final project advanced mechanics of materials course

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9+3+ Bcrdc`fkbs gb btr j`iy`f+ Qy`kc`q`f gb jfs wydidhfs ~`ywrdjbs+ + + + + + + + + 41

9+3+4+ Bcrdc`fkbs gb btr`j iy`f bk w·bym`kf gb jfs gbsqjdxdm`bkwfs+ + + + + 47

9+7+ Mfgbj`xdc` ·fk qfy bjbmbkwfs fflk`wfs+ + + + + + + + + + + + + + + + + + + + + + + 42

9+7+4+ Nfymrjdc`·fk g·bi`j+ M·bwfgf gb jfs ybs`grfs qfkgbydgfs+ + + + + + + 42

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2



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u

pu4

u9

ε

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u9

u3

=

cfs ε s`k ε 1∙ s`k ε cfs ε 1

1 1 4

upx

= _J]

upx

%9+4)

@kwyfgrc`mfs bj wbksfy gb wbks`fkbs _σ]Q

bk cffygbkdgds gbj qyfijbmd* p _σ]M

bk cffy-gbkdgds mdwby`djbs*

_σ]Q =

σuu σup σux

σup σpp σpx

σux σpx σxx

? _σ]M =

σ44 σ49 σ43

σ49 σ99 σ93

σ43 σ93 σ33

%9+9)

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>



9+4 Bcrdc`· fk cfksw`wrw`~d gb rkd j · dm`kd

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_]Q = _J]W _]M _J] ? _]M = _J] _]Q _J]W %9+3)

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σ99

σ49

=

T44 T49 1T49 T99 1

1 1 T>>

β4β9β>

%9+7)

σ43

σ93

=

T77 1

1 T22

β7β2

gfkgb sb edk rw`j`xdgf jds gbfflk`c`fkbs

β4 = β44 ? β9 = β99 ? β7 = 9β93 ? β2 = 9β43 ? β> = 9β49

p gfkgb T`h sb gbkfm`kdk cfbfflc`bkwbs gb y`l`gbx ybgrc`gd gb wbks`· fk qjdkd p sb bkcrbkwydkgdgfs qfy*

T44 =B 4

4 ∙ ν 49ν 94? T49 = ν 49B 9

4∙ν 49ν 94? T99 =

B 94 ∙ ν 49ν 94

T>> = L49 ? T77 = L93 ? T22 = L43 %9+2)

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ν h 8 gbnfymdc`·fk bk jd g`ybcc`·fk `gbi`gd d rkd gbnfymdc`·fk rk`wdy`d bk jd g`ybcc`·fk h

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σuu

σpp

σup

=

¦T44¦T49

¦T4>¦T49

¦T99¦T9>

¦T4>¦T9>

¦T>>

βuuβppγ up

σpx

σux = ¦T77

¦T72

¦T72 ¦T22 γ px

γ ux %9+>)

gfkgb sb edk rw`j`xdgf jds gbfflk`c`fkbs*

γ px = 9βpx ? γ ux = 9βux ? γ up = 9βup

<



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p gfkgb ¦T`h sfk jfs cfbfflc`bkwbs gb y`l`gbx wbks`·fk qjdkd ybgrc`gd wydksnfymdgfs dcffygbkdgds gbj qyfijbmd* p sb bkcrbkwydk gdgfs qfy*

¦T44 = T44 cfs7 ε / 9%T49 / 9T>>)s`k9 ε cfs9 ε / T99 s`k7 ε %9+<d)

¦T49 = %T44 / T99 ∙ 7T>>)s`k9 ε cfs9 ε / T49%s`k7 ε / cfs7 ε) %9+<i)

¦T99 = T44 s`k7 ε / 9%T49 / 9T>>)s`k9 ε cfs9 ε / T99 cfs7 ε %9+<c)¦T4> = %T44 ∙ T49 ∙ 9T>>)s`k ε cfs3 ε / %T44 ∙ T49 / 9T>>)s`k3 ε cfs ε %9+<g)

¦T9> = %T44 ∙ T49 ∙ 9T>>)s`k3 ε cfs ε / %T44 ∙ T49 / 9T>>)s`k ε cfs3 ε %9+<b)

¦T>> = %T44 / T99 ∙ 9T49 ∙ 9T>>)s`k9 ε cfs9 ε / T>>%s`k7 ε / cfs7 ε) %9+<n)

¦T77 = T77 cfs9 ε / T22 s`k9 ε %9+<l)¦T72 = %T22 ∙ T77)s`k ε cfs ε %9+<e)

¦T22 = T22 cfs9 ε / T77 s`k9 ε %9+<`)

9+9+ Jd wbfy·Ĵd gb cfywb gb qy`mby fygbk qdyd qjdcds jdm`kdgds+

9+9+4+ Ybjdc`fkbs c`kbm·dw`cds+

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up

x

N`lryd 9+98 Gbfflk`c`·fk gbj s`swbmd gb cffygbkdgds gbj qyfijbmd+

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5



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e

9

e

9

x4x9

xo/4xo

o

u

x

4

9

N`lryd 9+38 Krmbydc`·fk gb jd sbcrbkc`d gb j ·dm`kds+

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• Jds j·dm`kds sb bkcrbkwydk qbynbcwdmbkwb rk`gds bkwyb s·Ĵ m`smds+

• Bj mdwby`dj gb cdgd j ·dm`kd bs bj·dsw`cf j`kbdj p fywfwy·fq`cf+

• Cdgd j ·dm`kd bs gb bsqbsfy rk`nfymb+

• Gbsqjdxdm`bkwfs wydks~bysdjbs sfk `kgbqbkg`bkwbs gb jd cffygbkdgd x

• Jd wbks` ·fk qbyqbkg`crjdy dj qjdkf mbg`f bs krjd σxx = 1

• Jfs gbsqjdxdm`bkwfs p gbnfymdc`fkbs sfk qbtrbkfs+

Bswds e`q·fwbs`s cf`kc`gbk cfk jd wbfy·Ĵd gb qjdcds gb Yb`skby–M`kgj`k _4]* trb bk fqfs`c`·fk

d jd wbfy·Ĵd gb qjdcds gb O`ycefnn %f gb qjdcds gbjldgds)* kf gbsqybc`d jds wbks`fkbs gb cfywbwydks~bysdjbs dj qjdkf mbg`f gb jd qjdcd+

Cfks`gbydkgf jds e`q·fwbs`s bkrkc`dgds bj cdmqf gb gbsqjdxdm`bkwf gb jd wbfy·Ĵd gbqy`mby fygbk qrbgb bscy`i`ysb cfmf*

r%u*p *x *w) = r1%u*p*w) / xώu%u*p*w) %9+5d)

~%u*p *x *w) = ~1%u*p*w) / xώp%u*p*w) %9+5i)

|%u*p *x *w) = |%u*p*w) %9+5c)

gfkgb %r*~*|) sfk jfs gbsqjdxdm`bkwfs sbl ·rk jds g`ybcc`fkbs %u*p*x) ybsqbcw`~dmbkwb*

p gfkgb

ώu =∉r

∉x* ώp =

∉~

∉x%9+0)

sfk jds yfwdc`fkbs gb rkd j·Ĵkbd wydks~bysdj kfymdj d jd qjdcd djybgbgfy gb jfs bhbs p –p– uybsqbcw`~dmbkwb+ Jds nrkc`fkbs %r1* ~1* | * ώu* ώp) sfk jfs lydgfs gb j`ibywdg d gbwbm`kdygbj qyfijbmd+

0



9+3 Bcrdc`fkbs gb btr`jìy`f+ Qy kc`q`f gb jfs wydidhfs ~`ywrdjbs+

Idhf jd e`q·fwbs`s gb qbtrbkds gbnfymdc`fkbs* jd ybjdc`·fk bkwyb bj cdmqf gb gbsqjdxd-m`bkwfs p bj cdmqf gb gbnfymdc`fkbs sb bkcrbkwyd gdgd qfy*

βuu =∉r

∉u/

4

9

∉|

∉u

9

%9+41d)

βpp =∉~

∉p/

4

9

∉|

∉p

9

%9+41i)

γ up =

∉r

∉p/

∉~

∉u/

∉|

∉u

∉|

∉p

%9+41c)

γ ux =

∉r

∉x/

∉|

∉u

%9+41g)

γ px =

∉~

∉x/

∉|

∉p

%9+41b)

βxx =∉|

∉x%9+41n)

Jfsw·bym`kfs mdycdgfs cfk rkd j·Ĵkbd* sfk jdsgbnfymdc`fkbs kf j`kbdjbs gb ~fk O· dymdk+ Bswfsw·bym`kfs sfk gbsqybc`dijbs bk jd wbfy·Ĵd j`kbdj qdyd jd cr ·dj bs qfsìjb fiwbkby sfjrc`fkbsdkdj·Ĵw`cds bk rk dmqj`f k ·rmbyf gb cdsfs+ Dj `kcjr`y bswfs w·bym`kfs* ybsrjwd qy·dcw`cdmbkwb`mqfsìjb jd fiwbkc`·fk gb sfjrc`fkbs dkdj·Ĵw`cds* qfy jf trb bs `kg`sqbksdijb ybcryy`y d sf-jrc`fkbs dqyfu`mdgds mbg`dkwb m·bwfgfs krm·by`cfs* wdj cfmf bj m·bwfgf gb jfs bjbmbkwfsfflk`wfs rw`j`xdgf bk bswb wydidhf+

@kwyfgrc`bkgf bj cdmqf gb gbsqjdxdm`bkwfs %9+5) bk %9+41) sb jjbld d jd buqybs`·fk gb jfsw·bym`kfs gbj wbksfy gb gbnfymdc`fkbs bk cffygbkdgds gbj qyfijbmd*

βuuβppγ pxγ uxγ up

=

∉ r1∉u / 4

9 ∉ |1∉u

9

∉ ~1∉p / 4

9∉ |1

∉p9

∉ |1∉p / ώp

∉ |1∉u / ώu

∉ r1∉p / ∉ ~1

∉u / ∉ |1∉u

∉ |1∉p

/ x

∉ ώu

∉u∉ ώp

∉u11

∉ ώu

∉p /∉ ώp

∉u

=

β%1)uu

β%1)pp

γ %1)px

γ %1)ux

γ %1)up

/ x

β%4)uu

β%4)pp

γ %4)px

γ %4)ux

γ %4)up

%9+44)

9+3+ Bcrdc`fkbs gb btr`j iy`f+ Qy`kc`q`f gb jfs wydidhfs ~`ywrdjbs+

Cfks`g·bybsb rkd qjdcd crpd srqbyfflc`b mbg`d gbfflkb rk gfm`k`f di`bywf p dcfwdgf ℮ bkbj qjdkf u

∙p* crpf cfkwfykf sb gbfflkb qfy jd cry~d Γ+

Cfks`gbyb trb jd qjdcd sb bkcrbkwyd sfmbw`gd d rk cdmqf gb wbks`fkbs gb cfkwfykf%σˎkk* σˎks* σˎkx) p d rkd cdyld wydks~bysdj t%u* p) wdj cfmf sb mrbswyd bk jd N`lryd 9+7+ %k* s)bs rk s`swbmd gb cffygbkdgds gbfflk`gf qfy jd g`ybcc ·fk kfymdj k p jd g`ybcc` ·fk wdklbkc`djs dj cfkwfykf+

Jds bcrdc fkbs gb btr`jìy`f sb bkcrbkwydk dqj cdkgf bj qy`kc`q`f gb jfs wydidhfs ~`ywrd-jbs* bj crdj gbwbym`kd trb gb wfgfs jfs cdmqfs gb gbsqjdxdm`bkwfs qfsìjbs* bj ·rk`cf trb

41




sdw`sndcb jd cfkg`c`·fk gb btr`j iy`f bsw ·dw`cf bs dtrbj qdyd bj crdj sb crmqjb jd ybjdc`·fk*

η%R / ^ ) = 1

gfkgb R bs jd bkbyl·Ĵd bj·dsw`cd qfwbkc`dj* p ^ bs bj wydidhf ~`ywrdj ybdj`xdgf qfy wfgds jdsnrbyxds buwbykds+

t%u* p)

σˎkkσˎks

σˎkx

℮

Γp

u

x

N`lryd 9+78 Gbfflk`c`·fk gbj gfm`k`f gbj qyfijbmd p cdmqf gb wbks`fkbs buwbykf+

Jd ~dy`dc`·fk gb jd bkbyl·Ĵd qfwbkc`dj bj·dsw`cd p bj wydidhf ~`ywrdj gb jds nrbyxds buwbykdssb bkcrbkwydk gdgfs qfy jds buqybs`fkbs*

ηR =

℮

e&9 ∙e&9

σuu

ηβ%1)uu / xηβ%4)uu

/ σpp

ηβ%1)pp / xηβ%4)pp

gx

gugp

/ ℮

e&9

∙e&9

σup ηγ %1)

up / xγ %4)

up / σuxηγ %1)

ux / σpxηγ %1)

px gx gugp

%9+49)

η^ = ∙ ℮

tη|1 gugp ∙ Γ

e&9 ∙e&9

_σˎkk %ηrk / xηώk) / σˎks %ηrs / xηώs) / σˎkxη|1]gxgs %9+43)

s`bkgf rk

rs

=

ku kp

∙kp ku

r1

~1

ώk

ώs = ku kp

∙kp ku ώu

ώp %9+47)

p gfkgb k = {ku* kp} bs bj ~bysfy kfymdj sdj`bkwb gbj cfkwfykf Γ+ Bj s·Ĵmifjf % ) `kg`cdbj cdmqf gb wbks`fkbs dqj`cdgf sfiyb jd qjdcd bk nfymd buwbykd+

Cfmf jfs wbksfybs gb gbsqjdxdm`bkwfsβ%1)

pβ%4)

sfk `kgbqbkg`bkwbs gb x* qrb-gbk sby buwyd·Ĵgfs nrbyd gb jd `kwblydj d jf jdylf gbj bsqbsfy bk %9+49) p %9+43)* p qfy jf wdkwfjd buqybs`·fk gbj qy`kc`q`f gb wydidhfs ~`ywrdjbs qrbgb sby bscy`wd cfmf*

44




1 =

℮

_K uuηβ%1)uu / M uuηβ%4)uu / K pp ηβ%1)pp / M pp ηβ%4)pp / K upηγ %1)up

/M upγ %4)up / Tuηγ %1)ux / Tp ηγ %1)px

∙t]gugp %9+42)

∙ Γ

Kˎ kkηrk / Mˎ kkηώk / Kˎ ksηrs / Mˎ ksηώs / Tˎkη|1

gs

gfkgb* K uuK ppK up

=

e&9 ∙e&9

σuu

σpp

σup

gx *

M uuM ppM up

=

e&9 ∙e&9

σuu

σpp

σup

x gx %9+4>)

Tp

Tu = θ

e&9

∙e&9σpx

σux x gx

Jds cdkw`gdgbs %K uu* K pp* K up) sfk jds nrbyxds qjdkdybs ybsrjwdkwbs* %M uu* M pp* M up) sfkjfs mfmbkwfs ybsrjwdkwbs* p %Tu* Tp ) sfk jds nrbyxds wydks~bysdjbs ybsrjwdkwbs* wdj cfmfsb mrbswydk bk jd N`lryd 9+2

K k

Tk

Tu

M uu

K uu

K up

K up

M ppTp

K k

K pp u

p

xM kM s

N`lryd 9+28 G`dlydmd gb nrbyxds p mfmbkwfs ybsrjwdkwbs sfiyb rk bjbmbkwf gb qjdcd+

Bj cfbfflc`bkwb θ trb dqdybcb bk jds buqybs`fkbs gb jds nrbyxds wydks~bysdjbs sb `kwyfgr-cb cfk bj fflk gb cfks`gbydy bj ebcef gb trb bk bj bswdgf gb wbks`fkbs ybdj* jds wbks`fkbswydks~bysdjbs sb dkrjdk bk x = é

9 + Jd wbfy·Ĵd gb qy`mby fygbk dj srqfkby rk bswdgf gbwbks`fkbs wydks~bysdj cfkswdkwb d jf jdylf gbj bsqbsfy iy`kgd rk ~djfy mdpfy trb bj ybdjqdyd jd bkbyl·Ĵd qfwbkc`dj bj ·dsw`cd qfy gbnfymdc`·fk gb cfywb wydks~bysdj+ Rsrdjmbkwb sbcfks`gbyd trb jd g`swyìrc`·fk gb wbks`fkbs wydks~bysdjbs ybsqfkgb dj mbkfs d rk qfj`kf-m`f gb sblrkgf lydgf* p qfy jf wdkwf gb djj·Ĵ sb gbgrcb trb bj cfbfflc`bkwb gb cfyybcc`·fkwfmd bj ~djfy gb θ = 2&>

@kwblydkgf qfy qdywbs jd bcrdc`·fk %9+42)* qdyd buqj·Ĵc`wdy jfs gbsqjdxdm`bkwfs ~`ywrdjbsgb jfs lydgfs gb jìbywdg gbj qyfijbmd %ηr1* η~1* η|1* ηώu* ηώp )* qbym`wb fflkdjmbkwb fiwb-

49




kby jd buqybs`·fk*

1 =

℮

∙

∉K uu∉u

/∉K up

∉p

ηr1 ∙

∉K up

∉u/

∉K pp∉p

η~1 ∙

∉M uu

∉u/

∉M up∉p

∙ Tu

ηώu

gugp

∙ ℮∉M up

∉u/

∉M pp

∉p ∙T

p ηώp

/ ∉Tu

∉u/

∉Tp

∉p/ K

%|1

) / t η|1gugp %9+4<)

/

Γ

K kk ∙ Kˎ kk

ηrk /

K ks ∙ Kˎ ks

ηrs /

Tk ∙ Tˎk

η|1

gs

/

Γ

M kk ∙ Mˎ kk

ηώk /

M ks ∙ Mˎ ks

ηώs

gs

gfkgb*

K k = K uuku / K upkp ? K s = K upku / K ppkp

M k = M uuku / M upkp ? M s = M upku / M ppkp

Tk =

Tu / K uu∉|1

∉u/ K up

∉|1

∉p

ku /

Tp / K up

∉|1

∉u/ K pp

∉|1

∉p

ku

Gb bswd nfymd* cfmf jfs gbsqjdxdm`bkwfs ~`ywrdjbs sfk dyi`wydy`fs bk bj gfm`k`f* edc`bk-gf cdgd buqybs`·fk bkwyb qdy·bkwbs`s gb jd qy`mby `kwblydj `g·bkw`cdmbkwb krjd* sb fiw`bkbbj s`swbmd gb bcrdc`fkbs gb btr`j`iy`f bk bj gfm`k`f+ Jd cfkg`c`·fk gb krj`gdg gb jfsw·bym`kfs gb jd `kwblydj sfiyb bj cfkwfykf* iy`kgd jds cfkg`c`fkbs bsbkc`djbs p kdwrydjbsgbj qyfijbmd+

Bcrdc`fkbs gb btr`j`iy`f bk ℮

ηr1 8∉K uu

∉u/

∉K up∉p

= 1 %9+45d)

η~1 8∉K up

∉u/

∉K pp∉p

= 1 %9+45i)

η|1 8∉Tu

∉u/

∉Tp

∉p/ K %|1) / t = 1 %9+45c)

ηώu 8∉M uu

∉u/

∉M up∉p

∙ Tu = 1 %9+45g)

ηώp 8∉M up

∉u/

∉M pp∉p

∙ Tp = 1 %9+45b)

Cfkg`c`fkbs gb ifygb bk Γ

Kdwrydjbs 8 rk* rs* |1* ώk* ώs %9+40d)

Bsbkc`djbs 8 K k* K s* Tk* M k* M s %9+40i)

gfkgb*

K %|1) =∉

∉u

K uu

∉|1

∉u/ K up

∉|1

∉p

/

∉

∉p

K up

∉|1

∉u/ K pp

∉|1

∉p

%9+91)

