Solucionario completo- Fundamentos de A teoria-electromagnetica-reitz-milford-4edpdf

Prévia do material em texto

http://www.elsolucionario.blogspot.com 
Daladier
Typewritten text
LIBROS UNIVERISTARIOS 
Y SOLUCIONARIOS DE 
MUCHOS DE ESTOS LIBROS

LOS SOLUCIONARIOS 
CONTIENEN TODOS LOS 
EJERCICIOS DEL LIBRO
RESUELTOS Y EXPLICADOS
DE FORMA CLARA

VISITANOS PARA
DESARGALOS GRATIS.
Capítulo 1
1. Exercício 1.1: Para demonstrar o paralelismo basta construir
AB = �A− �B = −ı̂− 2̂+ k̂
CD = �C − �D = 3ı̂+ 6̂− 3k̂
e fazer o protudo vetorial entre eles. Se forem paralelos mesmo, deverá
dar zero.
AB ×CD =
∣∣∣∣∣∣
ı̂ ̂ k̂
−1 −2 1
2 6 −3
∣∣∣∣∣∣ = 0
para ver que é zero, basta notar que a coluna 2 e a coluna 3 são propor-
cionais (ou então faz o cálculo na unha).
2. Exercício 1.2: Banal. Basta fazer o produto escalar e mostrar que dá
zero.
3. Exercício 1.3: Banal. Basta mostrar que AB − �C = 0, mostrando que
os pontos perfazem um triângulo e que o produto escalar de dois deles (a
serem verificados) dá zero. Na verdade, é fácil ver que são �A e �B que são
perpendiculares.
4. Exercício 1.4: Temos que∣∣∣ �A∣∣∣2 = A2 = B2 +C2 − 2BC cos θ,
onde θ é o ângulo entre �B e �C. Geometricamente, temos que �A, �B e �C
formam um triângulo, que é o conteúdo da fórmula
�A = �B − �C,
assim, é só desenhar o triângulo e a lei dos cossenos aparece imediatamente.
5. Exercício 1.5: Façamos o produto escalar de �A com �B. Temos que
�A · �B = AB cos (θAB) = cosα cosβ + sinα sinβ,
onde θAB é o ângulo entre �A e �B, evidentemente. Este ângulo pode ser
imediatamente relacionado com os ângulos α e β, bastando para isso fazer
um desenho de �A e �B num plano cartesiano. Assim, temos que θAB = α−β
e, portanto,
cos (α− β) = cosα cosβ + sinα sinβ,
como queríamos demonstrar.
1
6. Exercício 1.6: Basta escrever tudo em termos de vetores unitários. Ter-
emos assim, considerando-se
�r = xı̂+ y̂+ zk̂, �A = axı̂+ ay ̂+ azk̂,
ficamos com (
�r − �A
)
· �A = 0
implica em
(x− ax)ax + (y − ay)ay + (z − az)az = 0,
ou ainda
axx+ ayy + azz − (a2x + a2y + a2z) = 0,
que é a equação de um plano.
7. Exercício 1.7: Agora, com as mesmas convenções anteriores, ficamos
com
(x− ax)x+ (y − ay) y + (z − az) z = 0
o que fornece
x2 − axx+ y2 − ayy + z2 − azz = 0
e que, completando quadrados, obtemos(
x− ax
2
)2
+
(
y − ay
2
)2
+
(
z − az
2
)2
=
a2x + a
2
y + a
2
z
4
.
Você seria capaz de dizer, sem desenhar, que tipo de esfera é essa? (não!!?,
credo!)
8. Exercício 1.8: A diagonal principal de um cubo é dada por (se precisar
de desenhar, é mal sinal)
�d = aı̂+ a̂+ ak̂,
já que todos os lados são iguais. Uma aresta é dada por �A = aı̂, por
exemplo. Assim, temos �d · �A = a2. Dependeria este resultado de qual
aresta escolhêssemos?
9. Exercício 1.9: Ver exercício 1.4 (lembrando de tomar agora o módulo,
pois trata-se de produto vetorial).
10. Exercício 1.10: Basta mostrar que este vetor é perpendicular aos vetores
AB e BC, por exemplo. Como estes vetores formam o plano, se o vetor
em questão é perpendicular a eles, será perpendicular ao plano. Óbvio!
Mostrar que o vetor
�A× �B + �B × �C + �C × �A
é perpendicular tanto a AB quanto a BC é fácil. Note que(
�A− �B
)
×
[
�A× �B + �B × �C + �C × �A
]
= 0,
de forma banal e óbvia. O mesmo pode ser dito do outro produto.
2
11. Exercício 1.11: Temos
�C = �A× �X
ao mesmo tempo que
�X =
�C × �A
A2
+ k �A,
de modo que (substituindo acima)
�C = �A×
[
�C × �A
A2
+ k �A
]
=
1
A2
�A×
(
�C × �A
)
=
�C
(
�A · �A
)
− �A
(
�C · �A
)
A2
= �C − �A
�C · �A
A2
Como �C é perpendicular a �A (da primeira expressão), temos que �C · �A = 0
e o resultado se segue.
12. Exercício 1.12: óbvio. Se temos o produto triplo igual a zero, então
temos que o determinante construído a partir das componentes é nulo.
Mas ele é nulo apenas se suas linhas são combinações lineares umas das
outras.
13. Exercício 1.13: Seja ϕ (x, y, z) = c, com c constante. Assim, demos que
dϕ = 0 =
∂ϕ
∂x
dx+
∂ϕ
∂y
dy +
∂ϕ
∂z
dz = 0
Mas isto é semelhante ao produto escalar(
∂ϕ
∂x
ı̂+
∂ϕ
∂y
̂+
∂ϕ
∂z
k̂
)
·
(
ı̂dx+ ̂dy + k̂dz
)
= 0.
Como o vetor d�s = ı̂dx+ ̂dy + k̂dz é tangente à superfície, temos que
∇ϕ = ∂ϕ
∂x
ı̂+
∂ϕ
∂y
̂+
∂ϕ
∂z
k̂
tem que ser perpendicular à superfície.
14. Exercício 1.14: Temos que ds = drâr + rdθâθ + dzk̂. Isto implica que
∂s
∂r
= 1,
∂s
∂θ
= r,
∂s
∂z
= 1,
de modo que
∇cyl = r̂ ∂
∂r
+ θ̂
1
r
∂
∂θ
+ ẑ
∂
∂z
3
15. Exercício 1.15: Basta escrever �F = �F (r, θ, z) = fr (r, θ, z) r̂+fθ (r, θ, z) θ̂+
fz (r, θ, z) ẑ e lembrar que
�F · n̂∆a = frr∆θ∆z + fθ∆r∆z + fzr∆r∆θ
e assim, usando a definição (1.33) do livro, temos
div �F = ∇ · �F = lim∆V→0 1r∆r∆θ∆z
{
∂
∂r (frr)∆θ∆z∆r
+∂fθ∂θ ∆r∆θ∆z +
∂
∂z (rfz)∆θ∆r∆z
} ,
e ficamos com
div �F =
∂
∂r
(frr) +
1
r
∂fθ
∂θ
+
∂fz
∂z
,
que é o resultado desejado.
16. Exercício 1.16: aplicação simples.
17. Exercício 1.17: Não... claro que não! Assim teremos �F · ∇ × �F = 0 e
podemos colocar isso em termos da matriz
�F ·
∣∣∣∣∣∣
ı̂ ̂ k̂
∂
∂x
∂
∂y
∂
∂z
fx fy fz
∣∣∣∣∣∣ =
fx
(
∂fz
∂y − ∂fy∂z
)
+ fy
(
∂fx
∂z − ∂fz∂x
)
+ fz
(
∂fy
∂x − ∂fx∂y
)
.
Não há qualquer razão para que este fator dê zero. Para ver isto, tome
fx = x, fy = 0 e fz = y, temos que a expressão anterior fica dada por x,
que é diferente de zero.
18. Exercício 1.18: Considere a expressão ∇2 (ϕψ) e reescreva-a como ∇ ·
∇ (ϕψ). Agora, expandindo este gradiente, ficamos com ∇· [ϕ∇ψ + ψ∇ϕ]
que, novamente expandida, fica
∇2 (ϕψ) = ϕ∇2ψ + ψ∇2ϕ+ 2∇ϕ · ∇ψ.
19. Exercício 1.19: Os dois primeiros eu me recuso, pois são ridiculamente
fáceis. O último é fácil também, mas vamos lá: temos que
�u · ∇ = ux ∂
∂x
+ uy
∂
∂y
+ uz
∂
∂z
e isso, aplicado a �r = xı̂+ y̂+ zk̂ , fornece
(�u · ∇)�r =
(
ux
∂
∂x
+ uy
∂
∂y
+ uz
∂
∂z
)[
xı̂+ y̂+ zk̂
]
= ı̂ux + ̂uy + k̂uz = �u,
como desejado.
4
20. Exercício 1.20: Seja �A um vetor constante. Temos que (1.1.6 da tabela)
∇
(
�A · �r
)
=
(
�A · ∇
)
�r + �A× (∇× �r) + (�r · ∇) �A+ �r ×
(
∇× �A
)
.
Ora, �A é constante, de forma que todos os termos que possuem derivadas
de �A são nulos (os últimos dois termos acima). O segundo termo é nulo
pelo problema anterior e o primeiro é o próprio �A.
21. Exercício 1.21: Farei, por preguiça, apenas o referente ao resultado 1.1.7.
Temos que
∇ ·
(
ϕ�F
)
= (∇ϕ) · �F + ϕ∇ · �F .
É fácil demais! Escrevam o divergente em coordenadas cartesianas e tam-
bém a função vetorial �F nestas mesmas coordenadas. Ficamos com
∇ ·
(
ϕ�F
)
=
∂
∂x
(ϕFx) +
∂
∂y
(ϕFy) +
∂
∂z
(ϕFz)
=
(
∂ϕ
∂x
Fx +
∂ϕ
∂y
Fy +
∂ϕ
∂z
Fz
)
+ ϕ
(
∂Fx
∂x
+
∂Fy
∂y
+
∂Fz
∂z
)
= (∇ϕ) · �F + ϕ∇ · �F .
22. Exercício 1.22: Ué!... nem sei o que fazer aqui! Se a função f depende
apenas de r, podemos escrever o gradiente em coordenadas esféricas e
ficamos imediatamente com o resultado.
23. Exercício 1.23: Vejam o anterior.
24. Exercício 1.24: Temos que
∇ϕ (ξ) = dϕ
dξ
∂ξ
∂x
+
dϕ
dξ
∂ξ
∂y
+
dϕ
dξ
∂ξ
∂z
e, como, ξ = �A · �r, temos que
∂ξ
∂x
= Ax,
∂ξ
∂y
= Ay,
∂ξ
∂z
= Az
de modo que
∇ϕ (ξ) = dϕ
dξ
Ax +
dϕ
dξ
Ay +
dϕ
dξ
Az = �A
dϕ
dξ
.
25. Exercício 1.25: Façam!
26. Exercício 1.26: Farei apenas o 1.2.4. Vou supor, portanto, que já foi
provado o item 1.2.2. Temos que provar que∫
V
(
∇ · �G+ �G · ∇
)
�Fdv =
∮
S
�F
(
�G · n̂
)
da.
5
O mais importante aqui é notar que podemos fazer tudo componente a
componente, ou seja, decompondo �F . Assim, considere o termo
ı̂
∫
V
(
∇ · �G+ �G · ∇
)
fxdv = ı̂
∫
V
[
fx
(
∇ · �G
)
+ �G · ∇fx
]
dv.
Note agora que este termo entre colchetes pode ser escrito como
ı̂
∫
V
∇ ·
(
fx �G
)
dv,
se usarmos a propriedade 1.1.7, tabela 1.1. Mas aplicando o teorema da
divergência sobre este termo, temos que
ı̂
∫
V
∇ ·
(
fx �G
)
dv = ı̂
∮
S
(
fx �G
)
· n̂dv = ı̂
∮
S
fx
(
�G · n̂
)
dv.
Repetindo isto para cada uma das outras componentes, ficamos com∫
V
(
∇ · �G+ �G · ∇
)
�Fdv =
∮
S
(
ı̂fx + ̂fy + k̂fz
)(
�G · n̂
)
dv
=
∮
S
�F
(
�G · n̂
)
da,
como queríamos demonstrar.
