Eq Acido Base 1

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AElig`cmeLfpi

Ykcmfm =

6



ekikcmep 66+

f|fì|ccedilpc`fp mi aelig`cmep s lfpiiplt+ Izehy`cethk bcpeth|c`f mih èkì~e miaelig`cme s lfpi+

6+6+ ]ie|ccedilf mi F||bikcyp+ Hcgcf`cekip+

lt+lt+ ]ie|ccedilf mi L|uacutekpimHew|s+lt+0+ ]ie|ccedilf mi Hiwcp

0+ Ivychcl|ce mi cekctf`cethk mih foyf+ekì~e mi ~B+

=+ Jyi|tf mi aelig`cmep s lfpip+=+6+ AElig`cmep s lfpip èkdyofmfp+=+lt+ ihf`cethk ik|i Af s Al+=+0+ aeligh`yhep mi èkìk|f`cekip ik ivychcl|ce(

~B( èkpfkip( o|fme mi mcpe`cf`cethk

lt



ekikcmep lt9+ if``cekip mi bcm|ethhcpcp mi pfhip

ipymce `yfhcfcze+ 9+6+ Pfhip ~|eìmikip mi aelig`cme jyi|i s lfpi matildelch+

9+lt+ Pfhip ~|eìmikip mi aelig`cme matildelch s lfpi jyi|i+

9+0+ Pfhip ~|eìmikip mi aelig`cme matildelch s lfpi matildelch+9+=+ Pfhip ~|eìmikip mi aelig`cme jyi|i s lfpi jyi|i+

9+9+ fh`yhe mi èkìk|f`cekip s ~B+

+ Mcpehy`cekip fge|coyfme|fp+ + Ckmc`fme|ip mi aelig`cmelfpi+

2+ Zfhe|f`cekip mi aelig`cmelfpi zehygi|ccedilfp+

2+6+ Kiy|fhctf`cethk ~|aelig`c`f mi hfle|fe|ce+

0



f|fì|ccedilpc`fp

AEligCMEP4 ]cikik pfle| fo|ce+ Pek è||epczep ~f|f hf

~cih+ Ik|ediìk `ci|ep

èhe|fkip zioifhip+ Mcpyihzik pypfk`cfp Ff`fk f hep gifhip

mip~|ikmcikme Blt+ ^ci|mik pyp ~|e~cimfmip fh

|if``cekf| èk lfpip+

LFPIP4 ]ciki pfle| fgf|oe+ Pyfzip fh fè ~i|e

è||epczep èk hf ~cih+ Mfk èhe| ftyh f `ci|ep

èhe|fkip zioifhip+ ^|i`c~cfk pypfk`cfp

mcpyihfp ~e| aelig`cmep+

Mcpyihzik o|fpfp+ ^ci|mik pyp ~|e~cimfmip fh

|if``cekf| èk aelig`cmep+

=



Mijckc`cethk mi F||bikcyp

^ylhc`f ik 622 py ie|ccedilf mirsquomcpe`cf`cethk cethkc`f+

$ Bfs pypfk`cfp ihi`|ehcep vyi ik mcpehy`cethkpi mcpe`cfk ik `fcekip s fkcekip+

AEligCME4 Pypfk`cf vyi ik mcpehy`cethk

f`yepf mcpe`cf `fcekip B+ LFPI4 Pypfk`cf vyi ik mcpehy`cethk f`yepf

mcpe`cf fkcekip EB ‐ +

9



Mcpe`cf`cethk

AEligCMEP4

BF ik mcpehy`cethk f`yepf B F ‐

Idig~hep4$ Bh ik mcpehy`cethk f`yepf B h ‐

$ BltPE= ik mcpehy`cethk f`yepf ltB PE=lt ‐

LFPIP4

LEB ik mcpehy`cethk f`yepf L EB ‐

Idig~he4

$ KfEB ik mcpehy`cethk f`yepf Kf

EB ‐



Kiy|fhctf`cethk

Pi ~|emyì fh |if``cekf| yk aelig`cme èk ykflfpi ~e| je|gf`cethk mi foyf4

B EB ‐ rdquo BltE Ih fkcethk vyi pi mcpe`ceth mih aelig`cme s ih `fcethk

vyi pi mcpe`ceth mi hf lfpi vyimfk ik

mcpehy`cethk ckfhi|fmep pfh mcpe`cfmf4 KfEB Bh rdquo BltE Kfh Kf h ‐



]ie|ccedilf mi L|uacutekpimHew|s+

AEligCMEP4

rsquo Pypfk`cf vyi ik mcpehy`cethk ìmi B sbquo+

LFPIP4

rsquo Pypfk`cf vyi ik mcpehy`cethk fì~f B sbquo+

2



^f| AElig`cmelfpi èkdyofme

Pcig~|i vyi ykf pypfk`cf pi èg~e|f ègeaelig`cme ìmi B bfs e|f vyi pi èg~e|fège lfpi `f~y|f mc`bep B+

yfkme yk aelig`cme ~ci|mi B pi èkzci|i ik pyrsquolfpi èkdyofmf s `yfkme ykf lfpi `f~y|fB pi èkzci|i ik py rsquoaelig`cme èkdyofme+

3

AEligCME BF LFPI EKD+ F ‐

‐ B

B

LFPI L AElig+ EKD+ BL B

‐ B



Idig~he mi ~f| AElig`cmelfpi

èkdyofmeMcpe`cf`cethk mi yk aelig`cme4 Bh o BltE h B0E

fv h ‐ fv

Ik ipi `fpe ih BltE fòcircf ège lfpi s ihBh fh ~i|mi| ih B pi |fkpje|gf ik h ‐ lfpi èkdyofmf

Mcpe`cf`cethk mi ykf lfpi4 KB0 o BltE h KB= fv EB ‐ fv

Ik ipi `fpe ih BltE fòcircf ège aelig`cme ~yipìmi B fh KB0 vyi pi |fkpje|gf ik KB=

aelig`cme èkdyofme

6gt



]ie|ccedilf mi Hiwcp

AEligCMEP4

rsquoPypfk`cf vyi èkciki fh gikep yk aeligege

`f~ft mi fì~f| yk ~f| mi ihi`|ekip sje|gf| yk ikhfì èzfhiki èe|mckfmesbquo+

LFPIP4


`f~ft mi f~e|f| yk ~f| mi ihi`|ekip ~f|fje|gf| yk ikhfì èzfhiki èe|mckfmesbquo+

66



]ie|ccedilf mi Hiwcp Idig~hep

Bh o BltE h B0Efv h ‐

fvIk ipi `fpe ih Bh ip yk aelig`cme ~e|vyièkciki yk aeligege mi B vyi fh mcpe`cf|pi

s vyimf| ège B zf f fì~f| yk ~f| miihi`|ekip mih BltE je|gfkme yk ikhfìèzfhiki èe|mckfme B0E+

KB0 o

BltE

h KB

=

fv

EB ‐ fvIk ipi `fpe ih KB0 ip ykf lfpi ~e|vyi

èkciki yk aeligege mi K `f~ft mi f~e|f|yk ~f| mi ihi`|ekip ik hf je|gf`cethk mih

ikhfì èzfhiki èe|mckfme KB=

+

6lt



]ie|ccedilf mi Hiwcp èk+

Mi ipf gfki|f( pypfk`cfp vyi ke cikikaeligegep mi bcm|ethoike( ège ih Fhh0 ~yimik

f`yf| ège aelig`cmep4 Fhh0 4KB0 h0Fh4KB0

h B h Bx x x xh ‐ Fh 4 K ‐ B h ‐ FhK ‐ Bx x x xh B h B

60



Ivychcl|ce mi cekctf`cethk mih foyf+

Hf ir~i|cik`cf migyip|f vyi ih foyf ciki ykf~ivyioumlf èkmy`czcmfm ihatilde`|c`f he vyi ckmc`f vyiipaelig ~f|`cfhgiki mcpe`cfme ik cekip4

lt BltE h B

0Efv EB ‐ fv

B0E iquest EB ‐ A` 7 rdquordquordquordquordquordquo

BltElt

ege BltE ip èkpfki ~e| |ff|pi mi yk

hccedilvycme( hhfgf|igep Aw 7 A` iquest BltElt

èke`cme ège rsquo~|emyè cethkcè mih foyfsbquo

6=

Q Wszlig Q W

w 0 A B E EB



ekì~e mi ~B+

Ih zfhe| mi mc`be ~|emyè cethkcè mih foyfip4 A_ lt9acute 7 6gt ‐ 6=

Ik ih `fpe mih foyf ~y|f4 rdquordquordquo‐ B0E 7 EB ‐ 7 6gt ‐ 6= Glt 7 6gt ‐ G Pi mikegckf ~B f4

S ~f|f ih `fpe mi foyf ~y|f( ègeB0E76gt ‐ G4

~B 7 ‐ heo 6gt ‐ 7

69

0~B heo QB E W



]c~ep mi mcpehy`cekip

AElig`cmfp4 B0E 6gt ‐ G ~B 8

Laeligpc`fp4 B0E 8 6gt ‐ G ~B

Kiy|fp4 B0E 7 6gt ‐ G ~B 7

Ik emep hep `fpep4 Aw 7 B0E iquest EB ‐

hyioe pc B0E

fygikf mcpe`cf`cethk mi ykaelig`cme( ikekìp EB ‐ mili mcpgckyc| ~f|fvyi ih ~|emyè mi fglfp èkìk|f`cekipèkckocirci zfhcikme 6gt ‐ 6=

6



O|aeligjc`f mi ~B ik pypfk`cfp

ègykip

6

AEligCME LAEligPCE

6= 6 lt 0 = 2 3 6gt 66 6lt 60 9

Tyge mi

hcgethk i|zitf

Hi`bi

Pfko|i

Foyf gf|

Fgekcfè Foyf mipchfmf



ekì~e mi ~EB+ F ziìp pi ypf ipi e|e èkì~e( `fpc

cmatildekcè fh mi ~B4

ege Aw 7 B0E iquest EB ‐ 7 6gt ‐ 6=

F~hc`fkme heof|cgep s `fglcfkme ih pcokeikm|ccedilfgep4

~B ~EB 7 6=

~f|f ykf ig~i|fy|f mi lt9acute+

~EB heo QEB W

62



Idig~he4 Ih ~B mi ykf mcpehy`cethk f`yepfip 6lt(+ microyfh pi|aelig hf EB ‐

s ih ~EB f hfig~i|fy|f mi lt9acute5

~B 7 ‐ heo B0E 7 6lt(( mi mekmi pi mimyìvyi4 B0E 7 6gt ‐ ~B 7 6gt ‐ 6lt( G 7 lt(9 iquest 6gt ‐ 60 G

ege Aw 7 B0E iquest EB ‐ 7 6gt ‐ 6= ikekìp4 A_ 6gt ‐ 6= Glt EB ‐ 7 rdquordquordquo 7 rdquordquordquordquordquordquo 7 gt(gt= G