43




9+3+4+ Bcrdc`fkbs gb btr jìy`f bk w·bym`kf gb jfs gbsqjdxdm`bkwfs+

Bs ·rw`j defyd fiwbkby rkd buqybs`·fk gb jds bcrdc`fkbs gb btr`jìy`f bk bj trb sb bkcrbk-wybk qybsbkwbsbk nfymd buq·Ĵc wd jds nrkc`fkbs gbj cdmqf gb gbsqjdxdm`bkwfs %r1* ~1* |1* ώu* ώp)

Rw`j`xdkgf jd buqybs`·fk gbj wbksfy gb gbnfymdc`fkbs %9+44)* jd ybjdc`·fk cfksw`wrw`~d %9+>)

b `kwyfgrc`bkgf bswds bk %9+4>) bs qfsìjb fiwbkby*

K uuK ppK up

=

D44 D49 D4>

D49 D99 D9>

D4> D9> D>>

∉ r1∉u / 4

9

∉ |1∉u

9∉ ~1∉u / 4

9

∉ |1∉u

9∉ r1∉p / ∉ ~1

∉u / ∉ |1∉u

∉ |1∉p

%9+94)

/

I44 I49 I4>

I49 I99 I9>

I4> I9> I>>

∉ ώu

∉u∉ ώp

∉p∉ ώu

∉p /∉ ώp

∉u

M uuM ppM up

=

I44 I49 I4>

I49 I99 I9>

I4> I9> I>>

∉ r1∉u / 4

9

∉ |1∉u

9∉ ~1∉u / 4

9

∉ |1∉u

9∉ r1∉p / ∉ ~1

∉u / ∉ |1∉u

∉ |1∉p

%9+99)

/

G44 G49 G4>

G49 G99 G9>

G4> G9> G>>

∉ ώu

∉u∉ ώp

∉p∉ ώu

∉p /∉ ώp

∉u

Tp

Tu = θ D77 D72

D72 D22 ∉ |1∉p / ώp

∉ |1∉u / ώu %9+93)

gfkgb jfs cfbfflc`bkwbs D`h* I`h* G`h sb bkcrbkwydk gdgfs qfy*

D`h =K

o=4

T%o)`h %xo/4 ∙ xo) %9+97d)

I`h =4

9

K o=4

T%o)`h %x9o/4 ∙ x9o) %9+97i)

G`h =4

3

K

o=4T%o)`h %x3o/4

∙x3o) %9+97c)

Bj ·Ĵkg`cb o `kg`cd jd sbcrbkc`d gb jdm`kdgf* gb dcrbygf d jd krmbydc`·fk gbfflk`gd bk jdN`lryd 9+3

Bs qfsìjb dsfc`dy d jfs cfbfflc`bkwbs gb y`l`gbx D`h cfk bj qyfijbmd gb gbnfymdc`·fk qjd-kd* p d jfs cfbfflc`bkwbs gb y`l`gbx G`h cfk bj qyfijbmd gb bu`·fk qryd+ Jfs cfbfflc`bkwbs

47



9+7 Mfgbj`xdc`· fk qfy bjbmbkwfs fflk`wfs+

I`h sb gbkfm`kdk cfm·rkmbkwb gb y`l`gbx bu`fkdj buwbks`fkdj dcfqjdgd* p bk cdsfs bsqbc`d-jbs gfkgb bswfs sfk wfgfs krjfs* dmifs qyfijbmds* bj gb bu` ·fk p gbnfymdc`·fk qjdkd sbbkcrbkwydk gbsdcfqjdgfs+

Jd kwyfgrcc ·fk gb %9+94) d %9+93) bk %9+45) qbym`wb bscyì`y fflkdjmbkwb jds bcrdc`fkbs gbbtr`jìy`f bk nrkc`·fk gb jfs gbsqjdxdm`bkwfs wdj cfmf s`lrb8

ηr 8η~ 8

ηώu 8ηώp 8

_G] ¼{S} = {1} %9+92)

η| 8 θD22

∉ 9|1

∉u9/

∉ώu

∉u

/ θD72

∉ 9|1

∉p∉u/

∉ώp

∉u

/ %9+9>)

θD72

∉ 9|1

∉p∉u/

∉ώu

∉p

/ θD77

∉ 9|1

∉p9/

∉ώu

∉u

/ K %|) / t = 1

gfkgb*

_G] =

D44 D49 D4> I44 I49 I4> D4> D9> D>> I4> I9> I>> 1 1D4> D9> D>> I4> I9> I>> D49 D99 D9> I49 I99 I9> 1 1I44 I49 I4> G44 G49 G4> I4> I9> I>> G4> G9> G>> D22 D72

I4> I9> I>> G4> G9> G>> I49 I99 I9> G49 G99 G9> D72 D77

%9+9<)

{S}4*< =

∉ 9r1∉u9 / ∉ |1

∉u∉ 9|1∉u9

∉ 9~1∉p∉u / ∉ |1

∉p∉ 9|1∉p∉u

∉ 9r1∉p∉u / ∉ 9~1

∉u9 / + + +

+ + + ∉ 9|1∉u9

∉ |1∉p / ∉ |1

∉u∉ 9|1∉p∉u

∉ 9ώu

∉u9

∉ 9ώu

∉p∉u∉ 9ώu

∉p∉u /∉ 9ώp

∉u9

∉ 9r1∉p∉u / ∉ |1

∉u∉ 9|1∉p∉u

? {S}5*47 =

∉ 9~1∉p9 / ∉ |1

∉p∉ 9|1

∉p∉ 9r1∉p9 /

∉ 9~1∉p∉u / + + +

+ + + ∉ 9|1∉p∉u

∉ |1∉p / ∉ |1

∉u∉ 9|1

∉p

∉ 9ώu∉u∉p∉ 9ώp

∉p9

∉ 9ώp

∉u∉p / ∉ 9ώu

∉p9

∙θ

∉ |1∉u / ώu

∙θ

∉ |1∉p / ώp

%9+95)

9+7+ Mfgbj`xdc` ·fk qfy bjbmbkwfs fflk`wfs+

9+7+4+ Nfymrjdc`·fk g·bi`j+ M·bwfgf gb jfs ybs`grfs qfkgbydgfs+

Jd nfymrjdc`·fk g·bi`j gb jds bcrdc`fkbs gb mf~`m`bkwf sb fiw`bkb dj mrjw`qj`cdy cdgdrkd gb jds buqybs`fkbs %9+92) p %9+9>) qfy jd ~dy`dc`·fk gbj lydgf gb jìbywdg dsfc`dgf dcdgd bcrdc ·fk b `kwblydy d bswd bk bj gfm`k`f ℮+

Dj ybdj`xdy jd `kwblydc`·fk qfy qdywbs sb ybgrcb bk rkf bj fygbk gb jd bcrdc`·fk g`nb-ybkc`dj+ Jds ~dy`dc`fkbs sfk cfkfc`gds cfmf nrkc`fkbs gb qbsf p jd bjbcc`·fk gb ·bswds bsdyi`wydy`d+

42




D cfkw`krdc`·fk sb g`~`gb bj gfm`k`f bk K srigfm`k`fs bjbmbkwdjbs ℮b cfk cfkwfykfΓb gb wdj nfymd trb jd rk`·fk gb wfgfs jfs srigfm`k`fs bjbmbkwdjbs criyb cfmqjbwdmbkwbbj gfm`k`f ℮* bs gbc`y* gdgd rkd ~dy`dijb %⋎) qrbgb bscy`i`ysb

℮ %)g℮

≅

K

=4 ℮b

%⋎)g℮b

Dgbm·ds jd g`~`s`·fk gbj gfm`k`f gbib bswdy srhbwd d jd ybswy`cc`·fk lbkbydj* ℮`b ∠ ℮ h

b = ∂ s`` = h

Buqj·Ĵc`wdkgf bj ybsrjwdgf trb sb fiw`bkb dj ybdj xdy bj qyfcbg`m`bkwf gbscy wf bk rksrigfm`k`f bjbmbkwdj ℮b sb w`bkb*

1 =

℮b

∉ηr1

∉uQ 4 /

∉ηr1

∉pQ 3

gugp ∙ Γb

K kηr1kgs %9+90d)

1 = ℮b

∉η~1∉p

Q 9 / ∉η~1∉u

Q 3 gugp ∙ Γb

K sηr1sgs %9+90i)

1 = θ

℮b

∉η|1

∉uT4%r1* ~1* |1) /

∉η|1

∉pT9%r1* ~1* |1)

gugp

/∉η|1

∉p

∉|1

∉pQ 9%r1* ~1* |1) /

∉|1

∉uQ 3%r1* ~1* |1)

∙ η|1t

gugp ∙

Γb

^ kη|1gs %9+90c)

1 =

℮b

∉ηώu

∉uY4 /

∉ηώu

∉pY3

gugp/θ

℮b

ηώuT9 ∙ Γb

M kηώkgs %9+90g)

1 = ℮b

∉ηώp

∉pY9 / ∉ηώp

∉uY3 gugp θ

℮b

ηώuT4 ∙ Γb

M kηώsgs %9+90b)

gfkgb*

Q =

D44 D49 D4> I44 I49 I4>

D49 D99 D9> I49 I99 I9>

D4> D9> D>> I4> I9> I>>

¼ { W } %9+31d)

T =

D22 D72

D72 D77

¼

∉ |1∉u / ώu

∉ |1∉p / ώp

%9+31i)

Y = I44 I49 I4> G44 G49 G4>

I49 I99 I9> G49 G99 G9>

I4> I9> I>> G4> G9> G>>

¼ { W } %9+31c)

{W } =

∉r1

∉u/

4

9

∉|1

∉u

9

*∉~1∉p

/4

9

∉|1

∉p

9

*∉r1

∉p/

∉~1∉u

/∉|1

∉u

∉|1

∉p*

∉ώu

∉u*

∉ώp

∉p*

∉ώu

∉p/

∉ώp

∉u

%9+34)

4>




9+7+9+ G`scybw`xdc`·fk qfy bjbmbkwfs fflk`wfs+

Cfks`gbybmfs trb sfiyb cdgd bjbmbkwf %fflk`wf) ℮b dqyfu`mdmfs jfs ~djfybs gb jfs lyd-gfs gb j`ibywdg gbj qyfijbmd %r1* ~1* |1* ώu* ώp) bk jd nfymd*

r1%u* p) =

m h=4

r hυ h%u* p) * ~1%u* p) =

m h=4

~ hυ h %u* p)

|1%u* p) =m

h=4

| hυ h%u* p) %9+39)

ώu%u* p) =

m h=4

ώuh υ h%u* p) * ώp%u* p) =

m h=4

ώph υ h%u* p)

gfkgb υ h sfk cfkfc`gds cfmf nrkc`fkbs gb `kwbyqfjdc`·fk jfcdjbs gbj bjbmbkwf fflk`wf pgfkgb bj sri`kg`cb h `kg`cd jfs ~djfybs gb jd nrkc`·fk bk jfs m kfgfs gbj bjbmbkwf+

Bk jd mfgbj xdc` ·fk qfy bjbmbkwfs fflk`wfs rw`j`xdgd bk bswb wydidhf sb ybcryyb dj m·bwfgfgb Ldjbyo`k* bk bj cr·dj jds nrkc`fkbs gb qbsf gb jd nfymrjdc`·fk g·bi`j sfk sbjbcc`fkdgds`lrdj d jds nrkc`fkbs gb nfymd+

@kwyfgrc`bkgf bkwfkcbs jds `kwbyqfjdc`fkbs %9+39) bk %9+90) p ybbmqjdxdkgf jds nrkc`f-kbs gb qbsf %ηr1* η~1* η|1* ηώu* ηώp ) gb dcrbygf dj m·bwfgf gb Ldjbyo`k sb fiw`bkb jd mf-gbj`xdc`·fk qfy bjbmbkwfs fflk`wfs gbj qyfijbmd* trb qrbgb sby buqybsdgd cfmf rk s`swbmdgb bcrdc`fkbs djlbiyd`cf bk nfymd mdwy`c`dj qfy jd buqybs`·fk*

N 4

N 9

N 3N 7N 2

=

O 44

O 49

O 43

O 47

O 42

O 49

W O 99

O 93

O 97

O 92

9 O 43

W 9 O 93

W

O 33 O 37 O 32O 47W O 97W O 73 O 77 O 72O 42

W O 92

W O 23

O 72

W O 22

{rb}{~b}

{|b

}{ώbu}ώb

p

%9+33)

gfkgb {%∜)b} sfk jfs ~djfybs gb jd nrkc`·fk %∜) bk jfs m kfgfs gbj bjbmbkwf+

O 44`h =

℮b

D44Υ

%4)`h / D>>Υ

%3)`h / D4>

Υ%9)`h / Υ

%9) h`

gugp %9+37d)

O 49`h =

℮b

D49Υ

%9)`h / D>>Υ

%9) h` / D9>Υ

%3)`h / D4>Υ

%4)`h

gugp %9+37i)

O 43`h =49

℮b

∉|1

∉u

D44Υ

%4)`h / D4>

Υ%9)`h / Υ

%9) h`

/ D>>Υ%3)`h

gugp %9+37c)

/4

9

℮b

∉|1

∉u

D49Υ

%9)`h / D4>Υ

%4)`h / D9>Υ

%3)`h / D>>Υ

%9) h`

gugp %9+37g)

4<




O 47`h =

℮b

I44Υ

%4)`h / I4>

Υ%9)`h / Υ

%9) h`

/ I>>Υ

%3)`h

gugp %9+37b)

O 42`h =

℮b

I4>Υ

%4)`h / I49Υ

%9)`h / I>>Υ

%9) h` / I9>Υ

%3)`h

gugp %9+37n)

O 99`h = D99Υ%3)`h / D>>Υ%4)

`h / D9> Υ%9)`h / Υ%9)

h` %9+37l)

O 93`h =4

9

℮b

∉|1

∉u

D49Υ

%9) h` / D9>Υ

%3)`h / D4>Υ

%4)`h / D>>Υ

%9)`h

gugp %9+37e)

/4

9

℮b

∉|1

∉p

D99Υ

%3)`h / D9>

Υ%9)`h / Υ

%9) h`

/ D>>Υ

%4)`h

gugp %9+37`)

O 97`h =

℮b

I4>Υ

%4)`h / I49Υ

%9) h` / I>>Υ

%9)`h / I9>Υ

%3)`h

gugp %9+37h)

O 92

`h=

℮bI

9> Υ%9)

`h/ Υ

%9)

h` / I99

Υ%3)

`h/ I

>>Υ%4)

`h gugp %9+37o)

O 33`h = θ

℮b

D22Υ

%4)`h / D72

Υ%9)`h / Υ

%9) h`

/ D77Υ

%3)`h

gugp %9+37j)

/4

9

℮b

D44

∉|1

∉u

9

/ D49

∉|1

∉p

9

/ 9D4>∉|1

∉u

∉|1

∉p

Υ%4)`h gugp

/4

9

℮b

D4>

∉|1

∉u

9

/ D9>

∉|1

∉p

9

/ 9D>>∉|1

∉u

∉|1

∉p

Υ%9)`h / Υ

%9) h`

gugp

/ 49 ℮b

D49∉|1∉u

9

/ D99∉|1∉p

9

/ 9D9> ∉|1∉u

∉|1∉p

Υ%3)`h gu gp

O 37`h = θ

℮b

D22Υ

%7)`h / D72Υ

%2)`h

gugp %9+37m)

/

℮b

∉|1

∉u

I44Υ

%4)`h / I4>

Υ%9)`h / Υ

%9) h`

/ I>>Υ

%3)`h

gugp

/

℮b

∉|1

∉p

I4>Υ

%4)`h / I>>Υ

%9)`h / I49Υ

%9) h` / I9>Υ

%3)`h

gu gp

O 32`h = θ ℮b

D72Υ%7)`h / D77Υ%2)`h gugp %9+37k)

/

℮b

∉|1

∉u

I49Υ

%9)`h / I4>Υ

%4)`h / I9>Υ

%3)`h / I>>Υ

%9) h`

gu gp

/

℮b

∉|1

∉p

I9>Υ

%9)`h / I>>Υ

%4)`h / I99Υ

%3)`h / I9>Υ

%9) h`

gu gp

45




O 73`h = θ

℮b

D22Υ

%7) h` / D72Υ

%2) h`

gugp %9+37k)

/4

9

℮b

∉|1

∉u

I44Υ

%4)`h / I4>

Υ%9)`h / Υ

%9) h`

/ I>>Υ

%3)`h

gu gp

/49

℮b

∉|1

∉p

I4>Υ

%4)`h / I>>Υ

%9) h` / I49Υ

%9)`h / I9>Υ

%3)`h

gu gp

O 77`h =

℮b

G44Υ

%4)`h / G4>

Υ%9)`h / Υ

%9) h`

/ G>>Υ

%3)`h / θD22υ`υ h

gugp %9+37f)

O 72`h =

℮b

G4>Υ

%4)`h / G49Υ

%9)`h / G>>Υ

%9) h` / G9>Υ

%3)`h / θD72υ`υ h

gu %9+37q)

O 23`h = θ

℮b

D72Υ

%7) h` / D77Υ

%2) h`

gugp %9+37t)

/ ℮b

∉|1

∉uI49Υ

%9) h` / I4>Υ

%4)`h / I9>Υ

%3)`h / I>>Υ

%9)`hgu gp

/

℮b

∉|1

∉p

I9>Υ

%9) h` / I>>Υ

%4)`h / I99Υ

%3)`h / I9>Υ

%9)`h

gu gp

O 22`h =

℮b

G>>Υ

%4)`h / G9>

Υ%9)`h / Υ

%9) h`

/ G99Υ

%3)`h / θD77υ`υ h

gugp %9+37y)

N 4

` = Γb

K kυ` gs %9+32d)

N 9` =

Γb

K sυ` gs %9+32i)

N 3` =

℮b

tυ` gugp/

Γb

^ kυ` gs %9+32c)

N 7` =

Γb

M kυ` gs %9+32g)

N 2`

= Γb

M s

υ`

gs%9+32b)

40




gfkgb

Υ%4)`h =

∉υ`

∉u

∉υ h

∉u? Υ

%9)`h =

∉υ`

∉u

∉υ h

∉p

Υ%3)`h =

∉υ`

∉p

∉υ h

∉p

? Υ%7)`h =

∉υ`

∉u

υ h

Υ%2)`h =

∉υ`

∉pυ h

Qrbgb fisby~dysb trb jd mdwy`x _O ] qfsbb w·bym`kfs trb gbqbkgbk gb jfs ~djfybs gb jdsfjrc`·fk d wyd~·bs gb jds gby`~dgds bsqdc`djbs gb |1* s`bkgf qfy jf wdkwf kbcbsdy`f* ybcryy`yd rkd bswydwbl`d gb sfjrc`·fk gb s`swbmds gb bcrdc`fkbs kf j`kbdjbs+ Cfk bswb fflk* sb rw`j`xdbj m·bwfgf gb Kb|wfk Ydqesfk* bj cr·dj gdgd rkd mdwy`x _O %{∎})] nrkc`·fk gb jd sfjrc`·fk{∎}* ybsrbj~b bk nfymd `wbydw`~d bj s`swbmd _O %{∎})] {∎} = {N } rw`j`xdkgf bj bstrbmd*

{η∎

}=

∉ {Y%{∎}y)}∉

{∎

} ∙4

{{N

} ∙_O %

{∎

}y)]

{∎

}y

}%9+3>d)

{∎}y/4 = {∎}y / {η∎} %9+3>i)

gfkgb {∎}y bs bj ~djfy gb jd sfjrc`·fk bk jd y∙·bs`md wbydc ·fk kp {Y%{∎}y)} sb gbkfm`kdybs`grf gbj s`swbmd p sb bkcrbkwyd gdgf qfy*

{Y%{∎}y)} ≤ _O %{∎}y)] {∎}y {N } %9+3<)

Bj bstrbmd `wbydw`~f %9+3>) sb gbw`bkb crdkgf qdyd rkd `wbydc`·fk y sb crmqjb trb