6
Wr= Vhswhpehu 4:/ 5336 Sdjh= 4
+Fkdswhu khdg=,Fdsðwxor 5=
t H{hufðflr 514= Dv gxdv sduwðfxodv hvwær vxvshqvdv sru �r gh frpsulphqwrv , d sduwlugh xp srqwrfrpxp1 Vxdv pdvvdv vær 6 h vxdv fdujdv vær ^1 Sdud fdofxodu r åqjxortxh fdgd frugd id} frp d yhuwlfdo edvwd qrwdu txh ghyhprv whu/ ghfrpsrqgr iruêdvvreuh fdgd sduwðfxod 6} c A ULt w ' fA t�? w c ^2eZ0f E2, t�? w�2 ' fDvvlp/ A ' 6} tiU w h 6} |@? w ' ^2eZ0f E2, t�? w�2gh prgr txh t�?� wULt w ' ^2�SZ0f6},2rx t�?� wULt� w �tiU2 w ' |@?� w� n |@?2 w ' ^2�SZ0f6},2 ctxh ì r uhvxowdgr ghvhmdgr1 Qrwh txh/ vh w � �/ hqwær srghuðdprv hvfuhyhu
w ' � ^2�SZ0f6},2
��*� �
t H{hufðflr 515= Dv fdujdv vær '� ' 2 e �f3b� h '2 ' cf�D e �f3b�1 D vhsdudêær ìo ' e e �f3261 Dvvlp/ d iruêd hqwuh hodv vhuä
8 ' '�'2eZ0fo2 ' c� e �f3�HeZ e H�HDe e �f3�2 e �S e �f3e� '' c �f32ZDSS�SDS ' cf�DS e �f3D��Vh dv hvihudv vær srvwdv hp frqwdwr/ d fdujd vh uhglvwulexl gh prgr txh whuhprv xpdfdujd oðtxlgd wrwdo ljxdo d 'A ' ��De �f3b� h fdgd hvihud �fduä frp xpd fdujd ljxdoã phwdgh ghvwh ydoru1 Dvvlp/ d iruêd �fduä
8 ' '�'2eZ0fo2 ' 2�2D e �f3�HeZ e H�HDe e �f3�2 e �S e �f3e� '' n��2S e �f3D�
Wr= Vhswhpehu 4:/ 5336 Sdjh= 5
t H{hufðflr 517= Whprv xp �r lq�qlwdphqwh orqjr/ frp ghqvlgdgh xqliruph gh fdujd bsru xqlgdgh gh frpsulphqwr1 D lqwhjudo sdud r fdpsr hoìwulfr/ sdud xp srqwr d xpdglvwåqfld Oo gd olqkd/ �fd +sru vlphwuld whprv dshqdv r fdpsr udgldo hp frrughqdgdvfloðqgulfdv/ frorfdprv r srqwr � vreuh r sodqr 5 ' f sru frqyhqlíqfld,
.o Eo� ' �eZ0f *�4u<"] nu3u bdo2 n 52o�*2_5 '' �eZ0f *�4u<" 2u-2S-2 n u2 ' �eZ0f *�4u<" 2-2t-2u2 n � '' �2Z0f-2 ctxh ì r uhvxowdgr surfxudgr1t H{hufðflr 518=
� +d, Whprv xp glvfr flufxodu gh udlr -/ frp xpd ghqvlgdgh vxshu�fldo gh fdujdj xqliruph1 Sdud ghwhuplqdu r fdpsr hoìwulfr hp xp srqwr � vreuh r hl{r grglvfr d xpd glvwåqfld 5 gh vhx sodqr edvwd frorfdu4 Eo�c w�c 5�� ' jB E5�� cgh prgr txh +hp xp srqwr txdotxhu Eoc wc 5�,
) E5c oc w� ' �eZ0f ]T jB E5��MOo c Oo�M o�_o�_w�_5� '' jeZ0f ] n"3"
] 2Z
f
] -
f
o�tEo c o��2 n E5 c 5��2_o�_w�_5�
Qr srqwr Efc fc 5� �fdprv frp
) E5c oc w� ' je0f ] -f 2o�So�2 n 52_o� ' j20f kS-2 n 52 c 5l �Sdud hqfrqwudu r fdpsr/ edvwd qrwdu txh/ sru vlphwuld/ vö ghyhprv whu r fdpsrqd gluhêær 5/ gh prgr txh
O. ' c	5Y)Y5 ' j20f
��c 5S-2 n 52� 	5�� Djrud whprv xp flolqgur flufxodu uhwr gh udlr - h dowxud u/ rulhqwdgr dr orqjrgr hl{r 51 Vxd ghqvlgdgh yroxpìwulfd gh fdujd ì 4 E5�� ' 4f n q5� hp uhodêær ãruljhp qr fhqwur gr flolqgur1 Sdud dfkdu d iruêd vreuh xpd fdujd sxqwliruph ^
Wr= Vhswhpehu 4:/ 5336 Sdjh= 6
qr fhqwur gr flolqgur/ edvwd hqfrqwudu r srwhqfldo qd ruljhp/ ghsrlv r fdpsr O.h �qdophqwh d iruêd/ sru vlpsohv pxowlsolfdêær1 Dvvlp/ r srwhqfldo �fd
) Efc fc 5� ' �eZ0f ] nu*23u*2
] 2Z
f
] -
f
4f n q5�to�2 n E5 c 5��2 o�_o�_w�_5� '
' �20f ] nu*23u*2 E4f n q5��
�t-2 n E5 c 5��2 c E5 c 5��� _5�
Id}hqgr/ sruwdqwr
O. ' .5 M5'f 	5 ' q20f
%u2
#u2 c
u-2 n u2e
$n-2 t�?�3� � u2-�
& c
txh ì r uhvxowdgr ghvhmdgr +ohpeuh0vh gd h{suhvvær gr t�?� hp whuprv gh orjdulw0prv1t H{hufðflr 519= Whprv xpd fdvfd hviìulfd �qd/ frqgxwrud/ gh udlr - txh hvwä xql0iruphphqwh fduuhjdgd frp xpd fdujd wrwdo '1 Dvvlp/ hvwd fdvfd hviìulfd srvvxl xpdghqvlgdgh vxshu�fldo gh fdujd j ' '*eZ-21 D lqwhjudo txh iruqhfh r srwhqfldo qxpsrqwr duelwuäulr qr lqwhulru rx qr h{whulru gd fdvfd �fd gdgd sru
) E5f� ' �eZ0f ] 2Zf
] Z
f
] "
f
jB Eo� c-�do�2 n 52f c 2o�5f ULt w�o�*2o�2 t�? w�_w�_�� '' 'HZ0f ] Zf t�? wd-2 n 52f c 2-5f ULt wo�*2_w '' 'HZ0f M-n 5fM c M-c 5fM-5f �Djrud/ sru vlphwuld/ wurfdprv 5f sru o/ mä txh frorfdu r srqwr � vreuh r hl{r 5 irl xph{shglhqwh pdwhpäwlfr dshqdv1 Ilfdprv/ sruwdqwr/ frp r uhvxowdgr
) ' 'HZ0f M-n oM c M-c oM-o �Vh r srqwr hvwä qr lqwhulru/ whprv o 	 - h �fdprv frp
) Eo� ' 'HZ0f -n o c E-c o�-o ' 'eZ0f-�Vh r srqwr hvwä qr h{whulru/ whprv o : - h �fdprv frp
) Eo� ' 'HZ0f -n o n E-c o�-o ' 'eZ0fo �Qrwh txh/ hp o ' - r srwhqfldo ì frqwðqxr1
Wr= Vhswhpehu 4:/ 5336 Sdjh= 7
t H{hufðflr 51:= Whprv c^ hp Efc fc f� h n^*2 hp E@c fc f�1 Sdud hqfrqwudu hp txhsrqwr gr hl{r { r fdpsr hoìwulfr vh dqxod/ edvwd id}huc^eZ0f%2 n ^*2eZ0f E%c @�2 ' fsdud rewhu %?�,J ' �2iS2� @�Sdud id}hu xp juä�fr gd vxshuiðflh htxlsrwhqfldo txh sdvvd shor srqwr %?�,J edvwdvdehu/ lqlfldophqwh/ txh r srwhqfldo qhvwh srqwr ì gdgr sru
� E%?�,J� ' ^eZ0f@
% c��2cS2� n �2 ��cS2�
& '
' 2�b�e2��DS2 ^eZ0f@�Dvvlp/ hp xqlgdghv gh ^* EeZ0f@� ghyhprv whu� E%c +c 5 ' f� ' c�s%2 n +2 n �2sE%c @�2 n +2 ' 2�b�e2��DS2�D fxuyd qr sodqr %+ txh vdwlvid} hvwd htxdêær ì d fxuyd gh srwhqfldo ghvhmdgd1R sureohpd d vhjxlu gä dv fxuydv jhudlv gh srwhqfldo dvvrfldgdv dr suhvhqwh h{0hpsor1 Dv fxuydv htxlsrwhqfldlv jhudlv srghp vhu sorwdgdv xvdqgr0vh r frpdqgr�frqwrxusorw+vxev+d@4/i,/ {@041811418 /|@041811418/julg@^83/83`/ wklfnqhvv@4/ �oohg@wuxh/frqwrxuv@^031;/0319/0317/0315/313/315/317/319/31;`,>� gr Pdsoh rqghs ' c�s%2 n +2 n �2sE%c @�2 n +2 �R uhvxowdgr ì r juä�fr d vhjxlu1
Wr= Vhswhpehu 4:/ 5336 Sdjh= 8
Yhmd r h{hpsor d vhjxlu1t H{hufðflr 51;= Sdud rewhu dv fxuydv htxlsrwhqfldlv sdud dv txdlv whprv � ' f/ edvwdid}hu c�s%2 n +2 n �2sE%c @�2 n +2 ' ffxmdv vroxêøhv vær b+2 n b%2 c 2e%@n �2@2 ' ftxh srgh vhu uhhvfulwd frpr
+2 n�%c e�@�2 ' �2�@�2 ctxh ì xpd flufxqihuíqfld gh udlr 2@*� fhqwudgd hp % ' e@*� +yhmd r h{hpsor dqwh0ulru,1 Qrwh txh/ qhvwh fdvr/ whuðdprv xpd frq�jxudêær gr wlsr prvwudgr dedl{r/ rqghdsuhvhqwdprv dv srvlêøhv gdv fdujdv h d srvlêær gd hvihud +dtxl dsuhvhqwdgd dshqdvqr sodqr %+,
Frqvlghuh djrud r sureohpd gh vh ghwhuplqdu r srwhqfldo gh xpd frq�jxudêær ghfdujdv hp txh whprv dshqdv xpd fdujd sxqwliruph c^ qd ruljhp h xpd hvihudphwäolfdqxpd frq�jxudêær h{dwdphqwh frpr prvwudgd qd �jxud dqwhulru +vhp d fdujd ^*2,� frqvlghuh txh vh wudwd gh ghwhuplqdu r srwhqfldo irud gd hvihud1 Frpr r srwhqfldovreuh d hvihud ghyh vhu qxor/ ylvwr txh ì xpd hvihud phwäolfd/ hqwær hvwh sureohpd ìh{dwdphqwh r phvpr gh vh hqfrqwudu r srwhqfldo sdud dv gxdv fdujdv sxqwliruphv +sruud}øhv gh xqlflgdgh gh vroxêøhv gd htxdêær gh Odsodfh/ txh yhuhprv pdlv dgldqwh,1Dvvlp/ srghuðdprv uhwludu d hvihud h rewhu d vroxêær sdud r fdpsr xvdqgr dshqdv dvgxdv fdujdv sxqwliruphv/ vlpsol�fdqgr hqruphphqwh rv fäofxorv1t H{hufðflr 51<= Whprv d vlwxdêær prvwudgd qd �jxud dedl{r= +r udlr gr flolqgur ì -h r frpsulphqwr ì u,
Wr= Vhswhpehu 4:/ 5336 Sdjh= 9
d lqwhjudo txh gä r srwhqfldo �fd/ gdgr txh Oo ' 5f	5/
) EOo� ' �eZ0f ] uf
] 2Z
f
] -
f
4to2 n E5 c 5f�2o_o_w_5 '
' 2Z4eZ0f ] u*23u*2
�tE5 c 5f�2 n-2 ctE5 c 5f�2� _5 '
' 4e0f
;?=c25fuc�5f c u2�
v-2 n�5f c u2�2n
n�5f n u2�
v-2 n�5f n u2�2n
n-22 *?