B0E lt(9 iquest 6gt ‐ 60 G

~EB 7 ‐ heo EB ‐ 7 ‐ heo gt(gt= G 7 6(=

eg~|elfgep ege ~B ~EB 7 6lt( 6(= 7 6=

63

Id c c F

ltgt^ lh m



Idi|`c`ce F4 Ykf mcpehy`cethk mi aelig`cme pyhjocirc|cè ciki ykfmikpcmfm mi 6(lt ogh s ykf|cvyitf mih ltgt ) ik ~ipe+ f fh`yhi pyèkìk|f`cethk ir~|ipfmf ik gehiphc|e s iko|fgephc|e+ l fh`yhi ih ~B mi ykf mcpehy`cethk~|i~f|fmf mchysikme gch ziìp hf fki|ce|+

f gp gp ) gfpf 7 rdquordquo r 6gtgt ) 7 rdquordquordquo r 6gtgt ) g

M

ZM

r m

gp ) r m ltgt ) r 6(lt o oH 7 rdquo 7 rdquordquordquo 7 rdquordquordquordquordquordquo 7 lt=gt oH

ZM 6gtgt ) 6gt ‐ 0 H r 6gtgt )

kp

gp G oH lt=gt oH

Gehf|cmfm 7 rdquordquo 7 rdquordquordquo 7 rdquordquordquo 7 rdquordquordquordquo ZM ZM G 32 ogeh

Gehf|cmfm 7 lt(=9 gehH

l ~B 7 ‐ heo QB0EW 7 ‐ heo lt r lt(=9r6gt ‐ 0 G7 lt(09

ltgt^|elhigf miPihi`czcmfmGf|te 3

lt6



Ihi`|ehcep jyi|ip s matildelchip

Ihi`|ehcep jyi|ip4 Ipaeligk efhgiki mcpe`cfmep

$ Idig~hep4 Bh fv B fv h ‐ fv

KfEB fv Kf fv EB ‐ fv

Ihi`|ehcep matildelchip4 Ipaeligk mcpe`cfmep ~f|`cfhgiki

$ Idig~hep4B0 ‐ EEBfv B0 ‐ EE ‐ fv BfvKB0fv BltE h KB=

fv EB ‐ fv

lt6

ltlt




ltlt

QF ‐W QBW

QBW QF ‐W

QBFW QBFW

AElig`cme jyi|i

QBFW

AElig`cme matildelch

lt0



Idig~he4 Dypcjc`f ~e|vyatilde ih cethk BE0 ‐

fòcircf ège aelig`cme j|iki fh KfEB s ègelfpi j|iki fh Bh+

Ih KfEB ~|e~e|`cekf EB ‐ f hf mcpehy`cethk4


~e| he vyi BE0

‐

EB ‐

E0

lt ‐

BltE ip mi`c|( ih cethk BE0 ‐ fòcircf ège aelig`cme+

Ih Bh ~|e~e|`cekf B f hf mcpehy`cethk4

Bh fv B

fv h ‐

fv ~e| he vyi BE0

‐ B BltE0 Elt BltE

ip mi`c|( ih cethk BE0 ‐ fòcircf ège lfpi+

lt0

lt=



Jyi|tf mi aelig`cmep+

Ik mcpehy`cekip f`yepfp mchycmfp BltE èkpfki hf jyi|tf mi yk aelig`cme BF mi~ikmi

mi hf èkpfki mi ivychcl|ce4 BFfv BltEh F ‐ fv B0Efv

F ‐ iquest B0E F ‐ iquest B0E A` 7 rdquordquordquordquordquordquo A` iquest BltE 7 rdquordquordquordquordquordquo

BF iquest BltE BF

lt=

0

lt

Q W Q WQ W

Q W f

F B E A B E A

BF

èkpfki mi mcpe`cf`cethk

A f`cmit

lt9



Jyi|tf mi aelig`cmep èk++

Pioocirck ih zfhe| mi Af bflhf|igep mi aelig`cmepjyi|ip e matildelchip4

Pc Af 6gtgt Ih aelig`cme ip jyi|i s ipf|aeligmcpe`cfme `fpc ik py efhcmfm+

Pc Af 8 6 Ih aelig`cme ip matildelch s ipf|aelig pethhe

~f|`cfhgiki mcpe`cfme+ ê| idig~he( ih aelig`cme fàtildecè B0 ‐ EEB

ip yk aelig`cme matildelch sf vyi py Af 7 6(2 iquest 6gt ‐ 9

lt9

lt



AElig`cmep ~ehc~|ethcèp Pek fvyihhep vyi ~yimik ìmi| gaeligp mi yk B

+ê| idig~he ih BltE0 ip mc~|ethcè+ Ircpik ~yip( fkep ivychcl|cep ège B

mcpe`ci4 BltE0

BltE BE0 ‐ B0E

BE0 ‐ BltE E0

lt ‐ B0E

BE0

‐ iquest B0

E E0

lt ‐ iquest B0

E Af6 7 rdquordquordquordquordquordquordquordquo Aflt 7 rdquordquordquordquordquordquordquo BltE0 BE0

‐

Af6 7 =(9 iquest 6gt ‐ Aflt 7 9(iquest 6gt ‐ 66

Hf èkpfkip pyìpczfp pcig~|i zfk mcpgckysikme+

lt

Id h P lc m h m lt



Idig~he4 Pflcikme vyi hfp èkpfkip mif`cmit mih aelig`cme jepjeth|cè pek4 Af6 7 (9 r 6gt ‐0(Aflt 7 (lt r 6gt ‐2 s Af0 7 lt(lt r 6gt ‐60( `fh`yhf| hfp

èkìk|f`cekip mi hep cekip B0E

( BltÊ=

‐

(BÊ=lt ‐ s Ê=

0 ‐ ik ykf mcpehy`cethk mi B0Ê= gt(gt2G+Ivychcl|ce 64 B0Ê= BltE BltÊ=

‐ B0E

Q Wgt gt(gt2 gt gt∊Q W ‐ r r r

∊Q Wiv gt(gt2 ‐ r r r

r 7 gt(gtlt6

lt

lt0lt = 0

6

0 =

Q W Q W (9 6gtQ W gt(gt2

f B ^ E B E r A G

B Ê r

lt = 0Q W Q W gt(gtlt6B Ê B E G

lt2



Ivychcl|ce lt4 BltÊ= ‐ BltE BÊ=

lt ‐ B0E `+ ck+gehh4 gt(gtlt6 gt gt(gtlt6`+ iv+gehh4 gt(gtlt6 ‐ s s gt(gtlt6 s

s 7 (lt r 6gt ‐ 2 G

Ivychcl|ce 04 BÊ=lt ‐ BltE Ê=

0 ‐ B0E `+ ck+gehh4 (lt r 6gt ‐ 2 gt gt(gtlt6`+ iv+gehh4 (lt r 6gt ‐ 2 ‐ t t gt(gtlt6 t

t 7 (9 r 6gt ‐ 63 G

lt 2

=Q W (lt 6gtBÊ G

lt2

lt2= 0

lt

lt =

Q W Q W gt(gtlt6 gt(gtlt6(lt 6gt

gt(gtlt6 gt(gtlt6Q Wf

B E B E s s s A G

s B Ê

600 = 0lt lt 2 2

=

Q W Q W gt(gtlt6 gt(gtlt6lt(lt 6gt

Q W (lt 6gt (lt 6gtf

B ^ E B E t t t A G

BÊ t

0 63

=Q W (9 6gtÊ G

lt3



Jyi|tf mi lfpip+

Ik mcpehy`cekip f`yepfp mchycmfp BltE èkpfki hf jyi|tf mi ykf lfpi LEB

mi~ikmi mi hf èkpfki mi ivychcl|ce4 Lfv BltE h LBfv EB ‐ fv LB r EB ‐ LB r EB ‐

A` 7 rdquordquordquordquordquordquo A` r BltE 7 rdquordquordquordquordquordquo

L r BltE L

lt3

lt

Q W Q WQ W

Q W l

LB EB A B E A

L A lfpc`cmfm

0gt



Jyi|tf mi aelig`cmep s lfpip~A

Fh coyfh vyi ih ~B pi mikegckf ~A f4

~Af7 ‐ heo Af 1 ~Al7 ‐ heo Al

yfke gfse| ip ih zfhe| mi Af e Al

gfse| ip hf jyi|tf mih aelig`cme e mi hf lfpi+

Coyfhgiki( `yfke gfse| ip ih zfhe| mi ~Afe ~Al gike| ip hf jyi|tf mih aelig`cme e mi hflfpi+

0gt

06



Idig~he4 Mii|gckf| ih ~B s ih ~EB miykf mcpehy`cethk gt(lt G mi KB0 pflcikmevyi A

llt9acute 7 6(2 iquest 6gt ‐9

Ivychcl|ce4 KB0fv BltEh KB=

fv EB ‐ fv

Q Wgt gt(lt gt gt

∊Q W ‐ r r r

∊Q Wiv gt(gt2 ‐ r r rKB=

r EB ‐ rlt Al 7 rdquordquordquordquordquordquordquo 7 rdquordquordquo 7 6(2 r 6gt ‐ 9

KB0

gt(lt ‐ r Mi mekmi pi mimyì vyi r 7 EB ‐ 7 6(3 r 6gt ‐ 0 G

~EB 7 ‐ heo EB ‐ 7 ‐ heo 6(3 r 6gt ‐ 0 7 lt(lt

~B 7 6= ‐ ~EB 7 6= ‐ lt(lt 7 66(lt2

06

0lt



ihf`cethk ik|i Af s Al

èkdyofmf Ivychcl|ce mi mcpe`cf`cethk mi yk aelig`cme4 BF BltE F ‐ B0E if``cethk mi hf lfpi èkdyofmf èk ih foyf4 F ‐ BltE BF EB ‐ F ‐ r B0E BF r EB ‐

Af 7 rdquordquordquordquordquordquo 1 Al 7 rdquordquordquordquordquordquo BF F ‐ F ‐ r B0E r BF r EB ‐

Af r Al 7 rdquordquordquordquordquordquordquordquordquordquordquordquo 7 A_ BF r F ‐