K

h=4z {η∎ h}y z9

K h=4

z {∎ h}y/4 z9 : ǯ %9+35)

gfkgb ǯ bs rkd cfkswdkwb srfflc`bkwbmbkwb qbtrbkd Qdyd ybsfj~by %9+3>) bs kbcbsdy`f

fiwbkby jd buqybs`·fk buqj·Ĵc`wd gb jd mdwy`x

∉ {Y%{∎}y)}∉ {∎}

trb gbkfm`kdybmfs _W ]* f mdwy`x

gb y`l`gbx wdklbkwb+

Ybdj`xdkgf bj wydidhf djlbiyd`cf kbcbsdy`f sb jjbld d*

91




W mk = O mk s` k = 3 %9+30d)

W 43`h =4

9

℮b

∉|1

∉u D44Υ

%4)`h / D4>

Υ%9)`h / Υ

%9) h`

/ D>>Υ

%3)`h

gugp %9+30i)

/4

9

℮b

∉|1

∉p

D49Υ

%9)`h / D4>Υ

%4)`h / D9>Υ

%3)`h / D>>Υ

%9) h`

gugp / O 43`h

W 93`h =4

9

℮b

∉|1

∉u

D49Υ

%9) h` / D9>Υ

%3)`h / D4>Υ

%4)`h / D>>Υ

%9)`h

gugp %9+30c)

/4

9

℮b

∉|1

∉p

D99Υ

%3)`h / D9>

Υ%9)`h / Υ

%9) h`

/ D>>Υ

%4)`h

gugp / O 93`h

W 73`h =4

9

℮b

∉|1

∉u

I44Υ

%4)`h / I4>

Υ%9)`h / Υ

%9) h`

/ I>>Υ

%3)`h

gugp %9+30g)

/4

9

℮b

∉|1

∉p

I4>Υ

%4)`h / I>>Υ

%9) h` / I49Υ

%9)`h / I9>Υ

%3)`h

gugp / O 73`h

W 23`h =4

9

℮b

∉|1

∉u

I49Υ

%9) h` / I4>Υ

%4)`h / I9>Υ

%3)`h / I>>Υ

%9)`h

gugp %9+30b)

/4

9

℮b

∉|1

∉p

I9>Υ

%9) h` / I>>Υ

%4)`h / I99Υ

%3)`h / I9>Υ

%9)`h

gugp / O 23`h

W 33

`h=

℮b R

gugp %9+30n)

R =

∉r1

∉u*

∉~1∉p

*∉r1

∉p*

∉~1∉u

¼

D44 D49 D4>

D49 D99 D9>

D4> D9> D>>

D4> D9> D>>

¼

Υ%4)`h

Υ%3)`h

Υ%9)

h` / Υ%9)`h

%9+71d)

/

∉ώu

∉u*

∉ώu

∉p*

∉ώp

∉p*

∉ώp

∉u

¼

I44 I49 I4>

I4> I9> I>>

I49 I99 I9>

I4> I9> I>>

¼

Υ%4)`h

Υ%3)`h

Υ%9)

h` / Υ%9)`h

/

∉|1

∉u

9

*

∉|1

∉p

9

*∉|1

∉u

∉|1

∉p

¼ D44 D>> 9D4>

D>> D99 9D9>

9D4> D49 / D>> 9D9>

¼

Υ%4)`h

Υ%3)`h

Υ%9)

h` / Υ%9)`h

94




9+7+3+ @kwblydc`·fk krm·by`cd

Jds nrkc`fkbs gb `kwbyqfjdc`·fk υ` sb buqybsdk bk nrkc`·fk gb jds cffygbkdgds gb jdscffygbkdgds kdwrydjbs %λ* μ) gb rk bjbmbkwf crdgy·dklrjdy gbkfm`kdgf bjbmbkwf mdswby℮ˎb qdyd bj crdj ∙4 λ 4? ∙4 μ 4* bs gbc`y υ` = υˎ`%λ* μ)

Cfmf jds kwblydjbs trb dqdybcbk bk jfs w·bym`kfs gb jds bcrdc`fkbs %9+37)* %9+32) p %9+35)sb bkcrbkwydk bk bj qjdkf lbfm·bwy`cf %u* p)* gbib `mqjbmbkwdysb rkd bswydwbl`d qdyd bu-qybsdy bswds `kwblydjbs bk bj qjdkf%λ* μ)+ Qdyd bjjf ybcryy`mfs d bjbmbkwfs `sfqdy·dmb-wy`cfs qdyd jds crdjbs sfk rw`j`xdgds jds m`smds nrkc`fkbs gb nfymd wdkwf qdyd dqyfu`-mdy jds ~dy`dijbs gbj qyfijbmd* cfmf jd lbfmbwy·Ĵd+ Bs gbc`y jds nrc`fkbs trb wydksnfy-mdk jds cffygbkdgds gbj bjbmbkwf mdswby bk jds cffygbkdgds gbj bjbmbkwf lbfm·bwy`cfu = u %λ* μ) ? p = p %λ* μ)sfk*

u =y

`=4

u`υˎ` ? p =y

`=4

p`υˎ`

gfkgb %u`* p`) sfk jds cffygbkdgds gbj kfgf jfcdj ` gbj bjbmbkwf +Bk bswb wydidhf sb rw`j`xd bj bjbmbkwf crdgy`j·dwbyf gb 0 kfgfs* crpds nrkc`fkbs gb `kwby-

qfjdc`·fk* sfk gb dcrbygf d jd krmbydc`·fk qybsbkwdgd bk jd N`l+ 9+>

{Υb} =

47%λ9 ∙ λ)%μ9 ∙ μ)47%λ9 / λ)%μ9 ∙ μ)47%λ9 / λ)%μ9 / μ)47%λ9 ∙ λ)%μ9 / μ)49 %4 ∙ λ9)%μ9 ∙ μ)49%λ9 / λ)%4 ∙ μ9)49 %4

∙λ9)%μ9 / μ)

49%λ9 ∙ λ)%4 ∙ μ9)%4 ∙ λ9)%4 ∙ μ9)

%9+74)

7

4 9

3

μ

λ

2

>

<

5 0

N`lryd 9+>8 Krmbydc`·fk gb kfgfs bk bj bjbmbkwf mdswby+

Gb bswd nfymd jds gby`~dgds bsqdc`djbs gb jds nrkc`fkbs gb nfymd bk bj bsqdc`f lbfm·bwy`-

99




cf gbj qyfijbmd qrbgbk bscy`i`ysb cfmf*∉ υˎ`

∉u∉ υˎ`

∉p

= _H ]∙4

∉ υˎ`

∉λ∉ υˎ`

∉μ

%9+79)

gfkgb H bs bj hdcfi`dkf gb jd wydksnfymdc`·fk gb cffygbkdgds bkwyb jfs s`swbmds gb cffy-gbkdgds gbj qyfijbmd p bj s`swbmd gb cffygbkdgds gbj bjbmbkwf mdswby*

H =

y=4

u`∉ υˎ`

∉λ

y=4

p`∉ υˎ`

∉λ

y=4

u`∉ υˎ`

∉μ

y=4

p`∉ υˎ`

∉μ

%9+73)

Cfks`g·bybsb bkwfkcbs jd s`lr`bkwb nfymd lbkbydj gb jds `kwblydjbs sfiyb rk bjbmbkwfdyi`wydy`f ℮%b)

O %b)`h =

℮%b)

N ∉ υˎ`

∉u* ∉ υˎ h

∉p* ∉ υˎ`

∉p* ∉ υˎ h

∉p* υˎ`* υˎ hgugp

Gb dcrbygf d jds wydksnfymdc`fkbs %9+30) jfs w·bym`kfs gb jd mdwy`x _O ] p bj ~bcwfy N

O %b)`h =

℮ˎ

Nˎ

∉ υˎ`

∉λ*

∉ υˎ`

∉μ*

∉ υˎ h

∉λ*

∉ υˎ h

∉μ* υˎ`* υˎ h* H

gbw Hgλgμ ≤

℮ˎ

Lˎ%λ* μ)gλgμ

pd trb wfgfs jfs w·bym`kfs trb sfk dylrmbkwf gb Nˎ sfk nrkc`fkbs gb λ p μ p gbw H =gbw H %λ* μ)

Gfkgb gbib kfwdysb trb sb ed wydksnfymdgf jd `kwblydj sfiyb rk bjbmbkwf dyi`wydy`f℮%b) bk jd `kwblydj sfiyb bj bjbmbkwf mdswby ℮ˎ

Qdyd b~djrdy bswd `kwblydj sb ybcryyb d jds n·fymrjds gb jd crdgydwryd gb Ldrss Jblbkgybgfkgb sb dqyfu`md bj ~djfy gb jd `kwblydj mbg`dkwb

℮ˎ

Lˎ%λ* μ)gλgμ =

K `=4

K h=4

Lˎ%λ`* μ h )\ \ h %9+77)

Bk jd s`lr`bkwb wdijd sb bstrbmdw`xdk jfs qrkwfs p jfs qbsfs gb jds g`nbybkwbs n·fymrjds

gb Ldrss rw`j`xdgds+

N ·fymrjd Qrkwfs λ` Qbsfs \

4 qrkwfs%Ybgrc`gd) 1+11 9+11

9 qrkwfs%Budcwd) ´1*2<3219>09 4+11

93



9+2 C · djcrjf gb wbks`fkbs+ Cy`wby`fs gb Ndjjd+

Bs `mqfywdkwb mbkc`fkdy trb jd n·fymrjd gb `kwblydc`·fk gb Ldrss gb k/49 qrkwfs `kwblyd

bk nfymd budcwd rk qfj`kfm`f gb lydgf k+

Gbib sby kfwdgf defyd trb bk jfs w·bym`kfs gb jd mdwy`x O bk %9+37) dsfc`dgfs d jdswbks`fkbs gb cfywb wydks~bysdjbs %b+l+ dtrbjjfs w·bym`kfs dnbcwdgfs qfy bj cfbfflc`bkwb θ)sfk qfj`kfm`fs gb rk lydgf mdpfy trb jfs ybswdkwbs w·bym`kfs trb cfmqfkbk jd mdwy`x+

Crdkgf jd ybjdc`·fk bk~byldgryd&bsqbsfy gb jd qjdcd bs mdpfy dj fygbk gb 21* jds wbks`f-kbs gb cfywb wydks~bysdjbs gbibk sby gbsqybc`dijbs+ Dj sby qfj`kfm`fs gb lydgf mdpfy* jfsw·bym`kfs dsfc`dgfs d jd wbks`·fk wydks~bysdj kf sb dkrjdk crdkgf g`sm`krpb bj bsqbsfy bkrk nbk·fmbkf cfkfc`gf cfmf ijftrbf gb jd sfjrc`· fk+ Qdyd b~`wdy bswb nbk·fmbkf s`k kbcbs`wdyybnfymrjdy jd e`q·fwbs`s gb kf gbsqybc`dm`bkwf gb jds wbks`fkbs gb cfywb wydks~bysdjbs* bstrb jfs w·bym`kfs dsfc`dgfs d bswds sb b~dj·rdk cfk rkd n·fymrjd gb Ldrss gb `kwblydc`·fkybgrc`gd m`bkwyds trb jfs ybswdkwbs w·bym`kfs sb b~dj·rdk cfk rkd n·fymrjd gb `kwblydc ·fkbudcwd+ Gb bswd nfymd bj mfgbjf qbym`wb jd dkrjdc`·fk gb jds wbks`fkbs wydks~bysdjbs crdk-gf bj bsqbsfy bs srfflc`bkwbmbkwb qbtrbkf+

9+2+ C ·djcrjf gb wbks`fkbs+ Cy`wby`fs gb Ndjjd+

Rkd ~bx fiwbk`gd jd sfjrc`·fk gbj s`swbmd %9+33) qdyd rkd gdgd cfkg`c`·fk gb cdyld*sb fiw`bkb* gdgd rkd cffygbkdgd %u*p*x)* bj wbksfy gb gbnfymdc`fkbs bk cffygbkdgdslbfm·bwy`cds rw`j`xdkgf jd buqybs`·fk %9+>)+ Jrblf* yfwdkgf bj wbksfy gb gbnfymdc`fkbs dcffygbkdgds mdwby`djbs d wyd~·bs gb %9+3)* p rw`j xdkgf jd ybjdc`·fk cfksw`wrw`~d %9+7) bs qf-s`ijb fiwbkby bj wbksfy gb wbks`fkbs bk cffygbkdgds mdwby`djbs+

Bs kbcbsdy`f mbkc`fkdy trb bj cdmqf gb wbks`fkbs bs cdjcrjdgf bk jfs qrkwfs gb Ldrssrw`j`xdgfs bk jd `kwblydc`·fk ybgrc`gd* cfkfc`gfs cfmf qrkwfs gb Idyjf|+

Rkd ~bx fiwbk`gf bj wbksfy gb wbks`fkbs* sb rw`j`xd rk cy`wby`f gb ndjjd qdyd gbwbym`kdybj bswdgf wbks`fkdj trb qyfgrcb jd yfwryd gb jd j·dm`kd cfks`gbydgd+

Bk bswb wydidhf sb rw`j`xdk wybs w`qfs gb cy`wby`fs gb ndjjd+

Cy`wby`f gb Wbks`·fk M·du`md

Bj cy`wby`f gb wbks`·fk m·du`md kf w`bkb bk crbkwd jd `kwbydcc`·fk bkwyb jfs g`sw`kwfs mf-gfs gb ndjjd* gb djj·Ĵ trb sb bkcrdgyd gbkwyf gb jfs cy`wby`fs cfkfc`gfs cfmf cy`wby`fs `k-gbqbkg`bkwbs gb ndjjd+ Bswb cy`wby`f qybg`cb jd ndjjd crdkgf sb sdw`sndcb crdjtr`byd gb jdss`lr`bkwbs cfkg`c`fkbs8

z σ4 z U * z σ9 z P %9+72)

z σ7 z Y z σ2 z S z σ> z W

Jfs fwyfs gfs cy`wby`fs gb ndjjd rw`j`xdgfs bk bswb wydidhf sb bkmdycdk gbkwyf gb jfs cy`-wby`fs gb ndjjd qfj`kfm`djbs* jfs crdjbs w`bkbk bk crbkwd jd `kwbydcc`·fk bkwyb jds wbks`fkbsqy`kc`qdjbs p rsrdjmbkwb iy`kgdk ybsrjwdgfs m·ds cfksby~dw`~fs trb jfs cy`wby`fs `kgb-qbkg`bkwbs+ Sb gbkfm`kdk qfj`kfm`djbs gbi`gf d trb w`bkbk jd nfymd lbkbydj*

N = N σ` / N hσ`σ h %9+7>)

97




gfkgb sb cfks`gbyd trb sb qyfgrcb jd ndjjd crdkgf N 4

Gbkwyf gb bswb w`qf gb cy`wby`fs sb edk `mqjbmbkwdgf jfs cy`wby`fs gb Wsd` E`jj p Wsd` \rjfs crdjbs w`bkbk jd nfymd lbkbydj*

Cy`wby`f gb Wsd` E`jjσ4

U

9/σ9

P

9 ∙

4

U 9/

4

P 9∙ 4

X 9

σ4σ9 %9+7<)

/σ7

Y

9/σ2

S

9/σ>

W

9 4

Cy`wby`f gb Wsd`\r

σ94

U W U C /

σ99

P W P C ∙

4∘U W U C P W P C

σ4σ9 %9+75)

/4

U W ∙4

U C σ4 / 4

P W ∙4

P C σ9 / σ7

Y 9

/ σ2

S 9

/ σ>

W 9 4

gfkgb

S u =4

U W U C ? S p = 4

P W P C? S x =

4

X W X C

U W * P W * X W 8 Wbks`·fk gb ndjjd d wydcc`·fk qryd bk jd g`ybcc`·fk mdwby`dj u4* u9* u3 ybsqbcw`-~dmbkwb+

U C * P C * X C 8 Wbks`·fk gb ndjjd d cfmqybs`·fk qryd bk jd g`ybcc`·fk mdwby`dj u4* u9* u3 ybs-qbcw`~dmbkwb+

Y*S*W 8 Wbks`fk gb ndjjd gb cfywb qryf bk jfs qjdkfs mdwby`djbs u93* u43* u49 ybsqbcw`~d-mbkwb+

Bk bj cy`wby`f gb Wbks`fk M·du`md p bj cy`wby`f gb Wsd`–E`jj U = U W s` σ4 ; 1 p U = U C

s` σ4 : 1+ @gbm qdyd P

9+2+4+ Cy`wby f gb qy`mby j·dm`kd ndjjdgd+

Bs gb `kwby·bs bk bswb wydidhf crdj bs bj bswdgf gb cdylds buwbykds trb qyfgrcb rk bswdgfwbks`fkdj wdj trb `kgrcb jd ndjjd bk rkd j·dm`kd p bk rk s·fjf qrkwf gbj gfm`k`f* idhfdjlrkf gb jfs cy`wby`fs gb ndjjd mbkc`fkdgfs+

Qdyd bjjf sb s`lrb bj s`lr`bkwb qyfcbg`m`bkwf+4+ Rkd ~bx bksdmijdgf bj ~bcwfy {N } gb %)* bj cr·dj w`bkb wfgd jd `knfymdc`·fk sfiyb

bj bswdgf gb cdylds* sb qybmrjw`qj`cd wfgfs jfs bjbmbkwfs gbj m`smf qfy rk ndcwfy trbgbkfm`kdybmfs δ+

9+ Sb cdjcrjd* qdyd cdgd bjbmbkwf* bk cdgd qrkwf gb Ldrss p bk cdgd j·dm`kd o* bj cdm-qf gb wbks`fkbs bk jds cffygbkdgds %xo*

xo/xo/4

9 * xo/4) trb cfyybsqfkgbk d jd srqbyfflc`b`knby`fy* mbg`d p srqby`fy gb jd j·dm`kd o ybsqbcw`~dmbkwb+

92




3+ Mbg`dkwb rk cy`wby`f gb ndjjd* sb cdjcrjd qdyd wfgfs jfs qrkwfs mbkc`fkdgfs bk bjqdsf 9* bj ndcwfy gb ndjjd N

7+ Sb djmdcbkd bj mdpfy ~djfy gb N bk wfgf bj gfm`k`f* p jd `knfymdc`·fk gb sr ri`cdc`·fk%bjbmbkwf* j·dm`kd* qrkwf gb Ldrss* qfs`c`·fk gbkwyf gb jd j·dm`kd)+

2+ Sb ybcdjcrjd bj ~djfy gbδ

rw`j`xdkgf bj cy`wby`f gb jd i`sbcc`·fk qdyd ybsfj~by jd bcrd-c`·fk N = 4* p sb ~rbj~b dj qdsf 4+

Dj fflkdj bswb qyfcbsf `wbydw`~f sb fiw`bkb rk ybsrjwdgf dqyfu`mdgf d wyd~·bs gb jfs gd-wfs g`scybwfs %bjbmbkwf* qrkwf gb Ldrss* j ·m`kd* qfs`c`·fk gbkwyf gb jd jdm`kd) gbj jrldylbfm·bwy`cf gb `k`c`f gb jd yfwryd gb jd qjdcd* p gb crdj bs bj bswdgf gb cdylds trb qyfgrcbbswb `k`c`f+

9>



3+ QYFLYDMD CfmqfsQjdwb

D qdyw`y gb jd mbwfgfjfl·Ĵd gbscy`wd bk jd Sbcc`·fk 9 gb bswb wydidhf* sb ed bscy`wf rk qyf-lydmd bk jbklrdhb Nfywydk 01 gbkfm`kdgf CfmqfsQjdwb* bj cr·dj ybsrbj~b jds bcrdc`fkbsgb btr`j`iy`f gb jdm`kdgfs gb mdwby`dj cfmqrbswf cfk ybnfyxdgf gb ffliyd rk`g`ybcc`fkdj+

Bj qyflydmd fnybcb jd fqc`·fk gb cdjcrjdy bj ndcwfy gb ndjjd p jd dmqj`fflcdc`·fk gbj bswdgf gbcdylds trb qyfgrcb bj `k`c`f gb ly`bwd bk jd qjdcd+ Bk bswd sbcc`·fk sb gbscy`ib iyb~bmbkwbsr bswyrcwryd+