57c5f n u2 nt-2 n �5f c u2 �2c5f c u2 nt-2 n �5f n u2 �2
68<@> c
txh ì r uhvxowdgr ghvhmdgr1t H{hufðflr 5143= R fdpsr hvwä qd gluhêær % hp wrgd d h{whqvær gr hvsdêr1 Vxsrqkdtxh hoh ghshqgh gd yduläyho +/ sru h{hpsor1 Hqwær qxpd shtxhqd uhjlær gr hvsdêr/whuhprv .% E%c +c 5� �' .�% E%c + n{+c 5� +vxsrqkd d uhjlær vx�flhqwhphqwh shtxhqdsdud txh r fdpsr vhmd hvvhqfldophqwh frqwðqxr h frqvwdqwh qr lqwhuydor d+c + n{+o,1Pdv hqwær/ frqvwuxlqgr xp shtxhqr flufxlwr txdgudgr frp yìuwlfh qrv srqwrv + h+ n{+ / doìp gh % h %n{%/ srghprv fdofxodu d lqwhjudo ihfkdgd
) ' L� O. d _Oo '
] %n{%
% .%_%c
] %
%n{%.�%_% ' E.% c .�%�{% �' fc
Wr= Vhswhpehu 4:/ 5336 Sdjh= :
r txh ì xpd frqwudglêær/ srlv vdehprv txh O. ' cU)/ gh prgr txh d lqwhjudoihfkdgd whp txh vh dqxodu sdud txdotxhu flufxlwr txh frqvlghuhprv1 D frqwudglêæryhlr gr idwr gh whuprv frqvlghudgr .% E%c +c 5� �' .�% E%c + n{+c 5�/ orjr hohv ghyhp vhuljxdlv1 Gdtxl ì iäflo frqfoxlu txh ghyhp vhu ljxdlv sdud txdlvtxhu grlv srqwrv E%c +c 5�h E%c +�c 5�/ ydohqgr r phvpr udflrfðqlr sdud d gluhêær 51 Lvwr hvwdehohfh r uhvxowdgr1t H{hufðflr 5145= Edvwd frqvlghudu d vxshuiðflh gh Jdxvv txh hqyroyh d vxshuiðflhlqwhuqd gd fdylgdgh h d fdujd qd ruljhp/ sulphludphqwh/ sdud frqfoxlu txh d fdujdlqgx}lgd dol ìn^1 Hqwær/ frqvwuxd xpd qryd vxshuiðflh gh Jdxvv txh hqjoreh dshqdv dvvxshuiðflh lqwhuqd h h{whuqd gd hvihud1 Qhvwh fdvr/ frpr qær kä fdujd +uhdo, hqyroylgd/ghyhprv whu xpd fdujd c^ qd vxshuiðflh h{whuqd1t H{hufðflr 5147= Whprv gxdv sodfdv frqgxwrudv lq�qlwdv vhsdudgdv sru xpd glvwåqfld_ h frp xpd ghqvlgdgh vxshuiðfldo gh fdujd krprjíqhd j h cj1 R fdpsr surgx}lgr�fd +ohpeuh0vh txh/ dr hvfrokhu xp srqwr qr lqwhulrugd uhjlær gholplwdgd shodv sodfdv/vö vhuä srvvðyho sdud d vxshuiðflh gh Jdxvv txh sdvvd shor srqwr hvfroklgr hqjoreduxpd gdv sodfdv/ pdv qær dpedv � d vxshuiðflh srgh vhu xp sdudohohsðshgr,O._e?|oJ ' j0f 	5�Qxp srqwr qr h{whulru gdv sodfdv/ whuhprv xpd vxshuiðflh hqjoredqgr wrgdv dv gxdvsodfdv/ id}hqgr frp txh r fdpsr qxp srqwr txdotxhu qd uhjlær irud grv sodqrv vhdqxoh/ rx vhmd/ O.sJo@ ' f�t H{hufðflr 5148= Whprv xpd glvwulexlêær hviìulfd gh fdujd txh vö ì ixqêær gh o1 Frpr�fd r fdpsr sdud hvwd glvwulexlêærB D glvwulexlêær ì= 4 Eo� ' �*o/ frp � frqvwdqwhsdud f y o y - h � ' f sdud o : -1 Srghprv xvdu d ohl gh Jdxvv1 Vh r srqwr hvwlyhuirud gd hvihud/ hqwær srghprv rewhu d fdujd wrwdo txh xpd vxshuiðflh gh Jdxvv txhsdvvd shor srqwr rqgh hvwdprv fdofxodqgr r fdpsr hqjored frpr vhqgr d fdujd wrwdogd hvihud1 Hvwd fdujd ì gdgd fdofxodqgr0vh
'A ' ] 2Zf
] Z
f
] -
f
�o� o�2 t�? w_o�_w�_�� ' 2Z�-2�Djrud r fdpsr srgh vhu fdofxodgr shod lqwhjudo] Z
f
] 2Z
f .oo2 t�? w_w_� ' 2Z�-20frx vhmd/ .o ' �-220fo2
Wr= Vhswhpehu 4:/ 5336 Sdjh= ;
R srwhqfldo �fd gdgr sru ) ' c ] "o .o_o ' �-220fo �Vh r srqwr hvwä ghqwur gd hvihud/ hqwær whuhprv txh d fdujd hqjoredgd shod vxshuiðflhgh Jdxvv txh sdvvd shor srqwr hp frqvlghudêær ì gdgd sru
'A ' ] of
] Z
f
] 2Z
f
�o�2o� t�? w_o�_w�_�� ' 2Z�o2gh prgr txh ] Z
f
] 2Z
f .oo2 t�? w_w_� ' 2Z�o20f crx vhmd/ .o ' �20f �Dvvlp/ r srwhqfldo �fd
) ' c ] oof �20f_o ' c�o20f n � Eof�Pdv qrwh txh/ shod vroxêær dqwhulru/ ) E-� ' �-*20f vreuh d hvihud1 Dvvlp/ sdud txhkdmd frqwlqxlgdgh gr srwhqfldo +txh ghyh h{lvwlu/ mä txh r fdpsr ì xpd ghulydgd grsrwhqfldo h vh r srwhqfldo irvvh ghvfrqwðqxr/ r fdpsr whuld xp vdowr lq�qlwr qr srqwr,ghyhprv frorfdu � ' �-0f �Ghvwd irupd/ r srwhqfldo �fd
) Eo� ' �0f �-c o2� ctxh ì r uhvxowdgr ghvhmdgr1t H{hufðflr 5149= Xpd eduud orqjd flufxodu gh udlr - frqwìp xpd ghqvlgdgh xqliruphgh fdujd 41 Sdud fdofxodu r fdpsr hoìwulfr sdud r fdvr +d, o : - srghprv xvdu d ohlgh Jdxvv sdud rewhu 2Zou.o ' 4Z-2u0fgh prgr txh .o ' 4-220fo+qrwh txh 4Z-2 ì d ghqvlgdgh *olqhdu* gh fdujd b gh prgr txh .o ì/ hvvhqfldophqwh/.o ' b* E2Z0fo�/ frpr mä hqfrqwudgr,1 Vh whprv +e, o 	 -/ hqwær srghprv xvdu
Wr= Vhswhpehu 4:/ 5336 Sdjh= <
qrydphqwh d ohl gh Jdxvv/ pdv revhuydqgr txh d txdqwlgdgh gh fdujd hqyroylgd shodvxshuiðflh gh Jdxvv ì gdgd sru ' ' 4Zo2ucgh prgr txh 2Zou.o ' 4Zo2u0fgdqgr .o ' 420f o�t H{hufðflr 514;= Sdud fdofxodu r urwdflrqdo h r glyhujhqwh gh Oo*o@ srghprv xvdu dvlghqwlgdghv yhwruldlv qd vhjxlqwh irupd
U d � Ooo@� ' �o@U d Oo n Oo d U �o@ ' �o@ c @o@3� �o d Oo ' �c @o@Ue � Ooo@� ' �o@Ue Oo cU� �o@� e Oo ' fc @o@3� �o e Oo ' fSdud hqfrqwudu d ghqvlgdgh gh fdujd txh surgx}luld r fdpsr
O. ' ^eZ0f Ooo@ cedvwd qrwdu txh ghyhprv whu/ shod ohl gh Jdxvv
U d O. ' 40f cgh prgr txh 4 ' 0f ^eZ0fU d
� Ooo@� ' êZ �c @o@ �R srwhqfldo gr fdpsr ì rewlgr fdofxodqgr0vh d lqwhjudo
) ' c ^eZ0f ] o o�3@_o ' ^eZ0f E@c 2� o@32 �
t H{hufðflr 514;= Vh whprv r fdvr hp txh r fdpsr gh Frxorpe ì gdgr sruO. ' ^eZ0fo�3BOochqwær whprv/ shor h{hufðflr dqwhulru/ txh @ ' �c B h d ghqvlgdgh ì gdgd sru
4 ' ^BeZo�3B �
Wr= Vhswhpehu 4:/ 5336 Sdjh= 43
D fdujd wrwdo +hvvhqfldophqwh U d O., qxp yroxph - �fd gdgd sru
'A ' eZ ] -f ^BeZo�3B o2_o ' ^B
] -
f oB3�_o ' ôB ���-ftxh glyhujh sdud o ' f/ rx vhmd/ glyhujh vreuh d fdujd1 Qrwh txh vh B ' f/ hqwær qærkdyhuld sureohpd1t H{hufðflr 514<= R srwhqfldo gh Frxorpe dwhqxdgr ì gdgr sru
) ' ^eZ0f e3o*bo �Ghvwd pdqhlud/ r fdpsr hoìwulfr dvvrfldgr �fd
O. ' 	o.o ' c	oY)Yo ' ^e3o*beZ0f
� Ooo� n Oobo2� ' ^e3o*beZ0f �� n ob� Ooo� ctxh ì r uhvxowdgr ghvhmdgr1 Sdud rewhu d ghqvlgdgh gh fdujd/ edvwd wrpdu r glyhujhqwhgr uhvxowdgr dflpd4 Eo�0f ' U d O. ' ^eZ0fU d
�e3o*b �� n ob� Ooo�� '' ^eZ0f
�	o YYo d �e3o*b � �o� n �bo2�Oo�� '' ^eZ0f
�Oo d 	o YYo �e3o*b � �o� n �bo2��n �e3o*b� �o� n �bo2��U d Oo� '
' ^eZ0f
%eZB EOo� e3o*b c oe3o*b �o2 n �bo n �b2�b2oe n �e3o*b Ebn o�bo�
& '
' ^e3o*beZ0f
�eZB EOo�c �b2o�Dvvlp/ whprv 4 EOo� ' ^e3o*b �B EOo�c e3o*beZb2o� cfrpr ghvhmdgr1 Qrwh txh d glvwulexlêær B EOo� gh Gludf dsduhfhx ghylgr d whuprvfdofxodgr/ hp fhuwr prphqwr/ r glyhujhqwh U d EOo*o��/ frpr mä ylvwr qr wh{wr1t H{hufðflr 5153= Sdud rewhu dv fxuydv htxlsrwhqfldlv/ edvwd qrwdu txh r srwhqfldo ìgdgr shod iöupxod ) ' �eZ0f OR d Ooo� �
Wr= Vhswhpehu 4:/ 5336 Sdjh= 44
Frofdqgr r glsror qd gluhêær % whprv/ hp frrughqdgdv sroduhv +h hp xqlgdghv gheZ0fR, ) ' %d%2 n +2 n 52o�*2h srghprv wudêdu r juä�fr idflophqwh1 +Frorfdprv 5 ' � sdud hylwdu d vlqjxodulgdghhp Efc fc f� sru txhvwøhv gr wudêdgru gr juä�fr,1 Ilfdprv frp d �jxud dedl{r
t H{hufðflr 5154=
� +d, Ghprqvwuh txh d iruêd txh dwxd qxp glsror OR frorfdgr hp xp fdpsr hoìwulfrh{whuqr O.e%| ì OR d UO.e%|1 Frqvlghuh d �jxud dedl{r=
Dwudyìv gd �jxud/ srghprv frqfoxlu txh d iruêd txh dwxd vreuh r glsror ì gdgdsru O8 ' n^ O.e%| EOo�c ^ O.e%| �Oo nO,� �
Wr= Vhswhpehu 4:/ 5336 Sdjh= 45
Djrud/ O,� O-/ gh prgr txh srghprv id}hu xpd h{sdqvær qr vhjxqgr whupr/ hpwruqr gh O,/ sdud rewhuO8 ' ^ O.e%| EOo�c ^ k O.e%| EOo� nO, d UO.e%| EOo�l ' c^O, d UO.e%| EOo�txh srgh vhu hvfulwd frpr +r vlqdo ghyh0vh ã ghliqlêær sduwlfxodu gr glsror,O8 ' cOR d UO.e%| EOo� �^Qrwd= r ohlwru ghyh id}hu d h{sdqvær frqwlgd pdlv dflpd sdud yhul�fdu dtxhohuhvxowdgr h{solflwdphqwh1`� +e, Prvwudu txh r wrutxh dwxdqwh qxp glsror qhvwh fdpsr ì gdgr sru
O� ' Oo e kOR d UO.e%|ln OR e O.e%|�Qhvwh fdvr/ ghyhprv whu
