fl i lorfu:1.ff'ä*t;' u e **,.1 l.€¦ · fgpr'e l az\ iettt auch vo,a kol, s =...

5
0ic Op{frrolsb,.er ble,r. r Hri der POE agibt *hl{csslrh da. lrfqrn& u^cutdlirhernerll'aaale ras{rirr6 tetk OP : rn{n tr1*e^-Iusdr+ ä[rW §e Y.fftnlr uell=L#t) i,t. lA(x) Yycxl ,Vvu) dr = §yol w)cr Vveffin| !.-<$g5'rrrd ü-3t)gd in c Y = frnts.1 _tr 'L FE-O[ (.te4[s fer .Ka c [i= LzCI) 5L Y;' §pan |.{r,t,,,r YrrS tlr=sf*&.t.-f Qr.l 2'B ünr..-,{L Y1,aUr.CI)= fiU il;c-r) [ria ute)= ä ur\o) v gctieY=f$nl M ttcr) eTi=LzA) u e fl & u ]tu'u)'= I lo"rfu:1".ff'ä*T;"' **,.1 L"..6 =i[r"r,-if"-Xl vfi[,uär V - tt--trr,,l \7--.-r\- 1 rSDf s.t. | - etv ( Ak) Q,*r) = ucr) , fulcorstauk t gth, =to)ä^O r ,re fl="t J $.of, lsfale cans{rorh{s , ifl; <§Gr,.ää; tr€o I Üßttqdc [- Co"tral coru{rair{r ] .. cr) ( ucr) 3 E crl, xefr.) \'/ti chu&|,

Upload: others

Post on 06-Oct-2020

0 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: fl I lorfu:1.ff'ä*T;' u e **,.1 L.€¦ · fgpr'e L az\ iettt Auch vo,a kol, S = 2plfual s{ qe( prab levn r He I § ?rl' ie{sl:.F-ohne Uq letchungs nebenbed, 1 d,h, mr=o t fr,t=rre

0ic

Op{frrolsb,.er ble,r. r Hri

der POE agibt *hl{csslrh

da. lrfqrn& u^cutdlirhernerll'aaale ras{rirr6 tetk OP :

rn{n tr1*e^-Iusdr+ ä[rW§e Y.fftnlr uell=L#t)

i,t. lA(x) Yycxl ,Vvu) dr = §yol w)cr Vveffin|

!.-<$g5'rrrd ü-3t)gd in

c Y = frnts.1 _tr

'LFE-O[ (.te4[s fer .Ka

c [i= LzCI)

5L

Y;' §pan |.{r,t,,,r YrrS

tlr=sf*&.t.-f Qr.l2'B

ünr..-,{LY1,aUr.CI)= fiU il;c-r)

[ria ute)= ä ur\o)

v gctieY=f$nl

M ttcr) eTi=LzA)

u e fl & u ]tu'u)'= I lo"rfu:1".ff'ä*T;"'**,.1 L"..6 =i[r"r,-if"-Xl vfi[,uär

V - tt--trr,,l \7--.-r\- 1 rSDfs.t. | - etv ( Ak) Q,*r) = ucr) , xä fulcorstauk

t gth, =to)ä^O r ,re fl="t J

$.of, lsfale cans{rorh{s , ifl; <§Gr,.ää; tr€o IÜßttqdc [- Co"tral coru{rair{r ] .. cr) ( ucr) 3 E crl, xefr.)

\'/tichu&|,

Page 2: fl I lorfu:1.ff'ä*T;' u e **,.1 L.€¦ · fgpr'e L az\ iettt Auch vo,a kol, S = 2plfual s{ qe( prab levn r He I § ?rl' ie{sl:.F-ohne Uq letchungs nebenbed, 1 d,h, mr=o t fr,t=rre

2

n'

erg ib+ das

t14H§&

rvg*Fi aetiecle 0P:

r u's uu=[rl)o=rn

(KfiHr yr ) =ln Vtr.Vvsdx VL*J'.ü q.,y,.etr

( F'1, !r, .trh) = .Lr.r.tvau)dx - r( -

( Hc Bnr in) = [ \alqod,, V ,r,*, <+ ur,!^ntl*

( Mr. Bh, !r) = § rn !,, dx Vupltuefi,vy*g*e[*

(grr,$n) =§fuo,1$h&)dr #y,,* Jre ,Pns

tr§s*.ä .fh'= [U;Ji=rG's

(§-,.§ a{

PS§§.ss

a- -lL.I-

,! -$r§1U

ü*LLg

.g^4,

-!l5

§§Ds§§.u-tUsU

§

u),' o?

,r.?;lr.ri. if,rfar - lue tnd '

*7'§ uf dr

s,t. lAß) [yrtr)'Vht*)d, * J u,;,ltrlut dv V vre Y,

!g :* lcr;) § Ui- !r$J) s f;'' $<rt), t = 6ft :=U Cr;) < ui:=t{r(rd}(A:=Ccri), 1'=ffi

t [(*r 16,!6) -(En,!r) *f ( M.s", %)JX-(lr,rhtre 6f=ß+4.

c{ (§) : (Krr 16;+); =e, i= ffiU-iiä1 ,3trt,fff'*,*l - üs3 O J Dl= 2fts4 Zrre-

..IigY;<[;i3@t(ü § ti!-sirri=T,no

s.t. K !*= Msc g6

,r(s)cr)=Orxenn

,s.t . ci

min[=4a21..,1M11

I

c;Ctt) § O r 1 = 7ta+41. . ,l Vtnl {tl1.

