j o flo., sf f g^4-jchaidez/notes/donaldson_flow.pdf · '-l- hc po..^ \j s o ., flo., o.\ sf...

4
'-l- hc Po..^ \J s o ., Flo., o.\ Sf *F Lr| i. f ] F" \a s g^4- lto liv..+ i^ J qwcfio..5 Sctrp + Obs<r,aulio..5 Dct i..\ \ir,^ .\ F lot r 9c-ri va,\ i... oFto*r f'{. t ivr^t tT A. g } io..5 (^1r.,.. Sy ^f tcc t ic rnor.i t" tU ( tf" r 6\, w hc,. c q^ hrc iC"|o g 1 u) to *o t!,u. Sy^f\ccti. r o^ pf".2 - Su-^-I of Ba,<,uttf I .. oF 0..,*uro.. lK.o,,. I t*.tt^"t , [-f = fe] e I't'(pr') S,Fh'<is.]? -r-r.r----r.r r.- | Co'jcc+ "rt : Yc I ( ?) ' 9.11r..fi. g.-.-*"^i$rfs trl-,s"1*.,^j .(^ro,".r, g T,.\, lbt w5,lf :1 e Pi$t Crt) r\ rr,. p_F ir 6 ro.,tty ,^rr^ '|"ltn U-iLt\ i-ylic5 c?x:HF(ra)? n ila6r"7. 6F-c^. Fhtr\clrl I ao^jclv<J\c&SLif lrr.,r-): Al\ "F .l',{k n^hri,.t it i.. I - l^ot<r. lr"ltpl 4 [a] = [r'"] tc u*<z-l+l c<r'ttnl- ^....,_^.1_ L\ &i$F-Fan^it,:3(t,:i4pl s,eY"=ll d V:, D Tt. no.-tr5o^ffi"[ y,.ul. '--"]' ' \e'rtz !E {':ll s Yrc--L') lc"^iFkn, [K.r,,,J' s Zotllzotg rF h = Cn^ S:*"f * Ott*-* ,'": : Ftt..d rFlo-u (,^6.y,,.x1 r.lg) .r' -Li"r,. conr.ccb s.1.,rp hrar6. Lct Ctt ,6 ,1 ,7\ L" syn";a\rcf it n F lt u, i l\ c L icc, "F co*Ja.,f;L t frJ p L, H Foc *T p sJ^Fkcli., *l tPJ=[^l snl , bc cc-\ |vn5.,. RP e Enlc^ltl ,drt) b7 Nc:= T- L:* o = -c =^P.o ?^f , JvnlrJo^ L{-F. lJ qe fs ^^ i^r.\rli,,. o^ n'yr *HT *s I on t w/ Li'rc* Al)cbc.. fwL+: 6i-c.. c,. vo\uc.,,c Fr.n v.r[ en'{lR" pori li -, L-^ I tt A+ c n- Rq | 1 a ,. it.* r'^<, t ci< ,-l r GA r (r.) vot;- vu\, + (.) Nld = Ar 3 C v., \ Vt eN C)o dc-F't- T^P a,r I =O A c^, fa- k I or. F P, 3 i-_it

Upload: others

Post on 03-Nov-2019

0 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: J o Flo., Sf F g^4-jchaidez/notes/donaldson_flow.pdf · '-l- hc Po..^ \J s o ., Flo., o.\ Sf *F Lr| i. f ] F" \a s g^4-lto liv..+ i^ J qwcfio..5 Sctrp + Obs

'-l- hc Po..^ \J s o ., Flo., o.\ Sf *F Lr| i. f ] F" \a s

g^4-lto liv..+ i^ J qwcfio..5

Sctrp + Obs<r,aulio..5

Dct i..\ \ir,^ .\ F lot r

9c-ri va,\ i... o€ Fto*r

f'{. t ivr^t tT A. g } io..5

(^1r.,.. Sy ^f tcc t ic rnor.i t" tU( tf" r 6\, w hc,. c q^hrc iC"|o g 1 u) to *o t!,u.Sy^f\ccti. r o^ pf".2

- Su-^-I of Ba,<,uttf I ..oF 0..,*uro.. lK.o,,. I t*.tt^"t , [-f = fe] e I't'(pr') S,Fh'<is.]?-r-r.r----r.r r.- | Co'jcc+ "rt : Yc I ( ?)

' 9.11r..fi. g.-.-*"^i$rfs trl-,s"1*.,^j .(^ro,".r, g T,.\, lbt w5,lf :1 € e Pi$t Crt)r\ rr,. p_F ir 6 ro.,tty ,^rr^ '|"ltn U-iLt\ i-ylic5 c?x:HF(ra)? n ila6r"7.