O� ' Oo e ^ O.e%| EOo�c �Oo nO,� e ^ O.e%| �Oo nO,� '' Oo e ^ O.e%| EOo�c Oo e ^ k O.e%| EOo� nO, d UO.e%| EOo�lcO, e ^ k O.e%| EOo� nO, d U O.e%| EOo�l '' cOo e k^O, d UO.e%| EOo�lc O, e ^ O.e%| c O, e ^O, d UO.e%| EOo� �
Frpr r ýowlpr whupr ì gh vhjxqgd rughp hp O,/ srghprv hvfuhyhu/ hp sulphludrughp/ O� ' cqOo e kOR d UO.e%| EOo�ln OR e O.e%| EOo�r ctxh ì r uhvxowdgr ghvhmdgr +d phqrv gr vlqdo sru ud}øhv mä doxglgdv,1� H{hufðflr 5155= Sdud d frqirupdêær flwdgd= n^ hp Efc fcc,� h Efc fcn,� h c2^hp Efc fc f�/ srghprv hvfuhyhu r srwhqfldo frpr
) ' ^*eZ0ft%2 n +2 n E5 n ,�2 n ^*eZ0ft%2 n +2 n E5 c ,�2 c 2^*eZ0fs%2 n +2 n 52txh srgh vhu uhhvfulwd frpr
) E%c +c 5� ' ^eZ0f
� �So2 n 25, n ,2 n �So2 c 25, n ,2 c 2o� '
' ^eZ0fo
;?= �t� n 25,n,2o2 n �t� n 325,n,2o2 c 2
<@> '
' ^eZ0fo
�c �o2 n �52oe � ,2 n� �,�� �
Wr= Vhswhpehu 4:/ 5336 Sdjh= 46
Frorfdqgr djrud 5 ' o ULt w/ �fdprv frp +dwì vhjxqgd rughp hp ,,
) Eoc wc �� ' ^,2eZ0fo� �� ULt2 w c �� �Sdud wudêdu dv vxshuiðflhv htxlsrwhqfldlv/ srghprv hvfuhyhu r srwhqfldo frpreZ0f) E%c +c 5�^,2 ' �52d%2 n +2 n 52oD*2 c �d%2 n +2 n 52o�*2 �Qr sodqr %5 �fdprv frp + ' f h
)� ' eZ0f) E%c +c 5�^,2 ' �52d%2 n 52oD*2 c �d%2 n 52o�*2R juä�fr gdv htxlsrwhqfldlv srgh vhu ihlwr gd phvpd pdqhlud txh irl ihlwr qrh{hufðflr 51: h �fd
t H{hufðflr 5156= Sdud rewhu d h{suhvvær sdud dv frpsrqhqwhv gr whqvru gh txdguxsror/edvwd xvdu d h{suhvvær jhudo ) ' �2 [�c� %�%�oD '�� crqgh '�� ' ] ] ] ��%��%�� c B��o�2� 4 EOo�� _%�_+�_5�h qrwdu txh 4 Eo�� ' B E%�� B E+�� d^B E5� c ,� n ^B E5� n ,�c 2^B E5��o/ gdqgr
'�� ' ] ] ] �2%�2 c +�2 c 5�2� B E%�� B E+�� d^B E5� c ,� n ^B E5� n ,�c 2^B E5��o _%�_+�_5� '
' c^ ] 5�2 dB E5� c ,� n B E5� n ,�c 2B E5��o _%�_+�_5� ' c2^,2
Wr= Vhswhpehu 4:/ 5336 Sdjh= 47
h
'22 ' ] ] ] �2+�2 c %�2 c 5�2� B E%�� B E+�� d^B E5� c ,� n ^B E5� n ,�c 2^B E5��o _%�_+�_5� '
' c^ ] 5�2 dB E5� c ,� n B E5� n ,�c 2B E5��o _%�_+�_5� ' c2^,2
h
'�� ' ] ] ] �25�2 c +�2 c %�2� B E%�� B E+�� d^B E5� c ,� n ^B E5� n ,�c 2^B E5��o _%�_+�_5� '
' c2^ ] 5�2 dB E5� c ,� n B E5� n ,�c 2B E5��o _%�_+�_5� ' ce^,2
Sdud fdofxodu rv whuprv fux}dgrv/ edvwd qrwdu txh r whupr �%��%�� vhpsuh gduä xpsurgxwr gh 5 frp % rx + rx xp surgxwr gh % frp +> ghylgr ãv ixqêøhv B E%�� h B E+�� ruhvxowdgr gd lqwhjudo vhuä vhpsuh qxor1 R whupr B�� vhuä vhpsuh qxor ghylgr dr ghowdgh Nurhqhfnhu1 Dvvlp/ wrgrv rv hohphqwrv irud gd gldjrqdo vh dqxoduær1 R whqvrutxdguxsror hoìwulfr sdud hvwd frq�jxudêær �fd
' ' 57 � f ff � ff f 2
68 2^,2�
t H{hufðflr 5157= D h{suhvvær sdud r prphqwr gh glsror ì
OR ' ] Oo�4 EOo�� _��c
pdv vh whprv xp glsror/ hqwær d ghqvlgdgh gh fdujd �fd
4 EOo�� ' ^B#Oo� c O,2
$c ^B#Oo� n O,2
$ c
gh prgrtxh
OR ' ^ ] Oo� %B#Oo� c O,2
$c B#Oo� n O,2
$& _�� '
' ^O,2 c
#c^O,2
$ ' ^O,c
frpr txhuðdprv ghprqvwudu1
Wr= Vhswhpehu 4:/ 5336 Sdjh= 48
t H{hufðflr 5159= R srwhqfldo ì gdgr sru
) Eoc wc �� ' �eZ0f OR d Ooo� ' R ULt weZ0fo2gh prgr txh r fdpsr/ xvdqgr d h{suhvvær sdud r judglhqwh hp frrughqdgdv hviìulfdvfrpr vhqgr U ' 	o YYo n 	w�o YYw n 	� �o t�? w YY�c�fdprv frp
O. ' cU) ' c�eZ0f
�c	oR ULt wo� n �o R t�? wo2 	w� '' ReZ0fo� k	o ULt w c 	w t�? wl ctxh ì r uhvxowdgr ghvhmdgr1 Qrwh dlqgd txh	5 ' 	o ULt w c 	w t�? wcgh prgr txh O. ' ReZ0fo� 	5�
Wr= Vhswhpehu 4</ 5336 Sdjh= 4
+Fkdswhu khdg=,Fdsðwxor 6=t H{hufðflr 614= Whprv txh r srwhqfldo dvvrfldgr dr sureohpd/ gdgd d vlphwuld/ ghyhsrghu vhu hvfulwr frpr ) ' �o n�rqgh � h � vær dv frqvwdqwhv d vhuhp ghwhuplqdgdv1 +d, Sdud rv srqwrv lqwhuqrv/whprv= sdud txh dv ghwhuplqhprv/ edvwd xvdu dv frqglêøhv gh frqwruqr/ gdgdv sru) Eo@� ' )@) EoK� ' )Ksdud rewhu r vlvwhpd � �o@ n� ' )@�oK n� ' )Kfxmdv vroxêøhv vær � ' oKo@ E)@ c )K�oK c o@ h � ' )KoK c )@o@oK c o@ cgh prgr txh qrvvr srwhqfldo �fd
) Eo� ' oKo@ E)@ c )K�oK c o@ �o n )KoK c )@o@oK c o@txh ì r uhvxowdgr ghvhmdgr1 +e, Sdud rv srqwrv h{whuqrv whprv vlpsohvphqwh +ohpeuh0vhgr hihlwr gd eolqgdjhp, ) Eo� ' oK)Ko �t H{hufðflr 615= Djrud d glvwulexlêær ì floðqgulfd1 D lgìld ì d phvpd gr h{hufðflrdqwhulru/ pxgdqgr dshqdv d irupd sduwlfxodu gr srwhqfldo/ txh hvfuhyhprv) ' � *? o n��Dv frqglêøhv gh frqwruqr lpsolfdp txh +d, sdud srqwrv lqwhuqrv=� )@ ' � *? o@ n�)K ' � *? oK n� cgh prgr txh � ' )K c )@*? EoK*o@� h � ' *? Eo)@K *o)K@ �*? EoK*o@� ch/ sruwdqwr/ ) Eo� ' )K c )@*? EoK*o@� *? o n *? Eo)@K *o)K@ �*? EoK*o@� �+e, Sdud srqwrv h{whuqrv/ whuhprv/ frpr dqwhulruphqwh) Eo� ' )K*? oK *? o�
Wr= Vhswhpehu 4</ 5336 Sdjh= 5
t H{hufðflrv 616= Vdehprv txh )� E%c +c 5� ì xpd vroxêær gd htxdêær gh Odsodfh1 Dvvlp/whprv U2)� E%c +c 5� ' f�Ghulydqgr dperv rv odgrv gd htxdêær frp uhodêær d txdotxhu yduläyho h xp qýphurtxdotxhu gh yh}hv/ �fdprv frpY?Y%�Y%2 d d d Y%?
�Y2)�Y%2 n Y2)�Y+2 n Y2)�Y52 � ' f�Frpr srghprv lqyhuwhu dv rughqv gh ghulydêær/ �fdprv frpY2)2Y%2 n Y2)2Y+2 n Y2)2Y52 ' fcrqgh )2 ' Y?)�Y%�Y%2 d d d Y%? �t H{hufðflr 617= Vdehprv txh ) vdwlvid} d htxdêær gh Odsodfh hp wrgd d uhjlær Tf1Sdud surydu txh r ydoru gh ) hp xp srqwr txdotxhu J ì d pìgld gh vhxv ydoruhv qxpdvxshuiðflh gh txdotxhu hvihud fhqwudgd hp J txh vh vlwxd lqwhludphqwh hp Tf/ rx vhmd/
) EJ� ' �eZ-2 L7 )_@csrghprv vhjxlu d vxjhvwær gr olyur h frorfdu � ' �*o qd htxdêær +408:, sdud rewhu]
T
��oU2)c )U2�o� _� ' L7
� �-U)c )U �-� d 	?_@�Qrwh djrud txh U2) ' f h txh U2 E�*o� ' ceZB EOo�/ gh prgr txh �fdprv frp
eZ) EJ� ' L7
� �-U)c )U �-� d 	?_@�R vhjxqgr whupr iruqhfh U E�*-� ' cO-*-� h frpr 	? ì udgldo/ srlv d vxshuiðflh ì xpdhvihud/ �fdprv frp U E�*-� ' O- d 	?*-� ' c�*-21 Qrvvr uhvxowdgr �fd
eZ) EJ� ' �-2 L7 )_@n
L
7
�-U) d 	?_@�Sdud surydu txh d ýowlpd lqwhjudo ì qxod/ ghyhprv qrv ohpeudu txh hvwdprv qxpduhjlær olyuh gh irqwhv gh fdujdv/ srlv d htxdêær gh Odsodfh ydoh1 Wdpeìp ghyhprv qrvohpeudu txh O. ' cU) h txh�- L7 U) d 	?_@ ' c �-
L
7 O. d 	?_@ ' c-̂0f c
Wr= Vhswhpehu 4</ 5336 Sdjh= 6
frp ^ ' f1 Dvvlp/ �fdprv frp
eZ) EJ� ' �-2 L7 )_@rx vhmd ) EJ� ' �eZ-2 L7 )_@txh ì r uhvxowdgr ghvhmdgr1t H{hufðflr 618= Sdud h{sdqglu d ixqêær
8 E�� ' ��c 2%+ n �2�3�*2edvwd xvdu d vìulh gh Wd|oru xvxdo=
8 E�� ' 8 Ef� n ��- Y8 E��Y� �����'f �� n �2- Y28 E��Y�2
�����'f �2 n J ���� '' � n %�n��2%2 c �2��2 n�D2%� c �2%��� n J ��e� �Vh frorfduprv hp ixqêær gh xpd vrpd h qrwduprv txh rv whuprv hp % vær rv srolq÷plrvgh Ohjhqguh/ whuhprv 8 E�� ' "[?'f �? E%� �?cfrpr txhuðdprv ghprqvwudu1t H{hufðflr 619= Sdud ghprqvwudu txh d phwdgh grv kdup÷qlfrv }rqdlv vær jhudgrvdwudyìv gd ghulydêær vxfhvvlyd gh o3� hp uhodêær ã frrughqdgd uhwdqjxodu 5 +5 'o ULt w,/ srghprv id}hu=YY5 ��o� ' c �o2 YoY5 ' co32 ULt w ' o32�� Ew�h wdpeìpY2Y52 ��o� ' c YY5 � �o2 YoY5� ' 2o3��YoY5�2 c �o2 Y2oY52 ' 2o3� ULt2 Ew� ���
t H{hufðflr 61:= Vdehprv txh U2 ' Y2Y%2 n Y2Y+2h txh % ' o ULt w h + ' o t�? w1 Dvvlp/ whprv/ sru lqyhuvær=o 's%2 n +2 h w ' @hU|@? E+*%�
Wr= Vhswhpehu 4</ 5336 Sdjh= 7
gh prgr txhYY% ' YoY% YYo n YwY% YYw ' %s%2 n +2 YYo c +%2 n +2 YYw ' ULt w YYo c t�? wo YYwYY+ ' YoY+ YYo n YwY+ YYw ' +s%2 n +2 YYo n %%2 n +2 YYw ' t�? w YYo n ULt wo YYwSdud rewhu dv ghulydgdv gh vhjxqgd rughp/ id}hprvY2Y%2 ' �ULt w YYo c t�? wo YYw��ULt w YYo c t�? wo YYw� '' ULt2 w Y2Yo2 n ULt w t�? wo2 YYw n t�?2 wo YYo n t�?2 wo2 Y2Yw2 n ULt w t�? wo2 YYwh wdpeìpY2Y+2 ' �t�? w YYo n ULt wo YYw��t�? w YYo n ULt wo YYw� '' t�?2 w Y2Yo2 c ULt w t�? wo2 YYw n ULt2 wo Y2Yo n ULt2 wo2 Y2Yw2 c ULt w t�? wo2 YYwtxh vrpdgrv gær
