%!PS-Adobe-2.0
%%Creator: dvips(k) 5.92b Copyright 2002 Radical Eye Software
%%Title: talk.dvi
%%Pages: 33
%%PageOrder: Ascend
%%BoundingBox: 0 0 596 842
%%DocumentFonts: CMR7 CMR12 CMSY10 CMMI12 CMR8 CMMI8 CMEX10 CMSY8 CMR6
%%+ CMBX12 CMMIB10 CMBX10
%%EndComments
%DVIPSWebPage: (www.radicaleye.com)
%DVIPSCommandLine: dvips talk -o
%DVIPSParameters: dpi=600, compressed
%DVIPSSource:  TeX output 2005.10.28:1122
%%BeginProcSet: texc.pro
%!
/TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S
N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72
mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0
0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{
landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize
mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[
matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round
exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{
statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0]
N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin
/FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array
/BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2
array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N
df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A
definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get
}B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub}
B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr
1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3
1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx
0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx
sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{
rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp
gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B
/chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{
/cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{
A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy
get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse}
ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp
fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17
{2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add
chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{
1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop}
forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn
/BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put
}if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{
bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A
mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{
SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{
userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X
1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4
index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N
/p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{
/Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT)
(LaserWriter 16/600)]{A length product length le{A length product exch 0
exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse
end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask
grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot}
imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round
exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto
fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p
delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M}
B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{
p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S
rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end

%%EndProcSet
%%BeginProcSet: f7b6d320.enc
% Thomas Esser, Dec 2002. public domain
%
% Encoding for:
%     cmb10 cmbx10 cmbx12 cmbx5 cmbx6 cmbx7 cmbx8 cmbx9 cmbxsl10
%     cmdunh10 cmr10 cmr12 cmr17cmr6 cmr7 cmr8 cmr9 cmsl10 cmsl12 cmsl8
%     cmsl9 cmss10cmss12 cmss17 cmss8 cmss9 cmssbx10 cmssdc10 cmssi10
%     cmssi12 cmssi17 cmssi8cmssi9 cmssq8 cmssqi8 cmvtt10
%
/TeXf7b6d320Encoding [
/Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /Omega
/ff /fi /fl /ffi /ffl /dotlessi /dotlessj /grave /acute /caron /breve
/macron /ring /cedilla /germandbls /ae /oe /oslash /AE /OE /Oslash
/suppress /exclam /quotedblright /numbersign /dollar /percent /ampersand
/quoteright /parenleft /parenright /asterisk /plus /comma /hyphen
/period /slash /zero /one /two /three /four /five /six /seven /eight
/nine /colon /semicolon /exclamdown /equal /questiondown /question /at
/A /B /C /D /E /F /G /H /I /J /K /L /M /N /O /P /Q /R /S /T /U /V /W /X
/Y /Z /bracketleft /quotedblleft /bracketright /circumflex /dotaccent
/quoteleft /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p /q /r /s /t /u
/v /w /x /y /z /endash /emdash /hungarumlaut /tilde /dieresis /suppress
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /space
/Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /.notdef
/.notdef /Omega /ff /fi /fl /ffi /ffl /dotlessi /dotlessj /grave /acute
/caron /breve /macron /ring /cedilla /germandbls /ae /oe /oslash /AE
/OE /Oslash /suppress /dieresis /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
] def

%%EndProcSet
%%BeginProcSet: pstricks.pro
%!
% PostScript prologue for pstricks.tex.
% Version 97 patch 3, 98/06/01
% For distribution, see pstricks.tex.
%
/tx@Dict 200 dict def tx@Dict begin
/ADict 25 dict def
/CM { matrix currentmatrix } bind def
/SLW /setlinewidth load def
/CLW /currentlinewidth load def
/CP /currentpoint load def
/ED { exch def } bind def
/L /lineto load def
/T /translate load def
/TMatrix { } def
/RAngle { 0 } def
/Atan { /atan load stopped { pop pop 0 } if } def
/Div { dup 0 eq { pop } { div } ifelse } def
/NET { neg exch neg exch T } def
/Pyth { dup mul exch dup mul add sqrt } def
/PtoC { 2 copy cos mul 3 1 roll sin mul } def
/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def }
def
/PathLength { flattenpath /z 0 def { /y1 ED /x1 ED /y2 y1 def /x2 x1 def
} { /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ }
/pathforall load stopped { pop pop pop pop } if z } def
/STP { .996264 dup scale } def
/STV { SDict begin normalscale end STP  } def
/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def
PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y
mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul
/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ]
0 } ifelse setdash stroke } def
/DotLine { /b PathLength def /a ED /z ED /y CLW def /z y z add def a 0 gt
{ /b b a div def } { a 0 eq { /b b y sub def } { a -3 eq { /b b y add
def } if } ifelse } ifelse [ 0 b b z Div round Div dup 0 le { pop 1 } if
] a 0 gt { 0 } { y 2 div a -2 gt { neg } if } ifelse setdash 1
setlinecap stroke } def
/LineFill { gsave abs CLW add /a ED a 0 dtransform round exch round exch
2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25
% DG/SR modification begin - Dec. 12, 1997 - Patch 2
%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a
itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a
% DG/SR modification end
Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict
/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1
% DG/SR modification begin - Jun.  1, 1998 - Patch 3 (from Michael Vulis)
% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore }
% def
a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore
pop pop } def
% DG/SR modification end
/BeginArrow { ADict begin /@mtrx CM def gsave 2 copy T 2 index sub neg
exch 3 index sub exch Atan rotate newpath } def
/EndArrow { @mtrx setmatrix CP grestore end } def
/Arrow { CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 h T 1 -1
scale } if w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fill
grestore } def
/Tbar { CLW mul add /z ED z -2 div CLW 2 div moveto z 0 rlineto stroke 0
CLW moveto } def
/Bracket { CLW mul add dup CLW sub 2 div /x ED mul CLW add /y ED /z CLW 2
div def x neg y moveto x neg CLW 2 div L x CLW 2 div L x y L stroke 0
CLW moveto } def
/RoundBracket { CLW mul add dup 2 div /x ED mul /y ED /mtrx CM def 0 CLW
2 div T x y mul 0 ne { x y scale } if 1 1 moveto .85 .5 .35 0 0 0
curveto -.35 0 -.85 .5 -1 1 curveto mtrx setmatrix stroke 0 CLW moveto }
def
/SD { 0 360 arc fill } def
/EndDot { { /z DS def } { /z 0 def } ifelse /b ED 0 z DS SD b { 0 z DS
CLW sub SD } if 0 DS z add CLW 4 div sub moveto } def
/Shadow { [ { /moveto load } { /lineto load } { /curveto load } {
/closepath load } /pathforall load stopped { pop pop pop pop CP /moveto
load } if ] cvx newpath 3 1 roll T exec } def
/NArray { aload length 2 div dup dup cvi eq not { exch pop } if /n exch
cvi def } def
/NArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop } if
f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def
/Line { NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub
def n { Lineto } repeat CP 4 2 roll ArrowB L pop pop } if } def
/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 }
ifelse { pop } repeat a } def
/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq
and { pop pop /n n 1 sub def } if } def
/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop }
repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1
ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1
moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto
Lineto pop pop closepath } ifelse } def
/Diamond { /mtrx CM def T rotate /h ED /w ED dup 0 eq { pop } { CLW mul
neg /d ED /a w h Atan def /h d a sin Div h add def /w d a cos Div w add
def } ifelse mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2
div /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
setmatrix } def
% DG modification begin - Jan. 15, 1997
%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq {
%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2
%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0
%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
%setmatrix } def
/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup
CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2
div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0
d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
% DG/SR modification begin - Jun.  1, 1998 - Patch 3 (from Michael Vulis)
% setmatrix } def
setmatrix pop } def
% DG/SR modification end
/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
def } def
/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
def } def
/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1
def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp
mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos
abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def
/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul
m mul neg def } def
/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if }
ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def }
def
/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def
/NC { CC x1 y1 x2 y2 x y curveto } def
/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def
/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def
/NAC { x2 y2 x y curveto CC x1 y1 } def
/EAC { x2 y2 x y ArrowB curveto pop pop } def
/OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub def
n { NC } repeat EOC } ifelse } def
/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload
/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop
pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def
/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt {
CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC }
repeat closepath pop pop } ifelse } def
/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def
/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def
/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore }
def
/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix
rotate matrix concatmatrix exch findfont exch makefont setfont } def
/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto
x1 y1 lineto closepath } def
/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1
y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div
exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse
/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto
x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath }
ifelse } def
/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add
/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq {
pop pop Rect } { OvalFrame } ifelse } def
/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop
} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ]
aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def
/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6
2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto }
ifelse } def
/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv {
6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def
/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1
sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore }
def
/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1
sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA
x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0
y0 x0 2 mul x1 sub y1 ] def } def
/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 }
if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if
/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy div
round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div
round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub
0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def
/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def }
if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def }
{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n
div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1
dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt {
dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt {
pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dup
stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg}
{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i i
w add def } repeat grestore gsave n 0 gt
% DG/SR modification begin - Nov. 7, 1997 - Patch 1
%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
% DG/SR modification end
{ 2 setlinecap } ifelse /i y1 def /f x1 dx mul
n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n
div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop
1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs
dup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt
{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto g
exch t L stroke /i i h add def } repeat grestore } def
/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0
1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add
exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
mul neg d } def
/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def
/Rot { CP CP translate 3 -1 roll neg rotate NET  } def
/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 }
def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngle
dup a add ] cvx def } def
/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ]
cvx def } def
/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s
abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b
div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } {
h1 abs h sub dup s mul abs } ifelse } def
/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s
mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q
{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add
exch } def
/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible
/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def
} if } ifelse } def
/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit
neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def
/IfVisible true def } def
end
% END pstricks.pro

%%EndProcSet
%%BeginProcSet: pst-dots.pro
%!PS-Adobe-2.0
%%Title: Dot Font for PSTricks
%%Creator: Timothy Van Zandt <tvz@Princeton.EDU>
%%Creation Date: May 7, 1993
%% Version 97 patch 1, 99/12/16
%% Modified by Etienne Riga <etienne.riga@skynet.be> - Dec. 16, 1999
%% to add /Diamond, /SolidDiamond and /BoldDiamond
10 dict dup begin
  /FontType 3 def
  /FontMatrix [ .001 0 0 .001 0 0 ] def
  /FontBBox [ 0 0 0 0 ] def
  /Encoding 256 array def
  0 1 255 { Encoding exch /.notdef put } for
  Encoding
    dup (b) 0 get /Bullet put
    dup (c) 0 get /Circle put
    dup (C) 0 get /BoldCircle put
    dup (u) 0 get /SolidTriangle put
    dup (t) 0 get /Triangle put
    dup (T) 0 get /BoldTriangle put
    dup (r) 0 get /SolidSquare put
    dup (s) 0 get /Square put
    dup (S) 0 get /BoldSquare put
    dup (q) 0 get /SolidPentagon put
    dup (p) 0 get /Pentagon put
    dup (P) 0 get /BoldPentagon put
% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga
    dup (l) 0 get /SolidDiamond put
    dup (d) 0 get /Diamond put
        (D) 0 get /BoldDiamond put
% DG/SR modification end
  /Metrics 13 dict def
  Metrics begin
    /Bullet        1000   def
    /Circle        1000   def
    /BoldCircle    1000   def
    /SolidTriangle 1344   def
    /Triangle      1344   def
    /BoldTriangle  1344   def
    /SolidSquare    886   def
    /Square         886   def
    /BoldSquare     886   def
    /SolidPentagon 1093.2 def
    /Pentagon      1093.2 def
    /BoldPentagon  1093.2 def
% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga
    /SolidDiamond  1008   def
    /Diamond       1008   def
    /BoldDiamond   1008   def
% DG/SR modification end
    /.notdef 0 def
  end
  /BBoxes 13 dict def
  BBoxes begin
    /Circle        { -550 -550 550 550 } def
    /BoldCircle    /Circle load def
    /Bullet        /Circle load def
    /Triangle      { -571.5 -330 571.5 660 } def
    /BoldTriangle  /Triangle load def
    /SolidTriangle /Triangle load def
    /Square        { -450 -450 450 450 } def
    /BoldSquare    /Square load def
    /SolidSquare   /Square load def
    /Pentagon      { -546.6 -465 546.6 574.7 } def
    /BoldPentagon  /Pentagon load def
    /SolidPentagon /Pentagon load def
% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga
    /Diamond       { -428.5 -742.5 428.5 742.5 } def
    /BoldDiamond   /Diamond load def
    /SolidDiamond  /Diamond load def
% DG/SR modification end
    /.notdef { 0 0 0 0 } def
  end
  /CharProcs 20 dict def
  CharProcs begin
    /Adjust {
      2 copy dtransform floor .5 add exch floor .5 add exch idtransform
      3 -1 roll div 3 1 roll exch div exch scale
    } def
    /CirclePath    { 0 0 500 0 360 arc closepath } def
    /Bullet        { 500 500 Adjust CirclePath fill } def
    /Circle        { 500 500 Adjust CirclePath .9 .9 scale CirclePath
                     eofill } def
    /BoldCircle    { 500 500 Adjust CirclePath .8 .8 scale CirclePath
                     eofill } def
    /BoldCircle    { CirclePath .8 .8 scale CirclePath eofill } def
    /TrianglePath  { 0  660 moveto -571.5 -330 lineto 571.5 -330 lineto
                     closepath } def
    /SolidTriangle { TrianglePath fill } def
    /Triangle      { TrianglePath .85 .85 scale TrianglePath eofill } def
    /BoldTriangle  { TrianglePath .7 .7 scale TrianglePath eofill } def
    /SquarePath    { -450 450 moveto 450 450 lineto 450 -450 lineto
                     -450 -450 lineto closepath } def
    /SolidSquare   { SquarePath fill } def
    /Square        { SquarePath .89 .89 scale SquarePath eofill } def
    /BoldSquare    { SquarePath .78 .78 scale SquarePath eofill } def
    /PentagonPath  {
      -337.8 -465   moveto
       337.8 -465   lineto
       546.6  177.6 lineto
         0    574.7 lineto
      -546.6  177.6 lineto
      closepath
    } def
    /SolidPentagon { PentagonPath fill } def
    /Pentagon      { PentagonPath .89 .89 scale PentagonPath eofill } def
    /BoldPentagon  { PentagonPath .78 .78 scale PentagonPath eofill } def
% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga
    /DiamondPath   { 0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto
                     428.5 0 lineto closepath } def
    /SolidDiamond  { DiamondPath fill } def
    /Diamond       { DiamondPath .85 .85 scale DiamondPath eofill } def
    /BoldDiamond   { DiamondPath .7 .7 scale DiamondPath eofill } def
% DG/SR modification end
    /.notdef { } def
  end
  /BuildGlyph {
    exch
    begin
      Metrics 1 index get exec 0
      BBoxes 3 index get exec
      setcachedevice
      CharProcs begin load exec end
    end
  } def
  /BuildChar {
    1 index /Encoding get exch get
    1 index /BuildGlyph get exec
  } bind def
end
/PSTricksDotFont exch definefont pop
%END pst-dots.pro

%%EndProcSet
%%BeginProcSet: bbad153f.enc
% Thomas Esser, Dec 2002. public domain
%
% Encoding for:
%     cmsy10 cmsy5 cmsy6 cmsy7 cmsy8 cmsy9
%
/TeXbbad153fEncoding [
/minus /periodcentered /multiply /asteriskmath /divide /diamondmath
/plusminus /minusplus /circleplus /circleminus /circlemultiply
/circledivide /circledot /circlecopyrt /openbullet /bullet
/equivasymptotic /equivalence /reflexsubset /reflexsuperset /lessequal
/greaterequal /precedesequal /followsequal /similar /approxequal
/propersubset /propersuperset /lessmuch /greatermuch /precedes /follows
/arrowleft /arrowright /arrowup /arrowdown /arrowboth /arrownortheast
/arrowsoutheast /similarequal /arrowdblleft /arrowdblright /arrowdblup
/arrowdbldown /arrowdblboth /arrownorthwest /arrowsouthwest /proportional
/prime /infinity /element /owner /triangle /triangleinv /negationslash
/mapsto /universal /existential /logicalnot /emptyset /Rfractur /Ifractur
/latticetop /perpendicular /aleph /A /B /C /D /E /F /G /H /I /J /K
/L /M /N /O /P /Q /R /S /T /U /V /W /X /Y /Z /union /intersection
/unionmulti /logicaland /logicalor /turnstileleft /turnstileright
/floorleft /floorright /ceilingleft /ceilingright /braceleft /braceright
/angbracketleft /angbracketright /bar /bardbl /arrowbothv /arrowdblbothv
/backslash /wreathproduct /radical /coproduct /nabla /integral
/unionsq /intersectionsq /subsetsqequal /supersetsqequal /section
/dagger /daggerdbl /paragraph /club /diamond /heart /spade /arrowleft
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/minus /periodcentered /multiply /asteriskmath /divide /diamondmath
/plusminus /minusplus /circleplus /circleminus /.notdef /.notdef
/circlemultiply /circledivide /circledot /circlecopyrt /openbullet
/bullet /equivasymptotic /equivalence /reflexsubset /reflexsuperset
/lessequal /greaterequal /precedesequal /followsequal /similar
/approxequal /propersubset /propersuperset /lessmuch /greatermuch
/precedes /follows /arrowleft /spade /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
] def

%%EndProcSet
%%BeginProcSet: aae443f0.enc
% Thomas Esser, Dec 2002. public domain
%
% Encoding for:
%     cmmi10 cmmi12 cmmi5 cmmi6 cmmi7 cmmi8 cmmi9 cmmib10
%
/TeXaae443f0Encoding [
/Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /Omega
/alpha /beta /gamma /delta /epsilon1 /zeta /eta /theta /iota /kappa
/lambda /mu /nu /xi /pi /rho /sigma /tau /upsilon /phi /chi /psi
/omega /epsilon /theta1 /pi1 /rho1 /sigma1 /phi1 /arrowlefttophalf
/arrowleftbothalf /arrowrighttophalf /arrowrightbothalf /arrowhookleft
/arrowhookright /triangleright /triangleleft /zerooldstyle /oneoldstyle
/twooldstyle /threeoldstyle /fouroldstyle /fiveoldstyle /sixoldstyle
/sevenoldstyle /eightoldstyle /nineoldstyle /period /comma /less /slash
/greater /star /partialdiff /A /B /C /D /E /F /G /H /I /J /K /L /M /N
/O /P /Q /R /S /T /U /V /W /X /Y /Z /flat /natural /sharp /slurbelow
/slurabove /lscript /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p
/q /r /s /t /u /v /w /x /y /z /dotlessi /dotlessj /weierstrass /vector
/tie /psi /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/space /Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi
/.notdef /.notdef /Omega /alpha /beta /gamma /delta /epsilon1 /zeta /eta
/theta /iota /kappa /lambda /mu /nu /xi /pi /rho /sigma /tau /upsilon
/phi /chi /psi /tie /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef
] def

%%EndProcSet
%%BeginProcSet: texps.pro
%!
TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2
index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll
exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]FontType 0
ne{/Metrics exch def dict begin Encoding{exch dup type/integertype ne{
pop pop 1 sub dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get
div def}ifelse}forall Metrics/Metrics currentdict end def}{{1 index type
/nametype eq{exit}if exch pop}loop}ifelse[2 index currentdict end
definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{dup
sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1 roll
mul exch}def/ReEncodeFont{CharStrings rcheck{/Encoding false def dup[
exch{dup CharStrings exch known not{pop/.notdef/Encoding true def}if}
forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def}def
end

%%EndProcSet
%%BeginProcSet: special.pro
%!
TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N
/vs 792 N/ho 0 N/vo 0 N/hsc 1 N/vsc 1 N/ang 0 N/CLIP 0 N/rwiSeen false N
/rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N
/@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc X}B/@hsize{
/hs X/CLIP 1 N}B/@vsize{/vs X/CLIP 1 N}B/@clip{/CLIP 2 N}B/@hoffset{/ho
X}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B
/@rhi{10 div/rhi X/rhiSeen true N}B/@llx{/llx X}B/@lly{/lly X}B/@urx{
/urx X}B/@ury{/ury X}B/magscale true def end/@MacSetUp{userdict/md known
{userdict/md get type/dicttype eq{userdict begin md length 10 add md
maxlength ge{/md md dup length 20 add dict copy def}if end md begin
/letter{}N/note{}N/legal{}N/od{txpose 1 0 mtx defaultmatrix dtransform S
atan/pa X newpath clippath mark{transform{itransform moveto}}{transform{
itransform lineto}}{6 -2 roll transform 6 -2 roll transform 6 -2 roll
transform{itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll
curveto}}{{closepath}}pathforall newpath counttomark array astore/gc xdf
pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack}
if}N/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1
-1 scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3
get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip
yflip not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub
neg 0 TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{
noflips{TR pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop
90 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get
neg sub neg TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr
1 get neg sub neg 0 TR}if yflip xflip not and{TR pop pop 270 rotate ppr
2 get ppr 0 get neg sub neg 0 S TR}if}ifelse scaleby96{ppr aload pop 4
-1 roll add 2 div 3 1 roll add 2 div 2 copy TR .96 dup scale neg S neg S
TR}if}N/cp{pop pop showpage pm restore}N end}if}if}N/normalscale{
Resolution 72 div VResolution 72 div neg scale magscale{DVImag dup scale
}if 0 setgray}N/psfts{S 65781.76 div N}N/startTexFig{/psf$SavedState
save N userdict maxlength dict begin/magscale true def normalscale
currentpoint TR/psf$ury psfts/psf$urx psfts/psf$lly psfts/psf$llx psfts
/psf$y psfts/psf$x psfts currentpoint/psf$cy X/psf$cx X/psf$sx psf$x
psf$urx psf$llx sub div N/psf$sy psf$y psf$ury psf$lly sub div N psf$sx
psf$sy scale psf$cx psf$sx div psf$llx sub psf$cy psf$sy div psf$ury sub
TR/showpage{}N/erasepage{}N/setpagedevice{pop}N/copypage{}N/p 3 def
@MacSetUp}N/doclip{psf$llx psf$lly psf$urx psf$ury currentpoint 6 2 roll
newpath 4 copy 4 2 roll moveto 6 -1 roll S lineto S lineto S lineto
closepath clip newpath moveto}N/endTexFig{end psf$SavedState restore}N
/@beginspecial{SDict begin/SpecialSave save N gsave normalscale
currentpoint TR @SpecialDefaults count/ocount X/dcount countdictstack N}
N/@setspecial{CLIP 1 eq{newpath 0 0 moveto hs 0 rlineto 0 vs rlineto hs
neg 0 rlineto closepath clip}if ho vo TR hsc vsc scale ang rotate
rwiSeen{rwi urx llx sub div rhiSeen{rhi ury lly sub div}{dup}ifelse
scale llx neg lly neg TR}{rhiSeen{rhi ury lly sub div dup scale llx neg
lly neg TR}if}ifelse CLIP 2 eq{newpath llx lly moveto urx lly lineto urx
ury lineto llx ury lineto closepath clip}if/showpage{}N/erasepage{}N
/setpagedevice{pop}N/copypage{}N newpath}N/@endspecial{count ocount sub{
pop}repeat countdictstack dcount sub{end}repeat grestore SpecialSave
restore end}N/@defspecial{SDict begin}N/@fedspecial{end}B/li{lineto}B
/rl{rlineto}B/rc{rcurveto}B/np{/SaveX currentpoint/SaveY X N 1
setlinecap newpath}N/st{stroke SaveX SaveY moveto}N/fil{fill SaveX SaveY
moveto}N/ellipse{/endangle X/startangle X/yrad X/xrad X/savematrix
matrix currentmatrix N TR xrad yrad scale 0 0 1 startangle endangle arc
savematrix setmatrix}N end

%%EndProcSet
%%BeginProcSet: color.pro
%!
TeXDict begin/setcmykcolor where{pop}{/setcmykcolor{dup 10 eq{pop
setrgbcolor}{1 sub 4 1 roll 3{3 index add neg dup 0 lt{pop 0}if 3 1 roll
}repeat setrgbcolor pop}ifelse}B}ifelse/TeXcolorcmyk{setcmykcolor}def
/TeXcolorrgb{setrgbcolor}def/TeXcolorgrey{setgray}def/TeXcolorgray{
setgray}def/TeXcolorhsb{sethsbcolor}def/currentcmykcolor where{pop}{
/currentcmykcolor{currentrgbcolor 10}B}ifelse/DC{exch dup userdict exch
known{pop pop}{X}ifelse}B/GreenYellow{0.15 0 0.69 0 setcmykcolor}DC
/Yellow{0 0 1 0 setcmykcolor}DC/Goldenrod{0 0.10 0.84 0 setcmykcolor}DC
/Dandelion{0 0.29 0.84 0 setcmykcolor}DC/Apricot{0 0.32 0.52 0
setcmykcolor}DC/Peach{0 0.50 0.70 0 setcmykcolor}DC/Melon{0 0.46 0.50 0
setcmykcolor}DC/YellowOrange{0 0.42 1 0 setcmykcolor}DC/Orange{0 0.61
0.87 0 setcmykcolor}DC/BurntOrange{0 0.51 1 0 setcmykcolor}DC
/Bittersweet{0 0.75 1 0.24 setcmykcolor}DC/RedOrange{0 0.77 0.87 0
setcmykcolor}DC/Mahogany{0 0.85 0.87 0.35 setcmykcolor}DC/Maroon{0 0.87
0.68 0.32 setcmykcolor}DC/BrickRed{0 0.89 0.94 0.28 setcmykcolor}DC/Red{
0 1 1 0 setcmykcolor}DC/OrangeRed{0 1 0.50 0 setcmykcolor}DC/RubineRed{
0 1 0.13 0 setcmykcolor}DC/WildStrawberry{0 0.96 0.39 0 setcmykcolor}DC
/Salmon{0 0.53 0.38 0 setcmykcolor}DC/CarnationPink{0 0.63 0 0
setcmykcolor}DC/Magenta{0 1 0 0 setcmykcolor}DC/VioletRed{0 0.81 0 0
setcmykcolor}DC/Rhodamine{0 0.82 0 0 setcmykcolor}DC/Mulberry{0.34 0.90
0 0.02 setcmykcolor}DC/RedViolet{0.07 0.90 0 0.34 setcmykcolor}DC
/Fuchsia{0.47 0.91 0 0.08 setcmykcolor}DC/Lavender{0 0.48 0 0
setcmykcolor}DC/Thistle{0.12 0.59 0 0 setcmykcolor}DC/Orchid{0.32 0.64 0
0 setcmykcolor}DC/DarkOrchid{0.40 0.80 0.20 0 setcmykcolor}DC/Purple{
0.45 0.86 0 0 setcmykcolor}DC/Plum{0.50 1 0 0 setcmykcolor}DC/Violet{
0.79 0.88 0 0 setcmykcolor}DC/RoyalPurple{0.75 0.90 0 0 setcmykcolor}DC
/BlueViolet{0.86 0.91 0 0.04 setcmykcolor}DC/Periwinkle{0.57 0.55 0 0
setcmykcolor}DC/CadetBlue{0.62 0.57 0.23 0 setcmykcolor}DC
/CornflowerBlue{0.65 0.13 0 0 setcmykcolor}DC/MidnightBlue{0.98 0.13 0
0.43 setcmykcolor}DC/NavyBlue{0.94 0.54 0 0 setcmykcolor}DC/RoyalBlue{1
0.50 0 0 setcmykcolor}DC/Blue{1 1 0 0 setcmykcolor}DC/Cerulean{0.94 0.11
0 0 setcmykcolor}DC/Cyan{1 0 0 0 setcmykcolor}DC/ProcessBlue{0.96 0 0 0
setcmykcolor}DC/SkyBlue{0.62 0 0.12 0 setcmykcolor}DC/Turquoise{0.85 0
0.20 0 setcmykcolor}DC/TealBlue{0.86 0 0.34 0.02 setcmykcolor}DC
/Aquamarine{0.82 0 0.30 0 setcmykcolor}DC/BlueGreen{0.85 0 0.33 0
setcmykcolor}DC/Emerald{1 0 0.50 0 setcmykcolor}DC/JungleGreen{0.99 0
0.52 0 setcmykcolor}DC/SeaGreen{0.69 0 0.50 0 setcmykcolor}DC/Green{1 0
1 0 setcmykcolor}DC/ForestGreen{0.91 0 0.88 0.12 setcmykcolor}DC
/PineGreen{0.92 0 0.59 0.25 setcmykcolor}DC/LimeGreen{0.50 0 1 0
setcmykcolor}DC/YellowGreen{0.44 0 0.74 0 setcmykcolor}DC/SpringGreen{
0.26 0 0.76 0 setcmykcolor}DC/OliveGreen{0.64 0 0.95 0.40 setcmykcolor}
DC/RawSienna{0 0.72 1 0.45 setcmykcolor}DC/Sepia{0 0.83 1 0.70
setcmykcolor}DC/Brown{0 0.81 1 0.60 setcmykcolor}DC/Tan{0.14 0.42 0.56 0
setcmykcolor}DC/Gray{0 0 0 0.50 setcmykcolor}DC/Black{0 0 0 1
setcmykcolor}DC/White{0 0 0 0 setcmykcolor}DC end

