------------------------------------#FG
#AD4C ,COMB9$ %APES
,IF TWO PR9T SYMBOLS H BE5 COMB9$ TO
=M A NEW PREVI\SLY UNDEF9$ SYMBOL1 !N X
M/ 2 DECID$ :E!R ! SECOND SYMBOL IS
5CLOS$1 SUP]IMPOS$1 COMB9$ ON ! "R OR
COMB9$ 2L4 ,EA* ( ! F\R COMPOSITE SYMBOL
9DICATORS SIGNALS A COMB9+ ( ! ITEM J
PRIOR ) ! ITEM IMMLY FOLL[+ X1 ": 8ITEM0
IS Z DEF9$ 9 ,SEC;N #G4
,EA* COMPOSITE SYMBOL 9DICATOR W NE$ A
GRADE #A SYMBOL 9DICATOR UN.S ! :OLE
EXPRES.N IS ALR 9 GRADE #A MODE4
#AD4C4A ,PHYSICAL ,5CLOSURE1 ;[
CIRCLE 5CLOS+ A PLUS SIGN
;$=["6 #AJJ
#AD ,%APE ,SYMBOLS A#FG
,9 ! EXAMPLE 2L1 ! CIRCLE 5CLOS+ A
PLUS SIGN IS 2+ US$ Z AN OP]A;N SIGN4 ,9
! F/ V].N ! OP]A;N SIGN IS UNSPAC$ S A
T]M9A;N SIGN IS NE$$ B NO GRADE
9DICATORS >E NE$$ 2C ! NUMB] SIGNS
9ITIATE NUM]IC MODE4 ,9 ! SECOND V].N !
OP]A;N SIGN IS SPAC$ = CL>;Y S NO
T]M9A;N SIGN IS NE$$ B ! %APE SYMBOLS D
NE$ GRADE #A 9DICATORS4
#B 8CIRCL$ PLUS0 #C EQUALS #C 8CIRCL$
PLUS0 #B
#B$=["6:#C "7 #C$=["6:#B
#B 8CIRCL$ PLUS0 #C EQUALS #C 8CIRCL$
PLUS0 #B
#B ;$=["6 #C "7 #C ;$=["6 #B
,NOTE3 ,SEE ,SEC;N #C4E IF NUMB]S >E
5CLOS$ 9 A SQU>E TO REPRES5T A
CALCULATOR KEY4
#AJA
#AD ,%APE ,SYMBOLS #FH
#AD4C4B ,SUP]POSI;N1 ;&
,NOTE T ? /RUCTURE %D N 2 US$ =
NEGA;N4 ,SEE 8L9E "? PREVI\S ITEM0 9
,SEC;N #AB4
;,R ) SUP]IMPOS$ ;X,-PRESCRIP;N SYMBOL
,R;&X
9TEGRAL SIGN ) A SMALL CIRCLE SUP]IMPOS$
HALF WAY UP,-CLOS$ 9TEGRAL DEF9$ 9
,SEC;N #AA4A
@!
9TEGRAL SIGN ) A SMALL SQU>E SUP]IMPOS$
HALF WAY UP,-! T]M9A;N CD 2 OMITT$ IF
"! 0 A FOLL[+ SPACE
;;!&$#D:
#AD4C4C ,V]TICAL ,JUXTAPOSI;N1 ;]
,! UPP] SYMBOL %D 2 GIV5 F/1 FOLL[$ BY
! V]TICAL JUXTAPOSI;N 9DICATOR1 !N ! L[]
SYMBOL4
,? /RUCTURE %D N 2 US$ = B>S1 #AJB
#AD ,%APE ,SYMBOLS A#FH
>R[S1 DOTS1 TILDES OR HATS OV] OR "U O!R
SYMBOLS "4 ,NEI %D X 2
US$ = SUP]SCRIPTS OR SUBSCRIPTS WRITT5
DIRECTLY OV] OR "U "4
A HOLL[ DOT ) AN EQUAL SIGN "UN1?
