ch7 problems

8/3/2019 Ch7 Problems

1/83

&RQFHSW6WXG\*XLGH3UREOHPV

(OHFWULFDODSSOLDQFHV79VWHUHRXVHHOHFWULFSRZHUDVLQSXW:KDWKDSSHQVWR

WKHSRZHU"$UHWKRVHKHDWHQJLQHV":KDWGRHVWKHVHFRQGODZVD\DERXWWKRVHGHYLFHV"

0RVWHOHFWULFDSSOLDQFHVVXFKDV799&5VWHUHRDQGFORFNVGLVVLSDWHSRZHULQHOHFWULFDOFLUFXLWVLQWRLQWHUQDOHQHUJ\WKH\JHWZDUPVRPHSRZHUJRHVLQWROLJKWDQGVRPHSRZHULQWRPHFKDQLFDOHQHUJ\7KHOLJKWLVDEVRUEHGE\WKHURRPZDOOVIXUQLWXUHHWFDQGWKHPHFKDQLFDOHQHUJ\LVGLVVLSDWHGE\IULFWLRQVRDOOWKHSRZHUHYHQWXDOO\HQGVXSDVLQWHUQDOHQHUJ\LQWKHURRPPDVVRIDLUDQG

RWKHUVXEVWDQFHV

7KHVHDUHQRWKHDWHQJLQHVMXVWWKHRSSRVLWHKDSSHQVQDPHO\HOHFWULFDOSRZHULVWXUQHGLQWRLQWHUQDOHQHUJ\DQGUHGLVWULEXWHGE\KHDWWUDQVIHU7KHVHDUHLUUHYHUVLEOHSURFHVVHV

$JDVROLQHHQJLQHSURGXFHVKSXVLQJN:RIKHDWWUDQVIHUIURPEXUQLQJIXHO

:KDWLVLWVWKHUPDOHIILFLHQF\DQGKRZPXFKSRZHULVUHMHFWHGWRWKHDPELHQW"

&RQYHUVLRQ7DEOH$KSN:N:

(IILFLHQF\K7+:

RXW4

+

(QHUJ\HTXDWLRQ4

/4

+:

RXWN:

4

+

4

/

: RXW


2/83

$UHIULJHUDWRUUHPRYHVN-IURPWKHFROGVSDFHXVLQJN-ZRUNLQSXW+RZPXFKHQHUJ\JRHVLQWRWKHNLWFKHQDQGZKDWLVLWVFRHIILFLHQWRISHUIRUPDQFH"

&95HIULJHUDWRU7KHHQHUJ\4+JRHVLQWRWKHNLWFKHQDLU

(QHUJ\(T 4+:4/N-

&23 E4/:

7KHEDFNVLGHRIWKHUHIULJHUDWRUKDVDEODFNJULOOH

WKDWKHDWVWKHNLWFKHQDLU2WKHUPRGHOVKDYHWKDWDWWKHERWWRPZLWKDIDQWRGULYHWKHDLURYHULW

$LULQ

$LURXW

$VVXPHZHKDYHDUHIULJHUDWRURSHUDWLQJDWVWHDG\VWDWHXVLQJ:RIHOHFWULFSRZHUZLWKD&23RI:KDWLVWKHQHWHIIHFWRQWKHNLWFKHQDLU"

7DNHD&9DURXQGWKHZKROHNLWFKHQ7KHRQO\HQHUJ\WHUPWKDWFURVVHV

WKHFRQWUROVXUIDFHLVWKHZRUNLQSXW:

DSDUWIURPHQHUJ\H[FKDQJHGZLWKWKH

NLWFKHQVXUURXQGLQJV7KDWLVWKHNLWFKHQLVEHLQJKHDWHGZLWKDUDWHRI:

5HPDUN7KHWZRKHDWWUDQVIHUUDWHVDUHERWKLQWHUQDOWRWKHNLWFKHQ4

+

JRHVLQWRWKHNLWFKHQDLUDQG4

/DFWXDOO\OHDNVIURPWKHNLWFKHQLQWRWKH

UHIULJHUDWHGVSDFHZKLFKLVWKHUHDVRQZHQHHGWRGULYHLWRXWDJDLQ


3/83

$ZLQGRZDLUFRQGLWLRQHUXQLWLVSODFHGRQDODERUDWRU\EHQFKDQGWHVWHGLQFRROLQJPRGHXVLQJ:RIHOHFWULFSRZHUZLWKD&23RI:KDWLVWKHFRROLQJSRZHUFDSDFLW\DQGZKDWLVWKHQHWHIIHFWRQWKHODERUDWRU\"

'HILQLWLRQRI&23 E4 /:

&RROLQJFDSDFLW\ 4

/E:

u:

)RUVWHDG\VWDWHRSHUDWLRQWKH4

/FRPHVIURPWKHODERUDWRU\DQG4

+JRHV

WRWKHODERUDWRU\JLYLQJDQHWWRWKHODERI:

4

+4

/:WKDWLV

KHDWLQJLW

*HRWKHUPDOXQGHUJURXQGKRWZDWHURUVWHDPFDQEHXVHGWRJHQHUDWHHOHFWULFSRZHU'RHVWKDWYLRODWHWKHVHFRQGODZ"

1R6LQFHWKHHDUWKLVQRWXQLIRUPZHFRQVLGHUWKHKRWZDWHURUVWHDPVXSSO\DVFRPLQJIURPRQHHQHUJ\VRXUFHWKHKLJK7DQGZHPXVWUHMHFWKHDWWRDORZWHPSHUDWXUHUHVHUYRLUDVWKHRFHDQDODNHRUWKHDWPRVSKHUHZKLFKLVDQRWKHUHQHUJ\UHVHUYRLU

,FHODQGXVHVDVLJQLILFDQWDPRXQWRIVWHDPWRKHDW

EXLOGLQJVDQGWRJHQHUDWHHOHFWULFLW\


4/83

$FDUHQJLQHWDNHVDWPRVSKHULFDLULQDWR&QRIXHODQGH[KDXVWVWKHDLUDW

R&SURGXFLQJZRUNLQWKHSURFHVV:KDWGRWKHILUVWDQGWKHVHFRQGODZVVD\DERXWWKDW"

(QHUJ\(T:4+

4/

FKDQJHLQHQHUJ\RIDLU2.

QG

ODZ([FKDQJHHQHUJ\ZLWKRQO\RQHUHVHUYRLU1272.7KLVLVDYLRODWLRQRIWKHVWDWHPHQWRI.HOYLQ3ODQFN

5HPDUN


5/83

$URRPLVKHDWHGZLWKD:HOHFWULFKHDWHU+RZPXFKSRZHUFDQEHVDYHGLIDKHDWSXPSZLWKD&23RILVXVHGLQVWHDG"

$VVXPHWKHKHDWSXPSKDVWRGHOLYHU:DVWKH4

+

+HDWSXPSEc4

+:

,1

:

,14

+Ec

:

6RWKHKHDWSXPSUHTXLUHVDQLQSXWRI:WKXVVDYLQJWKHGLIIHUHQFH

:

VDYHG:::

H4

:

L4

7L

+3

5RRP

LQFE

,IWKHHIILFLHQF\RIDSRZHUSODQWJRHVXSDVWKHORZWHPSHUDWXUHGURSVZK\GR

WKH\QRWMXVWUHMHFWHQHUJ\DWVD\R&"

,QRUGHUWRUHMHFWKHDWWKHDPELHQWPXVWEHDWWKHORZWHPSHUDWXUH2QO\LIZHPRYHGWKHSODQWWRWKH1RUWK3ROHZRXOGZHVHHVXFKDORZ7

5HPDUN


6/83

,IWKHHIILFLHQF\RIDSRZHUSODQWJRHVXSDVWKHORZWHPSHUDWXUHGURSVZK\QRW

OHWWKHKHDWUHMHFWLRQJRWRDUHIULJHUDWRUDWVD\R&LQVWHDGRIDPELHQWR&"

7KHUHIULJHUDWRUPXVWSXPSWKHKHDWXSWRR&WRUHMHFWLWWRWKHDPELHQW

7KHUHIULJHUDWRUPXVWWKHQKDYHDZRUNLQSXWWKDWZLOOH[DFWO\RIIVHWWKHLQFUHDVHGZRUNRXWSXWRIWKHSRZHUSODQWLIWKH\DUHERWKLGHDO$VZHFDQQRWEXLOGLGHDOGHYLFHVWKHDFWXDOUHIULJHUDWRUZLOOUHTXLUHPRUHZRUN

WKDQWKHSRZHUSODQWZLOOSURGXFHH[WUD

$FRDOILUHGSRZHUSODQWRSHUDWHVZLWKDKLJK7RIR&ZKHUHDVDMHWHQJLQHKDVDERXW.'RHVWKDWPHDQZHVKRXOGUHSODFHDOOSRZHUSODQWVZLWKMHWHQJLQHV"

7KHWKHUPDOHIILFLHQF\LVOLPLWHGE\WKH&DUQRWKHDWHQJLQHHIILFLHQF\

7KDWLVWKHORZWHPSHUDWXUHLVDOVRLPSRUWDQW+HUHWKHSRZHUSODQWKDVD

PXFKORZHU7LQWKHFRQGHQVHUWKDQWKHMHWHQJLQHKDVLQWKHH[KDXVWIORZVRWKHMHWHQJLQHGRHVQRWKDYHDKLJKHUHIILFLHQF\WKDQWKHSRZHUSODQW

*DVWXUELQHVDUHXVHGLQSRZHUSODQWVZKHUHWKH\FDQFRYHUSHDNSRZHUGHPDQGVQHHGHGIRUVKRUWHUWLPHSHULRGVDQGWKHLUKLJKWHPSHUDWXUHH[KDXVWFDQ

EHXVHGWRERLODGGLWLRQDOZDWHUIRUWKHVWHDPF\FOH

:7

4+

4/

:3LQ

IURPFRDO

WRDPELHQW


7/83

$KHDWWUDQVIHUUHTXLUHVDWHPSHUDWXUHGLIIHUHQFHVHHFKDSWHUWRSXVKWKH4

:KDWLPSOLFDWLRQVGRWKDWKDYHIRUDUHDOKHDWHQJLQH"$UHIULJHUDWRU"

7KLVPHDQVWKDWWKHUHDUHWHPSHUDWXUHGLIIHUHQFHVEHWZHHQWKHVRXUFHRIHQHUJ\DQGWKHZRUNLQJVXEVWDQFHVR7+LVVPDOOHUWKDQWKHVRXUFHWHPSHUDWXUH

7KLVORZHUVWKHPD[LPXPSRVVLEOHHIILFLHQF\$VKHDWLVUHMHFWHGWKHZRUNLQJ

VXEVWDQFHPXVWKDYHDKLJKHUWHPSHUDWXUH7/WKDQWKHDPELHQWUHFHLYLQJWKH4

/

ZKLFKORZHUVWKHHIILFLHQF\IXUWKHU

)RUDUHIULJHUDWRUWKHKLJKWHPSHUDWXUHPXVWEHKLJKHUWKDQWKHDPELHQWWR

ZKLFKWKH4 +LVPRYHG/LNHZLVHWKHORZWHPSHUDWXUHPXVWEHORZHUWKDQWKH

FROGVSDFHWHPSHUDWXUHLQRUGHUWRKDYHKHDWWUDQVIHUIURPWKHFROGVSDFHWRWKHF\FOHVXEVWDQFH6RWKHQHWHIIHFWLVWKHF\FOHWHPSHUDWXUHGLIIHUHQFHLVODUJHUWKDQWKHUHVHUYRLUWHPSHUDWXUHGLIIHUHQFHDQGWKXVWKH&23LVORZHUWKDQWKDWHVWLPDWHGIURPWKHFROGVSDFHDQGDPELHQWWHPSHUDWXUHV