U2 ' Y2Y%2 n Y2Y+2 ' � Y2Yo2 n �o YYo�n �o2 Y2Yw2 ' �o YYo �o YYo�n �o2 Y2Yw2 ctxh ì r uhvxowdgr ghvhmdgr1t H{hufðflr 61;= Qr h{hufðflr 5155/ fdsðwxor 5/ rewlyhprv txh
) Eoc wc �� ' E2^,2�eZ0fo�
��2 ULt2 w c �2�h frpr �2 Ew� ' ��2 ULt2 w c �2�/ �fd hvwdehohflgr r uhvxowdgr1t H{hufðflr 61<= Whprv xp glsror srqwxdo orfdol}dgr qr fhqwur gh xpd fdvfd hviìulfdfrqgxwrud frqhfwdgd ã whuud +srwhqfldo qxor,1 Sdud ghwhuplqdu r srwhqfldo qr lqwhulrugd fdvfd/ srghprv xvdu rv kdup÷qlfrv }rqdlv txh vær �qlwrv qd ruljhp Eo ' f�/ mätxh ghyhprv whu vroxêær ehp frpsruwdgd dð/ h{fhwr shor idwr gh whuprv xp glsrorsrqwxdo qd ruljhp h d glyhujíqfld ghyhu vhu gr wlsr dvvrfldgr d hvwd glvwulexlêær ghfdujd1 Dvvlp/ qrvvr srwhqfldo �fd gdgr sru
) Eoc w� ' "[?'f ��?o? n�?o3E?n����? Ew� c
Wr= Vhswhpehu 4</ 5336 Sdjh= 8
h d lgìld ì rewhu dv frqvwdqwhv �? h �? gdv frqglêøhv gh frqwruqr gr sureohpd1Hvwdv frqglêøhv gh frqwruqr srghp vhu idflophqwh gdgdv vdehqgr0vh txh sdud o pxlwrshtxhqrv/ ghyhuhprv whu r srwhqfldo sudwlfdphqwh ljxdo ãtxhoh gh xp glsror srqwxdo/mä txh ì xp glsror srqwxdo txh vh hqfrqwud qd ruljhp1 Dvvlp/ vdehqgr0vh txh rsrwhqfldo gr glsror srqwxdo ì gdgr sru
)_�R ' �eZ0f R ULt wo2 c�fd fodur txh +ohpeuh0vh txh qd ruljhp rv whuprv hp �? vh fdqfhodp, ghyhprv dqxoduwrgrv rv frh�flhqwhv �? sdud ? �' �/ mä txh gær glyhujíqfld glvwlqwd gd txh hvshudprvsdud d glvwulexlêær gh fdujd hp txhvwær1 Pdlv dlqgd/ �� ' R/ hylghqwhphqwh1 Djrud/vdehqgr0vh txh d hvihud hvwä dwhuudgd/ hqwær vdehprv txh hp o ' @ +udlr gd hvihud,/ghyhprv whu ) E@c w� ' f +txh ì d rxwud frqglêær gh frqwruqr gr sureohpd,1 Ohydqgrqd h{suhvvær sdud r ) gdgd dflpd/ whprv
) E@c w� ' "[?'f�?@?�? Ew� n �eZ0f R ULt w@2 ' f�Qrwh txh r whupr hp ? ' f ì xp whupr frqvwdqwh h qær id} glihuhqêd qd dqäolvh ghxp srwhqfldo1 Dvvlp/ qrvvd dqäolvh �fd gdgd sru
) E@c w� ' ���@n �eZ0f R@2
� ULt w n "[?'2�?@?�? Ew� ' fcrqgh mä lvrodprv r sulphlur whupr hp ULt w1 Djrud qrwh txh rv kdup÷qlfrv }rqdlv �? Ew�vær olqhduphqwh lqghshqghqwhv1 Dvvlp/ srghprv dqxodu r sulphlur whupr frorfdqgr
�� ' c �eZ0f R@� cpdv rv rxwurv whuprv vö srghuær vhu dqxodgrv vh frorfduprv �? ' f vh ? z 21 Dvvlp/qrvvr srwhqfldo �fd frpsohwdphqwh ghwhuplqdgr h ì gdgr sru
) Eoc w� ' �eZ0f
��c o�@�� R ULt wo2 ctxh ì r uhvxowdgr ghvhmdgr1t H{hufðflr 6143= Mä hqfrqwudprv r srwhqfldo gh xpd hvihud frqgxwrud qær fduuhjdgd/vlwxdgd qxp fdpsr hoìwulfr lqlfldophqwh xqliruph1 R srwhqfldo ì gdgr sru
) Eoc w� ' c��c @�o��.fo ULt w '' c.fo ULt w n .f@�o ULt wo�
Wr= Vhswhpehu 4</ 5336 Sdjh= 9
R sulphlur whupr ì r whupr gh fdpsr frqvwdqwh/ hqtxdqwr txh r vhjxqgr ì gdgr sru
)W Eoc w� ' �.f@�	&� d Ooo� �D frpsdudêær ghvwh whupr frp r srwhqfldo ghylgr d xp glsror srqwxdo/ gdgr sru
)_�R Eoc w� ' OR d OoeZ0fo�prvwud txh )W Eoc w� uhsuhvhqwd xp srwhqfldo gh glsror srqwxdo qd ruljhp frpprphqwrgh glsror hoìwulfr gdgr sru OR ' eZ0f@�.f	&�R srwhqfldo )W Eoc w� ì r srwhqfldo ghylgr ã hvihud/ mä txh d sduwh gh fdpsr frqvwdqwhmä irl uhwludgd h qær kä rxwudv irqwhv sdud r srwhqfldo1t H{hufðflr 6144= D hvihud whp udlr @ h srvvxl xpd fdujd ' h hvwä qxp fdpsr hoìwulfrlqlfldophqwh xqliruph1 Hvwh sureohpd ì vlplodu dr txh irl uhvroylgr qr frusr gr olyur/kdyhqgr dshqdv d dowhudêær gh txh/ djrud/ d hvihud frqgxwrud srvvxl xpd fdujd oðtxlgd1D vlphwuld ì hviìulfd +ghylgr ãv frqglêøhv gh frqwruqr, h r srqwhqfldo srgh vhu hvfulwrfrpr
) Eoc w� ' "[?'f ��?o? n�?o3E?n����? EULt w� '' �f n��o ULt wn "[?'2 �?o?�? EULt w� nn��o n �2o2 ULt w n "[?'2 �?o?n��? EULt w� �D frqglêær gh frqwruqr qr lq�qlwr gl} txh ) E�c w� ' c.fo ULt w/ gh prgr txh ghyh0prv dqxodu wrgrv rv whuprv gr wlsr o& frp & z 21 Doìp glvvr/ �� ' c.f1 Ilfdprvhqwær frp
) Eoc w� ' �f c.fo ULt w n ��o n �2o2 ULt w n "[?'2 �?o?n��? EULt w� �
Qrwh djrud txh d hvihud hvwä fduuhjdgd/ gh prgr txh r whupr ��*o qær srgh vh dqxoduh/ dlqgd sru flpd/ ghyh gdu r uhvxowdgr �� ' '*eZ0f/ mä txh vreuh d vxshuiðflh gdhvihud ghyhprv whu xp srwhqfldo
) E@c w� ' 'eZ0f@�
Wr= Vhswhpehu 4</ 5336 Sdjh= :
Dvvlp/ d frqglêær gh frqwruqr vreuh d vxshuiðflh gd hvihud �fd +�f ' f,
) E@c w� ' 'eZ0f@ n
��2@2 c .f@� ULt w n "[?'2 �?@?n��? EULt w� ' 'eZ0f@crx vhmd ��2@2 c .f@� ULt w n "[?'2 �?@?n��? EULt w� ' fcsdud txdotxhu w1 Frpr rv srolq÷plrv gh Ohjhqguh vær olqhduphqwh lqghshqghqwhv/ghyhprv whu txh fdgd frh�flhqwh gh �? EULt w� dflpd +lqfoxlqgr r ULt w ' �� EULt w�,ghyh dqxodu0vh1 Dvvlp/ �fdprv frp�2 ' .f@� h �? ' f vh ? z 2�R srwhqfldo �fd/ sruwdqwr/
) E@c w� ' 'eZ0fo n
�.f@�o2 c.fo� ULt wtxh qdgd pdlv ì gr txh r srwhqfldo sdud xpd hvihud ghvfduuhjdgd qxp fdpsr hoìwulfrxqliruph +uhvxowdgr rewlgr qr frusr gr wh{wr, dglflrqdgd dr srwhqfldo gh xpd hvihudfduuhjdgd frp fhqwur qd ruljhp +ohpeuh0vh txh ydoh d vxshusrvlêær sdud dv vroxêøhvgd htxdêær gh Odsodfh,1t H{hufðflr 6145= Djrud whprv xp frqgxwru floðqgulfr ghvfduuhjdgr/ phwäolfr/ qd suh0vhqêd gh xp fdpsr hoìwulfr lqlfldophqwh frqvwdqwh1 R hl{r 5 ghyh vhu frorfdgr qd gl0uhêær gr hl{r gr flolqgur h r srwhqfldo qr lq�qlwr �fd gdgr sru ) E�c w� ' c.fo ULt w/frpr dqwhulruphqwh +pdv hp frrughqdgdv floðqgulfdv/ rx vhmd/ r o dtxl whp vljql�fdgrglvwlqwr gr o hp frrughqdgdv hviìulfdv/ dvvlp frpr r w,1 D frqglêær gh frqwruqr vreuhd vxshuiðflh gr flolqgur srgh vhu hvfulwd frpr ) E@c w� ' f1 R srwhqfldo ì xpd vroxêærjhudo gd htxdêær gh Odsodfh hp frrughqdgdv floðqgulfdv +rqgh whprv vlphwuld sodqdutxh qrv srvvlelolwrx holplqdu rv whuprv Y2*Y52 gr odsodfldqr, h ì gdgr sru
) Eoc w� ' �f n�f *? o n "[?'� ��?o3? n�?o?� d�? ULt E?w� n(? t�? E?w�o �R whupr hp �f ì xpd frqvwdqwh lqhvvhqfldo/ gh prgr txh �f ' f vhp shugd ghjhqhudolgdgh1 R flolqgur qær ì fduuhjdgr/ gh prgr txh �f ' f1 Doìp glvvr/ d frqglêærgh frqwruqr hp o � � lpsolfd txh �? ' f vh ? z 21 Ilfdprv/ sruwdqwr/ dwì dtxl/frp r srwhqfldo
) Eoc w� ' ���o ULt w n����o t�? w n "[?'� o3? d� �? ULt E?w� n(�? t�? E?w�o c
Wr= Vhswhpehu 4</ 5336 Sdjh= ;
rqgh mä *dvvlplodprv* d frqvwdqwh �? hp ��? h (�?1 Qrwh djrud txh d frqglêær ghfrqwruqr qr lq�qlwr qrv frpsurphwh hp frorfdu r hl{r % qd gluhêær gr fdpsr hoìwulfrfrqvwdqwh/ rx vhmd/ hvwlyhprv vxsrqgr dwì dtxl txh O. ' .f	%1 Frp hvwd vlphwuld/ qærhvshudprv txh r srwhqfldo srvvd vh dowhudu txdqgr id}hprv w � cw1 Ghvwh prgr/ghyhprv holplqdu rv whuprv hp t�? w gd h{suhvvær dflpd sdud rewhu
) Eoc w� ' ���o ULt w n "[?'� � �?o3? ULt E?w� �Dvvlp/ frp o � � �fdprv dshqdv frp r sulphlur whupr h frqfoxlprv idflophqwh txh��� ' c.f1 Djrud/ sdud d frqglêær gh frqwruqr vreuh r flolqgur/ whprv
) Eoc w� ' �c.f@n � ��@ � ULt w n "[?'2 � �?@3? ULt E?w� ' f�Frpr dv ixqêøhv ULt w vær olqhduphqwh lqghshqghqwhv/ �fdprv frp � �? ' f vh ? z 2 h� �� ' .f@21 R uhvxowdgr �qdo sdud r srwhqfldo �fd) Eoc w� ' c.f�o c @2o � ULt w�Dv fxuydv gh srwhqfldo �fdp frpr prvwudgr qd �jxud dedl{r +@ ' �,
D ghqvlgdgh vxshu�fldo gh fdujd �fd gdgd sru
j Ew� ' c.f�� n @2o2� ULt wR juä�fr gd glvwulexlêær gh fdujdv �fd gdgr shod �jxud d vhjxlu=
Wr= Vhswhpehu 4</ 5336 Sdjh= <