"0;]"7
B9OMIAL COE6ICI5T "[
"
#AD4C4D ,HORIZONTAL ,JUXTAPOSI;N1 ;=
8,HORIZONTAL JUXTAPOSI;N0 IS TO 2
9VOK$ ONLY :5 TWO SYMBOLS >E WRITT5 9
CLOSE PROXIM;Y & X IS CLE> F ! USAGE T A
NEW S+LE SYMBOL1 4T9CT F ! ELE;T>Y
SYMBOLS 3SID]$ 9 SEQU;E1 IS 9T5D$4
,O!RWISE1 SYMBOLS WRITT5 "O AF ! O!R %D
SIMPLY 2 BRLD ACLY4
#AJC
#AE ,MATRICES & VECTORS #FI
#AE ,MATRICES & VECTORS
#AE4A ,5L>G$ GR\P+ SYMBOLS
,:5 5L>G$ BRACKETS >E US$ 9 PR9T =
VECTORS1 MATRICES1 SY/EMS ( EQUA;NS1
FUNC;N DEF9I;NS ETC41 ! APPROPRIATE
5L>G$ GR\P+ SYMBOLS %D 2 US$ 9 BRL4 ,^!
>E ! USUAL GR\P+ SYMBOLS PREC$$ BY A DOT
#F4 ,SEE ! FULL LI/ 9 ,SEC;N #E4 ,^! %D
2 PLAC$ DIRECTLY "U EA* O!R4 ,BLANK L9ES
2F & AF S* >RANGE;TS MAY 2 NE$$ = CL>;Y4
#AE4B ,MATRICES
,! COLUMNS %D 2 LEFT ADJU/$ EXCEPT =
M9US SIGNS : %D 2 BRLD TO /& \4 ,"O
COLUMN ( BLANK CELLS %D 2 LEFT 2T
COLUMNS4 ,MAT]IAL \TSIDE ! MATRIX1 S* Z
SIGNS ( OP]A;N & COMP>ISON1 %D 2 PLAC$
ON ! TOP L9E1 EV5 IF !Y >E C5T]$ 9 PR9T4
,I "7 ,"<#A #J,">
,"<#J #A,">
#AJD
#AE ,MATRICES & VECTORS A#FI
,.<#A #B #C,.>,.< #A #B,.>
,.<#D #E #F,.>,.<"-#C #D,.>
,.< #E "-#F,.>
,"< A "-B,">
,"<"-C D,">
-------------------------------------#GJ
#AE4C ,DET]M9ANTS
,^! H ! SAME /RUCTURE Z MATRICES B >E
NORMALLY 5CLOS$ 9 PR9T ) 5L>G$ V]TICAL
B>S4
;;;_\,P_\ "7 ,_\A B_\ "7 AD"-BC;'
,_\C D_\
#AE4D ,OMIS.N DOTS
,! PLACE;T ( DOTS US$ TO 9DICATE !
OMIS.N ( "O OR M R[S OR COLUMNS C FOLL[
! PR9T4
#AJE
#AE ,MATRICES & VECTORS A#GJ
;;;,_\A5#AA A5#AB 444 A5<#AN>,_\
,_\A5#BA A5#BB 444 A5<#BN>,_\
,_\ 4 4 444 4 ,_\
,_\A5 A5 444 A5 ,_\;'
-------------------------------------#GA
#AE4E ,D1L+ ) WIDE MATRICES
,IF A MATRIX OR DET]M9ANT IS TOO WIDE
= ! BRL PAGE1 RUNOV]S )9 5TRIES MAY 2
NEC4 ,IF "! IS N ROOM TO 9D5T ^!