%%EndProcSet
%%BeginFont: CMBX10
%!PS-AdobeFont-1.1: CMBX10 1.00B
%%CreationDate: 1992 Feb 19 19:54:06
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMBX10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMBX10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-301 -250 1164 946}readonly def
/UniqueID 5000768 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMMIB10
%!PS-AdobeFont-1.1: CMMIB10 1.100
%%CreationDate: 1996 Jul 23 07:54:00
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMIB10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMIB10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-15 -250 1216 750}readonly def
/UniqueID 5087392 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMBX12
%!PS-AdobeFont-1.1: CMBX12 1.0
%%CreationDate: 1991 Aug 20 16:34:54
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMBX12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMBX12 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-53 -251 1139 750}readonly def
/UniqueID 5000769 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMR6
%!PS-AdobeFont-1.1: CMR6 1.0
%%CreationDate: 1991 Aug 20 16:39:02
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR6 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-20 -250 1193 750}readonly def
/UniqueID 5000789 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMSY8
%!PS-AdobeFont-1.1: CMSY8 1.0
%%CreationDate: 1991 Aug 15 07:22:10
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-30 -955 1185 779}readonly def
/UniqueID 5000818 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMEX10
%!PS-AdobeFont-1.1: CMEX10 1.00
%%CreationDate: 1992 Jul 23 21:22:48
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMEX10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMEX10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 16 /parenleftBig put
dup 17 /parenrightBig put
dup 48 /parenlefttp put
dup 49 /parenrighttp put
dup 64 /parenleftbt put
dup 65 /parenrightbt put
dup 66 /parenleftex put
dup 67 /parenrightex put
dup 112 /radicalbig put
dup 114 /radicalbigg put
readonly def
/FontBBox{-24 -2960 1454 772}readonly def
/UniqueID 5000774 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMMI8
%!PS-AdobeFont-1.1: CMMI8 1.100
%%CreationDate: 1996 Jul 23 07:53:54
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-24 -250 1110 750}readonly def
/UniqueID 5087383 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMR8
%!PS-AdobeFont-1.1: CMR8 1.0
%%CreationDate: 1991 Aug 20 16:39:40
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-36 -250 1070 750}readonly def
/UniqueID 5000791 def
currentdict end
currentfile eexec
D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891
016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171
9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F
D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758
469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8
2BDBF16FBC7512FAA308A093FE5CF4E9D2405B169CD5365D6ECED5D768D66D6C
68618B8C482B341F8CA38E9BB9BAFCFAAD9C2F3FD033B62690986ED43D9C9361
3645B82392D5CAE11A7CB49D7E2E82DCD485CBA1772CE422BB1D7283AD675B65
48A7EA0069A883EC1DAA3E1F9ECE7586D6CF0A128CD557C7E5D7AA3EA97EBAD3
9619D1BFCF4A6D64768741EDEA0A5B0EFBBF347CDCBE2E03D756967A16B613DB
0FC45FA2A3312E0C46A5FD0466AB097C58FFEEC40601B8395E52775D0AFCD7DB
8AB317333110531E5C44A4CB4B5ACD571A1A60960B15E450948A5EEA14DD330F
EA209265DB8E1A1FC80DCD3860323FD26C113B041A88C88A21655878680A4466
FA10403D24BB97152A49B842C180E4D258C9D48F21D057782D90623116830BA3
9902B3C5F2F2DD01433B0D7099C07DBDE268D0FFED5169BCD03D48B2F058AD62
D8678C626DC7A3F352152C99BA963EF95F8AD11DB8B0D351210A17E4C2C55AD8
9EB64172935D3C20A398F3EEEEC31551966A7438EF3FEE422C6D4E05337620D5
ACC7B52BED984BFAAD36EF9D20748B05D07BE4414A63975125D272FAD83F76E6
10FFF8363014BE526D580873C5A42B70FA911EC7B86905F13AFE55EB0273F582
83158793B8CC296B8DE1DCCF1250FD57CB0E035C7EDA3B0092ED940D37A05493
2EC54E09B984FCA4AB7D2EA182BCF1263AA244B07EC0EA901C077A059F709F30
4384CB5FA748F2054FAD9A7A43D4EA427918BD414F766531136B60C3477C6632
BEFE3897B58C19276A301926C2AEF2756B367319772C9B201C49B4D935A8267B
041D6F1783B6AEA4DAC4F5B3507D7032AA640AAB12E343A4E9BDCF419C04A721
3888B25AF4E293AACED9A6BDC78E61DA1C424C6503CC1885F762BCA9D2C2FD74
7B8DD210DB4E177D8A09775620378F0FBC2B1C40C5013A1E11E9A3E76E1B034E
C68313C04770F82A407F9FF0425BABD1C747B7F763AFEF16FA51495566C64B12
E6A9B24A5A06FC5FC16A2895A454561AADD8CF579FC1781AB3D4964204184A10
11D5B65AB67156156FBC9EBF192D83D0C0ADA5D818CD2A23FE224235E175131C
AC8D4B252A7335A4EFB0B22C6287E3D34AD9DE0CEC449C306EA79CE681B973D6
7B01F006988C391D2E6B5B74E58EF8D8BEF04CDFD22F33C8BBEF96DCDC7842D0
63AEBBC03C4D4B81779F88554B6F007A23C1A791A48F05F22F1B02B59FF903E2
590B52472BD331E0537B4284F2D6BBF2244E7B90BBEDD2175F3806FC588D1023
4D2360F20FD31D305E967B2143E9E0E6779A9A8BC73A5EA75AF92BA7570949AD
E667920FEC658D9D87CEBACCBF203F017C429892F7341F480A4D6B7534B6A28B
DDC79DB02C19B3648A3B17899BC52D9FDD181640DF29330D3ADBC39967F4AD36
5FDE0F4C14B8CCB89766BD15F4DBC6581E4415CDF365573E7E16A78898075C5A
217ED50DCC27CD47EE147EBC22CEF1681A9B16CD0881E0B556BB4DB4EF683553
62E8B790958AC2FEABB6404B96364D8F47CAE4DE767BB2A833C1FD91DC19FDAB
DA850CA2B815E45E966EEAD2F8C35E436EC6B6CE0636EE892DDCA13A0390856E
3666142C2B0279540460D822B83AAF096EF36653774C0B66C58CD0EF07C53938
DA0F8795127619F4809BE820A36AB62E4E132C74727D518087A210BFD02A3DDF
0FC4479D6A5FC93540743B090C13452D2925D42E36B15BCB22C4E885D1678E2A
32680F79614195A4E24655C4E8948AB8529749E8654D91781ADD6E58CA3A0B25
6749691CC20A35AFAB1ED04BCA4E34AA32E5136FEEBAB867B6BD16802A5930AE
CBDF40007068136560339704D5640DD25D9B13A2F0A0414C6B77106A2F8738CE
8F2B2380848935064BE7F1B567CE3D9B2EA4F6C69B9607DFE3343D3F2B59B681
F03D67D99BD55C096AA988E97070558CAE729ECF18C559BD362A46F05DBA48D3
35E7CB91E20E14E0B60A8959C545E63998E9A6179DAFFFAB0327CAE4F0A64CF2
5BABE4A73073F06D301BA79AEB13BDA26E95EDB5DC596E9C98997A02DA5521A2
23CCA2162BB46219745584CD47B70EB1F8AE8FEE4B0023DEC9B87D6DB1FB73FD
6DAB9D4A30F34B6FFCF9D6C0FB2D1053FC2B351B3968081DDBD477BC8C1DEDAE
9AFB5DBDE09155079B9C19AD128404B7C4FDAF15C859D0DDD2CA9B74A827C069
E2DC35645E604235B1A223F21A0B3C3009F4A7D527CD51A877BA3FF2A04BAFE2
F2DD4071B49D7F07C42FAB7F973972522B3BC0611C93C4EC6924208E35DC2A8D
7BB71F1C4CB33347C1C2A5B20F9EEA38F33ABBDC
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMMI12
%!PS-AdobeFont-1.1: CMMI12 1.100
%%CreationDate: 1996 Jul 27 08:57:55
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI12 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-30 -250 1026 750}readonly def
/UniqueID 5087386 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMSY10
%!PS-AdobeFont-1.1: CMSY10 1.0
%%CreationDate: 1991 Aug 15 07:20:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-29 -960 1116 775}readonly def
/UniqueID 5000820 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMR12
%!PS-AdobeFont-1.1: CMR12 1.0
%%CreationDate: 1991 Aug 20 16:38:05
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR12 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-34 -251 988 750}readonly def
/UniqueID 5000794 def
currentdict end
currentfile eexec
D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891
016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171
9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F
D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758
469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8
2BDBF16FBC7512FAA308A093FE5CF4E9D2405B169CD5365D6ECED5D768D66D6C
68618B8C482B341F8CA38E9BB9BAFCFAAD9C2F3FD033B62690986ED43D9C9361
3645B82392D5CAE11A7CB49D7E2E82DCD485CBA04C77322EB2E6A79D73DC194E
59C120A2DABB9BF72E2CF256DD6EB54EECBA588101ABD933B57CE8A3A0D16B28
51D7494F73096DF53BDC66BBF896B587DF9643317D5F610CD9088F9849126F23
DDE030F7B277DD99055C8B119CAE9C99158AC4E150CDFC2C66ED92EBB4CC092A
AA078CE16247A1335AD332DAA950D20395A7384C33FF72EAA31A5B89766E635F
45C4C068AD7EE867398F0381B07CB94D29FF097D59FF9961D195A948E3D87C31
821E9295A56D21875B41988F7A16A1587050C3C71B4E4355BB37F255D6B237CE
96F25467F70FA19E0F85785FF49068949CCC79F2F8AE57D5F79BB9C5CF5EED5D
9857B9967D9B96CDCF73D5D65FF75AFABB66734018BAE264597220C89FD17379
26764A9302D078B4EB0E29178C878FD61007EEA2DDB119AE88C57ECFEF4B71E4
140A34951DDC3568A84CC92371A789021A103A1A347050FDA6ECF7903F67D213
1D0C7C474A9053866E9C88E65E6932BA87A73686EAB0019389F84D159809C498
1E7A30ED942EB211B00DBFF5BCC720F4E276C3339B31B6EABBB078430E6A09BB
377D3061A20B1EB98796B8607EECBC699445EAA866C38E03ED7D4F3EDBCA1926
2AF6A41F67AFCFBF3630C943FA111E4CCD988A7363F7C2B75EAF5830B049460E
0D2B337988F150B9182E989E7750C51BA83DF37685483F86D1F47478883F3F6A
4B7F768DA5AA89E8F163029ADD4A9209DE8A4F285766C06EA859639B92CCCDCA
F59B1C2BB8D588CA754D1257BFF76B53984DF4937093AAEF79009D32A29A4C16
FB610C7D6713482C48D7F9E8410C0F00AD6E67021056B6035534E79F05D14EF2
4E8D809887B0CF1D5838DCF799FFC9B26E95F24C1DC198ACE17601674B530E8E
4D8AC45859998240584B596B6142F07AC9CF8A8AE53D47917BDD44D96BD45D7A
F5F9D9A2CC839EF41C5367884DC0C84F8B533040D4352BE05487185AF31A4765
BA04396E0F82944C5B74A96A49ABDD4F119EDFA964A5A01FCA9705B837B24761
D70F23CD5FDF3A44DD192043E4BD1EE3BB700DE97266C157C814BE779EE41265
EBAD211ADAB2FA3F3C27BA469182936BCD139D5953435734DAB709701074F7A9
D2B80433AFD276020F7D64D22D748DB19E8DB82D2468B8B3D55B1B9AB50E5EFC
3C5C9720F11E545F1B6CB94DD479B921BFF4770B370764CF948A5F48C25AAE17
8CD086863E1BCDF50B126334F4153CC14D1C4EE8BA063541388F2B4BF578B1B1
E003E6502ED4895502E8AD8C5619AC31308194769901D4AD8983D2E967C3A85F
23222744B7535926BD811CCF9BBCA1AF06D341ABAFC541491E92BE02D43314B5
B4418C87A581F2E9762A2A6EA5B7104003339AA8232E51F5706B0D35AB5D85DA
E2AAE90E0A2348E014E40DBF1D08166E5997749EF97CA7CA0F6D147EDEC8552E
0ECCDE099770636849845CC301B23934FDE6BBAD188045F2184A2A54B418C102
32F4C5FDA546D09865DDF141EAD287BB6C31183C66070BF4AA92B264D4B848A7
DC159688373BC99B819065653DD85B4FBDF337527588D3B0AD013B5DADD0B842
9A1C2DA7992CE05AE2F3296552F7AC718D6CE3BD9DF83900437BF665BA51ECB9
42BAAC08DE0FB578C662F59A9F02E9010E6858779EFEDE90797F130DC4839E2E
719733CF61E8C14FBB83B3C730436803120AF2EFF99EA31C4F973C1193D241F6
BC88683C19C4F7EB1D923BD35F772FD02037CE90C577032A1A02ADDEAFA989D5
D62CF83C20BE3C825354B7391DEC7CB5D8E31BDDE5F65CD4DE7679855A02D42D
A8A3FBD95877FF19965B6A1BD97102106BEC859DDE12F6F1DA56FFE396423ECC
43A369003CDCBD66F5DCAF9FDEED45F81D44122CBBA8FEB618E3EF699B27BAEA
EDFB610A691366ADBAE1EF4BEA8A9FCEAE11381F2DB54D23AE96FD2E1B9C778A
518433E73C73ED94C90969AE3BC51E510A70ACBA5D666D3DEEDCC8C27F0BCB15
355A476754ED7F9E28EA86D04AD1DF076CAAD3C3C1F58C704A313C773DA5C9A9
141FA639FF8A122EB0936A9892840472B59E17F68B7F1EDF07BAB45CA11C8DE3
C34B9CEB8EF04F85560F7F11F8428E225B8E68F234BBD21D68803638E42E259B
0FB83DEBB96CAE73F6B8B4C6719DBD05BC071ABE0ACFC0E75B0B5C5480430D51
F4B70E6BC36A4670B3A8B3FB11492EB1B74ACADD2CA732CDD541FA5ADB62E7B1
57729FA05BDCD05E4E7D2B00FD7CD67CB94F0FB8D4BB381BC4BA210193F9DD2D
1F80F61F62DEF14071603A53A3C0194599ABEBDB2646EE6A17CF0BC794A4AEEB
714633BB80AB0C5B71BC3C5539FF8D04828664EFBCFB2E0194DA5ED5E20F27D4
768EADAC85D1A2E278B379B938C8556940EA4D83A4FE92D81EC4F68618A9F3B2
8EB5E392F5D9141DBDC61F64885A286C87FAEB01FB28FEA6D5174A4CEECF483B
EBD585473A359ADA26F00BFA3A44607F1415B57C0E969B44A71A9D1EDC67085A
86AB6FA7583CEDE0EFEDD29E350AFD9F981B9E8FD9A873B84F358F00427DA74E
A7DAB692E47133A2233C2EC0942211106D750147BC85535D047180F930A57C9C
26BBC61447C28265934F7FF208EC728945ECE0815E8A0A4DA287834814E25A28
36DD4CF3C31E78587A79AACEB67A3A18E902CBDAE6C25C2DCCEC7D598322DD23
03CE022CDE6319906C1025AEE6EA376D68B156C700700EF66A65713DA077A4B6
C0FA45AFC659753730DBEE96C4871441BF1283E669012AA9D69E01C68AA511CA
99BBF548035BEA8588577C88E24EA46737C28639A0DD78EE9B210055E4B7D1BC
7CCA2F4F2137834D5D1F6F34D91846C6003513C357E7FD5CDD73377DC7AC09F9
F62F3A207EC434499F0558CFEAB7A2B4F2B6AF560490E8CE39423429A2709C11
EDB494690000DEF575E607D0EFBDDC19508D8916A1E88BDBEC5B2D741CD012BA
07A0435DCA2861B44FAB1CDB94B41EB7203DF7E25B2CA302BA42CEBEF0155BD2
F089F3E96176A0E442C98698E690253DC8CC48AF44E2E7B0F7FC80262185A3A3
0CEC80F6996D8E6E4CD22D63B3896196B9507BEE8DFDC232DFAC098E058B27FD
4F1C173CE5278ECF49A32243B2C05805E31312DFD83322EAE83F6D0501ABFECB
AAB4D5EE5F9D89398E6FBAF704C6F78F94076449599D86752C510C0AAAF113CF
3DC33B195ECCCBB03D30DF69DAF118186F2C90F124ED7789ADBB43030BD59890
54797EFC79380B01055C3F7118891644574B76600BAB9CA1382B501C8B85364D
2D781EB35241BB592CC4949E9D13D97290C886DA8E979EDC34696CE45AA20323
C9988C5A0EE68DC76C8CEAF87A3CFE40977A66FFAA7AFD5166A564A42A371BC8
DE5ECADDC9AB07C1E542778A334E6BDC740281450A9B6D956FCA67893D64D964
B79AD29846D261FCE349CED0EC89213B2A35A26F0F9C7376FCFA285B29671188
9BEE7F6DE95C7DA957C3DAF81113CEF41ECF559A35F8D80ED42BA19C47B6F71C
93228052068060CF51C8F468F2A23E057372FA92D5669A63D711F56745C484E8
10729A8A057845B7C9B936F2392978DCC6518E7307324F2C23608C6FDF3AF77A
F4CACE00B9A3CEB8AC4DE3294D54C8425D918C0F0E832AAF7AEA0B7830318DDB
401975FB86CC892D6B650B240607991E956551F6177447F02ACD4DBF0A515D13
53A4642F1347EA56A523B50A4038FEE1C1BA56B126EB9D39E2F5CDC09255C8DF
8BA32E6B2611B784369D88A9421770FD6D8377C251A281E55E0D7E48C99EF2A3
5A3252C7792E4774DD1FB411A55A71B5C14A71EA7207464B80470725B902B9F5
DCF63D08B72AC1925E1CD48B0B5494EEE71A7EB19FBF865E0B8826CC35FD8E4E
85410EEF6009B01F3D33FEC5A986A944173B7EB79B12FC1CD9F932E682920386
F1C93CFA57E3011172C31BDB62B92CCEFD33404E88F1F06788B6CF55DED77A2D
900A522658BC18618B9F07D310E1328C8D5AA562596E1853CF1B7894D29551B0
AB92B65094A4DDEF6DEFE1340526CDAE0291F84A1274B7D881545A35B455FC94
31806648A7D99D29B3443FF0F690916666E073F192DFDAEFC57B0E5C5B3F45D0
0BAB95D1B1CB4C42BFF92A5D650D310AEFC5BFB053E25AB4DCF09D344E3C49C2
762E012DE0F6174EE8B7A146F491ED89561D11D7E7D286E7A1A524123FE304C4
7AACADA43A16F4FB980D6463D398F13B4EADA6B77733F4D60B1EAF090E3C1AE9
0681812442C09D3775E0AE667EA84BDD95809AF36652B2B59A72B380170D72CE
7EB793F70CD832CBE8ED9E492522835CAB80761A674A40A1AB7026F952EEF605
673DE8F88C6F2EC85D163086B98667AEC3EDE2C6F96227062420C7E863275CDE
456993A63E58CAF623A82319CBC6152D09FD0D11ECBC8B8CA965417F5F396191
F0C6244ED7E2292DAE37E6B0909E7FDD6ABB67664E1682CAB9ED068AD5C27009
83113B40A2519B9CFCA76CF150D784C9DA17A52A0968B0380ACD65B1F11CF46E
522293E7CE8473965FDEE562538A8001FDCEF8BEF01AC1FC3EB85CBC5DA3AA2C
D4264E7776AA5C43B9D4B0084194ACD5BBA17DBCE2B6A77095CD9D566BEEB5D0
855DF7E50A85B18362C963E19DB9E03AD4E3D1B075D6D795F9288FC601EA9919
84E6CA8B4C3CED995DCF0A7D7CD5E236BB44E63A7FB5A925928395025DA68F29
9EF80077B711C99E4E65537DDD972E328FD3122F0DF7D26B263AE7CD72FB5076
62946C97D08CFD81D5392FD5FCBDA432058764AB190924D47FEB94A1EEFA83D6
85CC9436CB441A1BC81B43341034ADD49847C19EE38EC6A16D31E23DB0E5B92E
1211B75A535DB93E8EF4DAB39CDD50A6F8981EA458B8BF7DD1E0C375EBC36349
D4CF919C239AEE60DEA196B7A3B820C38982EC5E6C3BC1528F1C954F1899B2A4
B0D196C270DFE8E7C2A073D04D244A3BABD2B66E127CDA088BA3C43B048C87D8
44FD6F90630D9B15F488476E36E912175A72D0D3ECD54FB2A4EFD1DCBB74E934
8A62BDDB068FA976C11235C5B634A510729DBE31AFA601B1FFB910615FCBF1AF
4C77F8BD29E4DA3C686E713A1A978E6527042BB30B919AF763F32F09ED054308
67260813E8A222ACE8B1075318AF170D6476D9F1C86432221FC64829BC64E35B
D323C25D58974DB3E291C49E316B597C066DFEBBC97A3FFFFE0A3572DE5062CA
D21168892370B0CA1FAC9BCCEAFBB285A07A85BC4B3F3F1CF916D63CCA7D148B
18C1AE08206ECADD17660A48E75D49330DAA7C989E25DC790347EBF24084DB27
F1DDF5DF5D0AD3F9A6852687E6B7F8AC46040FAF74586B23D12C27F05502203D
269E72089DAA4DF8875599DD5466DF16ACC33A5CF7A0603DA32628548D4FF310
01C803A3F2BC5C8BDFC66B73CE981C203F8513E8D899E78D4E2E8A5FF2A47AF3
647FED0A9030A7240CFD2BE70967CCDE642182A660EDBF809EC5BB4501AD2CBD
9402FC48C83D9F2FEF1DA226FD29F8B26EF5F6DF6A07BFDBC7B86CF67E8DB1D9
5E19A454FA2BC9B8F2AD750E3AD5365B2D09A1448A123140C8261F3F4F296636
1B5EEBF83F727B9F5094FC1FB2104A05F4B7110E135848DA6FDE3DFE9776A59B
9B8DDF85EC8E706B5F04BFCDFA487EBC0687715FC7C0010F843CBBF974B6743C
A254A6367C81FDE7D8710186A0DB18154E64FEDF608E99C966CD59FE2169932C
044B8B7C7EB47F6ECA3013CDDD84244D894700AC089CDA8971468F827A5E0387
EEC922A50D1F24C02CCCA85DC22555CDA82042B1944989DC8D48B0517B7AB807
8829188EAB394EF6063173B560198BE12D0ADF0D8FF22726094560922820A9EB
455FF15128090F5772BDA849DEF6106A6D0A027725D8D13E4F6D42497EBBE293
E4CF07F0843DF64A11857034D52DDAE74C4C564B797C386CE51184DF5C22D361
B1D9F993AC5D74D17A3F348CA04EFD553D86295C0C420A2273A8FC477398457F
D330DA88091A72BE3CCF7DDD271D4DFCBAE1133449DE9370CACF512ACB53D111
35595EDBC5F43F0D7901822C79D191E470B45A135B36FBBF2D686E6E47C99E17
334D0B361C8B082EE3EB7B69C105665186F263F020F4117ECEFF1A653D0D203E
D3109789A0DDF6920FD861846C4A4018CD38A2261A7412A6606B0412DB01F4BF
FA3F49C8C60538D43249372744E8BF953AF07272824557FD5ADFB216F3CEF49D
37F75DFCA05CA2190181BF476A2CBCBBC1ABE92197E6E442E692E5D00DD129A8
9DBF37703A19BD5FE153B47D5351E7B5A8180C148DEC4ADA3F76B760156B6F84
D09067EDA36DE8E602C22E498CE7A18504750271846A5FD9F91D30BD312E6069
CC18CA47B40EDDB1497F56FF43D0FD6E56235D7680648E8973F5E174E7E0F784
B63389ABA1D1CD5623D4E78981E0AA22E3EAA14196F0C5734118FB6F203492EB
5F4A3D4899699592BA5B9C20B92A973245FD5E8177C7A40192C63CA19970DE1D
FE5F9EA3693B5B04C4CFF3417D9E66D20394EF7DB910E64EF724190C76A45BC7
AB2DFFBDC4C5C1138509E1E17548F1ACB554E13185967F4B367EB3A965FB98D6
4A7C20B0D998708A371AA1F8F5CD5B4308E8286E93756A8F408671B0CB07AC38
0DEBC92B99D7B719C7B37442E91EB6A08CF35FE009466262747AACEE383E9E2C
17533B6D19A07BB15C41995C6C764E264E1000E0523ABC974E020FD155BB9FCD
05EA06A49AD74DF0CD3DFC8E6DEDB6537423119F742A2364DC1CD7DCE7A315A9
AEBB0E3C3DD734DB27FEB0F9938E6E579DED8C582D414A79F05D9BD5F62092AF
227B8430F3D020112266BC0982E827C82C9C547D47CF774A9079FEF114D6188B
9D17E1B8A5996620F5F1F8642DE8F4D74A42F754B6965D1584221C9AD39D8D40
10A0DAC362411972A3089D02C94FCD320393549F839B66067E02FBC14FFC9F77
33E87C886BB783C3E61EA3CE168D402C7903BE821670FC6FAD36B8B77FF2D496
8AD73EB64CE9D867EDF29DE06263C0543909F9E289E78D4AB1C7CE35E0FB960D
0B9EF6228E9997EEF07EF6DD4D2CF54450AE3F07F045ACE21C5B6EF8DE696296
7408159CE0B6BA0B11E303F9A2869B213C7D6F815908CF2C4556AA4317D03AA4
84491A1B499F64DDFF7A826F6EDAC70A10B671344520CC460C7D0BD7EA7B3AEB
847CA50B8904CE8AFF81250F4548C302C78E94A9EC8A0886481A123BDEA4440A
9DB8ECD5340A75A2E973F163B95C63E45E7F48F3F39113A84D5E8206016F6D6E
0BB6543665D64BDD08E828287D8DC431CA6E712A81E408F14A2A0E9180CF7B4B
E9296681703275D0F2FD2377E4B3D78762E451963A6464198F3AEFFCBE231DDA
6F063164940D3A07CC0CB638F252B591C444D80E666C85864D2DDA4CAE30CA06
996D7B35E236BA6D8E598D247F6D5CD1472D7EA2EC4006057E4C8B26B87B9AA2
B448D1D7D7DF9CFABCD79DF2B16BA02D01E98B89E5D7F9E5EF4F9F76457E158E
D5838729261013110E3ACA06056DF07C00535777E71DD3834D098E201B8AD60A
9A852B3EAE3A5383DDFB1B8B99A5D3A13BAA7155BA4E30FB52949A560067FE54
A82F913F348AA5D04255418C0E76274B024817B37F14E75E83D7D85BED3F20EC
E2D07F7DA5E6DD3FA327796498AEC6B782D17BC91FC1320C01287DB1E28C027E
7B585931D39E636BD8EE5C25C6D8F4F1201F9ADD6AB41A04B1B366BE9CB3FD89
08E7152B3E78D93BF6EE537C651E84351966CBB188664B13361075E250B6939B
25B97F50309B7275E81C13F115EF59536071B4E2946A6DC9A9D465A0EC1F5CC0
3880C99FB6E01D4239E6A0B5ED8E6FF9A3D792D819AAD20B9D6FA9C1E39C49D0
E33142E0EF1EBF5C27F6E3D1E5BBFA3FF27B6834F5621123F6C8CCD1D2618624
792DAB89CC5073B841BF678E00F3DEB0BCA9AA37716FF2B91F52FFDD411A1C22
5A05ADEC59BA64C37C142089AB6D50F3893A5FB3B646F79DD9907754CD0E1402
8329B2E2E5DE54FF8C6D9300D469075DC277FEB8508F4E46F027FB0C14733092
9CB9DFCCEA9581691628B8AA1A76E7EF31B523EA3498334368259C93DCB52D18
B64A7CA0B97BC17A5F02D4FAB0FCD55343654667E34ABBFD86AE9B4B8D7AEBBF
DA54FFECE7620AC04A560480930066A4FD5EBC1D5DAFA10E4D8C7588F6345AD3
4CBD72459E317FCB32A52801A04F8C692BF4BA5554B9BC53652BFEB062906D13
4FEDB3A7CAB0EECEB41B035853966D9699535578CBB326C7C328772A3B8EB501
0D0BBA0C396BA83EDED1F0E24E2B4B1550C818C3EB0F08BE7EC86B8241549EE4
3C7A61B5B34149B1DE57C03DE56A0A02D60824E2DA6C2A1D321102FD7560E07D
247FE9818AB3CF35501E4808384D9DEAFAE96681B1C36522F1E1E2A8EEEEC0BA
B7B84246EE3295FEB462F8FF8DAE67F22F7324B052EEFE66DD93C30D4C355523
A7ABB6B9C9D123B661625228173128CB0F19042BD9E7DF468ACFBD3D98784680
5C3CDC315269658D6DC4266FD09A99AA3525D2C56184282D316BD10C3BB4963F
472A9774D5FA429B17A04256FA734166E234AA518B73F29590C8A2920F0C523E
D2C1CEF77892BBA6BFA803201F38E6233ABD64A12194AB9173EF1690ACC8C46D
BE885C1FECB54C9A524CA158C7DC1ACABDF2E16431CBAF4ADB455C6324BFBB50
C315356B9C8AC66A02923136AEE08605590C45E857AB11ED8B50DCE70CAFD933
474B98E1C00B21CC9115A58A035953C25502DD1AA3F7C57FE830842412702CC7
7E8BA09628FFFB705E14E90A522A79A0EAC2A53B9DCBA2CA85F9B84AFC475872
1E6122E29BDD2FDE4C09CEC2EAAF6A3C5872005AC670920CADB600D6080AB939
EB0A00888C6A98C24DC48566AFE88CE131B4DBB7E3497BA59846A84C57265223
01ABA417C99108292D37CDFEBEFFFE31F7DF6EABEE9657A94B0AE5C7933494E0
D57977EF10A128B85C59BBA9DF7F147FB9ACF26591EC333707D2CB3DE46DBD0D
B6814FE30A410F14BF40326374DCC1A3EC1CF9604273E09DA48A5C1462D5CBBF
1D95556C6D32D4C8BAC3F26E58F5CD1F18EF8FDE382110F0D9F1838189B67964
53CFB0C7F48B8971ED251FEBBCEE2EDEBB2B47504BA5003418C7291FF5C71DCA
930A570C890C90C5F3A8741CED13ECE3E405DE5309915440111A69860391E6F7
2149C444702F429321C70D118677AD56E98A193176EE3807E2AEAD3E33C43B08
411C6212780666F0428A6A3EEE195FD2C5DA4875C75E50B553C9EDC542649785
7FF3E373742E2397250ACD8B88595C3BA1826595AE47E1696B7982F090294954
0F133C876735EE84D32A0C2F06D7125AFE21BEABFA871FC671517E3390CAD5F6
41D2BCD4F4EFEC910F7475BEF41DA97A5B89C73B70E5303423517F6A858589DF
E7A4B9931910329F8AB7E433020F0FEF566C54150757F2AC1FDE39AA19B1B11F
D0CCDEF651B46DFEF6A0EFED2880EB552E1F10EC697370BF20D81449C8FF9FB0
975B4C21A9BBA3FFACE380B37A5704B22B7C9E21AC5A5B580C445335CBBBED02
1276B6CB80AAE0723FBA315FAAC7FA538D03E8E1E68FE67FF8EC9C20A41BDFF3
BF2D98AC785E62F25B3B4E3B435D6A71DD26F1373CA55FDFBB0A46312B21F968
FD70C727A6710732308C34BF40BD4D5BCBC0077A4BCC59F435B5541283D5BBDD
1C2B18A08E2F1FAA5119A43AFD530292D996C085D28C5EE2DA0959162EF5BB99
9524A9195E4B2E22F2619939163234CB4593954BC6353A8AF5426A8DD9FA73DD
DEB2F477117DCA644CD441E46BF8CA7AD2290491B7D669F606DA8804CF25D0A6
94CB5304703B08EFA468C0DEFBE7E5B208536B79D1A382D5EC58C08F830FE8FC
72FE477883AF1AF97287F0EB06CC0C5E1E29F00CA10DCCE671658B09D072B602
1B7C8F19B26CCE1D19D6FCD6E11DEA568964A478EAF828F678C81A41482D5EC3
F44012C0B82A7F64BD16E344F8EA591A20FC3A72075183E0315F4D8D52304E38
9E41876299F190C14C18F146211EADAB1B58CD5DE8DE4E48AFC7CA7C4173D392
A4EC30DBCE9E47EB6E5BFCE37FA2226DB52849828BF6BA195EF74E61D64C2BE8
C16C355649DAE36F59C2076F3B95ABECC2FD3851D72F099B547274CAAD26519B
1BEE078BA50B0EA620C7032F6C8F5D222C6ECFD093B086F7B3D9B6DDD87BBADF
199F909E370236721C8EF9362012DDCEC0363F773545144C5ADF387C0AAD7E9F
9512DA0AA6CF2920F41D4D55C2F786FC8045D86715743667709678F5EE9AAC41
E22D87757716D34EEF1AF0774EB9FD4328DB4E260E82F3CE9B7AE205F683A513
8D089B9B1DC48A1D7FD6F46F4A526C1CEDB0494B350E93EBA23398B8C7AA874D
8DE33C519EC0195656D42A5126186827861B2C71F1E93BE141D289B0E2E5B8F7
12AA2A624E02C2F7670099FEB7C136A2D3CEAC24EE199891F3820C359647948E
6AD5E8C714E5134EECE3FC72861BB7F1E49C9674B34D940B6FB8389E475211F3
8E7E0ED44D111BDE09A4EE31A595963D71F729767A8A3FD30A161AE826CF53E9
A999DEC42D08884F3B579BC5235E550A5467FC8E966CD7D4ACEBCC731E62127C
DCBA3C97217CBCAA57923D3767D0ACD93490A88327846CFD4E0E51D7D7AA626F
29F1F5057CFF82339F5DF641239F8DA739852725E074ECED4C9AB3471C0606B6
93B224F49AE7F653B4D79613EE007614453F57DF5E82D250E1E0F77B58525BAF
3BD09D89E01AEFFB2635CD98ED636D1F98083B2D23130224A80CF3F6B39A9F2E
85A2B4E7E9CAAF0A75EB26006B251D27229C5D48223256F311C5BA623AF41540
02E155B49BCA5D3E5006F232C8E4AE8D8DFD8F1193DB60DE59B788B6EA0D59A1
9DC3B75D4A71A2B16AD022080D370695D0ED6B1894A7E625F2BA25A437E7A27B
39AA066A9A40CEB4EDBAD47F019F341AED7B77F15257356859148E210CA34FD7
64B089B6ED43EA90CA9E2253A5E0D2B94E974A88601B8C8C33C58A7666251A93
5948A9068439EA99CFAFC35189F965EFD3D78A11390DDA9C7A79F67846C566F4
A9AD42F64A3F6056759EE8BD4586DD26BBDD066DEEFBDE51B8E22B21BE7C7BC6
F5C4D2EF59C01ADCE612BD045C098B8DB272AD76419F3E20B84C478937E64F9B
1C43D44C3594A7FFC8F9B11421DE9C0E01274D9A9E7A3CAEE3B4B548A0CCFEB7
4B777926B8DE7F00ED120E386D95C9838D3F7EA006552F3A06B757B17ADC076C
88D17902366FB6A93B52FB2EFD190C9CEE3FBFCADEB497C77F1AFE59680C9A3E
30B2525F97125714C19A2B319A68013667913F96DB9A46BB656E4D2881609BA3
74637EDAB1EE96F5419F7F8ACB637D1BBC96860A9FDAA63F5A4C19C1A54CBDE5
B85A51BA7F0B732F55DC4DE44AE2CF095010ECA5A067F1083475AE315D9B754C
B6AA815EF520A48D2C7F70DB275BCC18135EA13749FC6083F64260F367AD340E
E20AFDD6A2094F7ED20E9F99EF2CE5B62645119C312BB978C3FCF9A98B35BA5B
C764AD4EF00A3760B7294668E87DC674B5C7C2E0A5EA1940C186C4D8E3134A7C
42C8E0497DE5919091689BC2F4D48C049979E672BFB71882794BABB3264DEC5C
46349B9FC3B684560BA7B2E2571E2FE78DD44E55BD2CF8283DAF8FA1643B8B31
EAAB773D593CFE493A31134E4655807D24F0A59CDDC863B5298C2A2AD313914E
00B4E0D978A9E19C734F83713C16FB91DA39125E0CA07242DA2505E3C951542A
8522EA7717832B9E356F336D9CB0ADE0D656F63C84049F5C7C05E03C72AA813D
416C6DA690BAE4D271FED01F4ABF46B92CDE4FFA5B98181127D4502D66B3C4A6
A0157505BEC98AD6FBC725A172A840758C69F2FC7771ED2B2E30B3F7062FF730
918419D77F6D600BE1C161B883CDBAF63F7A47034ADF35395B0B79C2A1CB5653
F83225B2BD95782BD965F3E7B08DCC2DBA54750BFEEF27D38ED605A46B351493
AE7CD1C5487300C8092FDCB06C936B4C3B4578EFC8DEA7F4A48983BD75EDF796
A5466AA04F754F9C9D5E87F332B82EF5C17AB99B68AC2F5F0250EBCBC4E42C06
4E20E14FDEE7043C24C2B0E9BD9580C8A1B280BCE7CF120281E3C9BB0A02C335
DA499B53ABDAD9888249F6D2F3840E2B7E4FC31F2FFDC16BC808946D69804F01
E695D733BCC8EA8C29BFD678FD45C35B4EFFCF8AE3B07E50ABA1ECF17595F742
9EDB1D5849FDF4A14FE067906F05B26C0E8C212070F41995954EEF249A5B4A9B
7BB11EEF13D015406E56743A43ABC3A0EABB59A74C774CF8AA59C99538B249EE
E1DE794CEA08D54CA4323CF5DDECA053196758951325D68D441E8E9C95C89369
DD468B9FBAD5658736F1550F7D3762289CFEF71C690769DF9EA55D0178A5384D
CE63AE3AF5FD3F3C9BD2367E45C67D7AE5A51CAB5CAB6429C676BF0467E89878
F4911FD1D31F6BA0123900C1BBAAE4E2C5BE84A05FC1255A8EC13432DD5AD9F9
4967AD6715603A1A034808264A80FA1F81FAFF0296D179DA62D85AF84353F9D8
9323405DE024729304BA195C7493AD8015E0416AD6CECF2BC49A5891C9376906
B491759D5DCA6A129E0680AD60C0C43168414B72BE7BF989F21811CCB4F0AF9D
3FB47D31E9882072B1E5B5525BEA94B47BE54EFA5D6A9FF0C0157AB32A7E8D64
728A51B0267A9D8C680B16CAFF325BC572A26583A69139854A0CB15EF51BEBBD
59903704A51AEEC17A5453ADB259E8701A5EB69455286017F33DB27DC9AD5858
1CF45A79C0039255AD103E267A0C9F96BB10956DC5114ECCB69F2C95A0AFDE79
B81A66C76147AAE32D608EB838A33EF7CEB3EE3DFAD55DB3ADEC761A5C0A81A4
F06C83B97263B5672B922025FF0CD869B5B6B195E6993C6D339CC4E61EFD8F74
08E75138A54EE6F4DFB5C588DB9E74BE932CB1E4F71E0C9A34B924EA43DE7B7D
1C68D991CFCA1CD56C6CBB89655317D269AEEF5C921C475AFE4EDA183664E967
5B7E2D2B4DD16E15D11A035F4BE93DFF6EB118E08A81449168D2C4C82866F5F7
4F31F7F9837070177460D2CDA4F122BAF6D87006BCCD98EAFBE7C1B405D4FEEE
0AC3C58580F8F382F820B0772B3EAA3ADC6C735EB711832A43AB6A9F332BB2B1
224C83FEF5110518B27E6BAB26EAEDDF8986AB0F63AF70D41707B0A23109964B
586D2511AE1F5BA93541C20E1433FE13BC30D7C7FC0FDFED6E39D2BA7D4CABFE
E730D42AB53745858A9AE17348E602F3E9E027CA28722AFFA75A1FA7F1DBB5ED
63D1CCA6C3C7EE7277A0F7B45D44E031CBAB7C0D852550DC59B6E2246072CC9C
AEEBA0D03FF50079E23FF50C88974D51160807C7754E5B85771EF86ECB28D689
B2759D1205BABC4A104CCBE4B95E7FFA03DC2571373D44CC15F3BCE288EECDBA
B94FE7409B6506D0C757860517DBB77B8C76F882C42455981EFB0DA9E64C3910
686789B1D120B80F0AB9DC3AA5FB90477FECDEB8EFA2C33A6DEAFD94B9F16758
FE71F24689909932E328F079D21B49CFE203F3E5F993C4CA380B7FCDB70E5484
E43D2C1B55FD81DF3085E16415F925BD6E4AF7EF127FD387DC772356EB09BD2A
F0A091C63EFA7D1B3881877B7764572EE352289A9E24A99C287D29E969AF290F
A9C435E4C5D97D66E99E26CB2245CA99705C7F6A90C0334DCC6FAE75DB5C7462
203DB1758BA2586AFB58CA7AFB58BADCA096B9AD0CDFEDE3365426933B90AD88
4D9878257C944172E504056233CFAD9159631C5831E2E9E463FF51F2AE9C3013
F38B41380FB0FBAC56EC9C355F6B280C7C0F3D09A293568E2D339EE81E8D2819
7EE197E5D6841DFD37BB3CE1040E515E8F6EC712FFAD46C04CE896BA7E31B7F4
813D567B2A866755E2C576F09066A17B0B4CC654D01C316962E7A6D6A3347FC6
D19E0E4AC53FA43B261FDB0F39C2930E4E9FB31B61FC2EE6FF628845A1A98CD1
16460281EDF27266BA4E9DBEC4E3489CB7E0F75491F34F8D1E6AB11229B2F4EF
6550ED7AC7ADAD0FA025941CAA0C0E9D65B8E6423DD4FE0324BB84A0708149B6
9DEEF27D6552EF5B8C45E3F9369E81F95004BCAC7C5F3F328921A1A40312C820
9741EE3475433EDFA8C3763EB688016A8B229E2143F137FAF66952B2C63DED02
0CF1AB40F456C4005964353B1ECCD462E0D41B4BB1EC403EE36670DD8D6E1B0D
DA5BF5026FD3AE6CCED6768C64DC31A5DA63BFE8CB9B67A2FC2A402633BEB2C4
2FE76D7DA6A4C06DC3A066607EC5C80C071FF8BA10F0B11DC53576D554C4A9A6
92AED788A887FFF1DED487D5F4FBE10462EB62033E5678B3E689EDACF28CB1BF
64F316B440846B86D58CA7701AAA178DCED96C957017861708E75E15F37A6DB8
335C5ADCFCA6DAC9EE7FF478B60333E4A6F4980DAE9E828E1021016CDAE3CB62
4575B2BEE11C78A8F951956B3A9AB76D918DC920DAA427CB75F226F2BE0450E1
AF594E3439A9F18A2A9212AC7D640EAC80C1E23F83EE313CC42BF6E9DA62E94F
9E9EB24429B9C947A1955508CF7EDDDF5ED2E089F4613AAFAA730589DB65AC4C
D849AD4C64DDC82350C3128C156B30DBD87EE3DECB0797790347D01C1657C401
DA800910BC009EC836FCD1205D44A67CCABC32CD550724F9A71F7800DD672461
FBFE2AAE976ED1F0AE8FF6BCBC8309023C908D254EAFA03CDEAC8BD76D070393
3001A46FEC583AA7AF0D5CDEBC5080BFDCDE4E20A7C196149E7BC47BC0C42D0F
34EFBD2F768E8666398829DE5345009597A6748CEFAE91061C7C650FA846CAF7
AB62506B5808E4DA45CB95F901CD12E71EB7940FAB10C23D788E484C08501B2C
466923EA39F3AE0249D05E60EF2F745DB09D8CE8CAFD52EF91F1177B73F9555A
1E590ECE1EB9AC7E12861CF73427310304DED363C8928C6D608A21E4C8CA10EB
50574DE4D1695F55F13F3CD491B8C0C639C7219D17E3BF687EB25BF924522063
69B25B749DD7125D7C66035240EDFF6591C307DF004E61B7D6B545890BA038C5
AD85C436F131F7D800BDB239DDF2085DA0899E6766233AA2A35BBC8BAF5624E0
DE78566984E4B16CAD1E2F17D50D1EA5CD63AC662E9D266EE632F737E031825C
926C65BCF5681FF7086CEB403DF91181EA153CA5F7C33502ED05100B3C3234A3
C6DF4147669CCA690FA85B18109CB9089E5AAC8A6F91ABA7785545716A8D2765
D00FD3EBAF289FF1CABCA5FCBC7FB5E2853395AB87BD3BC521769727A27BCB84
A0BAED7EBBD9FB3D4FEF9077D83B59DD492204F388C9A6898CB01400BE9213E4
364123E1B189D8B98D74BCE0146F5EB0AC54FE914304AA98B12FD911E068DF16
5FE2FFC425F86F44265D18FFB4B17876B3F08C0061E60B2D549DA1DF7542BF62
B015BF104581847F6A492B126A9366F4FA2FBD47507C1ADBAA71F2266012369C
D75069F1BD3061592DF8A5D6E26FE176EBA8173C4DE5BA68CA0AB2CD1FBA174B
77A9181F0966413C7E020C0B4820A7F1CE9665914E9DD354356638F2F318D3A4
0E1DC596278817BBD1C34083C6A88AAC910FAF1748F5CD0A886A5D03FFED1AA5
900828B689F96E59DD41CBEDB7566D43FAB35EFBDE918EACB84B5E79A49E97CD
DEBEB071132D98E44E8B6575F190178C91A02B17A497155F39605C19210C2413
78DB97CF44153E81EB17C48A5A57B6083771FFC97C5938065ED593CDA9C1FDD7
7AFC9CCD914E537D9ED33564B1D8FE4DA679B50CACDB8692953CAB424F767B1A
E2E916125F6E4B23F4B1F0E98765002C39FD26F39596A0273D597B2DABE7AFA8
13A95259A063D660499E5A3D66CE646A345403B3542CA7E1B0228526B758F883
82E0E0AF17C1A69B74227BDDDF6344995334D1E443098D00829C2D1B036C7341
F6DB61C1D267516C57E1F1F7417EA10331B29AC3141A404F8DFEACAB49CCCE90
DA7EBA824274ACAD8684840A05437403E7F9F3FCBE2B380C353B8A16BD4FF853
D5709D236645D9677A98AB89F89F88AF3867C20D7A0DA158FE29F156AD4CE435
2492CA9FEFC1895079AFA85AAD497950D64509ED20F9F91BA6BD80CD4CBED304
B8D2C7E0C7E7C181C3E24B2B67543A7DC26C18B9797019A0360E73A05F7FFF2D
B84118FDA804BD47ADBB623E81D7D173A94DC7705E95A1A1F4A6D6E5A61EF1CE
8F4F2FB9A327AFD0D2CEE23ADB1444CDFFEDA970BAA3F198E4F37361E23B8FBF
C066C6011FEDCAA8FDA96DB448633B79EF2A3B1AF0C40B8A3FBD2F9CBD746E0E
06BB47A5FD85B0EA295BCEBD263CC19ECAFF2DF31E008ED5FEE44324D55EAE45
3931BC19E0BA4A46F71922C2318A2D572AE4906B095369891408CCAF2977E5E0
6278BEB9856997A69EB9928FE5F4B738E7FE84AFC20EC354ABE35B3A8E2469C6
A778B11820D2F95C33514640B4F44890552A914887725FFA3CF13BD078DDA535
9E9419B0F22C06C5B03E78F2DAC6D52530075EDAF3BC540DCE99FF0141E4E902
67A71409D3DC80E45195D9694CB837C01ACC5E5285E62157FAE4C36B9CCA7859
C64127705FBD0E4788E895A9C07E54D1854950A43B3B7162E24E3C5DF6258B68
A0E0C04EC6077E3A3B38462EFA27D91392E6D532BB2C4F67076BAE9971DCDF63
49A3AE7E196B54F7AA2A80F51ED3429B008C17E0E5A842D305B6AC1CD1BCF7A0
A43EFA747C28718F2AE11C0FCCC79FDAD9E671DF9F1CC49B00687F53A6CB2024
D05340842198615A3F2E5536C0D42E40A41D990FF7D9118777DE482147168A65
6553C5BF1F4CC7696BEE80F0579EFEFA1F8C49AA24CD46F620905C5F37286718
B5C7786DC07A2836F6458DAC129424E4623D4C112740308A43A5F6B33D0196A2
C1ADBB1EC69654DF35AEEA481DC2B9CF494A64C271B2FBD5564CC951A1DF0364
3CEBC4F7B46E4CDB4E8A98DC829246A310B00F8892F880DA4610B7E7265678A9
EDA0D20115BD617DB1A39200F8766D741043B17A84FD6D286D3BE98B601981E1
D33817216C25DA16AFF7E79B4F41FAB1AF710ADD4F2FDE04D87051212F5FF4C5
24C5502D9DBE5B39EBF144BA3C2497ADD921CED0DF60B563F8F6D2CAE177EA09
5059E7B74FCD98477AC8D4176F08663476DE2DF202261794DCBA62B4D6402CA6
495809BF711096A939AB97847FC9E62F23229720039EF64C3D20815807426C0B
E2CA235B50A5578611CD945D1069702208B45DF9A5139040D4A3A53C71F1358A
673E395BB60157D754DC6057CA3A11C775A42425BC6510D1616E55BBE81BEEBC
8F9ABED1256F53DF63E92B018E293724D15F82CB77E9C55AF2D9BF55DE995E1A
C055CE02960527AB4FC06DB922EA46E6D6BF3FD2FF64C65E578A16F516AF9D07
DAC1B154444AB5D3FB6A4E0CEF6BA9490944D1AA9F6C92F9CE40A0246A18E7A8
653FB05AE768EB67BC0C84F816F70C8A11DACF3D76AB4A37B3C9E67ACA4BDEB5
DDCA2F41BC71BF9872E85C1CC16FD8697C3FD41AF47138C084780D304176D64E
8A7AE13941BD3C21CAE0F9C0464A23843E6E8D6FC6A7A633815FF51D8587C17F
9859B0C2EC60C3CDFE637E420BBCEC93CCE4A9F4767F3F05E1291D59CEDC8A72
1DAA5D21AF7EA177B107720EF22FB6CD6C955754B00C2A0F3367E1C17CD32887
F56AFBF04C262B0B5876E72883F29DEA0E187D5769F19429A69BF8E5F857D55F
F8CAA3E545B6384952706F2CAB5C7998739A0D79C048F8951F7031ADE2C13C91
94B8EF993784E7A626CF75A7B543AA422FB35C5FC3BE6125A92007D49ABAB819
53B6BDDA823E59166AB9CA97C51BCFAB3D9C6BA4D98855A784074C768FDC3527
21FCEEAC08DA90663094F59871391CFB10E6E320502683508088137313EF332D
F8619C6F483981A8471023CA40D1434D9CFA9D644C8AEFA21D8BD68B0C35EEE1
D3CB9FF1B0A7701B1F2946EF149B5FA0BDEAE5C55BB3B27D64BAFB9C996BCA3B
FD3A9967B6D54A55D82B843460D7242244EE0FAE49DB2C2DFF5EF8400FF1CD4F
A395CB30B580BE20D78EB87A3040CEF0D771B6D582A1AC59768533CFC16CE479
43248868757851101C7ECBB07BAA78E5096D24DAD64777B1C0BF3E50D1A061ED
A8D1F6514F602E6598AEBEF4307696C7B130D527B81381BC6AC3E9EA8E9DA185
6C1488F138DCDF7B6735D5BA4E1364D3A5831936E9038CEFF4DF5CB4AB51010C
25F6118680EF271F0961FEC2AD8FA8BB201EA5637DD88B26363753D541454E4C
AA3C5A3AD4FFF22AD4BA153DF2DC3B25CDF462CE2451591579BDA3EABC75D9A3
1C9EE79DD540A979EB47A434157844AF6D05EE2C0028B3406142737FE501CA52
3887A29B3ABE47758E8131CEB71198356523A95AE8ADADEDDF4B4C0A1855E490
C6BD9E1BFC074286F7132FD1312D118A31201EB5FB44505D755D61CAE391A78F
8B1C8B6F23454696F48F5DB88D701CB2EC3CEF2C5A49D24E9BF722578F1CAB30
2388F084AEE7A9464884CFC5250936365D0F5AF8BB6AF16CB6096432ACA0596A
851AB8CB0D633952464BFD0A32A6E630142D45BBD73F447BEDBEBBC67B322C02
21CC003967B78AB478C33FCDC1CACA155B94F9539EB6C0177FD51C28EC7AB093
200ACABD14E3FDAC38EEA53C1F3D74ADA49A8C4E2B67412EE7BE424389CB0088
555C24429A64EC334F78B726E883A8EB9DD2368D9BA8811923C6B78353B00A29
DE61F2803BAAF47920550733C457F2F2669D255D32E43309165292C89D51542A
42B80407C177591469A2B15F33D452B0BC23E2A51991318BA054BF8722C7258A
2CB088C7381DCD880E7F9670CF9C898AF7C148B961A1D582B16881C19192BFE1
56F46A5482AC4B4C954B7B04B888ECC1E077997C793619A8564320F5462BCB2B
E5FF44EBD4DD6C56FC36C9FE6EEAB5BF798E875C304030D4AC1BAEEC6C5665F6
9031FDCF58EABD643AD317644F24648EDF07FAAE7023D1B375B38A9DC37198A2
A78FB7C99FCE71223C2DF253186262EF29C5A9B521C6CA598F384CC9E3E71CC7
77C2E542087410DB18D69721548152EBCADDBF345437E8F8EF528367AF442673
F11D9E4EDD5C4B704B354BA5B9CC357175D6A21DF7DA86FF6F5AA37258345194
49A6DE09E4C195AF7D815742E8C277CE
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMR7
%!PS-AdobeFont-1.1: CMR7 1.0
%%CreationDate: 1991 Aug 20 16:39:21
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-27 -250 1122 750}readonly def
/UniqueID 5000790 def
currentdict end
currentfile eexec
D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891
016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171
9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F
D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758
469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8
2BDBF16FBC7512FAA308A093FE5CF5B8CABB9FFC6CC3F1E9AE32F234EB60FE7D
E34995B1ACFF52428EA20C8ED4FD73E3935CEBD40E0EAD70C0887A451E1B1AC8
47AEDE4191CCDB8B61345FD070FD30C4F375D8418DDD454729A251B3F61DAE7C
8882384282FDD6102AE8EEFEDE6447576AFA181F27A48216A9CAD730561469E4
78B286F22328F2AE84EF183DE4119C402771A249AAC1FA5435690A28D1B47486
1060C8000D3FE1BF45133CF847A24B4F8464A63CEA01EC84AA22FD005E74847E
01426B6890951A7DD1F50A5F3285E1F958F11FC7F00EE26FEE7C63998EA1328B
C9841C57C80946D2C2FC81346249A664ECFB08A2CE075036CEA7359FCA1E90C0
F686C3BB27EEFA45D548F7BD074CE60E626A4F83C69FE93A5324133A78362F30
8E8DCC80DD0C49E137CDC9AC08BAE39282E26A7A4D8C159B95F227BDA2A281AF
A9DAEBF31F504380B20812A211CF9FEB112EC29A3FB3BD3E81809FC6293487A7
455EB3B879D2B4BD46942BB1243896264722CB59146C3F65BD59B96A74B12BB2
9A1354AF174932210C6E19FE584B1B14C00E746089CBB17E68845D7B3EA05105
EEE461E3697FCF835CBE6D46C75523478E766832751CF6D96EC338BDAD57D53B
52F5340FAC9FE0456AD13101824234B262AC0CABA43B62EBDA39795BAE6CFE97
563A50AAE1F195888739F2676086A9811E5C9A4A7E0BF34F3E25568930ADF80F
0BDDAC3B634AD4BA6A59720EA4749236CF0F79ABA4716C340F98517F6F06D9AB
7ED8F46FC1868B5F3D3678DF71AA772CF1F7DD222C6BF19D8EF0CFB7A76FC6D1
0AD323C176134907AB375F20CFCD667AB094E2C7CB2179C4283329C9E435E7A4
1E042AD0BAA059B3F862236180B34D3FCED833472577BACD472A4EA03B9F08F8
DE0B33CFC11789C704BD5C7E91973E12EE6140D5EA01E9AC5C458605FD9DC8ED
1038FA9147FA415D64EFEC2C1232A5055C11F53D7FB2953A387B7990C40D7388
D792D5E503928B6C1ED09EBA119448FD99C6EEA561F0CBBE92FE7013A0678BCA
F013111BCECA962ECA0A8A6A0F8A24F1E64105173B259E3DC42D81F36B623CDC
D249833E49287ABF137F97C85B2D40F70C585ACE1FC0FA1F262237C3E0BA0E5A
34D26254A46282FE003D92A42237F9729E39A863E33EAF676CEA4D6FDF53F3B5
C86035C91E28C179BC5FCF7C961708BA4B0055267B3EE256C88AE0638FA7C93A
AA9A3C2ED4380B053B2FE5629443189C1509A44C13B936FDC9FAE14A4645C5E2
2AF38538F0859E49BB997A0F6927F153DA31CDD588DE18DBB80FD9B52174043C
B08045D6A908398DB1EA5EC05AFC57076F20CB337ADFC9ACE0B2C930AC741D2F
A18BDBBCB47E75C59412477F5DA65DE0F8BA928E1269309889C5532053991565
31425FCB8B60EF0224206E316DCD30ABD589353060301BD003518F03ADAF89EB
52D52B4EDAEF9E1DDA987DAEC448C8D797FD55AF8F8C772B68EBB010381CC65D
02177A85487004D5A5AE889F94736A7F36E86579725504F992172A56B144F5D8
B42BF4495024006B5C12E81A58156309C705394A9D42D57E761DCB64106BBC44
56F0CCDED2083650B30A68A566384C216D749230F82A33C558CC353A8222391B
193DD9E4167CABF448B0E08AA8D9D3232827B77BA51172A48953A3623515B3E6
1B4E895910E8E9D561D70046FB27E401F9F57DEDE227FD5FA581164C0C1D39A6
C17AE3CA4DD696CA746444BA6941B422B5AEB3DAFDBFC8F3038B32A3BF1DD1C3
0DE109B7F2AEF21BB303905EF40F7BDB42E4784884E33B3B31220D5753BA8720
9B87562034F3277F89F5444CE8CB5B2726C85CE3B49D6E60DF6E4B4BB0AFA1EF
A31E0947DF8C78159E27296BD9C109857F9A29331145BBB2E5C46EF3E491BB6C
A6CD85DE9C6D3BAE3370733B9D2AF609D9947B59EE1ECD873257074782D908D6
F8BEF1954D5955779FF85F37FE7B9978489F9D6DF1F4A49C78819CB664ABA334
A885D9E5F8ABE1EFF1A5ECFB1835B4334E0D0F5A62A2B90C03905AE42F4E20AA
25366D9618212C9F055BE6CA6F9FE542DBE1FEBBD762824F548A5AFB4FB3FD76
7F0648C1112953C4C5916A4FFD265B5C39D695B804726A425925837C2C80F84B
E67FFC6D714345D842A5EB35A1F110BECBDC95A720C9AE46E0E11B0973B7AFD7
C9C10CC3C21B60043C3014542A93C8A5D11BFE05293D9165C066487FE141F70C
B02A286FBBD12DD1CB52F3A59AC46003DB33BFC85E016636E54283BA5CE52544
7A850208FD0628FDF47F43EF5C7609D49822A6AAA476AA75DD5B97F2CC39E2D5
A3AC1912E5097C6F6E0BAC76580BDD8071FCE229ED580BF4852ACB8C2A59BFED
A19BF91873B4BDF7C63C8AC8AA0831D5792A38AE1329DB42EBF9C9E43B809D91
6F43F910245F754D855072252D2BC8741B5F689D3391E2190115DD0FD4F06627
00920AFF02BA7A6FA0D0823650ABC335FFD1D600BCDC8CF2524FDA2871817163
0735AA873B43D050637B1FD10D8B87A35D77DCBDC166FB4E5CB0A449C21F8AFB
146C4F819F43B837DC59ECF2E9F54D2F408589BBAF02ECC49FA7BDE8B9FEF882
76A2386458C92DF9E6C6EC22A372280B3CE26B47B5E5E35F938E5D7CA8DA3914
94FACD392C085A7A93867E085F0EAD18E11EDB4A955192648A1A40A26A37F88E
598066C8707F356EA640182927C35656966F83A25B291FBA1DA894AEEE3B40C1
DA53143F8B61EB59846A1D1527187537563C682724BFEAD9D723089B73761E8E
4635BEF5E4A0D64318A5DB70211C02F6A2ED822ED92D35B0CE94B33F8BB57929
E038E26750FB542B7FFBFD315D46604B0C533C4D5CADF95518CE258B0E08A7D6
63B5AD9C63FF553FBD681D1DBDE81F70604F99D94048EA5CE2D113A32B66B9FA
6A1FFD0DCC4DD0E92EC0835C39E2C945BA493035DB90AC6434F932E68216DB42
7506A92D1D80FAC2ADF599591F1D9E9A16E07BAB221144DD28F9EF3709FDADCA
4AF10A11B5E5402A38EB6EEC6E6616047E06D022C531A3BF9A4A1F3F075C503E
B7234B27A5DC75B493F5FE82FC662C762D4438F54A11B36163A6D5D3FABD46FC
D06217D76FA2D9F0AFD71F572A7AE4CB768C0B2F5FB33BCFB68B68BB268A3BB2
3231A3443D745B70547ECE43E8760656F64CC5475D2DC24293F1F8E1FACD040E
C6E63F86CACAEEEFB64E409966A8FD185EE5BF989CA4D7AFC2CCFEEC63EC72B9
A2ED2A07A05B22485C3D8D2A9C328DA1CD2A9503C257D07453C01AB95A074421
5C7E7E6669EE79E41372F2DE00C067E575111A7388D16AF5A2D086186E72E40F
2BB35F3882EF912F1BACF03EA0C7CDB41B62CC343D1FC545C63D8A426F4640F0
F3A4A11C07E400ABD8DF36A4903F0EC61FA078F55FCAB253E9D615E4DB8AECFF
538372CC8CB87DC3C9E98816DEEA89F6C64CB5544A436A7E8C33B11A8C355B51
FA3520F4AB711ADC9C1FA8B89C206AD1DBB8
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
TeXDict begin 39158280 55380996 1728 600 600 (talk.dvi)
@start /Fa 204[82 82 82 49[{ TeXf7b6d320Encoding ReEncodeFont }3
143.462 /CMBX10 rf /Fb 142[112 45[169 8[66 58[{
 TeXaae443f0Encoding ReEncodeFont }3 206.585 /CMMIB10
rf /Fc 141[95 20[65 1[65 6[162 40[181 43[{
 TeXf7b6d320Encoding ReEncodeFont }5 206.585 /CMBX12
rf /Fd 204[53 53 53 49[{ TeXf7b6d320Encoding ReEncodeFont }3
86.0772 /CMR6 rf /Fe 134[54 8[102 63[33 44[61 2[95{
 TeXbbad153fEncoding ReEncodeFont }5 114.77 /CMSY8 rf
/Ff 141[172 1[172 44[151 151 151 151 14[151 151 30[103
103 16[{}10 172.154 /CMEX10 rf /Fg 138[71 44 56 1[54
2[74 108 36 63 49 42 3[57 63 53 52 65 50 11[71 74 4[97
117 83 103 7[87 5[61 32[54 2[70 1[60 73 10[78 11[{
 TeXaae443f0Encoding ReEncodeFont }29 114.77 /CMMI8 rf
/Fh 204[61 61 61 61 4[95 41[102 1[{ TeXf7b6d320Encoding ReEncodeFont }6
114.77 /CMR8 rf /Fi 133[78 82 96 1[81 96 61 79 76 75
1[81 101 147 50 88 70 58 1[81 83 78 88 73 72 88 71 8[159
98 114 99 104 1[134 109 1[135 163 115 1[93 74 140 2[125
140 121 1[126 89 1[131 84 131 47 47 24[105 110 3[73 4[83
101 98 2[79 3[75 87 95 107 11[{ TeXaae443f0Encoding ReEncodeFont }58
172.154 /CMMI12 rf /Fj 143[143 5[48 29[119 10[137 7[96
96 1[0 12[172 1[134 5[172 8[134 3[134 2[134 1[86 8[134
3[134 1[134{ TeXbbad153fEncoding ReEncodeFont }17 172.154
/CMSY10 rf /Fk 134[107 107 146 107 112 79 80 79 1[112
101 112 169 56 107 1[56 112 101 62 90 112 90 112 101
9[208 152 152 146 112 1[157 138 157 152 185 126 1[104
73 152 1[132 1[154 146 143 152 1[96 4[56 2[101 1[101
2[101 1[101 1[56 67 56 2[79 79 40[{ TeXf7b6d320Encoding ReEncodeFont }
53 206.585 /CMR12 rf /Fl 133[75 89 89 122 89 94 66 66
66 89 94 84 94 140 47 89 52 47 94 84 52 75 94 75 94 84
3[47 84 47 1[126 1[173 126 126 122 94 124 131 115 131
126 154 105 131 87 61 126 132 110 115 129 122 119 126
1[80 1[131 1[47 47 84 84 84 84 84 84 84 84 84 84 84 47
56 47 131 1[66 66 47 4[84 47 10[84 8[94 94 98 9[140 1[{
 TeXf7b6d320Encoding ReEncodeFont }82 172.154 /CMR12
rf /Fm 198[57 57 57 57 57 57 57 57 57 57 48[{
 TeXf7b6d320Encoding ReEncodeFont }10 100.423 /CMR7 rf
end
%%EndProlog
%%BeginSetup
%%Feature: *Resolution 600dpi
TeXDict begin
%%PaperSize: A4
 end
%%EndSetup
%%Page: 1 1
TeXDict begin 1 0 bop 4500 6000 a
 tx@Dict begin 90 Rot  end
 4500 6000 a 10688 1267
a Fm(1)p 0 TeXcolorgray 1 TeXcolorgray 4729 1377 a Fl(.)p
1 TeXcolorgray 1 TeXcolorgray 5716 2212 a @beginspecial
@setspecial
 tx@Dict begin STP newpath 0.8 SLW 0  setgray  0. true 3.8 neg 6.59999
neg 292.12639 13.79999 .5 Frame  gsave 3.0 -45 PtoC Shadow .25  setgray
gsave fill grestore stroke grestore gsave 1  setgray gsave fill grestore
stroke grestore gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
end
 