6F-c^. Fhtr\clrl I ao^jclv<J\c&SLif lrr.,r-):

Al\ "F .l',{k n^hri,.t it i.. I - l^ot<r. lr"ltpl 4 [a] = [r'"] tc u*<z-l+lc<r'ttnl- ^....,_^.1_

L\ &i$F-Fan^it,:3(t,:i4pl s,eY"=ll d V:,D Tt. no.-tr5o^ffi"[ y,.ul. '--"]' ' \e'rtz !E {':ll s Yrc--L')

lc"^iFkn, [K.r,,,J' s Zotllzotg rF h = Cn^

S:*"f * Ott*-* ,'": : Ftt..d rFlo-u (,^6.y,,.x1 r.lg) .r' -Li"r,. conr.ccb s.1.,rp hrar6.

Lct Ctt ,6 ,1 ,7\ L" syn";a\rcf it n F lt u, i l\ c L icc, "F co*Ja.,f;L t frJ p L,H

Foc *T p sJ^Fkcli., *l tPJ=[^l snl , bc cc-\|vn5.,. RP e Enlc^ltl ,drt) b7

Nc:= T- L:* o = -c =^P.o?^f , JvnlrJo^ L{-F. lJqe fs ^^ i^r.\rli,,. o^ n'yr *HT *s I on t w/

Li'rc* Al)cbc.. fwL+: 6i-c.. c,. vo\uc.,,c Fr.n v.r[ en'{lR"pori li -, L-^ I tt A+ c n- Rq | 1 a ,. it.* r'^<, t ci< ,-l

rGA r (r.) vot;- vu\, + (.) Nld = Ar3 C v., \ Vt eN

C)o

dc-F't-

T^Pa,r I

=O A

c^, fa- k

I or. F P,

3

i-_it

Page 2: J o Flo., Sf F g^4-jchaidez/notes/donaldson_flow.pdf · '-l- hc Po..^ \J s o ., Flo., o.\ Sf *F Lr| i. f ] F" \a s g^4-lto liv..+ i^ J qwcfio..5 Sctrp + Obs

Saf.,f + 0Lkr'".ti^t (c.^,t) '.

'7" ? | w.. c, \ r t Tocr'rl. u^il,"g Rl<.ot...,.', ^ F...}^L 9p Lt:

(r) dvrtgr = Cvolr= Av.l- i Cr) Airtnt = RaA3CH)

-r nr\.or 0a - ti^. nnFrI .ric"f;,l'f;rl:f:r:i$ti;"*.*,. tr _ lrpt :r,o1Jw I oo - A ir. lQ, i erl ara f e- 5 trvch., ra c>S to..

/t'L-- Sv-rCmr[.d) |i"l + 1fl(lt) <r. AfFi^. r]e-o<.\ nFrd.

4 ]Sy-(rr,[.,o:) =' Jr\'(11)

t,rctrir-&-tn'. (F,i),, = S^^*tS wl f \=f ,lS=frdr?\: drrg = 9l

Th"1 , ha.<- oo-Arat YZicAarv.rl'a, AFtd. Cr+ i(,>).p

" f ini tioa .F F lr.-' . 0o o(\

' ( ,n r'r lc " enurgl F, * f i-^*l :

brnrt /S*.o if yot(itt"\

E-(il=tttP.'l' tJ" rrtr\'- \ ftf

t"K-lv,\, : p+r " fl dv'l

f^P

It,

\,^

- P.^*\Ar.^ Ft"-' il n,c.j.,bi'c C"r.lirn I Flo,- oF e u, .r. t (; .)p

)ep yL _ i . u = &volpq= J xPJ OP OP i= l5l"r

Page 3: J o Flo., Sf F g^4-jchaidez/notes/donaldson_flow.pdf · '-l- hc Po..^ \J s o ., Flo., o.\ Sf *F Lr| i. f ] F" \a s g^4-lto liv..+ i^ J qwcfio..5 Sctrp + Obs

Y\ore Dafiv-\io"

Pro.rF " \1r. (t\ e =

f r it'cll

d,"C0,lo.)acJu., lo.

dl^, : T,tt -. tlJ";l"-(\,, ( fn(ul , 0\ = ( H, Fi(+\ ?

-oi (-dt'x;, e) : 5;,(e,d{ "Xt)

Yi"tU e,rvt\ F,^.^tin^ L o^ N , narw-|1 :

t(0\ = i Tllni\f* , L' tLa R

ernlicat t(r-.F g q.r.c,b ( ,)*?d a Cet 0 = Z 4 < lri{ ri} ) tcf,, .F r'rr.a.r A1e

= -/rr.; ( # oxn, ,f^ l af 'Xtr, , t)fr- ft"*n"fil=-i<r'.'F(T,.)

trto\6.