8/83

$ODUJHVWDWLRQDU\GLHVHOHQJLQHSURGXFHV0:ZLWKDWKHUPDOHIILFLHQF\RI7KHH[KDXVWJDVZKLFKZHDVVXPHLVDLUIORZVRXWDW.DQGWKHLQWDNH

LV.+RZODUJHDPDVVIORZUDWHLVWKDWLIWKDWDFFRXQWVIRUKDOIWKH4

/"&DQ

WKHH[KDXVWIORZHQHUJ\EHXVHG"

+HDWHQJLQH 4

+:

RXWK7+

0:

(QHUJ\HTXDWLRQ4

/4

+:

RXWN:

([KDXVWIORZ

4

/P

DLUK K

P

DLU

4

/

KK

u

NJV

+RWFRPEXVWLRQJDVHVDLUDW.LVXVHGDVKHDWVRXUFHLQDKHDWHQJLQHZKHUHWKHJDVLVFRROHGWR.DQGWKHDPELHQWLVDW.7KLVLVQRWDFRQVWDQW7VRXUFH+RZGRHVWKDWDIIHFWWKHHIILFLHQF\"

6ROXWLRQ

,IWKHHIILFLHQF\LVZULWWHQDV

K7+:

QHW4

+7/7+

WKHQ7+LVVRPHZKHUHEHWZHHQ.

DQG.DQGLWLVQRWDOLQHDUDYHUDJH

+4

:

/4

7/

+(

FE

$IWHUVWXG\LQJFKDSWHUDQGZHFDQVROYHWKLVSUREOHPDQGILQGWKHSURSHUDYHUDJHKLJKWHPSHUDWXUHEDVHGRQSURSHUWLHVDWVWDWHVDQG


9/83

$UHPRWHORFDWLRQZLWKRXWHOHFWULFLW\RSHUDWHVDUHIULJHUDWRUZLWKDERWWOHRISURSDQHIHHGLQJDEXUQHUWRFUHDWHKRWJDVHV6NHWFKWKHVHWXSLQWHUPVRIF\FOLF

GHYLFHVDQGJLYHDUHODWLRQIRUWKHUDWLRRI4

/LQWKHUHIULJHUDWRUWR4

IXHOLQWKH

EXUQHULQWHUPVRIWKHYDULRXVUHVHUYRLUWHPSHUDWXUHV

7KHZRUNRIWKHKHDWHQJLQHDVVXPLQJ&DUQRWHIILFLHQF\LV

:

K+(

4

IXHO

7DPE7IXHO

4

IXHO

7KHZRUNUHTXLUHGE\WKHUHIULJHUDWRUDVVXPLQJUHYHUVLEOH&23LV

:

/4

7+

+4

7/

5()

)XHO4

+(

/HQJ4

)8(/

:

4

/EUHI4

/

7DPE7/7/

6HWWKHWZRZRUNWHUPVHTXDODQGVROYHIRU4

/

4

/7/

7DPE7/:

7/

7DPE7/

7DPE7IXHO

4

IXHO

5HPDUN7KLVUHVXOWLVRSWLPLVWLFVLQFHZHXVHG&DUQRWF\FOHHIILFLHQF\

DQGFRHIILFLHQWRISHUIRUPDQFH6HFRQGO\WKHKHDWWUDQVIHUUHTXLUHVD'7VRWKHKHDWHQJLQHHIILFLHQF\LVORZHUDQGWKH&23LVORZHU


10/83

+HDW(QJLQHVDQG5HIULJHUDWRUV

&DOFXODWHWKHWKHUPDOHIILFLHQF\RIWKHVWHDPSRZHUSODQWF\FOHGHVFULEHGLQ

([DPSOH 6ROXWLRQ

)URPVROXWLRQWR([DPSOH

ZQHW

ZWZS

N-NJ

T+TEN-NJ

K7+

ZQHWT+

:7

4+

4/

:3LQ

4

1RWLFHZHFDQQRWZULWHZQHWT+ T/DVWKHUHLVDQH[WUDKHDWWUDQVIHU4

DVDORVVLQWKHOLQH7KLVQHHGVWREHDFFRXQWHGIRULQWKHRYHUDOOHQHUJ\HTXDWLRQ


11/83

&DOFXODWHWKHFRHIILFLHQWRISHUIRUPDQFHRIWKH5DUHIULJHUDWRUJLYHQLQ([DPSOH 6ROXWLRQ

)URPWKHGHILQLWLRQ

E4

/:

,1

1RWLFHZHFDQQRWZULWH:

,14

+4

/

DVWKHUHLVDVPDOO4

LQWKHFRPSUHVVRU7KLVQHHGVWREHDFFRXQWHGIRULQWKHRYHUDOOHQHUJ\HTXDWLRQ

4+

:&

4 /

FE

(YDSRUDWRU

&RQGHQVHU

4 ORVV


12/83

&DOFXODWHWKHWKHUPDOHIILFLHQF\RIWKHVWHDPSRZHUSODQWF\FOHGHVFULEHGLQ3UREOHP 6ROXWLRQ

)URPVROXWLRQWR3UREOHP7XUELQH$S

P

9P

Y$PV

K N-NJ

Z7N-NJ

: 7P Z7 N:

:

1(7N:

)URPWKHVROXWLRQWR3UREOHP

(FRQRPL]HU$S'P

YPNJ

99P Y$PV

9YY9PV| 9VRNLQHWLFHQHUJ\FKDQJHXQLPSRUWDQW

T(&21KKN-NJ

4

(&21P

T(&21N:

*HQHUDWRU$S'P

YPNJ

9P

Y$PV

T*(1N-NJ

4

*(1 N:

7KHWRWDODGGHGKHDWWUDQVIHULV

4

+N:

K7+

:

1(74

+


13/83

&DOFXODWHWKHFRHIILFLHQWRISHUIRUPDQFHRIWKH5KHDWSXPSF\FOHGHVFULEHGLQ3UREOHP 6ROXWLRQ

)URPVROXWLRQWR3UREOHP

&9&RQGHQVHU

4

&21'P

K K

N:

7KHQZLWKWKHZRUNDV:

,1N:ZH

KDYH

4+

:&

4 /

FE

(YDSRUDWRU

&RQGHQVHU

4 ORVV

+HDWSXPSEc4

+:

,1


14/83

$IDUPHUUXQVDKHDWSXPSZLWKDN:PRWRU,WVKRXOGNHHSDFKLFNHQKDWFKHU\

DWR&ZKLFKORVHVHQHUJ\DWDUDWHRIN:WRWKHFROGHUDPELHQW7DPE:KDW

LVWKHPLQLPXPFRHIILFLHQWRISHUIRUPDQFHWKDWZLOOEHDFFHSWDEOHIRUWKHKHDWSXPS"6ROXWLRQ

3RZHULQSXW :

N:

(QHUJ\(TIRUKDWFKHU\ 4

+4

/RVVN:

'HILQLWLRQRI&23 E&23

4

+

:

4 OHDN4 4+/

:N:

+3FE


15/83

$SRZHUSODQWJHQHUDWHV0:RIHOHFWULFDOSRZHU,WXVHVDVXSSO\RI0:IURPDJHRWKHUPDOVRXUFHDQGUHMHFWVHQHUJ\WRWKHDWPRVSKHUH)LQGWKH

SRZHUWRWKHDLUDQGKRZPXFKDLUVKRXOGEHIORZHGWRWKHFRROLQJWRZHUNJVLI

LWVWHPSHUDWXUHFDQQRWEHLQFUHDVHGPRUHWKDQR&

6ROXWLRQ

&97RWDOSRZHUSODQW

(QHUJ\HTXDWLRQJLYHVWKHDPRXQWRIKHDWUHMHFWLRQWRWKHDWPRVSKHUHDV

4

/4

+:

0:

7KHHQHUJ\HTXDWLRQIRUWKHDLUIORZWKDWDEVRUEVWKHHQHUJ\LV

4

/P

DLU'KP

DLU&S '7

P

DLU4

/

&S'7

uu NJV

3UREDEO\WRRODUJHWRPDNHVRVRPHFRROLQJE\OLTXLGZDWHURUHYDSRUDWLYHFRROLQJVKRXOGEHXVHG

+4

:

7/

/4

+(

$LU

FE


16/83

$FDUHQJLQHGHOLYHUVKSWRWKHGULYHVKDIWZLWKDWKHUPDOHIILFLHQF\RI7KHIXHOKDVDKHDWLQJYDOXHRIN-NJ)LQGWKHUDWHRIIXHOFRQVXPSWLRQDQGWKHFRPELQHGSRZHUUHMHFWHGWKURXJKWKHUDGLDWRUDQGH[KDXVW

6ROXWLRQ

+HDWLQJYDOXH+94

+P

+9

)URPWKHGHILQLWLRQRIWKHWKHUPDOHIILFLHQF\

:

K4

+K P

+9

P

:

K+9uuNJVJV

&RQYHUVLRQRISRZHUIURPKSWRN:LQ7DEOH$

4

/4

+:

:

K:

K :

uN:

([KDXVWIORZ

$LULQWDNHILOWHU

6KDIW

)DQ

SRZHU

)XHOOLQH

FE


17/83

)RUHDFKRIWKHFDVHVEHORZGHWHUPLQHLIWKHKHDWHQJLQHVDWLVILHVWKHILUVWODZHQHUJ\HTXDWLRQDQGLILWYLRODWHVWKHVHFRQGODZ

D4

+N: 4

/N: :

N:

E4

+N: 4

/N: :

N:

F4

+N: 4

/N: :

N:

G4

+N: 4

/N: :

N:

6ROXWLRQ

VW

ODZ QG

ODZD


18/83

,QDVWHDPSRZHUSODQW0:LVDGGHGLQWKHERLOHU0:LVWDNHQRXWLQWKHFRQGHQVHUDQGWKHSXPSZRUNLV0:)LQGWKHSODQWWKHUPDOHIILFLHQF\,IHYHU\WKLQJFRXOGEHUHYHUVHGILQGWKHFRHIILFLHQWRISHUIRUPDQFHDVDUHIULJHUDWRU

6ROXWLRQ

:7

4+

4/

:3LQ

&97RWDOSODQW

(QHUJ\(T

4

+:

3LQ:

74

/

:

70:

K7+

:

7:

3LQ

4

+

E4

/

:

7:

3LQ


19/83

(OHFWULFVRODUFHOOVFDQSURGXFHSRZHUZLWKHIILFLHQF\&RPSDUHWKDWWRDKHDWHQJLQHGULYLQJDQHOHFWULFJHQHUDWRUZLWKHIILFLHQF\:KDWVKRXOGWKHKHDWHQJLQHHIILFLHQF\EHWRKDYHWKHVDPHRYHUDOOHIILFLHQF\DVWKHVRODUFHOOV"