@endspecial 0 0 1 TeXcolorrgb 57 w Fk(Leptonic)68
b(Mixings)g(from)f(a)g(V)-17 b(ariational)68 b(Principle)p
1 TeXcolorgray 1 0 0 TeXcolorrgb 1 0 0 TeXcolorrgb 1 0 0
TeXcolorrgb 7185 3164 a(P)-6 b(aul)69 b(Harrison)p 0.0 0.6 0.0
TeXcolorrgb 0.0 0.6 0.0 TeXcolorrgb 0.0 0.6 0.0 TeXcolorrgb
6816 3892 a(Univ)-6 b(ersit)g(y)67 b(of)h(W)-17 b(arwic)-6
b(k)6977 4280 y(27th)67 b(Octob)6 b(er)67 b(2005)p 0 0 1
TeXcolorrgb 10871 5612 a
 0 setgray
 10871 5612 a 0 TeXcolorgray
0 0 1 TeXcolorrgb 4500 6000 a
 tx@Dict begin -90 Rot  end
 4500 6000 a eop end
%%Page: 2 2
TeXDict begin 2 1 bop 0 0 1 TeXcolorrgb 4500 6000 a
 tx@Dict begin 90 Rot  end
 4500
6000 a 10688 1267 a Fm(2)p 0.0 0.6 0.0 TeXcolorrgb 1 0 0
TeXcolorrgb 1 TeXcolorgray 0 TeXcolorgray Black 0 TeXcolorgray
1 TeXcolorgray 4729 1377 a Fl(.)p 0 TeXcolorgray 4729
1684 a Fk(Outline)68 b(of)g(T)-17 b(alk)p 4729 1712 1355
7 v 0 0 1 TeXcolorrgb 0 0 1 TeXcolorrgb 4862 2121 a Fj(\017)p
0 0 1 TeXcolorrgb 84 w Fl(Fla)-5 b(v)g(our)57 b(Ph)-5
b(ysics)56 b(-)h(the)e(Issues.)p 0 0 1 TeXcolorrgb 4862
2476 a Fj(\017)p 0 0 1 TeXcolorrgb 84 w Fl(Common)j(Origin)d(of)h
(Masses)i(and)e(Mixing)g(in)g(the)f(Standard)g(Mo)5 b(del)p
0 0 1 TeXcolorrgb 4862 2832 a Fj(\017)p 0 0 1 TeXcolorrgb
84 w Fl(Historical)57 b(A)-5 b(ttempts)56 b(to)g(Constrain)f(Masses)j
(and)e(Mixings)p 0 0 1 TeXcolorrgb 4862 3187 a Fj(\017)p
0 0 1 TeXcolorrgb 84 w Fl(Jarlsk)-5 b(og)57 b(Co)-5 b(v)c(ariance)p
0 0 1 TeXcolorrgb 4862 3543 a Fj(\017)p 0 0 1 TeXcolorrgb
84 w Fl(Fla)k(v)g(our-Symmetric)56 b(Jarlsk)-5 b(og)57
b(In)-5 b(v)c(arian)k(ts)p 0 0 1 TeXcolorrgb 4862 3898
a Fj(\017)p 0 0 1 TeXcolorrgb 84 w Fl(Co)g(v)c(arian)k(t)56
b(Constrain)-5 b(ts)56 b(from)g(Extremisation)p 0 0 1
TeXcolorrgb 4862 4253 a Fj(\017)p 0 0 1 TeXcolorrgb 84
w Fl(Some)h(Examples)p 0 0 1 TeXcolorrgb 4862 4609 a
Fj(\017)p 0 0 1 TeXcolorrgb 84 w Fl(The)f(F)-14 b(uture)p
0 TeXcolorgray 1 0 0 TeXcolorrgb 4729 4964 a(W)g(ork)56
b(done)g(in)f(collab)5 b(oration)56 b(with)f(Bill)h(Scott)f(\(RAL\))h
(-)g(hep-ph/0508012.)p 0.0 0.6 0.0 TeXcolorrgb 4729 5271
a(Dra)-5 b(ws)56 b(hea)-5 b(vily)56 b(on)g(and)g(extends)f(the)h
(seminal)g(con)-5 b(tributions)55 b(of)h(Cecilia)f(Jarlsk)-5
b(og)57 b(to)4729 5578 y(\015a)-5 b(v)g(our)56 b(ph)-5
b(ysics)57 b(from)f(1985)h Fj(!)f Fl(1988.)10871 5612
y
 0 setgray
 10871 5612 a 0 TeXcolorgray 0.0 0.6 0.0 TeXcolorrgb
4500 6000 a
 tx@Dict begin -90 Rot  end
 4500 6000 a eop end
%%Page: 3 3
TeXDict begin 3 2 bop 0.0 0.6 0.0 TeXcolorrgb 4500 6000
a
 tx@Dict begin 90 Rot  end
 4500 6000 a 10688 1267 a Fm(3)p 1 0 0 TeXcolorrgb 0
TeXcolorgray 1 TeXcolorgray 0 TeXcolorgray Black 0 TeXcolorgray
0 TeXcolorgray 0 TeXcolorgray 6221 1558 a @beginspecial
@setspecial
 tx@Dict begin STP newpath 0.8 SLW 0  setgray  0. true 3.8 neg 3.8
neg 221.8306 13.79999 .5 Frame  gsave 3.0 -45 PtoC Shadow .25  setgray
gsave fill grestore stroke grestore gsave 1  setgray gsave fill grestore
stroke grestore gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
end
 
@endspecial 0 0 1 TeXcolorrgb 56 w Fk(P)-6
b(arameters)66 b(of)h(the)g(Standard)i(Mo)6 b(del)p 0
TeXcolorgray 1 0 0 TeXcolorrgb 4729 2056 a Fl(The)56
b(Standard)e(Mo)5 b(del)56 b(\(minimally)g(extended)e(to)i(accommo)5
b(date)57 b(neutrino)d(masses,)4729 2363 y(analogously)j(to)f(the)f
(other)g(fermions\))h(has)h Fj(\030)f Fl(25)g(free)f(parameters:)p
0 0 1 TeXcolorrgb 0 0 1 TeXcolorrgb 4862 2719 a Fj(\017)p
0 0 1 TeXcolorrgb 84 w Fl(3)i(gauge)g(coupling)e(constan)-5
b(ts)56 b(-)p 0.0 0.6 0.0 TeXcolorrgb 57 w Fi(g)7265
2745 y Fh(1)7332 2719 y Fl(,)g Fi(g)7516 2745 y Fh(2)7584
2719 y Fl(,)g Fi(g)7768 2745 y Fh(3)p 0 0 1 TeXcolorrgb
0 0 1 TeXcolorrgb 4862 3076 a Fj(\017)p 0 0 1 TeXcolorrgb
84 w Fl(2)h(Higgs)g(parameters)f(-)p 0.0 0.6 0.0 TeXcolorrgb
57 w Fi(\026)p Fl(,)g Fi(\025)p 0 0 1 TeXcolorrgb 0 0 1
TeXcolorrgb 4862 3432 a Fj(\017)p 0 0 1 TeXcolorrgb 84
w Fl(6)h(quark)f(masses)i(-)p 0.0 0.6 0.0 TeXcolorrgb
56 w Fi(m)6465 3458 y Fg(d)6536 3432 y Fl(,)e Fi(m)6786
3458 y Fg(s)6850 3432 y Fl(,)g Fi(m)7100 3458 y Fg(b)7159
3432 y Fl(,)g Fi(m)7409 3458 y Fg(u)7488 3432 y Fl(,)g
Fi(m)7738 3458 y Fg(c)7798 3432 y Fl(,)g Fi(m)8048 3458
y Fg(t)p 0 0 1 TeXcolorrgb 0 0 1 TeXcolorrgb 4862 3788
a Fj(\017)p 0 0 1 TeXcolorrgb 84 w Fl(6)h(lepton)e(masses)j(-)p
0.0 0.6 0.0 TeXcolorrgb 57 w Fi(m)6503 3814 y Fg(e)6567
3788 y Fl(,)e Fi(m)6817 3814 y Fg(\026)6898 3788 y Fl(,)g
Fi(m)7148 3814 y Fg(\034)7223 3788 y Fl(,)g Fi(m)7473
3814 y Fh(1)7541 3788 y Fl(,)g Fi(m)7791 3814 y Fh(2)7860
3788 y Fl(,)g Fi(m)8110 3814 y Fh(3)p 0 0 1 TeXcolorrgb
0 0 1 TeXcolorrgb 4862 4144 a Fj(\017)p 0 0 1 TeXcolorrgb
84 w Fl(3)h(quark)f(mixing)g(angles)g(and)g(a)h(phase)f(-)p
0.0 0.6 0.0 TeXcolorrgb 56 w Fi(\022)7843 4170 y Fg(us)7977
4144 y Fl(,)g Fi(\022)8159 4170 y Fg(cb)8271 4144 y Fl(,)g
Fi(\022)8453 4170 y Fg(ub)8582 4144 y Fl(,)g Fi(\016)8760
4170 y Fg(q)p 0 0 1 TeXcolorrgb 0 0 1 TeXcolorrgb 4862
4500 a Fj(\017)p 0 0 1 TeXcolorrgb 84 w Fl(3)h(leptonic)e(mixing)h
(angles)h(and)e(another)g(phase)i(-)p 0.0 0.6 0.0 TeXcolorrgb
56 w Fi(\022)8480 4526 y Fh(12)8609 4500 y Fl(,)f Fi(\022)8791
4526 y Fh(23)8919 4500 y Fl(,)g Fi(\022)9101 4526 y Fh(13)9230
4500 y Fl(,)g Fi(\016)9408 4526 y Fg(l)9453 4500 y Fl(.)p
0 0 1 TeXcolorrgb 0.0 0.6 0.0 TeXcolorrgb 0 0 1 TeXcolorrgb
0.0 0.6 0.0 TeXcolorrgb 0 0 1 TeXcolorrgb 0.0 0.6 0.0
TeXcolorrgb 0 0 1 TeXcolorrgb 0.0 0.6 0.0 TeXcolorrgb
0 0 1 TeXcolorrgb 0.0 0.6 0.0 TeXcolorrgb 0 0 1 TeXcolorrgb
1 0 0 TeXcolorrgb 4729 4857 a(No)h(accepted)e(theory)g(for)g
(predicting)f(an)-5 b(y)57 b(of)f(these)g(\(or)f(relating)g(them)h(to)g
(eac)-5 b(h)56 b(other\).)p 0 TeXcolorgray 4729 5213
a(There)f(are,)h(of)g(course,)g(man)-5 b(y)56 b(e\013orts)h
(\(unsuccessful)e(or)h(unpro)-5 b(v)g(en\).)p 0.0 0.6 0.0
TeXcolorrgb 4729 5569 a(This)56 b(is)g(a)h(new)e(\(and)h(quite)f
(original\))g(one.)10871 5612 y
 0 setgray
 10871 5612 a 0 TeXcolorgray
0.0 0.6 0.0 TeXcolorrgb 4500 6000 a
 tx@Dict begin -90 Rot  end
 4500 6000 a eop end
%%Page: 4 4
TeXDict begin 4 3 bop 0.0 0.6 0.0 TeXcolorrgb 4500 6000
a
 tx@Dict begin 90 Rot  end
 4500 6000 a 10688 1267 a Fm(4)p 0 TeXcolorgray 1 0 0
TeXcolorrgb 0 0 1 TeXcolorrgb 1 0 0 TeXcolorrgb 0 TeXcolorgray
Black 0 TeXcolorgray 0 TeXcolorgray 0 TeXcolorgray 6551
1558 a @beginspecial @setspecial
 tx@Dict begin STP newpath 0.8 SLW 0  setgray  0. true 3.8 neg 6.59999
neg 175.72954 13.79999 .5 Frame  gsave 3.0 -45 PtoC Shadow .25  setgray
gsave fill grestore stroke grestore gsave 1  setgray gsave fill grestore
stroke grestore gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
end
 
@endspecial 0 0 1 TeXcolorrgb
57 w Fk(Fla)-6 b(v)g(our)68 b(Ph)-6 b(ysics:)90 b(the)67
b(Issues)p 0 TeXcolorgray 1 0 0 TeXcolorrgb 4729 2087
a Fl(20/25)58 b(of)e(SM)g(parameters)g(di\013eren)-5
b(tiate)54 b(b)5 b(et)-5 b(w)g(een)55 b(the)g(\015a)-5
b(v)g(ours)57 b(or)f(relate)f(them)h(to)g(eac)-5 b(h)4729
2399 y(other.)p 0 0 1 TeXcolorrgb 4729 2763 a(Most)57
b(of)f(the)f(phenomena)h(of)g(the)f(SM)i(are)e(parameterised)h(b)-5
b(y)56 b(these)g(quan)-5 b(tities)55 b(-)4729 3075 y
(mass-di\013erences)i(b)5 b(et)-5 b(w)g(een)55 b(fermions,)h(branc)-5
b(hing)55 b(fractions)g(in)h(w)-5 b(eak)56 b(deca)-5
b(ys,)57 b(CP)4729 3387 y(violation...)p 0.0 0.6 0.0
TeXcolorrgb 4729 3751 a(Gauge)g(sector)f(of)f(SM)i(has)f(only)g(3)h
(parameters)f(\(plus)f(2)h(Higgs)i(couplings\).)74 b(SM)56
b(is)4729 4063 y(in)-5 b(ternally)55 b(consisten)-5 b(t)55
b(with)g(only)h(one)g(family)g(of)g(quarks)g(and)g(leptons.)p
0 TeXcolorgray 4729 4427 a(Wh)-5 b(y)56 b(3)h(families?)p
1 0 0 TeXcolorrgb 74 w(I)f(can't)g(answ)-5 b(er)56 b(that.)p
0 TeXcolorgray 4729 4791 a(What)e(are)g(the)g(unmeasured)f(parameters?)
p 1 0 0 TeXcolorrgb 74 w(W)-14 b(e)54 b(are)h(w)-5 b(orking)54
b(on)g(neutrino)e(exp)5 b(erimen)-5 b(ts)54 b(to)4729
5103 y(try)h(to)h(answ)-5 b(er)56 b(that.)10871 5612
y
 0 setgray
 10871 5612 a 0 TeXcolorgray 1 0 0 TeXcolorrgb 4500
6000 a
 tx@Dict begin -90 Rot  end
 4500 6000 a eop end
%%Page: 5 5
TeXDict begin 5 4 bop 1 0 0 TeXcolorrgb 4500 6000 a
 tx@Dict begin 90 Rot  end
 4500
6000 a 10688 1267 a Fm(5)p 0 TeXcolorgray 1 0 0 TeXcolorrgb
0 TeXcolorgray 0.0 0.6 0.0 TeXcolorrgb 0 0 1 TeXcolorrgb
1 0 0 TeXcolorrgb 0 TeXcolorgray Black 0 TeXcolorgray
0 TeXcolorgray 0 TeXcolorgray 5925 1558 a @beginspecial
@setspecial
 tx@Dict begin STP newpath 0.8 SLW 0  setgray  0. true 3.8 neg 6.59999
neg 263.02844 13.79999 .5 Frame  gsave 3.0 -45 PtoC Shadow .25  setgray
gsave fill grestore stroke grestore gsave 1  setgray gsave fill grestore
stroke grestore gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
end
 
@endspecial 0 0 1 TeXcolorrgb 56 w Fk(Wh)-6
b(y)68 b(Suc)-6 b(h)69 b(P)-6 b(eculiar)68 b(Quark)f(Mass)h(Sp)6
b(ectra?)p 0 TeXcolorgray 1 0 0 TeXcolorrgb 5572 2099
a Fl(Charge)55 b(=)i(+)6488 2032 y Fh(2)p 6488 2060 61
7 v 6488 2159 a(3)8758 2099 y Fl(Charge)e(=)i Fj(\000)9677
2032 y Fh(1)p 9677 2060 V 9677 2159 a(3)p 1 0 0 TeXcolorrgb
1 0 0 TeXcolorrgb 4590 5381 a @beginspecial 20 @llx 40
@lly 350 @urx 360 @ury 2069 @rwi @setspecial
%%BeginDocument: mass1.eps
%!PS-Adobe-2.0 EPSF-2.0
%%BoundingBox:  20 40 350 360
%%Title: /home/phucal/Root/mass1.eps: Example2
%%Creator: ROOT Version 5.02/00
%%CreationDate: Fri Sep  2 14:56:09 2005
%%EndComments
%%BeginProlog
80 dict begin
/s {stroke} def /l {lineto} def /m {moveto} def /t {translate} def
/sw {stringwidth} def /r {rotate} def /rl {roll}  def /R {repeat} def
/d {rlineto} def /rm {rmoveto} def /gr {grestore} def /f {eofill} def
/c {setrgbcolor} def /lw {setlinewidth} def /sd {setdash} def
/cl {closepath} def /sf {scalefont setfont} def /black {0 setgray} def
/box {m dup 0 exch d exch 0 d 0 exch neg d cl} def
/NC{systemdict begin initclip end}def/C{NC box clip newpath}def
/bl {box s} def /bf {box f} def /Y { 0 exch d} def /X { 0 d} def 
/mp {newpath /y exch def /x exch def} def
/side {[w .77 mul w .23 mul] .385 w mul sd w 0 l currentpoint t -144 r} def
/mr {mp x y w2 0 360 arc} def /m24 {mr s} def /m20 {mr f} def
/mb {mp x y w2 add m w2 neg 0 d 0 w neg d w 0 d 0 w d cl} def
/mt {mp x y w2 add m w2 neg w neg d w 0 d cl} def
/m21 {mb f} def /m25 {mb s} def /m22 {mt f} def /m26{mt s} def
/m23 {mp x y w2 sub m w2 w d w neg 0 d cl f} def
/m27 {mp x y w2 add m w3 neg w2 neg d w3 w2 neg d w3 w2 d cl s} def
/m28 {mp x w2 sub y w2 sub w3 add m w3 0 d  0 w3 neg d w3 0 d 0 w3 d w3 0 d  0 w3 d w3 neg 0 d 0 w3 d w3 neg 0 d
 0 w3 neg d w3 neg 0 d cl s } def
/m29 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t
 4 {side} repeat cl fill gr} def
/m30 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t
 4 {side} repeat cl s gr} def
/m31 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d x w2 sub y w2 add m w w neg d x w2 sub y w2
 sub m w w d s} def
/m2 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d s} def
/m5 {mp x w2 sub y w2 sub m w w d x w2 sub y w2 add m w w neg d s} def
/reencdict 24 dict def /ReEncode {reencdict begin /nco&na exch def
/nfnam exch def /basefontname exch def /basefontdict basefontname findfont def
/newfont basefontdict maxlength dict def basefontdict {exch dup /FID ne
{dup /Encoding eq {exch dup length array copy newfont 3 1 roll put} {exch 
newfont 3 1 roll put} ifelse} {pop pop} ifelse } forall newfont
/FontName nfnam put nco&na aload pop nco&na length 2 idiv {newfont
/Encoding get 3 1 roll put} repeat nfnam newfont definefont pop end } def
/accvec [ 176 /agrave 181 /Agrave 190 /acircumflex 192 /Acircumflex
201 /adieresis 204 /Adieresis 209 /ccedilla 210 /Ccedilla 211 /eacute
212 /Eacute 213 /egrave 214 /Egrave 215 /ecircumflex 216 /Ecircumflex
217 /edieresis 218 /Edieresis 219 /icircumflex 220 /Icircumflex
221 /idieresis 222 /Idieresis 223 /ntilde 224 /Ntilde 226 /ocircumflex
228 /Ocircumflex 229 /odieresis 230 /Odieresis 231 /ucircumflex 236 /Ucircumflex
237 /udieresis 238 /Udieresis 239 /aring 242 /Aring 243 /ydieresis
244 /Ydieresis 246 /aacute 247 /Aacute 252 /ugrave 253 /Ugrave] def
/Times-Roman /Times-Roman accvec ReEncode
/Times-Italic /Times-Italic accvec ReEncode
/Times-Bold /Times-Bold accvec ReEncode
/Times-BoldItalic /Times-BoldItalic accvec ReEncode
/Helvetica /Helvetica accvec ReEncode
/Helvetica-Oblique /Helvetica-Oblique accvec ReEncode
/Helvetica-Bold /Helvetica-Bold accvec ReEncode
/Helvetica-BoldOblique /Helvetica-BoldOblique  accvec ReEncode
/Courier /Courier accvec ReEncode
/Courier-Oblique /Courier-Oblique accvec ReEncode
/Courier-Bold /Courier-Bold accvec ReEncode
/Courier-BoldOblique /Courier-BoldOblique accvec ReEncode
/oshow {gsave [] 0 sd true charpath stroke gr} def
/stwn { /fs exch def /fn exch def /text exch def fn findfont fs sf
 text sw pop xs add /xs exch def} def
/stwb { /fs exch def /fn exch def /nbas exch def /textf exch deftextf length /tlen exch def nbas tlen gt {/nbas tlendef} iffn findfont fs sf textf dup length nbas sub nbas getinterval sw
pop neg xs add /xs exch def} def
/accspe [ 65 /plusminus  66 /bar  67 /existential  68 /universal 
69 /exclam  70 /numbersign 71 /greater  72 /question  73 /integral 
74 /colon  75 /semicolon  76 /less  77 /bracketleft  78 /bracketright
79 /greaterequal 80 /braceleft 81 /braceright 82 /radical
83 /spade 84 /heart 85 /diamond 86 /club 87 /lessequal
88 /multiply 89 /percent 90 /infinity 48 /circlemultiply 49 /circleplus
50 /emptyset  51 /lozenge 52 /bullet 53 /arrowright 54 /arrowup
55 /arrowleft 56 /arrowdown 57 /arrowboth 48 /degree 44 /comma 43 /plus 45 /angle 42 /angleleft 47 /divide 61 /notequal 40 /equivalence 41 /second 97 /approxequal 98 /congruent 99 /perpendicular 100 /partialdiff 101 /florin 102 /intersection
 103 /union 104 /propersuperset 105 /reflexsuperset 106 /notsubset 107 /propersubset 108 /reflexsubset 109 /element 110 /notelement 111 /gradient 112 /logicaland 113 /logicalor 114 /arrowdblboth 115 /arrowdblleft 116 /arrowdblup 117 /arrowdblright
 118 /arrowdbldown 119 /ampersand 120 /omega1 121 /similar 122 /aleph ] def
/Symbol /Special accspe ReEncode
%%EndProlog
%%BeginSetup
newpath  gsave  .25 .25 scale 
%%EndSetup
 gsave  0 0 t black[  ] 0 sd 3 lw 1 1 1 c 2268 1538 0 0 bf 0 0 m 2 2 d 1534 Y 2264 X 2 2 d -2268 X -1538 Y f 0 0 m 2 2 d 2264 X 1534 Y 2 2 d -1538 Y -2268 X f black 340 192 m 1154 Y s
 gsave  212 1026
 t 90 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (Mass \(GeV\)) show  gr  391 192 m -51 X s
 gsave  283 192
 t 0 r 0 0 m /Helvetica-Bold findfont 39.0986 sf 0 0 m (-3) show  gr 
 gsave  218 163
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (10) show  gr  366 250 m -26 X s 366 284 m -26 X s 366 308 m -26 X s 366 327 m -26 X s 366 342 m -26 X s 366 355 m -26 X s 366 366 m -26 X s 366 376 m -26 X s 391 384 m -51 X s
 gsave  283 378
 t 0 r 0 0 m /Helvetica-Bold findfont 39.0986 sf 0 0 m (-2) show  gr 
 gsave  218 352
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (10) show  gr  366 442 m -26 X s 366 476 m -26 X s 366 500 m -26 X s 366 519 m -26 X s 366 534 m -26 X s 366 547 m -26 X s 366 558 m -26 X s 366 568 m -26 X s 391 577 m -51 X s
 gsave  290 570
 t 0 r 0 0 m /Helvetica-Bold findfont 39.0986 sf 0 0 m (-1) show  gr 
 gsave  225 544
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (10) show  gr  366 635 m -26 X s 366 668 m -26 X s 366 692 m -26 X s 366 711 m -26 X s 366 726 m -26 X s 366 739 m -26 X s 366 750 m -26 X s 366 760 m -26 X s 391 769 m -51 X s
 /xs 0 def (1) /Helvetica-Bold 58.6478 stwn  gsave  322 745
 t 0 r  xs neg 0 t 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (1) show  gr  366 827 m -26 X s 366 861 m -26 X s 366 885 m -26 X s 366 903 m -26 X s 366 919 m -26 X s 366 931 m -26 X s 366 943 m -26 X s 366 952 m -26 X s 391 961 m -51 X s
 /xs 0 def (10) /Helvetica-Bold 58.6478 stwn  gsave  322 938
 t 0 r  xs neg 0 t 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (10) show  gr  366 1019 m -26 X s 366 1053 m -26 X s 366 1077 m -26 X s 366 1096 m -26 X s 366 1111 m -26 X s 366 1124 m -26 X s 366 1135 m -26 X s 366 1145 m -26 X s 391 1153 m -51 X
 s
 gsave  296 1147
 t 0 r 0 0 m /Helvetica-Bold findfont 39.0986 sf 0 0 m (2) show  gr 
 gsave  231 1121
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (10) show  gr  366 1211 m -26 X s 366 1245 m -26 X s 366 1269 m -26 X s 366 1288 m -26 X s 366 1303 m -26 X s 366 1316 m -26 X s 366 1327 m -26 X s 366 1337 m -26 X s 391 1346 m -51 X s
 gsave  296 1342
 t 0 r 0 0 m /Helvetica-Bold findfont 39.0986 sf 0 0 m (3) show  gr 
 gsave  231 1313
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (10) show  gr 
 gsave  860 1176
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (t ~ 174 GeV) show  gr 
 gsave  860 766
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (c ~ 1.3 GeV) show  gr 
 gsave  828 303
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (u ~ 0.005 GeV) show  gr 
 gsave  1004 1352
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (3) show  gr 
 gsave  1004 1411
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (2) show  gr  6 lw 1004 1404 m 32 X s 1 0 0 c 340 1200 m 454 X s 0 1 0 c 340 791 m 454 X s 0 0 1 c 340 327 m 454 X s
 gr  gr 
showpage
end
%%EOF

%%EndDocument
 @endspecial 1 0 0 TeXcolorrgb 1 0 0 TeXcolorrgb 3126
w @beginspecial 20 @llx 40 @lly 350 @urx 360 @ury 2069
@rwi @setspecial
%%BeginDocument: mass2.eps
%!PS-Adobe-2.0 EPSF-2.0
%%BoundingBox:  20 40 350 360
%%Title: /home/phucal/Root/mass2.eps: Example2
%%Creator: ROOT Version 5.02/00
%%CreationDate: Fri Sep  2 15:24:18 2005
%%EndComments
%%BeginProlog
80 dict begin
/s {stroke} def /l {lineto} def /m {moveto} def /t {translate} def
/sw {stringwidth} def /r {rotate} def /rl {roll}  def /R {repeat} def
/d {rlineto} def /rm {rmoveto} def /gr {grestore} def /f {eofill} def
/c {setrgbcolor} def /lw {setlinewidth} def /sd {setdash} def
/cl {closepath} def /sf {scalefont setfont} def /black {0 setgray} def
/box {m dup 0 exch d exch 0 d 0 exch neg d cl} def
/NC{systemdict begin initclip end}def/C{NC box clip newpath}def
/bl {box s} def /bf {box f} def /Y { 0 exch d} def /X { 0 d} def 
/mp {newpath /y exch def /x exch def} def
/side {[w .77 mul w .23 mul] .385 w mul sd w 0 l currentpoint t -144 r} def
/mr {mp x y w2 0 360 arc} def /m24 {mr s} def /m20 {mr f} def
/mb {mp x y w2 add m w2 neg 0 d 0 w neg d w 0 d 0 w d cl} def
/mt {mp x y w2 add m w2 neg w neg d w 0 d cl} def
/m21 {mb f} def /m25 {mb s} def /m22 {mt f} def /m26{mt s} def
/m23 {mp x y w2 sub m w2 w d w neg 0 d cl f} def
/m27 {mp x y w2 add m w3 neg w2 neg d w3 w2 neg d w3 w2 d cl s} def
/m28 {mp x w2 sub y w2 sub w3 add m w3 0 d  0 w3 neg d w3 0 d 0 w3 d w3 0 d  0 w3 d w3 neg 0 d 0 w3 d w3 neg 0 d
 0 w3 neg d w3 neg 0 d cl s } def
/m29 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t
 4 {side} repeat cl fill gr} def
/m30 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t
 4 {side} repeat cl s gr} def
/m31 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d x w2 sub y w2 add m w w neg d x w2 sub y w2
 sub m w w d s} def
/m2 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d s} def
/m5 {mp x w2 sub y w2 sub m w w d x w2 sub y w2 add m w w neg d s} def
/reencdict 24 dict def /ReEncode {reencdict begin /nco&na exch def
/nfnam exch def /basefontname exch def /basefontdict basefontname findfont def
/newfont basefontdict maxlength dict def basefontdict {exch dup /FID ne
{dup /Encoding eq {exch dup length array copy newfont 3 1 roll put} {exch 
newfont 3 1 roll put} ifelse} {pop pop} ifelse } forall newfont
/FontName nfnam put nco&na aload pop nco&na length 2 idiv {newfont
/Encoding get 3 1 roll put} repeat nfnam newfont definefont pop end } def
/accvec [ 176 /agrave 181 /Agrave 190 /acircumflex 192 /Acircumflex
201 /adieresis 204 /Adieresis 209 /ccedilla 210 /Ccedilla 211 /eacute
212 /Eacute 213 /egrave 214 /Egrave 215 /ecircumflex 216 /Ecircumflex
217 /edieresis 218 /Edieresis 219 /icircumflex 220 /Icircumflex
221 /idieresis 222 /Idieresis 223 /ntilde 224 /Ntilde 226 /ocircumflex
228 /Ocircumflex 229 /odieresis 230 /Odieresis 231 /ucircumflex 236 /Ucircumflex
237 /udieresis 238 /Udieresis 239 /aring 242 /Aring 243 /ydieresis
244 /Ydieresis 246 /aacute 247 /Aacute 252 /ugrave 253 /Ugrave] def
/Times-Roman /Times-Roman accvec ReEncode
/Times-Italic /Times-Italic accvec ReEncode
/Times-Bold /Times-Bold accvec ReEncode
/Times-BoldItalic /Times-BoldItalic accvec ReEncode
/Helvetica /Helvetica accvec ReEncode
/Helvetica-Oblique /Helvetica-Oblique accvec ReEncode
/Helvetica-Bold /Helvetica-Bold accvec ReEncode
/Helvetica-BoldOblique /Helvetica-BoldOblique  accvec ReEncode
/Courier /Courier accvec ReEncode
/Courier-Oblique /Courier-Oblique accvec ReEncode
/Courier-Bold /Courier-Bold accvec ReEncode
/Courier-BoldOblique /Courier-BoldOblique accvec ReEncode
/oshow {gsave [] 0 sd true charpath stroke gr} def
/stwn { /fs exch def /fn exch def /text exch def fn findfont fs sf
 text sw pop xs add /xs exch def} def
/stwb { /fs exch def /fn exch def /nbas exch def /textf exch deftextf length /tlen exch def nbas tlen gt {/nbas tlendef} iffn findfont fs sf textf dup length nbas sub nbas getinterval sw
pop neg xs add /xs exch def} def
/accspe [ 65 /plusminus  66 /bar  67 /existential  68 /universal 
69 /exclam  70 /numbersign 71 /greater  72 /question  73 /integral 
74 /colon  75 /semicolon  76 /less  77 /bracketleft  78 /bracketright
79 /greaterequal 80 /braceleft 81 /braceright 82 /radical
83 /spade 84 /heart 85 /diamond 86 /club 87 /lessequal
88 /multiply 89 /percent 90 /infinity 48 /circlemultiply 49 /circleplus
50 /emptyset  51 /lozenge 52 /bullet 53 /arrowright 54 /arrowup
55 /arrowleft 56 /arrowdown 57 /arrowboth 48 /degree 44 /comma 43 /plus 45 /angle 42 /angleleft 47 /divide 61 /notequal 40 /equivalence 41 /second 97 /approxequal 98 /congruent 99 /perpendicular 100 /partialdiff 101 /florin 102 /intersection
 103 /union 104 /propersuperset 105 /reflexsuperset 106 /notsubset 107 /propersubset 108 /reflexsubset 109 /element 110 /notelement 111 /gradient 112 /logicaland 113 /logicalor 114 /arrowdblboth 115 /arrowdblleft 116 /arrowdblup 117 /arrowdblright
 118 /arrowdbldown 119 /ampersand 120 /omega1 121 /similar 122 /aleph ] def
/Symbol /Special accspe ReEncode
%%EndProlog
%%BeginSetup
newpath  gsave  .25 .25 scale 
%%EndSetup
 gsave  0 0 t black[  ] 0 sd 3 lw 1 1 1 c 2268 1538 0 0 bf 0 0 m 2 2 d 1534 Y 2264 X 2 2 d -2268 X -1538 Y f 0 0 m 2 2 d 2264 X 1534 Y 2 2 d -1538 Y -2268 X f black 340 256 m 1026 Y s
 gsave  212 964
 t 90 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (Mass \(GeV\)) show  gr  386 256 m -46 X s
 gsave  283 254
 t 0 r 0 0 m /Helvetica-Bold findfont 39.0986 sf 0 0 m (-3) show  gr 
 gsave  218 225
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (10) show  gr  363 333 m -23 X s 363 379 m -23 X s 363 411 m -23 X s 363 435 m -23 X s 363 456 m -23 X s 363 473 m -23 X s 363 488 m -23 X s 363 501 m -23 X s 386 513 m -46 X s
 gsave  283 508
 t 0 r 0 0 m /Helvetica-Bold findfont 39.0986 sf 0 0 m (-2) show  gr 
 gsave  218 482
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (10) show  gr  363 590 m -23 X s 363 635 m -23 X s 363 667 m -23 X s 363 692 m -23 X s 363 712 m -23 X s 363 729 m -23 X s 363 744 m -23 X s 363 757 m -23 X s 386 769 m -46 X s
 gsave  290 762
 t 0 r 0 0 m /Helvetica-Bold findfont 39.0986 sf 0 0 m (-1) show  gr 
 gsave  225 736
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (10) show  gr  363 846 m -23 X s 363 891 m -23 X s 363 923 m -23 X s 363 948 m -23 X s 363 968 m -23 X s 363 986 m -23 X s 363 1000 m -23 X s 363 1014 m -23 X s 386 1025 m -46 X s
 /xs 0 def (1) /Helvetica-Bold 58.6478 stwn  gsave  322 1002
 t 0 r  xs neg 0 t 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (1) show  gr  363 1102 m -23 X s 363 1148 m -23 X s 363 1180 m -23 X s 363 1204 m -23 X s 363 1225 m -23 X s 363 1242 m -23 X s 363 1257 m -23 X s 363 1270 m -23 X s 386 1282 m -46 X
 s
 /xs 0 def (10) /Helvetica-Bold 58.6478 stwn  gsave  322 1258
 t 0 r  xs neg 0 t 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (10) show  gr 
 gsave  860 1170
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (b ~ 4.5 GeV) show  gr 
 gsave  828 808
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (s ~ 0.175 GeV) show  gr 
 gsave  828 489
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (d ~ 0.010 GeV) show  gr 
 gsave  1020 1307
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (3) show  gr 
 gsave  1023 1365
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (1) show  gr  6 lw 1020 1359 m 32 X s
 gsave  984 1342
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (-\040) show  gr  1 0 0 c 340 1193 m 454 X s 0 1 0 c 340 831 m 454 X s 0 0 1 c 340 513 m 454 X s
 gr  gr 
showpage
end
%%EOF