5;x. l',(a , dQ') tn

5 l',c', do' ) ^ 'rxn

l*'",($,do')^ dl{

t h^(r-,c6,d$.),Jl^

la

,a

c

c'

vo

It

,,\I

.N

=) i7L= - lliJq'xsi r.. {r*t,ci AalHi.= --' dvo 16

(du, lq\

' Jtrl6ilvr,l6.

(P"r' t.l) ,n [S^rl

qi t ^.) * fi.rc 1 ^dir^* flo-,|.

u 9 c Pa'.= q,)* a |o 1. + svol'. of P e

) Do *l8son fto., o^ f t"\( Pu orr nc tr<rir^h ior..1 f f S) .

Cutc<^l, !t^.bvf l1\g'llt oI po^*\l/on tsro*

,) [?o^^l A ro"]

z) Lr,^^lAr.^1

f\ Lt< . r.) I)o^,.. \ar'"k it t;? <,.ou3\'

[5.^, \c 1 .*n {- tl i s

A\\ o lkt ge'\\ic^'\

nni,,initcr oF e.

" o r^ [yt- K^uto" b&sn t1t's

g b '\t'L

".t"t"t, tL

["\ \a x

FL,*, Gxirh Fo, rL.rF ii^" n ir b#?5'::T,i-'fHft4uL^t /

J

0 ns.. Po\Lt*|r) Lu^1 - ii"-.' cxr] Vsn'tc:

(a) vc\pr -\t' @ oc

tb) 11 t^r\\ W?rk' 'V o,o

q tDa^\ * | 5,^"J L\<- f t, i^

o

i^ F,',i k ti rnc

Jc'*la,l C.e,-t<

i ". to trr -ftra .J

Page 4: J o Flo., Sf F g^4-jchaidez/notes/donaldson_flow.pdf · '-l- hc Po..^ \J s o ., Flo., o.\ Sf *F Lr| i. f ] F" \a s g^4-lto liv..+ i^ J qwcfio..5 Sctrp + Obs

f)criv-*io\.(F\.- .. $o- dil ?0.*llt.n'ss-g vp wi lL lt^i17

(tt..(i &t ttt4*\<r -q' ( 5,6;,T) c.r\ K,^\\c).

(}\.9,m,-},T.,5J,T,)o|T;5ehiF1i^3ivar}ecnioo,icLooI< at n"tt! (m-J,'^.) of Ji$t.or*c,rg\^ilons:

rgtr hl"s

rv* 't4 forrl .l

{+' (tl ,s) : (n ,j 16,5) a) f* [.,1 = lal- /L hns"hr [iot:Iili'-r;* cr,,. pr\s! bo.^.k Fro,.

-T+X = f (s ,dTH) ; i,6 e T+lt t\c'. &.F1^,s..

rz,($,6) j= \ f ,(C,i) d'.1 c , ltq*,: Ti iS y ^-jk"' f ''' { F-r t - {t rr-r,..+,^rcjlr:

,.

-A h,,,l c'cti o^ b1 9Y-pH".- (n, c) =; A j

ACJr;/+H.

, (c,fr)q = S^ai ,fr)1 Jvol'P'tVr\^^,\\'a

Sr.r(yt,/L/co.( Crr - G)i"r)

t,o1)

0eri.^tt^ cpnti"<- 4

- A ct io^ Gr- c:-l* is "Ho-i \|o"'1*" O.ln^,tt;

-olzvio.1\1 lL', it i^vsia,'| ,,-\, G o,<.h,.on, So i5 1,1^pt ..Si. a!ti,*.

- ca,. rcylric \ lo 3o = F n"i\t ^ir.n wchrf'a lJ r on h,- Tt^,r X"z W Jf.-"(vrl r ll"(h)/g , r r,.. fr^,c i^hi^',v5ih-\

f,"c!',.. oF 1$ on J1 n.r*litt C \1 rn*p..

ll* 1:*' --Fc \d r"'r't c

V: g, +--ryc,c+(L\: Ff ,--r t+ " -J+"X[ el-(N,Q'Tu)=T+;[LJ

- ls s.c+;,on "F 5, 3i.r^ LI n^or.c^t n^."F( l,ci , 4 -n-"CU) ? YC>l

- Rcr,',..Is: ry\o^^cn+ga i, lr:H- d s,€ f (S)=Xaa^,rr.- |'4.*p ir ;

, i^i(4,)'= AUdvrt 6

p;: A -"+ -(L"(n)