RUNOV]S1 !Y C 2 BLOCK$ & A BLANK L9E
LEFT 2T R[S4
#AJF
#AE ,MATRICES & VECTORS A#GA
""=;;;
,"
,"<"6B5#AX5#B "6B5#AY5#B "6B5#AZ5#B,">
,"<"6C5#AX5#C "6C5#AY5#C "6C5#AZ5#C,">
,"< ,">
,"
,"<"6B5#BX5#B "6B5#BY5#B "6B5#BZ5#B,">
,"<"6C5#BX5#C "6C5#BY5#C "6C5#BZ5#C,">
,"< ,">
,"
,"<"6B5#CX5#B "6B5#CY5#B "6B5#CZ5#B,">
,"<"6C5#CX5#C "6C5#CY5#C "6C5#CZ5#C,">
""=;'
,ANO!R APPROA* IS TO COMPLETE ! F/
COLUMN )\T OV]RUNS & !N TO PLACE ! NEXT
COLUMN 2L ?1 9D5T$ TWO CELLS4
#AJG
#AE ,MATRICES & VECTORS B#GA
""=;;;
,"
A5#BZ5#A"6B5#BZ5#B"6C5#BZ5#C,">
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""=;'
,NOTICE T 9 ! F/ EXAMPLE ! /RUCTURE (
! MATRIX IS CLE>] B 9 ! SECOND EXAMPLE !
9DIVIDUAL 5TRIES >E EASI] TO R1D4
,NOTICE AL ! DI6]5T PLACE;T ( ! 5L>G$
GR\P+ SIGNS 9 ! TWO EXAMPLES4
-------------------------------------#GB
,A TRANSCRIB]'S NOTE %D 2 9CLUD$ 9 EI
CASE TO EXPLA9 ! PLACE;T ( EA* 5TRY4
#AJH
#AE ,MATRICES & VECTORS A#GB
#AE4F ,VECTORS
,LRS REPRES5T+ VECTORS >E (T5 PR9T$ 9
BOLD FONT & MAY H >R[S OR B>S ABV OR 2L4
,BOLDFACE ONLY NE$S TO 2 %[N 9 BRL IF X
IS ! ONLY ME?OD US$4 ,= >R[S & B>S ABV &
2L SEE ,SEC;N #AB4
,IF ! VECTOR 8#B OV] M9US #A0 0 CALL$
;P & W5T F PO9T ,A TO PO9T ;,B "H >E "S
( ! MO/ LIKELY =MS3
;P ) A B> "U EQUALS 5L>G$ R.D BRACKETS1
#B AT ! TOP & M9US #A AT ! BOTTOM
P,: "7 ,"< #B,">
,"<"-#A,">
;P ) A B> OV]
P;:
BOLD ;P
^2;P
#AJI
#AE ,MATRICES & VECTORS B#GB
;,,AB ) AN >R[ OV]
;;<,,AB>^:
;,,AB ) A B> "U
;;<,,AB>,:
-------------------------------------#GC
#AE4G ,GR\P+ ( EQUA;NS
,OP5+ 5L>G$ CURLY BRACES >E (T5 US$ TO
GR\P EQUA;NS4 ,PR9T SPAC+ %D 2 FOLL[$ ":
POSSIBLE4
,SOLVE3
,_< X"6#BY "7 #G
,_<#BX"- ;Y "7 "-#D
;;;F" "7 ,_<#J IF X @< #J
,_ #J;'
#AAJ
#AF ,*EMI/RY #GD
#AF ,*EMI/RY
.=@_7 EQUILIBRIUM >R[1 TR5D TO ! LEFT
.="_7 EQUILIBRIUM >R[1 TR5D TO ! "R
.=^_7 EQUILIBRIUM >R[ "POONS">
.=,- DA% OR S+LE L9E BOND
.=.,- D\BLE L9E BOND
.=_,- TRIPLE L9E BOND
.=@_,- QUADRUPLE L9E BOND
.="5 S+LE DA%$ L9E
.=."5 D\BLE DA%$ L9E
.=_"5 TRIPLE DA%$ L9E
.=@_"5 QUADRUPLE DA%$ L9E
.="4 S+LE DOT