%%EndDocument
 @endspecial 10871 5612 a
 0 setgray
 10871 5612 a 0 TeXcolorgray
1 0 0 TeXcolorrgb 4500 6000 a
 tx@Dict begin -90 Rot  end
 4500 6000 a eop end
%%Page: 6 6
TeXDict begin 6 5 bop 1 0 0 TeXcolorrgb 4500 6000 a
 tx@Dict begin 90 Rot  end
 4500
6000 a 10688 1267 a Fm(6)p 0 TeXcolorgray Black 0 TeXcolorgray
0 TeXcolorgray 0 TeXcolorgray 5893 1558 a @beginspecial
@setspecial
 tx@Dict begin STP newpath 0.8 SLW 0  setgray  0. true 3.8 neg 6.59999
neg 267.53006 13.79999 .5 Frame  gsave 3.0 -45 PtoC Shadow .25  setgray
gsave fill grestore stroke grestore gsave 1  setgray gsave fill grestore
stroke grestore gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
end
 
@endspecial 0 0 1 TeXcolorrgb 56 w Fk(Wh)-6
b(y)68 b(Suc)-6 b(h)69 b(P)-6 b(eculiar)67 b(Lepton)i(Mass)e(Sp)6
b(ectra?)p 0 TeXcolorgray 1 0 0 TeXcolorrgb 5572 2077
a Fl(Charge)55 b(=)i Fj(\000)p Fl(1)2360 b(Charge)55
b(=)i(0)p 1 0 0 TeXcolorrgb 1 0 0 TeXcolorrgb 4345 5359
a @beginspecial 20 @llx 40 @lly 340 @urx 360 @ury 2069
@rwi @setspecial
%%BeginDocument: mass3.eps
%!PS-Adobe-2.0 EPSF-2.0
%%BoundingBox:  20 40 340 360
%%Title: /home/phucal/Root/mass3.eps: Example2
%%Creator: ROOT Version 5.02/00
%%CreationDate: Fri Sep  2 14:57:53 2005
%%EndComments
%%BeginProlog
80 dict begin
/s {stroke} def /l {lineto} def /m {moveto} def /t {translate} def
/sw {stringwidth} def /r {rotate} def /rl {roll}  def /R {repeat} def
/d {rlineto} def /rm {rmoveto} def /gr {grestore} def /f {eofill} def
/c {setrgbcolor} def /lw {setlinewidth} def /sd {setdash} def
/cl {closepath} def /sf {scalefont setfont} def /black {0 setgray} def
/box {m dup 0 exch d exch 0 d 0 exch neg d cl} def
/NC{systemdict begin initclip end}def/C{NC box clip newpath}def
/bl {box s} def /bf {box f} def /Y { 0 exch d} def /X { 0 d} def 
/mp {newpath /y exch def /x exch def} def
/side {[w .77 mul w .23 mul] .385 w mul sd w 0 l currentpoint t -144 r} def
/mr {mp x y w2 0 360 arc} def /m24 {mr s} def /m20 {mr f} def
/mb {mp x y w2 add m w2 neg 0 d 0 w neg d w 0 d 0 w d cl} def
/mt {mp x y w2 add m w2 neg w neg d w 0 d cl} def
/m21 {mb f} def /m25 {mb s} def /m22 {mt f} def /m26{mt s} def
/m23 {mp x y w2 sub m w2 w d w neg 0 d cl f} def
/m27 {mp x y w2 add m w3 neg w2 neg d w3 w2 neg d w3 w2 d cl s} def
/m28 {mp x w2 sub y w2 sub w3 add m w3 0 d  0 w3 neg d w3 0 d 0 w3 d w3 0 d  0 w3 d w3 neg 0 d 0 w3 d w3 neg 0 d
 0 w3 neg d w3 neg 0 d cl s } def
/m29 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t
 4 {side} repeat cl fill gr} def
/m30 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t
 4 {side} repeat cl s gr} def
/m31 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d x w2 sub y w2 add m w w neg d x w2 sub y w2
 sub m w w d s} def
/m2 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d s} def
/m5 {mp x w2 sub y w2 sub m w w d x w2 sub y w2 add m w w neg d s} def
/reencdict 24 dict def /ReEncode {reencdict begin /nco&na exch def
/nfnam exch def /basefontname exch def /basefontdict basefontname findfont def
/newfont basefontdict maxlength dict def basefontdict {exch dup /FID ne
{dup /Encoding eq {exch dup length array copy newfont 3 1 roll put} {exch 
newfont 3 1 roll put} ifelse} {pop pop} ifelse } forall newfont
/FontName nfnam put nco&na aload pop nco&na length 2 idiv {newfont
/Encoding get 3 1 roll put} repeat nfnam newfont definefont pop end } def
/accvec [ 176 /agrave 181 /Agrave 190 /acircumflex 192 /Acircumflex
201 /adieresis 204 /Adieresis 209 /ccedilla 210 /Ccedilla 211 /eacute
212 /Eacute 213 /egrave 214 /Egrave 215 /ecircumflex 216 /Ecircumflex
217 /edieresis 218 /Edieresis 219 /icircumflex 220 /Icircumflex
221 /idieresis 222 /Idieresis 223 /ntilde 224 /Ntilde 226 /ocircumflex
228 /Ocircumflex 229 /odieresis 230 /Odieresis 231 /ucircumflex 236 /Ucircumflex
237 /udieresis 238 /Udieresis 239 /aring 242 /Aring 243 /ydieresis
244 /Ydieresis 246 /aacute 247 /Aacute 252 /ugrave 253 /Ugrave] def
/Times-Roman /Times-Roman accvec ReEncode
/Times-Italic /Times-Italic accvec ReEncode
/Times-Bold /Times-Bold accvec ReEncode
/Times-BoldItalic /Times-BoldItalic accvec ReEncode
/Helvetica /Helvetica accvec ReEncode
/Helvetica-Oblique /Helvetica-Oblique accvec ReEncode
/Helvetica-Bold /Helvetica-Bold accvec ReEncode
/Helvetica-BoldOblique /Helvetica-BoldOblique  accvec ReEncode
/Courier /Courier accvec ReEncode
/Courier-Oblique /Courier-Oblique accvec ReEncode
/Courier-Bold /Courier-Bold accvec ReEncode
/Courier-BoldOblique /Courier-BoldOblique accvec ReEncode
/oshow {gsave [] 0 sd true charpath stroke gr} def
/stwn { /fs exch def /fn exch def /text exch def fn findfont fs sf
 text sw pop xs add /xs exch def} def
/stwb { /fs exch def /fn exch def /nbas exch def /textf exch deftextf length /tlen exch def nbas tlen gt {/nbas tlendef} iffn findfont fs sf textf dup length nbas sub nbas getinterval sw
pop neg xs add /xs exch def} def
/accspe [ 65 /plusminus  66 /bar  67 /existential  68 /universal 
69 /exclam  70 /numbersign 71 /greater  72 /question  73 /integral 
74 /colon  75 /semicolon  76 /less  77 /bracketleft  78 /bracketright
79 /greaterequal 80 /braceleft 81 /braceright 82 /radical
83 /spade 84 /heart 85 /diamond 86 /club 87 /lessequal
88 /multiply 89 /percent 90 /infinity 48 /circlemultiply 49 /circleplus
50 /emptyset  51 /lozenge 52 /bullet 53 /arrowright 54 /arrowup
55 /arrowleft 56 /arrowdown 57 /arrowboth 48 /degree 44 /comma 43 /plus 45 /angle 42 /angleleft 47 /divide 61 /notequal 40 /equivalence 41 /second 97 /approxequal 98 /congruent 99 /perpendicular 100 /partialdiff 101 /florin 102 /intersection
 103 /union 104 /propersuperset 105 /reflexsuperset 106 /notsubset 107 /propersubset 108 /reflexsubset 109 /element 110 /notelement 111 /gradient 112 /logicaland 113 /logicalor 114 /arrowdblboth 115 /arrowdblleft 116 /arrowdblup 117 /arrowdblright
 118 /arrowdbldown 119 /ampersand 120 /omega1 121 /similar 122 /aleph ] def
/Symbol /Special accspe ReEncode
%%EndProlog
%%BeginSetup
newpath  gsave  .25 .25 scale 
%%EndSetup
 gsave  0 0 t black[  ] 0 sd 3 lw 1 1 1 c 2268 1538 0 0 bf 0 0 m 2 2 d 1534 Y 2264 X 2 2 d -2268 X -1538 Y f 0 0 m 2 2 d 2264 X 1534 Y 2 2 d -1538 Y -2268 X f black 340 220 m 1098 Y s
 gsave  212 1000
 t 90 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (Mass \(GeV\)) show  gr  389 220 m -49 X s
 gsave  283 215
 t 0 r 0 0 m /Helvetica-Bold findfont 39.0986 sf 0 0 m (-4) show  gr 
 gsave  218 189
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (10) show  gr  364 286 m -24 X s 364 325 m -24 X s 364 352 m -24 X s 364 373 m -24 X s 364 391 m -24 X s 364 405 m -24 X s 364 418 m -24 X s 364 429 m -24 X s 389 439 m -49 X s
 gsave  283 437
 t 0 r 0 0 m /Helvetica-Bold findfont 39.0986 sf 0 0 m (-3) show  gr 
 gsave  218 407
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (10) show  gr  364 506 m -24 X s 364 544 m -24 X s 364 572 m -24 X s 364 593 m -24 X s 364 610 m -24 X s 364 625 m -24 X s 364 638 m -24 X s 364 649 m -24 X s 389 659 m -49 X s
 gsave  283 655
 t 0 r 0 0 m /Helvetica-Bold findfont 39.0986 sf 0 0 m (-2) show  gr 
 gsave  218 629
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (10) show  gr  364 725 m -24 X s 364 764 m -24 X s 364 791 m -24 X s 364 813 m -24 X s 364 830 m -24 X s 364 845 m -24 X s 364 857 m -24 X s 364 869 m -24 X s 389 879 m -49 X s
 gsave  290 873
 t 0 r 0 0 m /Helvetica-Bold findfont 39.0986 sf 0 0 m (-1) show  gr 
 gsave  225 847
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (10) show  gr  364 945 m -24 X s 364 984 m -24 X s 364 1011 m -24 X s 364 1032 m -24 X s 364 1050 m -24 X s 364 1064 m -24 X s 364 1077 m -24 X s 364 1088 m -24 X s 389 1098 m -49 X s
 /xs 0 def (1) /Helvetica-Bold 58.6478 stwn  gsave  322 1075
 t 0 r  xs neg 0 t 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (1) show  gr  364 1165 m -24 X s 364 1203 m -24 X s 364 1231 m -24 X s 364 1252 m -24 X s 364 1269 m -24 X s 364 1284 m -24 X s 364 1297 m -24 X s 364 1308 m -24 X s 389 1318 m -49 X
 s
 /xs 0 def (10) /Helvetica-Bold 58.6478 stwn  gsave  322 1295
 t 0 r  xs neg 0 t 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (10) show  gr 
 gsave  857 1127
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m ( ~ 1.777 GeV) show  gr 
 gsave  831 1127
 t 0 r 0 0 m /Symbol findfont 58.6478 sf 0 0 m (t) show  gr 
 gsave  863 867
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m ( ~ 0.105 GeV) show  gr 
 gsave  828 867
 t 0 r 0 0 m /Symbol findfont 58.6478 sf 0 0 m (m) show  gr 
 gsave  811 349
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (e ~ 0.0005 GeV) show  gr 
 gsave  987 1359
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (- 1) show  gr  1 0 0 c 6 lw 340 1153 m 454 X s 0 1 0 c 340 883 m 454 X s 0 0 1 c 340 373 m 454 X s
 gr  gr 
showpage
end
%%EOF

%%EndDocument
 @endspecial 1 0 0 TeXcolorrgb 1 0 0 TeXcolorrgb 7472
5216 a @beginspecial 30 @llx 50 @lly 420 @urx 320 @ury
2494 @rwi @setspecial
%%BeginDocument: mass4.eps
%!PS-Adobe-2.0 EPSF-2.0
%%BoundingBox:  30 50 420 320
%%Title: /home/phucal/Root/mass4.eps: Example2
%%Creator: ROOT Version 5.02/00
%%CreationDate: Fri Sep  2 15:05:44 2005
%%EndComments
%%BeginProlog
80 dict begin
/s {stroke} def /l {lineto} def /m {moveto} def /t {translate} def
/sw {stringwidth} def /r {rotate} def /rl {roll}  def /R {repeat} def
/d {rlineto} def /rm {rmoveto} def /gr {grestore} def /f {eofill} def
/c {setrgbcolor} def /lw {setlinewidth} def /sd {setdash} def
/cl {closepath} def /sf {scalefont setfont} def /black {0 setgray} def
/box {m dup 0 exch d exch 0 d 0 exch neg d cl} def
/NC{systemdict begin initclip end}def/C{NC box clip newpath}def
/bl {box s} def /bf {box f} def /Y { 0 exch d} def /X { 0 d} def 
/mp {newpath /y exch def /x exch def} def
/side {[w .77 mul w .23 mul] .385 w mul sd w 0 l currentpoint t -144 r} def
/mr {mp x y w2 0 360 arc} def /m24 {mr s} def /m20 {mr f} def
/mb {mp x y w2 add m w2 neg 0 d 0 w neg d w 0 d 0 w d cl} def
/mt {mp x y w2 add m w2 neg w neg d w 0 d cl} def
/m21 {mb f} def /m25 {mb s} def /m22 {mt f} def /m26{mt s} def
/m23 {mp x y w2 sub m w2 w d w neg 0 d cl f} def
/m27 {mp x y w2 add m w3 neg w2 neg d w3 w2 neg d w3 w2 d cl s} def
/m28 {mp x w2 sub y w2 sub w3 add m w3 0 d  0 w3 neg d w3 0 d 0 w3 d w3 0 d  0 w3 d w3 neg 0 d 0 w3 d w3 neg 0 d
 0 w3 neg d w3 neg 0 d cl s } def
/m29 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t
 4 {side} repeat cl fill gr} def
/m30 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t
 4 {side} repeat cl s gr} def
/m31 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d x w2 sub y w2 add m w w neg d x w2 sub y w2
 sub m w w d s} def
/m2 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d s} def
/m5 {mp x w2 sub y w2 sub m w w d x w2 sub y w2 add m w w neg d s} def
/reencdict 24 dict def /ReEncode {reencdict begin /nco&na exch def
/nfnam exch def /basefontname exch def /basefontdict basefontname findfont def
/newfont basefontdict maxlength dict def basefontdict {exch dup /FID ne
{dup /Encoding eq {exch dup length array copy newfont 3 1 roll put} {exch 
newfont 3 1 roll put} ifelse} {pop pop} ifelse } forall newfont
/FontName nfnam put nco&na aload pop nco&na length 2 idiv {newfont
/Encoding get 3 1 roll put} repeat nfnam newfont definefont pop end } def
/accvec [ 176 /agrave 181 /Agrave 190 /acircumflex 192 /Acircumflex
201 /adieresis 204 /Adieresis 209 /ccedilla 210 /Ccedilla 211 /eacute
212 /Eacute 213 /egrave 214 /Egrave 215 /ecircumflex 216 /Ecircumflex
217 /edieresis 218 /Edieresis 219 /icircumflex 220 /Icircumflex
221 /idieresis 222 /Idieresis 223 /ntilde 224 /Ntilde 226 /ocircumflex
228 /Ocircumflex 229 /odieresis 230 /Odieresis 231 /ucircumflex 236 /Ucircumflex
237 /udieresis 238 /Udieresis 239 /aring 242 /Aring 243 /ydieresis
244 /Ydieresis 246 /aacute 247 /Aacute 252 /ugrave 253 /Ugrave] def
/Times-Roman /Times-Roman accvec ReEncode
/Times-Italic /Times-Italic accvec ReEncode
/Times-Bold /Times-Bold accvec ReEncode
/Times-BoldItalic /Times-BoldItalic accvec ReEncode
/Helvetica /Helvetica accvec ReEncode
/Helvetica-Oblique /Helvetica-Oblique accvec ReEncode
/Helvetica-Bold /Helvetica-Bold accvec ReEncode
/Helvetica-BoldOblique /Helvetica-BoldOblique  accvec ReEncode
/Courier /Courier accvec ReEncode
/Courier-Oblique /Courier-Oblique accvec ReEncode
/Courier-Bold /Courier-Bold accvec ReEncode
/Courier-BoldOblique /Courier-BoldOblique accvec ReEncode
/oshow {gsave [] 0 sd true charpath stroke gr} def
/stwn { /fs exch def /fn exch def /text exch def fn findfont fs sf
 text sw pop xs add /xs exch def} def
/stwb { /fs exch def /fn exch def /nbas exch def /textf exch deftextf length /tlen exch def nbas tlen gt {/nbas tlendef} iffn findfont fs sf textf dup length nbas sub nbas getinterval sw
pop neg xs add /xs exch def} def
/accspe [ 65 /plusminus  66 /bar  67 /existential  68 /universal 
69 /exclam  70 /numbersign 71 /greater  72 /question  73 /integral 
74 /colon  75 /semicolon  76 /less  77 /bracketleft  78 /bracketright
79 /greaterequal 80 /braceleft 81 /braceright 82 /radical
83 /spade 84 /heart 85 /diamond 86 /club 87 /lessequal
88 /multiply 89 /percent 90 /infinity 48 /circlemultiply 49 /circleplus
50 /emptyset  51 /lozenge 52 /bullet 53 /arrowright 54 /arrowup
55 /arrowleft 56 /arrowdown 57 /arrowboth 48 /degree 44 /comma 43 /plus 45 /angle 42 /angleleft 47 /divide 61 /notequal 40 /equivalence 41 /second 97 /approxequal 98 /congruent 99 /perpendicular 100 /partialdiff 101 /florin 102 /intersection
 103 /union 104 /propersuperset 105 /reflexsuperset 106 /notsubset 107 /propersubset 108 /reflexsubset 109 /element 110 /notelement 111 /gradient 112 /logicaland 113 /logicalor 114 /arrowdblboth 115 /arrowdblleft 116 /arrowdblup 117 /arrowdblright
 118 /arrowdbldown 119 /ampersand 120 /omega1 121 /similar 122 /aleph ] def
/Symbol /Special accspe ReEncode
%%EndProlog
%%BeginSetup
newpath  gsave  .25 .25 scale 
%%EndSetup
 gsave  0 0 t black[  ] 0 sd 3 lw 1 1 1 c 2268 1538 0 0 bf 0 0 m 2 2 d 1534 Y 2264 X 2 2 d -2268 X -1538 Y f 0 0 m 2 2 d 2264 X 1534 Y 2 2 d -1538 Y -2268 X f black 340 308 m 922 Y s
 gsave  218 1212
 t 90 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (\)) show  gr 
 gsave  192 1189
 t 90 r 0 0 m /Helvetica-Bold findfont 39.0986 sf 0 0 m (2) show  gr 
 gsave  218 1082
 t 90 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m ( \(eV) show  gr 
 gsave  195 1059
 t 90 r 0 0 m /Helvetica-Bold findfont 39.0986 sf 0 0 m (2) show  gr 
 gsave  218 896
 t 90 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m ( Mass) show  gr 
 gsave  218 860
 t 90 r 0 0 m /Symbol findfont 58.6478 sf 0 0 m (D) show  gr  381 308 m -41 X s
 gsave  283 306
 t 0 r 0 0 m /Helvetica-Bold findfont 39.0986 sf 0 0 m (-3) show  gr 
 gsave  218 277
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (10) show  gr  361 400 m -21 X s 361 454 m -21 X s 361 493 m -21 X s 361 523 m -21 X s 361 547 m -21 X s 361 568 m -21 X s 361 585 m -21 X s 361 601 m -21 X s 381 615 m -41 X s
 gsave  283 609
 t 0 r 0 0 m /Helvetica-Bold findfont 39.0986 sf 0 0 m (-2) show  gr 
 gsave  218 583
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (10) show  gr  361 708 m -21 X s 361 762 m -21 X s 361 800 m -21 X s 361 830 m -21 X s 361 854 m -21 X s 361 875 m -21 X s 361 893 m -21 X s 361 909 m -21 X s 381 923 m -41 X s
 gsave  290 919
 t 0 r 0 0 m /Helvetica-Bold findfont 39.0986 sf 0 0 m (-1) show  gr 
 gsave  225 893
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (10) show  gr  361 1015 m -21 X s 361 1069 m -21 X s 361 1108 m -21 X s 361 1138 m -21 X s 361 1162 m -21 X s 361 1183 m -21 X s 361 1200 m -21 X s 361 1216 m -21 X s 381 1230 m -41 X s
 /xs 0 def (1) /Helvetica-Bold 58.6478 stwn  gsave  322 1207
 t 0 r  xs neg 0 t 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (1) show  gr 
 gsave  1548 844
 t 0 r 0 0 m /Helvetica-Bold findfont 39.0986 sf 0 0 m (2) show  gr 
 gsave  1460 818
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m ( eV) show  gr 
 gsave  1424 847
 t 0 r 0 0 m /Helvetica-Bold findfont 39.0986 sf 0 0 m (-3) show  gr 
 gsave  1342 818
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m ( 10) show  gr 
 gsave  1313 818
 t 0 r 0 0 m /Symbol findfont 58.6478 sf 0 0 m (´) show  gr 
 gsave  1131 818
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (| ~ 2.5\040) show  gr 
 gsave  1108 837
 t 0 r 0 0 m /Helvetica-Bold findfont 39.0986 sf 0 0 m (2) show  gr 
 gsave  1108 798
 t 0 r 0 0 m /Helvetica-Bold findfont 39.0986 sf 0 0 m (1) show  gr 
 gsave  1007 818
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m ( - m) show  gr 
 gsave  984 844
 t 0 r 0 0 m /Helvetica-Bold findfont 39.0986 sf 0 0 m (2) show  gr 
 gsave  984 785
 t 0 r 0 0 m /Helvetica-Bold findfont 39.0986 sf 0 0 m (3) show  gr 
 gsave  919 818
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (|m) show  gr 
 gsave  1522 613
 t 0 r 0 0 m /Helvetica-Bold findfont 39.0986 sf 0 0 m (2) show  gr 
 gsave  1434 586
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m ( eV) show  gr 
 gsave  1398 616
 t 0 r 0 0 m /Helvetica-Bold findfont 39.0986 sf 0 0 m (-5) show  gr 
 gsave  1316 586
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m ( 10) show  gr 
 gsave  1287 586
 t 0 r 0 0 m /Symbol findfont 58.6478 sf 0 0 m (´) show  gr 
 gsave  1157 586
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (| ~ 8\040) show  gr 
 gsave  1134 606
 t 0 r 0 0 m /Helvetica-Bold findfont 39.0986 sf 0 0 m (2) show  gr 
 gsave  1134 570
 t 0 r 0 0 m /Helvetica-Bold findfont 39.0986 sf 0 0 m (1) show  gr 
 gsave  1033 586
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m ( - m) show  gr 
 gsave  1010 616
 t 0 r 0 0 m /Helvetica-Bold findfont 39.0986 sf 0 0 m (2) show  gr 
 gsave  1010 557
 t 0 r 0 0 m /Helvetica-Bold findfont 39.0986 sf 0 0 m (2) show  gr 
 gsave  945 586
 t 0 r 0 0 m /Helvetica-Bold findfont 58.6478 sf 0 0 m (|m) show  gr 
 gsave  1228 1000
 t 0 r 0 0 m /Symbol findfont 58.6478 sf 0 0 m (n) show  gr  1 0 0 c 6 lw 340 830 m 454 X s 0 0 1 c 340 600 m 454 X s
 gr  gr 
showpage
end
%%EOF

%%EndDocument
 @endspecial 10871 5612 a
 0 setgray
 10871 5612 a 0 TeXcolorgray
1 0 0 TeXcolorrgb 4500 6000 a
 tx@Dict begin -90 Rot  end
 4500 6000 a eop end
%%Page: 7 7
TeXDict begin 7 6 bop 1 0 0 TeXcolorrgb 4500 6000 a
 tx@Dict begin 90 Rot  end
 4500
6000 a 10688 1267 a Fm(7)p 0 TeXcolorgray Black 0 TeXcolorgray
0 TeXcolorgray 0 TeXcolorgray 5711 1558 a @beginspecial
@setspecial
 tx@Dict begin STP newpath 0.8 SLW 0  setgray  0. true 3.8 neg 6.59999
neg 292.90475 13.79999 .5 Frame  gsave 3.0 -45 PtoC Shadow .25  setgray
gsave fill grestore stroke grestore gsave 1  setgray gsave fill grestore
stroke grestore gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
end
 
@endspecial 0 0 1 TeXcolorrgb 56 w Fk(Wh)-6
b(y)68 b(Suc)-6 b(h)69 b(P)-6 b(eculiar)67 b(F)-17 b(ermion)68
b(Mixing)g(Matrices?)p 0 TeXcolorgray 1 0 0 TeXcolorrgb
4729 1956 a Fl(MNS)57 b(\()p Fi(U)5340 1982 y Fg(M)12
b(N)g(S)5666 1956 y Fl(\))56 b(and)f(CKM)i(\()p Fi(V)6743
1982 y Fg(C)8 b(K)g(M)7085 1956 y Fl(\))56 b(matrices)g(parameterise)g
(couplings)f(of)h(mass)4729 2249 y(eigenstates)g(to)g
Fi(W)23 b Fl(:)p 0.0 0.6 0.0 TeXcolorrgb 6094 2802 a
Fi(d)470 b(s)552 b(b)p 1 0 0 TeXcolorrgb 0 TeXcolorgray
4729 3527 a Fj(j)p Fi(V)4875 3553 y Fg(C)8 b(K)g(M)5218
3527 y Fj(j)47 b(\030)p 1 0 0 TeXcolorrgb 5495 3235 a
Fi(u)5507 3547 y(c)5512 3859 y(t)p 0 TeXcolorgray 5702
3026 a Ff(0)5702 3329 y(B)5702 3433 y(B)5702 3536 y(B)5702
3646 y(@)p 0 0 1 TeXcolorrgb 5891 3235 a Fl(0)p Fi(:)p
Fl(974)p 0 TeXcolorgray 0 0 1 TeXcolorrgb 224 w(0)p Fi(:)p
Fl(224)p 0 TeXcolorgray 0 0 1 TeXcolorrgb 265 w(0)p Fi(:)p
Fl(004)p 0 TeXcolorgray 0 0 1 TeXcolorrgb 5891 3547 a(0)p
Fi(:)p Fl(224)p 0 TeXcolorgray 0 0 1 TeXcolorrgb 224
w(0)p Fi(:)p Fl(974)p 0 TeXcolorgray 0 0 1 TeXcolorrgb
307 w(0)p Fi(:)p Fl(04)p 0 TeXcolorgray 0 0 1 TeXcolorrgb
5933 3859 a(0)p Fi(:)p Fl(01)p 0 TeXcolorgray 0 0 1 TeXcolorrgb
308 w(0)p Fi(:)p Fl(04)p 0 TeXcolorgray 0 0 1 TeXcolorrgb
307 w(0)p Fi(:)p Fl(999)p 0 TeXcolorgray 7612 3026 a
Ff(1)7612 3329 y(C)7612 3433 y(C)7612 3536 y(C)7612 3646
y(A)p 1 0 0 TeXcolorrgb 0 TeXcolorgray 1 0 0 TeXcolorrgb
0.0 0.6 0.0 TeXcolorrgb 6019 4508 a Fi(\027)6102 4534
y Fh(1)6641 4508 y Fi(\027)6724 4534 y Fh(2)7262 4508
y Fi(\027)7345 4534 y Fh(3)p 1 0 0 TeXcolorrgb 0 TeXcolorgray
4729 5234 a Fj(j)p Fi(U)4891 5260 y Fg(M)12 b(N)g(S)5217
5234 y Fj(j)48 b(\030)p 1 0 0 TeXcolorrgb 5506 4941 a
Fi(e)5495 5253 y(\026)5499 5565 y(\034)p 0 TeXcolorgray
5707 4733 a Ff(0)5707 5036 y(B)5707 5139 y(B)5707 5243
y(B)5707 5353 y(@)5939 4941 y Fl(0)p Fi(:)p Fl(82)p 0 0 1
TeXcolorrgb 307 w(0)p Fi(:)p Fl(58)p 0 TeXcolorgray 0 0 1
TeXcolorrgb 226 w Fi(<)g Fl(0)p Fi(:)p Fl(17)p 0 TeXcolorgray
0 TeXcolorgray 5939 5253 a(0)p Fi(:)p Fl(41)p 0 TeXcolorgray
307 w(0)p Fi(:)p Fl(58)p 0 0 1 TeXcolorrgb 315 w(0)p
Fi(:)p Fl(71)p 0 TeXcolorgray 5939 5565 a(0)p Fi(:)p
Fl(41)307 b(0)p Fi(:)p Fl(58)315 b(0)p Fi(:)p Fl(71)7549
4733 y Ff(1)7549 5036 y(C)7549 5139 y(C)7549 5243 y(C)7549
5353 y(A)p 1 0 0 TeXcolorrgb 0 TeXcolorgray 1 0 0 TeXcolorrgb
1 0 0 TeXcolorrgb 1 0 0 TeXcolorrgb 7575 4223 a @beginspecial
30 @llx 120 @lly 180 @urx 210 @ury 1984 @rwi @setspecial
%%BeginDocument: Figs/Feyn/via.eps
%!PS-Adobe-2.0 EPSF-2.0
%%BoundingBox: 30 120 180 210
%%Title: via.eps
%%Creator: HIGZ Version 1.29/04
%%CreationDate: 2005/10/21   14.45
%%EndComments
%%BeginProlog
80 dict begin
/s {stroke} def /l {lineto} def /m {moveto} def /t {translate} def
/sw {stringwidth} def /r {rotate} def /rl {roll}  def /R {repeat} def
/d {rlineto} def /rm {rmoveto} def /gr {grestore} def /f {eofill} def
/c {setrgbcolor} def /lw {setlinewidth} def /sd {setdash} def
/cl {closepath} def /sf {scalefont setfont} def /black {0 setgray} def
/box {m dup 0 exch d exch 0 d 0 exch neg d cl} def
/NC{systemdict begin initclip end}def/C{NC box clip newpath}def
/bl {box s} def /bf {box f} def /Y { 0 exch d} def /X { 0 d} def 
/mp {newpath /y exch def /x exch def} def
/side {[w .77 mul w .23 mul] .385 w mul sd w 0 l currentpoint t -144 r} def
/mr {mp x y w2 0 360 arc} def /m24 {mr s} def /m20 {mr f} def
/mb {mp x y w2 add m w2 neg 0 d 0 w neg d w 0 d 0 w d cl} def
/mt {mp x y w2 add m w2 neg w neg d w 0 d cl} def
/m21 {mb f} def /m25 {mb s} def /m22 {mt f} def /m26  {mt s} def
/m23 {mp x y w2 sub m w2 w d w neg 0 d cl f} def
/m27 {mp x y w2 add m w3 neg w2 neg d w3 w2 neg d w3  w2 d cl s} def
/m28 {mp x w2 sub y w2 sub w3 add m w3 0 d 0 w3 neg d w3 0 d 0 w3 d w3 0 d
 0 w3 d w3 neg 0 d 0 w3 d w3 neg 0 d
 0 w3 neg d w3 neg 0 d cl s } def
/m29 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t
 4 {side} repeat cl fill gr} def
/m30 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t
 5 {side} repeat s gr} def
/m31 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d
 x w2 sub y w2 add m w w neg d x w2 sub y w2
 sub m w w d s} def
/m2 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d s} def
/m5 {mp x w2 sub y w2 sub m w w d x w2 sub y w2 add m w w neg d s} def
/reencdict 24 dict def /ReEncode {reencdict begin /nco&na exch def
/nfnam exch def /basefontname exch def /basefontdict basefontname findfont def
/newfont basefontdict maxlength dict def basefontdict {exch dup /FID ne
{dup /Encoding eq {exch dup length array copy newfont 3 1 roll put} {exch
newfont 3 1 roll put} ifelse} {pop pop} ifelse } forall newfont
/FontName nfnam put nco&na aload pop nco&na length 2 idiv {newfont
/Encoding get 3 1 roll put} repeat nfnam newfont definefont pop end } def
/accvec [ 176 /agrave 181 /Agrave 190 /acircumflex 192 /Acircumflex
201 /adieresis 204 /Adieresis 209 /ccedilla 210 /Ccedilla 211 /eacute
212 /Eacute 213 /egrave 214 /Egrave 215 /ecircumflex 216 /Ecircumflex
217 /edieresis 218 /Edieresis 219 /icircumflex 220 /Icircumflex
221 /idieresis 222 /Idieresis 223 /ntilde 224 /Ntilde 226 /ocircumflex
228 /Ocircumflex 229 /odieresis 230 /Odieresis 231 /ucircumflex 236 /Ucircumflex
237 /udieresis 238 /Udieresis 239 /aring 242 /Aring 243 /ydieresis
244 /Ydieresis 246 /aacute 247 /Aacute 252 /ugrave 253 /Ugrave] def
/Times-Roman /Times-Roman accvec ReEncode
/Times-Italic /Times-Italic accvec ReEncode
/Times-Bold /Times-Bold accvec ReEncode
/Times-BoldItalic /Times-BoldItalic accvec ReEncode
/Helvetica /Helvetica accvec ReEncode
/Helvetica-Oblique /Helvetica-Oblique accvec ReEncode
/Helvetica-Bold /Helvetica-Bold accvec ReEncode
/Helvetica-BoldOblique /Helvetica-BoldOblique  accvec ReEncode
/Courier /Courier accvec ReEncode
/Courier-Oblique /Courier-Oblique accvec ReEncode
/Courier-Bold /Courier-Bold accvec ReEncode
/Courier-BoldOblique /Courier-BoldOblique accvec ReEncode
/oshow {gsave [] 0 sd true charpath stroke gr} def
/stwn { /fs exch def /fn exch def /text exch def fn findfont fs sf
 text sw pop xs add /xs exch def} def
/stwb { /fs exch def /fn exch def /nbas exch def /textf exch def
textf length /tlen exch def nbas tlen gt {/nbas tlen  def} if
fn findfont fs sf textf dup length nbas sub nbas getinterval sw
pop neg xs add /xs exch def} def
/accspe [ 65 /plusminus 66 /bar 67 /existential 68 /universal
69 /exclam 70 /numbersign 71 /greater 72 /question 73 /integral
74 /colon 75 /semicolon 76 /less 77 /bracketleft 78 /bracketright
79 /greaterequal 80 /braceleft 81 /braceright 82 /radical
83 /spade 84 /heart 85 /diamond 86 /club 87 /lessequal
88 /multiply 89 /percent 90 /infinity 48 /circlemultiply 49 /circleplus
50 /emptyset 51 /lozenge 52 /bullet 53 /arrowright 54 /arrowup
55 /arrowleft 56 /arrowdown 57 /arrowboth 48 /degree 44 /comma 43 /plus
 45 /angle 42 /angleleft 47 /divide 61 /notequal 40 /equivalence 41 /second
 97 /approxequal 98 /congruent 99 /perpendicular 100 /partialdiff 101 /florin
 102 /intersection 103 /union 104 /propersuperset 105 /reflexsuperset
 106 /notsubset 107 /propersubset 108 /reflexsubset 109 /element 110 /notelement
 111 /gradient 112 /logicaland 113 /logicalor 114 /arrowdblboth
 115 /arrowdblleft 116 /arrowdblup 117 /arrowdblright 118 /arrowdbldown
 119 /ampersand 120 /omega1 121 /similar 122 /aleph ] def
/Symbol /Special accspe ReEncode
%%EndProlog
%%BeginSetup
newpath  gsave  .25 .25 scale 
%%EndSetup
 gsave 0 0 t black [] 0 sd 1 lw 1132 1132 0 0 C 3 lw 453 623 m -283 X s 1 lw 307
 623 m -4 8 d 27 -8 d -27 -9 d f
 /xs 0 def 
(q)
 /Helvetica     37 stwn 
( \040)
 /Helvetica     26 stwn 
 gsave  311 643
 t   0 r  xs 2 div neg 0 t 0 0 m
 /Helvetica findfont   37 sf 0    0 m 
(q)
 show 
 currentpoint pop 0 t 
 /Helvetica findfont   26 sf 0  -12 m 
( \040)
 show 
 gr  1 0 0 c
 /xs 0 def 
( \040)
 /Helvetica     37 stwn 
(i)
 /Helvetica     26 stwn 
 gsave  311 643
 t   0 r  xs 2 div neg 0 t 0 0 m
 /Helvetica findfont   37 sf 0    0 m 
( \040)
 show 
 currentpoint pop 0 t 
 /Helvetica findfont   26 sf 0  -12 m 
(i)
 show 
 gr  3 lw black 679 532 m -226 91 d s 1 lw 562 579 m -1 9 d 22 -17 d -28 2 d f
 /xs 0 def 
(q)
 /Helvetica     37 stwn 
(   \040)
 /Helvetica     26 stwn 
 gsave  579 595
 t   0 r  xs 2 div neg 0 t 0 0 m
 /Helvetica findfont   37 sf 0    0 m 
(q)
 show 
 currentpoint pop 0 t 
 /Helvetica findfont   26 sf 0  -12 m 
(   \040)
 show 
 gr  0 1 0 c
 /xs 0 def 
(\040)
 /Helvetica     37 stwn 
(a)
 /Symbol     26 stwn 
 gsave  579 595
 t   0 r  xs 2 div neg 0 t 0 0 m
 /Helvetica findfont   37 sf 0    0 m 
(\040)
 show 
 currentpoint pop 0 t 
/Helvetica findfont   37 sf 
(\040)
 dup length 1 sub 1 getinterval 
 stringwidth pop 2 div neg    0 rm 
 /Helvetica findfont   26 sf 0  -26 rm 
(\040)
 stringwidth pop 2 div neg 0 rm 
(\040)
 show
 /Symbol findfont   26 sf 0  -12 m 
(a)
 show 
 gsave  gr  gr  3 lw 0 0 1 c 453 623 m 6 4 d -2 7 d -2 6 d 2 Y 3 X 5 -3 d 6 -5 d
 5 -4 d 5 -3 d 3 X 2 Y -1 6 d -3 6 d -3 7 d -1 6 d 2 Y 3 X 4 -3 d 6 -5 d 6 -4 d
 5 -3 d 2 X 1 2 d -2 6 d -3 6 d -2 7 d -2 5 d 1 3 d 2 X 5 -3 d 6 -5 d 5 -4 d 5
 -3 d 3 -1 d 3 Y -1 5 d -3 7 d -3 7 d -1 5 d 3 Y 3 X 4 -3 d 6 -5 d 6 -4 d 5 -3 d
 2 -1 d 1 3 d -2 5 d -2 7 d -3 7 d -2 5 d 1 3 d 2 X 5 -3 d 6 -5 d 6 -4 d 4 -3 d
 3 -1 d 3 Y -1 5 d -3 7 d -3 7 d -1 5 d 3 Y 3 X 5 -3 d 5 -5 d 6 -4 d 5 -3 d 2 -1
 d 1 3 d -2 5 d -2 7 d -3 7 d -2 5 d 1 3 d 2 -1 d 5 -3 d 6 -4 d 6 -5 d 4 -3 d 3
 X 3 Y -1 5 d -3 7 d -3 7 d -1 5 d 3 Y 3 -1 d 5 -3 d 5 -4 d 6 -5 d 5 -3 d 3 X 3
 Y -2 5 d -2 7 d -3 7 d -2 5 d 1 3 d 3 -1 d 4 -3 d 6 -4 d 6 -5 d 4 -3 d 3 X 1 3
 d -2 5 d -3 7 d -2 7 d -2 5 d 3 Y 3 -1 d 5 -3 d 6 -4 d 5 -5 d 5 -3 d 3 X 3 Y -1
 5 d -3 7 d -3 6 d -1 6 d 2 Y 3 X 4 -3 d 6 -4 d 6 -5 d 5 -3 d 2 X 1 2 d -2 6 d
 -3 7 d -2 6 d -2 6 d 1 2 d 2 X 5 -3 d 6 -4 d 6 4 d s black
 /xs 0 def 
(W)
 /Helvetica     37 stwn 
(+)
 /Helvetica     26 stwn 
 gsave  537 732
 t   0 r  xs 2 div neg 0 t 0 0 m
 /Helvetica findfont   37 sf 0    0 m 
(W)
 show 
 currentpoint pop 0 t 
 /Helvetica findfont   26 sf 0   19 m 
(+)
 show 
 gr  1 0 0 c
 /xs 0 def 
(i\040)
 /Helvetica     26 stwn 
 gsave  461 581
 t   0 r  xs 2 div neg 0 t 0 0 m
 /Helvetica findfont   26 sf 0  -12 m 
(i\040)
 show 
 gr  0 1 0 c
 /xs 0 def 
(a)
 /Symbol     26 stwn 
 gsave  470 581
 t   0 r  xs 2 div neg 0 t 0 0 m
 /Symbol findfont   26 sf 0  -12 m 
(a)
 show 
 gr  black
 /xs 0 def 
(V)
 /Helvetica     37 stwn 
 gsave  441 581
 t   0 r  xs 2 div neg 0 t 0 0 m
 /Helvetica findfont   37 sf 0    0 m 
(V)
 show 
 gr 
 gr  gr 
showpage
end
%%EOF