0lt

00




èkdyofmf èk++ Ik hf ~|aelig`c`f( ipf |ihf`cethk Af r Al 7 A_

pcokcjc`f vyi4

Pc yk aelig`cme ip jyi|i py lfpi èkdyofmf ipmatildelch+

Pc yk aelig`cme ip matildelch py lfpi èkdyofmf ip

jyi|i+ F hf èkpfki mih aelig`cme e lfpi èkdyofmf

ik hf |if``cethk èk ih foyf pi hi pyihi hhfgf|

èkpfki mi bcm|ethhcpcp Ab+

00

0=



Idig~he4 fh`yhf| hf Al mih AK pc pfligepvyi hf Af mih BK zfhi =(3 iquest 6gt ‐6gt G+

Ih BK ip yk aelig`cme matildelch èkpfki gys~ivyioumlf+ ê| fke( py lfpi èkdyofmf( ih

K ‐

( pi|aelig ykf lfpi |ihfczfgiki jyi|i+ Py|if``cethk èk ih foyf pi|aelig4 K ‐ BltE BK EB ‐

A_ 6gt ‐ 6=

Glt

Al 7 rdquordquo 7 rdquordquordquordquordquordquo 7 lt(gt r 6gt ‐ 9 G Af =(3 r 6gt ‐ 6gt G

0=

h ceth h 09



ihf`cethk ik|i hf èkpfkis ih o|fme mi mcpe`cf`cethk lsquo Ik hf mcpe`cf`cethk mi yk aelig`cme e ykf lfpi

Coyfhgiki4

Ik ih `fpe mi aelig`cmep e lfpip gys matildelchip

Af ` e Al ` 8 6gt ‐ =( pi mip~|i`cf j|iki f6 èk he vyi4 Af 7 ` lt Al 7 ` lt

Mi mekmi4

09

l

` A

lt

6

lt0

6 6

Q W Q W

Q W f

F B E ` ` ` A

BF `

f

A

`

l

A

`

Idig~he4 Ykf mcpehy`cethk mi BLE 6gtlt G

0^|elhigf mi



Idig~he4 Ykf mcpehy`cethk mi BLElt 6gt lt Gciki yk mi ~B mi 9(+ f fteki pc ih aelig`cme s py

lfpi èkdyofmf pi|aeligk jyi|ip e matildelchip+ l fh`yhihf èkpfki mi mcpe`cf`cethk mih aelig`cme Af+ ` fh`yhi( pc ip ~epclhi( hf èkpfki mi lfpc`cmfm mihcek le|fe Al+ m Pc 6gtgt gh mi ipf mcpehy`cethk miBLElt pi git`hfk èk 6gtgt gh mi ykf mcpehy`cethk 6gt

lt G mi bcm|ethrcme pethmcè( microvyatilde èkìk|f`cethk mi hf

lfpi èkdyofmf pi elikm|aelig5f QB0EW 7 6gt ‐ ~B 7 6gt ‐ 9( 7 lt(96 r 6gt ‐ G 7QB0EW` 7 lt(96 r 6gt ‐ G 6gtlt G 7 lt(96 r6gt ‐ = he vyi pcokcjc`f vyi ipaelig mcpe`cfme ik yk gt(gtlt9 )

hyioe pi |ff mi yk aelig`cme matildelch+ Py lfpièkdyofmf( LElt ‐ ( pi|aelig ~yip( |ihfczfgiki jyi|i+

l Af 7 ` r lt 7 6gtlt G rlt(96 r 6gt ‐ =lt 7 (0 r 6gt ‐ 6gt

` Al 7 Aw Af 7 6gt ‐ 6= (0 r 6gt ‐ 6gt 7 6(92 r 6gt ‐ 9

m Pi kiy|fhctfk irf`fgiki4 QLElt ‐ W 7 9 r 6gt ‐ 0 G

0Pihi`czcmfmGf|te 32

Idi|`c`ce L4 Ik yk hfle|fe|ce pi cikik mep

0^|elhigf



Idi|`c`ce L4 Ik yk hfle|fe|ce pi cikik mepgf|fìp( yke èkikcikme 69 gh mi Bh `ysf

èkìk|f`cethk ip gt(gt9 G s ih e|e 69 gh mi aelig`cmeifkecè fàtildecè mi èkìk|f`cethk gt(gt9 Gf fh`yhi ih ~B mi `fmf ykf mi ihhfp+ l microVyatilde`fkcmfm mi foyf pi mili|aelig foumlfmc| f hf gaeligp aelig`cmf~f|f vyi ih ~B mi hfp mep mcpehy`cekip pif ihgcpge5 Mfe4 Af aelig`cme ifkecè 7 6(2 r 6gt9

f Bh ip aelig`cme jyi|i hyioe ipaelig efhgiki mcpe`cfme(~e| he vyi QB0EW 7 gt(gt9 G

~B 7 ‐ heo QB0EW 7 ‐ heo gt(gt9 7 6(0gtB0EEB ip aelig`cme matildelch ~e| he vyi4

Af 6(2 iquest6gt9 G 7 rdquordquo 7 rdquordquordquordquordquo 7 gt(gt63` gt(gt9 G

QB0EW 7 ` 7 gt(gt9 G r gt(gt63 7 3(9 r 6gt= G

~B 7 ‐ heo QB0EW 7 ‐ heo 3(9 r 6gt= 7 0(gt

0Pihi`czcmfmDykce 32


02^|elhigf





l k B0E ik Bh 7 Z r Gehf|cmfm 7 gt(gt69 h r gt(gt9 G 77 (9 r 6gt= geh+

^f|f vyi ih ~B pif 0(gt QB0EW 7 6gt0 G vyi pi|aelig fglcatildek

hf QBhW sf vyi ipaelig efhgiki mcpe`cfme+Ih zehygik ik ih vyi mili|aeligk ipf| mcpyihep ipep gehip ip4

Z 7 kGehf|cmfm 7 (9 r 6gt= geh 6gt0 gehiquesth6 7 gt(9 hc|ep

Hyioe bfl|aelig vyi foumlfmc| gt(9 ‐ gt(gt69 hc|ep 7 09 gh


03



Bcm|ethhcpcp mi pfhip

Ip hf |if``cethk mi hep cekip mi ykf pfh èk ihfoyf+

Pethhe ip f~|i`cflhi `yfkme ipep cekip

~|eìmik mi yk aelig`cme e ykf lfpi matildelch4 Bcm|ethhcpcp aelig`cmf mi yk `fcethk4

KB= BltE KB0

B0E

Bcm|ethhcpcp laeligpc`f mi yk fkcethk4 B0 ‐ EE ‐ BltE B0 ‐ EEB EB ‐

03

=gt



]c~ep mi bcm|ethhcpcp+ Pioocirck ~|eìmfk ih `fcethk s ih fkcethk mi yk

aelig`cme e ykf lfpi jyi|i e matildelch( hfp pfhip pi`hfpcjc`fk ik4 Pfhip ~|eìmikip mi aelig`cme jyi|i s lfpi jyi|i+

$ Idig~he4 Kfh Pfhip ~|eìmikip mi aelig`cme matildelch s lfpi jyi|i+

$ Idig~he4 KfK

Pfhip ~|eìmikip mi aelig`cme jyi|i s lfpi matildelch+ $ Idig~he4 KB=h

Pfhip ~|eìmikip mi aelig`cme matildelch s lfpi matildelch+ $ Idig~he4 KB=K

=gt

=6



Pfhip ~|eìmikip mi aelig`cmejyi|i s lfpi jyi|i+

Idig~he4 Kfh

KE PI ÊMYI BCMETHHCPCP sf vyi

fke ih Kf

vyi ip yk aelig`cme gys matildelchège ih h ‐ vyi ip ykf lfpi gys matildelchf~ikfp |if``cekfk èk foyf+ Ip mi`c| hepivychcl|cep4

Kf lt BltE KfEB B0E

h ‐ BltE Bh EB ‐

ipaeligk gys mip~hftfme bf`cf hf ctvyci|mf+

=lt



Pfhip ~|eìmikip mi aelig`cme

matildelch s lfpi jyi|i+ Idig~he4 KfB0 ‐ EE ‐

PI ÊMYI BCMETHHCPCP LAEligPCF

sf vyi ih Kf ip yk aelig`cme gys matildelch sf~ikfp |if``cekf èk foyf( ~i|e ihB0 ‐ EE ‐ ip ykf lfpi jyi|i s pc

|if``cekf èk atildepf mi je|gf pcokcjc`fczf4 B0 ‐ EE ‐ BltE B0 ‐ EEB EB ‐

he vyi ~|eze`f vyi ih ~B mcp+ laeligpc`f+

=0




jyi|i s lfpi matildelch+ Idig~he4 KB=h

PI ÊMYI BCMETHHCPCP AEligCMF sf

vyi ih KB= ip yk aelig`cme |ihfczfgikijyi|i s |if``cekf èk foyf gcik|fp vyi ihh ‐ ip ykf lfpi matildelch s ke he bfì mi je|gf

pcokcjc`fczf4 KB=

BltE KB0 B0E

he vyi ~|eze`f vyi ih ~B 8 mcp+ aelig`cmf+

==




matildelch s lfpi matildelch+ Idig~he4 KB=K

Ik ipi `fpe fke ih `fcethk KB=

ège ih

fkcethk K ‐ pi bcm|ehctfk s hf mcpehy`cethk pi|aeligaelig`cmf e laeligpc`f pioocirck vyatilde cek pi bcm|ehcì ikgfse| o|fme+

ege AlK ‐ 7 lt iquest 6gt ‐ 9 G sAfKB=

7 9( iquest 6gt ‐ 6gt G ( ik ipi `fpe( hfmcpehy`cethk ip laeligpc`f sf vyi AlK ‐ ip

gfse| vyi AfKB=

=9



Idig~he4 Pflcikme vyi Af BK 7 =(gt iquest 6gt ‐6gt

G( `fh`yhf| ih ~B s ih o|fme mi bcm|ethhcpcp miykf mcpehy`cethk f`yepf mi KfK gt(gt6 G+

Hf |if``cethk mi bcm|ethhcpcp pi|aelig4

K ‐ BltE BK EB ‐

BK iquest EB ‐ A_ AbK ‐ 7 rdquordquordquordquordquordquo 7 rdquordquordquordquordquordquo 7K ‐ =(gt iquest 6gt ‐ 6gt G