6ROXWLRQ

:

HO4

+KFHOOKJHQ:

HQJKJHQKHQJ4

+HQJ

!KFHOOKJHQKHQJ

KHQJKFHOOKJHQ


20/83

)RUHDFKRIWKHFDVHVLQSUREOHPGHWHUPLQHLIDKHDWSXPSVDWLVILHVWKHILUVWODZHQHUJ\HTXDWLRQDQGLILWYLRODWHVWKHVHFRQGODZ

D4

+N: 4

/N: :

N:

E4

+N: 4

/N: :

N:

F4

+N: 4

/N: :

N:

G4

+N: 4

/N: :

N:

6ROXWLRQ

VWODZ

QGODZ

D6DWLVILHG'RHVQRWYLRODWHE6DWLVILHG'RHVQRWYLRODWH

F9LRODWHG'RHVQRWYLRODWHEXWVW

ODZG 6DWLVILHG'RHVYLRODWH&ODXVLXV

H4

:

L4

7L

7+

+3FE


21/83

$QDLUFRQGLWLRQHUGLVFDUGVN:WRWKHDPELHQWZLWKDSRZHULQSXWRIN:)LQGWKHUDWHRIFRROLQJDQGWKHFRHIILFLHQWRISHUIRUPDQFH

6ROXWLRQ

,QWKLVFDVH4 +N:JRHVWRWKHDPELHQWVR

(QHUJ\(T4

/4

+:

N:

E5()5,*

4

/

:

H4N:

:N:

L4

7L

7DPE

5()


22/83

&DOFXODWHWKHDPRXQWRIZRUNLQSXWDUHIULJHUDWRUQHHGVWRPDNHLFHFXEHVRXWRID

WUD\RINJOLTXLGZDWHUDWR&$VVXPHWKHUHIULJHUDWRUKDVEDQGDPRWRUFRPSUHVVRURI:+RZPXFKWLPHGRHVLWWDNHLIWKLVLVWKHRQO\FRROLQJORDG"

6ROXWLRQ&9:DWHULQWUD\:HQHJOHFWWUD\PDVV

(QHUJ\(T PX X4 :3URFHVV 3FRQVWDQW3R

:3G93RPY Y

4PX X:PK K

7EO%KN-NJ7EO%KN-NJ

4N-

&RQVLGHUQRZUHIULJHUDWRU

E4/::4/E4EN-

)RUWKHPRWRUWRWUDQVIHUWKDWDPRXQWRIHQHUJ\WKHWLPHLVIRXQGDV

::

GW:

'W

'W::

uV

&RPPHQW:HQHJOHFWHGDEDVHORDGRIWKHUHIULJHUDWRUVRQRWDOOWKH:DUHDYDLODEOHWRPDNHLFHDOVRRXUFRHIILFLHQWRISHUIRUPDQFHLVYHU\

RSWLPLVWLFDQGILQDOO\WKHKHDWWUDQVIHULVDWUDQVLHQWSURFHVV$OOWKLVPHDQVWKDWLWZLOOWDNHPXFKPRUHWLPHWRPDNHLFHFXEHV


23/83

$KRXVHVKRXOGEHKHDWHGE\DKHDWSXPSEcDQGPDLQWDLQHGDWR&DWDOOWLPHV,WLVHVWLPDWHGWKDWLWORRVHVN:SHUGHJUHHWKHDPELHQWLVORZHUWKDQ

WKHLQVLGH$VVXPHDQRXWVLGHWHPSHUDWXUHRIR&DQGILQGWKHQHHGHGSRZHUWRGULYHWKHKHDWSXPS"

6ROXWLRQ$PELHQW7/

R&

+HDWSXPS Ec4

+:

+RXVH 4

+4

OHDN7+7/

:

4

+Ec4

OHDNEc7+7/Ec

>@N:

4 OHDN4 4+/

:

+3FE


24/83

5HIULJHUDQWDWq&[ IORZLQJDWNJVLVEURXJKWWRVDWXUDWHGYDSRULQDFRQVWDQWSUHVVXUHKHDWH[FKDQJHU7KHHQHUJ\LVVXSSOLHGE\DKHDWSXPSZLWKD

FRHIILFLHQWRISHUIRUPDQFHRIEc)LQGWKHUHTXLUHGSRZHUWRGULYHWKHKHDWSXPS

6ROXWLRQ

&9+HDWH[FKDQJHU

P

P

P

K

4

+P

K

*LYHQFRHIILFLHQWRISHUIRUPDQFH

Ec4

+

:

+4

:

/4

7/

+3

FE

7DEOH%

K

KI[

K

IJuN-NJ

K

KJ

N-NJ

(QHUJ\HTXDWLRQIRUOLQH 4

+P

5K

K

N:

:

4

+

Ec

N:


25/83

6HFRQG/DZDQG3URFHVVHV

3URYHWKDWDF\FOLFGHYLFHWKDWYLRODWHVWKH.HOYLQ3ODQFNVWDWHPHQWRIWKHVHFRQGODZDOVRYLRODWHVWKH&ODXVLXVVWDWHPHQWRIWKHVHFRQGODZ

6ROXWLRQ 3URRIYHU\VLPLODUWRWKHSURRILQVHFWLRQ

+(YLRODWLQJ.HOYLQUHFHLYHV4+

IURP

7+

DQGSURGXFHVQHW:4+

7KLV:LQSXWWR+3UHFHLYLQJ4/IURP7/

+3GLVFKDUJHV4+

4/

WR7+

1HW4WR

7+

LV4+

4+

4/

4/

+(+3WRJHWKHUWUDQVIHUV4/

IURP7/

WR7+

ZLWKQR:WKXVYLRODWHV&ODXVLXV

4

:

+( +3

+

4 /

4+ 4/

7+

7/

&97RWDO


26/83

'LVFXVVWKHIDFWRUVWKDWZRXOGPDNHWKHSRZHUSODQWF\FOHGHVFULEHGLQ3UREOHPDQLUUHYHUVLEOHF\FOH

6ROXWLRQ

*HQHUDOGLVFXVVLRQEXWKHUHDUHDIHZRIWKHPRVWVLJQLILFDQWIDFWRUV &RPEXVWLRQSURFHVVWKDWJHQHUDWHVWKHKRWVRXUFHRIHQHUJ\

+HDWWUDQVIHURYHUILQLWHWHPSHUDWXUHGLIIHUHQFHLQERLOHU

)ORZUHVLVWDQFHDQGIULFWLRQLQWXUELQHUHVXOWVLQOHVVZRUNRXW

)ORZIULFWLRQDQGKHDWORVVWRIURPDPELHQWLQDOOSLSLQJV


27/83

$VVXPHDF\FOLFPDFKLQHWKDWH[FKDQJHVN:ZLWKDR&UHVHUYRLUDQGKDV

D4

/N::

N:

E 4

/N::

N:

DQG4

/LVH[FKDQJHGZLWKDR&DPELHQW:KDWFDQ\RXVD\DERXWWKH

SURFHVVHVLQWKHWZRFDVHVDDQGELIWKHPDFKLQHLVDKHDWHQJLQH"5HSHDWWKHTXHVWLRQIRUWKHFDVHRIDKHDWSXPS

6ROXWLRQ

+HDWHQJLQH

D 6LQFH4/

LPSRVVLEOH.HOYLQ3ODQFN

E 3RVVLEOHLUUHYHUVLEOHKHQJ

+HDWSXPS

D 3RVVLEOHLUUHYHUVLEOHOLNHDQHOHFWULFKHDWHU

E ,PSRVVLEOHE o f&ODXVLXV


28/83

'LVFXVVWKHIDFWRUVWKDWZRXOGPDNHWKHKHDWSXPSGHVFULEHGLQ3UREOHPDQLUUHYHUVLEOHF\FOH

6ROXWLRQ

*HQHUDOGLVFXVVLRQEXWKHUHDUHDIHZRIWKHPRVWVLJQLILFDQWIDFWRUV

8QZDQWHGKHDWWUDQVIHULQWKHFRPSUHVVRU

3UHVVXUHORVVEDFNIORZOHDNLQFRPSUHVVRU

+HDWWUDQVIHUDQGSUHVVXUHGURSLQOLQH!

3UHVVXUHGURSLQDOOOLQHV

7KURWWOHSURFHVV!


29/83

7KHZDWHULQDVKDOORZSRQGKHDWVXSGXULQJWKHGD\DQGFRROVGRZQGXULQJWKHQLJKW+HDWWUDQVIHUE\UDGLDWLRQFRQGXFWLRQDQGFRQYHFWLRQZLWKWKHDPELHQWWKXVF\FOHVWKHZDWHUWHPSHUDWXUH,VVXFKDF\FOLFSURFHVVUHYHUVLEOHRU

LUUHYHUVLEOH"

6ROXWLRQ

$OOWKHKHDWWUDQVIHUWDNHVSODFHRYHUDILQLWH'7DQGWKXVDOOWKHKHDWWUDQVIHUSURFHVVHVDUHLUUHYHUVLEOH

&RQGXFWLRQDQGFRQYHFWLRQKDYH'7LQWKHZDWHUZKLFKLVLQWHUQDOO\LUUHYHUVLEOHDQG'7RXWVLGHWKHZDWHUZKLFKLVH[WHUQDOO\LUUHYHUVLEOH7KHUDGLDWLRQLVDEVRUEHGRUJLYHQRXWDWWKHZDWHUWHPSHUDWXUHWKXVLQWHUQDOO\IRUDEVRUSWLRQDQGH[WHUQDOO\IRUHPLVVLRQLUUHYHUVLEOH


30/83

&RQVLGHUDKHDWHQJLQHDQGKHDWSXPSFRQQHFWHGDVVKRZQLQILJXUH3$VVXPH7+7+!7DPEDQGGHWHUPLQHIRUHDFKRIWKHWKUHHFDVHVLIWKHVHWXS

VDWLVI\WKHILUVWODZDQGRUYLRODWHVWKHQG

ODZ

4

+ 4

/ :

4

+ 4

/ :

D E F

6ROXWLRQ

VW

ODZ

QG

ODZD


31/83

&RQVLGHUWKHIRXUFDVHVRIDKHDWHQJLQHLQSUREOHPDQGGHWHUPLQHLIDQ\RIWKRVHDUHSHUSHWXDOPDFKLQHVRIWKHILUVWRUVHFRQGNLQG

D4

+N: 4

/N: :

N:

E4

+N: 4

/N: :

N:

F4

+N: 4

/N: :

N:

G4

+N: 4

/N: :

N:

H4

:

L4

7L

7+

+(FE

6ROXWLRQ

VW

ODZ QG

ODZD


32/83

&DUQRW&\FOHVDQG$EVROXWH7HPSHUDWXUH

&DOFXODWHWKHWKHUPDOHIILFLHQF\RID&DUQRWF\FOHKHDWHQJLQHRSHUDWLQJEHWZHHQ

UHVHUYRLUVDWR&DQGR&&RPSDUHWKHUHVXOWWRWKDWRI3UREOHP

6ROXWLRQ

K7+:QHW4+7/7+

&DUQRW

KHIILFLHQF\DERXWRIWKH&DUQRW


33/83

$WDIHZSODFHVZKHUHWKHDLULVYHU\FROGLQWKHZLQWHUOLNHR&LWLVSRVVLEOH

WRILQGDWHPSHUDWXUHRIR&GRZQEHORZJURXQG:KDWHIILFLHQF\ZLOODKHDWHQJLQHKDYHRSHUDWLQJEHWZHHQWKHVHWZRWKHUPDOUHVHUYRLUV"

6ROXWLRQ

K7+

7/7+

7KHJURXQGEHFRPHVWKHKRWVRXUFHDQGWKHDWPRVSKHUHEHFRPHVWKHFROGVLGHRIWKHKHDWHQJLQH

K7+

7KLVLVORZEHFDXVHWKHPRGHVWWHPSHUDWXUHGLIIHUHQFH


34/83

&DOFXODWHWKHFRHIILFLHQWRISHUIRUPDQFHRID&DUQRWF\FOHKHDWSXPSRSHUDWLQJ

EHWZHHQUHVHUYRLUVDWq&DQGq&&RPSDUHWKHUHVXOWZLWKWKDWRI3UREOHP

6ROXWLRQ7

/&.7

+&.