%%EndDocument
 @endspecial 1 0 0 TeXcolorrgb 1 0 0 TeXcolorrgb 1560
x @beginspecial 30 @llx 120 @lly 180 @urx 210 @ury 1984
@rwi @setspecial
%%BeginDocument: Figs/Feyn/uia.eps
%!PS-Adobe-2.0 EPSF-2.0
%%BoundingBox: 30 120 180 210
%%Title: uia.eps
%%Creator: HIGZ Version 1.29/04
%%CreationDate: 2005/10/21   14.40
%%EndComments
%%BeginProlog
80 dict begin
/s {stroke} def /l {lineto} def /m {moveto} def /t {translate} def
/sw {stringwidth} def /r {rotate} def /rl {roll}  def /R {repeat} def
/d {rlineto} def /rm {rmoveto} def /gr {grestore} def /f {eofill} def
/c {setrgbcolor} def /lw {setlinewidth} def /sd {setdash} def
/cl {closepath} def /sf {scalefont setfont} def /black {0 setgray} def
/box {m dup 0 exch d exch 0 d 0 exch neg d cl} def
/NC{systemdict begin initclip end}def/C{NC box clip newpath}def
/bl {box s} def /bf {box f} def /Y { 0 exch d} def /X { 0 d} def 
/mp {newpath /y exch def /x exch def} def
/side {[w .77 mul w .23 mul] .385 w mul sd w 0 l currentpoint t -144 r} def
/mr {mp x y w2 0 360 arc} def /m24 {mr s} def /m20 {mr f} def
/mb {mp x y w2 add m w2 neg 0 d 0 w neg d w 0 d 0 w d cl} def
/mt {mp x y w2 add m w2 neg w neg d w 0 d cl} def
/m21 {mb f} def /m25 {mb s} def /m22 {mt f} def /m26  {mt s} def
/m23 {mp x y w2 sub m w2 w d w neg 0 d cl f} def
/m27 {mp x y w2 add m w3 neg w2 neg d w3 w2 neg d w3  w2 d cl s} def
/m28 {mp x w2 sub y w2 sub w3 add m w3 0 d 0 w3 neg d w3 0 d 0 w3 d w3 0 d
 0 w3 d w3 neg 0 d 0 w3 d w3 neg 0 d
 0 w3 neg d w3 neg 0 d cl s } def
/m29 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t
 4 {side} repeat cl fill gr} def
/m30 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t
 5 {side} repeat s gr} def
/m31 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d
 x w2 sub y w2 add m w w neg d x w2 sub y w2
 sub m w w d s} def
/m2 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d s} def
/m5 {mp x w2 sub y w2 sub m w w d x w2 sub y w2 add m w w neg d s} def
/reencdict 24 dict def /ReEncode {reencdict begin /nco&na exch def
/nfnam exch def /basefontname exch def /basefontdict basefontname findfont def
/newfont basefontdict maxlength dict def basefontdict {exch dup /FID ne
{dup /Encoding eq {exch dup length array copy newfont 3 1 roll put} {exch
newfont 3 1 roll put} ifelse} {pop pop} ifelse } forall newfont
/FontName nfnam put nco&na aload pop nco&na length 2 idiv {newfont
/Encoding get 3 1 roll put} repeat nfnam newfont definefont pop end } def
/accvec [ 176 /agrave 181 /Agrave 190 /acircumflex 192 /Acircumflex
201 /adieresis 204 /Adieresis 209 /ccedilla 210 /Ccedilla 211 /eacute
212 /Eacute 213 /egrave 214 /Egrave 215 /ecircumflex 216 /Ecircumflex
217 /edieresis 218 /Edieresis 219 /icircumflex 220 /Icircumflex
221 /idieresis 222 /Idieresis 223 /ntilde 224 /Ntilde 226 /ocircumflex
228 /Ocircumflex 229 /odieresis 230 /Odieresis 231 /ucircumflex 236 /Ucircumflex
237 /udieresis 238 /Udieresis 239 /aring 242 /Aring 243 /ydieresis
244 /Ydieresis 246 /aacute 247 /Aacute 252 /ugrave 253 /Ugrave] def
/Times-Roman /Times-Roman accvec ReEncode
/Times-Italic /Times-Italic accvec ReEncode
/Times-Bold /Times-Bold accvec ReEncode
/Times-BoldItalic /Times-BoldItalic accvec ReEncode
/Helvetica /Helvetica accvec ReEncode
/Helvetica-Oblique /Helvetica-Oblique accvec ReEncode
/Helvetica-Bold /Helvetica-Bold accvec ReEncode
/Helvetica-BoldOblique /Helvetica-BoldOblique  accvec ReEncode
/Courier /Courier accvec ReEncode
/Courier-Oblique /Courier-Oblique accvec ReEncode
/Courier-Bold /Courier-Bold accvec ReEncode
/Courier-BoldOblique /Courier-BoldOblique accvec ReEncode
/oshow {gsave [] 0 sd true charpath stroke gr} def
/stwn { /fs exch def /fn exch def /text exch def fn findfont fs sf
 text sw pop xs add /xs exch def} def
/stwb { /fs exch def /fn exch def /nbas exch def /textf exch def
textf length /tlen exch def nbas tlen gt {/nbas tlen  def} if
fn findfont fs sf textf dup length nbas sub nbas getinterval sw
pop neg xs add /xs exch def} def
/accspe [ 65 /plusminus 66 /bar 67 /existential 68 /universal
69 /exclam 70 /numbersign 71 /greater 72 /question 73 /integral
74 /colon 75 /semicolon 76 /less 77 /bracketleft 78 /bracketright
79 /greaterequal 80 /braceleft 81 /braceright 82 /radical
83 /spade 84 /heart 85 /diamond 86 /club 87 /lessequal
88 /multiply 89 /percent 90 /infinity 48 /circlemultiply 49 /circleplus
50 /emptyset 51 /lozenge 52 /bullet 53 /arrowright 54 /arrowup
55 /arrowleft 56 /arrowdown 57 /arrowboth 48 /degree 44 /comma 43 /plus
 45 /angle 42 /angleleft 47 /divide 61 /notequal 40 /equivalence 41 /second
 97 /approxequal 98 /congruent 99 /perpendicular 100 /partialdiff 101 /florin
 102 /intersection 103 /union 104 /propersuperset 105 /reflexsuperset
 106 /notsubset 107 /propersubset 108 /reflexsubset 109 /element 110 /notelement
 111 /gradient 112 /logicaland 113 /logicalor 114 /arrowdblboth
 115 /arrowdblleft 116 /arrowdblup 117 /arrowdblright 118 /arrowdbldown
 119 /ampersand 120 /omega1 121 /similar 122 /aleph ] def
/Symbol /Special accspe ReEncode
%%EndProlog
%%BeginSetup
newpath  gsave  .25 .25 scale 
%%EndSetup
 gsave 0 0 t black [] 0 sd 1 lw 1132 1132 0 0 C 3 lw 453 623 m -283 X s 1 lw 307
 623 m -4 8 d 27 -8 d -27 -9 d f
 /xs 0 def 
(l)
 /Helvetica     37 stwn 
(-)
 /Helvetica     26 stwn 
 gsave  311 643
 t   0 r  xs 2 div neg 0 t 0 0 m
 /Helvetica findfont   37 sf 0    0 m 
(l)
 show 
 currentpoint pop 0 t 
 /Helvetica findfont   26 sf 0   19 m 
(-)
 show 
 gr  1 0 0 c
 /xs 0 def 
(\040)
 /Helvetica     37 stwn 
(i)
 /Helvetica     26 stwn 
 gsave  311 643
 t   0 r  xs 2 div neg 0 t 0 0 m
 /Helvetica findfont   37 sf 0    0 m 
(\040)
 show 
 currentpoint pop 0 t 
 /Helvetica findfont   26 sf 0  -12 m 
(i)
 show 
 gr  3 lw black 679 532 m -226 91 d s 1 lw 562 579 m -1 9 d 22 -17 d -28 2 d f
 /xs 0 def 
(n)
 /Symbol     37 stwn 
( \040)
 /Helvetica     26 stwn 
 gsave  579 595
 t   0 r  xs 2 div neg 0 t 0 0 m
 /Symbol findfont   37 sf 0    0 m 
(n)
 show 
 currentpoint pop 0 t 
 /Helvetica findfont   26 sf 0  -12 m 
( \040)
 show 
 gr  0 1 0 c
 /xs 0 def 
(\040)
 /Helvetica     37 stwn 
(a)
 /Symbol     26 stwn 
 gsave  579 595
 t   0 r  xs 2 div neg 0 t 0 0 m
 /Helvetica findfont   37 sf 0    0 m 
(\040)
 show 
 currentpoint pop 0 t 
/Helvetica findfont   37 sf 
(\040)
 dup length 1 sub 1 getinterval 
 stringwidth pop 2 div neg    0 rm 
 /Helvetica findfont   26 sf 0  -26 rm 
(\040)
 stringwidth pop 2 div neg 0 rm 
(\040)
 show
 /Symbol findfont   26 sf 0  -12 m 
(a)
 show 
 gsave  gr  gr  3 lw 0 0 1 c 453 623 m 6 4 d -2 7 d -2 6 d 2 Y 3 X 5 -3 d 6 -5 d
 5 -4 d 5 -3 d 3 X 2 Y -1 6 d -3 6 d -3 7 d -1 6 d 2 Y 3 X 4 -3 d 6 -5 d 6 -4 d
 5 -3 d 2 X 1 2 d -2 6 d -3 6 d -2 7 d -2 5 d 1 3 d 2 X 5 -3 d 6 -5 d 5 -4 d 5
 -3 d 3 -1 d 3 Y -1 5 d -3 7 d -3 7 d -1 5 d 3 Y 3 X 4 -3 d 6 -5 d 6 -4 d 5 -3 d
 2 -1 d 1 3 d -2 5 d -2 7 d -3 7 d -2 5 d 1 3 d 2 X 5 -3 d 6 -5 d 6 -4 d 4 -3 d
 3 -1 d 3 Y -1 5 d -3 7 d -3 7 d -1 5 d 3 Y 3 X 5 -3 d 5 -5 d 6 -4 d 5 -3 d 2 -1
 d 1 3 d -2 5 d -2 7 d -3 7 d -2 5 d 1 3 d 2 -1 d 5 -3 d 6 -4 d 6 -5 d 4 -3 d 3
 X 3 Y -1 5 d -3 7 d -3 7 d -1 5 d 3 Y 3 -1 d 5 -3 d 5 -4 d 6 -5 d 5 -3 d 3 X 3
 Y -2 5 d -2 7 d -3 7 d -2 5 d 1 3 d 3 -1 d 4 -3 d 6 -4 d 6 -5 d 4 -3 d 3 X 1 3
 d -2 5 d -3 7 d -2 7 d -2 5 d 3 Y 3 -1 d 5 -3 d 6 -4 d 5 -5 d 5 -3 d 3 X 3 Y -1
 5 d -3 7 d -3 6 d -1 6 d 2 Y 3 X 4 -3 d 6 -4 d 6 -5 d 5 -3 d 2 X 1 2 d -2 6 d
 -3 7 d -2 6 d -2 6 d 1 2 d 2 X 5 -3 d 6 -4 d 6 4 d s black
 /xs 0 def 
(W)
 /Helvetica     37 stwn 
(-)
 /Helvetica     26 stwn 
 gsave  537 732
 t   0 r  xs 2 div neg 0 t 0 0 m
 /Helvetica findfont   37 sf 0    0 m 
(W)
 show 
 currentpoint pop 0 t 
 /Helvetica findfont   26 sf 0   19 m 
(-)
 show 
 gr  1 0 0 c
 /xs 0 def 
(i\040)
 /Helvetica     26 stwn 
 gsave  461 581
 t   0 r  xs 2 div neg 0 t 0 0 m
 /Helvetica findfont   26 sf 0  -12 m 
(i\040)
 show 
 gr  0 1 0 c
 /xs 0 def 
(a)
 /Symbol     26 stwn 
 gsave  470 581
 t   0 r  xs 2 div neg 0 t 0 0 m
 /Symbol findfont   26 sf 0  -12 m 
(a)
 show 
 gr  black
 /xs 0 def 
(U)
 /Helvetica     37 stwn 
 gsave  441 581
 t   0 r  xs 2 div neg 0 t 0 0 m
 /Helvetica findfont   37 sf 0    0 m 
(U)
 show 
 gr 
 gr  gr 
showpage
end
%%EOF

%%EndDocument
 @endspecial 10871 5612 a
 0 setgray
 10871 5612 a 0 TeXcolorgray
1 0 0 TeXcolorrgb 4500 6000 a
 tx@Dict begin -90 Rot  end
 4500 6000 a eop end
%%Page: 8 8
TeXDict begin 8 7 bop 1 0 0 TeXcolorrgb 4500 6000 a
 tx@Dict begin 90 Rot  end
 4500
6000 a 10688 1267 a Fm(8)p 0 TeXcolorgray Black 0 TeXcolorgray
0 TeXcolorgray 0 TeXcolorgray 5572 1558 a @beginspecial
@setspecial
 tx@Dict begin STP newpath 0.8 SLW 0  setgray  0. true 3.8 neg 6.59999
neg 312.25784 13.79999 .5 Frame  gsave 3.0 -45 PtoC Shadow .25  setgray
gsave fill grestore stroke grestore gsave 1  setgray gsave fill grestore
stroke grestore gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
end
 
@endspecial 0 0 1 TeXcolorrgb 56 w Fk(Common)67
b(Origin)i(of)e(Masses)g(and)i(Mixing)f(in)g(the)f(SM)p
0 TeXcolorgray 1 0 0 TeXcolorrgb 4729 2077 a Fl(Masses)58
b(and)e(mixings)h(in)e(the)h(Standard)e(Mo)5 b(del)56
b(ha)-5 b(v)g(e)57 b(common)g(origin)f(in)f(the)h(\\Y)-14
b(uk)-9 b(a)k(w)g(a)4729 2389 y(couplings")56 b(of)g(the)f(fermions)h
(to)g(the)g(Higgs.)p 0.0 0.6 0.0 TeXcolorrgb 4729 2701
a(First)g(w)-5 b(e)56 b(need)f(to)h(de\014ne)f(some)i(notation:)p
0 0 1 TeXcolorrgb 4729 3013 a(Will)f(fo)5 b(cus)56 b(on)g(leptons)f(-)i
(consider)e(3)i(families)f(of)g(leptonic)f Fi(S)10 b(U)18
b Fl(\(2\))55 b(doublets:)p 0 TeXcolorgray 6072 3619
a Fi( )6182 3645 y Fg(a)6302 3619 y Fl(=)6481 3273 y
Ff(0)6481 3583 y(@)p 0.0 0.6 0.0 TeXcolorrgb 6640 3483
a Fi(\027)6723 3508 y Fg(a)p 0 TeXcolorgray 1 0 0 TeXcolorrgb
6631 3795 a Fi(`)6702 3732 y Fe(\000)6702 3837 y Fg(a)p
0 TeXcolorgray 6804 3273 a Ff(1)6804 3583 y(A)6983 3619
y Fi(;)197 b( )7337 3645 y Fg(b)7444 3619 y Fl(=)7623
3273 y Ff(0)7623 3583 y(@)p 0.0 0.6 0.0 TeXcolorrgb 7789
3483 a Fi(\027)7872 3508 y Fg(b)p 0 TeXcolorgray 1 0 0
TeXcolorrgb 7774 3795 a Fi(`)7845 3723 y Fe(\000)7845
3843 y Fg(b)p 0 TeXcolorgray 7947 3273 a Ff(1)7947 3583
y(A)8126 3619 y Fi(;)g( )8480 3645 y Fg(c)8587 3619 y
Fl(=)8766 3273 y Ff(0)8766 3583 y(@)p 0.0 0.6 0.0 TeXcolorrgb
8932 3483 a Fi(\027)9015 3508 y Fg(c)p 0 TeXcolorgray
1 0 0 TeXcolorrgb 8917 3795 a Fi(`)8988 3732 y Fe(\000)8988
3837 y Fg(c)p 0 TeXcolorgray 9090 3273 a Ff(1)9090 3583
y(A)p 0 0 1 TeXcolorrgb 4729 4225 a Fl(Eac)-5 b(h)56
b(transforms)g(among)h(itself)f(under)e Fi(S)10 b(U)18
b Fl(\(2\))56 b(w)-5 b(eak)56 b(transformations)g(in)g(usual)g(w)-5
b(a)g(y)-14 b(.)p 1 0 0 TeXcolorrgb 4729 4537 a(W)g(e)56
b(de\014ne)f(also)i(t)-5 b(w)g(o)57 b(three-comp)5 b(onen)-5
b(t)54 b(v)-5 b(ectors)56 b(in)g(family-space:)p 0 TeXcolorgray
6252 4979 a Fi(\027)p 6252 5006 95 7 v 59 w Fl(=)6573
4788 y Ff(\020)p 0.0 0.6 0.0 TeXcolorrgb 210 x Fi(\027)6759
5024 y Fg(a)6831 4998 y Fi(;)29 b(\027)6990 5024 y Fg(b)7049
4998 y Fi(;)g(\027)7208 5024 y Fg(c)p 0 TeXcolorgray
7268 4788 a Ff(\021)7400 4979 y Fi(;)197 b(`)p 7644 5006
71 7 v 47 w Fl(=)7941 4788 y Ff(\020)p 1 0 0 TeXcolorrgb
210 x Fi(`)8115 4936 y Fe(\000)8115 5041 y Fg(a)8217
4998 y Fi(;)29 b(`)8364 4927 y Fe(\000)8364 5046 y Fg(b)8465
4998 y Fi(;)g(`)8612 4936 y Fe(\000)8612 5041 y Fg(c)p
0 TeXcolorgray 8713 4788 a Ff(\021)8845 4979 y Fi(;)10871
5612 y
 0 setgray
 10871 5612 a 0 TeXcolorgray 0 TeXcolorgray 4500
6000 a
 tx@Dict begin -90 Rot  end
 4500 6000 a eop end
%%Page: 9 9
TeXDict begin 9 8 bop 0 TeXcolorgray 4500 6000 a
 tx@Dict begin 90 Rot  end
 4500
6000 a 10688 1267 a Fm(9)p 1 0 0 TeXcolorrgb 0 0 1 TeXcolorrgb
0 TeXcolorgray 0 0 1 TeXcolorrgb 0.0 0.6 0.0 TeXcolorrgb
1 0 0 TeXcolorrgb 0 TeXcolorgray Black 0 TeXcolorgray
0 TeXcolorgray 0 TeXcolorgray 6095 1570 a @beginspecial
@setspecial
 tx@Dict begin STP newpath 0.8 SLW 0  setgray  0. true 3.8 neg 7.4
neg 239.41371 14.59999 .5 Frame  gsave 3.0 -45 PtoC Shadow .25  setgray
gsave fill grestore stroke grestore gsave 1  setgray gsave fill grestore
stroke grestore gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
end
 
@endspecial 0 0 1 TeXcolorrgb 56 w Fk(Origin)68
b(of)f(Masses)h(and)g(Mixing)g(\(con)-6 b(td.\))p 0 TeXcolorgray
1 0 0 TeXcolorrgb 4729 2100 a Fl(Will)56 b(accommo)5
b(date)57 b(neutrino)d(masses)k(in)-5 b(to)56 b(SM)g(with)f(simplest)i
(extension,)e(namely)h(that)4729 2412 y(neutrinos)f(ha)-5
b(v)g(e)56 b(Dirac)g(masses.)p 0.0 0.6 0.0 TeXcolorrgb
4729 2776 a(After)f(sp)5 b(on)-5 b(taneous)56 b(symmetry)h(breaking,)e
(mass)j(terms)e(app)5 b(ear)55 b(in)h(the)f(Lagrangian)i(as)4729
3088 y(follo)-5 b(ws)56 b(\(ha)-5 b(v)g(e)57 b(simpli\014ed)e(some)j
(details\):)p 0 TeXcolorgray 6737 3530 a Fj(L)6856 3556
y Fg(mass)7196 3530 y Fl(=)7387 3485 y(\026)7375 3530
y Fi(`)p 7375 3557 71 7 v 28 w(L)29 b(`)p 7618 3557 V
38 w Fl(+)47 b(\026)-93 b Fi(\027)p 7896 3557 95 7 v
40 w(N)46 b(\027)p 8200 3557 V 50 w Fl(+)38 b Fi(H)t(:C)s(:)p
0 0 1 TeXcolorrgb 4729 4024 a Fl(The)56 b(mass)h(matrices,)p
0 TeXcolorgray 56 w Fi(L)p 0 0 1 TeXcolorrgb 56 w Fl(and)p
0 TeXcolorgray 56 w Fi(N)p 0 0 1 TeXcolorrgb 18 w Fl(,)f(are)g
(arbitrary)-14 b(,)54 b(3)39 b Fj(\002)f Fl(3)56 b(Hermitian)g
(matrices.)p 1 0 0 TeXcolorrgb 4729 4387 a(The)g(c)-5
b(harged-curren)g(t)54 b(w)-5 b(eak)56 b(in)-5 b(teraction)55
b(ma)-5 b(y)57 b(also)g(b)5 b(e)55 b(written:)p 0 TeXcolorgray
5463 4826 a Fj(L)5582 4852 y Fg(cc)5742 4826 y Fl(=)48
b Fi(g)6 b Fl(\()6086 4780 y(\026)6074 4826 y Fi(`)p
6074 4853 71 7 v 28 w(:)29 b(\027)p 6249 4853 95 7 v
10 w Fl(\))p Fi(W)6590 4755 y Fh(+)6731 4826 y Fl(+)38
b Fi(H)t(:C)s(:)p 1 0 0 TeXcolorrgb 1 0 0 TeXcolorrgb
1 0 0 TeXcolorrgb 7982 5286 a @beginspecial 30 @llx 120
@lly 180 @urx 210 @ury 1417 @rwi @setspecial
%%BeginDocument: Figs/Feyn/uia_diag.eps
%!PS-Adobe-2.0 EPSF-2.0
%%BoundingBox: 30 120 180 210
%%Title: uia_diag.eps
%%Creator: HIGZ Version 1.29/04
%%CreationDate: 2005/10/27   15.39
%%EndComments
%%BeginProlog
80 dict begin
/s {stroke} def /l {lineto} def /m {moveto} def /t {translate} def
/sw {stringwidth} def /r {rotate} def /rl {roll}  def /R {repeat} def
/d {rlineto} def /rm {rmoveto} def /gr {grestore} def /f {eofill} def
/c {setrgbcolor} def /lw {setlinewidth} def /sd {setdash} def
/cl {closepath} def /sf {scalefont setfont} def /black {0 setgray} def
/box {m dup 0 exch d exch 0 d 0 exch neg d cl} def
/NC{systemdict begin initclip end}def/C{NC box clip newpath}def
/bl {box s} def /bf {box f} def /Y { 0 exch d} def /X { 0 d} def 
/mp {newpath /y exch def /x exch def} def
/side {[w .77 mul w .23 mul] .385 w mul sd w 0 l currentpoint t -144 r} def
/mr {mp x y w2 0 360 arc} def /m24 {mr s} def /m20 {mr f} def
/mb {mp x y w2 add m w2 neg 0 d 0 w neg d w 0 d 0 w d cl} def
/mt {mp x y w2 add m w2 neg w neg d w 0 d cl} def
/m21 {mb f} def /m25 {mb s} def /m22 {mt f} def /m26  {mt s} def
/m23 {mp x y w2 sub m w2 w d w neg 0 d cl f} def
/m27 {mp x y w2 add m w3 neg w2 neg d w3 w2 neg d w3  w2 d cl s} def
/m28 {mp x w2 sub y w2 sub w3 add m w3 0 d 0 w3 neg d w3 0 d 0 w3 d w3 0 d
 0 w3 d w3 neg 0 d 0 w3 d w3 neg 0 d
 0 w3 neg d w3 neg 0 d cl s } def
/m29 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t
 4 {side} repeat cl fill gr} def
/m30 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t
 5 {side} repeat s gr} def
/m31 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d
 x w2 sub y w2 add m w w neg d x w2 sub y w2
 sub m w w d s} def
/m2 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d s} def
/m5 {mp x w2 sub y w2 sub m w w d x w2 sub y w2 add m w w neg d s} def
/reencdict 24 dict def /ReEncode {reencdict begin /nco&na exch def
/nfnam exch def /basefontname exch def /basefontdict basefontname findfont def
/newfont basefontdict maxlength dict def basefontdict {exch dup /FID ne
{dup /Encoding eq {exch dup length array copy newfont 3 1 roll put} {exch
newfont 3 1 roll put} ifelse} {pop pop} ifelse } forall newfont
/FontName nfnam put nco&na aload pop nco&na length 2 idiv {newfont
/Encoding get 3 1 roll put} repeat nfnam newfont definefont pop end } def
/accvec [ 176 /agrave 181 /Agrave 190 /acircumflex 192 /Acircumflex
201 /adieresis 204 /Adieresis 209 /ccedilla 210 /Ccedilla 211 /eacute
212 /Eacute 213 /egrave 214 /Egrave 215 /ecircumflex 216 /Ecircumflex
217 /edieresis 218 /Edieresis 219 /icircumflex 220 /Icircumflex
221 /idieresis 222 /Idieresis 223 /ntilde 224 /Ntilde 226 /ocircumflex
228 /Ocircumflex 229 /odieresis 230 /Odieresis 231 /ucircumflex 236 /Ucircumflex
237 /udieresis 238 /Udieresis 239 /aring 242 /Aring 243 /ydieresis
244 /Ydieresis 246 /aacute 247 /Aacute 252 /ugrave 253 /Ugrave] def
/Times-Roman /Times-Roman accvec ReEncode
/Times-Italic /Times-Italic accvec ReEncode
/Times-Bold /Times-Bold accvec ReEncode
/Times-BoldItalic /Times-BoldItalic accvec ReEncode
/Helvetica /Helvetica accvec ReEncode
/Helvetica-Oblique /Helvetica-Oblique accvec ReEncode
/Helvetica-Bold /Helvetica-Bold accvec ReEncode
/Helvetica-BoldOblique /Helvetica-BoldOblique  accvec ReEncode
/Courier /Courier accvec ReEncode
/Courier-Oblique /Courier-Oblique accvec ReEncode
/Courier-Bold /Courier-Bold accvec ReEncode
/Courier-BoldOblique /Courier-BoldOblique accvec ReEncode
/oshow {gsave [] 0 sd true charpath stroke gr} def
/stwn { /fs exch def /fn exch def /text exch def fn findfont fs sf
 text sw pop xs add /xs exch def} def
/stwb { /fs exch def /fn exch def /nbas exch def /textf exch def
textf length /tlen exch def nbas tlen gt {/nbas tlen  def} if
fn findfont fs sf textf dup length nbas sub nbas getinterval sw
pop neg xs add /xs exch def} def
/accspe [ 65 /plusminus 66 /bar 67 /existential 68 /universal
69 /exclam 70 /numbersign 71 /greater 72 /question 73 /integral
74 /colon 75 /semicolon 76 /less 77 /bracketleft 78 /bracketright
79 /greaterequal 80 /braceleft 81 /braceright 82 /radical
83 /spade 84 /heart 85 /diamond 86 /club 87 /lessequal
88 /multiply 89 /percent 90 /infinity 48 /circlemultiply 49 /circleplus
50 /emptyset 51 /lozenge 52 /bullet 53 /arrowright 54 /arrowup
55 /arrowleft 56 /arrowdown 57 /arrowboth 48 /degree 44 /comma 43 /plus
 45 /angle 42 /angleleft 47 /divide 61 /notequal 40 /equivalence 41 /second
 97 /approxequal 98 /congruent 99 /perpendicular 100 /partialdiff 101 /florin
 102 /intersection 103 /union 104 /propersuperset 105 /reflexsuperset
 106 /notsubset 107 /propersubset 108 /reflexsubset 109 /element 110 /notelement
 111 /gradient 112 /logicaland 113 /logicalor 114 /arrowdblboth
 115 /arrowdblleft 116 /arrowdblup 117 /arrowdblright 118 /arrowdbldown
 119 /ampersand 120 /omega1 121 /similar 122 /aleph ] def
/Symbol /Special accspe ReEncode
%%EndProlog
%%BeginSetup
newpath  gsave  .25 .25 scale 
%%EndSetup
 gsave 0 0 t black [] 0 sd 1 lw 1132 1132 0 0 C 3 lw 453 623 m -283 X s 1 lw 307
 623 m -4 8 d 27 -8 d -27 -9 d f
 /xs 0 def 
(l)
 /Helvetica     37 stwn 
(-)
 /Helvetica     26 stwn 
 gsave  311 643
 t   0 r  xs 2 div neg 0 t 0 0 m
 /Helvetica findfont   37 sf 0    0 m 
(l)
 show 
 currentpoint pop 0 t 
 /Helvetica findfont   26 sf 0   19 m 
(-)
 show 
 gr  1 0 0 c
 /xs 0 def 
(\040)
 /Helvetica     37 stwn 
(a)
 /Helvetica     26 stwn 
 gsave  311 643
 t   0 r  xs 2 div neg 0 t 0 0 m
 /Helvetica findfont   37 sf 0    0 m 
(\040)
 show 
 currentpoint pop 0 t 
 /Helvetica findfont   26 sf 0  -12 m 
(a)
 show 
 gr  3 lw black 679 532 m -226 91 d s 1 lw 562 579 m -1 9 d 22 -17 d -28 2 d f
 /xs 0 def 
(n)
 /Symbol     37 stwn 
( \040)
 /Helvetica     26 stwn 
 gsave  579 595
 t   0 r  xs 2 div neg 0 t 0 0 m
 /Symbol findfont   37 sf 0    0 m 
(n)
 show 
 currentpoint pop 0 t 
 /Helvetica findfont   26 sf 0  -12 m 
( \040)
 show 
 gr  0 1 0 c
 /xs 0 def 
(\040)
 /Helvetica     37 stwn 
(a)
 /Helvetica     26 stwn 
 gsave  579 595
 t   0 r  xs 2 div neg 0 t 0 0 m
 /Helvetica findfont   37 sf 0    0 m 
(\040)
 show 
 currentpoint pop 0 t 
 /Helvetica findfont   26 sf 0  -12 m 
(a)
 show 
 gr  3 lw 0 0 1 c 453 623 m 6 4 d -2 7 d -2 6 d 2 Y 3 X 5 -3 d 6 -5 d 5 -4 d 5
 -3 d 3 X 2 Y -1 6 d -3 6 d -3 7 d -1 6 d 2 Y 3 X 4 -3 d 6 -5 d 6 -4 d 5 -3 d 2
 X 1 2 d -2 6 d -3 6 d -2 7 d -2 5 d 1 3 d 2 X 5 -3 d 6 -5 d 5 -4 d 5 -3 d 3 -1
 d 3 Y -1 5 d -3 7 d -3 7 d -1 5 d 3 Y 3 X 4 -3 d 6 -5 d 6 -4 d 5 -3 d 2 -1 d 1
 3 d -2 5 d -2 7 d -3 7 d -2 5 d 1 3 d 2 X 5 -3 d 6 -5 d 6 -4 d 4 -3 d 3 -1 d 3
 Y -1 5 d -3 7 d -3 7 d -1 5 d 3 Y 3 X 5 -3 d 5 -5 d 6 -4 d 5 -3 d 2 -1 d 1 3 d
 -2 5 d -2 7 d -3 7 d -2 5 d 1 3 d 2 -1 d 5 -3 d 6 -4 d 6 -5 d 4 -3 d 3 X 3 Y -1
 5 d -3 7 d -3 7 d -1 5 d 3 Y 3 -1 d 5 -3 d 5 -4 d 6 -5 d 5 -3 d 3 X 3 Y -2 5 d
 -2 7 d -3 7 d -2 5 d 1 3 d 3 -1 d 4 -3 d 6 -4 d 6 -5 d 4 -3 d 3 X 1 3 d -2 5 d
 -3 7 d -2 7 d -2 5 d 3 Y 3 -1 d 5 -3 d 6 -4 d 5 -5 d 5 -3 d 3 X 3 Y -1 5 d -3 7
 d -3 6 d -1 6 d 2 Y 3 X 4 -3 d 6 -4 d 6 -5 d 5 -3 d 2 X 1 2 d -2 6 d -3 7 d -2
 6 d -2 6 d 1 2 d 2 X 5 -3 d 6 -4 d 6 4 d s black
 /xs 0 def 
(W)
 /Helvetica     37 stwn 
(-)
 /Helvetica     26 stwn 
 gsave  537 732
 t   0 r  xs 2 div neg 0 t 0 0 m
 /Helvetica findfont   37 sf 0    0 m 
(W)
 show 
 currentpoint pop 0 t 
 /Helvetica findfont   26 sf 0   19 m 
(-)
 show 
 gr 
 /xs 0 def 
(1)
 /Helvetica     37 stwn 
 gsave  441 581
 t   0 r  xs 2 div neg 0 t 0 0 m
 /Helvetica findfont   37 sf 0    0 m 
(1)
 show 
 gr 
 gr  gr 
showpage
end
%%EOF

%%EndDocument
 @endspecial 1 0 0 TeXcolorrgb 4729 5410 a Fl(It)56 b(is)g
(\\diagonal":)75 b(only)56 b(leptons)g(from)g(the)f(same)j(doublet)c
(couple)i(to)g(eac)-5 b(h)56 b(other.)10871 5612 y
 0 setgray
 10871
5612 a 0 TeXcolorgray 1 0 0 TeXcolorrgb 4500 6000 a
 tx@Dict begin -90 Rot  end
 4500
6000 a eop end
%%Page: 10 10
TeXDict begin 10 9 bop 1 0 0 TeXcolorrgb 4500 6000 a
 tx@Dict begin 90 Rot  end

4500 6000 a 10631 1267 a Fm(10)p 1 0 0 TeXcolorrgb 0 0 1
TeXcolorrgb 0 TeXcolorgray 0 0 1 TeXcolorrgb 0 TeXcolorgray
0 0 1 TeXcolorrgb 0 TeXcolorgray 0.0 0.6 0.0 TeXcolorrgb
1 0 0 TeXcolorrgb 0 TeXcolorgray Black 0 TeXcolorgray
0 TeXcolorgray 0 TeXcolorgray 6095 1570 a @beginspecial
@setspecial
 tx@Dict begin STP newpath 0.8 SLW 0  setgray  0. true 3.8 neg 7.4
neg 239.41371 14.59999 .5 Frame  gsave 3.0 -45 PtoC Shadow .25  setgray
gsave fill grestore stroke grestore gsave 1  setgray gsave fill grestore
stroke grestore gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
end
 
@endspecial 0 0 1 TeXcolorrgb 56 w Fk(Origin)68
b(of)f(Masses)h(and)g(Mixing)g(\(con)-6 b(td.\))p 0 TeXcolorgray
1 0 0 TeXcolorrgb 4729 2051 a Fl(W)-14 b(e)56 b(wish)g(to)g
(diagonalise)h(b)5 b(oth)55 b(matrices,)h(in)f(order)h(to)g(obtain)f
(the)g(\\ph)-5 b(ysical")57 b(states.)p 0.0 0.6 0.0 TeXcolorrgb
4729 2381 a(So,)f(w)-5 b(e)56 b(mak)-5 b(e)57 b(the)f(follo)-5
b(wing)55 b(unitary)g(transformation)g(on)h(the)g(\014elds:)p
0 TeXcolorgray 6499 2777 a Fi(`)p 6499 2805 71 7 v 47
w Fj(!)48 b Fi(`)p 6837 2805 V 6937 2706 a Fg(m)7100
2777 y Fl(=)g Fi(U)7393 2803 y Fg(`)7479 2777 y Fi(`)p
7479 2805 V 28 w(;)366 b(\027)p 7991 2805 95 7 v 59 w
Fj(!)48 b Fi(\027)p 8353 2805 V 8447 2706 a Fg(m)8610
2777 y Fl(=)g Fi(U)8903 2803 y Fg(\027)9007 2777 y Fi(\027)p
9007 2805 V 0 0 1 TeXcolorrgb 4729 3173 a Fl(Then)p 0
TeXcolorgray 6278 3570 a Fj(L)6397 3595 y Fg(mass)6833
3570 y Fl(=)7119 3524 y(\026)7107 3570 y Fi(`)p 7107
3597 71 7 v 7207 3498 a Fg(m)7351 3570 y Fi(U)7465 3595
y Fg(`)7522 3570 y Fi(LU)7769 3488 y Fe(y)7751 3618 y
Fg(`)7859 3570 y Fi(`)p 7859 3597 V 7959 3498 a Fg(m)8112
3570 y Fl(+)g(\026)-94 b Fi(\027)p 8281 3597 95 7 v 8404
3498 a Fg(m)8548 3570 y Fi(U)8662 3595 y Fg(\027)8737
3570 y Fi(N)18 b(U)9022 3498 y Fe(y)9004 3612 y Fg(\027)9112
3570 y Fi(\027)p 9112 3597 V 9207 3498 a Fg(m)6833 3905
y Fl(=)7119 3860 y(\026)7107 3905 y Fi(`)p 7107 3933
71 7 v 7207 3834 a Fg(m)7322 3905 y Fi(D)7462 3931 y
Fg(`)7547 3905 y Fi(`)p 7547 3933 V 7647 3834 a Fg(m)7800
3905 y Fl(+)48 b(\026)-93 b Fi(\027)p 7970 3933 95 7
v 8092 3834 a Fg(m)8207 3905 y Fi(D)8347 3931 y Fg(\027)8451
3905 y Fi(\027)p 8451 3933 V 8545 3834 a Fg(m)p 0 0 1
TeXcolorrgb 4729 4301 a Fl(where)p 0 TeXcolorgray 55
w Fi(D)5356 4327 y Fg(`)5461 4301 y Fj(\021)47 b Fi(U)5756
4327 y Fg(`)5814 4301 y Fi(LU)6061 4220 y Fe(y)6043 4349
y Fg(`)p 0 0 1 TeXcolorrgb 0 0 1 TeXcolorrgb 6179 4301
a Fl(and)p 0 TeXcolorgray 55 w Fi(D)6646 4327 y Fg(\027)6769
4301 y Fj(\021)h Fi(U)7065 4327 y Fg(\027)7140 4301 y
Fi(N)18 b(U)7425 4239 y Fe(y)7407 4344 y Fg(\027)p 0 0 1
TeXcolorrgb 0 0 1 TeXcolorrgb 7543 4301 a Fl(are)56 b(diagonal)g(mass)i
(matrices.)p 1 0 0 TeXcolorrgb 75 w(Also)p 0 TeXcolorgray
0 TeXcolorgray 5055 4686 a Fj(L)5174 4712 y Fg(cc)5430
4686 y Fl(=)144 b Fi(g)6 b Fl(\()5870 4641 y(\026)5858
4686 y Fi(`)p 5858 4714 71 7 v 5956 4615 a Fg(m)6100
4686 y Fi(U)6214 4712 y Fg(`)6272 4686 y Fi(U)6404 4615
y Fe(y)6386 4729 y Fg(\027)6494 4686 y Fi(\027)p 6494
4714 95 7 v 6588 4615 a Fg(m)6703 4686 y Fl(\))p Fi(W)6951
4615 y Fh(+)7092 4686 y Fl(+)38 b Fi(H)t(:C)s(:)5430
5041 y Fl(=)144 b Fi(g)6 b Fl(\()5870 4996 y(\026)5858
5041 y Fi(`)p 5858 5069 71 7 v 5956 4970 a Fg(m)6071
5041 y Fi(U)6185 5067 y Fg(M)12 b(N)g(S)6541 5041 y Fi(\027)p
6541 5069 95 7 v 6635 4970 a Fg(m)6750 5041 y Fl(\))p
Fi(W)6998 4970 y Fh(+)7138 5041 y Fl(+)39 b Fi(H)t(:C)s(:)p
0 TeXcolorgray 0 TeXcolorgray 0 TeXcolorgray 7982 5438
a @beginspecial 30 @llx 120 @lly 180 @urx 210 @ury 1417
@rwi @setspecial
%%BeginDocument: Figs/Feyn/uia.eps
%!PS-Adobe-2.0 EPSF-2.0
%%BoundingBox: 30 120 180 210
%%Title: uia.eps
%%Creator: HIGZ Version 1.29/04
%%CreationDate: 2005/10/21   14.40
%%EndComments
%%BeginProlog
80 dict begin
/s {stroke} def /l {lineto} def /m {moveto} def /t {translate} def
/sw {stringwidth} def /r {rotate} def /rl {roll}  def /R {repeat} def
/d {rlineto} def /rm {rmoveto} def /gr {grestore} def /f {eofill} def
/c {setrgbcolor} def /lw {setlinewidth} def /sd {setdash} def
/cl {closepath} def /sf {scalefont setfont} def /black {0 setgray} def
/box {m dup 0 exch d exch 0 d 0 exch neg d cl} def
/NC{systemdict begin initclip end}def/C{NC box clip newpath}def
/bl {box s} def /bf {box f} def /Y { 0 exch d} def /X { 0 d} def 
/mp {newpath /y exch def /x exch def} def
/side {[w .77 mul w .23 mul] .385 w mul sd w 0 l currentpoint t -144 r} def
/mr {mp x y w2 0 360 arc} def /m24 {mr s} def /m20 {mr f} def
/mb {mp x y w2 add m w2 neg 0 d 0 w neg d w 0 d 0 w d cl} def
/mt {mp x y w2 add m w2 neg w neg d w 0 d cl} def
/m21 {mb f} def /m25 {mb s} def /m22 {mt f} def /m26  {mt s} def
/m23 {mp x y w2 sub m w2 w d w neg 0 d cl f} def
/m27 {mp x y w2 add m w3 neg w2 neg d w3 w2 neg d w3  w2 d cl s} def
/m28 {mp x w2 sub y w2 sub w3 add m w3 0 d 0 w3 neg d w3 0 d 0 w3 d w3 0 d
 0 w3 d w3 neg 0 d 0 w3 d w3 neg 0 d
 0 w3 neg d w3 neg 0 d cl s } def
/m29 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t
 4 {side} repeat cl fill gr} def
/m30 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t
 5 {side} repeat s gr} def
/m31 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d
 x w2 sub y w2 add m w w neg d x w2 sub y w2
 sub m w w d s} def
/m2 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d s} def
/m5 {mp x w2 sub y w2 sub m w w d x w2 sub y w2 add m w w neg d s} def
/reencdict 24 dict def /ReEncode {reencdict begin /nco&na exch def
/nfnam exch def /basefontname exch def /basefontdict basefontname findfont def
/newfont basefontdict maxlength dict def basefontdict {exch dup /FID ne
{dup /Encoding eq {exch dup length array copy newfont 3 1 roll put} {exch
newfont 3 1 roll put} ifelse} {pop pop} ifelse } forall newfont
/FontName nfnam put nco&na aload pop nco&na length 2 idiv {newfont
/Encoding get 3 1 roll put} repeat nfnam newfont definefont pop end } def
/accvec [ 176 /agrave 181 /Agrave 190 /acircumflex 192 /Acircumflex
201 /adieresis 204 /Adieresis 209 /ccedilla 210 /Ccedilla 211 /eacute
212 /Eacute 213 /egrave 214 /Egrave 215 /ecircumflex 216 /Ecircumflex
217 /edieresis 218 /Edieresis 219 /icircumflex 220 /Icircumflex
221 /idieresis 222 /Idieresis 223 /ntilde 224 /Ntilde 226 /ocircumflex
228 /Ocircumflex 229 /odieresis 230 /Odieresis 231 /ucircumflex 236 /Ucircumflex
237 /udieresis 238 /Udieresis 239 /aring 242 /Aring 243 /ydieresis
244 /Ydieresis 246 /aacute 247 /Aacute 252 /ugrave 253 /Ugrave] def
/Times-Roman /Times-Roman accvec ReEncode
/Times-Italic /Times-Italic accvec ReEncode
/Times-Bold /Times-Bold accvec ReEncode
/Times-BoldItalic /Times-BoldItalic accvec ReEncode
/Helvetica /Helvetica accvec ReEncode
/Helvetica-Oblique /Helvetica-Oblique accvec ReEncode
/Helvetica-Bold /Helvetica-Bold accvec ReEncode
/Helvetica-BoldOblique /Helvetica-BoldOblique  accvec ReEncode
/Courier /Courier accvec ReEncode
/Courier-Oblique /Courier-Oblique accvec ReEncode
/Courier-Bold /Courier-Bold accvec ReEncode
/Courier-BoldOblique /Courier-BoldOblique accvec ReEncode
/oshow {gsave [] 0 sd true charpath stroke gr} def
/stwn { /fs exch def /fn exch def /text exch def fn findfont fs sf
 text sw pop xs add /xs exch def} def
/stwb { /fs exch def /fn exch def /nbas exch def /textf exch def
textf length /tlen exch def nbas tlen gt {/nbas tlen  def} if
fn findfont fs sf textf dup length nbas sub nbas getinterval sw
pop neg xs add /xs exch def} def
/accspe [ 65 /plusminus 66 /bar 67 /existential 68 /universal
69 /exclam 70 /numbersign 71 /greater 72 /question 73 /integral
74 /colon 75 /semicolon 76 /less 77 /bracketleft 78 /bracketright
79 /greaterequal 80 /braceleft 81 /braceright 82 /radical
83 /spade 84 /heart 85 /diamond 86 /club 87 /lessequal
88 /multiply 89 /percent 90 /infinity 48 /circlemultiply 49 /circleplus
50 /emptyset 51 /lozenge 52 /bullet 53 /arrowright 54 /arrowup
55 /arrowleft 56 /arrowdown 57 /arrowboth 48 /degree 44 /comma 43 /plus
 45 /angle 42 /angleleft 47 /divide 61 /notequal 40 /equivalence 41 /second
 97 /approxequal 98 /congruent 99 /perpendicular 100 /partialdiff 101 /florin
 102 /intersection 103 /union 104 /propersuperset 105 /reflexsuperset
 106 /notsubset 107 /propersubset 108 /reflexsubset 109 /element 110 /notelement
 111 /gradient 112 /logicaland 113 /logicalor 114 /arrowdblboth
 115 /arrowdblleft 116 /arrowdblup 117 /arrowdblright 118 /arrowdbldown
 119 /ampersand 120 /omega1 121 /similar 122 /aleph ] def
/Symbol /Special accspe ReEncode
%%EndProlog
%%BeginSetup
newpath  gsave  .25 .25 scale 
%%EndSetup
 gsave 0 0 t black [] 0 sd 1 lw 1132 1132 0 0 C 3 lw 453 623 m -283 X s 1 lw 307
 623 m -4 8 d 27 -8 d -27 -9 d f
 /xs 0 def 
(l)
 /Helvetica     37 stwn 
(-)
 /Helvetica     26 stwn 
 gsave  311 643
 t   0 r  xs 2 div neg 0 t 0 0 m
 /Helvetica findfont   37 sf 0    0 m 
(l)
 show 
 currentpoint pop 0 t 
 /Helvetica findfont   26 sf 0   19 m 
(-)
 show 
 gr  1 0 0 c
 /xs 0 def 
(\040)
 /Helvetica     37 stwn 
(i)
 /Helvetica     26 stwn 
 gsave  311 643
 t   0 r  xs 2 div neg 0 t 0 0 m
 /Helvetica findfont   37 sf 0    0 m 
(\040)
 show 
 currentpoint pop 0 t 
 /Helvetica findfont   26 sf 0  -12 m 
(i)
 show 
 gr  3 lw black 679 532 m -226 91 d s 1 lw 562 579 m -1 9 d 22 -17 d -28 2 d f
 /xs 0 def 
(n)
 /Symbol     37 stwn 
( \040)
 /Helvetica     26 stwn 
 gsave  579 595
 t   0 r  xs 2 div neg 0 t 0 0 m
 /Symbol findfont   37 sf 0    0 m 
(n)
 show 
 currentpoint pop 0 t 
 /Helvetica findfont   26 sf 0  -12 m 
( \040)
 show 
 gr  0 1 0 c
 /xs 0 def 
(\040)
 /Helvetica     37 stwn 
(a)
 /Symbol     26 stwn 
 gsave  579 595
 t   0 r  xs 2 div neg 0 t 0 0 m
 /Helvetica findfont   37 sf 0    0 m 
(\040)
 show 
 currentpoint pop 0 t 
/Helvetica findfont   37 sf 
(\040)
 dup length 1 sub 1 getinterval 
 stringwidth pop 2 div neg    0 rm 
 /Helvetica findfont   26 sf 0  -26 rm 
(\040)
 stringwidth pop 2 div neg 0 rm 
(\040)
 show
 /Symbol findfont   26 sf 0  -12 m 
(a)
 show 
 gsave  gr  gr  3 lw 0 0 1 c 453 623 m 6 4 d -2 7 d -2 6 d 2 Y 3 X 5 -3 d 6 -5 d
 5 -4 d 5 -3 d 3 X 2 Y -1 6 d -3 6 d -3 7 d -1 6 d 2 Y 3 X 4 -3 d 6 -5 d 6 -4 d
 5 -3 d 2 X 1 2 d -2 6 d -3 6 d -2 7 d -2 5 d 1 3 d 2 X 5 -3 d 6 -5 d 5 -4 d 5
 -3 d 3 -1 d 3 Y -1 5 d -3 7 d -3 7 d -1 5 d 3 Y 3 X 4 -3 d 6 -5 d 6 -4 d 5 -3 d
 2 -1 d 1 3 d -2 5 d -2 7 d -3 7 d -2 5 d 1 3 d 2 X 5 -3 d 6 -5 d 6 -4 d 4 -3 d
 3 -1 d 3 Y -1 5 d -3 7 d -3 7 d -1 5 d 3 Y 3 X 5 -3 d 5 -5 d 6 -4 d 5 -3 d 2 -1
 d 1 3 d -2 5 d -2 7 d -3 7 d -2 5 d 1 3 d 2 -1 d 5 -3 d 6 -4 d 6 -5 d 4 -3 d 3
 X 3 Y -1 5 d -3 7 d -3 7 d -1 5 d 3 Y 3 -1 d 5 -3 d 5 -4 d 6 -5 d 5 -3 d 3 X 3
 Y -2 5 d -2 7 d -3 7 d -2 5 d 1 3 d 3 -1 d 4 -3 d 6 -4 d 6 -5 d 4 -3 d 3 X 1 3
 d -2 5 d -3 7 d -2 7 d -2 5 d 3 Y 3 -1 d 5 -3 d 6 -4 d 5 -5 d 5 -3 d 3 X 3 Y -1
 5 d -3 7 d -3 6 d -1 6 d 2 Y 3 X 4 -3 d 6 -4 d 6 -5 d 5 -3 d 2 X 1 2 d -2 6 d
 -3 7 d -2 6 d -2 6 d 1 2 d 2 X 5 -3 d 6 -4 d 6 4 d s black
 /xs 0 def 
(W)
 /Helvetica     37 stwn 
(-)
 /Helvetica     26 stwn 
 gsave  537 732
 t   0 r  xs 2 div neg 0 t 0 0 m
 /Helvetica findfont   37 sf 0    0 m 
(W)
 show 
 currentpoint pop 0 t 
 /Helvetica findfont   26 sf 0   19 m 
(-)
 show 
 gr  1 0 0 c
 /xs 0 def 
(i\040)
 /Helvetica     26 stwn 
 gsave  461 581
 t   0 r  xs 2 div neg 0 t 0 0 m
 /Helvetica findfont   26 sf 0  -12 m 
(i\040)
 show 
 gr  0 1 0 c
 /xs 0 def 
(a)
 /Symbol     26 stwn 
 gsave  470 581
 t   0 r  xs 2 div neg 0 t 0 0 m
 /Symbol findfont   26 sf 0  -12 m 
(a)
 show 
 gr  black
 /xs 0 def 
(U)
 /Helvetica     37 stwn 
 gsave  441 581
 t   0 r  xs 2 div neg 0 t 0 0 m
 /Helvetica findfont   37 sf 0    0 m 
(U)
 show 
 gr 
 gr  gr 
showpage
end
%%EOF