6 iquest 6gt ‐ 6= Glt

AbK ‐ 7 rdquordquordquordquordquordquo 7 lt(9 iquest 6gt ‐ 9 G

=(gt iquest 6gt ‐ 6gt G

Id h P lc m A BK = gt 6gt 6gt

=






ek` ckck+ G gt(gt6 gt gt ek` ivych+ G gt(gt66 ‐ gt(gt6 gt(gt6

BK r EB ‐ gt(gt6 lt Glt lt(9 iquest 6gt ‐ 9 G 7 rdquordquordquordquordquordquo 7 rdquordquordquordquordquordquo

K ‐ gt(gt66 ‐ G Mip~|i`cfkme j|iki f 6( pi elciki vyi 7 gt(gt9 A_ 6gt ‐ 6= Glt B0E 7 rdquordquordquo 7 rdquordquordquordquordquordquo 7 lt(gt r 6gt ‐ 66 G

EB ‐ gt(gt6 G r gt(gt9

~B 7 ‐ heo B0E 7 ‐ heo lt(gt r 6gt ‐ 66 G 7 6gt(

Idi|`c`ce 4 fteki ychctfkme hep

=

^|elhigf miP h c cm m



Idi|`c`ce 4 fteki ychctfkme hepivychcl|cep è||ip~ekmcikip( pc hep ~B mi hfp

mcpehy`cekip vyi pi |ihf`cekfk pioycmfgiki pekaelig`cmep( laeligpcèp e kiy|ep+ f Fìfe ~eaeligpcè gt(gt6G1 l Kc|fe pethmcè gt(gt6 G1 ` Pyhjfe fgethkcègt(gt6 G1 m Bcm|ethrcme mi lf|ce gt(gt6 G+

f Fìfe ~eaeligpcè4 ~B laeligpcè( sf vyiB0 ‐ EE ‐ BltE B0 ‐ EEB EB ‐ ~e| pi| ih aelig`+ fìcè matildelch( gcik|fp vyi ih A ke|if``cekf èk foyf ~e| pi| ih AEB lfpi jyi|i+

l kc|fe pethmcè4 ~B kiy|e( sf vyi kc ih fkcethkKE0 ‐

kc ih `fcethk Kf |if``cekfk èk foyf ~e|~|eìmi| ih ~|cgi|e mih BKE0 s mih KfEB ihpioykme( fglep ihi`|ehcep jyi|ip+

Pihi`czcmfmPi~cigl|i 32


=2






` Pyhjfe fgethkcè4 ~B aelig`cme( sf vyi

KB= BltE KB0 B0E ~e| pi| ih fgekcfè matildelch( gcik|fp vyi ih PE=

lt ‐ ke|if``cekf èk foyf ~e| pi| ih BltPE= aelig`cme jyi|i+

m bcm|ethrcme mi lf|ce4 ~B laeligpcè ~yip pi |ff mi ykflfpi jyi|i hep bcm|ethrcmep mi hep gifhip fh`fhckeps fh`fhckeatilde||iep pek lfpip lfpfkip jyi|ip


=3



Mcpehy`cekipfge|coyfme|fp fg~ethk Pek `f~fìp mi gfkiki| ih ~B mip~yatildep mi

foumlfmc| ~ivyioumlfp `fkcmfmip fke mi aelig`cmeège mi lfpi+ Ipaeligk je|gfmfp ~e|4

Mcpehy`cekip mi aelig`cme matildelch pfh mi mc`beaelig`cme matildelch èk `fcethk kiy|e4$ Idig~he4 aelig`cme fàtildecè fìfe mi pemce+

Mcpehy`cekip mi lfpi matildelch pfh mi mc`bflfpi matildelch èk fkcethk kiy|e4$ Idig~he4 fgekcfè s `he|y|e mi fgekce+

9gt



Zf|cf`cethk mih ~B fh foumlfmc| ~ivyioumlfp`fkcmfmip mi KfEB e Bh

pound Im+ Pfkchhfkf

Id h96



Idig~he4 fh`yhf| ih ~B mi ykf mcpehy`cethkfg~ethk je|gfmf ~e| ykf èkìk|f`cethkgt(lt G mi aelig`cme fàtildecè s gt(lt G mi fìfemi pemce+ Af B0 ‐EEB 7 6(2 iquest 6gt ‐9 G+

Ih fìfe ipaelig efhgiki mcpe`cfme4

B0 ‐ EEKf B0 ‐ EE ‐

Kf

Ih aelig`cme fàtildecè pi ik`yik|f ik ivychcl|ce

èk py lfpi èkdyofmf fìfe4

BltE B0 ‐ EEB B0 ‐ EE ‐

B0E

`ck G gt(lt gt(lt gt

ìv G gt(lt ‐ r gt(lt r r

Id h

9lt



Idig~he4 fh`yhf| ih ~B mi ykf mcpehy`cethkfg~ethk je|gfmf ~e| ykf èkìk|f`cethkgt(lt G mi aelig`cme fàtildecè s gt(lt G mi fìfemi pemce+ Af B0 ‐EEB 7 6(2 iquest 6gt ‐9 G

B0 ‐ EE ‐ iquest B0E gt(ltr iquest r Glt 6(2 iquest 6gt ‐ 9 G 7 rdquordquordquordquordquordquordquordquordquo 7 rdquordquordquordquordquordquo

B0 ‐ EEB gt(lt ‐ r G

Mi mekmi pi mimyì vyi4

r 7 B0E

7 6(2 iquest 6gt ‐ 9

G

~B 7 ‐ heo B0E 7 =(=

C mc m m B99



Ckmc`fme|ip mi ~Baelig`cme lfpi

Pek pypfk`cfp vyi `fglcfk mi èhe| fh~fpf| mi hf je|gf aelig`cmf f hf laeligpc`f4

BCk BltE Ck ‐ B0E

je|gf aelig`cmf je|gf laeligpc`f

Ih `fglce mi èhe| pi èkpcmi|f f~|i`cflhi

`yfkme QBCkW 6gtiquestQCk ‐

W e QBCkW8 66gtiquestQCk ‐

W Ck ‐ iquest B0E BCk

Af 7 rdquordquordquordquordquordquo B0E 7 Af iquest rdquordquordquo BCk Ck ‐

~B 7 ~Af heo Ck ‐ BCk 7 ~Af 6

9



Fhoykep ckmc`fme|ip mi ~B

Ckmc`fme| ehe| je|gf

aelig`cmf ehe| je|gf

laeligpc`f Tekf mizc|fdi ~B

Zcehif mi

giche Fgf|chhe Zcehif gtlt

ede ekoe Ftyh ede 09

ede mi

gicheede Fgf|chhe =

]e|kfpeh ede Ftyh 2

Jikehjfhiccedilkf Ckèhe|e epf 26gt

9



Zfhe|f`cekip aelig`cmelfpi Zfhe|f| ip gimc| hf

èkìk|f`cethk mi ykmii|gckfme aelig`cme e

lfpi f ~f|c| mihfkaelighcpcp zehygatilde|cèmi hf lfpi e aelig`cmeychctfme ik hf|if``cethk mikiy|fhctf`cethk+

92



O|aeligjc`f mi zfhe|f`cethk mi

zckfo|i èk KfEB

Tekf mi zc|fdi jikehjfhiccedilkf

ltgt =gt gt Z KfEBgh

6lt

6gt2

=

lt

~B

93



Zfhe|f`cekip aelig`cmelfpi+ Hf kiy|fhctf`cethk mi yk aelig`cmelfpi èk ykf

lfpiaelig`cme mi èkìk|f`cethk èke`cmf pièkpcoyi `yfkme kEB ‐ 7 kB0E+

Hf |if``cethk mi kiy|fhctf`cethk ~yimiip`|clc|pi4l BfF f LEBl LfFl fiquestl BltE

Ik |ifhcmfm( hf pfh LfFl fLl

lFf ‐

piik`yik|f mcpe`cfmf( ~e| he vyi hf ocirckc`f|if``cethk ip4 B0E EB ‐ lt BltE

kaelig`cme r f 7 klfpi r l

gtPcgyhf`cethk



Zfhe|f`cekip aelig`cmelfpi Zaelig`cme r Qaelig`cmeW r f 7 Zlfpi r QlfpiW r l ]emfzccedilf pi ypf gy`be hf èkìk|f`cethk

ir~|ipfmf ège Ke|gfhcmfm4

Ke|gfhcmfm 7 Gehf|cmfm r k B y EB

Zaelig`cme r Kaelig`cme 7 Zlfpi r Klfpi

Ik ih `fpe mi pfhip ~|eìmikip mi aelig`cme elfpi matildelchip mili ychctf|pi yk ckmc`fme|vyi zc|i fh ~B mi hf pfh |ipyhfki mi hf

kiy|fhctf`cethk+

Idig~he4 6gtgt gh mi ykf mcpehy`cethk mi B PE

6



Idig~he4 6gtgt gh mi ykf mcpehy`cethk mi BltPE=

pi kiy|fhctfk èk lt9 gh mi ykf mcpehy`cethkltG mi FhEB0 microyaeligh pi|aelig hf QBltPE=W5

0 BltPE= lt FhEB0 0PE=lt ‐ ltFh0 BltE

lt9 gh r lt G r 0 7 6gtgt gh r Gaelig`cme r lt

Mi mekmi4 lt9 gh r lt G r 0Gaelig`cme 7 rdquordquordquordquordquordquordquo 7 gt(9 G

6gtgt gh r lt QBltPE=W 7 gt(9 G

Zaelig`cme r Kaelig`cme 7 Zlfp r Klfpi Klfpi7 0 r Glfpi

6gtgt gh r Kaelig`cme 7 lt9 gh r K K

aelig`cme 7 6(9 K G

aelig`cme7 K

aelig`cme lt 7 gt(9 G

Zccedilmie


lt





êm|ccedilfgep bfli| `fh`yhfme kBltPE= f~f|c| mih àeligh`yhe ipivycegatilde|cè( ~yipèkeìgep

kFhEB0 7 Ziquest G 7 lt9 gh iquest ltG 7 9gtggehip0 BltPE= lt FhEB0 0PE=

lt ‐ ltFh0 BltE

0 geh BltPE= lt geh FhEB0 rdquordquordquordquordquo 7 rdquordquordquordquordquordquo kBltPE= 9gt ggehip

kBltPE= 7 9 ggeh

k BltPE= 9 ggeh7 rdquordquordquordquordquo 7 rdquordquordquordquo 7

Idi|`c`ce M4 Pc 6gt(6 gh mi zckfo|i bfk

0^|elhigf miPihi`czcmfm



di ` ` ekiìpcfme 9gt(9 gh mi ykf lfpi gt(lt K ~f|f py

kiy|fhctf`cethk+ f yaeligh pi|aelig hf ke|gfhcmfm mihaelig`cme ik ih zckfo|i1 l Py~ekcikme vyi py f`cmit

pi mili fh aelig`cme fàtildecè aelig`cme ifkecè+ microyaelighip ih ~e|ìkfdi ik ~ipe mih aelig`cme fàtildecè pc hfmikpcmfm mih zckfo|i ip mi 6(gt ogh5

f Zaelig`cme r Kaelig`cme 7 Zlfpi r Klfpi

9gt(9 gh r gt(lt KKaelig`cme 7 rdquordquordquordquordquordquo 7 6 K Gaelig`cme 7 6 G6gt(6 gh

l Py~ekofgep vyi ikigep yk hc|e mi zckfo|i4 gaelig+ fàtildecè 7 Gehf|cmfm r G r Z 7