.=."4 D\BLE DOT
.=_"4 TRIPLE DOT
.=@_"4 QUADRUPLE DOT
.="8 S+LE CROSS
.=."8 D\BLE CROSS #AAA
#AF ,*EMI/RY A#GD
.=_"8 TRIPLE CROSS
.=@_"8 QUADRUPLE CROSS
.="0 S+LE SMALL CIRCLE
.=."0 D\BLE SMALL CIRCLE
.=_"0 TRIPLE SMALL CIRCLE
.=@_"0 QUADRUPLE SMALL CIRCLE
-------------------------------------#GE
#AF4A ,*EMICAL "NS
CYCLOHEXANE ) ! F/ FIVE LRS 9 ITALIC
.1CYCLO.'HEXANE
#B COMMA #B HYPH5 ,DIME?YLPROPANE
#B1B-,DIME?YLPROPANE
#A HYPH5 ,HYDROXYL COMMA #B HYPH5
NITROB5Z5E
#A-,HYDROXYL1#B-NITROB5Z5E
,COPP] OP5 P>5!SIS ,ROMAN CAPITAL TWO
CLOSE P>5!SIS SPACE ,SULPHATE
,COPP]"<,,II"> ,SULPHATE
#AAB
#AF ,*EMI/RY A#GE
,COPP] SUP]SCRIPT ,ROMAN CAPITAL TWO
SPACE ,SULPHATE
,COPP];;9<,,II> ,SULPHATE
#AF4B ,*EMICAL =MULAE
,USE ( CAPITAL 9DICATORS & T]M9ATORS3
,! G5]AL ,,UEB PR9CIPLES ON ! *OICE (
S+LE LR1 ^W OR PASSAGE MODE APPLY2 9
"PICUL>1 A CAPITAL T]M9ATOR %D N 2 US$
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S+LE CAPITAL 9DICATORS = *EMICAL =MULAE
PROVIDES A UNI=M APPE>.E TO ! BRL2
N"E!.S1 "! MAY 2 A CLE> ADVANTAGE 9 US+
CAPITAL PASSAGE MODE 9 "S CASES4 ,LRS
REPRES5T+ *EMICAL ELE;TS %D N"E 2
3TRACT$4
,O
,FE
,N,O
,NA,CL
;,AL OP5 P>5!SIS ,O CLOSE P>5!SIS ,CL
,AL"<,O">,CL #AAC
#AF ,*EMI/RY B#GE
,O SUB #B
,O;5#B
-------------------------------------#GF
;,H SUB #B ,O
,H;5#B,O
,CA "<,O ;,H"> SUB #B
,CA"<,O,H">;5#B
,CU ;,S ,O SUB #D DOT #E ;,H SUB #B ,O
,CU,S,O;5#D"4#E,H5#B,O
;,H SUP] PLUS
,H;9"6
;,S ,O SUB #D SUP] M9US M9US
,S,O;5#D9<"-"->
,AN EXAMPLE ( US+ CAPITAL PASSAGE
MODE3
#AAD
#AF ,*EMI/RY A#GF
;,R DOT ;,,,C ;H " DOT ;,C ;,H
SUB #B DOT ;,C ;,H SUB #B DOT ;,C ,O
SUB #B ;,H
,,,R"4CH""4CH;5#B"4CH5#B
"4CO;5#B;H,'
,NOTE T ,ROMAN NUM]ALS >E CAPITALIS$ Z
A S+LE GR\P3
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;;,FE9<,,III>,CL5#C
#AF4C ,ATOMIC MASS NUMB]S
,^! >E (T5 %[N ) LEFT-H& SUP]SCRIPT &
SUBSCRIPT NUMB]S3
SUB #IB SUP] #BCH ;,U
;5#IB9#BCH,U
#AF4D ,ELECTRONIC 3FIGURA;N
,S* NOTA;N C 9VOLVE LEFT-H&
SUP]SCRIPTS1 & A SPACE OR HALF-SPACE 9
PR9T NE$S TO 2 RETA9$ 9 ! BRL TO MAKE !
