9j - math.cuhk.edu.hk

18
Lecture 14: !"#$%% & ’((") *)+,-#. $(, (+)/ 011-/" 2 3 3 ’! +) 4 5 6"78(8.8+( & 9". : ;" $ <"#.+) 1*$#" +<") 2 5 0( 8((")*)+,--". +( : 81 $ /$* 1 5 = 5 > 3 3 :? : @ 2 18. 5 :’5 A" : $(, BA2 = 8. 1$.8178"1 & B$ C B’DA = > E B ’5 > . 1 A5 FG H ; C IB’ = > E B9’ = > 3 H#C 9’ = > E 9J = > H,C B 28? > GK 87 .+ 0 ’! L

Upload: others

Post on 15-Jun-2022

3 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: 9J - math.cuhk.edu.hk

Lecture 14: !"#$%% &

'((") *)+,-#. $(, (+)/

011-/" 2 3

3 '! +) 4 5

6"78(8.8+( & 9". : ;" $ <"#.+) 1*$#" +<") 25 0( 8((")*)+,--".

+( : 81 $ /$* 1 5

=

5 >3

3 :? : @ 2 18. 5 :'5 ' A" :

$(, BA2 =8. 1$.8178"1 &

B$ C B'DA = ' > E B '5 ' > . 1 A5 FG

H ; C IB'= ' > E B9' = ' >

3

H#C 9' = ' > E 9J =' >

H,C B 28? > GK 87 ' .+0'!

L

Page 2: 9J - math.cuhk.edu.hk

M)+*+18.8+( & 9". : ;" $( 8((") *)+,-#. 1*$#" 5 DN"(=

:'5 J8 AA:

$(, 'BA 2 =O" N$<" &

H$C 9'= 'DA > E # ' = ' > .$? =

A >

B;% # ' = BJ > E #3# '8 FG

H#C 9'=J > E

.+ =' > E +

H,C 9' = ' > E+ 877 FEP

H"C '7 1 ' = ' > E 1 ' = AQ 7+) .8? " :=

.N"( 2EA 5

L

Page 3: 9J - math.cuhk.edu.hk

M)++7 &

#$ C $ ' = '. ' G E B'.RE ST=?>U9AE $F . BA5'D E $ '5 ' > .#?5AI

B;% 9'= B' G E 1#T5'D E ##Q.3##Q5'D

E ' B2 =JGH#C # ' =

PG E 9 '=J .+ > E 9'

=PG .$?

=P >

I+=

S ' =J > E +

5 I8/8%$)%Q =S '

=' > E +

H,C '7 ' E J=.N"( S ' = ' > E V ;Q ## C

'7 ' .+=

.N"( S '=' > > + ;Q ,"78(8.8+(

5

Page 4: 9J - math.cuhk.edu.hk

H"C '7 B'= FGEWF =

A > 7+) $%% ' #3 :5

.N"( $ '= J 3 ' > E + .N" :

5

'( *$).8#-%$) = O" #$( #N++1" FEF 3 A5

DN"( & $ ' 3 A= ' 3 A > E+ X ' 3 A 3

3' B ;Q B, CC

X ' 3

3 A5

!"/$)Y & ' $. . B; C .+Z".N") 1$Q .N$. .N" 8((") *)+,-#.

81 #+(T-Z$." %8("$) 8( .N" 1"#+(, $)Z-/"(. 5

L

Page 5: 9J - math.cuhk.edu.hk

6"78(8.8+( 55 9". : ;" $( 8((") *)+,-#. 1*$#" 5

2+) ' A:=

O" #$( ,"78(" .N" %"(Z.N +) (+)/ +7 ' ;Q 8

['\ &] J9'5'DM)+*+18.8+( & 9". < ;" $( 8((") *)+,-#. 1*$#" +<") 2

5DN"( =

[' = ' A: $(, :BA2 =O" N$<" &

B$ C ^^B '%% E %+% 5 ['\

H;C ['99 GK=

$(, _D[ E + 877 ' E D5

H#C `' = ' > ' A ^^F^^^^F^^ H B$-#NQ 3 I#NO$)R '("a-$%8.Q C

B , C %.?.Q%% A ['\ 3^^^F^^ H D)8$(Z%" 8("a-$%8.QC

X5

)

Page 6: 9J - math.cuhk.edu.hk

M)++7 & #$ C %8#?%% Eb E

D8?[R

'B'

H ; C c'[ E 2'A d+ H ;Q,"78(8.8+(=

e,2D'!