7 6 gehH r gt ogeh r 6 H 7 gt o gpehye gt o

) 7 rdquordquordquordquo r 6gtgt 7 rdquordquordquo r 6gtgt 7 9( )

Pi i` mfmPi~cigl|i 3



ekikcmep 66+

f|fì|ccedilpc`fp mi aelig`cmep s lfpiiplt+ Izehy`cethk bcpeth|c`f mih èkì~e miaelig`cme s lfpi+

6+6+ ]ie|ccedilf mi F||bikcyp+ Hcgcf`cekip+

lt+lt+ ]ie|ccedilf mi L|uacutekpimHew|s+lt+0+ ]ie|ccedilf mi Hiwcp

0+ Ivychcl|ce mi cekctf`cethk mih foyf+ekì~e mi ~B+

=+ Jyi|tf mi aelig`cmep s lfpip+=+6+ AElig`cmep s lfpip èkdyofmfp+=+lt+ ihf`cethk ik|i Af s Al+=+0+ aeligh`yhep mi èkìk|f`cekip ik ivychcl|ce(

~B( èkpfkip( o|fme mi mcpe`cf`cethk

lt











0



f|fì|ccedilpc`fp












=









9



Mcpe`cf`cethk

AEligCMEP4




LFPIP4


Idig~he4


EB ‐



Kiy|fhctf`cethk








AEligCMEP4


LFPIP4


2






3


‐ B

B


‐ B





fv h ‐ fv




aelig`cme èkdyofme

6gt




AEligCMEP4



LFPIP4



66







KB0 o

BltE

h KB

=

fv




+

6lt







60





lt BltE h B

0Efv EB ‐ fv


BltElt




6=

Q Wszlig Q W

w 0 A B E EB



ekì~e mi ~B+




~B 7 ‐ heo 6gt ‐ 7

69

0~B heo QB E W








hyioe pc B0E


6




ègykip

6

AEligCME LAEligPCE

6= 6 lt 0 = 2 3 6gt 66 6lt 60 9

Tyge mi

hcgethk i|zitf

Hi`bi

Pfko|i

Foyf gf|








~B ~EB 7 6=


~EB heo QEB W

62










63

Id c c F

ltgt^ lh m





M

ZM

r m



kp

gp G oH lt=gt oH





lt6









fv EB ‐ fv

lt6

ltlt




ltlt

QF ‐W QBW

QBW QF ‐W

QBFW QBFW

AElig`cme jyi|i

QBFW


lt0







~e| he vyi BE0

‐

EB ‐

E0

lt ‐



Bh fv B

fv h ‐

fv ~e| he vyi BE0



lt0

lt=







BF iquest BltE BF

lt=

0

lt

Q W Q WQ W

Q W f

F B E A B E A

BF


A f`cmit

lt9









lt9

lt





mcpe`ci4 BltE0

BltE BE0 ‐ B0E

BE0 ‐ BltE E0

lt ‐ B0E

BE0

‐ iquest B0

E E0

lt ‐ iquest B0


‐



lt

Id h P lc m h m lt





( BltÊ=

‐

(BÊ=lt ‐ s Ê=


‐ B0E



r 7 gt(gtlt6

lt

lt0lt = 0

6

0 =


f B ^ E B E r A G

B Ê r


lt2





s 7 (lt r 6gt ‐ 2 G



t 7 (9 r 6gt ‐ 63 G

lt 2

=Q W (lt 6gtBÊ G

lt2

lt2= 0

lt

lt =



B E B E s s s A G

s B Ê

600 = 0lt lt 2 2

=



B ^ E B E t t t A G

BÊ t

0 63

=Q W (9 6gtÊ G

lt3



Jyi|tf mi lfpip+




L r BltE L

lt3

lt

Q W Q WQ W

Q W l

LB EB A B E A

L A lfpc`cmfm

0gt









0gt

06






fv EB ‐ fv

Q Wgt gt(lt gt gt

∊Q W ‐ r r r



KB0



~B 7 6= ‐ ~EB 7 6= ‐ lt(lt 7 66(lt2

06

0lt







0lt

00





pcokcjc`f vyi4






00

0=





K ‐


A_ 6gt ‐ 6=

Glt


0=

h ceth h 09




Coyfhgiki4



Mi mekmi4

09

l

` A

lt

6

lt0

6 6

Q W Q W

Q W f

F B E ` ` ` A

BF `

f

A

`

l

A

`


0^|elhigf mi













0^|elhigf












02^|elhigf











03







KB= BltE KB0

B0E


03

=gt






$ Idig~he4 KfK



=gt

=6




Idig~he4 Kfh


fke ih Kf


Kf lt BltE KfEB B0E



=lt









=0







pcokcjc`fczf4 KB=

BltE KB0 B0E


==






ège ih




gfse| vyi AfKB=

=9












=












=











=2











=3







9gt




pound Im+ Pfkchhfkf

Id h96






Kf




B0E



Id h

9lt







r 7 B0E


G

~B 7 ‐ heo B0E 7 =(=

C mc m m B99





BCk BltE Ck ‐ B0E








9







Zcehif mi



ede mi

gicheede Fgf|chhe =

]e|kfpeh ede Ftyh 2


9






92




zckfo|i èk KfEB



6lt

6gt2

=

lt

~B

93







lFf ‐



gtPcgyhf`cethk








kiy|fhctf`cethk+


6











aelig`cme 7 6(9 K G

aelig`cme7 K


Zccedilmie


lt







lt ‐ ltFh0 BltE


kBltPE= 7 9 ggeh

























0



f|fì|ccedilpc`fp












=









9



Mcpe`cf`cethk

AEligCMEP4




LFPIP4


Idig~he4


EB ‐



Kiy|fhctf`cethk








AEligCMEP4


LFPIP4


2






3


‐ B

B


‐ B





fv h ‐ fv




aelig`cme èkdyofme

6gt




AEligCMEP4



LFPIP4



66







KB0 o

BltE

h KB

=

fv




+

6lt







60





lt BltE h B

0Efv EB ‐ fv


BltElt




6=

Q Wszlig Q W

w 0 A B E EB



ekì~e mi ~B+




~B 7 ‐ heo 6gt ‐ 7

69

0~B heo QB E W








hyioe pc B0E


6




ègykip

6

AEligCME LAEligPCE

6= 6 lt 0 = 2 3 6gt 66 6lt 60 9

Tyge mi

hcgethk i|zitf

Hi`bi

Pfko|i

Foyf gf|








~B ~EB 7 6=


~EB heo QEB W

62










63

Id c c F

ltgt^ lh m





M

ZM

r m



kp

gp G oH lt=gt oH





lt6









fv EB ‐ fv

lt6

ltlt




ltlt

QF ‐W QBW

QBW QF ‐W

QBFW QBFW

AElig`cme jyi|i

QBFW


lt0







~e| he vyi BE0

‐

EB ‐

E0

lt ‐



Bh fv B

fv h ‐

fv ~e| he vyi BE0



lt0

lt=







BF iquest BltE BF

lt=

0

lt

Q W Q WQ W

Q W f

F B E A B E A

BF


A f`cmit

lt9









lt9

lt





mcpe`ci4 BltE0

BltE BE0 ‐ B0E

BE0 ‐ BltE E0

lt ‐ B0E

BE0

‐ iquest B0

E E0

lt ‐ iquest B0


‐



lt

Id h P lc m h m lt





( BltÊ=

‐

(BÊ=lt ‐ s Ê=


‐ B0E



r 7 gt(gtlt6

lt

lt0lt = 0

6

0 =


f B ^ E B E r A G

B Ê r


lt2





s 7 (lt r 6gt ‐ 2 G



t 7 (9 r 6gt ‐ 63 G

lt 2

=Q W (lt 6gtBÊ G

lt2

lt2= 0

lt

lt =



B E B E s s s A G

s B Ê

600 = 0lt lt 2 2

=



B ^ E B E t t t A G

BÊ t

0 63

=Q W (9 6gtÊ G

lt3



Jyi|tf mi lfpip+




L r BltE L

lt3

lt

Q W Q WQ W

Q W l

LB EB A B E A

L A lfpc`cmfm

0gt









0gt

06






fv EB ‐ fv

Q Wgt gt(lt gt gt

∊Q W ‐ r r r



KB0



~B 7 6= ‐ ~EB 7 6= ‐ lt(lt 7 66(lt2

06

0lt







0lt

00





pcokcjc`f vyi4






00

0=





K ‐


A_ 6gt ‐ 6=

Glt


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69

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G

~B 7 ‐ heo B0E 7 =(=

C mc m m B99





BCk BltE Ck ‐ B0E








9







Zcehif mi



ede mi

gicheede Fgf|chhe =

]e|kfpeh ede Ftyh 2


9






92




zckfo|i èk KfEB



6lt

6gt2

=

lt

~B

93







lFf ‐



gtPcgyhf`cethk








kiy|fhctf`cethk+


6











aelig`cme 7 6(9 K G

aelig`cme7 K


Zccedilmie


lt







lt ‐ ltFh0 BltE


kBltPE= 7 9 ggeh




















3


‐ B

B


‐ B





fv h ‐ fv




aelig`cme èkdyofme

6gt




AEligCMEP4



LFPIP4



66







KB0 o

BltE

h KB

=

fv




+

6lt







60





lt BltE h B

0Efv EB ‐ fv


BltElt




6=

Q Wszlig Q W

w 0 A B E EB



ekì~e mi ~B+




~B 7 ‐ heo 6gt ‐ 7

69

0~B heo QB E W








hyioe pc B0E


6




ègykip

6

AEligCME LAEligPCE

6= 6 lt 0 = 2 3 6gt 66 6lt 60 9

Tyge mi

hcgethk i|zitf

Hi`bi

Pfko|i

Foyf gf|








~B ~EB 7 6=


~EB heo QEB W

62










63

Id c c F

ltgt^ lh m





M

ZM

r m



kp

gp G oH lt=gt oH





lt6









fv EB ‐ fv

lt6

ltlt




ltlt

QF ‐W QBW

QBW QF ‐W

QBFW QBFW

AElig`cme jyi|i

QBFW


lt0







~e| he vyi BE0

‐

EB ‐

E0

lt ‐



Bh fv B

fv h ‐

fv ~e| he vyi BE0



lt0

lt=







BF iquest BltE BF

lt=

0

lt

Q W Q WQ W

Q W f

F B E A B E A

BF


A f`cmit

lt9









lt9

lt





mcpe`ci4 BltE0

BltE BE0 ‐ B0E

BE0 ‐ BltE E0

lt ‐ B0E

BE0

‐ iquest B0

E E0

lt ‐ iquest B0


‐



lt

Id h P lc m h m lt





( BltÊ=

‐

(BÊ=lt ‐ s Ê=


‐ B0E



r 7 gt(gtlt6

lt

lt0lt = 0

6

0 =


f B ^ E B E r A G

B Ê r


lt2





s 7 (lt r 6gt ‐ 2 G



t 7 (9 r 6gt ‐ 63 G

lt 2

=Q W (lt 6gtBÊ G

lt2

lt2= 0

lt

lt =



B E B E s s s A G

s B Ê

600 = 0lt lt 2 2

=



B ^ E B E t t t A G

BÊ t

0 63

=Q W (9 6gtÊ G

lt3



Jyi|tf mi lfpip+




L r BltE L

lt3

lt

Q W Q WQ W

Q W l

LB EB A B E A

L A lfpc`cmfm

0gt









0gt

06






fv EB ‐ fv

Q Wgt gt(lt gt gt

∊Q W ‐ r r r



KB0



~B 7 6= ‐ ~EB 7 6= ‐ lt(lt 7 66(lt2

06

0lt







0lt

00





pcokcjc`f vyi4






00

0=





K ‐


A_ 6gt ‐ 6=

Glt


0=

h ceth h 09




Coyfhgiki4



Mi mekmi4

09

l

` A

lt

6

lt0

6 6

Q W Q W

Q W f

F B E ` ` ` A

BF `

f

A

`

l

A

`


0^|elhigf mi













0^|elhigf












02^|elhigf











03







KB= BltE KB0

B0E


03

=gt






$ Idig~he4 KfK



=gt

=6




Idig~he4 Kfh


fke ih Kf


Kf lt BltE KfEB B0E



=lt









=0







pcokcjc`fczf4 KB=

BltE KB0 B0E


==






ège ih




gfse| vyi AfKB=