&DUQRW Ec7

+

7+

7/

KDVEc

)URPVROXWLRQWR3UREOHP&9&RQGHQVHU

4

&21'P

K K

N:

7KHQZLWKWKHZRUNDV:

,1N:ZHKDYH

4+

:&

4 /

FE

(YDSRUDWRU

&RQGHQVHU

4 ORVV

+HDWSXPSEc4

+:

,1


35/83

)LQGWKHSRZHURXWSXWDQGWKHORZ7KHDWUHMHFWLRQUDWHIRUD&DUQRWF\FOHKHDW

HQJLQHWKDWUHFHLYHVN:DWR&DQGUHMHFWVKHDWDWR&DVLQ3UREOHP

6ROXWLRQ

)URPWKHGHILQLWLRQRIWKHDEVROXWHWHPSHUDWXUH(T

KFDUQRW7/7+

'HILQLWLRQRIWKHKHDWHQJLQHHIILFLHQF\JLYHVWKHZRUNDV

:

K4

+uN:

$SSO\WKHHQHUJ\HTXDWLRQ

4

/4

+:

N:


36/83

$FDUHQJLQHEXUQVNJIXHOHTXLYDOHQWWRDGGLWLRQRI4+DW.DQGUHMHFWV

HQHUJ\WRWKHUDGLDWRUDQGWKHH[KDXVWDWDQDYHUDJHWHPSHUDWXUHRI.,IWKHIXHOSURYLGHVN-NJZKDWLVWKHPD[LPXPDPRXQWRIZRUNWKHHQJLQHFDQ

SURYLGH"

6ROXWLRQ

$KHDWHQJLQH 4+

PTIXHO

uN-

$VVXPHD&DUQRWHIILFLHQF\PD[LPXPWKHRUHWLFDOZRUN

K7/7+

: K4+N-

([KDXVWIORZ

$LULQWDNHILOWHU

&RRODQWIORZ

$WP

DLU6KDIW

)DQ

SRZHU

5DGLDWRU


37/83

'LIIHUHQFHVLQVXUIDFHZDWHUDQGGHHSZDWHUWHPSHUDWXUHFDQEHXWLOL]HGIRUSRZHUJHQHUDWLRQ,WLVSURSRVHGWRFRQVWUXFWDF\FOLFKHDWHQJLQHWKDWZLOORSHUDWHQHDU

+DZDLLZKHUHWKHRFHDQWHPSHUDWXUHLVq&QHDUWKHVXUIDFHDQGq&DWVRPHGHSWK:KDWLVWKHSRVVLEOHWKHUPDOHIILFLHQF\RIVXFKDKHDWHQJLQH"

6ROXWLRQ

7+

&.7/

&.

K7+0$;

7

+7

/

7+

7KLVLVDYHU\ORZHIILFLHQF\VRLWKDVWREHGRQHRQDYHU\ODUJHVFDOHWREHHFRQRPLFDOO\IHDVLEOHDQGWKHQLWZLOOKDYHVRPHHQYLURQPHWDOLPSDFW


38/83

)LQGWKHPD[LPXPFRHIILFLHQWRISHUIRUPDQFHIRUWKHUHIULJHUDWRULQ\RXUNLWFKHQDVVXPLQJLWUXQVLQD&DUQRWF\FOH

6ROXWLRQ

7KHUHIULJHUDWRUFRHIILFLHQWRISHUIRUPDQFHLV

E4/

:4/

4+

4/

7/

7+

7/

$VVXPLQJ7/

a&7+

a&

E d

$FWXDOZRUNLQJIOXLGWHPSHUDWXUHVPXVWEHVXFKWKDW7/7UHIULJHUDWRUDQG7+!7URRP

$UHIULJHUDWRUGRHVQRWRSHUDWHLQD

&DUQRWF\FOH7KHDFWXDOYDSRUFRPSUHVVLRQF\FOHLVH[DPLQHGLQ&KDSWHU


39/83

$QDLUFRQGLWLRQHUSURYLGHVNJVRIDLUDWq&FRROHGIURPRXWVLGHDWPRVSKHULFDLUDWq&(VWLPDWHWKHDPRXQWRISRZHUQHHGHGWRRSHUDWHWKHDLUFRQGLWLRQHU&OHDUO\VWDWHDOODVVXPSWLRQVPDGH

6ROXWLRQ&RQVLGHUWKHFRROLQJRIDLUZKLFKQHHGVDKHDWWUDQVIHUDV

4

DLUP

'K#P

&S'7NJVuN-NJ.u.N:

$VVXPH&DUQRWF\FOHUHIULJHUDWRU

E4

/

:4

/ 4

+4

/ #

7/

7+7/

:

4

/ E

N:

7KLVHVWLPDWHLVWKHWKHRUHWLFDOPD[LPXP

SHUIRUPDQFH7RGRWKHUHTXLUHGKHDWWUDQVIHU7/ #&DQG7+&DUHPRUHOLNHO\VHFRQGO\

EEFDUQRW+4

:

/4

5()

& &FE RR


40/83

:HSURSRVHWRKHDWDKRXVHLQWKHZLQWHUZLWKDKHDWSXPS7KHKRXVHLVWREH

PDLQWDLQHGDWq&DWDOOWLPHV:KHQWKHDPELHQWWHPSHUDWXUHRXWVLGHGURSVWRq&WKHUDWHDWZKLFKKHDWLVORVWIURPWKHKRXVHLVHVWLPDWHGWREHN::KDWLVWKHPLQLPXPHOHFWULFDOSRZHUUHTXLUHGWRGULYHWKHKHDWSXPS"

6ROXWLRQ

0LQLPXPSRZHULIZH

DVVXPHD&DUQRWF\FOH

4

+4

OHDNN:

4 OHDN4 4 +/

:

+3

Ec4

+

:

,1

7

+

7+

7/

:

,1

N:


41/83

$VDOHVSHUVRQVHOOLQJUHIULJHUDWRUVDQGGHHSIUHH]HUVZLOOJXDUDQWHHDPLQLPXPFRHIILFLHQWRISHUIRUPDQFHRI\HDUURXQG+RZZRXOG\RXHYDOXDWHWKDW"$UHWKH\DOOWKHVDPH"

6ROXWLRQ$VVXPHDKLJKWHPSHUDWXUHRI&,IDIUHH]HUFRPSDUWPHQWLVLQFOXGHG

7/

a&GHHSIUHH]HUDQGIOXLGWHPSHUDWXUHLVWKHQ7/

a&

EGHHSIUHH]HUd7/7+7/>@

$KRWVXPPHUGD\PD\UHTXLUHDKLJKHU7+

WRSXVK4+

RXWLQWRWKHURRPVR

HYHQORZHUE

&ODLPLVSRVVLEOHIRUDUHIULJHUDWRUEXWQRWIRUDGHHSIUHH]HU


42/83

$F\FOLFPDFKLQHVKRZQLQ)LJ3UHFHLYHVN-IURPD.HQHUJ\UHVHUYRLU,WUHMHFWVN-WRD.HQHUJ\UHVHUYRLUDQGWKHF\FOHSURGXFHVN-RIZRUNDVRXWSXW,VWKLVF\FOHUHYHUVLEOHLUUHYHUVLEOHRULPSRVVLEOH"

6ROXWLRQ

K&DUQRW7

/

7+

KHQJ:

4+

!K&DUQRW

7KLVLVLPSRVVLEOH

H4N-

:N-

L4N-

7.+

+(FE

7.L


43/83

$QLQYHQWRUKDVGHYHORSHGDUHIULJHUDWLRQXQLWWKDWPDLQWDLQVWKHFROGVSDFHDW

q&ZKLOHRSHUDWLQJLQDq&URRP$FRHIILFLHQWRISHUIRUPDQFHRILVFODLPHG+RZGR\RXHYDOXDWHWKLV"

6ROXWLRQ

E&DUQRW4

/

:LQ

7/

7+

7/

!E&DUQRW LPSRVVLEOHFODLP

H4

:

L4

7&L

7&+

5()


44/83

$KRXVHKROGIUHH]HURSHUDWHVLQDURRPDWq&+HDWPXVWEHWUDQVIHUUHGIURPWKHFROGVSDFHDWDUDWHRIN:WRPDLQWDLQLWVWHPSHUDWXUHDWq&:KDWLVWKHWKHRUHWLFDOO\VPDOOHVWSRZHUPRWRUUHTXLUHGWRRSHUDWHWKLVIUHH]HU"

6ROXWLRQ

$VVXPHD&DUQRWF\FOHEHWZHHQ7/

&DQG

7+

&

E4

/

:

LQ

7

/

7+

7/

:

LQ4

/EN:

7KLVLVWKHWKHRUHWLFDOPLQLPXPSRZHULQSXW$Q\DFWXDOPDFKLQHUHTXLUHVDODUJHULQSXW

H4

:

L4

7L

7DPE

5()

N:


45/83

,QDFU\RJHQLFH[SHULPHQW\RXQHHGWRNHHSDFRQWDLQHUDWq&DOWKRXJKLWJDLQV:GXHWRKHDWWUDQVIHU:KDWLVWKHVPDOOHVWPRWRU\RXZRXOGQHHGIRUD

KHDWSXPSDEVRUELQJKHDWIURPWKHFRQWDLQHUDQGUHMHFWLQJKHDWWRWKHURRPDW

q&"

6ROXWLRQ

:HGRQRWNQRZWKHDFWXDOGHYLFHVRILQGWKHZRUNIRUD&DUQRWF\FOH

E5()

4

/:

7/

7+

7/

! : 4/

E5():


46/83

$WHPSHUDWXUHRIDERXW.FDQEHDFKLHYHGE\PDJQHWLFFRROLQJ,QWKLVSURFHVVDVWURQJPDJQHWLFILHOGLVLPSRVHGRQDSDUDPDJQHWLFVDOWPDLQWDLQHGDW.E\WUDQVIHURIHQHUJ\WROLTXLGKHOLXPERLOLQJDWORZSUHVVXUH7KHVDOWLVWKHQ

WKHUPDOO\LVRODWHGIURPWKHKHOLXPWKHPDJQHWLFILHOGLVUHPRYHGDQGWKHVDOW

WHPSHUDWXUHGURSV$VVXPHWKDWP-LVUHPRYHGDWDQDYHUDJHWHPSHUDWXUHRI.WRWKHKHOLXPE\D&DUQRWF\FOHKHDWSXPS)LQGWKHZRUNLQSXWWRWKHKHDW

SXPSDQGWKHFRHIILFLHQWRISHUIRUPDQFHZLWKDQDPELHQWDW.