E `' [A[ 5

^^F^^EK f 9 F=FGEK 877 FEP

H#C '7 FEP = .N"( .N" 8("a-$%8.Q N+%,1 5

I+=

$11-/" ' .+ 5c+O =

: # A2 =

g A%%' 3 B'^^W E9' 3 B' = ' 3 $. > E

$.=' 3 B' > 3 #$. =

' 3 -*

+ h# .8? > 3 ' 1.$Q > 3 #$. =' > . BA 1.$Q >

Page 7: 9J - math.cuhk.edu.hk

+ f# ' = ' G 3 ' 1.$Q > 3 # BJ =' > . BA 1.$Q >

I". # E1'

S ' = ' Ge

)

DN"( & + " $.=' > 3

'E 8(.) 3 .Z'8

X 'B' = ' > D " ^^F_W^^G^^W

' $ ' = ' > ' A ^^F^^^^F^^5

Page 8: 9J - math.cuhk.edu.hk

H,C

%%'.Q%D39i.Q8?.QG3#?D?G.#?DQ1.#QD?j7.#Q5QkE ['\

e. W !" 1.$Q > .NQ 'D ['D

A :''' e. W^1. = ' > ' H$ e A.; C^3 8%Q 'D RE$

A ['\e

. W^^F^^^^F^^ 3^^^F^^W

E B['[ . ['\Cl

X [' . '%% ' ^^F^^ 3^^^F^^5

Page 9: 9J - math.cuhk.edu.hk

0**%Q ' B C $(, B, C .+ .N" 1.$(,$), <"#.+) 1*$#" 2(

O8.N .N"

1.$(,$), 8((")*)+,-#. m &

D8 3

3 B$8=0R

= m 3 3 '$( C =' E H ;"

=5 5 =

;( C

'''5$8;8. e1 H A5 8$88%Y8.R%;88 Cl

H '1`$8.;8. CYA8' %$8. Cl

. H A5 %;88 Cl

L

Page 10: 9J - math.cuhk.edu.hk

V).N+Z+($%8.Q6"78(8.8+( & 9". : ;" $( 8((") *)+,-#. 1*$#" 5 n" 1$Q '

=J A:

$)" +).N+Z+($% H +) *")*"(,8#-%$)C 87 B '=' > E V 5

0 1-;1". I#< 81 #$%%", +).N+Z+($% 87 $(Q .O+ ,81.8(#.

<"#.+)1 8( I $)" +).N+Z+($% 5

0 -(8. <"#.+) 8( : 81 $ )"#.+) ' A: O8.N ^^F^^E^5

0 1-;1". IB: 81 #$%%", +).N+(+)/$% 87 I 81 +).N+Z+($%

$(, $%% <"#.+)1 8( I $)" -(8. <"#.+)1 5

L

Page 11: 9J - math.cuhk.edu.hk

" 5 o 5 9". [ ;" .N" 1*$#" +7 #+(.8(-+-1 #+/*%"? 3 <$%-", 7-(#.8+(1

+( p K=W^D q5

n" N$<" 8((") *)+,-#. ,"78(", ;Q &

S 7= Z >

,8. $. Jrl

78. C Z". C,. 7+) 7 = Z".

2+) $(Q (" d? 8(."Z") = ". 7 =.

8(. ,"77 N. C E " & E #+1 N..8 18((. 7+)." 3s=W0 q

$(, #+(18,") I 3

3 t 7( 8( A W u B['a pT#+1#/(%.,.