%%EndDocument
 @endspecial 1 0 0 TeXcolorrgb 4729 5684 a Fl(where)p
0 TeXcolorgray 55 w Fi(U)5330 5710 y Fg(M)12 b(N)g(S)5704
5684 y Fj(\021)48 b Fi(U)6000 5710 y Fg(`)6058 5684 y
Fi(U)6190 5621 y Fe(y)6172 5726 y Fg(\027)p 1 0 0 TeXcolorrgb
6308 5684 a Fl(is)56 b(the)f(MNS)i(lepton)e(mixing)h(matrix.)p
0.0 0.6 0.0 TeXcolorrgb 75 w(NB.)g(Analogous)i(for)d(quarks.)10871
5612 y
 0 setgray
 10871 5612 a 0 TeXcolorgray 0.0 0.6 0.0 TeXcolorrgb
4500 6000 a
 tx@Dict begin -90 Rot  end
 4500 6000 a eop end
%%Page: 11 11
TeXDict begin 11 10 bop 0.0 0.6 0.0 TeXcolorrgb 4500
6000 a
 tx@Dict begin 90 Rot  end
 4500 6000 a 10631 1267 a Fm(11)p 1 0 0 TeXcolorrgb
0 TeXcolorgray 1 0 0 TeXcolorrgb 0 TeXcolorgray 1 0 0
TeXcolorrgb 0 0 1 TeXcolorrgb 0 0 1 TeXcolorrgb 0 0 1
TeXcolorrgb 0 TeXcolorgray 0 0 1 TeXcolorrgb 0 TeXcolorgray
0.0 0.6 0.0 TeXcolorrgb 1 0 0 TeXcolorrgb 0 TeXcolorgray
Black 0 TeXcolorgray 0 TeXcolorgray 0 TeXcolorgray 4976
1558 a @beginspecial @setspecial
 tx@Dict begin STP newpath 0.8 SLW 0  setgray  0. true 3.8 neg 6.59999
neg 395.40016 13.79999 .5 Frame  gsave 3.0 -45 PtoC Shadow .25  setgray
gsave fill grestore stroke grestore gsave 1  setgray gsave fill grestore
stroke grestore gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
end
 
@endspecial 0 0 1 TeXcolorrgb
56 w Fk(Historical)67 b(A)-6 b(ttempts)66 b(to)h(Constrain)h(F)-17
b(ermion)67 b(Masses)g(and)i(Mixings)p 0 TeXcolorgray
1 0 0 TeXcolorrgb 4729 1987 a Fl(Inspired)55 b(b)-5 b(y)56
b(some)h(phenomenological)f(relationships)f(in)h(quark)g(mixing,)g(eg.)
p 0 TeXcolorgray 5953 2436 a(tan)28 b Fi(\022)6304 2462
y Fg(C)6454 2436 y Fj(')47 b Fl(0)p Fi(:)p Fl(23)i Fj(')7165
2197 y Ff(r)p 7337 2197 252 7 v 7354 2320 a Fi(m)7501
2345 y Fg(d)p 7354 2396 218 7 v 7357 2554 a Fi(m)7504
2580 y Fg(s)7589 2436 y Fl(;)365 b(tan)28 b Fi(\022)8352
2462 y Fg(cb)8512 2436 y Fj(')48 b Fl(0)p Fi(:)p Fl(04)g
Fj(')9223 2197 y Ff(r)p 9395 2197 252 7 v 9412 2320 a
Fi(m)9559 2345 y Fg(d)p 9412 2396 218 7 v 9417 2554 a
Fi(m)9564 2580 y Fg(b)p 1 0 0 TeXcolorrgb 4729 2885 a
Fl(and)56 b(the)f(kno)-5 b(wn)56 b(common)h(origin)f(of)g(masses)i(and)
e(mixings,)g(man)-5 b(y)57 b(attempts)f(ha)-5 b(v)g(e)57
b(b)5 b(een)4729 3177 y(made)57 b(to)f(relate)f(them.)p
0 0 1 TeXcolorrgb 4729 3507 a(Best)i(kno)-5 b(wn)55 b(is)i(b)-5
b(y)56 b(H.)g(F)-14 b(ritzsc)-5 b(h)56 b(from)g(1977)h(and)f(1978:)76
b(Mass)58 b(matrices:)p 0 TeXcolorgray 5483 4173 a Fi(M)5681
4055 y Fd(2)p 5681 4076 53 6 v 5681 4147 a(3)5806 4173
y Fl(=)5985 3672 y Ff(0)5985 3975 y(B)5985 4078 y(B)5985
4182 y(B)5985 4292 y(@)6217 3880 y Fl(0)333 b Fi(a)327
b Fl(0)6181 4192 y Fi(a)6269 4130 y Fe(\003)6636 4192
y Fl(0)335 b Fi(b)6217 4504 y Fl(0)307 b Fi(b)6680 4442
y Fe(\003)7055 4504 y Fi(c)7209 3672 y Ff(1)7209 3975
y(C)7209 4078 y(C)7209 4182 y(C)7209 4292 y(A)7388 4173
y Fl(;)366 b Fi(M)7982 4102 y Fe(\000)8094 4055 y Fd(1)p
8094 4076 V 8094 4147 a(3)8219 4173 y Fl(=)8398 3672
y Ff(0)8398 3975 y(B)8398 4078 y(B)8398 4182 y(B)8398
4292 y(@)8630 3880 y Fl(0)339 b Fi(\013)347 b Fl(0)8584
4192 y Fi(\013)8692 4130 y Fe(\003)9065 4192 y Fl(0)h
Fi(\014)8630 4504 y Fl(0)307 b Fi(\014)9126 4442 y Fe(\003)9501
4504 y Fi(\015)9679 3672 y Ff(1)9679 3975 y(C)9679 4078
y(C)9679 4182 y(C)9679 4292 y(A)p 0.0 0.6 0.0 TeXcolorrgb
4729 4889 a Fl(Predicts)55 b(\(after)f(some)k(reasonable)e(appro)-5
b(ximations\))56 b(ab)5 b(o)-5 b(v)g(e)56 b Fi(\022)8911
4915 y Fg(C)9069 4889 y Fl(relation,)f(but)g(also)p 0
TeXcolorgray 6503 5348 a(tan)28 b Fi(\022)6854 5374 y
Fg(cb)7013 5348 y Fi(>)7192 5109 y Ff(r)p 7364 5109 246
7 v 7381 5231 a Fi(m)7528 5257 y Fg(s)p 7381 5308 212
7 v 7383 5466 a Fi(m)7530 5492 y Fg(b)7648 5348 y Fj(\000)7820
5109 y Ff(r)p 7992 5109 242 7 v 8009 5231 a Fi(m)8156
5257 y Fg(c)p 8009 5308 208 7 v 8013 5466 a Fi(m)8160
5492 y Fg(t)8282 5348 y Fj(')48 b Fl(0)p Fi(:)p Fl(09)p
Fi(;)p 0.0 0.6 0.0 TeXcolorrgb 4785 5797 a Fl(no)-5 b(w)56
b(excluded.)10871 5612 y
 0 setgray
 10871 5612 a 0 TeXcolorgray
0.0 0.6 0.0 TeXcolorrgb 4500 6000 a
 tx@Dict begin -90 Rot  end
 4500 6000 a eop end
%%Page: 12 12
TeXDict begin 12 11 bop 0.0 0.6 0.0 TeXcolorrgb 4500
6000 a
 tx@Dict begin 90 Rot  end
 4500 6000 a 10631 1267 a Fm(12)p 0 TeXcolorgray
0.0 0.6 0.0 TeXcolorrgb 0 TeXcolorgray 0 0 1 TeXcolorrgb
1 0 0 TeXcolorrgb 0 TeXcolorgray 1 0 0 TeXcolorrgb 0
TeXcolorgray Black 0 TeXcolorgray 0 TeXcolorgray 0 TeXcolorgray
6469 1570 a @beginspecial @setspecial
 tx@Dict begin STP newpath 0.8 SLW 0  setgray  0. true 3.8 neg 7.4
neg 187.2444 14.59999 .5 Frame  gsave 3.0 -45 PtoC Shadow .25  setgray
gsave fill grestore stroke grestore gsave 1  setgray gsave fill grestore
stroke grestore gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
end
 
@endspecial 0 0 1
TeXcolorrgb 56 w Fk(Historical)67 b(A)-6 b(ttempts)66
b(\(Con)-6 b(td.\))p 0 TeXcolorgray 1 0 0 TeXcolorrgb
4729 2059 a Fl(Ho)h(w)57 b(do)5 b(es)56 b(F)-14 b(ritzsc)-5
b(h)55 b Fi(Ansatz)65 b Fl(w)-5 b(ork?)p 0 TeXcolorgray
4729 2371 a(Mass)55 b(matrices)f(enco)5 b(de)53 b(10)h(pieces)f(of)h
(information)f(-)g(6)h(masses)i(and)d(4)h(mixing)g(parameters.)p
0.0 0.6 0.0 TeXcolorrgb 4729 2683 a(Ansatz)i(uses)h(only)f(6)h
(magnitudes)f(and)f(one)h(phase,)104 b(=)-29 b Fj(\))105
b Fl(3)56 b(constrain)-5 b(ts.)p 0 0 1 TeXcolorrgb 4729
2996 a(F)-14 b(ritzsc)-5 b(h's)56 b Fi(Ansatz)65 b Fl(has)56
b(spa)-5 b(wned)56 b(a)h(host)f(of)g(immitators,)g(some)h(who)f(can)g
(do)g(b)5 b(etter)54 b(in)4729 3308 y(terms)i(of)g(predictions.)p
1 0 0 TeXcolorrgb 4729 3620 a(Although)f(initially)-14
b(,)55 b(just)g(a)i(mathematical)f(device,)f(mo)5 b(dern)56
b(mo)5 b(dels)56 b(app)5 b(eal)56 b(to)g(\\\015a)-5 b(v)g(our)4729
3932 y(symmetries")57 b(to)f(enforce)f(the)g(zero)5 b(es.)p
0 TeXcolorgray 4729 4244 a(Man)-5 b(y)57 b(build-in)d(sup)5
b(ersymmetry)-14 b(,)56 b(and/or)g(extra)f(dimensions,)h(complicated)g
(Higgs)4729 4556 y(structures)f(etc.)p 0.0 0.6 0.0 TeXcolorrgb
4729 4868 a(Ho)-5 b(w)g(ev)g(er,)57 b(all)f(seem)h(to)f(assume)h(the)f
(same)h(basic)f(premise,)g(that)f Fj(9)h Fl(a)h(\\sp)5
b(ecial")56 b(basis,)h(in)4729 5180 y(whic)-5 b(h)55
b(the)h(mass)i(matrices)e(tak)-5 b(e)56 b(some)h(\\sp)5
b(ecial")57 b(form)f(whic)-5 b(h)55 b(limits)h(the)f(n)-5
b(um)g(b)5 b(er)56 b(of)4729 5492 y(parameters)g(to)g(few)-5
b(er)55 b(than)g(10.)10871 5612 y
 0 setgray
 10871 5612 a 0 TeXcolorgray
0.0 0.6 0.0 TeXcolorrgb 4500 6000 a
 tx@Dict begin -90 Rot  end
 4500 6000 a eop end
%%Page: 13 13
TeXDict begin 13 12 bop 0.0 0.6 0.0 TeXcolorrgb 4500
6000 a
 tx@Dict begin 90 Rot  end
 4500 6000 a 10631 1267 a Fm(13)p 0 TeXcolorgray
1 0 0 TeXcolorrgb 0 0 1 TeXcolorrgb 0.0 0.6 0.0 TeXcolorrgb
0 TeXcolorgray 1 0 0 TeXcolorrgb 0 TeXcolorgray Black
0 TeXcolorgray 0 TeXcolorgray 0 TeXcolorgray 6878 1558
a @beginspecial @setspecial
 tx@Dict begin STP newpath 0.8 SLW 0  setgray  0. true 3.8 neg 6.59999
neg 130.18675 13.79999 .5 Frame  gsave 3.0 -45 PtoC Shadow .25  setgray
gsave fill grestore stroke grestore gsave 1  setgray gsave fill grestore
stroke grestore gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
end
 
@endspecial 0 0 1 TeXcolorrgb
56 w Fk(Jarlsk)-6 b(og)68 b(Co)-6 b(v)-11 b(ariance)p
0 TeXcolorgray 0.0 0.6 0.0 TeXcolorrgb 4729 2028 a Fl(Instead)56
b(of)g(diagonalising,)g(w)-5 b(e)56 b(could)f(ha)-5 b(v)g(e)57
b(made)g(the)e(follo)-5 b(wing)56 b Fi(simul)t(taneous)h
Fl(arbitrary)4729 2321 y(unitary)e(transformation:)p
0 TeXcolorgray 6650 2717 a Fi(`)p 6650 2745 71 7 v 48
w Fj(!)48 b Fi(`)p 6989 2745 V 7088 2646 a Fe(0)7176
2717 y Fl(=)g Fi(U)18 b(`)p 7487 2745 V 29 w(;)366 b(\027)p
8000 2745 95 7 v 59 w Fj(!)48 b Fi(\027)p 8362 2745 V
8456 2646 a Fe(0)8544 2717 y Fl(=)g Fi(U)18 b(\027)p
8855 2745 V 0 0 1 TeXcolorrgb 4729 3113 a Fl(Then)p 0
TeXcolorgray 6490 3510 a Fj(L)6609 3535 y Fg(mass)7045
3510 y Fl(=)7331 3464 y(\026)7319 3510 y Fi(`)p 7319
3537 71 7 v 7419 3438 a Fe(0)7487 3510 y Fi(U)g(LU)7866
3438 y Fe(y)7957 3510 y Fi(`)p 7957 3537 V 8057 3438
a Fe(0)8135 3510 y Fl(+)48 b(\026)-94 b Fi(\027)p 8304
3537 95 7 v 8399 3438 a Fe(0)8468 3510 y Fi(U)18 b(N)g(U)8885
3438 y Fe(y)8975 3510 y Fi(\027)p 8975 3537 V 9070 3438
a Fe(0)7045 3845 y Fl(=)7331 3800 y(\026)7319 3845 y
Fi(`)p 7319 3873 71 7 v 7419 3774 a Fe(0)7459 3845 y
Fi(L)7574 3774 y Fe(0)7642 3845 y Fi(`)p 7642 3873 V
7742 3774 a Fe(0)7820 3845 y Fl(+)48 b(\026)-93 b Fi(\027)p
7990 3873 95 7 v 8084 3774 a Fe(0)8124 3845 y Fi(N)8277
3774 y Fe(0)8346 3845 y Fi(\027)p 8346 3873 V 8440 3774
a Fe(0)p 0 0 1 TeXcolorrgb 4729 4241 a Fl(where)p 0 TeXcolorgray
55 w Fi(L)5331 4179 y Fe(0)5419 4241 y Fj(\021)47 b Fi(U)18
b(LU)5979 4179 y Fe(y)p 0 0 1 TeXcolorrgb 0 0 1 TeXcolorrgb
6098 4241 a Fl(and)p 0 TeXcolorgray 55 w Fi(N)6578 4179
y Fe(0)6666 4241 y Fj(\021)48 b Fi(U)18 b(N)g(U)7265
4179 y Fe(y)p 0 0 1 TeXcolorrgb 0 0 1 TeXcolorrgb 7384
4241 a Fl(are)56 b(new)f(arbitrary)f(Hermitian)i(mass)i(matrices.)p
1 0 0 TeXcolorrgb 75 w(In)4729 4534 y(this)e(basis,)g(the)g(c)-5
b(harged)56 b(curren)-5 b(t)54 b(is:)p 0 TeXcolorgray
6611 4930 a Fj(L)6730 4956 y Fg(cc)6986 4930 y Fl(=)143
b Fi(g)6 b Fl(\()7425 4885 y(\026)7413 4930 y Fi(`)p
7413 4958 71 7 v 7512 4859 a Fe(0)7581 4930 y Fi(U)18
b(U)7845 4859 y Fe(y)7936 4930 y Fi(\027)p 7936 4958
95 7 v 8030 4859 a Fe(0)8070 4930 y Fl(\))p Fi(W)8318
4859 y Fh(+)8459 4930 y Fl(+)38 b Fi(H)t(:C)s(:)6986
5266 y Fl(=)143 b Fi(g)6 b Fl(\()7425 5220 y(\026)7413
5266 y Fi(`)p 7413 5293 71 7 v 7512 5195 a Fe(0)7552
5266 y Fi(:)29 b(\027)p 7628 5293 95 7 v 7722 5195 a
Fe(0)7762 5266 y Fl(\))p Fi(W)8010 5195 y Fh(+)8151 5266
y Fl(+)38 b Fi(H)t(:C)s(:)p 1 0 0 TeXcolorrgb 4729 5662
a Fl(In)56 b(terms)g(of)g(new)f(\014elds,)h(CC)g(is)g(still)g
(diagonal,)g(but)f(mass)j(matrices)e(ha)-5 b(v)g(e)57
b(c)-5 b(hanged.)10871 5612 y
 0 setgray
 10871 5612 a 0 TeXcolorgray
1 0 0 TeXcolorrgb 4500 6000 a
 tx@Dict begin -90 Rot  end
 4500 6000 a eop end
%%Page: 14 14
TeXDict begin 14 13 bop 1 0 0 TeXcolorrgb 4500 6000 a
 tx@Dict begin 90 Rot  end

4500 6000 a 10631 1267 a Fm(14)p 0 TeXcolorgray 1 0 0
TeXcolorrgb 0 0 1 TeXcolorrgb 0 0 1 TeXcolorrgb 0 0 1
TeXcolorrgb 0 TeXcolorgray 0 0 1 TeXcolorrgb 0 TeXcolorgray
0.0 0.6 0.0 TeXcolorrgb 0 TeXcolorgray Black 0 TeXcolorgray
0 TeXcolorgray 0 TeXcolorgray 6909 1558 a @beginspecial
@setspecial
 tx@Dict begin STP newpath 0.8 SLW 0  setgray  0. true 3.8 neg 6.59999
neg 125.87349 13.79999 .5 Frame  gsave 3.0 -45 PtoC Shadow .25  setgray
gsave fill grestore stroke grestore gsave 1  setgray gsave fill grestore
stroke grestore gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
end
 
@endspecial 0 0 1 TeXcolorrgb 56 w Fk(Jarlsk)-6
b(og)68 b(In)-6 b(v)-11 b(ariance)p 0 TeXcolorgray 0.0 0.6 0.0
TeXcolorrgb 4729 2077 a Fl(New)53 b(basis)g(\(with)f(transformed)f
(mass)k(matrices\))d(lo)5 b(oks)54 b(lik)-5 b(e)52 b(just)g(as)i(go)5
b(o)g(d)53 b(a)g(starting)f(p)5 b(oin)-5 b(t)p 1 0 0
TeXcolorrgb 4729 2433 a(But)56 b(what)f(ab)5 b(out)55
b(the)h(observ)-9 b(ables)56 b(\(masses)i(and)d(mixing)h(matrix)g
(elemen)-5 b(ts\)?)p 0 0 1 TeXcolorrgb 4729 2790 a(No)g(w:)p
0 TeXcolorgray 6615 3110 a Fi(`)p 6615 3137 71 7 v 6714
3039 a Fg(m)6877 3110 y Fl(=)48 b Fi(U)7170 3135 y Fg(`)7256
3110 y Fi(U)7388 3039 y Fe(y)7450 3110 y Fi(`)p 7450
3137 V 7550 3039 a Fe(0)7590 3110 y Fi(;)366 b(\027)p
8003 3137 95 7 v 8097 3039 a Fg(m)8260 3110 y Fl(=)48
b Fi(U)8553 3135 y Fg(\027)8656 3110 y Fi(U)8788 3039
y Fe(y)8850 3110 y Fi(\027)p 8850 3137 V 8944 3039 a
Fe(0)p 0 0 1 TeXcolorrgb 4729 3489 a Fl(and)p 0 TeXcolorgray
6609 3921 a Fj(L)6728 3947 y Fg(mass)7164 3921 y Fl(=)7450
3875 y(\026)7438 3921 y Fi(`)p 7438 3948 71 7 v 7538
3850 a Fg(m)7653 3921 y Fi(D)7798 3850 y Fe(0)7793 3963
y Fg(`)7878 3921 y Fi(`)p 7878 3948 V 7978 3850 a Fg(m)8131
3921 y Fl(+)g(\026)-94 b Fi(\027)p 8300 3948 95 7 v 8423
3850 a Fg(m)8538 3921 y Fi(D)8683 3850 y Fe(0)8678 3963
y Fg(\027)8782 3921 y Fi(\027)p 8782 3948 V 8876 3850
a Fg(m)p 0 0 1 TeXcolorrgb 4729 4353 a Fl(where)p 0 TeXcolorgray
55 w Fi(D)5361 4291 y Fe(0)5356 4398 y Fg(`)5461 4353
y Fj(\021)47 b Fi(U)5756 4379 y Fg(`)5814 4353 y Fi(U)5946
4291 y Fe(y)6008 4353 y Fi(L)6123 4291 y Fe(0)6163 4353
y Fi(U)18 b(U)6427 4271 y Fe(y)6409 4401 y Fg(`)6537
4353 y Fl(=)48 b Fi(D)6856 4379 y Fg(`)p 0 0 1 TeXcolorrgb
0 0 1 TeXcolorrgb 6969 4353 a Fl(and)p 0 TeXcolorgray
56 w Fi(D)7442 4291 y Fe(0)7437 4396 y Fg(\027)7559 4353
y Fj(\021)g Fi(U)7855 4379 y Fg(\027)7930 4353 y Fi(U)8062
4291 y Fe(y)8124 4353 y Fi(N)8277 4291 y Fe(0)8317 4353
y Fi(U)18 b(U)8581 4291 y Fe(y)8563 4396 y Fg(\027)8691
4353 y Fl(=)48 b Fi(D)9010 4379 y Fg(\027)p 0 0 1 TeXcolorrgb
0 0 1 TeXcolorrgb 9141 4353 a Fl(are)56 b(unc)-5 b(hanged.)p
1 0 0 TeXcolorrgb 73 w(Also)p 0 TeXcolorgray 6353 4785
a Fj(L)6472 4811 y Fg(cc)6728 4785 y Fl(=)144 b Fi(g)6
b Fl(\()7168 4740 y(\026)7156 4785 y Fi(`)p 7156 4813
71 7 v 7255 4714 a Fg(m)7398 4785 y Fi(U)7512 4811 y
Fg(`)7570 4785 y Fi(U)7702 4714 y Fe(y)7764 4785 y Fi(U)18
b(U)8028 4714 y Fe(y)8010 4828 y Fg(\027)8119 4785 y
Fi(\027)p 8119 4813 95 7 v 8213 4714 a Fg(m)8328 4785
y Fl(\))p Fi(W)8576 4714 y Fh(+)8716 4785 y Fl(+)39 b
Fi(H)t(:C)s(:)6728 5136 y Fl(=)144 b Fi(g)6 b Fl(\()7168
5091 y(\026)7156 5136 y Fi(`)p 7156 5164 71 7 v 7255
5065 a Fg(m)7370 5136 y Fi(U)7502 5065 y Fe(0)7484 5179
y Fg(M)12 b(N)g(S)7839 5136 y Fi(\027)p 7839 5164 95
7 v 7933 5065 a Fg(m)8048 5136 y Fl(\))p Fi(W)8296 5065
y Fh(+)8437 5136 y Fl(+)38 b Fi(H)t(:C)s(:)p 1 0 0 TeXcolorrgb
4729 5568 a Fl(where)p 0 TeXcolorgray 55 w Fi(U)5348
5506 y Fe(0)5330 5612 y Fg(M)12 b(N)g(S)5704 5568 y Fj(\021)48
b Fi(U)6000 5594 y Fg(`)6058 5568 y Fi(U)6190 5506 y
Fe(y)6251 5568 y Fi(U)18 b(U)6515 5506 y Fe(y)6497 5611
y Fg(\027)6626 5568 y Fl(=)47 b Fi(U)6918 5594 y Fg(M)12
b(N)g(S)p 1 0 0 TeXcolorrgb 7301 5568 a Fl(is)57 b(also)g(unc)-5
b(hanged.)10871 5612 y
 0 setgray
 10871 5612 a 0 TeXcolorgray 1 0 0
TeXcolorrgb 4500 6000 a
 tx@Dict begin -90 Rot  end
 4500 6000 a eop end
%%Page: 15 15
TeXDict begin 15 14 bop 1 0 0 TeXcolorrgb 4500 6000 a
 tx@Dict begin 90 Rot  end

4500 6000 a 10631 1267 a Fm(15)p 0 TeXcolorgray 1 0 0
TeXcolorrgb 0 TeXcolorgray 1 0 0 TeXcolorrgb 0 0 1 TeXcolorrgb
0 0 1 TeXcolorrgb 0 0 1 TeXcolorrgb 0 TeXcolorgray 0 0 1
TeXcolorrgb 0 TeXcolorgray 0 0 1 TeXcolorrgb 1 0 0 TeXcolorrgb
0.0 0.6 0.0 TeXcolorrgb 0 TeXcolorgray Black 0 TeXcolorgray
0 TeXcolorgray 0 TeXcolorgray 6131 1570 a @beginspecial
@setspecial
 tx@Dict begin STP newpath 0.8 SLW 0  setgray  0. true 3.8 neg 7.4
neg 234.3638 14.59999 .5 Frame  gsave 3.0 -45 PtoC Shadow .25  setgray
gsave fill grestore stroke grestore gsave 1  setgray gsave fill grestore
stroke grestore gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
end
 
@endspecial 0 0 1 TeXcolorrgb 56 w Fk(Summary)67
b(of)g(Jarlsk)-6 b(og)68 b(Co\(In\)v)-11 b(ariance)p
0 TeXcolorgray 1 0 0 TeXcolorrgb 4729 2100 a Fl(Giv)-5
b(en)56 b(t)-5 b(w)g(o)57 b(mass)g(matrices)g Fi(L)f
Fl(and)f Fi(N)74 b Fl(whic)-5 b(h,)56 b(when)f(diagonalised,)h(giv)-5
b(e)56 b(correct)f(mass)4729 2412 y(eigen)-5 b(v)c(alues)56
b(and)g(mixing)g(angles,)g(can)g(alw)-5 b(a)g(ys)58 b(mak)-5
b(e)57 b Fi(simul)t(taneous)g Fl(unitary)4729 2724 y(transformations)f
(on)g(b)5 b(oth)55 b(and)h(use)g(resulting)f(matrices.)74
b(All)57 b(observ)-9 b(ables)55 b(\(eigen)-5 b(v)c(alues)4729
3036 y(and)56 b(mixing)g(matrix)g(elemen)-5 b(ts\))56
b(are)g(in)-5 b(v)c(arian)k(t)55 b(under)f(this)i(transformation.)p
0.0 0.6 0.0 TeXcolorrgb 4729 3400 a([Related)f(to)h(issue)h(of)f(extra)
f(degrees)h(of)g(freedom)g(in)f(the)h(mass)i(matrices:)4729
3712 y(W)-14 b(ell)56 b(kno)-5 b(wn)56 b(that)f(only)h(6)g(masses)j
(and)c(4)i(mixing)f(parameters)g(are)g(observ)-9 b(able,)55
b(but)g(t)-5 b(w)g(o)4729 4024 y(distinct)55 b(\(Hermitian,)g(3)38
b Fj(\002)g Fl(3\))56 b(mass)i(matrices)f(require)d(18)j(parameters)f
(to)g(b)5 b(e)55 b(sp)5 b(eci\014ed.)74 b(8)4729 4336
y(degrees)56 b(of)g(freedom)f(are)h(therefore)e(unobserv)-9
b(able)55 b(and)h(the)f(mass)j(matrices)e(cannot)g(b)5
b(e)4729 4648 y(unique.)73 b(Extra)56 b(d.o.f.s)f(corresp)5
b(ond)55 b(to)h(the)f(arbitrary)g(parameters)h(in)f(the)h(unkno)-5
b(wn)4729 4960 y(transformation)55 b(matrix)h(U.])p 0 0 1
TeXcolorrgb 4729 5324 a(NB.)h(Is)f(not)g(a)g(\\symmetry")i(-)e(that)f
(w)-5 b(ould)56 b(b)5 b(e)55 b(if)h Fi(L)8126 5262 y
Fe(0)8214 5324 y Fl(=)47 b Fi(L)p Fl(.)10871 5612 y
 0 setgray
 10871
5612 a 0 TeXcolorgray 0 0 1 TeXcolorrgb 4500 6000 a
 tx@Dict begin -90 Rot  end
 4500
6000 a eop end
%%Page: 16 16
TeXDict begin 16 15 bop 0 0 1 TeXcolorrgb 4500 6000 a
 tx@Dict begin 90 Rot  end

4500 6000 a 10631 1267 a Fm(16)p 0.0 0.6 0.0 TeXcolorrgb
1 0 0 TeXcolorrgb 0 TeXcolorgray Black 0 TeXcolorgray
0 TeXcolorgray 0 TeXcolorgray 6230 1558 a @beginspecial
@setspecial
 tx@Dict begin STP newpath 0.8 SLW 0  setgray  0. true 3.8 neg 3.8
neg 220.53564 13.79999 .5 Frame  gsave 3.0 -45 PtoC Shadow .25  setgray
gsave fill grestore stroke grestore gsave 1  setgray gsave fill grestore
stroke grestore gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
end
 
@endspecial 0 0 1 TeXcolorrgb 56 w Fk(Nomenclature)67
b(for)g(P)-6 b(articular)67 b(Bases)p 0 TeXcolorgray
1 0 0 TeXcolorrgb 1 0 0 TeXcolorrgb 4862 2025 a Fj(\017)p
1 0 0 TeXcolorrgb 84 w Fl(\\Mass)59 b(basis")e(-)f(\(sp)5
b(eci\014ed)55 b(b)-5 b(y)56 b(the)f(\\)p Fi(m)p Fl(")i(sup)5
b(erscript\))54 b(is)i(unique,)f(up)h(to)g(a)g(bunc)-5
b(h)55 b(of)5032 2317 y(p)5 b(ossible)56 b(re-phasings)h(\(whic)-5
b(h)54 b(I)i(ma)-5 b(y)58 b(come)e(bac)-5 b(k)57 b(to\).)p
0 TeXcolorgray 0 TeXcolorgray 4862 2647 a Fj(\017)p 0
TeXcolorgray 84 w Fl(\\W)-14 b(eak)57 b(\(or)f(gauge\))g(basis")h(-)g
(An)-5 b(y)56 b(basis)h(in)f(whic)-5 b(h)55 b(the)g(w)-5
b(eak)57 b(in)-5 b(teraction)54 b(is)j(diagonal)5032
2940 y(\(eg.)75 b(those)56 b(sp)5 b(eci\014ed)55 b(b)-5
b(y)56 b(the)f(un-sup)5 b(erscripted)53 b(\014elds,)j(and/or)g(b)-5
b(y)56 b(the)f(\\primed")5032 3232 y(\014elds\).)74 b(WB)57
b(is)g(not)e(unique)g(-)h(di\013eren)-5 b(t)55 b(ones)i(are)f(all)g
(related)f(b)-5 b(y)56 b(the)f Fi(U)5032 3525 y Fl(transformation.)74
b(An)-5 b(y)57 b(WB)f(can)g(b)5 b(e)56 b(used)g(to)g(sho)-5
b(w)56 b(gauge)h(in)-5 b(v)c(ariance,)55 b(etc.)p 0.0 0.6 0.0
TeXcolorrgb 0.0 0.6 0.0 TeXcolorrgb 4862 3854 a Fj(\017)p
0.0 0.6 0.0 TeXcolorrgb 84 w Fl(\\Fla)-5 b(v)g(our)57
b(basis")g(-)g(a)f(particular)e(c)-5 b(hoice)56 b(of)g(WB)h(in)f(whic)
-5 b(h)55 b(the)g(c)-5 b(harged)56 b(lepton)f(mass)5032
4147 y(matrix,)h Fi(L)5742 4084 y Fe(0)5782 4147 y Fl(,)g(is)h
(diagonal)f(\(while)f Fi(N)7388 4084 y Fe(0)7484 4147
y Fl(is)h(not\).)74 b(Corresp)5 b(onds)55 b(to)h(a)h(sp)5
b(ecial)56 b(c)-5 b(hoice)56 b(of)g Fi(U)18 b Fl(,)5032
4439 y(and)56 b(is)h(unique)e(\(up)g(to)h(the)f(de\014nition)f(of)i
(the)f(phases)i(of)f(the)f(c)-5 b(harged)56 b(lepton)f(\014elds\).)5032
4732 y(It)f(is)h(the)e(basis)i(in)f(whic)-5 b(h)53 b(all)h(6)h(leptons)
f(carry)f(one)h(of)g(the)g(\015a)-5 b(v)g(our)54 b(indices)g
Fi(e;)29 b(\026;)g(\034)19 b Fl(.)74 b(It)53 b(is)5032
5024 y(the)j Fi(conv)6 b(entional)59 b Fl(basis.)p 0 0 1
TeXcolorrgb 0 0 1 TeXcolorrgb 4862 5354 a Fj(\017)p 0 0 1
TeXcolorrgb 84 w Fl(\\Neutrino)d(Mass)i(basis")f(-)f(the)g(particular)e
(WB)j(for)e(whic)-5 b(h)55 b Fi(N)9171 5291 y Fe(0)9268
5354 y Fl(is)h(diagonal)h(and)e Fi(L)10554 5291 y Fe(0)10650
5354 y Fl(is)5032 5646 y(not.)75 b(Is)56 b(not)g(often)f(used.)p
0.0 0.6 0.0 TeXcolorrgb 0 TeXcolorgray 1 0 0 TeXcolorrgb
0 TeXcolorgray 10871 5612 a
 0 setgray
 10871 5612 a 0 TeXcolorgray
0 TeXcolorgray 4500 6000 a
 tx@Dict begin -90 Rot  end
 4500 6000 a eop end
%%Page: 17 17
TeXDict begin 17 16 bop 0 TeXcolorgray 4500 6000 a
 tx@Dict begin 90 Rot  end
 4500
6000 a 10631 1267 a Fm(17)p Black 0 TeXcolorgray 0 TeXcolorgray
0 TeXcolorgray 5437 1558 a @beginspecial @setspecial
 tx@Dict begin STP newpath 0.8 SLW 0  setgray  0. true 3.8 neg 6.59999
neg 331.09924 13.79999 .5 Frame  gsave 3.0 -45 PtoC Shadow .25  setgray
gsave fill grestore stroke grestore gsave 1  setgray gsave fill grestore
stroke grestore gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
end