qrwh txh/ vreuh r hl{r %/ whprv xpd glvwulexlêær gh fdujdv qhjdwlydv sdud % : f hsrvlwlydv sdud % 	 f/ frpr hvshudgr1t H{hufðflr 6146= R srwhqfldo ì
) Eoc w� ' �o�*2 t�? w2 ' W4��S5� 1Hp frrughqdgdv floðqgulfdv/ whprvY)Yo ' �2So t�? w2 h Y)Yw ' So2 ULt w2gh prgr txh Y2)Yo2 ' c �eo�*2 t�? w2 h �o2 Y2)Yw2 ' c �eo�*2 t�? w2h/ sruwdqwr/Y2)Yo2 n �o Y)Yo n �o2 Y2)Yw2 ' c �eo�*2 t�? w2 n �o �2So t�? w2 c �eo�*2 t�? w2 ' f�Gl}0vh txh hvwh srwhqfldo srgh vhu xvdgr sdud ghvfuhyhu r sureohpd gh xp sodqrfduuhjdgr frqgxwru hp %5 +rx vhmd/ + ' f,1 Hvwh srwhqfldo ì ghvfrqwðqxr hp w ' f/srlv d ixqêær qær uhwruqd d vhxv ydoruhv gh dqwhv vh gdprv xpd yrowd frpsohwd qrsodqr w � w n 2Z1 D ixqêær dflpd/ S5 ì xpd ixqêær pxowlydorudgd h/ sdud wruqdu0vhxqlydorudgd/ ghyhprv frqvwuxlu sdud hod xpd vxshuiðflh gh Ulhpdqq gh gxdv irokdv1 Dghqvlgdgh gh fdujd vreuh r sodqr �fd gdgd sruY)Y+ ����+'f ' �2So YoY+ t�? w2 n �2So ULt w2 YwY+ '' +2o t�? w2 n %2o ULt w2 '' �2 �t�? w t�? w2 n ULt w ULt w2� ' �2 ULt�w c w2� ' �2 ULt w2 �
Wr= Vhswhpehu 4</ 5336 Sdjh= 43
R juä�fr gdv fxuydv htxlsrwhqfldlv �fd
rqgh srghprv qrwdu r hqfxuydphqwr gdv htxlsrwhqfldlv/ lqglfdqgr txh r fdpsr/ shuwrgd erugd gr sodqr +uhsuhvhqwdgr shod olqkd suhwd fkhld, whqghuä d glyhujlu *sdud irud*/uhsuhvhqwdqgr rv hihlwrv gh erugd1t H{hufðflr 6147= Shor pìwrgr gdv lpdjhqv/ whprv txh r srwhqfldo �fd gdgr sru
) E%c +c 5� ' ^eZ0f
57 �tE%c _�2 n +2 n 52 c �tE%n _�2 n +2 n 52
68
gh prgr txh d ghqvlgdgh vxshu�fldo gh fdujd �fd gdgd sru +r sodqr hvwä hp +5,
j Efc +c 5� ' c0f Y)Y% ����%'f ' c_^2Z �d_2 n +2 n 52o�*2h d fdujd wrwdo lqgx}lgd �fd
j|J|@, ' c_^2Z ] n"3"
] n"
3"
�d_2 n +2 n 52o�*2_5_+ '' c_^2Z ] n"3" 2_2 n 52_5 ' c^cfrpr hvshudgr1t H{hufðflr 6148= Whprv dv fdujdv sxqwliruphv ^� h ^2 orfdol}dgdv suö{lpdv d xp sodqrfrqgxwru ghvfduuhjdgr +) ' f,1 Dv fdujdv lpdjhqv vhuær c^� h c^2 orfdol}dgdv hvshfx0oduphqwh d ^� h ^2/ uhvshfwlydphqwh1 Ì öeylr/ sruwdqwr/ txh ghyhprv vhpsuh hvfrokhu/qxpd glvwulexlêær 4 EOo� frqwðqxd/ d glvwulexlêær c4 EOo�/ hvshfxoduphqwh srvlflrqdgdfrp uhodêær dr sodqr frqgxwru1
Wr= Vhswhpehu 4</ 5336 Sdjh= 44
t H{hufðflr 6149= D srvlêær grv sodqrv ì gdgd shod �jxud dedl{r/ ehp frpr d srvlêærgdv fdujdv srqwxdlv1
Dv srvlêøhv gdv fdujdv wdpeìp hvwær prvwudgdv h vær rv uh h{rv hvshfxoduhv gdvphvpdv frp uhodêær drv sodqrv1 Irupdp xp kh{djrqr/ srlv d fdujd lqlfldo +uhdo,/irupd gxdv lpdjhqv hvshfxoduhv +yhuphokdv, txh/ sru vxd yh}/ irupdp gxdv lpdjhqvhvshfxoduhv +yhughv, txh irupdp d phvpd lpdjhp hvshfxodu +d}xo,/ gdqgr r kh{djrqrgd �jxud dqwhulru1t H{hufðflr 614:= Whprv xpd vlwxdêær frpr d prvwudgd qd �jxud d vhjxlu=
Wr= Vhswhpehu 4</ 5336 Sdjh= 45
h d iruêd �fd
8 ' ^2eZ0f
�c �E2_c 2%�2 c �E2%�2 n �E2_�2 n �E2_�2 c �E2_n 2%�2 c �Ee_c 2%�2 n �Ee_�2 d d d � '' ^2�SZ0f_2
� ��2 n 2c �E�c ��2 c �E� n ��2 c �E2c ��2 n �2
�
' ^2�SZ0f_2
+ ��2 n "[?'�
� 2?2 c� �E?n ��2 n �E?c ��2
��,
rqgh � ' %*_1 D glihuhqêd sdud r uhvxowdgr gr olyur ghyh0vh drv srqwrv rqgh irudpfrorfdgrv rv sodqrv1t H{hufðflr 614;= Sdud hqfrqwudu d iruêd hqwuh d fdujd sxqwliruph h d hvihud fduuhjdgd/srghprv frqvlghudu r sureohpd htxlydohqwh shor pìwrgr gdv lpdjhqv/ vhjxqgr r txdokä dshqdv gxdv fdujdv sxqwliruphv1 Xpd gh ydoru ^/ vlwxdgd d xpd glvwåqfld _ gdruljhp h xpd vhjxqgd gh fdujd ^� ' c@^*_ vlwxdgd d xpd glvwåqfld K ' @2*_ gdruljhp/ rqgh @ ì r udlr gd hvihud1 Dvvlp/ d iruêd hqwuh hodv �fd gdgd sru
8^^� ' ^^�eZ0f E_c @2*_�2 ' c@^2eZ0f E_2 c @2�2 �t H{hufðflr 614<= Whprv xpd hvihud frqgxwrud qd suhvhqêd gh xp fdpsr hoìwulfrxqliruph qd gluhêær 51 Hvwh fdpsr srgh vhu uhsuhvhqwdgr shor fdpsr gh gxdv fdujdvsxqwxdlv ' h c' vlwxdgdv vreuh r hl{r 5 hp 5 ' cu h 5 ' nu/ frp u � �1 Rsrwhqfldo ghvwd frq�jxudêær ì
)e%| E%c +c 5� ' 'eZ0f
57 �t%2 n +2 n E5 n u�2 c �t%2 n +2 n E5 c u�2
68 '
' 'eZ0f
� �So2 n 2ou ULt w n u2 c �So2 c 2ou ULt w n u2� '
' 'eZ0fu
57 �t� n 2 ou ULt w n o2u2 c �t�c 2 ou ULt w n o2u2
68 '
' 'eZ0fu
���c ou ULt w c o22u2�c�� n ou ULt w c o22u2�� '' 'eZ0fu 2o ULt wu ' '2Z0fu2 o ULt w�Gh irupd txh vh frorfduprv .f ' '*2Z0fu2/ whprv sdud u � �/ hp sulphlud rughp/txh )e%| Eoc w� ' c.fo ULt w�
Wr= Vhswhpehu 4</ 5336 Sdjh= 46
Djrud whprv xpd frq�jxudêær qd txdo whprv xpd hvihud frqgxwrud qær fduuhjdgd qdsuhvhqêd gh gxdv fdujdv ' h c' gd irupd dvvlqdodgd dflpd1 Shor pìwrgr gdv lpdjhqv/srghprv ghvfrqvlghudu d hvihud h vxevwlwxð0od shodv fdujdv lpdjhqv
'� ' c @u' h '�� ' c@u Ec'� ' @'u csdud fdujdv srvlwlydv h qhjdwlydv/ uhvshfwlydphqwh/ qdv srvlêøhv
K� ' c@2u h K�� ' @2u �R sureohpd vh wruqd xp sureohpd gh txdwur fdujdv sxqwxdlv qdv srvlêøhv lqglfdgdvghprgr txh r srwhqfldo �fd gdgr sru +r sulphlur whupr yhp gdv fdujdv qr lq�qlwr/rx vhmd/ mä �}hprv u � � qhohv/ r vhjxqgr whupr ì ghylgr ãv fdujdv qdv srvlêøhv K� hK,
) ' c.fo ULt w n c'�eZ0f
57 �t%2 n +2 n E5 c K��2 c �t%2 n +2 n E5 c K���2
68 '
' c.fo ULt w n c'�eZ0f
� �So2 c 2oK� ULt w n K�2 c �So2 c 2oK�� ULt w n K��2� �Qrwh djrud txh vh whprv u � �/ hqwær vær rv whuprv hp o txh vær *judqghv* frpuhodêær d K� h K�� +hvwhv ýowlprv yær sdud }hur frp u � �,1 Dvvlp/ �fdprv frp
) Eoc w� ' c.fo ULt w n c'�eZ0fo
57 �t�c 2 K�o ULt w n K�2o2 c �t�c 2 K��o ULt w n K��2o2
68 '
' c.fo ULt w n c'�eZ0fo
��� n K�o ULt w c K�22o2�c �� n K��o ULt w c K��22o2�� '' c.fo ULt w n c'�eZ0fo
�K� c K��o � ULt w ' c.fo ULt w n '2Z0fu2 @�o2 ULt w '' c.fo ULt w n.f ULt w@�o2 ' c.f�o c @�o2� ULt wctxh ì r uhvxowdgr ghvhmdgr1t H{hufðflr 6153= Qrwh txh djrud d fdujd hvwä qr lqwhulru gd fdvfd hviìulfd/ d qxdglvwåqfld o� gr fhqwur gd phvpd/ txh srvvxl udlr @1 Whprv txh r srwhqfldo srgh vhuhvfulwr frpr
) Eoc w� ' �eZ0f
� ^So2 n o�2 c 2oo� ULt w n ^�So2 n K2 c 2oK ULt w�
Wr= Vhswhpehu 4</ 5336 Sdjh= 47
rqgh ghyhprv hqfrqwudu K h ^�/ dfhuwdqgr dv frqglêøhv gh frqwruqr1 D hvihud ì frq0gxwrud/ gh prgr txh ghyhprv whu ) ' SJ?r|� ' )f1 Dvvlp/ whuhprv/ uhwludqgr dfrqvwdqwh ^So�2 n @2 c 2o�@ ULt w ' c^�S@2 n K2 c 2@K ULt wrx vhmd/ ^2 �@2 n K2 c 2@K ULt w� ' ^�2 �o�2 n @2 c 2@o� ULt w�txh ghyh ydohu sdud txdotxhu w1 Dvvlp/ ljxdodqgr rv whuprv hp w/ �fdprv frp^2K ' ^�2o�h wdpeìp ^2 �@2 n K2� ' ^�2 �o�2 n @2� �Vxevwlwxlqgr d sulphlud qd vhjxqgd/ whprv�@2^e n ^�eo�2� ' ^2^�2 �o�2 n @2�h/ sruwdqwr/ o�2 �^�2�2 c ^2 �o�2 n @2� �^�2�n @2^e ' f�Hvwd htxdêær whp gxdv udð}hv= ^� ' ^ h ^�2 ' ^2@2*o�21 D sulphlud vroxêær qær srghvhu dfhlwd1 D vhjxqgd iruqhfh ^� ' c @o� ^�Ohydqgr lvwr qd htxdêær sdud K dflpd/ �fdprv frp
^2K ' ^2@2o�2 o�gh prgr txh K ' @2o� �Dvvlp/ qrvvr srwhqfldo �fd
) Eoc w� ' )f n �eZ0f
57 ^So2 n o�2 c 2oo� ULt w c @o� ^to2 n @eo�2 c 2o@2o� ULt w
68
Dvvlp/ d ghqvlgdgh gh fdujd qd vxshuiðflh �fd
j Ew� ' c Y) Eoc w�Yo ����o'@ '
�c@2o� n o�� ULt wd@2 n o�2 c 2@o� ULt wo�*2 ctxh ì r uhvxowdgr hvshudgr1
Wr= Vhswhpehu 4</ 5336 Sdjh= 48
Iljxuh 4=
t H{hufðflr 6154= Ghyhprv frqvlghudu sulphludphqwh gxdv olqkdv gh fdujd lq�qlwdvfrp ghqvlgdghv olqhduhv gh fdujd b sdudohodv h srvlflrqdgdv hp % ' f/ sdud nb h% ' c2_ sdud cb/ frpr qd �jxud dedl{r1R srwhqfldo dvvrfldgr ã frq�jxudêær grvgrlv �rv gh ghqvlgdghv nb h cb �fd +r vlvwhpd gh frrughqdgdv hvwä vreuh d olqkd ghfdujd srvlwlyd,
) Eo� ' b2Z *?