=9












=












=











=2











=3







9gt




pound Im+ Pfkchhfkf

Id h96






Kf




B0E



Id h

9lt







r 7 B0E


G

~B 7 ‐ heo B0E 7 =(=

C mc m m B99





BCk BltE Ck ‐ B0E








9







Zcehif mi



ede mi

gicheede Fgf|chhe =

]e|kfpeh ede Ftyh 2


9






92




zckfo|i èk KfEB



6lt

6gt2

=

lt

~B

93







lFf ‐



gtPcgyhf`cethk








kiy|fhctf`cethk+


6











aelig`cme 7 6(9 K G

aelig`cme7 K


Zccedilmie


lt







lt ‐ ltFh0 BltE


kBltPE= 7 9 ggeh



















fv h ‐ fv




aelig`cme èkdyofme

6gt




AEligCMEP4



LFPIP4



66







KB0 o

BltE

h KB

=

fv




+

6lt







60





lt BltE h B

0Efv EB ‐ fv


BltElt




6=

Q Wszlig Q W

w 0 A B E EB



ekì~e mi ~B+




~B 7 ‐ heo 6gt ‐ 7

69

0~B heo QB E W








hyioe pc B0E


6




ègykip

6

AEligCME LAEligPCE

6= 6 lt 0 = 2 3 6gt 66 6lt 60 9

Tyge mi

hcgethk i|zitf

Hi`bi

Pfko|i

Foyf gf|








~B ~EB 7 6=


~EB heo QEB W

62










63

Id c c F

ltgt^ lh m





M

ZM

r m



kp

gp G oH lt=gt oH





lt6









fv EB ‐ fv

lt6

ltlt




ltlt

QF ‐W QBW

QBW QF ‐W

QBFW QBFW

AElig`cme jyi|i

QBFW


lt0







~e| he vyi BE0

‐

EB ‐

E0

lt ‐



Bh fv B

fv h ‐

fv ~e| he vyi BE0



lt0

lt=







BF iquest BltE BF

lt=

0

lt

Q W Q WQ W

Q W f

F B E A B E A

BF


A f`cmit

lt9









lt9

lt





mcpe`ci4 BltE0

BltE BE0 ‐ B0E

BE0 ‐ BltE E0

lt ‐ B0E

BE0

‐ iquest B0

E E0

lt ‐ iquest B0


‐



lt

Id h P lc m h m lt





( BltÊ=

‐

(BÊ=lt ‐ s Ê=


‐ B0E



r 7 gt(gtlt6

lt

lt0lt = 0

6

0 =


f B ^ E B E r A G

B Ê r


lt2





s 7 (lt r 6gt ‐ 2 G



t 7 (9 r 6gt ‐ 63 G

lt 2

=Q W (lt 6gtBÊ G

lt2

lt2= 0

lt

lt =



B E B E s s s A G

s B Ê

600 = 0lt lt 2 2

=



B ^ E B E t t t A G

BÊ t

0 63

=Q W (9 6gtÊ G

lt3



Jyi|tf mi lfpip+




L r BltE L

lt3

lt

Q W Q WQ W

Q W l

LB EB A B E A

L A lfpc`cmfm

0gt









0gt

06






fv EB ‐ fv

Q Wgt gt(lt gt gt

∊Q W ‐ r r r



KB0



~B 7 6= ‐ ~EB 7 6= ‐ lt(lt 7 66(lt2

06

0lt







0lt

00





pcokcjc`f vyi4






00

0=





K ‐


A_ 6gt ‐ 6=

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0=

h ceth h 09




Coyfhgiki4



Mi mekmi4

09

l

` A

lt

6

lt0

6 6

Q W Q W

Q W f

F B E ` ` ` A

BF `

f

A

`

l

A

`


0^|elhigf mi













0^|elhigf












02^|elhigf











03







KB= BltE KB0

B0E


03

=gt






$ Idig~he4 KfK



=gt

=6




Idig~he4 Kfh


fke ih Kf


Kf lt BltE KfEB B0E



=lt









=0







pcokcjc`fczf4 KB=

BltE KB0 B0E


==






ège ih




gfse| vyi AfKB=

=9












=












=











=2











=3







9gt




pound Im+ Pfkchhfkf

Id h96






Kf




B0E



Id h

9lt







r 7 B0E


G

~B 7 ‐ heo B0E 7 =(=

C mc m m B99





BCk BltE Ck ‐ B0E








9







Zcehif mi



ede mi

gicheede Fgf|chhe =

]e|kfpeh ede Ftyh 2


9






92




zckfo|i èk KfEB



6lt

6gt2

=

lt

~B

93







lFf ‐



gtPcgyhf`cethk








kiy|fhctf`cethk+


6











aelig`cme 7 6(9 K G

aelig`cme7 K


Zccedilmie


lt







lt ‐ ltFh0 BltE


kBltPE= 7 9 ggeh


















AEligCMEP4



LFPIP4



66







KB0 o

BltE

h KB

=

fv




+

6lt







60





lt BltE h B

0Efv EB ‐ fv


BltElt




6=

Q Wszlig Q W

w 0 A B E EB



ekì~e mi ~B+




~B 7 ‐ heo 6gt ‐ 7

69

0~B heo QB E W








hyioe pc B0E


6




ègykip

6

AEligCME LAEligPCE

6= 6 lt 0 = 2 3 6gt 66 6lt 60 9

Tyge mi

hcgethk i|zitf

Hi`bi

Pfko|i

Foyf gf|








~B ~EB 7 6=


~EB heo QEB W

62










63

Id c c F

ltgt^ lh m





M

ZM

r m



kp

gp G oH lt=gt oH





lt6









fv EB ‐ fv

lt6

ltlt




ltlt

QF ‐W QBW

QBW QF ‐W

QBFW QBFW

AElig`cme jyi|i

QBFW


lt0







~e| he vyi BE0

‐

EB ‐

E0

lt ‐



Bh fv B

fv h ‐

fv ~e| he vyi BE0



lt0

lt=







BF iquest BltE BF

lt=

0

lt

Q W Q WQ W

Q W f

F B E A B E A

BF


A f`cmit

lt9









lt9

lt





mcpe`ci4 BltE0

BltE BE0 ‐ B0E

BE0 ‐ BltE E0

lt ‐ B0E

BE0

‐ iquest B0

E E0

lt ‐ iquest B0


‐



lt

Id h P lc m h m lt





( BltÊ=

‐

(BÊ=lt ‐ s Ê=


‐ B0E



r 7 gt(gtlt6

lt

lt0lt = 0

6

0 =


f B ^ E B E r A G

B Ê r


lt2





s 7 (lt r 6gt ‐ 2 G



t 7 (9 r 6gt ‐ 63 G

lt 2

=Q W (lt 6gtBÊ G

lt2

lt2= 0

lt

lt =



B E B E s s s A G

s B Ê

600 = 0lt lt 2 2

=



B ^ E B E t t t A G

BÊ t

0 63

=Q W (9 6gtÊ G

lt3



Jyi|tf mi lfpip+




L r BltE L

lt3

lt

Q W Q WQ W

Q W l

LB EB A B E A

L A lfpc`cmfm

0gt









0gt

06






fv EB ‐ fv

Q Wgt gt(lt gt gt

∊Q W ‐ r r r



KB0



~B 7 6= ‐ ~EB 7 6= ‐ lt(lt 7 66(lt2

06

0lt







0lt

00





pcokcjc`f vyi4






00

0=





K ‐


A_ 6gt ‐ 6=

Glt


0=

h ceth h 09




Coyfhgiki4



Mi mekmi4

09

l

` A

lt

6

lt0

6 6

Q W Q W

Q W f

F B E ` ` ` A

BF `

f

A

`

l

A

`


0^|elhigf mi













0^|elhigf












02^|elhigf











03







KB= BltE KB0

B0E


03

=gt






$ Idig~he4 KfK



=gt

=6




Idig~he4 Kfh


fke ih Kf


Kf lt BltE KfEB B0E



=lt









=0







pcokcjc`fczf4 KB=

BltE KB0 B0E


==






ège ih




gfse| vyi AfKB=

=9












=












=











=2











=3







9gt




pound Im+ Pfkchhfkf

Id h96






Kf




B0E



Id h

9lt







r 7 B0E


G

~B 7 ‐ heo B0E 7 =(=

C mc m m B99





BCk BltE Ck ‐ B0E








9







Zcehif mi



ede mi

gicheede Fgf|chhe =

]e|kfpeh ede Ftyh 2


9






92




zckfo|i èk KfEB



6lt

6gt2

=

lt

~B

93







lFf ‐



gtPcgyhf`cethk








kiy|fhctf`cethk+


6











aelig`cme 7 6(9 K G

aelig`cme7 K


Zccedilmie


lt







lt ‐ ltFh0 BltE


kBltPE= 7 9 ggeh





















KB0 o

BltE

h KB

=

fv




+

6lt







60





lt BltE h B

0Efv EB ‐ fv


BltElt




6=

Q Wszlig Q W

w 0 A B E EB



ekì~e mi ~B+




~B 7 ‐ heo 6gt ‐ 7

69

0~B heo QB E W








hyioe pc B0E


6




ègykip

6

AEligCME LAEligPCE

6= 6 lt 0 = 2 3 6gt 66 6lt 60 9

Tyge mi

hcgethk i|zitf

Hi`bi

Pfko|i

Foyf gf|








~B ~EB 7 6=


~EB heo QEB W

62










63

Id c c F

ltgt^ lh m





M

ZM

r m



kp

gp G oH lt=gt oH





lt6









fv EB ‐ fv

lt6

ltlt




ltlt

QF ‐W QBW

QBW QF ‐W

QBFW QBFW

AElig`cme jyi|i

QBFW


lt0







~e| he vyi BE0

‐

EB ‐

E0

lt ‐



Bh fv B

fv h ‐

fv ~e| he vyi BE0



lt0

lt=







BF iquest BltE BF

lt=

0

lt

Q W Q WQ W

Q W f

F B E A B E A

BF


A f`cmit

lt9









lt9

lt





mcpe`ci4 BltE0

BltE BE0 ‐ B0E

BE0 ‐ BltE E0

lt ‐ B0E

BE0

‐ iquest B0

E E0

lt ‐ iquest B0


‐



lt

Id h P lc m h m lt





( BltÊ=

‐

(BÊ=lt ‐ s Ê=


‐ B0E



r 7 gt(gtlt6

lt

lt0lt = 0

6

0 =


f B ^ E B E r A G

B Ê r


lt2





s 7 (lt r 6gt ‐ 2 G



t 7 (9 r 6gt ‐ 63 G

lt 2

=Q W (lt 6gtBÊ G

lt2

lt2= 0

lt

lt =



B E B E s s s A G

s B Ê

600 = 0lt lt 2 2

=



B ^ E B E t t t A G

BÊ t

0 63

=Q W (9 6gtÊ G

lt3



Jyi|tf mi lfpip+




L r BltE L

lt3

lt

Q W Q WQ W

Q W l

LB EB A B E A

L A lfpc`cmfm

0gt









0gt

06






fv EB ‐ fv

Q Wgt gt(lt gt gt

∊Q W ‐ r r r



KB0



~B 7 6= ‐ ~EB 7 6= ‐ lt(lt 7 66(lt2

06

0lt







0lt

00





pcokcjc`f vyi4






00

0=





K ‐


A_ 6gt ‐ 6=

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0=

h ceth h 09




Coyfhgiki4



Mi mekmi4

09

l

` A

lt

6

lt0

6 6

Q W Q W

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F B E ` ` ` A

BF `

f

A

`

l

A

`


0^|elhigf mi













0^|elhigf












02^|elhigf











03







KB= BltE KB0

B0E


03

=gt






$ Idig~he4 KfK



=gt

=6




Idig~he4 Kfh


fke ih Kf


Kf lt BltE KfEB B0E



=lt









=0







pcokcjc`fczf4 KB=

BltE KB0 B0E


==






ège ih