Page 3: fl I lorfu:1.ff'ä*T;' u e **,.1 L.€¦ · fgpr'e L az\ iettt Auch vo,a kol, S = 2plfual s{ qe( prab levn r He I § ?rl' ie{sl:.F-ohne Uq letchungs nebenbed, 1 d,h, mr=o t fr,t=rre

fgpr'e L az\ iettt Auch vo,a kol, S

= 2plfual s{ €qe( prab levn r He I § ?rl'ie{sl:.F- ohne Uq letchungs nebenbed, 1 d,h, mr=o t fr,t=rre Z

r = tl,Xr6 ßn=ns+ n,Wx' Y't) - ::'CqW"'47

=: tlx)s.L ,KJ.-[Yo g=0 qA) := [K!- f{at]; = O

(,s4,2r-..1fr4 = fn=?§

o CQ = Constrainl Auoh'(icalion,ranl G,(x.) = ?an1t HJom = rorJtK,MJ=r=trs

ßlxos

c ann gi(lt ! =+ K-4Mscq = Qg. nr'l S;= +K-tl"l* ,

l,h. ( / )rop is* dryivalenl ?eu f rcien op

(4)ro,'rnfnLeß'rc

-

min

li(us ss.r,sr.s.)-(ft,$r)+;u,,,r[

g e 6tre ä(rslurs,.r#M. s,s)-(&,0)

g e lRn"l (sIM. S..r 414.) g = sJ ra

(uJ 4-1',M. K 4l'1rr+ 4%)s =*mJK'r,

'$!geßn feltr 4>o

(4).q,

fr,s0

rea,

3

Page 4: fl I lorfu:1.ff'ä*T;' u e **,.1 L.€¦ · fgpr'e L az\ iettt Auch vo,a kol, S = 2plfual s{ qe( prab levn r He I § ?rl' ie{sl:.F-ohne Uq letchungs nebenbed, 1 d,h, mr=o t fr,t=rre

Lorrante-Funfiton: m-ns r X= ([,g) € lfl,n=no*q

f,= ()rq,...,,t. ) = LaXcony Mqlt;pli(atorcn = adjottl shlc

L(r, l) = fcx) + Arccr) =ftr)*f Li.;t0es{

= Lr( Msr,t)-(!r,!)+/(t't a,g)* [trg-Hns)

o KKT'-S8etern, V L(x*,trt) =O

VI L(-U,rrÄ)=0Vu L (f ,8,f,)=07,rL(I,t,A)=Q

MsL *xIq Hcs - t4|l.

= J.l

=Q=QK1 - lfsc g,

h)sr

a

M§O6r0 aYc -Mr.K, -Ms6 O

@\11d.;r:'r

lul=&j

grl0l0)

K!{f -$*ln brn = }p[tlnal,h]o sgekn (rol,r,srl- 00ilt1)

^.(,tl* 2,

.'.

t"ts=lY.T > O, J,[.,§p0 &,arhrlt'los.rawefii(

f,lc. M.tr2 Ot d,h, tP0 Ko^fn(lh4witxrhlr

M., . Mr: - ( n. x il§ ) - Hafuir

gffi(!,g), a ) e ntt5ilts'nt, (a)*n idg,-rtal !x3=(t,s) fsl efaJe*{iücr Nhpaakt tce fc*),J. h, (4 )rop ha* erh e einlei,r{ly Lösung ,

dre r,ni{ lttl[c voa t4) wfi ber."hrul uirl*

Page 5: fl I lorfu:1.ff'ä*T;' u e **,.1 L.€¦ · fgpr'e L az\ iettt Auch vo,a kol, S = 2plfual s{ qe( prab levn r He I § ?rl' ie{sl:.F-ohne Uq letchungs nebenbed, 1 d,h, mr=o t fr,t=rre

5 o Sc hur-Konple wtettl bi Eun{ Redur,rzr,le 0p},haf;friftsgs{a w

@ Elr'rrd nieren X- nnd L qus (4 ) vff :

4. Ä E- 6-4 Msg + 6-4!e UGKT )8. & = f K'r Mscu = Sr.g tnnit So=+ K-4Mro

hal rn d;e 2. GletchunT erhSe{xn:

4t4ce -M;: ?K4&r * 14^4il) = O

d fl"L + MI X'M. u l Mf K'' 9t

or H6 r + Mr[ y-r Hr K^a P1s"L ?- 11{ K-'!,

(a)got

@q

( n'f K- '' M4 14^4M..+orM") us MrIKi

@ §f; rninieren

a) eut g. 4trs Ut)a«r m,[ der 2, Gle;chun&

!= *|4;n UII ---ä s.

:[ V lir,,Mr]l tl=[ä]ß) Md dann s dtß @q nil der 4,G[acbr1

! =-M;4 K'^+ M.-t!i -

g,

(rc M;r Kr* * l,l""14/ M,l )Ä = KMf re@q

= redu+iellq }pttnaLJ{eTgs3elau" bau , red, Kl(T^*{lü,

ff)