3C s%2 n +2tE%n 2_�2 n +2
4D
h xpd vxshuiðflh htxlsrwhqfldo ) ' )f lpsolfd txh
i T�2Z)fb � ' � '
s%2 n +2tE%n 2_�2 n +2
gh prgr txh e�2_2�c�2 ' %2 c e% �2_E�c�2� n +2rx dlqgd �%c 2�2�c�2_�2 n +2 ' �2_2E�c�2�2gh irupd txh whprv xpd vxshuiðflh gh srwhqfldo qxp fðufxor frp udlr �_* E�c�2�h fhqwur hp % ' 2�2* E�c�2�/ + ' f1 Dvvlp/ whprv txh
@ ' �_�c�2
Wr= Vhswhpehu 4</ 5336 Sdjh= 49
h/ shod �jxud/ %f c _ ' 2�2�c�2_�Dvvlp/ %f ' �2 n ��c�2_ ' �2 n ��c�2 E�c�2�� @rx vhmd/ %f@ ' �2 n �� �Uhvroyhqgr hvwd htxdêær hp � / �fdprv frp
�2 c %f@ � n � ' f � � ' %f2@ n 2
u %2f2@2 c �txh ì r uhvxowdgr surfxudgr1t H{hufðflr 6155= D ghqvlgdgh ì gdgd sru 4 EOo� ' 4f sdud o y - h 4 EOo� ' f sdudo : -1 Sdud fdofxodu r srwhqfldo xvdqgr d htxdêær gh Srlvvrq/ edvwd qrwdu txh hvwdhtxdêær �fd gdgd sru U2) Eoc wc �� ' c4 EOo�0f �Frpr d ghqvlgdgh ì ixqêær dshqdv gh o/ whprv txh�o2 __o �o2_) Eo�_o � ' c4 Eo�0f �Srghprv lqwhjudu hvwd htxdêær gluhwdphqwh sdud rewhu] o
f
__o� �o�2 _)_o�� _o� ' c �0f ] of o�24 Eo�� _o�h/ sruwdqwr/ sdud o : -/ whprv
o2_)e%|_o ' c ��0f-�gh prgr txh ] o
f
_)e%|_o� ' c-��0f ] �o�2_o�gdqgr )e%| Eo� ' -��0fo �Vh o 	 -/ hqwær whprv o2_)�?|_o ' c ��0fo�
Wr= Vhswhpehu 4</ 5336 Sdjh= 4:
gh prgr txh ] _)�?|_o� ' c ��0f ] o�_o�h )�?| Eo� ' )f c �S0f o2�Frpr hp o ' - ghyhprv whu )e%| E-� ' )�?| E-�/ srghprv hvfuhyhu-2�0f ' )f c �S0f-2cgh prgr txh )f ' -220f �Dvvlp/
)�?| Eo� ' -220f
��c o2�-2�)e%| Eo� ' -��0fo+frpsduh frp r uhvxowdgr gr h{hufðflr 2��DK,1t H{hufðflr 6156= Whprv xp glsror rulhqwdgr shushqglfxoduphqwh d xp sodqr frqgxwrulq�qlwr h d xpd glvwåqfld _ gr phvpr1 Sdud fdofxodu d iruêd h{huflgd shor glsror vreuhr sodqr/ edvwd xvdu r pìwrgr gdv lpdjhqv1 Vdehprv txh/ vh d srvlêær gdv fdujdv uhdlvvær= n^ hp 5 ' _ h c^ hp 5 ' _n ,/ hqwær dv fdujdv lpdjhp hvwduær qdv srvlêøhv= c^hp 5 ' c_ h n^ hp 5 ' c_c ,1 R srwhqfldo jhudgr shodv fdujdv uhdlv/ �fd sruwdqwr
) E%c +c 5� ' ^eZ0f
57 �t%n +2 n E5 c _�2 c �t%2 n +2 n E5 c _c ,�2
68 �
D iruêd h{huflgd shor glsror vreuh r sodqr ì gdgd shod iruêd txh dv fdujdv uhdlv id}hpvreuh dv fdujdv lpdjhqv/ vrpdgdv yhwruldophqwh1 Whprv iruêd dshqdv qd gluhêær 	5/ sruvlphwuld/ gh prgr txh srghprv fdofxodu dshqdv 851 R fdpsr hoìwulfr .5 dvvrfldgr drsrwhqfldo dqwhulru �fd
.5 E%c +c 5� ' cY)Y5 ' ^eZ0f
+ 5 c _�%n +2 n E5 c _�2��*2 c 5 c _c ,�%2 n +2 n E5 c _c ,�2��*2
, �
D iruêd vreuh d fdujd lpdjhp c^ vlwxdgd hp 5 ' c_ �fd
c^.5 Efc fcc_� ' ^2eZ0f
� 2_E2_�� c 2_n ,E2_n ,��
� ' ^2eZ0f
� �e_2 c �E2_n ,�2
�
Wr= Vhswhpehu 4</ 5336 Sdjh= 4;
hqtxdqwr txh d iruêd vreuh d fdujd lpdjhp n^ vlwxdgd hp 5 ' c_c , �fd
n^.5 Efc fcc_c ,� ' ^2eZ0f
�c �E2_n ,�2 n �e E_n ,�2
�
h d iruêd wrwdo �fd
85 ' c^.5 Efc fcc_� n ^.5 Efc fcc_c ,� '' ^2�SZ0f_2
%�c 2�� n ,2_�2 n ��� n ,_�2
& '
' ^2�SZ0f_2
+�c 2%�c 2 ,2_ n �� ,2_�2
&n %�c 2 ,_ n �� ,_�2
&, '
' ^2�SZ0f_2
�c�2 ,2_2 n � ,2_2� ' �^2,2�2Z0f_e ' �R2�2Z0f_e crx vhmd 85 ' �R2�2Z0f_etxh ì xpd iruêd gh dwudêær1t H{hufðflr 6158= Frqvlghuh dv h{sdqvøhv=
) E%n _c +c 5� ' )n _Y)Y% n �2_2 Y2)Y%2) E%c _c +c 5� ' )c _Y)Y% n �2_2 Y2)Y%2) E%c + n _c 5� ' )n _Y)Y+ n �2_2 Y2)Y+2) E%c + c _c 5� ' )c _Y)Y+ n �2_2 Y2)Y+2) E%c +c 5 n _� ' )n _Y)Y5 n �2_2 Y2)Y52) E%c +c 5 c _� ' )c _Y)Y5 n �2_2 Y2)Y52
�
Vrpdqgr0dv/ whprv [ ' S)n _2 �Y2)Y%2 n Y2)Y+2 n Y2)Y52 � �Rud/ vh ) E%c +c 5� vdwlvid} d htxdêær gh Odsodfh/ hqwær �fdprv frp
) E%c +c 5� ' �S[ctxh ì r uhvxowdgr ghvhmdgr1
Wr= Rfwrehu 9/ 5336 Sdjh= 4
+Fkdswhu khdg=,Fdsðwxor 7=t H{hufðflr 714= D ghqvlgdgh yroxpìwulfd gh fdujd gh srodul}dêær srgh vhu hqfrqwudgdvlpsohvphqwh id}hqgr0vh U d O� ' c4�gh prgr txh 4� ' c2@%�Qdv h{wuhplgdghv whuhprv +sdud xpd eduud txh vh h{whqgh gh f d u, rv ydoruhv
j� Eu� ' O� ���%'u d 	? ' �@u2 n K�j� Eu� ' O� ���%'f d 	? ' cKrqgh qrwdprv txh 	?%'f ' c	?%'u1t H{hufðflr 715= Whprv xp fxer frp srodul}dêær gdgd sru O� ' �Oo h frp ruljhp qrfhqwur gr fxer1 D ghqvlgdgh yroxpìwulfd gh fdujd gh srodul}dêær ì4� ' c��cmä txh UdOo ' �1 Dv ghqvlgdghv gh fdujd vxshu�fldlv qdv glyhuvdv sduhghv gr fxer vær=
j%M%'nu*2 ' �u2 c j%M%'3u*2 ' �u2j+M+'nu*2 ' �u2 c j+ M+'3u*2 ' �u2j5 M5'nu*2 ' �u2 c j5 M5'3u*2 ' �u2D vxshu�fldo wrwdo srgh vhu fdofxodgd frpr
't�T ' �j%M%'nu*2 n j%M%'3u*2 n j+ M+'nu*2 n j+ M+'3u*2 n j5 M5'nu*2 n j5 M5'3u*2�u2' ��u�hqtxdqwr txh d fdujd yroxpìwulfd wrwdo ì gdgd sru +xvdqgr0vh txh 4� ' c��,'�J, ' c��u��Dvvlp/ 't�T n'�J, ' f/ frpr txhuðdprv ghprqvwudu1t H{hufðflr 716= Whprv xpd eduud ihlwd gh glhoìwulfr qd irupd floðqgulfd frp udlr -h frpsulphqwr u/ srodul}dgd xqliruphphqwh qd gluhêær gr frpsulphqwr u1 Frpr dsrodul}dêær ì xqliruph/ whprv txh 4� ' f1 Whprv/ dlqgd/ txhjuM5'3u*2 ' � h juM5'3u*2 ' c��
Wr= Rfwrehu 9/ 5336 Sdjh= 5
Qrwh txh d fdujd wrwdo ì qxod +fi1 sureohpd dqwhulru,1 Frp hvwdv ghqvlgdghv vxshu�fldlvgh fdujd/ whprv txh r srwhqfldo �fd gdgr sru
) Eoc wc 5� ' �eZ0f ]t�T jMOo c Oo�M o�_o�_w�fdofxodgd qdv gxdv vxshuiðflhv frqvlghudgdv +txh vær dv srqwdv gd eduud,1 Qxp srqwrvreuh r hl{r gd eduud �fdprv frp Oo� ' o�	4 n u*2	& qd vxshuiðflh qr odgr *srvlwlyr* hOo� ' o�	4c u*2	& qr odgr *qhjdwlyr* gd eduud +fxmr fhqwur irl srvlflrqdgr qd ruljhp grvlvwhpd gh frrughqdgdv, h Oo ' 5	&1 D lqwhjudo �fd
) Efc fc 5� ' E2Z� �eZ0f
%] -
f
o�_o�so�2 n E5 c u*2�2 c ] -f o�_o�so�2 n E5 n u*2�2
& '
' E2Z� �eZ0f
57v-2 n�5 c u2�2 c ����5 c u2 ����c
v-2 n�5 n u2�2 n ����5 n u2 ����
68 �
+d, sdud srqwrv irud gd eduud/ whprv 5 : u*2 h/ sruwdqwr/
c ����5 c u2 ����n ����5 n u2 ���� ' ugh prgr txh r fdpsr hoìwulfr �fd +vö kä fdpsr qd gluhêær 5,= =
.5 ' c �20f
57 E5 c u*2�t-2 n �5 c u2 �2 c
E5 n u*2�t-2 n�5 n u2 �2
68 �
Sdud srqwrv qr lqwhulru gd eduud whprv 5 	 u*2 h
c ����5 c u2 ����n ����5 n u2 ���� ' 25h r fdpsr hoìwulfr �fd
.5 ' c �20f
57 E5 c u*2�t-2 n �5 c u2 �2 c
E5 n u*2�t-2 n �5 n u2 �2 n 2
68 �
t H{hufðflr 717= Whprv txh surydu txh]
T O�_� '
]
T 4�Oo_� n
]
7 j�Oo_@�
Wr= Rfwrehu 9/ 5336 Sdjh= 6
Ohpeudprv txh 4� ' cUd O� h txh O� d 	? ' j� 1 Dvvlp/ srghprv hvfuhyhu r odgr gluhlwrgd h{suhvvær dflpd frpr
u_�o ' c ]T �U d O��Oo_� n
]
7
�O� d 	?�Oo_@�
Djrud qrwdprv/ shod vxjhvwær gr olyur/ txh
U d �%O�� ' �% n %�U d O��U d �+ O�� ' �+ n + �U d O��U d �5 O�� ' �5 n 5 �U d O��gh prgr txh srghprv hvfuhyhu
U d �%O�� 	%nU d �+ O�� �+ nU d �5 O�� 	5 ' O� n Oo �U d O�� �
Lqwhjudqgr qr yroxph/ �fdprv frp]
T
kU d �%O�� 	%nU d �+ O�� �+ nU d �5 O�� 	5l _� ' ]T O�_� n
]
T
�U d O��Oo_��
Dsolfdqgr r whruhpd gd glyhujíqfld qr whupr ã hvtxhugd/ �fdprv frp]
7 E%	%n +�+ n 5	5��O� d 	?� _@ '
]
T O�_� n
]
T
�U d O��Oo_�c
rx vhmd ]
T O�_� ' c
]
T
�U d O��Oo_� n ]7 �O� d 	?�Oo_@txh ì r uhvxowdgr ghvhmdgr1t H{hufðflr 718= Whprv txh dv srodul}dêøhv vær frqvwdqwhv +xqliruphv, hp wrgrv rvglhoìwulfrv1 Hvwhv hvwær d xpd glvwåqfld shtxhqd hqwuh vl/ frp dshqdv xpd hvwuhlwdihqgd vhsdudqgr0rv1 D srodul}dêær O� irupd xp åqjxor � frp d qrupdo drv sodqrv txholplwdp d ihqgd1 Frp hvwdv srodul}dêøhv/ �fdprv frp ghqvlgdghv vxshu�fldlv gh fdujdljxdlv d j� ' O� d 	? ' i� ULt �hp fdgd xp grv sodqrv txh frqvwlwxhp d ihqgd1D ihqgd ì ihlwd gh du> dvvlp whprv xpdfrq�jxudêær gh grlv sodqrv sdudohorv frp ghqvlgdghv xqliruphv gh fdujd j� frprdflpd1 R fdpsr qd ihqgd srgh vhu rewlgr gluhwdphqwh gd ohl gh Jdxvv h iruqhfh
. ' � ULt �0f cfrpr ghvhmdgr +r fdpsr hvwä qd gluhêær gh O� / hylghqwhphqwh,1
Wr= Rfwrehu 9/ 5336 Sdjh= 7
t H{hufðflr 719= Xp orqjr flolqgur frqgxwru gh udlr @ h ghqvlgdgh olqhdu gh fdujd b hvwäqxp phlr glhoìwulfr gh shuplvvlylgdgh frqvwdqwh 01 Sdud hqfrqwudu r fdpsr hoìwulfr dxpd glvwåqfld o : @ gr hl{r gr floðqgur/ ohpeudprv txh ghyhprv whu d htxdêær
U d O( ' bu�Srghprv id}hu d lqwhjudêær xvdqgr0vh xpd vxshuiðflh gh Jdxvv txh hqyroyh flqolqgursdud rewhu L
7 O( d 	?_@ ' buh/ sruwdqwr/ 2Zou(4 ' bucgh prgr txh (4 ' b2Zo�Dvvlp/ r fdpsr hoìwulfr �fd .4 ' b2Z0o �t H{hufðflr 71:= Dv frqglêøhv gh frqwruqr vær +qær kä fdujd h{whuqd vreuh d lqwhuidfh,=(�? c(2? ' j ' f.�| c .2| ' fWrpdqgr d olqkd phqflrqdgd qr wh{wr frpr edvh/ whprv txh(�? ULt w� ' (2? ULt w2.� t�? w� ' .2 t�? w2Gd sulphlud htxdêær/ whprv 0�.� ULt w� ' 02.2 ULt w2gh prgr txh/ glylglqgr0vh d htxdêær dflpd shod htxdêær sdud r . dqwhulru/ rewhprv