gfse| vyi AfKB=

=9












=












=











=2











=3







9gt




pound Im+ Pfkchhfkf

Id h96






Kf




B0E



Id h

9lt







r 7 B0E


G

~B 7 ‐ heo B0E 7 =(=

C mc m m B99





BCk BltE Ck ‐ B0E








9







Zcehif mi



ede mi

gicheede Fgf|chhe =

]e|kfpeh ede Ftyh 2


9






92




zckfo|i èk KfEB



6lt

6gt2

=

lt

~B

93







lFf ‐



gtPcgyhf`cethk








kiy|fhctf`cethk+


6











aelig`cme 7 6(9 K G

aelig`cme7 K


Zccedilmie


lt







lt ‐ ltFh0 BltE


kBltPE= 7 9 ggeh





















60





lt BltE h B

0Efv EB ‐ fv


BltElt




6=

Q Wszlig Q W

w 0 A B E EB



ekì~e mi ~B+




~B 7 ‐ heo 6gt ‐ 7

69

0~B heo QB E W








hyioe pc B0E


6




ègykip

6

AEligCME LAEligPCE

6= 6 lt 0 = 2 3 6gt 66 6lt 60 9

Tyge mi

hcgethk i|zitf

Hi`bi

Pfko|i

Foyf gf|








~B ~EB 7 6=


~EB heo QEB W

62










63

Id c c F

ltgt^ lh m





M

ZM

r m



kp

gp G oH lt=gt oH





lt6









fv EB ‐ fv

lt6

ltlt




ltlt

QF ‐W QBW

QBW QF ‐W

QBFW QBFW

AElig`cme jyi|i

QBFW


lt0







~e| he vyi BE0

‐

EB ‐

E0

lt ‐



Bh fv B

fv h ‐

fv ~e| he vyi BE0



lt0

lt=







BF iquest BltE BF

lt=

0

lt

Q W Q WQ W

Q W f

F B E A B E A

BF


A f`cmit

lt9









lt9

lt





mcpe`ci4 BltE0

BltE BE0 ‐ B0E

BE0 ‐ BltE E0

lt ‐ B0E

BE0

‐ iquest B0

E E0

lt ‐ iquest B0


‐



lt

Id h P lc m h m lt





( BltÊ=

‐

(BÊ=lt ‐ s Ê=


‐ B0E



r 7 gt(gtlt6

lt

lt0lt = 0

6

0 =


f B ^ E B E r A G

B Ê r


lt2





s 7 (lt r 6gt ‐ 2 G



t 7 (9 r 6gt ‐ 63 G

lt 2

=Q W (lt 6gtBÊ G

lt2

lt2= 0

lt

lt =



B E B E s s s A G

s B Ê

600 = 0lt lt 2 2

=



B ^ E B E t t t A G

BÊ t

0 63

=Q W (9 6gtÊ G

lt3



Jyi|tf mi lfpip+




L r BltE L

lt3

lt

Q W Q WQ W

Q W l

LB EB A B E A

L A lfpc`cmfm

0gt









0gt

06






fv EB ‐ fv

Q Wgt gt(lt gt gt

∊Q W ‐ r r r



KB0



~B 7 6= ‐ ~EB 7 6= ‐ lt(lt 7 66(lt2

06

0lt







0lt

00





pcokcjc`f vyi4






00

0=





K ‐


A_ 6gt ‐ 6=

Glt


0=

h ceth h 09




Coyfhgiki4



Mi mekmi4

09

l

` A

lt

6

lt0

6 6

Q W Q W

Q W f

F B E ` ` ` A

BF `

f

A

`

l

A

`


0^|elhigf mi













0^|elhigf












02^|elhigf











03







KB= BltE KB0

B0E


03

=gt






$ Idig~he4 KfK



=gt

=6




Idig~he4 Kfh


fke ih Kf


Kf lt BltE KfEB B0E



=lt









=0







pcokcjc`fczf4 KB=

BltE KB0 B0E


==






ège ih




gfse| vyi AfKB=

=9












=












=











=2











=3







9gt




pound Im+ Pfkchhfkf

Id h96






Kf




B0E



Id h

9lt







r 7 B0E


G

~B 7 ‐ heo B0E 7 =(=

C mc m m B99





BCk BltE Ck ‐ B0E








9







Zcehif mi



ede mi

gicheede Fgf|chhe =

]e|kfpeh ede Ftyh 2


9






92




zckfo|i èk KfEB



6lt

6gt2

=

lt

~B

93







lFf ‐



gtPcgyhf`cethk








kiy|fhctf`cethk+


6











aelig`cme 7 6(9 K G

aelig`cme7 K


Zccedilmie


lt







lt ‐ ltFh0 BltE


kBltPE= 7 9 ggeh



















lt BltE h B

0Efv EB ‐ fv


BltElt




6=

Q Wszlig Q W

w 0 A B E EB



ekì~e mi ~B+




~B 7 ‐ heo 6gt ‐ 7

69

0~B heo QB E W








hyioe pc B0E


6




ègykip

6

AEligCME LAEligPCE

6= 6 lt 0 = 2 3 6gt 66 6lt 60 9

Tyge mi

hcgethk i|zitf

Hi`bi

Pfko|i

Foyf gf|








~B ~EB 7 6=


~EB heo QEB W

62










63

Id c c F

ltgt^ lh m





M

ZM

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kp

gp G oH lt=gt oH





lt6









fv EB ‐ fv

lt6

ltlt




ltlt

QF ‐W QBW

QBW QF ‐W

QBFW QBFW

AElig`cme jyi|i

QBFW


lt0







~e| he vyi BE0

‐

EB ‐

E0

lt ‐



Bh fv B

fv h ‐

fv ~e| he vyi BE0



lt0

lt=







BF iquest BltE BF

lt=

0

lt

Q W Q WQ W

Q W f

F B E A B E A

BF


A f`cmit

lt9









lt9

lt





mcpe`ci4 BltE0

BltE BE0 ‐ B0E

BE0 ‐ BltE E0

lt ‐ B0E

BE0

‐ iquest B0

E E0

lt ‐ iquest B0


‐



lt

Id h P lc m h m lt





( BltÊ=

‐

(BÊ=lt ‐ s Ê=


‐ B0E



r 7 gt(gtlt6

lt

lt0lt = 0

6

0 =


f B ^ E B E r A G

B Ê r


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s 7 (lt r 6gt ‐ 2 G



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=



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lt3



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06

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pcokcjc`f vyi4






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l

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KB= BltE KB0

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$ Idig~he4 KfK



=gt

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Idig~he4 Kfh


fke ih Kf


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=0







pcokcjc`fczf4 KB=

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==






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9gt




pound Im+ Pfkchhfkf

Id h96






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Id h

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C mc m m B99





BCk BltE Ck ‐ B0E








9







Zcehif mi



ede mi

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9






92




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6











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ekì~e mi ~B+




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69

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6




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fv EB ‐ fv

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‐

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BF iquest BltE BF

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0

lt

Q W Q WQ W

Q W f

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BF


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lt9

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mcpe`ci4 BltE0

BltE BE0 ‐ B0E

BE0 ‐ BltE E0

lt ‐ B0E

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‐



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( BltÊ=

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6

0 =


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KB= BltE KB0

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==






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pound Im+ Pfkchhfkf

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9






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BF iquest BltE BF

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0

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lt9

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mcpe`ci4 BltE0

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‐ iquest B0

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‐



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Id h P lc m h m lt





( BltÊ=

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6

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KB= BltE KB0

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pound Im+ Pfkchhfkf

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9







Zcehif mi



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BF iquest BltE BF

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0

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Q W Q WQ W

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BF


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lt9

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mcpe`ci4 BltE0

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BE0 ‐ BltE E0

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‐



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( BltÊ=

‐

(BÊ=lt ‐ s Ê=