6ROXWLRQ

E4 /: ,17

/7

+7

/

:

,1

u

-

5HPDUN7KLVLVDQH[WUHPHO\ODUJHWHPSHUDWXUHGLIIHUHQFHIRUDKHDWSXPS


47/83

7KHORZHVWWHPSHUDWXUHWKDWKDVEHHQDFKLHYHGLVDERXWu.7RDFKLHYHWKLVDQDGGLWLRQDOVWDJHRIFRROLQJLVUHTXLUHGEH\RQGWKDWGHVFULEHGLQWKH

SUHYLRXVSUREOHPQDPHO\QXFOHDUFRROLQJ7KLVSURFHVVLVVLPLODUWRPDJQHWLFFRROLQJEXWLWLQYROYHVWKHPDJQHWLFPRPHQWDVVRFLDWHGZLWKWKHQXFOHXVUDWKHU

WKDQWKDWDVVRFLDWHGZLWKFHUWDLQLRQVLQWKHSDUDPDJQHWLFVDOW6XSSRVHWKDWP-LVWREHUHPRYHGIURPDVSHFLPHQDWDQDYHUDJHWHPSHUDWXUHRI.WHQPLFURMRXOHVLVDERXWWKHSRWHQWLDOHQHUJ\ORVVRIDSLQGURSSLQJPP)LQGWKHZRUNLQSXWWRD&DUQRWKHDWSXPSDQGLWVFRHIILFLHQWRISHUIRUPDQFHWRGRWKLVDVVXPLQJWKHDPELHQWLVDW.

6ROXWLRQ

4/

P-u-DW7/

.

4+

4/

u7

+

7/

uu

-

:LQ

4+

4/

u # -

E4

/

:LQ

u

u


48/83

$FHUWDLQVRODUHQHUJ\FROOHFWRUSURGXFHVDPD[LPXPWHPSHUDWXUHRIq&7KHHQHUJ\LVXVHGLQDF\FOLFKHDWHQJLQHWKDWRSHUDWHVLQDq&HQYLURQPHQW:KDWLVWKHPD[LPXPWKHUPDOHIILFLHQF\":KDWLVLWLIWKHFROOHFWRULVUHGHVLJQHGWR

IRFXVWKHLQFRPLQJOLJKWWRSURGXFHDPD[LPXPWHPSHUDWXUHRIq&"

6ROXWLRQ

)RU 7+

&.7/

.

KWKPD[

7+7/

7+

)RU 7+&.7/.

KWKPD[

7+7/

7+


49/83

+HOLXPKDVWKHORZHVWQRUPDOERLOLQJSRLQWRIDQ\RIWKHHOHPHQWVDW.$WWKLVWHPSHUDWXUHWKHHQWKDOS\RIHYDSRUDWLRQLVN-NPRO$&DUQRWUHIULJHUDWLRQF\FOHLVDQDO\]HGIRUWKHSURGXFWLRQRINPRORIOLTXLGKHOLXPDW

.IURPVDWXUDWHGYDSRUDWWKHVDPHWHPSHUDWXUH:KDWLVWKHZRUNLQSXWWRWKH

UHIULJHUDWRUDQGWKHFRHIILFLHQWRISHUIRUPDQFHIRUWKHF\FOHZLWKDQDPELHQWDW."

6ROXWLRQ

)RUWKH&DUQRWF\FOHWKHUDWLRRIWKHKHDWWUDQVIHUVLVWKHUDWLRRIWHPSHUDWXUHV

4+

4/

u7

+

7/

u

N-

:,1

4+

4/

N-

E4

/

:,1

>

7/

7+

7/

@


50/83

&DOFXODWHWKHDPRXQWRIZRUNLQSXWDUHIULJHUDWRUQHHGVWRPDNHLFHFXEHVRXWRID

WUD\RINJOLTXLGZDWHUDWR&$VVXPHWKHUHIULJHUDWRUZRUNVLQD&DUQRW

F\FOHEHWZHHQR&DQGR&ZLWKDPRWRUFRPSUHVVRURI:+RZPXFKWLPHGRHVLWWDNHLIWKLVLVWKHRQO\FRROLQJORDG"

6ROXWLRQ&9:DWHULQWUD\:HQHJOHFWWUD\PDVV

(QHUJ\(T PX X4 :3URFHVV 3FRQVWDQW3R

:3G93RPY Y

4PX X:PK K

7EO%KN-NJ7EO%KN-NJ

4N-

&RQVLGHUQRZUHIULJHUDWRU

E4/:

4

/

4+4/

7/

7+7/

:4/

E 4

E

N-

)RUWKHPRWRUWRWUDQVIHUWKDWDPRXQWRIHQHUJ\WKHWLPHLVIRXQGDV

::

GW:

'W

'W:

:

u

V

&RPPHQW:HQHJOHFWHGDEDVHORDGRIWKHUHIULJHUDWRUVRQRWDOOWKH:DUHDYDLODEOHWRPDNHLFHDOVRRXUFRHIILFLHQWRISHUIRUPDQFHLVYHU\RSWLPLVWLFDQGILQDOO\WKHKHDWWUDQVIHULVDWUDQVLHQWSURFHVV$OOWKLV

PHDQVWKDWLWZLOOWDNHPXFKPRUHWLPHWRPDNHLFHFXEHV


51/83

$VWHHOERWWOH9PFRQWDLQV5DDWq&N3D,WLVSODFHGLQDGHHSIUHH]HUZKHUHLWLVFRROHGWRq&7KHGHHSIUHH]HUVLWVLQDURRPZLWKDPELHQWWHPSHUDWXUHRIq&DQGKDVDQLQVLGHWHPSHUDWXUHRIq&)LQGWKHDPRXQWRIHQHUJ\WKHIUHH]HUPXVWUHPRYHIURPWKH5DDQGWKHH[WUDDPRXQWRIZRUN

LQSXWWRWKHIUHH]HUWRGRWKHSURFHVV

6ROXWLRQ

&95DRXWWRWKH&VSDFH

(QHUJ\HTXDWLRQPX X4 :

3URFHVV9&RQVW!YY!:

7DEOH%YPNJXN-NJ

P9YNJ

6WDWHYYYJ7DEOH%!SKDVH

![YYI

YIJ

XuN-NJ

4PX XN-

&RQVLGHUWKHIUHH]HUDQGDVVXPH&DUQRWF\FOH

E4/:

4

/

4+4/

7/

7+7/

:LQ4/EN-


52/83

/LTXLGVRGLXPOHDYHVDQXFOHDUUHDFWRUDWq&DQGLVXVHGDVWKHHQHUJ\VRXFHLQDVWHDPSRZHUSODQW7KHFRQGHQVHUFRROLQJZDWHUFRPHVIURPDFRROLQJWRZHU

DWq&'HWHUPLQHWKHPD[LPXPWKHUPDOHIILFLHQF\RIWKHSRZHUSODQW,VLWPLVOHDGLQJWRXVHWKHWHPSHUDWXUHVJLYHQWRFDOFXODWHWKLVYDOXH"

6ROXWLRQ

LIQ Na

800oC

REACTOR

ENERGY

TO H O2

COND.

COOLING

TOWER

ENERGY

FROM

STEAMPOWER

PLANT

7+

&.7/

&.

K7+0$;

7

+7

/

7+

,WPLJKWEHPLVOHDGLQJWRXVH&DVWKHYDOXHIRU7+VLQFHWKHUHLVQRWD

VXSSO\RIHQHUJ\DYDLODEOHDWDFRQVWDQWWHPSHUDWXUHRI&OLTXLG1DLVFRROHGWRDORZHUWHPSHUDWXUHLQWKHKHDWH[FKDQJHU

7KH1DFDQQRWEHXVHGWRERLO+2DW&

6LPLODUO\WKH+2OHDYHVWKHFRROLQJWRZHUDQGHQWHUVWKHFRQGHQVHUDW&

DQGOHDYHVWKHFRQGHQVHUDWVRPHKLJKHUWHPSHUDWXUH

7KHZDWHUGRHVQRWSURYLGHIRUFRQGHQVLQJVWHDPDWD

FRQVWDQWWHPSHUDWXUHRI&


53/83

$WKHUPDOVWRUDJHLVPDGHZLWKDURFNJUDQLWHEHGRIPZKLFKLVKHDWHGWR

.XVLQJVRODUHQHUJ\$KHDWHQJLQHUHFHLYHVD4+IURPWKHEHGDQGUHMHFWV

KHDWWRWKHDPELHQWDW.7KHURFNEHGWKHUHIRUHFRROVGRZQDQGDVLWUHDFKHV

.WKHSURFHVVVWRSV)LQGWKHHQHUJ\WKHURFNEHGFDQJLYHRXW:KDWLVWKHKHDWHQJLQHHIILFLHQF\DWWKHEHJLQQLQJRIWKHSURFHVVDQGZKDWLVLWDWWKHHQGRIWKHSURFHVV"

6ROXWLRQ

$VVXPHWKHZKROHVHWXSLVUHYHUVLEOHDQGWKDWWKHKHDWHQJLQHRSHUDWHVLQD

&DUQRWF\FOH7KHWRWDOFKDQJHLQWKHHQHUJ\RIWKHURFNEHGLV XXT&'7N-NJ

P U9uNJ4PTuN-

7RJHWWKHHIILFLHQF\XVHWKH&$5127DV

K7R7+DWWKHEHJLQQLQJRISURFHVV

K7R7+DWWKHHQGRISURFHVV

:

4 4+ /

+(


54/83

$KHDWHQJLQHKDVDVRODUFROOHFWRUUHFHLYLQJN:SHUVTXDUHPHWHULQVLGHZKLFKDWUDQVIHUPHGLDLVKHDWHGWR.7KHFROOHFWHGHQHUJ\SRZHUVDKHDW

HQJLQHZKLFKUHMHFWVKHDWDWR&,IWKHKHDWHQJLQHVKRXOGGHOLYHUN:ZKDWLVWKHPLQLPXPVL]HDUHDVRODUFROOHFWRU"

6ROXWLRQ

7+.7/R&.