Bj qyflydmd jbb jfs gdwfs gb cdgd qyfijbmd trb sb gbsbb ybsfj~by gb gfs dyce`~fs gbwbuwf trb sb gbkfm`kdk GDWFSQJDCD+wuw p qybqyfcbsf+wuw+

Jd bscy`wryd gb dmifs dyce`~fs sb ybdj`xd d qdyw`y gbj sfnw|dyb gb qyb p qfsw qyfcbsf gbc·djcrjf krm·by`cf qfy bjbmbkwfs p ~fj·rmbkbs fflk`wfs L@G 0+1+ Bswb sfnw|dyb* gbsdyyfjjdgfbk bj Cbkwyf @kwbykdc`fkdj gb M·bwfgfs Krm·by`cfs bk @klbk`by·Ĵd %C@MKB) gb Idycbjfkd*qrbgb sby gbscdyldgf cfk rkd j`cbkc`d wbmqfydj lydwr wd gbj |bis`wb |||+l`g+c`mkb+rqc+bs

Bk L@G 0+1 sb `mqjbmbkw ·f rk m·fgrjf trb qbym`wb8

• Wydxdgf gb jd lbfmbwy·Ĵd gb jd qjdcd+

• Dqj`cdc`·fk gb cfkg`c`fkbs gb ifygb+

• @mqfs`c`·fk gb cdylds+

• Cfkg`c`fkbs gb mdjjdgf p g`scybw`xdc`·fk gb jd qjdcd+

• @kwyfgrcc`·fk gb cfkswdkwbs bj·dsw`cds p wbks`fkbs gb ndjjd gbj mdwby`dj gb jds j·dm`kdsgb jd qjdcd+

•@kwyfgrcc`·fk gb jd sbcrbkc`d gb jdm`kdgf

• @kwyfgrcc`·fk gbj w`qf gb cy`wby`f gb ndjjd d rw`j`xdy+

• ^`srdj`xdc`·fk gb jfs ybsrjwdgfs fiwbk`gfs cfk CfmqfsQjdwb+

D cfkw`krdc` ·fk sb ybsrmb bj qyfcbg`m`bkwf trb ybdj`xd bj qyflydmd CfmqfsQjdwb* crpfc·fg`lf nrbkwb sb dghrkwd bk bj Dq·bkg`cb+

3+4+ Qyflydmd Qy`kc`qdj CfmqfsQjdwb+

4+ Jbcwryd gb gdwfs gbj qyfijbmd+ @kcjrpb8 cfkbcw`~`gdgbs gb bjbmbkwfs p cffygbkd-

gds gb jfs kfgfs gb jd mdjjd? cfkg`c`fkbs gb cfkwfykf? Bhbcrwd bk bj fygbk qybsbk-wdgf* bj jjdmdgf d jds s`lr`bkwbs sriyrw`kds8

9+ CFKSW@WRW@^D

Cdjcrjd jfs ~djfybs gb jds cfkswdkwbs bj·dsw`cds gb jd qjdcd+

9<



3+4 Qyflydmd Qy`kc`qdj CfmqfsQjdwb+

3+ CFKWFYKF

Ybdj`xd rkd mdycdc`·fk gb jds cfkg`c`fkbs gb cfkwfykf kdwrydjbs gbj qyfijbmd* dfflk gb bj`m`kdy qfswby`fymbkwb jds ffljds p cfjrmkds dsfc`dgds d jfs m`smfs* bk bjs`swbmd gb bcrdc`fkbs %9+33)

7+ YESJbb jds cfkg`c`fkbs gb cdyld gbj qyfijbmd p fiw`bkb jfs w·bym`kfs gbj ~bcwfy gbnrbyxds {N } gb %9+33)

2+ DSSBMIJP

Fiw`bkb jfs w·bym`kfs gb jd mdwy`x _O ] bk %9+37) p jfs w·bym`kfs gb jd mdwy`x wdklbkwb_W ] %9+35) mbg`dkwb `kwblydc`·fk krm·by`cd gb Ldrss* rw`j`xdkgf `kwblydc`·fk ybgrc`gdbk jfs w ·bym`kfs dsfc`dgfs d jds gbnfymdc`fkbs gb cfywb wydks~bysdjbs+

>+ SFJ^BJR Ybsrbj~b mbg`dkwb gbscfmqfs`c`·fk JR cfk q`~fwbf bj bstrbmd gbj m·bwf-gf gb Kb|wfk–Ydqesfk %9+3>) S` kf sb crmqjb jd cfkg`c`·fk %9+35) sb ybwfykd dj qdsf

dkwby`fy rw`j`xdkgf bj krb~f ~djfy gb jd sfjrc`·fk+<+ SWYBSSN@BJG

Cdjcrjd bj wbksfy gb wbks`fkbs bk cdgd qrkwf gb Ldrss rw`j`xdgf bk jd `kwblydc`·fkybgrc`gd p bk cdgd j·dm`kd* wdkwf bk cffygbkdgds mdwby`djbs cfmf gbj qyfjbmd+Dgbmds cdjcrjd bj bswdgf gb nrbyxds p mfmbkwfs ybsrjwdkwbs dqj`cdkgf jd bcrdc`·fk%9+4>)

5+ ND@JCY@W

Cdjcrjd bj ndcwfy gb ndjjd* sbl ·rk bj cy wby`f gb ndjjd sbjbcc`fkdgf* wdj cfmf sb qybsbkwdbk jd sbcc`·fk 9+2 S` sb ybtr`byb jd irstrbgd gb jd cfkg`c`·fk gb qy`mby j·dm`kd ndjjdgdsb s`lrb bj qyfcbg`m`bkwf gbscy`wf bk jd sbcc`·fk mbkc`fkdgd+

0+ QFSWL@G

Bscy`ib jfs ybsrjwdgfs bk rk dyce`~f gb sdj`gd* gb nfymd wdj trb qrbgdk sby ~`srdj`-xdgfs qfswby`fymbkwb bk L@G 0+1

95



7+ Ybsrjwdgfs

Sb qybsbkwdk d cfkw`krdc`·fk rkd sby`b gb ybsrjwdgfs krm·by`cfs fiwbk`gfs cfk bj c·fg`lfCfmqfsQjdwb+ Jds gfs qy`mbyds sby`bs gb ybsrjwdgfs sb fy`bkwdk d mfswydy bj bnbcwf gb jdscfkg`c`fkbs gb cfkwfykf* p bj drmbkwf gbj k·rmbyf gb j ·dm`kds bk jd ybsqrbswd bsw·dw`cd gb

qjdcds ybcwdklrjdybs gb mdwby`dj cfmqrbswf dkwb rkd cdyld rk`nfymbmbkwb g`swyìr`gd+N`kdjmbkwb sb qybsbkwdk ybsrjwdgfs fiwbk`gfs gb jds cdylds trb qyfgrcbk jd ndjjd gb jdqy`mby j·dm`kd* qdyd gfs w`qfs gb cfkg`c`fkbs gb cdyld8 rk`nfymbmbkwb g`swyìr`gd p rkdnrbyxd gb wydcc ·fk qjdkd dcwrdkgf bk rkf gb jfs ifygbs+ Jfs ybsrjwdgfs sfk cfmqdydgfsbk cdgd rkf gb jfs cdsfs cfk dtrbjjfs qybsbkwdgfs bk _7]+

7+4+ Cdsf 4+ Bnbcwf gb jds cfkg`c`fkbs gb ifygb

Sb qybsbkwdk ybsrjwdgfs qdyd jd gbbu` ·fk kf j`kbdj bsw·dw`cd gb rkd qjdcd ybcwdklrjdy dk-wb rkd cdyld wydks~bysdj T1 rk`nfymbmbmbkwb g`swyìr·Ĵgd* qdyd gfs w`qfs gb cfkg`c`fkbsgb ifygb8 s`mqjbmbkwb dqfpdgf %SS-3) p bmqfwydgf %CC) bk wfgfs jfs ifygbs+

Jd qjdcd sb bkcrbkwyd cfmqrbswd qfy crdwyf j·dm`kds g`sqrbswds gb dcrbygf d jd sbcrbk-c`d gb jdm`kdgf %1&01&01&1)

Jds cfkswdkwbs bj ·dsw`cds gbj mdwby`dj gb jd j·dm`kd sfk*

B 4 = 4+5959Ü41>qs` * B 9 = 4+5342Ü41>qs` * L49 = L43 = L93 = 1+3492Ü41>qs` * ν 49 = 1+9302

Jds g`mbks`fkbs gb jd qjdcd gb dcrbygf d jd kfmbkcjdwryd gb jd N`l+ 7+4 sfk d = i = 49 `k+Bj bsqbsfy gb jd qjdcd bs e = 1+10> `k % cdgd j·dm`kd bs gb 1+197 `k gb bsqbsfy )

u

p

i&9

i&9

d&9 d&9

N`lryd 7+48 Gbfflk`c`·fk gb g`mbks`fkbs gb jd qjdcd+

90



7+3 Cdsf 3+ Dkdj·Ĵs`s gb ndjjd gb qy`mby j· dm`kd+

7+3+ Cdsf 3+ Dkdj·Ĵs`s gb ndjjd gb qy`mby j·dm`kd+

7+3+4+ Ndjjd dkwb cdyld rk`nfymbmbkwb g`swy ir`gd

Sb qybsbkwdk ybsrjwdgfs qdyd jd wbks`·fk gb ndjjd gb jd qy`mby j·dm`kd gb rkd qjdcd ybc-

wdklrjdy dkwb rkd cdyld rk`nfymbmbkwb g`sw`ir`gd T+ Jds g`mbks`fkbs gb jd qjdcd gbdcrbygf d jd N`l 7+4 sfk* d = 0 `k * i = 2 `k

Bj mdwby`dj gb jds j·dm`kds cfyybsqfkgb dj gbj mdwby`dj cfmqrbswf gb ffliyds gb lydfflwfbk mdwy`x bqfu` %W311&2915)* crpds qyfq`bgdgbs bj·dsw`cds sfk*

B 4 = 40+91Ü41>qs` * B 9 = 4+2>Ü41>qs` * L49 = L43 = 1+59Ü41> * L93 = 1*70Ü41> * ν 49 = 1+97

Jds qyfq`bgdgbs gb ybs`swbkc`d d jd wydcc`·fk* cfmqybs`·fk p cfywb sfk* gb dcrbygf d jdkfmbkcjdwryd gbfflk`gd bk jd Sbcc`·fk 9+2*

U W = 940+21 Ü 413qs` * U C = 97>+11 Ü 413qs` * P W = >+32 Ü 413qs` * P C = >+32 Ü 413qs`

Y = 0+51 Ü 413qs` * S = W = 49+>1 Ü 413qs`

Bj bsqbsfy eqjp gb cdgd j·dm`kd bs eqjp = 1+112 `k+

Sb rw`j`xdk wybs bstrbmds gb jdm`kdgf* jfs crdjbs sb gbkfm`kdk cfmf sb `kg`cd8

D 8 Jdm`kdgf dklrjdy s`m·bwy`cf* %72&-72&72)

I 8 Jdm`kdgf cyrxdgf s`m·bwy`cf* %1&01&01&1)

C 8 Jdm`kdgf cyrxdgf dkw`s`m·bwy`cf* %1&01&1&01)

Jds cfkg`c`fkbs gb ifygb cfyybsqfkgbk d dtrbjjds cfk wfgfs jfs jdgfs s`mqjbmbkwbdqfpdgfs gb w`qf SS-4* jds crdjbs sb bkcrbkwydk gdgds* gb dcrbygf d jd kfmbkcjdwrydgbfflk`gd bk jd N`l+ 7+4 qfy*

Qjdcd s`mqjbmbkwb dqfpdgd SS-4

bk u = ∙i&9 * i&9 8 ~ = | = ώp = 1

bk p = ∙d&9 * d&9 8 r = | = ώu = 1

Bk jfs jdm`kdgfs I p C sb rw`j`xd jd s`mbwy·Ĵd gbj qyfijbmd qdyd mfgbjdy s ·fjf rk crdywfgb jd qjdcd %bj crdgydkwb qfs`w`~f) * `kwyfgrc`bkgf jds s`lr`bkwbs cfkg`c`fkbs d jf jdylf gbjds j·Ĵkbds gb s`mbwy·Ĵd*

bk u = 1 8 r = ώu = 1 bk p = 1 8 ~ = ώp = 1

Bk jds ffllryds 7+7 p 7+2 sb mrbswyd jd krmbydc`·fk gb jfs bjbmbkwfs gb jd mdjjd rw`j`-xdgd bk jd mfgbj`xdc`·fk gb jd qjdcd bkwbyd* p jd mfgbj`xdc`·fk gb rk crdywf gb jd qjdcdybsqbcw`~dmbkwb* ds·Ĵ cfmf jd krmbydc` ·fk gb jfs qrkwfs gb Ldrss+

37



7+3 Cdsf 3+ Dkdj·Ĵs`s gb ndjjd gb qy`mby j· dm`kd+

N`lryd 7+78 Krmbydc`·fk gb jfs bjbmbkwfs rw`j`xdgfs bk jd mfgbj`xdc`·fk gb jd qjdcd bkwbyd%bstrbmd gb jdm`kdgf D)+

N`lryd 7+28 Krmbydc`·fk gb jfs bjbmbkwfs rw`j`xdgfs bk jd mfgbj`xdc`·fk gb rk crdywf gb qjdcd%bstrbmds gb jdm`kdgf I p C)+

Bk jd Wdijd 7+2 sb qybsbkwdk jfs ybsrjwdgfs fiwbk`gfs qdyd jd cdyld gb ndjjd kfymdj`xdgdT&B 9%d&e)7 gb jd qy mby j·dm`kd* sbl·rk jfs cy`wby`fs gb m·du`md wbks`·fk kfymdj* Wsd` \r pWsd` E`jj+ Sb cfmqdydk jfs ybsrjwdgfs cfk dtrbjjfs qybsbkwdgfs bk Ybggp _7]+ Dgbm·ds* sbfiw`bkb jd ri`cdc`·fk gb jd j·dm`kd ndjjdgd g·fkgb sb ed rw`j xdgf jd s`lr`bkwb kfmbkcjdwryd*

NBJ %Nd`jbg Bjbmbkw) Bjbmbkwf ndjjdgf

NJDP %Nd`jbg Jdpby) J·dm`kd ndjjdgd

NQFS %Nd`jbg Qfs`w`fk) 48 Ifwwfm * 9 8 M`ggjb * 3 8 Wfq

NLQ %Nd`jbg Ldrss Qf`kw) Qrkwf gb Ldrss gb ndjjd

32



2+ Cfkcjrs`fkbs+

Bk bj qybsbkwb wydidhf sb ed `mqjbmbkwdgf bj m·bwfgf gb jfs bjbmbkwfs fflk`wfs qdydfiwbkby jd sfjrc` ·fk gb jds bcrdc`fkbs gb btr`jìy`f bsw·dw`cf gb qjdcds gb jdm`kdgf gb md-wby`dj cfmqrbswf+ Sb rw`j`x·f jd wbfy·Ĵd gb gbnfymdc` ·fk gb cfywb gb qy`mby fygbk gb Yb`skby

M`kgj`k* `kcjrpbkgf jds gbnfymdc`fkbs kf j`kbdjbs gb ^fk Odymdk+ Bj cdmqf gb wbks`f-kbs fiwbk`gf qbym`w`·f jd `mqjbmbkwdc`·fk gb rk bstrbmd gb c·djcrjf gbj bswdgf gb cdyldsbuwbykf trb qyfgrcb jd ndjjd gb jd qy`mby j ·dm`kd* rw`j x·dkgfsb qdyd bjjf cy`wby`fs gb ndjjdgb mdwby`djbs fyw ·fwyfqfs* wdjbs cfmf bj gb wbks` ·fk m·du`md* Wsd` \r p Wsd` E`jj+

Sb fiwr~`byfk ybsrjwdgfs gb jd cry~d gb gbbu`·fk m·du`md ~s cdyld qdyd rkd qjdcd ybc-wdklrjdy idhf rkd cdyld rk`nfymbmbkwb g`swyìr`gd+ Sb dkdj`xdyfk jfs bnbcwfs sfiyb jdy`l`g`xdc`·fk gb jd qjdcd trb qyfgrcbk jds g`nbybkwbs cfkg`c`fkbs gb cfkwfykf p gb jdm`-kdgf+ Qfy bhbmqjf* sb fiwr~f trb qdyd rkd m`smd sbcrbkc`d gb jdm`kdgf* bj drmbkwfgbj k ·rmbyf gb j·dm`kds drmbkwd jd y`l`gbx d jd bu`·fk gb jd qjdcd+

Sb fiwr~`byfk ybsrjwdgfs qdyd jd cdyld gb ndjjd gb jd qy`mby j·dm`kd gb rkd qjdcd ybcwdk-lrjdy wdkwf idhf rkd cdyld wydks~bysdj rk`nfymbmbkwb g`swyìr`gd* cfmf qdyd rkd cdyldgb wydcc`·fk dcw ·rdkgf bk rkf gb srs ifygbs+ Sb dkdj`xdyfk jfs bnbcwfs trb wbk·Ĵdk sfiyb jdybs`swbkc`d* jds g`nbybkwbs sbcrbkc`ds gb jdm`kdgf+ Qfy bhbmqjf* sb bkcfkwy·f trb bj jdm`-kdgf cyrxdgf s`m ·bwy`cf %1&01&01&1) gb mdwby`dj cfmqrbswf lydfflwf–bqfu`* sfqfywd dqyf-u`mdgdmbkwb rk 92 " m ·ds gb cdyld dkwbs gb jd ndjjd gb jd qy`mby j·dm`kd trb rkd g`s-qfs`c`·fk ds`m·bwy`cd %1&01&1&01) qdyd crdjtr`byd gb jfs gfs bswdgfs gb cdyld+ Wdmi`·bk sbfiwr~f trb rk jdm`kdgf s`m·bwy`cf %72& ∙ 72&72) qybsbkwd ~bkwdhds gb ybs`swbkc`d nybkwb djfs gfs dkwby`fybs* crdkgf jd cdyld buwbykd dqj`cdgd bs wydks~bysdj* p gbs~bkwdhds crdkgfbswd bs qjdkdy+

Wfgfs jfs ybsrjwdgfs nrbyfk cfmqdydgfs cfk dtrbjjfs qybsbkwdgfs qfy fwyfs drwfybs _7]fiwbk`·bkgfsb rkd irbkd cfkcfygdkc`d lbkbydj bk wfgfs jfs cdsfs+

Sb cfkcjrpb trb bj bstrbmd krm·by`cf `mqjbmbkwdgf* bs ~`dijb qdyd sby rw`j`xdgf cf-mf rkd ebyydm`bkwd y·dq`gd gb g`sbkf bk jd b~djrdc`·fk gb jd cdqdc`gdg gb ybs`swbkc`dgb g`nbybkwbs bstrbmds gb jdm`kdc`·fk* gdgds jds qyfq`bgdgbs mbc·dk`cds gb rk mdwby`djcfmqrbswf p rk bswdgf gb cdyld+

35



Ybnbybkc`ds

_4] O+M+ J`b| ^`iydw`fk fn M`kgj`k Qjdwbs* Bjsb~`by Sc`bkcb* 4005+

_9] W+P+ Odm* E+N+ Seby* W+K+ Cedf * Qybg`cw fks fn Gbbcw`fk dkg N`ysw-Qjp Nd`jryb Jfdg

fn We`k Jdm`kdwbg Cfmqfs`wb Qjdwbs ~`d web N`k`wb Bjbmbkw Dqqyfdce* @kw+ H+ Sfj`gsSwyrcwrybs* ^fj 33* Kf+ 3* qq 3<2 -305* 400>

_3] H+K+ Ybggp Mbcedk`cs fn Jdm`kdwbg Cfmqfs`wb Qjdwbs dkg Sebjjs* 9kg Bg`w`fk* CYCQybss* 9117+

_7] H+K+ Ybggp* N`k`wb Bjbmbkw Dkdjps`s fn Cfmqfs`wb Jdm`kdwbs* Ojr|by Dcdgbm`cQrij`sebys* 9112+