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6

0 =


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s 7 (lt r 6gt ‐ 2 G



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=



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==






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pound Im+ Pfkchhfkf

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BCk BltE Ck ‐ B0E








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9






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BF iquest BltE BF

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0

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Q W Q WQ W

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BF


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lt9

lt





mcpe`ci4 BltE0

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BE0 ‐ BltE E0

lt ‐ B0E

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‐



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Id h P lc m h m lt





( BltÊ=

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lt

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6

0 =


f B ^ E B E r A G

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s 7 (lt r 6gt ‐ 2 G



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=



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pound Im+ Pfkchhfkf

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63

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0

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6

0 =


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s 7 (lt r 6gt ‐ 2 G



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0 63

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pound Im+ Pfkchhfkf

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s 7 (lt r 6gt ‐ 2 G



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fv EB ‐ fv

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BF iquest BltE BF

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pound Im+ Pfkchhfkf

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lt







lt ‐ ltFh0 BltE


kBltPE= 7 9 ggeh


























=












=











=2











=3







9gt




pound Im+ Pfkchhfkf

Id h96






Kf




B0E



Id h

9lt







r 7 B0E


G

~B 7 ‐ heo B0E 7 =(=

C mc m m B99





BCk BltE Ck ‐ B0E








9







Zcehif mi



ede mi

gicheede Fgf|chhe =

]e|kfpeh ede Ftyh 2


9






92




zckfo|i èk KfEB



6lt

6gt2

=

lt

~B

93







lFf ‐



gtPcgyhf`cethk








kiy|fhctf`cethk+


6











aelig`cme 7 6(9 K G

aelig`cme7 K


Zccedilmie


lt







lt ‐ ltFh0 BltE


kBltPE= 7 9 ggeh


























=











=2











=3







9gt




pound Im+ Pfkchhfkf

Id h96






Kf




B0E



Id h

9lt







r 7 B0E


G

~B 7 ‐ heo B0E 7 =(=

C mc m m B99





BCk BltE Ck ‐ B0E








9







Zcehif mi



ede mi

gicheede Fgf|chhe =

]e|kfpeh ede Ftyh 2


9






92




zckfo|i èk KfEB



6lt

6gt2

=

lt

~B

93







lFf ‐



gtPcgyhf`cethk








kiy|fhctf`cethk+


6











aelig`cme 7 6(9 K G

aelig`cme7 K


Zccedilmie


lt







lt ‐ ltFh0 BltE


kBltPE= 7 9 ggeh
























=2











=3







9gt




pound Im+ Pfkchhfkf

Id h96






Kf




B0E



Id h

9lt







r 7 B0E


G

~B 7 ‐ heo B0E 7 =(=

C mc m m B99





BCk BltE Ck ‐ B0E








9







Zcehif mi



ede mi

gicheede Fgf|chhe =

]e|kfpeh ede Ftyh 2


9






92




zckfo|i èk KfEB



6lt

6gt2

=

lt

~B

93







lFf ‐



gtPcgyhf`cethk








kiy|fhctf`cethk+


6











aelig`cme 7 6(9 K G

aelig`cme7 K


Zccedilmie


lt







lt ‐ ltFh0 BltE


kBltPE= 7 9 ggeh
























=3







9gt




pound Im+ Pfkchhfkf

Id h96






Kf




B0E



Id h

9lt







r 7 B0E


G

~B 7 ‐ heo B0E 7 =(=

C mc m m B99





BCk BltE Ck ‐ B0E








9







Zcehif mi



ede mi

gicheede Fgf|chhe =

]e|kfpeh ede Ftyh 2


9






92




zckfo|i èk KfEB



6lt

6gt2

=

lt

~B

93







lFf ‐



gtPcgyhf`cethk








kiy|fhctf`cethk+


6











aelig`cme 7 6(9 K G

aelig`cme7 K


Zccedilmie


lt







lt ‐ ltFh0 BltE


kBltPE= 7 9 ggeh





















9gt




pound Im+ Pfkchhfkf

Id h96






Kf




B0E



Id h

9lt







r 7 B0E


G

~B 7 ‐ heo B0E 7 =(=

C mc m m B99





BCk BltE Ck ‐ B0E








9







Zcehif mi



ede mi

gicheede Fgf|chhe =

]e|kfpeh ede Ftyh 2


9






92




zckfo|i èk KfEB



6lt

6gt2

=

lt

~B

93







lFf ‐



gtPcgyhf`cethk








kiy|fhctf`cethk+


6











aelig`cme 7 6(9 K G

aelig`cme7 K


Zccedilmie


lt







lt ‐ ltFh0 BltE


kBltPE= 7 9 ggeh


















pound Im+ Pfkchhfkf

Id h96






Kf




B0E



Id h

9lt







r 7 B0E


G

~B 7 ‐ heo B0E 7 =(=

C mc m m B99





BCk BltE Ck ‐ B0E








9







Zcehif mi



ede mi

gicheede Fgf|chhe =

]e|kfpeh ede Ftyh 2


9






92




zckfo|i èk KfEB



6lt

6gt2

=

lt

~B

93







lFf ‐



gtPcgyhf`cethk








kiy|fhctf`cethk+


6











aelig`cme 7 6(9 K G

aelig`cme7 K


Zccedilmie


lt







lt ‐ ltFh0 BltE


kBltPE= 7 9 ggeh




















Kf




B0E



Id h

9lt







r 7 B0E


G

~B 7 ‐ heo B0E 7 =(=

C mc m m B99





BCk BltE Ck ‐ B0E








9







Zcehif mi



ede mi

gicheede Fgf|chhe =

]e|kfpeh ede Ftyh 2


9






92




zckfo|i èk KfEB



6lt

6gt2

=

lt

~B

93







lFf ‐



gtPcgyhf`cethk








kiy|fhctf`cethk+


6











aelig`cme 7 6(9 K G

aelig`cme7 K


Zccedilmie


lt







lt ‐ ltFh0 BltE


kBltPE= 7 9 ggeh





















r 7 B0E


G

~B 7 ‐ heo B0E 7 =(=

C mc m m B99





BCk BltE Ck ‐ B0E








9







Zcehif mi



ede mi

gicheede Fgf|chhe =

]e|kfpeh ede Ftyh 2


9






92




zckfo|i èk KfEB



6lt

6gt2

=

lt

~B

93







lFf ‐



gtPcgyhf`cethk








kiy|fhctf`cethk+


6











aelig`cme 7 6(9 K G

aelig`cme7 K


Zccedilmie


lt







lt ‐ ltFh0 BltE


kBltPE= 7 9 ggeh



















BCk BltE Ck ‐ B0E








9







Zcehif mi



ede mi

gicheede Fgf|chhe =

]e|kfpeh ede Ftyh 2


9






92




zckfo|i èk KfEB



6lt

6gt2

=

lt

~B

93







lFf ‐



gtPcgyhf`cethk








kiy|fhctf`cethk+


6











aelig`cme 7 6(9 K G

aelig`cme7 K


Zccedilmie


lt







lt ‐ ltFh0 BltE


kBltPE= 7 9 ggeh





















Zcehif mi



ede mi

gicheede Fgf|chhe =

]e|kfpeh ede Ftyh 2


9






92




zckfo|i èk KfEB



6lt

6gt2

=

lt

~B

93







lFf ‐



gtPcgyhf`cethk








kiy|fhctf`cethk+


6











aelig`cme 7 6(9 K G

aelig`cme7 K


Zccedilmie


lt







lt ‐ ltFh0 BltE


kBltPE= 7 9 ggeh




















92




zckfo|i èk KfEB



6lt

6gt2

=

lt

~B

93







lFf ‐



gtPcgyhf`cethk








kiy|fhctf`cethk+


6











aelig`cme 7 6(9 K G

aelig`cme7 K


Zccedilmie


lt







lt ‐ ltFh0 BltE


kBltPE= 7 9 ggeh


















zckfo|i èk KfEB



6lt

6gt2

=

lt

~B

93







lFf ‐



gtPcgyhf`cethk








kiy|fhctf`cethk+


6











aelig`cme 7 6(9 K G

aelig`cme7 K


Zccedilmie


lt







lt ‐ ltFh0 BltE


kBltPE= 7 9 ggeh





















lFf ‐



gtPcgyhf`cethk








kiy|fhctf`cethk+


6











aelig`cme 7 6(9 K G

aelig`cme7 K


Zccedilmie


lt







lt ‐ ltFh0 BltE


kBltPE= 7 9 ggeh






















kiy|fhctf`cethk+


6











aelig`cme 7 6(9 K G

aelig`cme7 K


Zccedilmie


lt







lt ‐ ltFh0 BltE


kBltPE= 7 9 ggeh

























aelig`cme 7 6(9 K G

aelig`cme7 K


Zccedilmie


lt







lt ‐ ltFh0 BltE


kBltPE= 7 9 ggeh





















lt ‐ ltFh0 BltE


kBltPE= 7 9 ggeh


























Documents

Eq Acido Base 1