@endspecial 0 0 1 TeXcolorrgb 56 w Fk(Our)68 b(Principles)f(for)g
(Constraining)i(Masses)e(and)i(Mixings)p 0 TeXcolorgray
1 0 0 TeXcolorrgb 4729 1987 a Fl(An)-5 b(y)57 b(theory)e(of)h(\015a)-5
b(v)g(our)56 b(whic)-5 b(h)55 b(constrains)h(masses)i(and)e(mixings)h
(should)e(resp)5 b(ect)55 b(certain)4729 2280 y(principles:)p
0 TeXcolorgray 0 TeXcolorgray 4862 2569 a Fj(\017)p 0
TeXcolorgray 84 w Fl(Jarlsk)-5 b(og)55 b(demonstrated)e(that)g(the)g
(SM)h(as)h(it)e(stands)h(has)g(no)g(preferred)d(basis)k(in)f(whic)-5
b(h)5032 2861 y(to)56 b(write)f(the)h(lepton)f(\(and)g(quark\))g(mass)j
(matrices.)75 b(The)55 b(mathematical)h(expressions)5032
3154 y(of)g Fi(bey)6 b(ond)56 b Fl(SM)g(constrain)-5
b(ts)56 b(should)g(therefore)e(b)5 b(e)55 b(Jarlsk)-5
b(og-co)g(v)c(arian)k(t.)75 b(If)56 b(they)f(are)5032
3446 y(not,)h(then)f(there)g(is)h(a)h(preferred)c(basis,)k(and)f(w)-5
b(e)56 b(kno)-5 b(w)56 b(of)g(no)g(ph)-5 b(ysics)56 b(whic)-5
b(h)56 b(should)5032 3739 y(prefer)f(one)h(basis)h(o)-5
b(v)g(er)56 b(another.)p 0.0 0.6 0.0 TeXcolorrgb 0.0 0.6 0.0
TeXcolorrgb 4862 4068 a Fj(\017)p 0.0 0.6 0.0 TeXcolorrgb
84 w Fl(The)g(SM)g(as)h(it)f(no)-5 b(w)56 b(stands)g(treats)g(all)g
(families)g(on)g(an)g(equal)g(fo)5 b(oting.)74 b(This)56
b(should)5032 4361 y(con)-5 b(tin)g(ue)56 b(to)g(b)5
b(e)55 b(the)g(case,)i(ie.)75 b(mass/mixing)58 b(constrain)-5
b(ts)56 b(should)f(b)5 b(e)5032 4653 y(\015a)-5 b(v)g(our-symmetric.)p
0 TeXcolorgray 1 0 0 TeXcolorrgb 0 0 1 TeXcolorrgb 4729
4942 a(A)g(t)56 b(lo)-5 b(w)g(er)57 b(priorit)-5 b(y)-14
b(,)54 b(mass/mixing)k(constrain)-5 b(ts)56 b(should)g(treat)f(c)-5
b(harged)56 b(leptons)f(and)4729 5235 y(neutrinos)g(symmetrically)-14
b(.)75 b(This)55 b(w)-5 b(ould)56 b(app)5 b(ear)55 b(to)h(b)5
b(e)56 b(in)f(line)h(with)f Fi(S)10 b(U)18 b Fl(\(2\))55
b(gauge)4729 5527 y(symmetry)-14 b(,)56 b(although)g(b)5
b(ecause)55 b(this)h(is)h(brok)-5 b(en)55 b(b)-5 b(y)56
b(w)-5 b(eak)57 b(h)-5 b(yp)5 b(erc)-5 b(harge,)54 b(there)h(is)i(p)5
b(erhaps)4729 5820 y(scop)g(e)56 b(to)g(relax)g(this)g(\(as)g(w)-5
b(e)56 b(will)g(need,)f(in)g(fact\).)10871 5612 y
 0 setgray
 10871
5612 a 0 TeXcolorgray 0 0 1 TeXcolorrgb 4500 6000 a
 tx@Dict begin -90 Rot  end
 4500
6000 a eop end
%%Page: 18 18
TeXDict begin 18 17 bop 0 0 1 TeXcolorrgb 4500 6000 a
 tx@Dict begin 90 Rot  end

4500 6000 a 10631 1267 a Fm(18)p 1 0 0 TeXcolorrgb 0
TeXcolorgray Black 0 TeXcolorgray 0 TeXcolorgray 0 TeXcolorgray
6042 1558 a @beginspecial @setspecial
 tx@Dict begin STP newpath 0.8 SLW 0  setgray  0. true 3.8 neg 6.59999
neg 246.77698 13.79999 .5 Frame  gsave 3.0 -45 PtoC Shadow .25  setgray
gsave fill grestore stroke grestore gsave 1  setgray gsave fill grestore
stroke grestore gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
end
 
@endspecial 0 0 1
TeXcolorrgb 56 w Fk(Fla)-6 b(v)g(our-Symmetric)67 b(Jarlsk)-6
b(og)68 b(In)-6 b(v)-11 b(arian)-6 b(ts)p 0 TeXcolorgray
1 0 0 TeXcolorrgb 4729 2015 a Fl(Con)h(v)g(en)g(tional)56
b(observ)-9 b(ables)56 b(are)g(not,)f(in)h(themselv)-5
b(es,)56 b(\015a)-5 b(v)g(our-symmetric.)75 b(eg.)g(the)4729
2318 y(electron)55 b(mass,)j Fi(m)5974 2344 y Fg(e)6038
2318 y Fl(,)e(carries)g(the)f(electron)g(\015a)-5 b(v)g(our)56
b(lab)5 b(el)55 b(and)h Fi(U)9009 2344 y Fg(e)p Fh(3)9134
2318 y Fl(,)g(for)g(example,)g(carries)4729 2622 y(the)f(ob)-5
b(vious)57 b(\015a)-5 b(v)g(our)56 b(and)g(mass)i(lab)5
b(els.)p 0 0 1 TeXcolorrgb 4729 2971 a(Jarlsk)-5 b(og)57
b(also)g(sho)-5 b(w)g(ed,)56 b(ho)-5 b(w)g(ev)g(er,)56
b(ho)-5 b(w)56 b(to)g(write)f(\015a)-5 b(v)g(our-symmetric)57
b(in)-5 b(v)c(arian)k(t)4729 3274 y(observ)c(ables.)p
0.0 0.6 0.0 TeXcolorrgb 4729 3578 a(Examples)56 b(are)g(\(all)g
(matrices)g(in)g(an)g(arbitrary)e(w)-5 b(eak-basis,)58
b(primes)e(dropp)5 b(ed\):)p 0 TeXcolorgray 4900 4000
a(T)-14 b(r)o(\()p Fi(L)p Fl(\))47 b(=)h Fi(m)5693 4026
y Fg(e)5795 4000 y Fl(+)39 b Fi(m)6112 4026 y Fg(\026)6231
4000 y Fl(+)f Fi(m)6547 4026 y Fg(\034)6622 4000 y Fl(;)197
b(T)-14 b(r)o(\()p Fi(L)7220 3929 y Fh(2)7288 4000 y
Fl(\))47 b(=)h Fi(m)7727 3929 y Fh(2)7727 4042 y Fg(e)7834
4000 y Fl(+)38 b Fi(m)8150 3929 y Fh(2)8150 4042 y Fg(\026)8270
4000 y Fl(+)g Fi(m)8586 3929 y Fh(2)8586 4042 y Fg(\034)8661
4000 y Fl(;)197 b(T)-14 b(r)o(\()p Fi(L)9259 3929 y Fh(3)9327
4000 y Fl(\))47 b(=)h Fi(m)9766 3929 y Fh(3)9766 4042
y Fg(e)9873 4000 y Fl(+)38 b Fi(m)10189 3929 y Fh(3)10189
4042 y Fg(\026)10308 4000 y Fl(+)h Fi(m)10625 3929 y
Fh(3)10625 4042 y Fg(\034)p 0.0 0.6 0.0 TeXcolorrgb 4729
4422 a Fl(whic)-5 b(h)55 b(form)h(a)h(complete)f(set)g(and)f(are)h(ob)
-5 b(viously)57 b(in)-5 b(v)c(arian)k(t:)p 0 TeXcolorgray
5921 4844 a(T)-14 b(r\()p Fi(L)6276 4772 y Fe(0)6315
4844 y Fl(\))143 b(=)h(T)-14 b(r)o(\()p Fi(U)18 b(LU)7417
4772 y Fe(y)7478 4844 y Fl(\))48 b(=)g(T)-14 b(r)o(\()p
Fi(LU)8257 4772 y Fe(y)8318 4844 y Fi(U)18 b Fl(\))48
b(=)g(T)-14 b(r)o(\()p Fi(L)p Fl(\);)5860 5190 y(T)g(r\()p
Fi(L)6215 5119 y Fe(0)p Fh(2)6315 5190 y Fl(\))143 b(=)h(T)-14
b(r)o(\()p Fi(U)18 b(LU)7417 5119 y Fe(y)7478 5190 y
Fi(U)g(LU)7857 5119 y Fe(y)7919 5190 y Fl(\))48 b(=)g(T)-14
b(r)o(\()p Fi(U)18 b(L)8698 5119 y Fh(2)8766 5190 y Fi(U)8898
5119 y Fe(y)8960 5190 y Fl(\))47 b(=)h(T)-14 b(r)o(\()p
Fi(L)9606 5119 y Fh(2)9674 5190 y Fl(\))p 0.0 0.6 0.0
TeXcolorrgb 4729 5612 a(etc.)10871 5612 y
 0 setgray
 10871 5612
a 0 TeXcolorgray 0.0 0.6 0.0 TeXcolorrgb 4500 6000 a
 tx@Dict begin -90 Rot  end

4500 6000 a eop end
%%Page: 19 19
TeXDict begin 19 18 bop 0.0 0.6 0.0 TeXcolorrgb 4500
6000 a
 tx@Dict begin 90 Rot  end
 4500 6000 a 10631 1267 a Fm(19)p 0 TeXcolorgray
0.0 0.6 0.0 TeXcolorrgb 0 TeXcolorgray 0.0 0.6 0.0 TeXcolorrgb
0 0 1 TeXcolorrgb 1 0 0 TeXcolorrgb 0 TeXcolorgray Black
0 TeXcolorgray 0 TeXcolorgray 0 TeXcolorgray 6987 1558
a @beginspecial @setspecial
 tx@Dict begin STP newpath 0.8 SLW 0  setgray  0. true 3.8 neg 6.59999
neg 115.02196 13.79999 .5 Frame  gsave 3.0 -45 PtoC Shadow .25  setgray
gsave fill grestore stroke grestore gsave 1  setgray gsave fill grestore
stroke grestore gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
end
 
@endspecial 0 0 1 TeXcolorrgb
56 w Fk(And)68 b(for)f(Mixing...)p 0 TeXcolorgray 1 0 0
TeXcolorrgb 4729 2037 a Fl(W)-14 b(e)56 b(deriv)-5 b(ed)55
b(earlier)g(that)p 0 TeXcolorgray 56 w Fi(U)6604 2063
y Fg(M)12 b(N)g(S)6978 2037 y Fj(\021)48 b Fi(U)7274
2063 y Fg(`)7331 2037 y Fi(U)7463 1975 y Fe(y)7445 2080
y Fg(\027)7525 2037 y Fl(.)p 0 0 1 TeXcolorrgb 4729 2341
a(Clearly)-14 b(,)55 b(if)h(w)-5 b(e)56 b(had)p 0 TeXcolorgray
56 w Fi(U)6192 2367 y Fg(\027)6314 2341 y Fl(=)48 b Fi(U)6607
2367 y Fg(`)p 0 0 1 TeXcolorrgb 6665 2341 a Fl(,)56 b(then)p
0 TeXcolorgray 55 w Fi(U)7266 2367 y Fg(M)12 b(N)g(S)7640
2341 y Fl(=)48 b Fi(I)p 0 0 1 TeXcolorrgb 70 w Fl(and)56
b(there)f(w)-5 b(ould)55 b(b)5 b(e)56 b(no)g(mixing.)p
0.0 0.6 0.0 TeXcolorrgb 4729 2644 a(Hence,)g(non-zero)f(mixing)p
0 TeXcolorgray 104 w(=)-29 b Fj(\))97 b Fi(U)7050 2670
y Fg(\027)7173 2644 y Fj(6)p Fl(=)48 b Fi(U)7466 2670
y Fg(`)p 0.0 0.6 0.0 TeXcolorrgb 7579 2644 a Fl(and)p
0 TeXcolorgray 56 w Fi(L)p 0.0 0.6 0.0 TeXcolorrgb 56
w Fl(and)p 0 TeXcolorgray 56 w Fi(N)p 0.0 0.6 0.0 TeXcolorrgb
74 w Fl(are)56 b(diagonalised)g(b)-5 b(y)56 b(di\013eren)-5
b(t)4729 2948 y(unitary)55 b(matrices,)h(ie.)74 b(they)55
b(are)h(not)g(sim)-5 b(ultaneously)56 b(diagonalisable.)p
0 TeXcolorgray 4729 3251 a(Undergraduate)f(quan)-5 b(tum)55
b(mec)-5 b(hanics)57 b(tells)f(us)g(that)f(if)h(t)-5
b(w)g(o)56 b(matrices)g(are)g(not)4729 3555 y(diagonalised)g(b)-5
b(y)56 b(the)g(same)h(op)5 b(erator,)55 b(then)g(they)g(do)h(not)g
(comm)-5 b(ute.)p 1 0 0 TeXcolorrgb 4729 3858 a(Hence,)56
b(a)g(signature)g(of)g(non-zero)f(mixing)h(m)-5 b(ust)57
b(b)5 b(e)56 b(that)f(the)g(comm)-5 b(utator)p 0 TeXcolorgray
7217 4280 a Fi(iC)60 b Fl(=)47 b([)p Fi(L;)29 b(N)18
b Fl(])47 b Fj(6)p Fl(=)h(0)p 0 0 1 TeXcolorrgb 4729
4702 a(Clearly)-14 b(,)55 b(under)g(a)h(c)-5 b(hange)56
b(of)g(w)-5 b(eak)57 b(basis,)p 0 TeXcolorgray 57 w(C)p
0 0 1 TeXcolorrgb 55 w(transforms)f(according)g(to)p
0 TeXcolorgray 56 w Fi(C)k Fj(!)48 b Fi(C)10113 4639
y Fe(0)10201 4702 y Fl(=)g Fi(U)18 b(C)12 b(U)10777 4639
y Fe(y)p 0 0 1 TeXcolorrgb 4729 5005 a Fl(and)56 b(an)-5
b(y)56 b(p)5 b(olynomial)56 b(of)p 0 TeXcolorgray 56
w Fi(C)p 0 0 1 TeXcolorrgb 68 w Fl(tranforms)g(lik)-5
b(ewise.)74 b(As)57 b(b)5 b(efore,)55 b(traces)h(are)g(in)-5
b(v)c(arian)k(t.)p 0.0 0.6 0.0 TeXcolorrgb 4729 5308
a(Ho)g(w)g(ev)g(er,)p 0 TeXcolorgray 57 w(T)-14 b(r)o
Fi(C)60 b Fl(=)48 b(0)p 0.0 0.6 0.0 TeXcolorrgb 56 w(for)56
b(an)-5 b(y)56 b(comm)-5 b(utator.)75 b(Therefore)54
b(only)i(t)-5 b(w)g(o)57 b(indep)5 b(enen)-5 b(t)4729
5612 y(comm)g(utator)57 b(in)-5 b(v)c(arian)k(ts)55 b(can)h(b)5
b(e)56 b(formed)f(from)p 0 TeXcolorgray 56 w Fi(C)12
b Fl(:)75 b(T)-14 b(r)o Fi(C)8517 5549 y Fh(2)p 0.0 0.6 0.0
TeXcolorrgb 8641 5612 a Fl(and)p 0 TeXcolorgray 56 w(T)g(r)o
Fi(C)9275 5549 y Fh(3)9344 5612 y Fl(.)10871 5612 y
 0 setgray
 10871
5612 a 0 TeXcolorgray 0 TeXcolorgray 4500 6000 a
 tx@Dict begin -90 Rot  end
 4500
6000 a eop end
%%Page: 20 20
TeXDict begin 20 19 bop 0 TeXcolorgray 4500 6000 a
 tx@Dict begin 90 Rot  end
 4500
6000 a 10631 1267 a Fm(20)p 0.0 0.6 0.0 TeXcolorrgb 0
TeXcolorgray 0.0 0.6 0.0 TeXcolorrgb 0 TeXcolorgray 0.0 0.6 0.0
TeXcolorrgb 0 0 1 TeXcolorrgb 0 TeXcolorgray 0 0 1 TeXcolorrgb
0 TeXcolorgray 0 0 1 TeXcolorrgb 0 TeXcolorgray 0 0 1
TeXcolorrgb 0 TeXcolorgray 1 0 0 TeXcolorrgb 0 TeXcolorgray
0.0 0.6 0.0 TeXcolorrgb 0 TeXcolorgray 0.0 0.6 0.0 TeXcolorrgb
0 TeXcolorgray 0.0 0.6 0.0 TeXcolorrgb 0 TeXcolorgray
0.0 0.6 0.0 TeXcolorrgb 0 0 1 TeXcolorrgb 0 TeXcolorgray
0 0 1 TeXcolorrgb 0 TeXcolorgray 0 0 1 TeXcolorrgb 0
TeXcolorgray 1 0 0 TeXcolorrgb 0 TeXcolorgray Black 0
TeXcolorgray 0 TeXcolorgray 0 TeXcolorgray 7217 1558
a @beginspecial @setspecial
 tx@Dict begin STP newpath 0.8 SLW 0  setgray  0. true 3.8 neg 3.8
neg 82.91566 13.79999 .5 Frame  gsave 3.0 -45 PtoC Shadow .25  setgray
gsave fill grestore stroke grestore gsave 1  setgray gsave fill grestore
stroke grestore gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
end
 
@endspecial 0 0 1 TeXcolorrgb
56 w Fk(Con)-6 b(tin)g(ued...)p 0 TeXcolorgray 1 0 0
TeXcolorrgb 4729 2026 a Fl(It)56 b(turns)f(out)g(that)p
0 TeXcolorgray 56 w(T)-14 b(r)o Fi(C)6324 1963 y Fh(3)p
1 0 0 TeXcolorrgb 6448 2026 a Fl(is)57 b(a)f(pure-)p
Fi(C)12 b(P)23 b Fl(-violating)55 b(observ)-9 b(able:)p
0 TeXcolorgray 4809 2468 a(T)-14 b(r)28 b Fi(C)5144 2396
y Fh(3)5212 2468 y Fi(=)p Fl(3)144 b(=)g(Det)27 b Fi(C)5524
2823 y Fl(=)144 b Fj(\000)p Fl(2\()p Fi(m)6230 2848 y
Fg(\026)6348 2823 y Fj(\000)39 b Fi(m)6668 2848 y Fg(\034)6743
2823 y Fl(\)\()p Fi(m)7022 2848 y Fg(\034)7134 2823 y
Fj(\000)f Fi(m)7453 2848 y Fg(e)7517 2823 y Fl(\)\()p
Fi(m)7796 2848 y Fg(e)7898 2823 y Fj(\000)g Fi(m)8217
2848 y Fg(\026)8298 2823 y Fl(\)\()p Fi(m)8577 2848 y
Fh(2)8683 2823 y Fj(\000)g Fi(m)9002 2848 y Fh(3)9071
2823 y Fl(\)\()p Fi(m)9350 2848 y Fh(3)9456 2823 y Fj(\000)g
Fi(m)9775 2848 y Fh(1)9843 2823 y Fl(\)\()p Fi(m)10122
2848 y Fh(1)10228 2823 y Fj(\000)g Fi(m)10547 2848 y
Fh(2)10616 2823 y Fl(\))p Fi(J)p 1 0 0 TeXcolorrgb 4729
3264 a Fl(where)p 0 TeXcolorgray 55 w Fi(J)p 1 0 0 TeXcolorrgb
72 w Fl(is)57 b(t)-5 b(wice)55 b(the)h(area)g(of)g(the)f(unitarit)-5
b(y)54 b(triangle.)74 b(It)56 b(is)g(manifestly)g(symmetric)4729
3576 y(among)h(all)f(\015a)-5 b(v)g(our)57 b(indices)e(and)h(all)g
(mass)i(indices.)p 0 TeXcolorgray 4729 3888 a(T)-14 b(r)o
Fi(C)5035 3826 y Fh(2)p 0.0 0.6 0.0 TeXcolorrgb 5160
3888 a Fl(is)56 b(a)h(pure-)p Fi(C)12 b(P)23 b Fl(-conserving)54
b(observ)-9 b(able,)56 b(and)f(is)i(a)f(somewhat)h(more)f(complicated)
4729 4200 y(\(but)f(also)i(manifestly)e(symmetric)i(among)g(\015a)-5
b(v)g(our)56 b(and)g(mass)i(lab)5 b(els\))55 b(function)f(of)i(lepton)
4729 4512 y(masses)i(and)e(mixing)g(in)-5 b(v)c(arian)k(ts.)p
0 0 1 TeXcolorrgb 4729 4876 a(If)56 b(mixing)g(is)g(zero,)g(then)f(b)5
b(oth)55 b(these)h(in)-5 b(v)c(arian)k(ts)55 b(are)h(zero.)74
b(Hence,)56 b(they)g(represen)-5 b(t)4729 5188 y(di\013eren)g(t)55
b(\015a)-5 b(v)g(our-symmetric)56 b Fi(measur)5 b(es)58
b Fl(of)e(mixing.)10871 5612 y
 0 setgray
 10871 5612 a 0 TeXcolorgray
0 0 1 TeXcolorrgb 4500 6000 a
 tx@Dict begin -90 Rot  end
 4500 6000 a eop end
%%Page: 21 21
TeXDict begin 21 20 bop 0 0 1 TeXcolorrgb 4500 6000 a
 tx@Dict begin 90 Rot  end

4500 6000 a 10631 1267 a Fm(21)p 0.0 0.6 0.0 TeXcolorrgb
0 TeXcolorgray 1 0 0 TeXcolorrgb 0 TeXcolorgray 1 0 0
TeXcolorrgb 0 TeXcolorgray 1 0 0 TeXcolorrgb 0 TeXcolorgray
1 0 0 TeXcolorrgb 0 TeXcolorgray Black 0 TeXcolorgray
0 TeXcolorgray 0 TeXcolorgray 5771 1558 a @beginspecial
@setspecial
 tx@Dict begin STP newpath 0.8 SLW 0  setgray  0. true 3.8 neg 6.59999
neg 284.5748 13.79999 .5 Frame  gsave 3.0 -45 PtoC Shadow .25  setgray
gsave fill grestore stroke grestore gsave 1  setgray gsave fill grestore
stroke grestore gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
end
 
@endspecial 0 0 1 TeXcolorrgb 56 w Fk(Jarlsk)-6
b(og-Co)g(v)-11 b(arian)-6 b(t)68 b(Constrain)-6 b(t)68
b(on)g(the)g(Mixing)p 0 TeXcolorgray 1 0 0 TeXcolorrgb
4729 2077 a Fl(Motiv)-9 b(ated)55 b(b)-5 b(y)56 b(quasi-maximal)i
(nature)d(of)h(the)f(leptonic)g(mixings,)i(w)-5 b(ere)55
b(motiv)-9 b(ated)56 b(to)g(try)4729 2389 y(to)g(\\explain")g(this)g(b)
-5 b(y)56 b(maximising)h(\(more)f(formally)-14 b(,)56
b(extremising\))f(a)h(\015a)-5 b(v)g(our-symmetric)4729
2701 y(Jarlsk)g(og)57 b(in)-5 b(v)c(arian)k(t,)p 0 TeXcolorgray
55 w Fj(A)48 b Fl(=)g(T)-14 b(r)o([)p Fi(f)18 b Fl(\()p
Fi(L;)29 b(N)18 b Fl(\)].)p 0 TeXcolorgray 4729 3013
a(Extremisation)55 b(means)i(\014nding)e(v)-9 b(alues)56
b(for)g(whic)-5 b(h)55 b(deriv)-9 b(ativ)k(es)55 b(of)h(in)-5
b(v)c(arian)k(t)55 b(is)i(zero.)p 0.0 0.6 0.0 TeXcolorrgb
4729 3325 a(Deriv)-9 b(ativ)k(e)55 b(wrt)g(what?)73 b(\(mixing)56
b(angles,)h(masses?\).)p 0 0 1 TeXcolorrgb 4729 3637
a(Doh!)74 b(Deriv)-9 b(ativ)k(es)56 b(wrt)f(elemen)-5
b(ts)56 b(of)g(matrices)g(themselv)-5 b(es,)57 b(of)f(course:)p
0 TeXcolorgray 5888 4079 a Fi(@)5977 4105 y Fg(L)6067
4079 y Fl(\()p Fj(A)p Fl(\))48 b(=)g Fi(@)9 b Fl(\()p
Fj(A)p Fl(\))p Fi(=@)g(L)48 b Fl(=)g(0;)366 b Fi(@)8040
4105 y Fg(N)8156 4079 y Fl(\()p Fj(A)p Fl(\))47 b(=)h
Fi(@)9 b Fl(\()p Fj(A)p Fl(\))p Fi(=@)g(N)66 b Fl(=)48
b(0)p Fi(:)p 1 0 0 TeXcolorrgb 4729 4521 a Fl(T)-14 b(reats)56
b(all)g(indices)f(symmetrically)-14 b(,)56 b(and)g(leads)g(inevitably)f
(to)h(Jarlsk)-5 b(og-co)g(v)c(arian)k(t)57 b(matrix)4729
4833 y(constrain)-5 b(ts!)p 0 TeXcolorgray 4729 5145
a(W)-14 b(e)56 b(re-disco)-5 b(v)g(ered)56 b(some)h(established)f
(results)f(on)h(di\013eren)-5 b(tiating)55 b(scalar)h(functions)f(of)
4729 5457 y(matrices)h(with)f(resp)5 b(ect)55 b(to)h(their)f(elemen)-5
b(ts.)10871 5612 y
 0 setgray
 10871 5612 a 0 TeXcolorgray 0 TeXcolorgray
4500 6000 a
 tx@Dict begin -90 Rot  end
 4500 6000 a eop end
%%Page: 22 22
TeXDict begin 22 21 bop 0 TeXcolorgray 4500 6000 a
 tx@Dict begin 90 Rot  end
 4500
6000 a 10631 1267 a Fm(22)p 1 0 0 TeXcolorrgb 0 TeXcolorgray
0 0 1 TeXcolorrgb 0.0 0.6 0.0 TeXcolorrgb 0 TeXcolorgray
0 TeXcolorgray 1 0 0 TeXcolorrgb 0 TeXcolorgray Black
0 TeXcolorgray 0 TeXcolorgray 0 TeXcolorgray 7217 1558
a @beginspecial @setspecial
 tx@Dict begin STP newpath 0.8 SLW 0  setgray  0. true 3.8 neg 3.8
neg 82.91566 13.79999 .5 Frame  gsave 3.0 -45 PtoC Shadow .25  setgray
gsave fill grestore stroke grestore gsave 1  setgray gsave fill grestore
stroke grestore gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
end
 
@endspecial 0 0 1 TeXcolorrgb
56 w Fk(Con)-6 b(tin)g(ued...)p 0 TeXcolorgray 0 TeXcolorgray
4729 2032 a Fl(Question)56 b(w)-5 b(as,)57 b(whic)-5
b(h)55 b(in)-5 b(v)c(arian)k(t?)73 b(\(W)-14 b(e)56 b(tried)f(sev)-5
b(eral!\))p 1 0 0 TeXcolorrgb 4729 2330 a(As)57 b(an)f(example,)g
(consider)p 0 TeXcolorgray 56 w(T)-14 b(r)o Fi(C)6882
2268 y Fh(3)6950 2330 y Fl(.)p 1 0 0 TeXcolorrgb 75 w(Extremisation)55
b(conditions)g(are:)p 0 TeXcolorgray 6611 2740 a Fi(@)6700
2766 y Fg(L)6819 2740 y Fl(T)-14 b(r)47 b Fi(C)7173 2669
y Fh(3)7241 2740 y Fi(=)p Fl(3)144 b(=)g Fj(\000)p Fi(i)p
Fl([)p Fi(N)9 b(;)29 b(C)8420 2669 y Fh(2)8486 2740 y
Fl(])8533 2669 y Fg(T)8676 2740 y Fl(=)48 b(0)p Fi(;)6585
3081 y(@)6674 3107 y Fg(N)6819 3081 y Fl(T)-14 b(r)47
b Fi(C)7173 3010 y Fh(3)7241 3081 y Fi(=)p Fl(3)144 b(=)g(+)p
Fi(i)p Fl([)p Fi(L;)29 b(C)8388 3010 y Fh(2)8454 3081
y Fl(])8501 3010 y Fg(T)8644 3081 y Fl(=)48 b(0)p Fi(:)p
0.0 0.6 0.0 TeXcolorrgb 4729 3491 a Fl(Manifestly)56
b(Jarlsk)-5 b(og-co)g(v)c(arian)k(t)56 b(\(ie.)g(basis-indep)5
b(enden)-5 b(t\))53 b(constrain)-5 b(ts:)75 b(b)5 b(oth)55
b(sides)h(of)g(the)4729 3789 y(equation)f(are)h(eviden)-5
b(tly)55 b(form-in)-5 b(v)c(arian)k(t)55 b(under)g(an)h(arbitrary)e
Fi(U)18 b Fl(\(3\))56 b(transformation)p 0 TeXcolorgray
4729 4087 a Fi(L)48 b Fj(!)g Fi(U)18 b(L)29 b(U)5520
4025 y Fe(y)5581 4087 y Fl(,)56 b Fi(N)66 b Fj(!)48 b
Fi(U)18 b(N)47 b(U)6551 4025 y Fe(y)6613 4087 y Fl(.)p
0.0 0.6 0.0 TeXcolorrgb 75 w(W)-14 b(e)56 b(w)-5 b(ould)56
b(obtain)f(the)g(same)j(constrain)-5 b(ts)55 b(p)5 b(erforming)55
b(the)4729 4385 y(extremisation)g(in)h(an)-5 b(y)57 b(basis.)p
0 0 1 TeXcolorrgb 4729 4684 a(The)f(equations)f(ob)-5
b(viously)57 b(treat)e(all)h(\015a)-5 b(v)g(our)56 b(and)g(mass)i(lab)5
b(els)56 b(symmetrically)g(and)4729 4982 y(therefore)e(satisfy)i(our)g
(t)-5 b(w)g(o)56 b(principal)f(requiremen)-5 b(ts.)p
1 0 0 TeXcolorrgb 4729 5280 a(This)56 b(is)g(a)h(general)f(prop)5
b(ert)-5 b(y)54 b(of)i(our)f(extremisation)h(pro)5 b(cedure.)p
0.0 0.6 0.0 TeXcolorrgb 4729 5578 a(Finally)-14 b(,)p
0 TeXcolorgray 55 w Fi(L)p 0.0 0.6 0.0 TeXcolorrgb 56
w Fl(and)p 0 TeXcolorgray 56 w Fi(N)p 0.0 0.6 0.0 TeXcolorrgb
74 w Fl(are)56 b(treated)f(symmetrically)h(in)g(this)f(case.)10871
5612 y
 0 setgray
 10871 5612 a 0 TeXcolorgray 0.0 0.6 0.0 TeXcolorrgb
4500 6000 a
 tx@Dict begin -90 Rot  end
 4500 6000 a eop end
%%Page: 23 23
TeXDict begin 23 22 bop 0.0 0.6 0.0 TeXcolorrgb 4500
6000 a
 tx@Dict begin 90 Rot  end
 4500 6000 a 10631 1267 a Fm(23)p 0 TeXcolorgray
0.0 0.6 0.0 TeXcolorrgb 0 TeXcolorgray 0.0 0.6 0.0 TeXcolorrgb
1 0 0 TeXcolorrgb 0 0 1 TeXcolorrgb 0.0 0.6 0.0 TeXcolorrgb
0 TeXcolorgray 0.0 0.6 0.0 TeXcolorrgb 0 TeXcolorgray
1 0 0 TeXcolorrgb 0 TeXcolorgray 1 0 0 TeXcolorrgb 0
TeXcolorgray 0 TeXcolorgray Black 0 TeXcolorgray 0 TeXcolorgray
0 TeXcolorgray 6815 1558 a @beginspecial @setspecial
 tx@Dict begin STP newpath 0.8 SLW 0  setgray  0. true 3.8 neg 3.8
neg 138.99165 13.79999 .5 Frame  gsave 3.0 -45 PtoC Shadow .25  setgray
gsave fill grestore stroke grestore gsave 1  setgray gsave fill grestore
stroke grestore gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
end


@endspecial 0 0 1 TeXcolorrgb 56 w Fk(Mak)-6 b(e)68
b(a)g(Mo)6 b(dest)67 b(Start)p 0 TeXcolorgray 1 0 0 TeXcolorrgb
4729 2067 a Fl(Before)56 b(pro)5 b(ceding,)54 b(decide)h(to)h
(extremise)g(at)g Fi(f)18 b(ixed)56 b Fl(lepton)f(masses.)p
0 TeXcolorgray 4729 2379 a(\(Allo)-5 b(wing)56 b(them)g(to)g(v)-9
b(ary)55 b(is)i(the)e(ultimate)g(goal,)i(but)e(w)-5 b(an)g(ted)56
b(a)g(mo)5 b(dest)56 b(start.\))p 0.0 0.6 0.0 TeXcolorrgb
4729 2691 a(Extremisation)f(with)g(constrain)-5 b(ts)104
b(=)-29 b Fj(\))104 b Fl(Lagrange)57 b(m)-5 b(ultipliers.)p
0 0 1 TeXcolorrgb 4729 3003 a(Outcome)56 b(is)h(to)f(mo)5
b(dify)55 b(RHS)h(of)g(equations:)p 0 TeXcolorgray 5671
3444 a(\()p Fi(@)5826 3470 y Fg(L)5944 3444 y Fl(T)-14
b(r)47 b Fi(C)6298 3373 y Fh(3)6366 3444 y Fi(=)p Fl(3\))6600
3373 y Fg(T)6743 3444 y Fl(=)h Fj(\000)p Fi(i)p Fl([)p
Fi(N)9 b(;)29 b(C)7514 3373 y Fh(2)7581 3444 y Fl(])191
b(=)g Fi(\025)8239 3470 y Fg(L)p Fh(0)8477 3444 y Fl(+)86
b Fi(\025)8792 3470 y Fg(L)p Fh(1)8972 3444 y Fi(L)g
Fl(+)g Fi(\025)9488 3470 y Fg(L)p Fh(2)9668 3444 y Fi(L)9783
3373 y Fh(2)5676 3800 y Fl(\()p Fi(@)5831 3825 y Fg(N)5976
3800 y Fl(T)-14 b(r)47 b Fi(C)6330 3728 y Fh(3)6398 3800
y Fi(=)p Fl(3\))6632 3728 y Fg(T)6775 3800 y Fl(=)h(+)p
Fi(i)p Fl([)p Fi(L;)29 b(C)7514 3728 y Fh(2)7581 3800
y Fl(])191 b(=)g Fi(\025)8239 3825 y Fg(N)12 b Fh(0)8483
3800 y Fl(+)68 b Fi(\025)8780 3825 y Fg(N)12 b Fh(1)8986
3800 y Fi(N)85 b Fl(+)67 b Fi(\025)9502 3825 y Fg(N)12
b Fh(2)9708 3800 y Fi(N)9861 3728 y Fh(2)p 0 0 1 TeXcolorrgb
4729 4241 a Fl(where)55 b(the)g(arbitrary)g(constan)-5
b(ts)56 b Fi(\025)h Fl(are)f(the)f(LMs.)76 b(\(Eqs.)e(still)56
b(Jarlsk)-5 b(og-co)g(v)c(arian)k(t\).)p 1 0 0 TeXcolorrgb
4729 4605 a(NB.)57 b(18)g(constrain)-5 b(t)55 b(eqns.)75
b(but)55 b(not)g(all)h(indep)5 b(enden)-5 b(t.)72 b(Should)55
b(exactly)h(\014x)f(the)h(mixings)g(to)4729 4917 y(some)h(v)-9
b(alues,)56 b(while)f(all)h(masses)j(are)d(\014xed)f(to)h(kno)-5
b(wn)56 b(v)-9 b(alues.)10871 5612 y
 0 setgray
 10871 5612 a 0 TeXcolorgray
1 0 0 TeXcolorrgb 4500 6000 a
 tx@Dict begin -90 Rot  end
 4500 6000 a eop end
%%Page: 24 24
TeXDict begin 24 23 bop 1 0 0 TeXcolorrgb 4500 6000 a
 tx@Dict begin 90 Rot  end

4500 6000 a 10631 1267 a Fm(24)p 0 0 1 TeXcolorrgb 0
TeXcolorgray 0 0 1 TeXcolorrgb 0.0 0.6 0.0 TeXcolorrgb
0 TeXcolorgray 1 0 0 TeXcolorrgb 0 TeXcolorgray Black
0 TeXcolorgray 0 TeXcolorgray 0 TeXcolorgray 7015 1558
a @beginspecial @setspecial
 tx@Dict begin STP newpath 0.8 SLW 0  setgray  0. true 3.8 neg 3.8
neg 111.11032 13.79999 .5 Frame  gsave 3.0 -45 PtoC Shadow .25  setgray
gsave fill grestore stroke grestore gsave 1  setgray gsave fill grestore
stroke grestore gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
end
 
@endspecial 0 0 1 TeXcolorrgb
56 w Fk(Solution)69 b(Metho)6 b(d)p 0 TeXcolorgray 1 0 0
TeXcolorrgb 4729 2067 a Fl(Use)57 b(co)-5 b(v)c(ariance)56
b(to)g(c)-5 b(ho)5 b(ose)56 b(an)-5 b(y)57 b(basis)g(in)e(whic)-5
b(h)56 b(to)g(solv)-5 b(e.)75 b(Cho)5 b(ose)57 b(\015a)-5
b(v)g(our)56 b(basis)h(\()p 0 TeXcolorgray Fi(L)p 1 0 0
TeXcolorrgb 55 w Fl(is)4729 2379 y(diagonal,)p 0 TeXcolorgray
56 w Fi(N)p 1 0 0 TeXcolorrgb 74 w Fl(is)g(not\))e(-)h(o\013)h
(diagonal)f(elemen)-5 b(ts)57 b(of)f Fi(@)8190 2404 y
Fg(L)8336 2379 y Fl(Eqn.)74 b(=)48 b(0.)p 0 0 1 TeXcolorrgb
4729 2691 a(F)-14 b(urther)54 b(c)-5 b(ho)5 b(ose)57
b(phase)f(con)-5 b(v)g(en)g(tion)56 b(in)f(whic)-5 b(h)56
b(imaginary)g(parts)g(of)p 0 TeXcolorgray 56 w Fi(N)p
0 0 1 TeXcolorrgb 74 w Fl(are)g(all)g(of)g(equal)4729
3003 y(mo)5 b(dulus:)p 0 TeXcolorgray 7303 3137 a Fi(e)552
b(\026)g(\034)6185 3863 y(N)114 b Fl(=)6672 3570 y Fi(e)6660
3882 y(\026)6665 4194 y(\034)6872 3362 y Ff(0)6872 3665
y(B)6872 3768 y(B)6872 3872 y(B)6872 3982 y(@)7281 3570
y Fi(a)489 b(z)47 b Fl(+)38 b Fi(id)233 b(y)45 b Fj(\000)38
b Fi(id)7104 3882 y(z)46 b Fj(\000)39 b Fi(id)495 b(b)415
b(x)38 b Fl(+)g Fi(id)7104 4194 y(y)45 b Fl(+)38 b Fi(id)306
b(x)38 b Fj(\000)g Fi(id)413 b(c)8977 3362 y Ff(1)8977
3665 y(C)8977 3768 y(C)8977 3872 y(C)8977 3982 y(A)p
0.0 0.6 0.0 TeXcolorrgb 4729 4615 a Fl(V)-14 b(ariables)p
0 TeXcolorgray 56 w Fi(a)p Fl(,)57 b Fi(b)p Fl(,)f Fi(c)p
Fl(,)f Fi(x)p Fl(,)h Fi(y)6 b Fl(,)56 b Fi(z)p 0.0 0.6 0.0
TeXcolorrgb 64 w Fl(and)p 0 TeXcolorgray 56 w Fi(d)p
0.0 0.6 0.0 TeXcolorrgb 85 w Fl(determine)e(the)i(three)e(neutrino)h
(masses)j(and)e(the)f(four)4729 4927 y(mixing)h(parameters)10871
5612 y
 0 setgray
 10871 5612 a 0 TeXcolorgray 0.0 0.6 0.0 TeXcolorrgb
4500 6000 a
 tx@Dict begin -90 Rot  end
 4500 6000 a eop end
%%Page: 25 25
TeXDict begin 25 24 bop 0.0 0.6 0.0 TeXcolorrgb 4500
6000 a
 tx@Dict begin 90 Rot  end
 4500 6000 a 10631 1267 a Fm(25)p 0 TeXcolorgray
0.0 0.6 0.0 TeXcolorrgb 0 TeXcolorgray 0.0 0.6 0.0 TeXcolorrgb
0 TeXcolorgray 0 0 1 TeXcolorrgb 0 TeXcolorgray 0 0 1
TeXcolorrgb 1 0 0 TeXcolorrgb 0 TeXcolorgray 1 0 0 TeXcolorrgb
0 TeXcolorgray 1 0 0 TeXcolorrgb 0 TeXcolorgray Black
0 TeXcolorgray 0 TeXcolorgray 0 TeXcolorgray 6948 1582
a @beginspecial @setspecial
 tx@Dict begin STP newpath 0.8 SLW 0  setgray  0. true 3.8 neg 3.8
neg 120.42616 15.47008 .5 Frame  gsave 3.0 -45 PtoC Shadow .25  setgray
gsave fill grestore stroke grestore gsave 1  setgray gsave fill grestore
stroke grestore gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
end
 