_2] H+K+ Ybggp* Dk @kwyfgrcw`fk wf web N`k`wb Bjbmbkw Mbwefg* McLyd|-E`jj* 4003+

_>] L+H+ Wry~bp* Budcw dkg Dqqyfu`mdwb J`kbdy dkg Kfkj`kbdy @k`w`dj Nd`jryb Dkdjps`s fn Jdm`kdwbg M`kgj`k Qjdwbs `k Njburyb* Cfmqfs`wb Swyrcwrybs* ^fj+ 2* qq+ 434-4<4*

4050+

30



>+ Dq ·bkg`cb

Sb wydkscy`ib d cfkw`krdc`·fk bj c·fg`lf nrbkwb gbj qyflydmd CfsmfsQjdwb+bub

QYFLYDM CFMQFSQJDWB

RSB DSSBMIJBYSRSB SFJ^BYS

RSB SWYBSS

RSB IFRKGDYP

RSB QFSW

@MQJ@C@W KFKB

CEDYDCWBY(21 88 GRMMP

GFRIJB QYBC@S@FK* DJJFCDWDIJB 88 OLJFI%8*8)

GFRIJB QYBC@S@FK* DJJFCDWDIJB 88 UKFGB%8)* PKFGB%8)*

+ WLJFI%8*8)*YESKJK%8)

GFRIJB QYBC@S@FK* DJJFCDWDIJB 88 NLJFIDJ%8)*\LJFIDJ%8)*RLJFIDJ%8)

@KWBLBY 88 BWPQ*KLQ*GFN*KBJBM*KKFGB*KBT*DI*KG

@KWBLBY 88 O*@*ND@JQJP%7)*DRU*H *Y*JDPBY *KKN

@KWBLBY* DJJFCDWDIJB 88 G@Y@CE%8)*CFKBCW%8*8)*W@YD%8)*SWBKC@J%8)*

+ DNNCFJ%8*8)*DRUKKN%8)

GFRIJB QYBC@S@FK 88 NDCWFY

GFRIJB QYBC@S@FK 88 NKB\*DMQ*KRM*GBK*YBS@GRF*GBJWD*NDCW

GFRIJB QYBC@S@FK* DJJFCDWDIJB 88RFJG%8)* RKB\%8)*SWY%8*8*8*8*8)*

+ SWYN%8*8*8*8*8)

GFRIJB QYBC@S@FK* DJJFCDWDIJB 88 KMTL%8*8*8)*YFWD%8*8)

FQBK%RK@W=41*N@JB=‐qybqyfcbsf+wuw‐)

FQBK%RK@W=91*N@JB=‐GDWFSQJDCD+WUW‐)

FQBK%RK@W=71*N@JB=‐NDJJD+WUW‐)

YB\@KG%91)

GF \E@JB%GRMMP+KB+‐KRMBYFVGBVCDQDS8‐)

YBDG%91*() GRMMP

BKG GFYBDG%91*() JDPBY

YB\@KG%91)

GF \E@JB%GRMMP+KB+‐DMQJ@WRGVCDYLD8‐)

YBDG%91*() GRMMP

BKG GF

YBDG%91*() DMQ

YB\@KG%91)

GF \E@JB%GRMMP+KB+‐GBJWDVCDYLD8‐)

YBDG%91*() GRMMP

BKG GF

YBDG%91*() GBJWD

YB\@KG%91)

CJFSB%91)

YB\@KG%41)GF \E@JB %GRMMP+KB+‐KRMBYFVGBVBJBMBKWFSVPVKFGFS‐)

YBDG%41*() GRMMP

BKG GF

YBDG%41*() KBJBM* KKFGB*BWPQ

SBJBCW CDSB %BWPQ)

CDSB%5*0)

KLQ=3

GFN=2

71



KKN=3

CDSB%7)

KLQ=9

GFN=2

KKN=9

BKG SBJBCW

DJJFCDWB%UKFGB%KKFGB)*PKFGB%KKFGB)*CFKBCW%KBJBM*BWPQ))

DJJFCDWB%W@YD%KKFGB(GFN)*SWBKC@J%BWPQ(GFN))

DJJFCDWB%\LJFIDJ%KKFGB))

DJJFCDWB%RLJFIDJ%KKFGB(GFN))

DJJFCDWB%G@Y@CE%KG))

DJJFCDWB%KMTL%KBJBM*%KLQ-4)((9*5))

$JBCWRYD CFKBCW@^@GDGBS

$SB FIW@BKB BJ DKCEF GB IDKGD

YB\@KG%41)

$SB JBBK JDS CFYGBKGDS GB JFS KFGFS

GF \E@JB %GRMMP+KB+‐CFFYGBKDGDS8‐)

YBDG%41*() GRMMP

BKG GF

GF @=4*KKFGBYBDG %41*() O* UKFGB%@)*PKFGB%@)

BKG GF

YB\@KG%41)

GF \E@JB %GRMMP+KB+‐CFKBCW@^@GDGBS8‐)

YBDG%41*() GRMMP

BKG GF

GF @=4*KBJBM

YBDG %41*() O* CFKBCW%@*8)

BKG GF

YB\@KG%41)

$JBCWRYD CFKBCW@^@GDGBS

$SB FIW@BKB BJ DKCEF GB IDKGD

CDJJ CFKWFYKF%W@YD*KG)

KBT=KKFGB(GFN-KGDRU=1

GF @=4*KBJBM

Y=4

GF H=4*BWPQ

GF O=4*GFN

@N %W@YD%GFN(%CFKBCW%@*H)-4)/O)+LW+1) WEBK

SWBKC@J%Y)=W@YD%GFN(%CFKBCW%@*H)-4)/O)

Y=Y/4

BKG @N

BKG GF

BKG GF

@N %%MDU^DJ%SWBKC@J%48Y-484))-M@K^DJ%SWBKC@J%48Y-484)))+LW+DRU)

+ WEBK

DRU=MDU^DJ%SWBKC@J%48Y-484))-M@K^DJ%SWBKC@J%48Y-484))BKG @N

BKG GF

DI=%DRU/4)(9-4

C SB FIW@BKB BJ KRMBYF GB BCRDC@FKBS

GBDJJFCDWB%G@Y@CE)

GBDJJFCDWB%SWBKC@J)

74



DJJFCDWB%OLJFI%KBT*DI))

DJJFCDWB%WLJFI%KBT*DI))

DJJFCDWB%NLJFIDJ%KBT))

DJJFCDWB%RFJG%KBT))

DJJFCDWB%RKB\%KBT)*YESKJK%KBT))

DJJFCDWB%SWY%KBJBM*JDPBY*3*%KLQ-4)((9*GFN)*

+ SWYN%KBJBM*JDPBY*3*%KLQ-4)((9*GFN))C N@K CFKG@C@FKBS GB CFKWFYKF

C DKDJ@S@S GB N@YSW QJP ND@JRYB

C--------------------------------------------------------

CDJJ CFKSW@WRW@^D

CDJJ YES%BWPQ*KLQ*GFN*KKN*UKFGB*PKFGB*CFKBCW*W@YD*NLJFIDJ)

C----------------------------------------------------------------

NDCW=4+1G/1

22 CFKW@KRB

RLJFIDJ=1+1G/1

RFJG=1+1G/1

4 OLJFI=1+1G/1

CDJJ DSSBMIJP%KBJBM*BWPQ*KLQ*GFN*UKFGB*PKFGB*CFKBCW*W@YD*

+ RLJFIDJ*OLJFI*WLJFI)

WLJFI=WLJFI/OLJFICDJJ MDWU^BC%OLJFI*RFJG*YESKJK)

c YESKJK=1+1G/1

CDJJ SFJ^BJR%WLJFI*RKB\*DMQ(NLJFIDJ-YESKJK)

C LFWF 7

RKB\=RKB\/RFJG

GF @=4*KKFGB(GFN

@N%W@YD%@)+LW+1) WEBK

RLJFIDJ%@)=RKB\%W@YD%@))

BKG @N

BKG GF

KRM=1+1G/1

GBK=1+1G/1

GF @=4*KBT

KRM=DIS%RKB\%@)-RFJG%@))((9+1G/1/KRMGBK=RKB\%@)((9+1/GBK

BKG GF

YBS@GRF=STYW%KRM&GBK)

\Y@WB%(*() ‐YBS@GRF‐* YBS@GRF

@N %YBS@GRF+JW+4+1B-7) WEBK

LFWF 7

BJSB

RFJG=RKB\

LFWF 4

BKG @N

3 CFKW@KRB

CDJJ SWYBSSN@BJG%BWPQ*KLQ-4*GFN

+*UKFGB*PKFGB*CFKBCW*RLJFIDJ*SWY*SWYN*KMTL)

CDJJ ND@JCY@W%SWY*ND@JQJP*NDCWFY)@N %DIS%NDCWFY-4+1)+JW+4B-7) WEBK

LFWF 7

BKG @N

@N %NDCWFY+JW+4+1) WEBK

GBJWD=GBJWD(NDCW

DMQ=GBJWD/DMQ

BJSB

79



NDCW=1+2

GBJWD=GBJWD(NDCW

DMQ=DMQ-GBJWD

BKG @N

LFWF 22

7 CFKW@KRB

CDJJ SWYBSSN@BJG%BWPQ*KLQ-4*GFN+*UKFGB*PKFGB*CFKBCW*RLJFIDJ*SWY*SWYN*KMTL)

CDJJ ND@JCY@W%SWY*ND@JQJP*NDCWFY)

CDJJ QFSWL@G%RLJFIDJ*SWY*KMTL)

\Y@WB%71*() ‐NDCWFYVGB NDJJD ‐*DMQ

\Y@WB%71*() ‐JRLDYVGB NDJJD ‐*ND@JQJP

BKG QYFLYDM

C --------------------------------------------------

MFGRJB DSSBMIJBYS

@MQJ@C@W KFKB

CFKWD@KS

SRIYFRW@KB DSSBMIJP%KBJBM*BWPQ*KLQ*GFN*UKFGB*PKFGB*CFKBCW*W@YD*

+ RLJFIDJ*OLJFI*WLJFI)

RSB SEDQB@KWBLBY*@KWBKW%@K) 88 BWPQ*KLQ*GFN

@KWBLBY* @KWBKW%@K) 88 W@YD%8)*CFKBCW%8*8)

GFRIJBQYBC@S@FK*@KWBKW%FRW) 88 OLJFI%8*8)*WLJFI%8*8)

GFRIJBQYBC@S@FK*@KWBKW%@K) 88 UKFGB%8)*PKFGB%8)*RLJFIDJ%8)

@KWBLBY 88 @*M*K*KBJBM*DIKG*@JFCDJ*HJFCDJ

@KWBLBY 88 DRU*Y*S*M@G*O*H*@LJFIDJ*HLJFIDJ

GFRIJBQYBC@S@FK 88 NBMGDWD%<*KLQ((9*BWPQ)

GFRIJBQYBC@S@FK*G@MBKS@FK%3) 88 LQ*L\*LQYBG*L\Y

GFRIJBQYBC@S@FK* G@MBKS@FK%KLQ((9*BWPQ) 88 GQS@GU@*GQS@GBWD*QS@

GFRIJBQYBC@S@FK* G@MBKS@FK%%KLQ-4)((9*BWPQ) 88 GQS@GU@Y*GQS@GBWDY* QS@Y

GFRIJB QYBC@S@FK* G@MBKS@FK%BWPQ(GFN*BWPQ(GFN) 88 OJFCDJ*WJFCDJ*OKJKJFC

GFRIJB QYBC@S@FK 88 UJFCDJ%BWPQ)*PJFCDJ%BWPQ)*RJFCDJ%GFN*BWPQ)

WLJFI=1+1G/1OLJFI=1+1G/1

DIKG=S@XB%OLJFI%4*8))

M@G=%DIKG/4)&9

CDJJ LDRSSQF@KWS%BWPQ*LQ*LQYBG*L\*L\Y)

CDJJ GBY@^DGDSNRKC@FKNFYMD%LQ*GQS@GU@*GQS@GBWD)

CDJJ GBY@^DGDSNRKC@FKNFYMD%LQYBG*GQS@GU@Y*GQS@GBWDY)

CDJJ NRKC@FKNFYMD%LQ*QS@)

CDJJ NRKC@FKNFYMD%LQYBG*QS@Y)

NBMGDWD%4*8*8)=QS@%8*8)

NBMGDWD%9*8*8)=GQS@GU@%8*8)

NBMGDWD%3*8*8)=GQS@GBWD%8*8)

GF Y=4*KLQ-4

GF S=4*KLQ-4M=%Y-4)(%KLQ-4)/S

NBMGDWD%7*M*8)=QS@Y%M*8)

NBMGDWD%2*M*8)=GQS@GU@Y%M*8)

NBMGDWD%>*M*8)=GQS@GBWDY%M*8)

BKG GF

BKG GF

NBMGDWD%<*48KLQ84*4)=L\%8)

73



NBMGDWD%<*48KLQ-484*9)=L\Y%8)

GF 911 @=4*KBJBM

UJFCDJ%48BWPQ84)=UKFGB%CFKBCW%@*48BWPQ84))

PJFCDJ%48BWPQ84)=PKFGB%CFKBCW%@*48BWPQ84))

OJFCDJ=1+1G/1

GF O=4*BWPQGF H=4*GFN

RJFCDJ%H*O)=RLJFIDJ%%CFKBCW%@*O)-4)(GFN/H)

BKG GF

BKG GF

$FIW@BKB JD MDWY@X JFCDJ

CDJJ OJFCKFKJ@KBDY%BWPQ*KLQ*GFN*UJFCDJ*PJFCDJ*

+ NBMGDWD%%&9*3*<&)*8*8)*RJFCDJ*OKJKJFC*WJFCDJ)

CDJJ MDWY@XOJFCDJ%BWPQ*KLQ*GFN*UJFCDJ*PJFCDJ*NBMGDWD*OJFCDJ)

OJFCDJ=OJFCDJ/OKJKJFC

$SB BKSDMIJDK JFS BJBMBKWFS GB JD MDWY@X JFCDJ BK JD MDWY@X LJFIDJ

GF M=4*BWPQ

$^DMFS D DQJ@CDY CFKG@C@FKBS GB CFKWFYKF

GF Y=4*GFN

@LJFIDJ=%CFKBCW%@*M)-4)(GFN/Y@N%W@YD%@LJFIDJ)+LW+1) WEBK

@JFCDJ=%M-4)(GFN/Y

GF K=4*BWPQ

GF S=4*GFN

HLJFIDJ=%CFKBCW%@*K)-4)(GFN/S

@N%W@YD%HLJFIDJ)+LW+1) WEBK

HJFCDJ=%K-4)(GFN/S

$S@ QBYWBKBCB D RKD CFJRMKD GFKGB KF EDP G@Y@CEJBW

$EDPTRB ^BY S@ JD CFJRMKD BS SRQBY@FY D JD N@JD SBLRK JD KRMBYDC@FK IDKGD

DRU=W@YD%HLJFIDJ)-W@YD%@LJFIDJ)/M@G

OLJFI%W@YD%@LJFIDJ)*DRU)=OJFCDJ%@JFCDJ*HJFCDJ)/OLJFI%W@YD%@LJFIDJ)*DRU)

WLJFI%W@YD%@LJFIDJ)*DRU)=WJFCDJ%@JFCDJ*HJFCDJ)/WLJFI%W@YD%@LJFIDJ)*DRU)

BKG @N

BKG GFBKG GF

BKG @N

BKG GF

BKG GF

911 CFKW@KRB

BKG SRIYFRW@KB

C--------------------------------------------------------------------------

SRIYFRW@KB MDWY@XOJFCDJ%BWPQ*KLQ*GFN*UJFCDJ*PJFCDJ*NBMGDWD*OBJBM)

@KWBLBY* @KWBKW%@K) 88 BWPQ*KLQ*GFN

GFRIJB QYBC@S@FK* @KWBKW%@K) 88 UJFCDJ%8)*PJFCDJ%8)*NBMGDWD%8*8*8)

GFRIJB QYBC@S@FK*@KWBKW%FRW) 88 OBJBM%8*8)

@KWBLBY 88 Y*S*@KGBU*O*J*@KGU*HKGU*M*KGFRIJB QYBC@S@FK*G@MBKS@FK%BWPQ)88 GQS@GU*GQS@GP

GFRIJB QYBC@S@FK* G@MBKS@FK%KLQ((9*BWPQ) 88 QS@*GQS@GU@*GQS@GBWD

GFRIJB QYBC@S@FK* G@MBKS@FK%%KLQ-4)((9*BWPQ) 88 GQS@GU@Y*GQS@GBWDY*QS@Y

GFRIJB QYBC@S@FK* G@MBKS@FK%BWPQ*BWPQ) 88 GUIGU*GPIGP*GUIGP*GUIQ*GPIQ*QIQ

GFRIJB QYBC@S@FK 88 L\%KLQ)*L\Y%KLQ-4)*H@K^%9*9)*GBW*NDCW

GFRIJB QYBC@S@FK 88 D%2*2)*I%3*3)*G%3*3)*@KBY%3)

GFRIJB QYBC@S@FK* G@MBKS@FK%GFN*GFN*BWPQ*BWPQ) 88 OJFC

77



CFMMFK &MDWBY@DJ& D*I*G*@KBY

QS@%8*8)=NBMGDWD%4*8*8)

GQS@GU@%8*8)=NBMGDWD%9*8*8)

GQS@GBWD%8*8)=NBMGDWD%3*8*8)

QS@Y=NBMGDWD%7*48%KLQ-4)((984*8)

GQS@GU@Y=NBMGDWD%2*48%KLQ-4)((984*8)GQS@GBWDY=NBMGDWD%>*48%KLQ-4)((984*8)

L\=NBMGDWD%<*48KLQ84*4)

L\Y=NBMGDWD%<*48KLQ-484*9)

$Q@SDMFS WFGDS JDS ^DY@DIJBS

OJFC=1+1G/1

QIQ=1+1G/1

GUIGU=1+1G/1

GPIGP=1+1G/1 GUIGP=1+1G/1

$JFS WBYM@KFS GB JD @KWBLYDC@FK KF YBGRC@GD SB CDJCRJDK QY@MBYF

GF Y=4*KLQ

GF S=4*KLQ

$HDCFI@DKF B @K^BYSD GBJ HDCFI@DKF@KGBU=S/KLQ(%Y-4)

H@K^%9*9)=gfwVqyfgrcw%UJFCDJ*GQS@GU@%@KGBU*8))

H@K^%4*9)=-gfwVqyfgrcw%PJFCDJ*GQS@GU@%@KGBU*8))

H@K^%9*4)=-gfwVqyfgrcw%UJFCDJ*GQS@GBWD%@KGBU*8))

H@K^%4*4)=gfwVqyfgrcw%PJFCDJ*GQS@GBWD%@KGBU*8))

GBW=H@K^%4*4)(H@K^%9*9)-H@K^%4*9)(H@K %9*4)

H@K^=H@K^&GBW

NDCW=GBW(L\%Y)(L\%S)

GQS@GU=H@K %4*4)(GQS@GU@%@KGBU*8)/H@K %4*9)(GQS@GBWD%@KGBU*8)

GQS@GP=H@K %9*4)(GQS@GU@%@KGBU*8)/H@K %9*9)(GQS@GBWD%@KGBU*8)

GF M=4*BWPQ

GF K=4*BWPQ

C JDS ^DY@DIJBS GUIGU S@LK@N@CD SFK JDS MRJW@QJ@CDC@FKBS YBQBW@GDS TRB DQDYBCBK BK 7+99>

C D BSWDS SB JDS @KWBLYDQIQ%M*K)=QS@%@KGBU*M)(QS@%@KGBU*K)(NDCW/QIQ%M*K)

GUIGU%M*K)=GQS@GU%M)(GQS@GU%K)(NDCW/GUIGU%M*K)

GPIGP%M*K)=GQS@GP%M)(GQS@GP%K)(NDCW/GPIGP%M*K)

GUIGP%M*K)=GQS@GU%M)(GQS@GP%K)(NDCW/GUIGP%M*K)