2+) m $(Q\.(

=O" N$<" &

,"7Q=

U e v re

18( '

/811.$."=

#7/7( > E

"8/.""58(.k,.35'$7k"8./3/.$.E9$757/(7A/(wb

V

E V

Page 12: 9J - math.cuhk.edu.hk

0%1+ = B7(=7( > E 'D= Cr

l

"8(.""581k(.,.ER'Jk^,.m E '

#

e

5I 81 +).N+(+)/$% 1-;1". +7 [ =

Page 13: 9J - math.cuhk.edu.hk

6"78(8.8+( & 9". : ;" $( 8((") *)+,-#. 1*$#" 5 0 1-;1". m +7 :

81 $( +).N+(+)/$% ;$181 7+) : 87 8. 81 $( +),")", ;$181

ON8#N 81 +).N+(+)/$% 5

M)+*+18.8+( & 9". : ;" $( 8((") *)+,-#. 1*$#" $(, IEt ' = =5 5 =JN u

;" $( +).N+Z+($% 1-;1". +7 : #+(181.8(Z +7 (+( 3 R")+ <"#.+)1 5

DN"( & ..Qe

A I*$(Y C =

'e

33 ''

5

'8[D'c

L

Page 14: 9J - math.cuhk.edu.hk

M)++7 & n)8." J E vW=

$8<8 7+) 1+/" $1=0R = 5 5 =

0`A25

D$Y" 8((") *)+,-#. O8.N DT +( ;+.N 18,"1 Z8<"1 &

S J = 3<T > E

=

$8#<8 = JT G E $T%%<TNe

_

B+)+%%$)Q l '7=

8( $,,8.8+( .+ $;+<"=

I 81 +).N+(+)/$%=

.N"( .Q" I*$(+ = ' E 9 '5 D8 > '8

L

Page 15: 9J - math.cuhk.edu.hk

B+)+%%$)Q W & 9". 1 ;" $( +).N+Z+($% 1-;1". m +7 $( m 8((") *)+,-#.

1*$#" : #+(181.8(Z +7 (+(3 R")+ <"#.+)1 3 DN"(

=I 81 %8("$)%Q

8(,"*"(,"(. 5

#51*$( H

D)8 = m3 3 D+(1 C

M)++7 & '7 $8<8 m EP 7+) 1+/" J8=

5 55

=DY AI $(,

8 3x 'o^

=0R

= m 33

=0Y A2

=

yQ *)"<8+-1 *)+*+18.8+( =

$8 mE

S KvzQ{ =*

E + 7+) 8 3_=W =5 m 5

=Y

5

|

Page 16: 9J - math.cuhk.edu.hk

M)+* & 9". : ;" $( 8((") *)+,-#. 1*$#" $(, I(Et '8= 5 m 58+( u

;" $ %8("$)%Q 8(,"*"(,"(. 1-;1". m +7 :5 6"78(" &

I(e

E t J8 ='$

=5

5 5

=

'( u ON")" '=

E 8(=

$(,

.)"" l m3 m l

'&] 8( 5

DN"( l I(e

81 +).N+Z+($% $(, I*$( 9 I(e C E 1*$( B I( C

DR T =

3

BD: = ON")" # =EBO<6l ^^P^^^W' =

E 3

3oD+

=

E :'

Page 17: 9J - math.cuhk.edu.hk

B+(18,") : E M}! C "a-8**", O8.N .N" 8((") *)+,-#.

S 7= Z G E9

e

=

7. Z".1 ,.5

9". *E t '=

?=

? k 3 3 5

=i

l

= m3

3 3 u ;" 1.$(,$), +),")", ;$181

7+) M[! C 5

D$Y" D=

E '5 V

=l l

DN"( & D<= E ? 3

B` =D

5 > 3

3 : =E ?[<5(+

W

81 5

5 8 5

$ {~Gz=3$?�< 8( E $3 '

R'' D$% �

L

Page 18: 9J - math.cuhk.edu.hk

885 $ $ &"8 5 81E W�

3 I'i $(, I+ +(8

33

3

7+) M}!C

DN81 *)+,-#"1 $( +).N+Z+($% ;$181 t D%=DR

=5

5

�=

ON+1"

"%"/"(.1 $)" #$%%", 9"Z"(,)" *+%Q(+/8$% 5

L