@endspecial 0 0 1 TeXcolorrgb
56 w Fk(Solution)69 b(for)e Fc(T)-19 b(r)o Fb(C)8531
1507 y Fa(3)p 0 TeXcolorgray 1 0 0 TeXcolorrgb 4729 2091
a Fl(Solution)55 b(is)h(giv)-5 b(en)57 b(b)-5 b(y)p 0
TeXcolorgray 6699 2295 a Fi(a)48 b Fl(=)g Fi(b)g Fl(=)f
Fi(c)260 b Fl(and)g Fi(x)48 b Fl(=)g Fi(y)54 b Fl(=)48
b Fi(z)p 1 0 0 TeXcolorrgb 4729 2681 a Fl(with)p 0 TeXcolorgray
55 w Fi(a;)29 b(x)p 1 0 0 TeXcolorrgb 56 w Fl(and)p 0
TeXcolorgray 56 w Fi(d)p 1 0 0 TeXcolorrgb 56 w Fl(\014xed)55
b(b)-5 b(y)56 b(the)f Fi(\027)68 b Fl(masses.)p 0 0 1
TeXcolorrgb 4729 2993 a(Corresp)5 b(onds)55 b(to)h(trimaximal)g(lepton)
f(mixing)i(\(an)e(old)h(friend\):)p 0 TeXcolorgray 6403
3755 a Fi(U)6517 3781 y Fg(M)12 b(N)g(S)6939 3755 y Fl(=)7255
3639 y(1)p 7183 3715 228 7 v 7183 3750 a Fj(p)p 7327
3750 85 7 v 7327 3892 a Fl(3)7457 3254 y Ff(0)7457 3557
y(B)7457 3660 y(B)7457 3764 y(B)7457 3874 y(@)7689 3462
y Fl(1)355 b(1)368 b(1)7689 3774 y(1)341 b Fi(!)313 b(!)8643
3712 y Fe(\003)7689 4086 y Fl(1)307 b Fi(!)8191 4024
y Fe(\003)8566 4086 y Fi(!)8759 3254 y Ff(1)8759 3557
y(C)8759 3660 y(C)8759 3764 y(C)8759 3874 y(A)p 0 0 1
TeXcolorrgb 4729 4561 a Fl(where)p 0 TeXcolorgray 55
w Fi(!)54 b Fl(=)48 b Fi(e)5632 4499 y Fh(2)p Fg(i\031)t(=)p
Fh(3)5986 4561 y Fl(=)f Fj(\000)6315 4493 y Fh(1)p 6315
4521 61 7 v 6315 4620 a(2)6432 4561 y Fl(+)38 b Fi(i)6676
4398 y Fe(p)p 6778 4398 61 6 v 95 x Fh(3)p 6676 4521
163 7 v 6727 4620 a(2)p 0 0 1 TeXcolorrgb 6856 4561 a
Fl(,)56 b(a)g(cub)5 b(e-ro)g(ot)55 b(of)h(unit)-5 b(y)-14
b(.)p 0.0 0.6 0.0 TeXcolorrgb 4729 4925 a(This)56 b(corresp)5
b(onds)55 b(\(unsurprisingly\))f(to)i(maximal)h Fi(C)12
b(P)79 b Fl(violation.)74 b(Suggestiv)-5 b(e,)56 b(but)4729
5237 y(excluded)f(b)-5 b(y)56 b(exp)5 b(erimen)-5 b(t.)10871
5612 y
 0 setgray
 10871 5612 a 0 TeXcolorgray 0.0 0.6 0.0 TeXcolorrgb
4500 6000 a
 tx@Dict begin -90 Rot  end
 4500 6000 a eop end
%%Page: 26 26
TeXDict begin 26 25 bop 0.0 0.6 0.0 TeXcolorrgb 4500
6000 a
 tx@Dict begin 90 Rot  end
 4500 6000 a 10631 1267 a Fm(26)p 0 0 1 TeXcolorrgb
0 TeXcolorgray 0 0 1 TeXcolorrgb 0 TeXcolorgray 0 0 1
TeXcolorrgb 1 0 0 TeXcolorrgb 0 TeXcolorgray 1 0 0 TeXcolorrgb
0 TeXcolorgray 1 0 0 TeXcolorrgb 0 TeXcolorgray 1 0 0
TeXcolorrgb 0 TeXcolorgray Black 0 TeXcolorgray 0 TeXcolorgray
0 TeXcolorgray 6953 1582 a @beginspecial @setspecial
 tx@Dict begin STP newpath 0.8 SLW 0  setgray  0. true 3.8 neg 6.59999
neg 119.71622 15.47008 .5 Frame  gsave 3.0 -45 PtoC Shadow .25  setgray
gsave fill grestore stroke grestore gsave 1  setgray gsave fill grestore
stroke grestore gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
end


@endspecial 0 0 1 TeXcolorrgb 56 w Fk(T)-17 b(ry)67
b(Instead)h Fc(T)-19 b(r)o Fb(C)8526 1507 y Fa(2)p 0
TeXcolorgray 1 0 0 TeXcolorrgb 4729 2099 a Fl(Constrain)-5
b(ts)56 b(are)g(no)-5 b(w:)p 0 TeXcolorgray 5716 2541
a(\()p Fj(\000)p Fi(@)6005 2567 y Fg(L)6095 2541 y Fl(T)-14
b(r)28 b Fi(C)6430 2470 y Fh(2)6498 2541 y Fi(=)p Fl(2\))6732
2470 y Fg(T)6875 2541 y Fl(=)48 b(+[)p Fi(N)9 b(;)29
b(C)12 b Fl(])142 b(=)i Fi(\025)8147 2567 y Fg(L)p Fh(0)8384
2541 y Fl(+)86 b Fi(\025)8699 2567 y Fg(L)p Fh(1)8879
2541 y Fi(L)g Fl(+)g Fi(\025)9395 2567 y Fg(L)p Fh(2)9575
2541 y Fi(L)9690 2470 y Fh(2)5716 2896 y Fl(\()p Fj(\000)p
Fi(@)6005 2922 y Fg(N)6121 2896 y Fl(T)-14 b(r)28 b Fi(C)6456
2825 y Fh(2)6524 2896 y Fi(=)p Fl(2\))6758 2825 y Fg(T)6901
2896 y Fl(=)48 b Fj(\000)p Fl([)p Fi(L;)29 b(C)12 b Fl(])142
b(=)i Fi(\025)8147 2922 y Fg(N)12 b Fh(0)8391 2896 y
Fl(+)67 b Fi(\025)8687 2922 y Fg(N)12 b Fh(1)8893 2896
y Fi(N)85 b Fl(+)67 b Fi(\025)9409 2922 y Fg(N)12 b Fh(2)9615
2896 y Fi(N)9768 2825 y Fh(2)9837 2896 y Fi(:)p 0 0 1
TeXcolorrgb 4729 3338 a Fl(Unsurprisingly)-14 b(,)55
b(here)g(w)-5 b(e)56 b(get)g(a)h Fi(C)12 b(P)23 b Fl(-conserving)55
b(solution:)p 0 TeXcolorgray 5110 3825 a Fi(x)47 b Fl(=)h
Fj(\006)5566 3669 y Ff(p)p 5738 3669 1140 7 v 156 x Fl(\()p
Fi(a)39 b Fj(\000)f Fi(b)p Fl(\)\()p Fi(c)f Fj(\000)h
Fi(a)p Fl(\))p Fi(E)418 b(E)57 b Fl(=)8181 3708 y(\()p
Fi(m)8394 3734 y Fg(e)8496 3708 y Fj(\000)39 b Fi(m)8816
3734 y Fg(\026)8897 3708 y Fl(\)\()p Fi(m)9176 3734 y
Fg(\034)9288 3708 y Fj(\000)f Fi(m)9607 3734 y Fg(e)9671
3708 y Fl(\))p 7665 3785 2590 7 v 7665 3943 a(\()p Fi(m)7878
3969 y Fg(e)7980 3943 y Fl(+)g Fi(m)8296 3969 y Fg(\026)8415
3943 y Fj(\000)g Fl(2)p Fi(m)8818 3969 y Fg(\034)8894
3943 y Fl(\)\()p Fi(m)9173 3969 y Fg(\034)9285 3943 y
Fl(+)g Fi(m)9601 3969 y Fg(e)9704 3943 y Fj(\000)g Fl(2)p
Fi(m)10107 3969 y Fg(\026)10188 3943 y Fl(\))5042 4358
y Fi(y)54 b Fl(=)48 b Fj(\006)5491 4202 y Ff(p)p 5663
4202 1169 7 v 156 x Fl(\()p Fi(b)37 b Fj(\000)i Fi(c)p
Fl(\)\()p Fi(a)e Fj(\000)h Fi(b)p Fl(\))p Fi(M)426 b(M)65
b Fl(=)8173 4241 y(\()p Fi(m)8386 4267 y Fg(\026)8505
4241 y Fj(\000)38 b Fi(m)8824 4267 y Fg(\034)8899 4241
y Fl(\)\()p Fi(m)9178 4267 y Fg(e)9280 4241 y Fj(\000)g
Fi(m)9599 4267 y Fg(\026)9680 4241 y Fl(\))p 7665 4318
2590 7 v 7665 4476 a(\()p Fi(m)7878 4501 y Fg(\026)7996
4476 y Fl(+)h Fi(m)8313 4501 y Fg(\034)8426 4476 y Fj(\000)f
Fl(2)p Fi(m)8829 4501 y Fg(e)8894 4476 y Fl(\)\()p Fi(m)9173
4501 y Fg(e)9274 4476 y Fl(+)h Fi(m)9591 4501 y Fg(\026)9710
4476 y Fj(\000)f Fl(2)p Fi(m)10113 4501 y Fg(\034)10188
4476 y Fl(\))5114 4890 y Fi(z)56 b Fl(=)48 b Fj(\006)5561
4735 y Ff(p)p 5733 4735 1111 7 v 155 x Fl(\()p Fi(c)37
b Fj(\000)h Fi(a)p Fl(\)\()p Fi(b)g Fj(\000)g Fi(c)p
Fl(\))p Fi(T)431 b(T)71 b Fl(=)8129 4774 y(\()p Fi(m)8342
4800 y Fg(\034)8455 4774 y Fj(\000)38 b Fi(m)8774 4800
y Fg(e)8838 4774 y Fl(\)\()p Fi(m)9117 4800 y Fg(\026)9236
4774 y Fj(\000)g Fi(m)9555 4800 y Fg(\034)9630 4774 y
Fl(\))p 7618 4851 2590 7 v 7618 5008 a(\()p Fi(m)7831
5034 y Fg(\034)7944 5008 y Fl(+)g Fi(m)8260 5034 y Fg(e)8362
5008 y Fj(\000)h Fl(2)p Fi(m)8766 5034 y Fg(\026)8847
5008 y Fl(\)\()p Fi(m)9126 5034 y Fg(\026)9244 5008 y
Fl(+)f Fi(m)9560 5034 y Fg(\034)9674 5008 y Fj(\000)g
Fl(2)p Fi(m)10077 5034 y Fg(e)10141 5008 y Fl(\))10224
4890 y Fi(:)p 0 0 1 TeXcolorrgb 4729 5436 a Fl(with)p
0 TeXcolorgray 55 w Fi(a;)29 b(b;)g(c)p 0 0 1 TeXcolorrgb
55 w Fl(\014xed)55 b(b)-5 b(y)56 b(the)g Fi(\027)67 b
Fl(masses.)10871 5612 y
 0 setgray
 10871 5612 a 0 TeXcolorgray 0 0 1
TeXcolorrgb 4500 6000 a
 tx@Dict begin -90 Rot  end
 4500 6000 a eop end
%%Page: 27 27
TeXDict begin 27 26 bop 0 0 1 TeXcolorrgb 4500 6000 a
 tx@Dict begin 90 Rot  end

4500 6000 a 10631 1267 a Fm(27)p 0 TeXcolorgray 0 0 1
TeXcolorrgb 0 TeXcolorgray 0 0 1 TeXcolorrgb 0 TeXcolorgray
1 0 0 TeXcolorrgb 0 TeXcolorgray Black 0 TeXcolorgray
0 TeXcolorgray 0 TeXcolorgray 6948 1582 a @beginspecial
@setspecial
 tx@Dict begin STP newpath 0.8 SLW 0  setgray  0. true 3.8 neg 3.8
neg 120.42616 15.47008 .5 Frame  gsave 3.0 -45 PtoC Shadow .25  setgray
gsave fill grestore stroke grestore gsave 1  setgray gsave fill grestore
stroke grestore gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
end
 
@endspecial 0 0 1 TeXcolorrgb 56 w Fk(Solution)69
b(for)e Fc(T)-19 b(r)o Fb(C)8531 1507 y Fa(2)p 0 TeXcolorgray
1 0 0 TeXcolorrgb 4729 2091 a Fl(In)-5 b(terestingly)-14
b(,)54 b(the)i(observ)-5 b(ed)56 b Fi(\027)67 b Fl(mass-squared)57
b(di\013erence)e(hierarc)-5 b(h)g(y)55 b(is)i(correctly)4729
2403 y(obtained)e(setting)p 0 TeXcolorgray 5993 2335
a Fg(b)p Fe(\000)p Fg(a)p 5992 2363 213 7 v 5992 2462
a(a)p Fe(\000)p Fg(c)6270 2403 y Fl(=)48 b(1)g(\()g(=)-29
b Fj(\))7082 2314 y Fh(\001)p Fg(m)7292 2273 y Fd(2)7292
2349 y(21)p 7082 2363 322 7 v 7082 2465 a Fh(\001)p Fg(m)7292
2425 y Fd(2)7292 2502 y(31)7469 2403 y Fl(=)48 b(0)p
Fi(:)p Fl(03\).)p 0 0 1 TeXcolorrgb 4729 2715 a(The)56
b(mixing)g(matrix)g Fj(!)p 0 TeXcolorgray 6468 3176 a
Fi(\027)6551 3202 y Fh(1)7171 3176 y Fi(\027)7254 3202
y Fh(2)7874 3176 y Fi(\027)7957 3202 y Fh(3)9128 3176
y Fi(\027)9211 3202 y Fh(1)9668 3176 y Fi(\027)9751 3202
y Fh(2)10207 3176 y Fi(\027)10290 3202 y Fh(3)4729 3902
y Fl(\()p Fj(j)p Fi(U)4957 3927 y Fg(M)12 b(N)g(S)5283
3902 y Fj(j)5331 3830 y Fh(2)5399 3902 y Fl(\))95 b(=)5799
3609 y Fi(e)5787 3921 y(\026)5832 4233 y(\034)5917 3401
y Ff(0)5917 3704 y(B)5917 3807 y(B)5917 3910 y(B)5917
4020 y(@)6149 3609 y Fi(:)p Fl(33333)308 b Fi(:)p Fl(33333)g
Fi(:)p Fl(33333)6149 3921 y Fi(:)p Fl(17079)g Fi(:)p
Fl(16257)g Fi(:)p Fl(66663)6149 4233 y Fi(:)p Fl(49587)g
Fi(:)p Fl(50409)g Fi(:)p Fl(00003)8249 3401 y Ff(1)8249
3704 y(C)8249 3807 y(C)8249 3910 y(C)8249 4020 y(A)8495
3902 y Fj(')8737 3609 y Fi(e)8725 3921 y(\026)8770 4233
y(\034)8855 3401 y Ff(0)8855 3704 y(B)8855 3807 y(B)8855
3910 y(B)8855 4020 y(@)9087 3609 y Fl(1)p Fi(=)p Fl(3)g(1)p
Fi(=)p Fl(3)226 b(1)p Fi(=)p Fl(3)9087 3921 y(1)p Fi(=)p
Fl(6)308 b(1)p Fi(=)p Fl(6)226 b(2)p Fi(=)p Fl(3)9087
4233 y(1)p Fi(=)p Fl(2)308 b(1)p Fi(=)p Fl(2)i(0)10378
3401 y Ff(1)10378 3704 y(C)10378 3807 y(C)10378 3910
y(C)10378 4020 y(A)10557 3902 y Fi(:)p 0 0 1 TeXcolorrgb
4729 4654 a Fl(whic)-5 b(h)55 b(is)i(inconsisten)-5 b(t)55
b(with)g(exp)5 b(erimen)-5 b(t.)p 0.0 0.6 0.0 TeXcolorrgb
4729 4966 a(BUT)57 b(it)e(is)i(a)f(simple)h(p)5 b(erm)-5
b(utation)54 b(of)i(the)f(\(viable\))g(tribimaximal)h(mixing)g(matrix!)
10871 5612 y
 0 setgray
 10871 5612 a 0 TeXcolorgray 0.0 0.6 0.0
TeXcolorrgb 4500 6000 a
 tx@Dict begin -90 Rot  end
 4500 6000 a eop end
%%Page: 28 28
TeXDict begin 28 27 bop 0.0 0.6 0.0 TeXcolorrgb 4500
6000 a
 tx@Dict begin 90 Rot  end
 4500 6000 a 10631 1267 a Fm(28)p 0 0 1 TeXcolorrgb
0 TeXcolorgray 0 0 1 TeXcolorrgb 0 TeXcolorgray 1 0 0
TeXcolorrgb 0 TeXcolorgray Black 0 TeXcolorgray 0 TeXcolorgray
0 TeXcolorgray 7212 1558 a @beginspecial @setspecial
 tx@Dict begin STP newpath 0.8 SLW 0  setgray  0. true 3.8 neg 3.8
neg 83.68906 13.79999 .5 Frame  gsave 3.0 -45 PtoC Shadow .25  setgray
gsave fill grestore stroke grestore gsave 1  setgray gsave fill grestore
stroke grestore gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
end


@endspecial 0 0 1 TeXcolorrgb 56 w Fk(What)67 b(Next?)p
0 TeXcolorgray 1 0 0 TeXcolorrgb 4729 2067 a Fl(W)-14
b(e)56 b(tried)f(the)g(ob)-5 b(vious)57 b(next)e(step,)h(ie.)g(a)g
(linear)f(com)-5 b(bination:)p 0 TeXcolorgray 7033 2508
a Fj(A)48 b Fl(=)g Fi(i)p Fl(T)-14 b(r)o Fi(C)7761 2437
y Fh(3)7867 2508 y Fl(+)38 b Fi(r)c Fl(T)-14 b(r)o Fi(C)8452
2437 y Fh(2)8520 2508 y Fi(:)p 1 0 0 TeXcolorrgb 4729
2950 a Fl(where)55 b Fi(r)61 b Fl(is)56 b(a)h(JI)e(constan)-5
b(t)56 b(of)g(dimensions)h Fi(m)7749 2888 y Fh(2)7817
2950 y Fl(.)p 0 TeXcolorgray 4729 3262 a(The)f(solution)f(giv)-5
b(es)57 b(a)g(tra)9 b(jectory)54 b(of)i(mixing)h(matrices,)f(as)h(a)f
(function)e(of)i Fi(r)61 b Fl(\(and)55 b(the)4729 3574
y(unkno)-5 b(wn)55 b(o\013set)i(of)f(the)f(neutrino)f(masses\).)p
0.0 0.6 0.0 TeXcolorrgb 4729 3886 a(Has)j(some)h(v)-5
b(ery)56 b(in)-5 b(teresting)54 b(prop)5 b(erties)55
b(\(see)h(b)5 b(elo)-5 b(w\),)55 b(including)f(viable)i(mixing)g
(matrices)4729 4198 y(and)g Fi(C)12 b(P)79 b Fl(violation.)p
0 0 1 TeXcolorrgb 4729 4510 a(Ho)-5 b(w)g(ev)g(er,)57
b(so)g(far,)e(ha)-5 b(v)g(e)57 b(failed)e(to)h(\014nd)f(a)i(solution)e
(whic)-5 b(h)56 b(sim)-5 b(ultaneously)56 b(\014ts)g(observ)-5
b(ed)4729 4822 y(masses)58 b(and)e(mixings.)p 1 0 0 TeXcolorrgb
4729 5134 a(Complete)g(c)-5 b(haracterisation)55 b(of)h(solution)f
(space)i(is)f(w)-5 b(ork)56 b(in)g(progress.)10871 5612
y
 0 setgray
 10871 5612 a 0 TeXcolorgray 1 0 0 TeXcolorrgb 4500
6000 a
 tx@Dict begin -90 Rot  end
 4500 6000 a eop end
%%Page: 29 29
TeXDict begin 29 28 bop 1 0 0 TeXcolorrgb 4500 6000 a
 tx@Dict begin 90 Rot  end

4500 6000 a 10631 1267 a Fm(29)p 0 0 1 TeXcolorrgb 0.0 0.6 0.0
TeXcolorrgb 0 TeXcolorgray 1 0 0 TeXcolorrgb 0 TeXcolorgray
1 0 0 TeXcolorrgb 0 TeXcolorgray Black 0 TeXcolorgray
0 TeXcolorgray 0 TeXcolorgray 4804 1558 a @beginspecial
@setspecial
 tx@Dict begin STP newpath 0.8 SLW 0  setgray  0. true 3.8 neg 6.59999
neg 419.29646 13.79999 .5 Frame  gsave 3.0 -45 PtoC Shadow .25  setgray
gsave fill grestore stroke grestore gsave 1  setgray gsave fill grestore
stroke grestore gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
end
 
@endspecial 0 0 1 TeXcolorrgb 56 w Fk(Complete)68
b(Set)f(of)g(Fla)-6 b(v)g(our-Symmetric,)68 b(In)-6 b(v)-11
b(arian)-6 b(t)68 b(Measures)g(of)f(Mixing)p 0 TeXcolorgray
1 0 0 TeXcolorrgb 4729 1953 a Fj(9)56 b Fl(four)f(observ)-9
b(ables)56 b(of)g(mixing)104 b(=)-29 b Fj(\))104 b Fl(m)-5
b(ust)57 b(b)5 b(e)56 b(p)5 b(ossible)56 b(to)g(\014nd)f(four)g(indep)5
b(enden)-5 b(t)4729 2264 y(\015a)g(v)g(our-symmetric)57
b(in)-5 b(v)c(arian)k(t)55 b(measures)i(of)f(mixing.)74
b(W)-14 b(e)57 b(extended)d(the)h(set)h(as)h(follo)-5
b(ws:)p 0.0 0.6 0.0 TeXcolorrgb 4729 2575 a(Comm)g(utators)57
b(of)f(p)5 b(o)-5 b(w)g(ers)56 b(of)p 0 TeXcolorgray
56 w Fi(L)p 0.0 0.6 0.0 TeXcolorrgb 56 w Fl(and)p 0 TeXcolorgray
56 w Fi(N)p 0.0 0.6 0.0 TeXcolorrgb 74 w Fl(are)g(indep)5
b(enden)-5 b(t)53 b(measures)k(of)f(mixing:)p 0 TeXcolorgray
7131 3015 a Fi(C)7252 3040 y Fg(ij)7404 3015 y Fj(\021)48
b Fl([)p Fi(L)7748 2944 y Fg(i)7796 3015 y Fi(;)29 b(N)8025
2944 y Fg(j)8088 3015 y Fl(])p Fi(:)p 0.0 0.6 0.0 TeXcolorrgb
4729 3454 a Fl(Complete)56 b(set)g(is)g(obtained)f(for)h
Fi(i;)29 b(j)56 b Fj(\024)48 b Fl(2)56 b(\(higher)f(p)5
b(o)-5 b(w)g(ers)56 b(of)p 0 TeXcolorgray 56 w Fi(L)p
0.0 0.6 0.0 TeXcolorrgb 56 w Fl(and)p 0 TeXcolorgray
56 w Fi(N)p 0.0 0.6 0.0 TeXcolorrgb 74 w Fl(ma)-5 b(y)57
b(b)5 b(e)55 b(reduced)g(to)4729 3766 y(functions)g(of)h(lo)-5
b(w)g(er)56 b(p)5 b(o)-5 b(w)g(ers)56 b(and)g(their)e(traces,)i(using)g
(the)g(c)-5 b(haracteristic)54 b(equation\).)p 0 0 1
TeXcolorrgb 4729 4077 a(While)i(these)f(are)h(not)g(in)-5
b(v)c(arian)k(ts,)55 b(it)h(is)g(easy)h(to)f(construct)f(\()p
Fi(C)12 b(P)23 b Fl(-conserving\))55 b(in)-5 b(v)c(arian)k(ts)4729
4388 y(b)g(y)56 b(analogy)h(with)p 0 TeXcolorgray 55
w(T)-14 b(r)p Fi(C)6277 4325 y Fh(2)6265 4430 y(11)p
0 0 1 TeXcolorrgb 6449 4388 a Fl(considered)55 b(already:)p
0 TeXcolorgray 7042 4828 a Fi(Q)7176 4853 y Fg(mn)7412
4828 y Fj(\021)48 b Fl(T)-14 b(r)o Fi(C)7888 4853 y Fg(ij)7992
4828 y Fi(:C)8160 4853 y Fg(k)s(l)p 0 0 1 TeXcolorrgb
4729 5267 a Fl(where)p 0 TeXcolorgray 55 w Fi(m)48 b
Fl(=)g Fi(i)38 b Fl(+)g Fi(k)44 b Fj(\000)38 b Fl(1)p
0 0 1 TeXcolorrgb 57 w(and)p 0 TeXcolorgray 55 w Fi(n)48
b Fl(=)g Fi(j)f Fl(+)39 b Fi(l)j Fj(\000)c Fl(1)p 0 0 1
TeXcolorrgb(.)75 b(There)55 b(are)h(exactly)g(9)g(of)g(these,)g(an)-5
b(y)56 b(four)f(of)4729 5578 y(whic)-5 b(h)55 b(are)h(indep)5
b(enden)-5 b(t.)10871 5612 y
 0 setgray
 10871 5612 a 0 TeXcolorgray
0 0 1 TeXcolorrgb 4500 6000 a
 tx@Dict begin -90 Rot  end
 4500 6000 a eop end
%%Page: 30 30
TeXDict begin 30 29 bop 0 0 1 TeXcolorrgb 4500 6000 a
 tx@Dict begin 90 Rot  end

4500 6000 a 10631 1267 a Fm(30)p 0 TeXcolorgray 0 0 1
TeXcolorrgb 0 TeXcolorgray 0 0 1 TeXcolorrgb 0 TeXcolorgray
0 0 1 TeXcolorrgb 0 TeXcolorgray 0 0 1 TeXcolorrgb 0.0 0.6 0.0
TeXcolorrgb 0 TeXcolorgray 0.0 0.6 0.0 TeXcolorrgb 0
TeXcolorgray 0.0 0.6 0.0 TeXcolorrgb 0 TeXcolorgray 0.0 0.6 0.0
TeXcolorrgb 0 TeXcolorgray 0.0 0.6 0.0 TeXcolorrgb 0
TeXcolorgray 0.0 0.6 0.0 TeXcolorrgb 1 0 0 TeXcolorrgb
0 TeXcolorgray Black 0 TeXcolorgray 0 TeXcolorgray 0
TeXcolorgray 7146 1558 a @beginspecial @setspecial
 tx@Dict begin STP newpath 0.8 SLW 0  setgray  0. true 3.8 neg 3.8
neg 92.7756 13.79999 .5 Frame  gsave 3.0 -45 PtoC Shadow .25  setgray
gsave fill grestore stroke grestore gsave 1  setgray gsave fill grestore
stroke grestore gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
end
 
@endspecial
0 0 1 TeXcolorrgb 57 w Fk(What)67 b(W)-17 b(orks?)p 0
TeXcolorgray 1 0 0 TeXcolorrgb 4729 2021 a Fl(Returning)54
b(to)i(our)g(extended)e(set)j(of)f(comm)-5 b(utator)56
b(in)-5 b(v)c(arian)k(ts,)55 b(w)-5 b(e)57 b(tried)d(another)h(linear)
4729 2315 y(com)-5 b(bination:)p 0 TeXcolorgray 6283
2611 a Fj(A)48 b Fl(=)g Fi(Q)6781 2637 y Fh(11)6948 2611
y Fl(+)38 b Fi(q)d(Q)7361 2637 y Fh(21)7538 2611 y Fl(=)47
b(T)-14 b(r)p Fi(C)8023 2540 y Fh(2)8011 2653 y(11)8178
2611 y Fl(+)38 b Fi(q)d Fl(T)-14 b(r)o([)p Fi(C)8798
2637 y Fh(11)8926 2611 y Fi(:C)9094 2637 y Fh(21)9223
2611 y Fl(])p Fi(;)1338 b Fl(\(1\))p 1 0 0 TeXcolorrgb
4729 2965 a(where)55 b Fi(q)62 b Fl(is)57 b(a)f(JI)g(constan)-5
b(t)56 b(of)g(dimensions)g Fi(m)7749 2903 y Fe(\000)p
Fh(1)7912 2965 y Fl(.)p 0 TeXcolorgray 4729 3259 a(This)g(will)f(ha)-5
b(v)g(e)57 b Fi(C)12 b(P)23 b Fl(-conserving)56 b(solutions.)p
0.0 0.6 0.0 TeXcolorrgb 4729 3553 a(The)g(solution)f(giv)-5
b(es)57 b(a)g(tra)9 b(jectory)54 b(of)i(mixing)h(matrices,)f(as)h(a)f
(function)e(of)i Fi(q)62 b Fl(\(and)56 b(the)4729 3847
y(unkno)-5 b(wn)55 b(o\013set)i(of)f(the)f(neutrino)f(masses\).)p
0 0 1 TeXcolorrgb 4729 4142 a(W)-14 b(e)56 b(\(arbitrarily\))d(c)-5
b(ho)5 b(ose)57 b Fi(m)6642 4167 y Fh(1)6759 4142 y Fl(=)47
b(0)57 b(\(for)e(simplicit)-5 b(y\))55 b(and)h(lo)5 b(ok)56
b(for)g(a)g(solution)g(\(to)g(\014t)f(the)4729 4436 y(phenomenology\))h
(with)f(the)g Fi(\027)6746 4461 y Fh(2)6870 4436 y Fl(mass)j
(eigenstate)e(trimaximally)g(mixed,)4729 4730 y(ie.)g
Fj(j)p Fi(U)5116 4756 y Fg(\013)p Fh(2)5263 4730 y Fj(j)5311
4667 y Fh(2)5426 4730 y Fl(=)48 b(1)p Fi(=)p Fl(3)p Fi(;)29
b Fj(8)g Fi(\013)q Fl(.)p 1 0 0 TeXcolorrgb 4729 5024
a(F)-14 b(or)56 b(\014xed)f(neutrino)g(masses-squared)j(di\013erences,)
d(ev)-5 b(erything)55 b(is)h(no)-5 b(w)56 b(determined.)73
b(W)-14 b(e)4729 5318 y(simply)56 b(need)g(to)g(\014nd)f
Fi(q)62 b Fl(to)56 b(\014t)f(the)h(neutrino)e(sp)5 b(ectrum)55
b(and)h(the)f(rest)h(of)g(the)f(mixing)4729 5612 y(matrix)h(follo)-5
b(ws.)10871 5612 y
 0 setgray
 10871 5612 a 0 TeXcolorgray 1 0 0
TeXcolorrgb 4500 6000 a
 tx@Dict begin -90 Rot  end
 4500 6000 a eop end
%%Page: 31 31
TeXDict begin 31 30 bop 1 0 0 TeXcolorrgb 4500 6000 a
 tx@Dict begin 90 Rot  end

4500 6000 a 10631 1267 a Fm(31)p 0 0 1 TeXcolorrgb 0.0 0.6 0.0
TeXcolorrgb 0 TeXcolorgray 1 0 0 TeXcolorrgb 0 TeXcolorgray
1 0 0 TeXcolorrgb 0 TeXcolorgray Black 0 TeXcolorgray
0 TeXcolorgray 0 TeXcolorgray 6134 1582 a @beginspecial
@setspecial
 tx@Dict begin STP newpath 0.8 SLW 0  setgray  0. true 3.8 neg 8.25275
neg 233.89188 15.47008 .5 Frame  gsave 3.0 -45 PtoC Shadow .25  setgray
gsave fill grestore stroke grestore gsave 1  setgray gsave fill grestore
stroke grestore gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
end
 
@endspecial 0 0 1 TeXcolorrgb 56 w Fk(Solution)69
b(for)e Fc(T)-19 b(r)o Fb(C)7717 1507 y Fa(2)7703 1646
y(11)7928 1582 y Fc(+)53 b Fb(q)47 b Fc(T)-19 b(r)o([)p
Fb(C)8792 1613 y Fa(11)8964 1582 y Fb(:C)9199 1613 y
Fa(21)9371 1582 y Fc(])p 0 TeXcolorgray 1 0 0 TeXcolorrgb
4729 2121 a Fl(Allo)-5 b(wing)56 b(masses)j(to)d(\015oat,)f(tra)9
b(jectory)55 b(\(as)i(function)d(of)i Fi(q)6 b Fl(\))55
b(has)i(in)-5 b(teresting)55 b(prop)5 b(erties:)p 0 TeXcolorgray
4729 2428 a(It)56 b(has)g(3)h(p)5 b(oles,)56 b(eac)-5
b(h)56 b(of)g(whic)-5 b(h)55 b(corresp)5 b(onds)55 b(to)h(a)h(p)5
b(erm)-5 b(utation)54 b(of)i(the)g(tribimaximal)4729
2735 y(form,)g(and)g(\(in)f(the)g(limit)h(as)h(w)-5 b(e)56
b(approac)-5 b(h)56 b(eac)-5 b(h)56 b(p)5 b(ole\))55
b(has)i(a)f(single)g Fi(\027)68 b Fl(mass)58 b(degeneracy)-14
b(.)p 0.0 0.6 0.0 TeXcolorrgb 4729 3042 a(As)57 b(w)-5
b(e)56 b(approac)-5 b(h)56 b(the)f(\\correct")h(p)5 b(ole,)p
0 TeXcolorgray 55 w(\001)p Fi(m)7667 2979 y Fh(2)7667
3084 y(21)p 0.0 0.6 0.0 TeXcolorrgb 7853 3042 a Fl(tends)56
b(to)g(zero)g(\(not)f(bad,)h(cf.)f(data\).)p 0.0 0.6 0.0
TeXcolorrgb 122 w(=)-29 b Fj(\))4729 3348 y Fl(smallness)58
b(of)p 0 TeXcolorgray 56 w(sin)28 b Fi(\022)5978 3374
y Fh(13)p 0.0 0.6 0.0 TeXcolorrgb 6163 3348 a Fl(related)55
b(to)h(smallness)i(of)p 0 TeXcolorgray 56 w(\001)p Fi(m)8153
3286 y Fh(2)8153 3391 y(21)8283 3348 y Fi(=)p Fl(\001)p
Fi(m)8654 3286 y Fh(2)8654 3391 y(31)8784 3348 y Fl(.)p
0 0 1 TeXcolorrgb 4729 3655 a(Of)e(course,)p 0 TeXcolorgray
56 w(\001)p Fi(m)5818 3593 y Fh(2)5818 3698 y(21)5948
3655 y Fi(=)p Fl(\001)p Fi(m)6319 3593 y Fh(2)6319 3698
y(31)p 0 0 1 TeXcolorrgb 6505 3655 a Fl(is)h(kno)-5 b(wn)55
b(\(appro)-5 b(ximately\))55 b(whic)-5 b(h)56 b(\014xes)p
0 TeXcolorgray 56 w Fi(q)p 0 0 1 TeXcolorrgb 62 w Fl(and)g(the)f
(mixing)4729 3962 y(matrix:)p 0 TeXcolorgray 6143 4166
a Fi(\027)6226 4192 y Fh(1)6846 4166 y Fi(\027)6929 4192
y Fh(2)7549 4166 y Fi(\027)7632 4192 y Fh(3)8844 4166
y Fi(\027)8927 4192 y Fh(1)9383 4166 y Fi(\027)9466 4192
y Fh(2)9923 4166 y Fi(\027)10006 4192 y Fh(3)4830 4886
y Fl(\()p Fj(j)p Fi(U)5058 4912 y Fg(l)q(\027)5170 4886
y Fj(j)5218 4815 y Fh(2)5286 4886 y Fl(\))95 b(=)5686
4594 y Fi(e)5674 4906 y(\026)5719 5218 y(\034)5804 4385
y Ff(0)5804 4688 y(B)5804 4792 y(B)5804 4895 y(B)5804
5005 y(@)6036 4594 y Fl(0)p Fi(:)p Fl(662)308 b(0)p Fi(:)p
Fl(333)g(0)p Fi(:)p Fl(005)6036 4906 y(0)p Fi(:)p Fl(219)g(0)p
Fi(:)p Fl(333)g(0)p Fi(:)p Fl(448)6036 5218 y(0)p Fi(:)p
Fl(120)g(0)p Fi(:)p Fl(333)g(0)p Fi(:)p Fl(547)7883 4385
y Ff(1)7883 4688 y(C)7883 4792 y(C)7883 4895 y(C)7883
5005 y(A)8130 4886 y Fj(')8371 4594 y Fi(e)8359 4906
y(\026)8404 5218 y(\034)8489 4385 y Ff(0)8489 4688 y(B)8489
4792 y(B)8489 4895 y(B)8489 5005 y(@)8721 4594 y Fl(2)p
Fi(=)p Fl(3)g(1)p Fi(=)p Fl(3)392 b(0)8721 4906 y(1)p
Fi(=)p Fl(6)308 b(1)p Fi(=)p Fl(3)g(1)p Fi(=)p Fl(2)8721
5218 y(1)p Fi(=)p Fl(6)g(1)p Fi(=)p Fl(3)g(1)p Fi(=)p
Fl(2)10175 4385 y Ff(1)10175 4688 y(C)10175 4792 y(C)10175
4895 y(C)10175 5005 y(A)10354 4886 y Fi(:)p 0 0 1 TeXcolorrgb
4729 5626 a Fl(whic)-5 b(h)55 b(is)i(consisten)-5 b(t)56
b(with)f(exp)5 b(erimen)-5 b(t.)10871 5612 y
 0 setgray
 10871 5612
a 0 TeXcolorgray 0 0 1 TeXcolorrgb 4500 6000 a
 tx@Dict begin -90 Rot  end
 4500 6000
a eop end
%%Page: 32 32
TeXDict begin 32 31 bop 0 0 1 TeXcolorrgb 4500 6000 a
 tx@Dict begin 90 Rot  end

4500 6000 a 10631 1267 a Fm(32)p 0 TeXcolorgray 0 0 1
TeXcolorrgb 0 TeXcolorgray 0 0 1 TeXcolorrgb 0 TeXcolorgray
0 0 1 TeXcolorrgb 0 TeXcolorgray 0.0 0.6 0.0 TeXcolorrgb
0 TeXcolorgray 0.0 0.6 0.0 TeXcolorrgb 0.0 0.6 0.0 TeXcolorrgb
0 TeXcolorgray 0.0 0.6 0.0 TeXcolorrgb 0 TeXcolorgray
1 0 0 TeXcolorrgb 0 TeXcolorgray Black 0 TeXcolorgray
0 TeXcolorgray 0 TeXcolorgray 7255 1558 a @beginspecial
@setspecial
 tx@Dict begin STP newpath 0.8 SLW 0  setgray  0. true 3.8 neg 3.8
neg 77.62576 13.79999 .5 Frame  gsave 3.0 -45 PtoC Shadow .25  setgray
gsave fill grestore stroke grestore gsave 1  setgray gsave fill grestore
stroke grestore gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
end
 
@endspecial 0 0 1 TeXcolorrgb 56 w Fk(The)68
b(F)-17 b(uture)p 0 TeXcolorgray 1 0 0 TeXcolorrgb 4729
2067 a Fl(W)j(e)56 b(do)g(not)g(consider)g(the)f(successful)h(in)-5
b(v)c(arian)k(t)p 0 TeXcolorgray 55 w(T)-14 b(r)o Fi(C)8279
2004 y Fh(2)8267 2109 y(11)8434 2067 y Fl(+)39 b Fi(q)34
b Fl(T)-14 b(r)o([)p Fi(C)9054 2092 y Fh(11)9183 2067
y Fi(:C)9351 2092 y Fh(21)9479 2067 y Fl(])p 1 0 0 TeXcolorrgb
56 w(to)56 b(b)5 b(e)56 b(the)f(last)4729 2379 y(w)-5
b(ord:)74 b(do)5 b(es)54 b(not)g(accommo)5 b(date)56
b Fi(C)12 b(P)77 b Fl(violation)54 b(and)g(extremisation)g(is)h(p)5
b(erformed)53 b(at)h(\014xed)4729 2691 y(masses.)p 0
TeXcolorgray 4729 3055 a(First)i(job)f(is)i(to)f(complete)g(the)f
(analysis)i(of)f(the)f(linear)g(com)-5 b(bination)56
b(of)g(T)-14 b(r)o Fi(C)9845 2992 y Fh(2)9970 3055 y
Fl(and)56 b(T)-14 b(r)o Fi(C)10604 2992 y Fh(3)10672
3055 y Fl(,)4729 3367 y(to)56 b(lo)5 b(ok)56 b(for)g(viable)f
Fi(C)12 b(P)23 b Fl(-violating)56 b(solutions.)p 0.0 0.6 0.0
TeXcolorrgb 4729 3731 a(W)-14 b(ould)56 b(lik)-5 b(e)56
b(to)g(\014nd)f(an)h(in)-5 b(v)c(arian)k(t)55 b(whic)-5
b(h)55 b(can)h(b)5 b(e)56 b(extremised)f(without)g(\014xing)g(masses,)j
(to)4729 4043 y(predict)c(them)i(also.)p 0 0 1 TeXcolorrgb
4729 4406 a(Need)g(to)g(understand)e(ho)-5 b(w)56 b(our)g(pro)5
b(cedure)54 b(can)i(b)5 b(e)56 b(applied)f(successfully)g(to)h(the)g
(quarks.)10871 5612 y
 0 setgray
 10871 5612 a 0 TeXcolorgray 0 0 1
TeXcolorrgb 4500 6000 a
 tx@Dict begin -90 Rot  end
 4500 6000 a eop end
%%Page: 33 33
TeXDict begin 33 32 bop 0 0 1 TeXcolorrgb 4500 6000 a
 tx@Dict begin 90 Rot  end

4500 6000 a 10631 1267 a Fm(33)p 0.0 0.6 0.0 TeXcolorrgb
0 TeXcolorgray 1 0 0 TeXcolorrgb 0 TeXcolorgray 1 0 0
TeXcolorrgb 0 TeXcolorgray Black 0 TeXcolorgray 0 TeXcolorgray
0 TeXcolorgray 7295 1556 a @beginspecial @setspecial
 tx@Dict begin STP newpath 0.8 SLW 0  setgray  0. true 3.8 neg 3.8
neg 71.98584 13.64 .5 Frame  gsave 3.0 -45 PtoC Shadow .25  setgray
gsave fill grestore stroke grestore gsave 1  setgray gsave fill grestore
stroke grestore gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
end


@endspecial 0 0 1 TeXcolorrgb 57 w Fk(Discussion)p 0
TeXcolorgray 1 0 0 TeXcolorrgb 4729 2064 a Fl(This)56
b(con)-5 b(tribution)54 b(is)i(not)g(an)g Fi(extension)f
Fl(of)h(the)g(Standard)e(Mo)5 b(del)56 b(-)h(there)d(are)i(no)g(new)
4729 2376 y(particles,)f(no)h(new)g(symmetries)h(and)e(no)h(new)g(in)-5
b(teractions.)p 0 TeXcolorgray 4729 2740 a(If)56 b(an)-5
b(ything,)55 b(it)g(is)i(a)f Fi(contr)5 b(action)54 b
Fl(of)i(the)g(SM.)g(It)f(relies)h(on)g(an)g(existing)g(co)-5
b(v)c(ariance)56 b(\(JC\))4729 3052 y(p)5 b(ostulating)55
b(a)h(new)g(principle,)e(\(extremisation)h(of)h(a)g(JI\))f(whic)-5
b(h)56 b(pro)-5 b(vides)55 b(constrain)-5 b(ts)4729 3364
y(whic)g(h)55 b(reduce)g(the)g(n)-5 b(um)g(b)5 b(er)56
b(of)g(free)f(parameters)h(in)f(the)h(Mo)5 b(del.)p 0.0 0.6 0.0
TeXcolorrgb 4729 3728 a(Though)55 b(original)h(in)g(the)f(con)-5
b(text)55 b(of)h(\015a)-5 b(v)g(our)57 b(ph)-5 b(ysics,)56
b(our)g(extremisation)f(pro)5 b(cedure)4729 4040 y(builds)55
b(on)h(treid)f(and)h(trusted)e(traditions)h(of)h(our)g(\014eld)f(-)i
(it)e(lo)5 b(oks)57 b(lik)-5 b(e)56 b(the)f(priciple)f(of)i(least)4729
4352 y(\(extremal\))f(action.)p 0 0 1 TeXcolorrgb 4729
4716 a(P)-5 b(erhaps)56 b(our)f(JI)h(\(expressed)f(in)h(appropriate)e
(dimensions\))i(could)g(b)5 b(e)55 b(added)h(to)g(the)f(SM)4729
5028 y(action)g(itself.)74 b(V)-14 b(ariations)56 b(wrt)e(the)h(mass)j
(matrices)e(result)e(in)i(new)f(\\constrain)-5 b(t)55
b(equations")4729 5340 y(whic)-5 b(h)55 b(determine)g(them.)10871
5612 y
 0 setgray
 10871 5612 a 0 TeXcolorgray 0 0 1 TeXcolorrgb
4500 6000 a
 tx@Dict begin -90 Rot  end
 4500 6000 a eop end
%%Trailer

userdict /end-hook known{end-hook}if
%%EOF