BKG GF

BKG GF

$WBYM@KD Y P S

BKG GF

BKG GF

GF M=4*BWPQ

GF K=4*BWPQ OJFC%4*4*M*K)=D%4*4)(GUIGU%M*K)/D%3*3)(GPIGP%M*K)/D%4*3)(%GUIGP%M*K)/GUIGP%K*M))

OJFC%4*9*M*K)=D%4*9)(GUIGP%M*K)/D%3*3)(GUIGP%K*M)/D%9*3)(GPIGP%M*K)/D%4*3)(GUIGU%M*K)

OJFC%4*7*M*K)=I%4*4)(GUIGU%M*K)/I%4*3)(GUIGP%M*K)/I%4*3)(GUIGP%K*M)/I%3*3)(GPIGP%M*K)

OJFC%4*2*M*K)=I%4*3)(GUIGU%M*K)/I%4*9)(GUIGP%M*K)/I%3*3)(GUIGP%K*M)/I%9*3)(GPIGP%M*K)OJFC%9*9*M*K)=D%9*9)(GPIGP%M*K)/D%3*3)(GUIGU%M*K)/D%9*3)(%GUIGP%M*K)/GUIGP%K*M))

OJFC%9*7*M*K)=I%4*9)(GUIGP%K*M)/I%9*3)(GPIGP%M*K)/I%4*3)(GUIGU%M*K)/I%3*3)(GUIGP%M*K)

OJFC%9*2*M*K)=I%9*3)(%GUIGP%M*K)/GUIGP%K*M))/I%9*9)(GPIGP%M*K)/I%3*3)(GUIGU%M*K)

OJFC%7*7*M*K)=G%4*4)(GUIGU%M*K)/G%4*3)(GUIGP%M*K)/G%4*3)(GUIGP%K*M)/G%3*3)(GPIGP%M*K)



OJFC%9*4*K*M)=OJFC%4*9*M*K)

72








BKG GF

BKG GFQIQ=1+1

GUIGU=1+1

GPIGP=1+1

GUIGP=1+1

GUIQ=1+1

GPIQ=1+1

$DEFYD SB CDJCRJDK JFS WBYM@KFS GB JD @KWBLYDC@FK YBGRC@GD

GF Y=4*KLQ-4

GF S=4*KLQ-4

$HDCFI@DKF B @K^BYSD GBJ HDCFI@DKF

@KGBU=S/%KLQ-4)(%Y-4)

H@K^%9*9)=gfwVqyfgrcw%UJFCDJ*GQS@GU@Y%@KGBU*8))

H@K^%4*9)=-gfwVqyfgrcw%PJFCDJ*GQS@GU@Y%@KGBU*8))

H@K^%9*4)=-gfwVqyfgrcw%UJFCDJ*GQS@GBWDY%@KGBU*8))H@K^%4*4)=gfwVqyfgrcw%PJFCDJ*GQS@GBWDY%@KGBU*8))

GBW=H@K^%4*4)(H@K^%9*9)-H@K^%4*9)(H@K %9*4)

H@K^=H@K^&GBW

GQS@GU=H@K %4*4)(GQS@GU@Y%@KGBU*8)/H@K %4*9)(GQS@GBWDY%@KGBU*8)

GQS@GP=H@K %9*4)(GQS@GU@Y%@KGBU*8)/H@K %9*9)(GQS@GBWDY%@KGBU*8)

NDCW=GBW(L\Y%Y)(L\Y%S)

GF M=4*BWPQ

GF K=4*BWPQ

GUIGU%M*K)=GQS@GU%M)(GQS@GU%K)(NDCW/GUIGU%M*K)

GPIGP%M*K)=GQS@GP%M)(GQS@GP%K)(NDCW/GPIGP%M*K)

GUIGP%M*K)=GQS@GU%M)(GQS@GP%K)(NDCW/GUIGP%M*K)

QIQ%M*K)=QS@Y%@KGBU*M)(QS@Y%@KGBU*K)(NDCW/QIQ%M*K)

GUIQ%M*K)= GQS@GU%M)(QS@Y%@KGBU*K)(NDCW/GUIQ%M*K)

GPIQ%M*K)=GQS@GP%M)(QS@Y%@KGBU*K)(NDCW/GPIQ%M*K)BKG GF

BKG GF

$WBYM@KD Y P S

BKG GF

BKG GF

GF M=4*BWPQ

GF K=4*BWPQ

OJFC%3*3*M*K)=D%2*2)(GUIGU%M*K)/D%7*2)(GUIGP%M*K)/ D%7*2)(GUIGP%K*M)/D%7*7)(GPIGP%M*K)

OJFC%3*7*M*K)=D%2*2)(GUIQ%M*K)/D%7*2)(GPIQ%M*K)

OJFC%3*2*M*K)=D%7*2)(GUIQ%M*K)/D%7*7)(GPIQ%M*K)

OJFC%7*7*M*K)=D%2*2)(QIQ%M*K)/OJFC%7*7*M*K)

OJFC%7*2*M*K)=D%7*2)(QIQ%M*K)/OJFC%7*2*M*K)

OJFC%2*2*M*K)=D%7*7)(QIQ%M*K)/OJFC%2*2*M*K)OJFC%7*3*K*M)=OJFC%3*7*M*K)



BKG GF

BKG GF

GF O=4*BWPQ

GF J=4*GFN

7>



@KGU=GFN(%O-4)/J

GF Y=4*BWPQ

GF S=4*GFN

HKGU=GFN(%Y-4)/S

OBJBM%@KGU*HKGU)=OJFC%J*S*O*Y)

BKG GF

BKG GFBKG GF

BKG GF

BKG SRIYFRW@KB

C--------------------------------------------------------------

SRIYFRW@KB OJFCKFKJ@KBDY%BWPQ*KLQ*GFN*UJFCDJ*PJFCDJ*NBMGDWD*RJFCDJ*OBJBM*WBJBM)

@KWBLBY* @KWBKW%@K) 88 BWPQ*KLQ*GFN

GFRIJB QYBC@S@FK* @KWBKW%@K) 88 UJFCDJ%8)*PJFCDJ%8)*NBMGDWD%8*8*8)

GFRIJB QYBC@S@FK* @KWBKW%@K) 88 RJFCDJ%8*8)

GFRIJB QYBC@S@FK*@KWBKW%FRW) 88 OBJBM%8*8)*WBJBM%8*8)

@KWBLBY 88 Y*S*@KGBU*@*H*O*J*@KGU*HKGU*^BC%7)

GFRIJB QYBC@S@FK*G@MBKS@FK%BWPQ)88 GQS@GU*GQS@GP

GFRIJB QYBC@S@FK* G@MBKS@FK%KLQ((9*BWPQ) 88 GQS@GU@*GQS@GBWD

GFRIJB QYBC@S@FK 88 L\%KLQ)*H@K^%9*9)*GBW*NDCW

GFRIJB QYBC@S@FK 88 D%2*2)*I%3*3)*G%3*3)*@KBY%3)GFRIJB QYBC@S@FK* G@MBKS@FK%GFN*GFN*BWPQ*BWPQ) 88 OJFC*WJFC

GFRIJB QYBC@S@FK88 QDY%3)*CFYCE%3)*GG%2*9)*^DRU%3)


OJFC=1+1G/1

WJFC=1+1G/1

GQS@GU@%8*8)=NBMGDWD%4*8*8)

GQS@GBWD%8*8)=NBMGDWD%9*8*8)

L\=NBMGDWD%3*48KLQ84*4)

$JFS WBYM@KFS GB JD @KWBLYDC@FK KF YBGRC@GD SB CDJCRJDK QY@MBYF

GF Y=4*KLQ

GF S=4*KLQ

$HDCFI@DKF B @K^BYSD GBJ HDCFI@DKF

@KGBU=S/KLQ(%Y-4)H@K^%9*9)=gfwVqyfgrcw%UJFCDJ*GQS@GU@%@KGBU*8))




GBW=H@K^%4*4)(H@K^%9*9)-H@K^%4*9)(H@K %9*4)

H@K^=H@K^&GBW

GQS@GU=H@K %4*4)(GQS@GU@%@KGBU*8)/H@K %4*9)(GQS@GBWD%@KGBU*8)

GQS@GP=H@K %9*4)(GQS@GU@%@KGBU*8)/H@K %9*9)(GQS@GBWD%@KGBU*8)


GF @=4*2

GG%@*4)=GFWVQYFGRCW%RJFCDJ%@*8)*GQS@GU)

GG%@*9)=GFWVQYFGRCW%RJFCDJ%@*8)*GQS@GP)

BKG GF

GF @=4*BWPQGF H=4*BWPQ

QDY%4)=GG%3*4)(GQS@GP%H)/GG%3*9)(GQS@GU%H)

CFYCE%4)=D%4*4)(GG%3*4)(GQS@GU%H)/D%4*9)(GG%3*9)(GQS@GP%H)/D%4*3)(QDY%4)


OJFC%4*3*@*H)=%GQS@GU%@)(CFYCE%4)/GQS@GP%@)(CFYCE%9))(1+2(NDCW/OJFC%4*3*@*H)


OJFC%9*3*@*H)=%GQS@GP%@)(CFYCE%4)/GQS@GU%@)(CFYCE%9))(1+2(NDCW/OJFC%9*3*@*H)

7<



CFYCE%4)=D%4*4)(GG%3*4)(GG%3*4)/D%4*9)(GG%3*9)(GG%3*9)/9+1(D%4*3)(GG%3*4)(GG%3*9)

CFYCE%9)=D%4*3)(GG%3*4)(GG%3*4)/D%9*3)(GG%3*9)(GG%3*9)/9+1(D%3*3)(GG%3*4)(GG%3*9)

QDY%4)=GQS@GU%@)(GQS@GP%H)/GQS@GU%H)(GQS@GP%@)

QDY%9)=D%4*9)(GG%3*4)(GG%3*4)/D%9*9)(GG%3*9)(GG%3*9)/9+1(D%9*3)(GG%3*4)(GG%3*9)

OJFC%3*3*@*H)=%GQS@GU%@)(GQS@GU%H)(CFYCE%4)/

+QDY%4)(CFYCE%9)/GQS@GP%@)(GQS@GP%H)(QDY%9))(1+2(NDCW/OJFC%3*3*@*H)

QDY%4)=I%4*4)(GQS@GU%H)/I%4*3)(GQS@GP%H)QDY%9)=I%4*3)(GQS@GU%H)/I%3*3)(GQS@GP%H)

CFYCE%4)=GG%3*4)(QDY%4)/GG%3*9)(QDY%9)

QDY%4)=I%4*9)(GQS@GU%H)/I%9*3)(GQS@GP%H)


OJFC%3*7*@*H)=%GQS@GU%@)(CFYCE%4)/GQS@GP%@)(CFYCE%9))(NDCW/OJFC%3*7*@*H)

QDY%4)=I%4*9)(GQS@GP%H)/I%4*3)(GQS@GU%H)





OJFC%3*2*@*H)=%GQS@GU%@)(CFYCE%4)/GQS@GP%@)(CFYCE%9))(NDCW/OJFC%3*2*@*H)

OJFC%3*4*H*@)=OJFC%4*3*@*H)(9+1

OJFC%3*9*H*@)=OJFC%9*3*@*H)(9+1

OJFC%7*3*H*@)=OJFC%3*7*@*H)(1+2OJFC%2*3*H*@)=OJFC%3*2*@*H)(1+2

^DRU%4)=GQS@GU%H)(GQS@GU%@)

^DRU%9)=GQS@GP%H)(GQS@GP%@)

^DRU%3)=GQS@GP%H)(GQS@GU%@)/GQS@GP%@)(GQS@GU%H)

CFYCE%4)=GFWVQYFGRCW%%&D%4*4)*D%4*9)*D%4*3)&)*^DRU)


WJFC%3*3*@*H)=%GG%4*4)(CFYCE%4)/GG%4*9)(CFYCE%9))(NDCW/WJFC%3*3*@*H)


WJFC%3*3*@*H)=%GG%9*9)(CFYCE%4)/GG%9*4)(CFYCE%9))(NDCW/WJFC%3*3*@*H)

QDY%4)=GG%3*4)(GQS@GU%H)

QDY%9)=GG%3*9)(GQS@GP%H)

QDY%3)=GG%3*4)(GQS@GP%H)/GG%3*9)(GQS@GU%H)

CFYCE%4)=D%4*4)(QDY%4)/D%4*9)(QDY%9)/D%4*3)(QDY%3)

CFYCE%9)=D%4*3)(QDY%4)/D%9*3)(QDY%9)/D%3*3)(QDY%3)CFYCE%3)=D%4*9)(QDY%4)/D%9*9)(QDY%9)/D%9*3)(QDY%3)

CFYCE%4)=CFYCE%4)(GQS@GU%@)(GG%3*4)

CFYCE%9)=CFYCE%9)(%GQS@GU%@)(GG%3*9)/GG%3*4)(GQS@GP%@))

CFYCE%3)=CFYCE%3)(GQS@GP%@)(GG%3*9) WJFC%3*3*@*H)=%CFYCE%4)/CFYCE%9)/CFYCE%3))(NDCW/WJFC%3*3*@*H)

QDY%4)=I%4*3)(GG%7*4)/I%3*3)(GG%7*9)

QDY%9)=I%4*4)(GG%7*4)/I%4*3)(GG%7*9)

CFYCE%4)=GQS@GU%H)(QDY%9)/GQS@GP%H)(QDY%4)

QDY%9)=I%4*9)(GG%7*4)/I%9*3)(GG%7*9)

CFYCE%9)=GQS@GP%H)(QDY%9)/GQS@GU%H)(QDY%4)

WJFC%3*3*@*H)=%CFYCE%4)(GQS@GU%@)/CFYCE%9)(GQS@GP%@))(NDCW/WJFC%3*3*@*H)

QDY%4)=I%9*3)(GG%2*9)/I%3*3)(GG%2*4)

QDY%9)=I%4*9)(GG%2*9)/I%4*3)(GG%2*4)

CFYCE%4)=GQS@GU%H)(QDY%9)/GQS@GP%H)(QDY%4)

QDY%9)=I%9*9)(GG%2*9)/I%9*3)(GG%2*4)CFYCE%9)=GQS@GP%H)(QDY%9)/GQS@GU%H)(QDY%4)

WJFC%3*3*@*H)=%CFYCE%4)(GQS@GU%@)/CFYCE%9)(GQS@GP%@))(NDCW/WJFC%3*3*@*H)

BKG GF

BKG GF

BKG GF

BKG GF

75



^BC=%&4*9*7*2&)

WJFC%^BC*3*8*8)=OJFC%^BC*3*8*8)

GF O=4*BWPQ

GF J=4*GFN

@KGU=GFN(%O-4)/J

GF Y=4*BWPQ

GF S=4*GFNHKGU=GFN(%Y-4)/S

OBJBM%@KGU*HKGU)=OJFC%J*S*O*Y)

WBJBM%@KGU*HKGU)=WJFC%J*S*O*Y)

BKG GF

BKG GF

BKG GF

BKG GF

BKG SRIYFRW@KB

c---------------------------------------------------------------------------------

SRIYFRW@KB YES%BWPQ*KLQ*GFN*KKN*UKFGB*PKFGB*CFKBCW*W@YD*NLJFIDJ)

RSB SEDQB

GFRIJBQYBC@S@FK*@KWBKW%@K) 88 UKFGB%8)*PKFGB%8)

@KWBLBY*@KWBKW%@K) 88 W@YD%8)*CFKBCW%8*8)

@KWBLBY* @KWBKW%@K) 88 BWPQ*KLQ*GFN*KKNGFRIJB QYBC@S@FK* @KWBKW%FRW) 88 NLJFIDJ%8)


@KWBLBY 88 KJFDGS*@KGBU*O*@KGU

GFRIJB QYBC@S@FK 88 H@K^%9*9)*GBW*NDCW

GFRIJB QYBC@S@FK 88 GQS@4G%KLQ*KKN)*QS@4G%KLQ*KKN)

@KWBLBY 88 @*M*@JFCDJ*Y*S*H

@KWBLBY* DJJFCDWDIJB 88 JFDG%8*8)

GFRIJBQYBC@S@FK* DJJFCDWDIJB 88 JFDGGDWD%8)

GFRIJBQYBC@S@FK 88 UJFCDJ%BWPQ)*PJFCDJ%BWPQ)


GFRIJBQYBC@S@FK* G@MBKS@FK%KLQ((9*BWPQ) 88 GQS@GU@*GQS@GBWD*QS@

GFRIJB QYBC@S@FK* G@MBKS@FK%BWPQ(GFN)88 NJFCDJ

@KWBLBY 88 @LJFIDJ

FQBK%RK@W=41*N@JB=‐qybqyfcbsf+wuw‐)YB\@KG%41)

GF \E@JB %GRMMP+KB+‐CDYLDS8‐)

YBDG%41*() GRMMP

BKG GF

@=1

GF \E@JB%GRMMP+KB+‐N@KVCDYLDS‐)

YBDG%41*() GRMMP

@=@/4

BKG GF

KJFDGS=@-4

YB\@KG%41)

DJJFCDWB%JFDG%KJFDGS*3))

DJJFCDWB%JFDGGDWD%KJFDGS))

GF \E@JB %GRMMP+KB+‐CDYLDS8‐)YBDG%41*() GRMMP

BKG GF

GF @=4*KJFDGS

YBDG%41*() JFDG%@*8)*JFDGGDWD%@)

BKG GF


CDJJ NRKC@FKNFYMD4G%BWPQ*KLQ*LQ*QS@4G*GQS@4G)

70



CDJJ GBY@^DGDSNRKC@FKNFYMD%LQ*GQS@GU@*GQS@GBWD)

CDJJ NRKC@FKNFYMD%LQ*QS@)

NLJFIDJ=1+1G/1

GF 911 H=4*KJFDGS

NJFCDJ=1+1

UJFCDJ%48BWPQ84)=UKFGB%CFKBCW%JFDG%H*4)*48BWPQ84))

PJFCDJ%48BWPQ84)=PKFGB%CFKBCW%JFDG%H*4)*48BWPQ84))

@N %JFDG%H*3)+BT+>) WEBK

GF Y=4*KLQ

GF S=4*KLQ

@KGBU=S/KLQ(%Y-4)

H@K^%9*9)=gfwVqyfgrcw%UJFCDJ*GQS@GU@%@KGBU*8))




GBW=H@K^%4*4)(H@K^%9*9)-H@K^%4*9)(H@K %9*4)


GF O=4*BWPQ

@KGU=%O-4)(GFN/3

NJFCDJ%@KGU)=JFDGGDWD%H)(QS@%@KGBU*O)(NDCW/NJFCDJ%@KGU)BKG GF

BKG GF

BKG GF

BJSB

CDJJ JFDGIFRKG%GFN*KKN*QS@4G*GQS@4G*KLQ*L\*JFDG%H*8)*JFDGGDWD%H)*UJFCDJ*PJFCDJ*NJFCDJ)

BKG @N

GF M=4*BWPQ

GF Y=4*GFN

@LJFIDJ=%CFKBCW%JFDG%H*4)*M)-4)(GFN/Y

@N%W@YD%@LJFIDJ)+LW+1) WEBK

@JFCDJ=%M-4)(GFN/Y

NLJFIDJ%W@YD%@LJFIDJ))=NJFCDJ%@JFCDJ)/NLJFIDJ%W@YD%@LJFIDJ))

BKG @N

BKG GFBKG GF

$N@K GB WFGF

911 CFKW@KRB

BKG SRIYFRW@KB

C-------------------------------------------------------------------------

SRIYFRW@KB JFDGIFRKG%GFN*KKN*QS@4G*GQS@4G*KLQ*L\*JFDG*JFDGGDWD*UJFC*PJFC*NJFCDJ)

@KWBLBY* @KWBKW%@K) 88 GFN*KKN*KLQ*JFDG%8)

GFRIJB QYBC@S@FK* @KWBKW%@K) 88 JFDGGDWD*L\%8)

GFRIJB QYBC@S@FK* @KWBKW%@K) 88 UJFC%8)*PJFC%8)*QS@4G%8*8)*GQS@4G%8*8)