ATTA*;T CLE>4 #AAE
#AF ,*EMI/RY B#GF
,AR #AS SUP] #B #BS SUP] #B #BP SUP] #F
#CS SUP] #B #CP SUP] #F
,AR #AS9#B#BS9#B#BP9#F#CS9#B#CP9#F
SUP] #A ;,S SUB #J
;9#A,S5#J
#D;D SUP] #I #ES SUP] #B SUP] #B ;,D SUB
#E_/#B
#D;D9#I#ES9#B ;9#B,D5<#E_/#B>
-------------------------------------#GG
#AF4E ,*EMICAL ,EQUA;NS
#B ,NA ,O ;,H PLUS ;,H SUB #B ;,S ,O SUB
#D "R >R[ ,NA SUB #B ;,S ,O SUB #D
PLUS #B ;,H SUB #B ,O
;;;#B,NA,O,H"6,H5#B,S,O5#D
\O ,NA5#B,S,O5#D"6#B,H5#B,O;'
#AAF
#AF ,*EMI/RY A#GG
;,N SUB #B "R >R[ ;,N ;,H SUB #C1 ) AN
;,H SUB #B WRITT5 ABV ! >R[ & 8,HAB]
PROCESS0 WRITT5 2L ! >R[
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,N,H5#C;'
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""=;;;
,H5#B
,N5#B \O ,N,H5#C
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""=;'
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;;;,H5#B ""6,I5#B "] "7 #B,H,I
";'
;,,,H ;N ;C O,' PLUS ;,,,R O ;H,' "R >R[
;,N ;,H SUB #B DOT ;,C ,O DOT ,O ;,R
"R >R[ ;,N ;,H SUB #B ;,C ,O DOT ;,N
;,H DOT ;,C ,O SUB #B ;,R
;;;,,,HNCO"6ROH \O NH5#B"4CO"4OR
\O NH5#B;CO"4NH"4CO5#BR,';' #AAG
#AF ,*EMI/RY B#GG
,PB " PLUS #B ;E
EQUILIBRIUM >R[ ,PB
;;;,PB9<"6"6>"6#B;E ^_7 ,PB;'
-------------------------------------#GH
#AF4F ,ELECTRONS
,ELECTRONS %[N Z DOTS1 CROSSES OR
CIRCLES ATTA*$ TO ELE;T SYMBOLS MAY 2
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M COMPLEX CASES " >E BETT] D1LT ) US+ ORD9>Y
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PURELY 9 BRL4
,CL ) A MIDL9E DOT AF ! ;L
,CL"4
#AAH
#AF ,*EMI/RY A#GH
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,O SURR.D$ BY SMALL CROSSES & CIRCLES
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"R1 TWO CROSSES 2L1 & A CIRCLE 2L A
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""=;;;
."8
,H "8"0 ,O "8"0 ,H
."8
""=;'
#AF4G ,/RUCTURAL ,=MULAE
,! G5]AL ,,UEB ME?OD = L9E DRAW+ MAY 2
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#AF ,*EMI/RY B#GH
TRANSCRIB] DEF9$ SYMBOLS4
""=;;;
,H
_
,H,-,C,-,H
_
,H,-,C,-,H
_
,H,-,C,-,H
_
,H
""=;'
-------------------------------------#GI
"37
> <
> <
<< >>
<< >>
"33
#ABJ
#AF ,*EMI/RY A#GI
""=;;;
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_ __ __
_ __ __
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,N
,H
""=;'
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#AF ,*EMI/RY B#GI
""=;;;,,,
CHO
_
HO "33W333 H
_
H "33W333 OH
_
HO "33W333 H
_
CH5#BOH
""=,';'
#ABB
#AF ,*EMI/RY #HJ
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> <<
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__ _
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""=;'
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NH
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< >
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""=,';'
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_ _
< >
<>
NO5#B
""=,';'
""=;;;,,,
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< >
< >
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> <
> <
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""=,';'
#ABD
#AF ,*EMI/RY #HB
>>< ><<
>> < > <<
_ __ _
_ __ _
<< > < >>
<<> <>>
,L9E> ,ME?OD
,A ME?OD IS AVAILABLE 9 : /RUCTURAL
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9 BRL4 ,H["E1 Z YET ? HAS N BE5 DOCU;T$
Z A ,,UEB TE*NIQUE4
-------------------------------------#HC
#AG ,COMPUT] ,NOTA;N
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L5G? ( ! BRL
-------------------------------------#HD
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