K+(7

/

7+

:

K4

+!4

+:

K

N:

4

+$!$4

+

P


55/83

6L[W\NLORJUDPVSHUKRXURIZDWHUUXQVWKURXJKDKHDWH[FKDQJHUHQWHULQJDVVDWXUDWHGOLTXLGDWN3DDQGOHDYLQJDVVDWXUDWHGYDSRU7KHKHDWLVVXSSOLHGE\

D&DUQRWKHDWSXPSRSHUDWLQJIURPDORZWHPSHUDWXUHUHVHUYRLUDWq&)LQGWKHUDWHRIZRUNLQWRWKHKHDWSXPS

6ROXWLRQ

&9+HDWH[FKDQJHU

P

P

P

K4

+P

K

7DEOH%KK

7+

7VDW3

4

+

N:

$VVXPHD&DUQRWKHDWSXPS

+4

:

/4

7/

+3

Ec4

+:

7+7+ 7/

:

4

+EcN:


56/83

$KHDWSXPSLVGULYHQE\WKHZRUNRXWSXWRIDKHDWHQJLQHDVVKRZQLQILJXUH

3,IZHDVVXPHLGHDOGHYLFHVILQGWKHUDWLRRIWKHWRWDOSRZHU4

/4

+WKDW

KHDWVWKHKRXVHWRWKHSRZHUIURPWKHKRWHQHUJ\VRXUFH4

+LQWHUPVRIWKHWHPSHUDWXUHV

E+3

4

+:

4

+4

+4

/

7URRP

7URRP

7DPE

:

K+(

4

+

7URRP

7+

4

+

:

4

+E

+3

7URRP

7URRP

7DPE

4

+

4

/4

+:

>7

URRP

7+

@4

+

4

+4

/

4

+

7URRP7

+

7

URRP

7+

7URRP

7DPE

7URRP

7

URRP

7+

7

URRP7

URRP7

+

7URRP

7DPE

7URRP

>

7+

7URRP

7+

7URRP

7DPE

@

7

URRP

7+

>7

+7

URRP

7URRP

7DPE

@

7URRP

7+

>7+7

DPE

7URRP

7DPE

@


57/83

,WLVSURSRVHGWREXLOGD0:HOHFWULFSRZHUSODQWZLWKVWHDPDVWKHZRUNLQJIOXLG7KHFRQGHQVHUVDUHWREHFRROHGZLWKULYHUZDWHUVHH)LJ37KH

PD[LPXPVWHDPWHPSHUDWXUHLVq&DQGWKHSUHVVXUHLQWKHFRQGHQVHUVZLOOEHN3D(VWLPDWHWKHWHPSHUDWXUHULVHRIWKHULYHUGRZQVWUHDPIURPWKHSRZHU

SODQW

6ROXWLRQ

:

1(7N:7

+&.

3&21'

N3Do7/

7*

3N3D&.

K7+&$5127

7+7/

7+

4

/0,1

uN:

%XWP

+

2

uu

NJVKDYLQJDQHQHUJ\IORZRI

4

/0,1P

+

2

'KP

+2&

3/,4+2'7

+20,1

'7+20,1

4

/0,1

P

+

2&

3/,4+2

u

u&


58/83

7ZRGLIIHUHQWIXHOVFDQEHXVHGLQDKHDWHQJLQHRSHUDWLQJEHWZHHQWKHIXHOEXUQLQJWHPSHUDWXUHDQGDORZWHPSHUDWXUHRI.)XHO$EXUQVDW.GHOLYHULQJN-NJDQGFRVWVNJ)XHO%EXUQVDW.GHOLYHULQJ

N-NJDQGFRVWVNJ:KLFKIXHOZLOO\RXEX\DQGZK\"

6ROXWLRQ

)XHO$ K7+$

7

/

7+

:$K7+$u4$uN-NJ

:$$N-

)XHO% K7+%

7

/

7+

:%

K7+%

u4%

uN-NJ

:%

%

N-

6HOHFWIXHO%IRUPRUHZRUNSHUGROODUWKRXJKLWKDVDORZHUWKHUPDOHIILFLHQF\


59/83

)LQLWH'7+HDW7UDQVIHU

$UHIULJHUDWRUNHHSLQJR

&LQVLGHLVORFDWHGLQDR

&URRP,WPXVWKDYHDKLJKWHPSHUDWXUH'7DERYHURRPWHPSHUDWXUHDQGDORZWHPSHUDWXUH'7EHORZWKHUHIULJHUDWHGVSDFHLQWKHF\FOHWRDFWXDOO\WUDQVIHUWKHKHDW)RUD'7RIDQGR&UHVSHFWLYHO\FDOFXODWHWKH&23DVVXPLQJD&DUQRWF\FOH

6ROXWLRQ )URPWKHGHILQLWLRQRI&23DQGDVVXPLQJ&DUQRWF\FOH

E4

/

:,1

7/

7+

7/

ZKHQ7VDUHDEVROXWHWHPSHUDWXUHV

'7 7+ 7+ 7/ 7/ ER& . R& .

D E

F

1RWLFHKRZWKH&23GURSVVLJQLILFDQWO\ZLWKWKHLQFUHDVHLQ'7


60/83

$UHIULJHUDWRUXVHVDSRZHULQSXWRIN:WRFRRODq&VSDFHZLWKWKHKLJKWHPSHUDWXUHLQWKHF\FOHDVq&7KH4+LVSXVKHGWRWKHDPELHQWDLUDWq&LQDKHDWH[FKDQJHUZKHUHWKHWUDQVIHUFRHIILFLHQWLV:P.)LQGWKHUHTXLUHGPLQLPXPKHDWWUDQVIHUDUHD

6ROXWLRQ

:

N:4

+E+3

4

+:

u E+3u>@N:K$'7

$

4

+

K'7u

u P


61/83

$KRXVHLVKHDWHGE\DKHDWSXPSGULYHQE\DQHOHFWULFPRWRUXVLQJWKHRXWVLGHDVWKHORZWHPSHUDWXUHUHVHUYRLU7KHKRXVHORVHVHQHUJ\GLUHFWO\SURSRUWLRQDOWRWKH

WHPSHUDWXUHGLIIHUHQFHDV4

ORVV.7+7/'HWHUPLQHWKHPLQLPXPHOHFWULF

SRZHUWRGULYHWKHKHDWSXPSDVDIXQFWLRQRIWKHWZRWHPSHUDWXUHV

6ROXWLRQ

+HDWSXPS&23 Ec4

+:

LQ d7+7+7/

+HDWORVVPXVWEHDGGHG 4

+

4

ORVV.7+

7/

6ROYHIRUUHTXLUHGZRUNDQGVXEVWLWXWHLQIRUEc

:

LQ4

+Ec t.7

+7

/u7

+7

/7

+

:

LQ t.7+7/7

+


62/83

$IDUPHUUXQVDKHDWSXPSZLWKDPRWRURIN:,WVKRXOGNHHSDFKLFNHQ

KDWFKHU\DWR&ZKLFKORVHVHQHUJ\DWDUDWHRIN:SHUGHJUHHGLIIHUHQFHWRWKHFROGHUDPELHQW7KHKHDWSXPSKDVDFRHIILFLHQWRISHUIRUPDQFHWKDWLVRID&DUQRWKHDWSXPS:KDWLVWKHPLQLPXPDPELHQWWHPSHUDWXUHIRUZKLFKWKH

KHDWSXPSLVVXIILFLHQW"

6ROXWLRQ&9+DWFKHU\VWHDG\VWDWH

7RKDYHVWHDG\VWDWHDWR&IRUWKHKDWFKHU\

(QHUJ\(T 4

+4

/RVVE $&:

3URFHVV(T 4/RVV

7+

7DPE

E $&E&$5127&23IRUWKHUHIHUHQFH&DUQRWKHDWSXPS

E&$5127

4

+

:

4

+

4

+4

/

7

+

7+

7/

7

+

7+

7DPE

6XEVWLWXWHWKHSURFHVVHTXDWLRQVDQGWKLVE&$5127

LQWRWKHHQHUJ\(T

7+

7DPE

7

+

7+

7DPE

:

7+

7DPE

7+

:

7+

:

u.

7+

7DPE

.

7DPER

&

&RPPHQW7KDWRIFRXUVHLVQRWDYHU\ORZWHPSHUDWXUHDQGWKHVL]HRIWKHV\VWHPLVQRWDGHTXDWHIRUPRVWORFDWLRQV

4 OHDN4 4+

/

:N:

+3FE


63/83

&RQVLGHUD&DUQRWF\FOHKHDWHQJLQHRSHUDWLQJLQRXWHUVSDFH+HDWFDQEHUHMHFWHGIURPWKLVHQJLQHRQO\E\WKHUPDOUDGLDWLRQZKLFKLVSURSRUWLRQDOWRWKHUDGLDWRU

DUHDDQGWKHIRXUWKSRZHURIDEVROXWHWHPSHUDWXUH4UDGa.$76KRZWKDWIRUD

JLYHQHQJLQHZRUNRXWSXWDQGJLYHQ7+WKHUDGLDWRUDUHDZLOOEHPLQLPXPZKHQ

WKHUDWLR7/7+

6ROXWLRQ

:1(7

4+

7+7/7

+4

/

7+7/7

/ DOVR4

/.$7

/

:1(7

.7

+

$7

/

7

+

7+

7/ $

7/

7+

7/

7+

FRQVW

'LIIHUHQWLDWLQJ

G$

7/7

+

7/7

+

$

7/7

+

7/7

+

G

7/7

+

G$G7

/7

+$

7/7

+

7/7

+

>

7/7

+

7/7

+

@

7/

7+

IRUPLQ$

&KHFNWKDWLWLVPLQLPXPDQGQRWPD[LPXPZLWKWKHQG

GHULYDWLYH!


64/83

$KRXVHLVKHDWHGE\DQHOHFWULFKHDWSXPSXVLQJWKHRXWVLGHDVWKHORZWHPSHUDWXUHUHVHUYRLU)RUVHYHUDOGLIIHUHQWZLQWHURXWGRRUWHPSHUDWXUHVHVWLPDWH

WKHSHUFHQWVDYLQJVLQHOHFWULFLW\LIWKHKRXVHLVNHSWDWq&LQVWHDGRIq&$VVXPHWKDWWKHKRXVHLVORVLQJHQHUJ\WRWKHRXWVLGHDVLQ(T

6ROXWLRQ

+HDW3XPS4

ORVV v7+7/

0D[3HUI

4

+

:

,1

7+

7+7/

.7+7/

:

,1

:

,1.7+7/

7+

$7+$

&. %7+%&.

7/&:

,1$.:

,1%

.VDYLQJ


65/83

$KRXVHLVFRROHGE\DQHOHFWULFKHDWSXPSXVLQJWKHRXWVLGHDVWKHKLJKWHPSHUDWXUHUHVHUYRLU)RUVHYHUDOGLIIHUHQWVXPPHURXWGRRUWHPSHUDWXUHV

HVWLPDWHWKHSHUFHQWVDYLQJVLQHOHFWULFLW\LIWKHKRXVHLVNHSWDWq&LQVWHDGRIq&$VVXPHWKDWWKHKRXVHLVJDLQLQJHQHUJ\IURPWKHRXWVLGHGLUHFWO\

SURSRUWLRQDOWRWKHWHPSHUDWXUHGLIIHUHQFHDVLQ(T

6ROXWLRQ

$LUFRQGLWLRQHU5HIULJHUDWRU4

/($. v7+7/

0D[3HUI

4

/

:

,1

7/7+7/

.7+7/

:

,1

:

,1

.7+7/

7/

$7/$

&. %7/%&.