GFRIJB QYBC@S@FK* @KWBKW%FRW) 88 NJFCDJ%8)

@KWBLBY 88 KNDCB%KKN)*H*@*@KGU

GFRIJB QYBC@S@FK*G@MBKS@FK%KKN) 88 U*P*DRU

GFRIJB QYBC@S@FK 88 DKW@CJFCO*GS

SBJBCW CDSB%JFDG%9))CDSB%4)

DKW@CJFCO=4+1

KNDCB=%&4*9*2&)

CDSB%9)

DKW@CJFCO=4+1

KNDCB= %&9*3*>&)

CDSB%3)

21



DKW@CJFCO=-4+1

KNDCB=%&7*3*<&)

CDSB%7)

DKW@CJFCO=-4+1

KNDCB=%&4*7*5&)

BKG SBJBCW

GF @=4*KKN

U%@)=UJFC%KNDCB%@))

P%@)=PJFC%KNDCB%@))

BKG GF

DRU=1+1G/1

GF H=4*KKN

GF @=4*KLQ

GS=GFWVQYFGRCW%U%48KKN84)*GQS@4G%@*48KKN84))((9+1G/1/

+ GFWVQYFGRCW%P%48KKN84)*GQS@4G%@*48KKN84))((9+1G/1

GS=STYW%GS)

DRU%H)=QS@4G%@*H)(L\%@)(GS/DRU%H)

BKG GF

BKG GF

DRU=DRU(DKW@CJFCOGF @=4*KKN

@KGU=%KNDCB%@)-4)(GFN/JFDG%3)

NJFCDJ%@KGU)=JFDGGDWD(DRU%@)

BKG GF

BKG SRIYFRW@KB

BKG MFGRJB

c------------------------------------------------

MFGRJB IFRKGDYP

@MQJ@C@W KFKB

CFKWD@KS

SRIYFRW@KB CFKWFYKF%W@YD*KG)


@KWBLBY* @KWBKW%FRW) 88 W@YD%8)* KG@KWBLBY 88 KFGB*@*IGPWPQB

@KWBLBY* DJJFCDWDIJB 88 G@Y@CE%8)

FQBK%RK@W=41*N@JB=‐qybqyfcbsf+wuw‐)

YB\@KG%41)

C CFKG@C@FKBS GB CFKWFYKF

GF \E@JB %GRMMP+KB+‐CFKG@C@FKBSVGBVCFKWFYKF8‐)

YBDG%41*() GRMMP

BKG GF

@=1

GF \E@JB%GRMMP+KB+‐N@KVCFKG@C@FKBSVGBVCFKWFYKF‐)

YBDG%41*() GRMMP

@=@/4

BKG GF

KG=@-4DJJFCDWB%G@Y@CE%KG))

YB\@KG%41)

GF \E@JB %GRMMP+KB+‐CFKG@C@FKBSVGBVCFKWFYKF8‐)

YBDG%41*() GRMMP

BKG GF

GF @=4*KG

YBDG%41*() KFGB*IGPWPQB

24



G@Y@CE%@)=%KFGB-4)(2/IGPWPQB

BKG GF

CDJJ CYBDW@YD%W@YD*G@Y@CE*KG)

BKG SRIYFRW@KB

SRIYFRW@KB CYBDW@YD%W@YD*G@Y@CE*KG)

$CYBD BJ ^BCWFY W@YD YBDJ@XDKGF RKD KRMBYDC@FK KBLDW@^D$QDYD DTRBJJDS N@JDS TRB WBKLDK FCKG@C@FK GB G@Y@CEJBW

$P QFS@W@ D QDYD JDS N@JDS S@K CFKG@C@FK

@KWBLBY 88 @*H*Y*S

@KWBLBY*@KWBKW%@KFRW) 88 G@Y@CE%8)

@KWBLBY* @KWBKW%FRW) 88 W@YD%8)*KG

$FIW@BKB JFS WBYM@KFS GB JD MDWY@X D WDJ TRB J(D(JW = O

CDJJ IRIIJBSFYW%G@Y@CE*KG)

H=4

Y=-4

S=4

GF @=4*S@XB%W@YD)

@N %G@Y@CE%H)+BT+@) WEBK

W@YD%@)=YY=Y-4

H=H/4

BJSB

W@YD%@)=S

S=S/4

BKG @N

BKG GF

BKG SRIYFRW@KB

SRIYFRW@KB IRIIJBSFYW%DYYBL*KBJBM)

$FYGBKD GB MDPFY D MBKFS JFS BJBMBKWFS GBJ ^BCWFY DYYBLJF BJ CRDJ

$QRBGB WBKBY BJBMBKWFS YBQBW@GFS * KBJBM BS BJ WDMDKF N@KDJ GB DYYBL

C S@K JFS BJBMBKWFS YBQBW@GFS

@KWBLBY 88 @*H*DRU*Q@KWBLBY*@KWBKW%@KFRW) 88 DYYBL%8)*KBJBM

GF @=4*S@XB%DYYBL)-4

GF H=4*S@XB%DYYBL)-@

@N%DYYBL%H)+LW+DYYBL%H/4)) WEBK

DRU=DYYBL%H/4)

DYYBL%H/4)=DYYBL%H)

DYYBL%H)=DRU

BKG @N

BKG GF

BKG GF

$DEFYD SDCDMFS JFS ^DJFYBS YBQBW@GFS

Q=4

GF H=9*S@XB%DYYBL)@N %DYYBL%H)+KB+DYYBL%Q)) WEBK

Q=Q/4

DYYBL%Q)=DYYBL%H)

BKG @N

BKG GF

KBJBM=Q

BKG SRIYFRW@KB

29



BKG MFGRJB

C--------------------------------------------------------

SRIYFRW@KB CFKSW@WRW@^D

@MQJ@C@W KFKB

CEDYDCWBY(21 88 GRMMP*CY@WBY@F

@KWBLBY 88 @*H*JDPBY *O

GFRIJB QYBC@S@FK 88 B4*B9*L49*L43*L93*KR49*KR94*YEFGFRIJB QYBC@S@FK* DJJFCDWDIJB 88 DKLJB%8)*T%8*8*8)

GFRIJB QYBC@S@FK 88 WY%7*9)*T44Q*T99Q*T49Q*T>>Q*T77Q*T22Q*SEN*NDCW%3)*XF*BSQ*EJDP*TIDY%2*2)


GFRIJB QYBC@S@FK 88 UW*UC*PW*PC*Y*S*W


CFMMFK &CFMQGDWD& JDPBY*BSQ

CFMMFK&SW@NNKBSS& TIDY

CFMMFK &ND@JRYB& UW*UC*PW*PC*Y*S*W*CY@WBY@F

GFRIJB QYBC@S@FK 88 Q@


SEN=2+1&>+1

Q@=DCFS%-4+1)

YB\@KG%41)

GF \E@JB%GRMMP+KB+‐GDWFSVGBVMDWBY@DJBS8‐)YBDG%41*() GRMMP

BKG GF

YBDG%41*() YEF*B4*B9*L49*L43*L93*KR49

YB\@KG%41)

GF \E@JB%GRMMP+KB+‐WBKS@FKBSVGBVNDJJD8‐)

YBDG%41*() GRMMP

BKG GF

YBDG%41*() UW*UC*PW*PC*Y*S*W

GF \E@JB%GRMMP+KB+‐KRMBYFVGBVCDQDS8‐)

YBDG%41*() GRMMP

BKG GF

YBDG%41*() JDPBY

YB\@KG%41)

GF \E@JB%GRMMP+KB+‐BSQBSFYVQJDCD8‐)YBDG%41*() GRMMP

BKG GF

YBDG%41*() BSQ

YB\@KG%41)

DJJFCDWB%DKLJB%JDPBY)*T%2*2*JDPBY))

GF \E@JB%GRMMP+KB+‐DKLRJFSVGBVCYRXDGF8‐)

YBDG%41*() GRMMP

BKG GF

YBDG%41*() DKLJB

YB\@KG%41)

GF \E@JB%GRMMP+KB+‐CY@WBY@FVGBVNDJJD8‐)

YBDG%41*() GRMMP

BKG GF

YBDG%41*() CY@WBY@FDKLJB=DKLJB(9+1(Q@&3>1+1

KR94=KR49(B9&B4

NDCW%4)=4+1&%4+1-KR49(KR94)

T44Q=B4(NDCW%4)

T99Q=B9(NDCW%4)

T49Q=B9(KR49(NDCW%4)

T>>Q=L49

23



T77Q=L93

T22Q=L43

TIDY%4*8)=%&T44Q*T49Q*1+1G/1*1+1G/1*1+1G/1&)

TIDY%9*8)=%&T49Q*T99Q*1+1G/1*1+1G/1*1+1G/1&)

TIDY%3*8)=%&1+1G/1*1+1G/1*T>>Q*1+1G/1*1+1G/1&)

TIDY%7*8)=%&1+1G/1*1+1G/1*1+1G/1*T77Q*1+1G/1&)

TIDY%2*8)=%&1+1G/1*1+1G/1*1+1G/1*1+1G/1*T22Q&)

GF O=4*JDPBY

NDCW%4)=CFS%DKLJB%O))

GF H=4*7

WY%H*4)=NDCW%4)((YBDJ%H)

BKG GF

NDCW%4)=S@K%DKLJB%O))

GF H=4*7


BKG GF

T%4*4*O)=T44Q(WY%7*4)/9+(%T49Q/9+(T>>Q)(WY%9*9)(WY%9*4)/ T99Q(WY%7*9)

T%4*9*O)=%T44Q/T99Q-7+(T>>Q)(WY%9*9)(WY%9*4)/T49Q(%WY%7*4)/WY%7*9))

T%9*9*O)=T44Q(WY%7*9)/9+(%T49Q/9+(T>>Q)(WY%9*4)(WY%9*9)/T99Q(WY%7*4)

T%4*3*O)=%T44Q-T49Q-9+(T>>Q)(WY%4*9)(WY%3*4)/%T49Q-T99Q/9+(T>>Q)(WY%3*9)(WY%4*4)T%9*3*O)=%T44Q-T49Q-9+(T>>Q)(WY%3*9)(WY%4*4)/%T49Q-T99Q/9+(T>>Q)(WY%4*9)(WY%3*4)

T%3*3*O)=%T44Q/T99Q-9(T49Q-9+(T>>Q)(WY%9*4)(WY%9*9)/T>>Q(%WY%7*4)/WY%7*9))

T%7*7*O)=%T77Q(WY%9*4)/T22Q(WY%9*9))

T%7*2*O)=%T22Q-T77Q)(WY%4*4)(WY%4*9)

T%2*2*O)=%T22Q(WY%9*4)/T77Q(WY%9*9))

BKG GF

EJDP=BSQ&YBDJ%JDPBY)

XF=-BSQ&9+1

D=1+1G/1

I=1+1G/1

G=1+1G/1

@KBY=1+1G/1

GF O=4*JDPBY

GF H=4*3NDCW%H)=%XF/EJDP)((YBDJ%H)-XF((YBDJ%H)

BKG GF

D=T%8*8*O)(NDCW%4)/D

I=T%483*483*O)(NDCW%9)/I

G=T%483*483*O)(NDCW%3)/G

@KBY=NDCW(YEF/@KBY

XF=XF/EJDP

BKG GF

I=I&9+1G/1

G=G&3+1G/1[D¤GF @=4*9

GF H=@/4*3

D%H*@)=D%@*H)

I%H*@)=I%@*H)G%H*@)=G%@*H)

BKG GF

BKG GF

D%7*7)=SEN(D%7*7)

D%7*2)=SEN(D%7*2)

D%2*2)=SEN(D%2*2)

D%2*7)=D%7*2)

27



CJFSB%41)

BKG SRIYFRW@KB

C---------------------------------------------------

MFGRJB SEDQB

@MQJ@C@W KFKB

CFKWD@KS

C--------------------------------------------------------------------SRIYFRW@KB GBY@^DGDSNRKC@FKNFYMD%LQ*GQS@GU@*GQS@GBWD)

@KWBLBY 88 Y*S*@KGBU*KLQ*BWPQ

GFRIJB QYBC@S@FK*@KWBKW%FRW)*G@MBKS@FK%8*8) 88 GQS@GU@*GQS@GBWD

GFRIJB QYBC@S@FK*@KWBKW%@K)* G@MBKS@FK%8) 88 LQ

KLQ=@KW%STYW%YBDJ%S@XB%GQS@GU@%8*4)))))

BWPQ=S@XB%GQS@GU@%4*8))

GF Y=4*KLQ

GF S=4*KLQ

@KGBU=S/KLQ(%Y-4)

GQS@GU@%@KGBU*4)=1+92(%9+1(LQ%Y)-4+1)(%LQ%S)(LQ%S)-LQ%S))

GQS@GU@%@KGBU*9)=1+92(%9+1(LQ%Y)/4+1)(%LQ%S)(LQ%S)-LQ%S))

GQS@GU@%@KGBU*3)=1+92(%9+1(LQ%Y)/4+1)(%LQ%S)(LQ%S)/LQ%S))

GQS@GU@%@KGBU*7)=1+92(%9+1(LQ%Y)-4+1)(%LQ%S)(LQ%S)/LQ%S))GQS@GU@%@KGBU*2)=-LQ%Y)(%LQ%S)(LQ%S)-LQ%S))

GQS@GU@%@KGBU*>)=1+2(%9+1(LQ%Y)/4+1)(%4+1-LQ%S)(LQ%S))

GQS@GU@%@KGBU*<)=-LQ%Y)(%LQ%S)(LQ%S)/LQ%S))

GQS@GU@%@KGBU*5)= 1+2(%9+1(LQ%Y)-4+1)(%4+1-LQ%S)(LQ%S))

GQS@GU@%@KGBU*0)= -9+1(LQ%Y)(%4+1-LQ%S)(LQ%S))

GQS@GBWD%@KGBU*4)= 1+92(%LQ%Y)(LQ%Y)-LQ%Y))(%9+1(LQ%S)-4+1)

GQS@GBWD%@KGBU*9) =1+92(%LQ%Y)(LQ%Y)/LQ%Y))(%9+1(LQ%S)-4+1)

GQS@GBWD%@KGBU*3)= 1+92(%LQ%Y)(LQ%Y)/LQ%Y))(%9+1(LQ%S)/4+1)

GQS@GBWD%@KGBU*7) = 1+92(%LQ%Y)(LQ%Y)-LQ%Y))(%9+1(LQ%S)/4+1)

GQS@GBWD%@KGBU*2)=1+2(%4-LQ%Y)(LQ%Y))(%9+1(LQ%S)-4+1)

GQS@GBWD%@KGBU*>)= -%LQ%Y)(LQ%Y)/LQ%Y))(LQ%S)

GQS@GBWD%@KGBU*<)= 1+2(%4-LQ%Y)(LQ%Y))(%9+1(LQ%S)/4+1)

GQS@GBWD%@KGBU*5)= -%LQ%Y)(LQ%Y)-LQ%Y))(LQ%S)

GQS@GBWD%@KGBU*0) = -9+1(%4+1-LQ%Y)(LQ%Y))(LQ%S)BKG GF

BKG GF

BKG SBJBCW

BKG SRIYFRW@KB

C------------------------------------------------------------------------

SRIYFRW@KB LDRSSQF@KWS%BWPQ*LQ*LQYBG*L\*L\YBG)

@KWBLBY* @KWBKW%@K) 88 BWPQ

GFRIJB QYBC@S@FK*G@MBKS@FK%8)*@KWBKW%FRW) 88 LQ*L\* LQYBG*L\YBG

LQ%4)=1+1111g/1

LQ%9)=1+<<720>>>09g/1

LQ%3)=-lq%9)

L\%4)=1+5555555550g/1

L\%9)=1+2222222222g/1

L\%3)=L\%9)LQYBG%4)=-1+2<<3219>09g/1

LQYBG%9)=-LQYBG%4)

L\YBG%4)=4+1111111111g/1

L\YBG%9)=L\YBG%4)

BKG SRIYFRW@KB

SRIYFRW@KB NRKC@FKNFYMD%LQ*QS@)

22



@KWBLBY 88 Y*S*@KGBU*KLQ*BWPQ

GFRIJB QYBC@S@FK*@KWBKW%@K) 88 LQ%8)

GFRIJB QYBC@S@FK*@KWBKW%FRW)88 QS@%8*8)

$IY@KGD JDS NRKC@FKBS GB NFYMD ^DJRDGDS BK JFS

$QRKWFS GB LDRSS LQ

KLQ=@KW%STYW%YBDJ%S@XB%QS@%8*4)))))

GF Y=4*KLQGF S=4*KLQ

@KGBU=S/KLQ(%Y-4)

QS@%@KGBU*4)=1+92(%LQ%Y)(LQ%Y)-LQ%Y))(%LQ%S)(LQ%S)-LQ%S))

QS@%@KGBU*9)=1+92(%LQ%Y)(LQ%Y)/LQ%Y))(%LQ%S)(LQ%S)-LQ%S))

QS@%@KGBU*3)=1+92(%LQ%Y)(LQ%Y)/LQ%Y))(%LQ%S)(LQ%S)/LQ%S))

QS@%@KGBU*7)=1+92(%LQ%Y)(LQ%Y)-LQ%Y))(%LQ%S)(LQ%S)/LQ%S))

QS@%@KGBU*2)=1+2(%4+1-LQ%Y)(LQ%Y))(%LQ%S)(LQ%S)-LQ%S))

QS@%@KGBU*>)=1+2(%LQ%Y)(LQ%Y)/LQ%Y))(%4+1-LQ%S)(LQ%S))

QS@%@KGBU*<)=1+2(%4+1-LQ%Y)(LQ%Y))(%LQ%S)(LQ%S)/LQ%S))

QS@%@KGBU*5)=1+2(%LQ%Y)(LQ%Y)-LQ%Y))(%4+1-LQ%S)(LQ%S))

QS@%@KGBU*0)=%4+1-LQ%Y)(LQ%Y))(%4+1-LQ%S)(LQ%S))

BKG GF

BKG GF

BKG SRIYFRW@KB

SRIYFRW@KB NRKC@FKNFYMD4G%BJBMWPQB*KLQ*LQ*QS@4G*GQS@4G)

@KWBLBY* @KWBKW%@K) 88 BJBMWPQB*KLQ

@KWBLBY 88 Y

GFRIJB QYBC@S@FK 88 LQ%KLQ)

GFRIJB QYBC@S@FK*@KWBKW%FRW)88 QS@4G%8*8)*GQS@4G%8*8)

$^DJRD JDS NRKC@FKBS GB NFYMD BK SR ^BYS@FK 4G SFIYB BJ CFKWFYKF

GF Y=4*KLQ

QS@4G%Y*4)=1+2(%LQ%Y)(LQ%Y)-LQ%Y))

QS@4G%Y*9)=1+2(%4/LQ%Y))(LQ%Y)

QS@4G%Y*3)=4+1-LQ%Y)(LQ%Y)

GQS@4G%Y*4)= -1+2/LQ%Y)

GQS@4G%Y*9)= 1+2/LQ%Y)GQS@4G%Y*3)= -9+1(LQ%Y)

BKG GF

BKG SRIYFRW@KB

BKG MFGRJB

C ----------------------------------------------------

MFGRJB SWYBSS

CFKWD@KS

SRIYFRW@KB SWYBSSN@BJG%BWPQ*KLQ*GFN*UKFGB*PKFGB*CFKBCW*RLJFIDJ*SWYBSS*SWYN@BJG*KMTL)

RSB SEDQB

@MQJ@C@W KFKB

@KWBLBY*@KWBKW%@K) 88 CFKBCW%8*8)

GFRIJB QYBC@S@FK*@KWBKW%@K)88RLJFIDJ%8)*UKFGB%8)*PKFGB%8)

GFRIJB QYBC@S@FK* @KWBKW%FRW) 88 SWYBSS%8*8*8*8*8)

GFRIJB QYBC@S@FK* @KWBKW%FRW) 88 SWYN@BJG%8*8*8*8*8)GFRIJB QYBC@S@FK* @KWBKW%FRW) 88 KMTL%8*8*8)

@KWBLBY*@KWBKW%@K) 88 BWPQ*GFN*KLQ

@KWBLBY 88 @

@KWBLBY 88 RI@CD*H*JDPBY*J

GFRIJB QYBC@S@FK 88 RJFCDJ%BWPQ(GFN)

GFRIJBQYBC@S@FK 88 NBMGDWD%3*KLQ((9*BWPQ)

GFRIJB QYBC@S@FK*DJJFCDWDIJB 88 YFWD%8*8*8)*T%8*8*8)

2>




GFRIJBQYBC@S@FK* G@MBKS@FK%KLQ((9*BWPQ)88GQS@GU@Y*GQS@GBWDY*QS@Y

GFRIJB QYBC@S@FK 88 SWY%KLQ((9*2)*SWYN%KLQ((9*2)

GFRIJB QYBC@S@FK 88 X*XI*EJDP*BSQ*YFWJFC%GFN*GFN)

GFRIJB QYBC@S@FK* G@MBKS@FK%BWPQ)88 UJFCDJ*PJFCDJ


DJJFCDWB%YFWD%GFN*GFN*JDPBY)*T%GFN*GFN*JDPBY))

CDJJ SW@NNKBSS%YFWD*T)


LQYBG=1+1

CDJJ GBY@^DGDSNRKC@FKNFYMD%LQYBG*GQS@GU@Y*GQS@GBWDY)

CDJJ NRKC@FKNFYMD%LQYBG*QS@Y)

EJDP=BSQ&YBDJ%JDPBY)

NBMGDWD%4*8*8)=QS@Y%8*8)

NBMGDWD%9*8*8)=GQS@GU@Y%8*8)

NBMGDWD%3*8*8)=GQS@GBWDY%8*8)

GF 911 @=4*S@XB%CFKBCW%8*4))

UJFCDJ=UKFGB%CFKBCW%@*48BWPQ84))

PJFCDJ=PKFGB%CFKBCW%@*48BWPQ84))GF H=4*BWPQ

RI@CD=%CFKBCW%@*H)-4)(GFN/4

RJFCDJ%%H-4)(GFN/48H(GFN84)=RLJFIDJ%RI@CD8RI@CD/GFN-484)

BKG GF

GF 411 H=4*JDPBY

XI=-BSQ&9+1/EJDP(%H-4)

YFWJFC%8*8)=YFWD%8*8*H)

GF J=4*3

X=XI/EJDP&9+1(%J-4)

CDJJ SWYD@KS%BWPQ*GFN*KLQ*UJFCDJ*PJFCDJ*

+ NBMGDWD*X*YFWJFC*RJFCDJ*T%8*8*H)*SWY*SWYN)

SWYBSS%@*H*J*8*8)=SWY%8*8)

SWYN@BJG%@*H*J*8*8)=SWYN%8*8)

BKG GF411 CFKW@KRB

CDJJ KMT%BWPQ*GFN*KLQ*UJFCDJ*PJFCDJ*NBMGDWD*RJFCDJ*KMTL%@*8*8))

911 CFKW@KRB

GBDJJFCDWB%YFWD*T)

BKG SRIYFRW@KB

C------------------------------------------------------------------------

SRIYFRW@KB SWYD@KS%BWPQ*GFN*KLQ*UJFCDJ*PJFCDJ*NBMGDWD*X*YFWD*RJFCDJ*T*SWYBSS*SWYN)

C SWYN@BJG BS BJ CDMQF GB WBKS@FKBS BK CFFYGBKDGDS GBJ QYFIJMBD

C S@LMDUU* S@LMDPP*S@LMDUP*

@MQJ@C@W KFKB

GFRIJB QYBC@S@FK*@KWBKW%@K) 88 YFWD%8*8)*RJFCDJ%8)*T%8*8)

GFRIJB QYBC@S@FK* @KWBKW%@K) 88 NBMGDWD%8*8*8)*UJFCDJ%8)*PJFCDJ%8)

@KWBLBY* @KWBKW%@K) 88 BWPQ*GFN*KLQGFRIJB QYBC@S@FK*@KWBKW%FRW) 88 SWYBSS%8*8)*SWYN%8*8)

GFRIJB QYBC@S@FK* @KWBKW%@K) 88 X

GFRIJB QYBC@S@FK 88 TIDY%2*2)

@KWBLBY 88 Y*S*@KGBU*@*H


GFRIJB QYBC@S@FK* G@MBKS@FK%KLQ((9*BWPQ) 88 GQS@GU@Y*GQS@GBWDY*QS@Y

GFRIJB QYBC@S@FK 88 H@K^%9*9)*GBW

2<



GFRIJB QYBC@S@FK 88 G@SQJ%GFN*BWPQ)

GFRIJB QYBC@S@FK 88 GBY@^%GFN*9)*SWYD@K%2)*SWYD@KIDY%2)

CFMMFK&SW@NNKBSS& TIDY

C SB YBFYGBKD BJ ^BCWFY GBSQJDXDM@BKWF

GF @=4*BWPQ

GF H=4*GFNG@SQJ%H*@)=RJFCDJ%GFN(%@-4)/H)

BKG GF

BKG GF

QS@Y%8*8)=NBMGDWD%4*8*8)

GQS@GU@Y%8*8)=NBMGDWD%9*8*8)

GQS@GBWDY%8*8)=NBMGDWD%3*8*8)

GF Y=4*KLQ

GF S=4*KLQ

@KGBU=S/KLQ(%Y-4)



H@K^%9*4)=-gfwVqyfgrcw%UJFCDJ*GQS@GBWDY%@KGBU*8))

H@K^%4*4)=gfwVqyfgrcw%PJFCDJ*GQS@GBWDY%@KGBU*8))GBW=H@K^%4*4)(H@K^%9*9)-H@K^%4*9)(H@K %9*4)

H@K^=H@K^&GBW



GF @=4*GFN

GBY@^%@*4)=GFWVQYFGRCW%G@SQJ%@*8)*GQS@GU)

GBY@^%@*9)=GFWVQYFGRCW%G@SQJ%@*8)*GQS@GP)

BKG GF

SWYD@K%4)=GBY@^%4*4)/1+2(GBY@^%3*4)(GBY@^%3*4)/X(GBY@^%7*4)

SWYD@K%9)=GBY@^%9*9)/1+2(GBY@^%3*9)(GBY@^%3*9)/X(GBY@^%2*9)

SWYD@K%7)= GBY@^%3*9)/GFWVQYFGRCW%G@SQJ%2*8)*QS@Y%@KGBU*8))

SWYD@K%2)=GBY@^%3*4)/GFWVQYFGRCW%G@SQJ%7*8)*QS@Y%@KGBU*8))

SWYD@K%3)=GBY@^%4*9)/GBY@^%9*4)/GBY@^%3*4)(GBY@^%3*9)/ X(%GBY@^%7*9)/GBY@^%2*4))

GF @=4*2

SWYD@KIDY%@)=GFWVQYFGRCW%YFWD%@*8)*SWYD@K)

BKG GF

GF @=4*2

SWYBSS%@KGBU*@)=GFWVQYFGRCW%TIDY%@*8)*SWYD@KIDY)

BKG GF

GF @=4*2

SWYN%@KGBU*@)=GFWVQYFGRCW%T%@*8)*SWYD@K)

BKG GF

BKG GF

BKG GF

BKG SRIYFRW@KB

C-------------------------------------------------------------------------

SRIYFRW@KB SW@NNKBSS%YFWD*T)@MQJ@C@W KFKB


@KWBLBY 88 @*H*O*JDPBY

GFRIJB QYBC@S@FK* @KWBKW%FRW) 88 YFWD%8*8*8)*T%8*8*8)

GFRIJB QYBC@S@FK 88 WY%7*9)*NDCW%3)*Q@*BSQ*TIDY%2*2)

GFRIJB QYBC@S@FK*DJJFCDWDIJB 88 DKLJB%8)

GFRIJB QYBC@S@FK 88 T44*T99*T49*T>>*T77*T22

25




CFMMFK &SW@NNKBSS& TIDY

DJJFCDWB%DKLJB%JDPBY))


Q@=DCFS%-4+1)

YBDG%41*() GRMMP

GF \E@JB%GRMMP+KB+‐DKLRJFSVGBVCYRXDGF8‐)YBDG%41*() GRMMP

BKG GF

YBDG%41*() DKLJB

DKLJB=DKLJB(9+1(Q@&3>1+1

T44=TIDY%4*4)

T49=TIDY%4*9)

T>>=TIDY%3*3)

T99=TIDY%9*9)

T77=TIDY%7*7)

T22=TIDY%2*2)

GF O=4*JDPBY

NDCW%4)=CFS%DKLJB%O))

GF H=4*7

WY%H*4)=NDCW%4)((YBDJ%H)BKG GF

NDCW%4)=S@K%DKLJB%O))

GF H=4*7


BKG GF

YFWD%4*8*O)=%&WY%9*4)*WY%9*9)*WY%4*4)(WY%4*9)*1+1G/1*1+1G/1&)

YFWD%9*8*O)=%&WY%9*9)*WY%9*4)*-WY%4*4)(WY%4*9)*1+1G/1*1+1G/1&)

YFWD%3*8*O)=%&-9+(WY%4*4)(WY%4*9)*9+(WY%4*4)(WY%4*9)*%WY%9*4)-WY%9*9))*1+1G/1*1+1G/1&)

YFWD%7*8*O)=%&1+1G/1*1+1G/1*1+1G/1*WY%4*4)*-WY%4*9)&)

YFWD%2*8*O)=%&1+1G/1*1+1G/1*1+1G/1*WY%4*9)*WY%4*4)&)

T%4*4*O)=T44(WY%7*4)/9+(%T49/9+(T>>)(WY%9*9)(WY%9*4)/T99(WY%7*9)

T%4*9*O)=%T44/T99-7+(T>>)(WY%9*9)(WY%9*4)/T49(%WY%7*4)/WY%7*9))

T%9*9*O)=T44(WY%7*9)/9+(%T49/9+(T>>)(WY%9*4)(WY%9*9)/T99(WY%7*4)

T%4*3*O)=%T44-T49-9+(T>>)(WY%4*9)(WY%3*4)/%T49-T99/9+(T>>)(WY%3*9)(WY%4*4)T%9*3*O)=%T44-T49-9+(T>>)(WY%3*9)(WY%4*4)/%T49-T99/9+(T>>)(WY%4*9)(WY%3*4)

T%3*3*O)=%T44/T99-9(T49-9+(T>>)(WY%9*4)(WY%9*9)/T>>(%WY%7*4)/WY%7*9))

T%7*7*O)=%T77(WY%9*4)/T22(WY%9*9))

T%7*2*O)=%%T22-T77)(WY%4*4)(WY%4*9))

T%2*2*O)=%T22(WY%9*4)/T77(WY%9*9))

BKG GF

GF @=4*9

GF H=@/4*3

T%H*@*8)=T%@*H*8)

BKG GF

BKG GF

T%2*7*8)=T%7*2*8)

GBDJJFCDWB%DKLJB)

CJFSB%41)BKG SRIYFRW@KB

C---------------------------------------------------------------------

SRIYFRW@KB KMT%BWPQ*GFN*KLQ*UJFCDJ*PJFCDJ*NBMGDWD*RJFCDJ*KMTJ)

@MQJ@C@W KFKB

GFRIJB QYBC@S@FK*@KWBKW%@K) 88 RJFCDJ%8)

GFRIJB QYBC@S@FK* @KWBKW%@K) 88 NBMGDWD%8*8*8)*UJFCDJ%8)*PJFCDJ%8)

20



@KWBLBY* @KWBKW%@K) 88 BWPQ*GFN*KLQ

GFRIJB QYBC@S@FK*@KWBKW%FRW) 88 KMTJ%8*8)

@KWBLBY 88 Y*S*@KGBU*@*H


GFRIJB QYBC@S@FK* G@MBKS@FK%KLQ((9*BWPQ) 88GQS@GU@Y*GQS@GBWDY*QS@Y

GFRIJB QYBC@S@FK 88 H@K^%9*9)*GBW

GFRIJB QYBC@S@FK 88 G@SQJ%GFN*BWPQ)*BQS1%GFN)*BQS4%3)GFRIJB QYBC@S@FK 88 GBY@^%GFN*9)



BQS1=1+1G/1

BQS4=1+1G/1

C SB YBFYGBKD BJ ^BCWFY GBSQJDXDM@BKWF

GF @=4*BWPQ

GF H=4*GFN

G@SQJ%H*@)=RJFCDJ%GFN(%@-4)/H)

BKG GF

BKG GF

QS@Y%8*8)=NBMGDWD%4*8*8)

GQS@GU@Y%8*8)=NBMGDWD%9*8*8)

GQS@GBWDY%8*8)=NBMGDWD%3*8*8)GF Y=4*KLQ

GF S=4*KLQ

@KGBU=S/KLQ(%Y-4)



H@K^%9*4)=-gfwVqyfgrcw%UJFCDJ*GQS@GBWDY%@KGBU*8))

H@K^%4*4)=gfwVqyfgrcw%PJFCDJ*GQS@GBWDY%@KGBU*8))

GBW=H@K^%4*4)(H@K^%9*9)-H@K^%4*9)(H@K %9*4)

H@K^=H@K^&GBW



GF @=4*GFN

GBY@^%@*4)=GFWVQYFGRCW%G@SQJ%@*8)*GQS@GU)

GBY@^%@*9)=GFWVQYFGRCW%G@SQJ%@*8)*GQS@GP)BKG GF

BQS1%4)=GBY@^%4*4)/1+2(GBY@^%3*4)(GBY@ %3*4)

BQS1%9)=GBY@^%9*9)/1+2(GBY@^%3*9)(GBY@ %3*9)

BQS1%7)=GBY@^%3*9)/GFWVQYFGRCW%G@SQJ%2*8)*QS@Y%@KGBU*8))

BQS1%2)=GBY@^%3*4)/GFWVQYFGRCW%G@SQJ%7*8)*QS@Y%@KGBU*8))

BQS1%3)=GBY@^%4*9)/GBY@ %9*4)/GBY@^%3*4)(GBY@^%3*9)

BQS4%4)=GBY@^%7*4)

BQS4%9)=GBY@^%2*9)

BQS4%3)=GBY@^%7*9)/GBY@^%2*4)

GF @=4*3

KMTJ%@KGBU*@)=GFWVQYFGRCW%D%@*48384)*BQS1%48384))/GFWVQYFGRCW%I%@*48384)*BQS4%48384))

KMTJ%@KGBU*@/3)=GFWVQYFGRCW%I%@*48384)*BQS1%48384))/GFWVQYFGRCW%G%@*48384)*BQS4%48384))

BKG GF

GF @=4*9KMTJ%@KGBU*0-@)=GFWVQYFGRCW%D%@/3*78284)*BQS1%78284))

BKG GF

BKG GF

BKG GF

BKG SRIYFRW@KB

C------------------------------------------------------------

SRIYFRW@KB ND@JCY@W%SWY*ND@JQJP*NDCWFY)

>1



@MQJ@C@W KFKB

CEDYDCWBY(21 88 CY@WBY@F

GFRIJB QYBC@S@FK* @KWBKW%@K) 88 SWY%8*8*8*8*8)

GFRIJB QYBC@S@FK* @KWBKW%FRW) 88 NDCWFY

@KWBLBY* @KWBKW%FRW) 88 ND@JQJP%8)

@KWBLBY 88 BJBM*JDPBY*WMI*LDRSS

GFRIJB QYBC@S@FK 88 UW*UC*PW*PC*Y*S*WGFRIJB QYBC@S@FK 88 SU*SP*U*P*N

GFRIJB QYBC@S@FK 88 SWYBSS%2)*NFJG

CFMMFK &ND@JRYB& UW*UC*PW*PC*Y*S*W*CY@WBY@F

NFJG=1+1

GF BJBM=4*S@XB%SWY%8*4*4*4*4))

GF JDPBY=4*S@XB%SWY%4*8*4*4*4))

GF WMI=4*S@XB%SWY%4*4*8*4*4))

GF LDRSS=4*S@XB%SWY%4*4*4*8*4))

SWYBSS%8)=SWY%BJBM*JDPBY*WMI*LDRSS*8)

@N%CY@WBY@F+BT+‐WSD@E@JJ‐) WEBK

@N%SWYBSS%4)+LW+1+1) WEBK

U=UWBJSB

U=UC

BKG @N


P=PW

BJSB

P=PC

BKG @N

N=%SWYBSS%4)&U)((9+1/%SWYBSS%9)&P)((9+1-

+ %4+1&%U(U))(SWYBSS%4)(SWYBSS%9)/

+%SWYBSS%7)&Y)((9+1/%SWYBSS%2)&S)((9+1/%SWYBSS%3)&W)((9+1

BJSB @N%CY@WBY@F+BT+‐WBKS@FKVMDU@MD‐) WEBK


U=UWBJSB

U=UC

BKG @N


P=PW

BJSB

P=PC

BKG @N

N=MDU%DIS%SWYBSS%4)&U)*DIS%SWYBSS%9)&P)*

+ DIS%SWYBSS%3)&W)*DIS%SWYBSS%7)&Y)*DIS%SWYBSS%2)&S))

BJSB @N%CY@WBY@F+BT+‐WSD@\R‐) WEBK

N=%4+1&UW-4+1&UC)(SWYBSS%4)/%4+1&PW-4+1&PC)(SWYBSS%9)/

+ 4+1&%UW(UC)(SWYBSS%4)((9+1/4+1&%PW(PC)(SWYBSS%9)((9+1/+ %SWYBSS%7)&Y)((9+1/%SWYBSS%2)&S)((9+1/%SWYBSS%3)&W)((9+1-

+ 1+2&%STYW%UW(UC(PW(PC))(SWYBSS%4)(SWYBSS%9)

BKG @N

@N %N+LW+NFJG) WEBK

NFJG=N

ND@JQJP=%&BJBM*JDPBY*WMI*LDRSS&)

>4



BKG @N

BKG GF

BKG GF

BKG GF

BKG GF

NDCWFY=NFJG

BKG SRIYFRW@KBBKG MFGRJB

C------------------------------------------------------------

MFGRJB SFJ^BYS

@MQJ@C@W KFKB

CFKWD@KS

SRIYFRW@KB SFJ^BJR%JR*U*I)

@KWBLBY 88 O*M*H*K*M@G*Y*DI

GFRIJB QYBC@S@FK* @KWBKW%@K) 88 I%8)

GFRIJB QYBC@S@FK* @KWBKW%FRW) 88 U%8)

GFRIJB QYBC@S@FK* @KWBKW%@KFRW) 88 JR%8*8)

GFRIJB QYBC@S@FK 88 SRMD

K=S@XB%JR%8*4))

M=S@XB%JR%4*8))M@G=%M/4)&9

DI=M@G-4

GF O=4*K

GF H=O*M@K%O/DI*K)

SRMD=1+1G/1

GF Y=MDU%H-DI*4)*O-4

SRMD=JR%O*Y-O/M@G)(JR%Y*H-Y/M@G)/SRMD

BKG GF

JR%O*H-O/M@G)=JR%O*H-O/M@G)-SRMD

BKG GF

GF H=O/4*M@K%O/DI*K)

SRMD=1+1G/1

GF Y=MDU%H-DI*4)*O-4

SRMD=JR%H*Y-H/M@G)(JR%Y*O-Y/M@G)/SRMDBKG GF

JR%H*O-H/M@G)=%JR%H*O-H/M@G)-SRMD)&JR%O*M@G)

BKG GF

BKG GF

GF O=4*K

SRMD=1+1G/1

GF Y=MDU%O-M@G/4*4)*O-4

SRMD=JR%O*Y-O/M@G)(U%Y)/SRMD

BKG GF

U%O)=I%O)-SRMD

BKG GF

GF O=K*4*-4

SRMD=1+1G/1

GF Y=O/4*M@K%O/M@G-4*K)SRMD=JR%O*Y-O/M@G)(U%Y)/SRMD

BKG GF

U%O)=%U%O)-SRMD)&JR%O*M@G)

BKG GF

BKG SRIYFRW@KB

BKG MFGRJB

>9

final project advanced mechanics of materials course

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