7+&:

,1$.:

,1%

.VDYLQJ


66/83

$KHDWSXPSKDVDFRHIILFLHQWRISHUIRUPDQFHWKDWLVRIWKHWKHRUHWLFDO

PD[LPXP,WPDLQWDLQVDKRXVHDWq&ZKLFKOHDNVHQHUJ\RIN:SHUGHJUHHWHPSHUDWXUHGLIIHUHQFHWRWKHDPELHQW)RUDPD[LPXPRIN:SRZHULQSXWILQGWKHPLQLPXPRXWVLGHWHPSHUDWXUHIRUZKLFKWKHKHDWSXPSLVDVXIILFLHQWKHDW

VRXUFH

6ROXWLRQ

4 OHDN4 4+/

:N:

+3

&9+RXVH)RUFRQVWDQWq&WKHKHDWSXPSPXVWSURYLGH4

OHDN'7

4

+4

OHDN7+7/Ec:

&9+HDWSXPS'HILQLWLRQRIWKHFRHIILFLHQWRISHUIRUPDQFHDQGWKHIDFWWKDW

WKHPD[LPXPLVIRUD&DUQRWKHDWSXPS

Ec4

+:

4

+4

+4

/Ec&DUQRW u7+7+7/

6XEVWLWXWHLQWRWKHILUVWHTXDWLRQWRJHW

7+7/>u7+7+7/@!

7+7/7+ uu

7+

7/

!7/

&


67/83

$QDLUFRQGLWLRQHUFRROVDKRXVHDW7/q&ZLWKDPD[LPXPRIN:SRZHULQSXW7KHKRXVHJDLQVN:SHUGHJUHHWHPSHUDWXUHGLIIHUHQFHWRWKHDPELHQW

DQGWKHUHIULJHUDWLRQ&23LVEE&DUQRW)LQGWKHPD[LPXPRXWVLGHWHPSHUDWXUH7

+IRUZKLFKWKHDLUFRQGLWLRQHUSURYLGHVVXIILFLHQWFRROLQJ

6ROXWLRQ

4 OHDN4 4+ /

:N:

+3 7/

+HUH

7/7KRXVH

7+7DPE

,QWKLVVHWXSWKHORZWHPSHUDWXUHVSDFHLVWKHKRXVHDQGWKHKLJK

WHPSHUDWXUHVSDFHLVWKHDPELHQW7KHKHDWSXPSPXVWUHPRYHWKHJDLQRUOHDNKHDWWUDQVIHUWRNHHSLWDWDFRQVWDQWWHPSHUDWXUH

4

OHDN7DPE7KRXVH4

/ZKLFKPXVWEHUHPRYHGE\WKHKHDWSXPS

E4

/:

EFDUQRW7KRXVH7DPE7KRXVH

6XEVWLWXWHLQIRU4

/DQGPXOWLSO\ZLWK7DPE7KRXVH:

7DPE7KRXVH7KRXVH:

6LQFH7KRXVH.DQG:

N:LWIROORZV

7DPE7KRXVH7KRXVH:

u.

6ROYLQJ7DPE7KRXVH7DPE.&


68/83

$&DUQRWKHDWHQJLQHVKRZQLQ)LJ3UHFHLYHVHQHUJ\IURPDUHVHUYRLUDW7UHVWKURXJKDKHDWH[FKDQJHUZKHUHWKHKHDWWUDQVIHUUHGLVSURSRUWLRQDOWRWKH

WHPSHUDWXUHGLIIHUHQFHDV4

+.7

UHV7

+,WUHMHFWVKHDWDWDJLYHQORZ

WHPSHUDWXUH7/7RGHVLJQWKHKHDWHQJLQHIRUPD[LPXPZRUNRXWSXWVKRZWKDW

WKHKLJKWHPSHUDWXUH7+LQWKHF\FOHVKRXOGEHVHOHFWHGDV7+ 7UHV7/

6ROXWLRQ

:K7+

4+

7

+7

/

7+

u.7UHV

7+

PD[LPL]H:7+

G:G7

+

G:G7+.7UHV 7+7/7+

.7/7+

7+ 7

UHV7/


69/83

,GHDO*DV&DUQRW&\FOHV

+\GURJHQJDVLVXVHGLQD&DUQRWF\FOHKDYLQJDQHIILFLHQF\RIZLWKDORZWHPSHUDWXUHRI.'XULQJWKHKHDWUHMHFWLRQWKHSUHVVXUHFKDQJHVIURPN3DWRN3D)LQGWKHKLJKDQGORZWHPSHUDWXUHKHDWWUDQVIHUDQGWKHQHWF\FOHZRUNSHUXQLWPDVVRIK\GURJHQ

6ROXWLRQ

$VWKHHIILFLHQF\LVNQRZQWKHKLJKWHPSHUDWXUHLVIRXQGDV

K7

/

7+!7

+

7/

.

1RZWKHYROXPHUDWLRQHHGHGIRUWKHKHDWWUDQVIHU777/LV

YY57357333

VRIURP(TZHKDYHZLWK5IURP7DEOH$

T/57/OQYYN-NJ

8VLQJWKHHIILFLHQF\IURP(TWKHQ

T+T/N-NJ

7KHQHWZRUNHTXDOVWKHQHWKHDWWUDQVIHU

ZT+T/N-NJ


70/83

$QLGHDOJDV&DUQRWF\FOHZLWKDLULQDSLVWRQF\OLQGHUKDVDKLJKWHPSHUDWXUHRI.DQGDKHDWUHMHFWLRQDW.'XULQJWKHKHDWDGGLWLRQWKHYROXPHWULSOHV)LQGWKHWZRVSHFLILFKHDWWUDQVIHUVTLQWKHF\FOHDQGWKHRYHUDOOF\FOH

HIILFLHQF\

6ROXWLRQ

7KH3YGLDJUDPRIWKHF\FOHLV

VKRZQWRWKHULJKW

)URPWKHLQWHJUDWLRQDORQJWKH

SURFHVVFXUYHVGRQHLQWKHPDLQ

WH[WZHKDYH(T

T+57+OQYY

uOQ

N-NJ

3

Y

.

.

6LQFHLWLVD&DUQRWF\FOHWKHNQRZOHGJHRIWKHWHPSHUDWXUHVJLYHVWKHF\FOH

HIILFLHQF\DV

K7+

K7+

7/7+

IURPZKLFKZHFDQJHWWKHRWKHUKHDWWUDQVIHUIURP(T

T/T+7/7+N-NJ


71/83

$LULQDSLVWRQF\OLQGHUJRHVWKURXJKD&DUQRWF\FOHZLWKWKH3YGLDJUDPVKRZQLQ)LJ7KHKLJKDQGORZWHPSHUDWXUHVDUH.DQG.UHVSHFWLYHO\7KHKHDWDGGHGDWWKHKLJKWHPSHUDWXUHLVN-NJDQGWKHORZHVWSUHVVXUHLQWKH

F\FOHLVN3D)LQGWKHVSHFLILFYROXPHDQGSUHVVXUHDIWHUKHDWUHMHFWLRQDQGWKH

QHWZRUNSHUXQLWPDVV

6ROXWLRQ

T+

N-NJ7+.7/.3N3D

7KHVWDWHVDVVKRZQLQILJXUH

..N3D..

6LQFHWKLVLVD&DUQRWF\FOHDQGZHNQRZWKHWHPSHUDWXUHVWKHHIILFLHQF\LV

K7

/

7+

DQGWKHQHWZRUNEHFRPHV

Z1(7

KT+u

N-NJ

7KHKHDWUHMHFWHGLV

3

Y

.

.

T/

T+

Z1(7

N-NJ

$IWHUKHDWUHMHFWLRQLVVWDWH)URPHTXDWLRQ o(T T

/57/OQYY

Y573uPNJ

YYH[ST/57/H[SuPNJ

357YuN3D


72/83

5HYLHZ3UREOHPV

$FDUHQJLQHRSHUDWHVZLWKDWKHUPDOHIILFLHQF\RI$VVXPHWKHDLU

FRQGLWLRQHUKDVDFRHIILFLHQWRISHUIRUPDQFHRIEZRUNLQJDVDUHIULJHUDWRUFRROLQJWKHLQVLGHXVLQJHQJLQHVKDIWZRUNWRGULYHLW+RZPXFKIXHOHQHUJ\VKRXOGEHVSHQGH[WUDWRUHPRYHN-IURPWKHLQVLGH"

6ROXWLRQ

&DUHQJLQH : KHQJ4IXHO

$LUFRQGLWLRQHU E4/

:

: KHQJ4IXHO4/

E

4IXHO4/KHQJ E

uN-

:

/4

7+

+4

7/

5()

)XHO4

+(

/HQJ4

)8(/


73/83

$QDLUFRQGLWLRQHUZLWKDSRZHULQSXWRIN:LVZRUNLQJDVDUHIULJHUDWRUERUDVDKHDWSXPSEc,WPDLQWDLQVDQRIILFHDWq&\HDUURXQGZKLFKH[FKDQJHVN:SHUGHJUHHWHPSHUDWXUHGLIIHUHQFHZLWKWKHDWPRVSKHUH)LQGWKHPD[LPXPDQGPLQLPXPRXWVLGHWHPSHUDWXUHIRUZKLFKWKLVXQLWLVVXIILFLHQW

6ROXWLRQ

$QDO\]HWKHXQLWLQKHDWSXPSPRGH

5HSODFHPHQWKHDWWUDQVIHUHTXDOVWKHORVV4

7+

7DPE

: 4

+Ec

7+

7DPE

7+

7DPE:

.

+HDWSXPSPRGH0LQXPXP7DPE&

7KHXQLWDVDUHIULJHUDWRUPXVWFRROZLWKUDWH4

7DPE7KRXVH

:

4

/

E 7DPE7KRXVH

7DPE7KRXVH:

.

5HIULJHUDWRUPRGH0D[LPXP7DPE

&


74/83

$ULJLGLQVXODWHGFRQWDLQHUKDVWZRURRPVVHSDUDWHGE\DPHPEUDQH5RRP$

FRQWDLQVNJDLUDWR&DQGURRP%KDVNJDLUDWR&ERWKURRPVDWN3D&RQVLGHUWZRGLIIHUHQWFDVHV

+HDWWUDQVIHUEHWZHHQ$DQG%FUHDWHVDILQDOXQLIRUP7

7KHPHPEUDQHEUHDNVDQGWKHDLUFRPHVWRDXQLIRUPVWDWH

)RUERWKFDVHVILQGWKHILQDOWHPSHUDWXUH$UHWKHWZRSURFHVVHVUHYHUVLEOHDQGGLIIHUHQW"([SODLQ

6ROXWLRQ

&97RWDO$%

(QHUJ\(T 884:

88P$88$P% 88%

#P$ &977$P% &977%

7P$

P$P%7$

P%P$P%

7%

u

u

R&

3$

3$

u7

7$

uN3D

3%3% u77% uN3D

6DPHHQHUJ\HT6LQFHLGHDOJDVX7VDPH7R&EXWQRZDOVRVDPH3

3P579 9 9$9%

9 P$57$3 P%57%3

3P57P$57$3 P %57%3

3 P7P$7$ P%7%

uu

N3D

%RWKFDVHVLUUHYHUVLEOH4RYHUDILQLWH'7DQGLQPL[LQJRIGLIIHUHQWVWDWHVLQWHUQDOXUHGLVWULEXWLRQ

&DVHLVPRUHLUUHYHUVLEOHDVWKHILQDOVWDWHLQFRXOGGULYHDWXUELQHEHWZHHQ

WKHWZRGLIIHUHQWSUHVVXUHVXQWLOHTXDO


75/83

$WFHUWDLQORFDWLRQVJHRWKHUPDOHQHUJ\LQXQGHUJRXQGZDWHULVDYDLODEOHDQGXVHGDVWKHHQHUJ\VRXUFHIRUDSRZHUSODQW&RQVLGHUDVXSSO\RIVDWXUDWHGOLTXLG

ZDWHUDWq&:KDWLVWKHPD[LPXPSRVVLEOHWKHUPDOHIILFLHQF\RIDF\FOLFKHDWHQJLQHXVLQJWKLVVRXUFHRIHQHUJ\ZLWKWKHDPELHQWDWq&":RXOGLWEHEHWWHUWRORFDWHDVRXUFHRIVDWXUDWHGYDSRUDWq&WKDQXVHWKHVDWXUDWHGOLTXLGDWq&"

6ROXWLRQ

70$;

&.7+

70LQ&.7/

K7+0$;7

+

7/

7+


76/83

:HZLVKWRSURGXFHUHIULJHUDWLRQDWq&$UHVHUYRLUVKRZQLQ)LJ3LVDYDLODEOHDWq&DQGWKHDPELHQWWHPSHUDWXUHLVq&7KXVZRUNFDQEHGRQH

E\DF\FOLFKHDWHQJLQHRSHUDWLQJEHWZHHQWKHq&UHVHUYRLUDQGWKHDPELHQW7KLVZRUNLVXVHGWRGULYHWKHUHIULJHUDWRU'HWHUPLQHWKHUDWLRRIWKHKHDW

WUDQVIHUUHGIURPWKHq&UHVHUYRLUWRWKHKHDWWUDQVIHUUHGIURPWKHq&UHVHUYRLUDVVXPLQJDOOSURFHVVHVDUHUHYHUVLEOH

6ROXWLRQ

(TXDWHWKHZRUNIURPWKHKHDWHQJLQHWRWKHUHIULJHUDWRU

4+

:

4 /

+(

4+

4 /

5()

7&+ 7&R

7&R 7&/

:4+

7+7

7+

DOVR

:4/

77/7

/

4+

4/

7R7/7

/

7+7

+7R


77/83

$/MXJRIPLONDWq&LVSODFHGLQ\RXUUHIULJHUDWRUZKHUHLWLVFRROHGGRZQWRq&7KHKLJKWHPSHUDWXUHLQWKH&DUQRWUHIULJHUDWLRQF\FOHLVq&DQGWKH

SURSHUWLHVRIPLONDUHWKHVDPHDVIRUOLTXLGZDWHU)LQGWKHDPRXQWRIHQHUJ\WKDWPXVWEHUHPRYHGIURPWKHPLONDQGWKHDGGLWLRQDOZRUNQHHGHGWRGULYHWKH

UHIULJHUDWRU

6ROXWLRQ

&9PLONRXWWRWKH&UHIULJHUDWRUVSDFH

(QHUJ\(T PX X4 :3URFHVV3FRQVWDQWDWP!:3PYY

6WDWH7DEOH%Y #YIPNJK #KIN-NJ

PP9YNJ

6WDWH7DEOH%K #KIN-NJ

4PX X:PX X3PYYPK K

4uN-

&95HIULJHUDWLRQF\FOH7/&7+&DVVXPH&DUQRW,GHDOE4/:4/4+4/7/7+ 7/

:4/EN-

0,/.FE

&

$,5

R


78/83

$FRPELQDWLRQRIDKHDWHQJLQHGULYLQJDKHDWSXPSVHH)LJ3WDNHVZDVWH

HQHUJ\DWq&DVDVRXUFH4ZWRWKHKHDWHQJLQHUHMHFWLQJKHDWDWq&7KHUHPDLQGHU4ZJRHVLQWRWKHKHDWSXPSWKDWGHOLYHUVD4+DWq&,IWKHWRWDOZDVWHHQHUJ\LV0:ILQGWKHUDWHRIHQHUJ\GHOLYHUHGDWWKHKLJKWHPSHUDWXUH

6ROXWLRQ

:DVWHVXSSO\4

Z4

Z0:

+HDW(QJLQH

:

K4

Z7/7+4

Z

+HDWSXPS

:

4

+E+34

:Ec

4

Z>7+7+7+@

(TXDWHWKHWZRZRUNWHUPV

:

4 /

4Z

+(

4Z

4+

+3

:DVWHVRXUFH

$PELHQW&

:DVWHVRXUFH

+($7&

7/7+4

Z4

Z u7+7+7+

6XEVWLWXWH4

Z0:4

Z

4

Z4

Z u

4

Z4

Z u!4

Z0:

4

Z0:

:

K4

Zu0:

4

+4

Z:

0:

)RUWKHKHDWSXPSEc


79/83

$LULQDULJLGPER[LVDW.N3D,WLVKHDWHGWR.E\KHDWWUDQVIHUIURPDUHYHUVLEOHKHDWSXPSWKDWUHFHLYHVHQHUJ\IURPWKHDPELHQWDW.

EHVLGHVWKHZRUNLQSXW8VHFRQVWDQWVSHFLILFKHDWDW.6LQFHWKHFRHIILFLHQWRISHUIRUPDQFHFKDQJHVZULWHG4PDLU&YG7DQGILQGG:,QWHJUDWHG:ZLWK

WHPSHUDWXUHWRILQGWKHUHTXLUHGKHDWSXPSZRUN

6ROXWLRQ

&23 Ec 4+:

4+

4+ 4/#

7+

7+ 7/

PDLU3957uuNJ

G4+

PDLU &YG7+Ec G:#7+

7+ 7/G:

!G:PDLU&Y >7+

7+ 7/@G7+

:PDLU&Y7/7

G7PDLU&Y7/7

G7

PDLU&Y>777/OQ77

@

u>OQ

@N-


80/83

&RQVLGHUWKHURFNEHGWKHUPDOVWRUDJHLQ3UREOHP8VHWKHVSHFLILFKHDWVR\RXFDQZULWHG4+LQWHUPVRIG7URFNDQGILQGWKHH[SUHVVLRQIRUG:RXWRIWKH

KHDWHQJLQH,QWHJUDWHWKLVH[SUHVVLRQRYHUWHPSHUDWXUHDQGILQGWKHWRWDOKHDW

HQJLQHZRUNRXWSXW

6ROXWLRQ

7KHURFNSURYLGHVWKHKHDW4+

G4+

G8URFNP&G7URFN

G:KG4+

7R7URFNP&G7URFN

PU9uNJ

:7R7URFNP&G7URFNP&>777ROQ77

@

u>OQ

@N-


81/83

$KHDWSXPSKHDWVDKRXVHLQWKHZLQWHUDQGWKHQUHYHUVHVWRFRROLWLQWKH

VXPPHU7KHLQWHULRUWHPSHUDWXUHVKRXOGEHq&LQWKHZLQWHUDQGq&LQWKHVXPPHU+HDWWUDQVIHUWKURXJKWKHZDOOVDQGFHLOLQJVLVHVWLPDWHGWREHN-

SHUKRXUSHUGHJUHHWHPSHUDWXUHGLIIHUHQFHEHWZHHQWKHLQVLGHDQGRXWVLGH

D,IWKHZLQWHURXWVLGHWHPSHUDWXUHLVq&ZKDWLVWKHPLQLPXPSRZHUUHTXLUHGWRGULYHWKHKHDWSXPS"

E)RUWKHVDPHSRZHUDVLQSDUWDZKDWLVWKHPD[LPXPRXWVLGHVXPPHUWHP

SHUDWXUHIRUZKLFKWKHKRXVHFDQEHPDLQWDLQHGDWq&"

6ROXWLRQ

D:LQWHU

+RXVHLV7+

DQGDPELHQW

LVDW7/

4 OHD4 4+/

:

+3

7+

&.7/

&.DQG4

+N-K

Ec4

+:

,1

:

,1

7+7

+7

/

:

,1N-KN:)RU&DUQRWF\FOH

E

4 OHDN4 4+ /

:

+3 7/

6XPPHU

7/7KRXVH

7+7DPE

7/

&.:

,1N-KDQG4

/7

+N-K

E4

/

:

,1

7

+

7/

7+

7/

7+

RU7+

u

7+

.&


82/83

$IXUQDFHVKRZQLQ)LJ3FDQGHOLYHUKHDW4+DW7+DQGLWLVSURSRVHGWR

XVHWKLVWRGULYHDKHDWHQJLQHZLWKDUHMHFWLRQDW7DWPLQVWHDGRIGLUHFWURRP

KHDWLQJ7KHKHDWHQJLQHGULYHVDKHDWSXPSWKDWGHOLYHUV4+DW7URRPXVLQJWKH

DWPRVSKHUHDVWKHFROGUHVHUYRLU)LQGWKHUDWLR4+4+DVDIXQFWLRQRIWKHWHPSHUDWXUHV,VWKLVDEHWWHUVHWXSWKDQGLUHFWURRPKHDWLQJIURPWKHIXUQDFH"

6ROXWLRQ

&9+HDW(QJ:

+(K4

+ZKHUHK7DWP7+

&9+HDW3XPS:

+34

+EcZKHUHEc7UP7UP7DWP

:RUNIURPKHDWHQJLQHJRHVLQWRKHDWSXPSVRZHKDYH

4

+Ec:

+3EcK4

+

DQGZHPD\VXEVWLWXWH7VIRUEcK,IIXUQDFHLVXVHGGLUHFWO\4

+4

+

VRLIEcK!WKLVSURSRVHGVHWXSLVEHWWHU,VLW")RU7+

!7DWPIRUPXODVKRZV

WKDWLWLVJRRGIRU&DUQRWF\FOHV,QDFWXDOGHYLFHVLWGHSHQGVZHWKHUEcK!LVREWDLQHG


83/83

$PWDQNRIDLUDWN3D.DFWVDVWKHKLJKWHPSHUDWXUHUHVHUYRLUIRUD

&DUQRWKHDWHQJLQHWKDWUHMHFWVKHDWDW.$WHPSHUDWXUHGLIIHUHQFHRIq&EHWZHHQWKHDLUWDQNDQGWKH&DUQRWF\FOHKLJKWHPSHUDWXUHLVQHHGHGWRWUDQVIHU

WKHKHDW7KHKHDWHQJLQHUXQVXQWLOWKHDLUWHPSHUDWXUHKDVGURSSHGWR.DQG

WKHQVWRSV$VVXPHFRQVWDQWVSHFLILFKHDWFDSDFLWLHVIRUDLUDQGILQGKRZPXFKZRUNLVJLYHQRXWE\WKHKHDWHQJLQH

6ROXWLRQ

4+:

4 /

+(

$,5

.

7+

7DLU&7/.

PDLU3957

u

uNJ

G:KG4+

7/7DLU

G4+

G4+

PDLUGXPDLU&YG7DLU

: G:PDLU&Y

7/

7DG7DPDLU&Y

7D

7D

7/

OQ7D

7D

uu

OQ

N-

ch7 problems

Documents