|@? w� ' g�g2 |@? w2cfrpr ghvhmdgr1t H{hufðflr 71;=
Wr= Rfwrehu 9/ 5336 Sdjh= 8
t H{hufðflr 71<= Whprv txh r srwhqfldo �fd gdgr sru +fi1 �jxud e�b gr olyur,
)� E%c +c 5� ' �eZ0�
57 ^tE%n _�2 n +2 n 52 n ^
�tE%c _�2 n +2 n 52
68
h )2 E%c +c 5� ' �eZ02 ^��tE%n _�2 n +2 n 52 �Vreuh r sodqr +5 rv srwhqfldlv ghyhp vhu ljxdlv/ ylvwr txh qær kä fdujdv olyuhv qdlqwhuidfh h/ sruwdqwr/ qær srgh kdyhu ghvfrqwlqxlgdgh gd frpsrqhqwh qrupdo gh O(1Rud/ srghprv fdofxodu (�? h (2? idflophqwh d sduwlu grv srwhqfldlv dflpd frpr vhqgr
(�? ' 0�.�c%M%'f ' c0� Y)�Y% ���%'f ' �eZ ^n^�d%2n+2n52o�*2_(2? ' 02.2c%M%'f ' c02 Y)2Y% ���%'f ' �eZ ^��d%2n+2n52o�*2_ �Dvvlp/ whprv xpd sulphlud htxdêær gdgd sru(�? c(2? ' f � E^ n ^�� ' ^���Sdud rewhu d vhjxqgd htxdêær/ ohpeudprv txh whprv d frqglêær gh frqwruqr qd frp0srqhqwh wdqjhqfldo gr fdpsr hoìwulfr +srghprv wrpdu + rx 5 frpr vhqgr xpd wdogluhêær,1 Dvvlp/ whprv txh
.�| ' c Y)�Y+ ����%'f ' �eZ0� ^ c ^�d+2 n 52o�*2_.2| ' c Y)2Y+ ����%'f ' �eZ02 ^��d+2 n 52o�*2_iruqhfhqgr d htxdêær .�| c.2| ' f � 02 E^ c ^�� ' 0�^���Dvvlp/ �fdprv frp r vlvwhpd gh htxdêøhv� ^�� c ^� ' ^0�02 ^�� n ^� ' ^fxmdv vroxêøhv vær ^� ' 02 c 0�0� n 02 ^c ^�� ' 2020� n 02 ^�
Wr= Rfwrehu 9/ 5336 Sdjh= 9
t H{hufðflr 7143= Whprv rv srwhqfldlv lqwhuqr h h{whuqr gdgrv sru
)�? ' �f n�f *? Eo� n "[?'� ��?o? n�?o3?� ULt E?w�)J�| ' �f *? Eo� n "[?'� ��?o? n(?o3?� ULt E?w�txh vær dv vroxêøhv gd htxdêær gh Odsodfh hp frrughqdgdv floðqgulfdv1 R whupr hpt�? Ew� mä irl holplqdgr sru ud}øhv gh vlphwuld ^qær srghprv whu rv srwhqfldlv yduldqgrtxdqgr id}hprv w � cw`1 Sdud r srwhqfldo lqwhuqr/ whprv txh qær kä glyhujíqfldvorjduðwlplfdv/ mä txh r flolqgur hvwä ghvfduuhjdgr1 Wdpeìp qær whprv txdotxhu rxwurwlsr gh glyhujíqfld1 Dvvlp/ ghyhprv sru �? ' f sdud wrgr ? h �fdu frp
)�? ' ��o ULt w n "[?'2�?o? ULt E?w� �Sdud r srwhqfldo h{whuqr/ srghprv hoplqdu r whupr orjdwðplfr shodv phvpdv ud}øhvdqwhulruhv doìp gh holplqduprv rv whuprv o? frp ? : �/ mä txh r srwhqfldo h{whuqrglyhujh frp o1 Dvvlp/ �fdprv frp
)J�| ' ���o n (�o � ULt w n "[?'2(?o3? ULt E?w� �D sulphlud frqglêær gh frqwruqr gl} uhvshlwr dr srwhqfldo qr lq�qlwr +)J�|/ sruwdqwr,1Hvwd frqglêær ì txh )J�| Eo � �� ' c.fo ULt wcgh prgr txh �� ' c.f1 Xpd vhjxqgd frqglêær gh frqwruqr ì)�? E@� ' )J�| E@�txh iruqhfh dv htxdêøhv@2�� c(� ' c.f@2 h �?@2? c(? ' f�D rxwud frqglêær gh frqwruqr txh idowd ì
c0f Y)J�|Yo ����o'@ ' c0� Y)�?Yo
����o'@txh iruqhfh dv htxdêøhvg@2�� n(� ' c.f@2 h g@2?�? n(? ' f1
Wr= Rfwrehu 9/ 5336 Sdjh= :
Ilfdprv/ srlv/ frp rv vlvwhpdv� @2�� c(� ' c.f@2g@2�� n(� ' c.f@2h � �?@2? c(? ' fg@2?�? n(? ' f �Hvwh ýowlpr vlvwhpd lpsolfd qhfhvvduldphqwh txh �? ' (? ' f/ sdud ? z 21 Rsulphlur vlvwhpd iruqhfh
�� ' c 2.fg n � h (� ' g c �g n �@2.f�Rv srwhqfldlv �fdp/ sruwdqwr/+ )�? ' 32gn�.fo ULt w)J�| ' k�c g3�gn� @2o2 l.fo ULt w ctxh vær rv uhvxowdgrv surfxudgrv1t H{hufðflr 7144= Whprv xp glsror srqwxdo OR qr fhqwur gd hvihud glhoìwulfd gh udlr @1Vdehprv txh r fdpsr irud gd hvihud ì glsrodu/ rx vhmd/ whprv
)J�| ' �OR d Ooo�rqgh � ì r frh�flhqwh d vh ghwhuplqdu1 Qr lqwhulru gd hvihud glhoìwulfd ghyhprv whu
)�? ' �o ULt w n �o2 ULt wcrqgh mä holplqdprv rv whuprv hp o3? +? z �, h rv whuprv o? +? z 2, d sduwlu ghfrqvlghudêøhv vlploduhv ãv ihlwdv hp h{hufðflrv ghvwh wlsr1 Wdpeìp vdehprv/ shodfrqglêær gh txh kä xp glsror srqwxdo qd ruljhp txh � ' R*eZ0�1 Ilfdprv/ sruwdqwr/frp rv srwhqfldlv
)�? ' ��o n ReZ0�o2
� ULt w
)J�| ' �R ULt wo2Dv frqglêøhv gh frqwruqr lpsolfdp txh ghyhprv whu frqwlqxlgdgh gr srwhqfldo qdvxshuiðflh gd hvihud1 Dvvlp/ )�? Eo ' @� ' )J�| Eo ' @�
Wr= Rfwrehu 9/ 5336 Sdjh= ;
rx vhmd ��@n ReZ0�@2
� ' � R@2 �Gd phvpd irupd/ ghyhprv whu frqwlqxlgdgh qd frpsrqhqwh gr yhwru ghvorfdphqwrhoìwulfr/ ylvwr txh d hvihud glhoìwulfd qær hvwä fduuhjdgd frp qhqkxpd ghqvlgdgh vx0shu�fldo gh fdujd1 Dvvlp/ ghyhprv whu wdpeìp(�? ' (J�|rx vhmd/ c0� Y)�?Yo ����o'@ ' c0f Y)J�|Yo
����o'@ �Hvwd ýowlpd ljxdogdgh iruqhfh
g �� c 2ReZ0�@�
� ' c2� R@� �Ilfdprv/ sruwdqwr/ frp r vlvwhpd gh htxdêøhv� @�� c R� ' c ReZ0�g@�� n 2R� ' 2RgeZ0� cfxmdv vroxêøhv vær
� ' �gg n 2 �eZ0� ' �g n 2 �eZ0f� ' R2Z0�@� Eg c ��Eg n 2�gh prgr txh rv srwhqfldlv �fdp
)�? ' � 2ReZ0�@� Eg c ��Eg n 2�o n ReZ0�o2
� ULt w
' R ULt weZ0�o2
�� n 2o�@� Eg c ��Eg n 2��h )J�| ' R ULt weZ0fo2 �g n 2 ctxh vær rv uhvxowdgrv ghvhmdgrv1t H{hufðflr 7145= Rv uhvxowdgrv vær+ )� ' c.f ��c g3�gn2 @�o��.fo ULt w)2 ' c �gn2.fo ULt w
Wr= Rfwrehu 9/ 5336 Sdjh= <
txh/ txdqgr id}hprv g � �/ �fdp+ )� ' c.fo ULt w ��c @�o��)2 ' f ctxh vær rv uhvxowdgrv sdud d hvihud frqgxwrud1t H{hufðflr 7146= Whprv xpd fkdsd �qd gh pdwhuldo frp frqvwdqwh glhoìwulfd g�olplwdgd sru dperv rv odgrv sru xp pdwhuldo gh frqvwdqwh glhoìwulfd g21 Vdehprvtxh r fdpsr qr phlr 2/ O.2/ ì gdgr frpr vhqgr xqliruph h shushqglfxodu drv frqwruqrv1Sdud hqfrqwudu r fdpsr O.� ghyhprv xvdu dv frqglêøhv gh frqwruqr gr sureohpd1 Qærkä fdujdv olyuhv qr sureohpd1 Dvvlp/ whprv(�? ' (2?.�| ' .2|Frpr O.2 ì shushqglfxodu drv frqwruqrv/ ghyhprv whu .2| ' f h/ sruwdqwr/ .�| ' f1Djrud vdehprv txh (2? ' 02.2? h (�? ' 0�.�?�Dvvlp/ .�? ' 020�.2?�Djrud/ frpr vdehprv txh O(� ' 0f O.� n O��c�fdprv frp ��? ' 02.2? c 0f.�?�2? ' E02 c 0f�.2?Hp whuprv gdv frqvwdqwhv g� ' 0�*0f srghprv hvfuhyhu rv uhvxowdgrv dflpd frpr
.�? ' g2g�.2?��? ' 0f�g� c �g�
�g2.2?
h �2? ' Eg2 c �� 0f.2?�Sruwdqwr/ frpr vö whprv srodul}dêær shushqglfxodu ã vxshuiðflh/ j� ' i��?1t H{hufðflr 7147= Srghprv id}hu g� � � qd vroxêær dqwhulru sdud rewhu.�? ' f h ��? ' 0fg2.2?�
Wr= Rfwrehu 9/ 5336 Sdjh= 43
Qrwhtxh/ djrud (�? ' ��? mä txh r fdpsr hoìwulfr .�? ì qxor1 Dvvlp/ whprv txh(�? ' 0fg2.2? ' j� ctxh frqfrugd frp d h{suhvvær +e�ee, gr olyur1t H{hufðflr 7148= Dv sodfdv vær sdudohodv/ frqgxwrudv h hvwær glvwdqwhv sru xp ydoru_1 Vær pdqwlgdv d xpd glihuhqêd gh srwhqfldo {)1 D fkdsd gh pdwhuldo glhoìwulfr ghfrqvwdqwh glhoìwulfd g ì lqvhulgd h srvvxl xpd hvshvvxud | 	 _1 R srwhqfldo srgh vhuhvfulwr frpr {) ' {)� n{)2crqgh {)�_c | ' j0f h {)2| ' j0�gh prgr txh {) ' j0f
�E_c |� n |g � ' j0f
�g_c Eg c �� |g � �R yhwru ghvorfdphqwr hoìwulfr ì ( ' jtxh/ frp d htxdêær sdud r srwhqfldo/ �fd
( ' g0f{)dg_c Eg c �� |o �Rv fdpsrv hoìwulfrv �fdp
.��@S ' (0f ' g{)dg_c Eg c �� |o._�e, ' (0� ' {)dg_c Eg c �� |ofrpr txhuðdprv hqfrqwudu1t H{hufðflr 7149= Sdud hqfrqwudu dv srodul}dêøhv/ srghprv xvdu rv uhvxowdgrv gr h{hu0fðflr dqwhulru sdud hvfuhyhu���@S ' c0f.��@S n( ' f�_�e, ' c0f.��@S n( ' 0f Eg c ��{)dg_c Eg c �� |oOhpeudprv dlqgd txh (R,@S@ c(_�e, ' j,�� ' jh j_�e, ' O�_�e, d 	? ' ijcr vlqdo ghshqghqgr gd idfh hp txh frqvlghudprv r fäofxor1
Wr= Rfwrehu 9/ 5336 Sdjh= 44
t H{hufðflr 714:= Whprv txh hqfrqwudu xp fdpsr hoìwulfr udgldo txh vdwlvidêd wrgdvdv frqglêøhv gh frqwruqr sdud d hvihud gh udlr - txh xwxd vxephuvd shod phwdgh qxpphlr oðtxlgr gh shuplvvlylgdgh 0�1 D fdujd wrwdo gd hvihud ì '1 Dvvlp/ surfxudprvxp srwhqfldo gr wlsr
)�? ' �o)J�| ' �oD sulphlud frqglêær gh frqwruqr +d frqwlqxlgdgh gr srwhqfldo, vlpsohvphqwh d�updtxh � ' �1 D vhjxqgd frqglêær gh frqwruqr ì gdgd sru
(�? c(2? ' 'eZ@2 cmä txh j ' '*eZ@21 Dvvlp/ whprv
c0� Y)�?Yo ����o'@ c 02 Y)J�|Yo
����o'@ ' 'eZ@2rx vhmd E02 n 0�� �@2 ' 'eZ@2h/ sruwdqwr/ � ' � ' 'eZ E02 n 0�� cgdqgr r srwhqfldo )�? ' )J�| ' 'eZ E0� n 02� o �Txh hvwh ì r uhvxowdgr yhugdghlur ghfruuh lphgldwdphqwh gd xqlflgdgh gdv vroxêøhv gdhtxdêær gh Odsodfh +qrwh txh rv srwhqfldlv dflpd vær vroxêøhv gd htxdêær gh Odsodfh,1t H{hufðflr 714;= Edvwd qrwdu txh hvwh sureohpd lpsolfd txh/ qr sureohpd uhvroylgrqr olyur/ ghyhprv whu 0f wurfdgr sru 0� +h ylfh0yhuvd,1 Dvvlp/ g ghyh vhu wurfdgr sru�*g1 R uhvxowdgr txh wðqkdprv hud
O.�? ' c�g n 2 O.f(frp d wurfd/ �fdprv frp
O.�? ' c��*g n 2 O.f ' c�g� n 2g O.f�
Wr= Rfwrehu 57/ 5336 Sdjh= 44 Fdsðwxor 9=t H{hufðflr 915= Ghyhprv qrv ohpeudu txh srghprv fdofxodu r yhwru ghvorfdphqwrhoìwulfr d sduwlu gd h{suhvvær +*ohl gh Jdxvv* sdud r yhwru O(,eZo2( ' ^�
Rewhprv/ dvvlp/ ( ' ^eZo2 h . ' ^eZ0o2 �D hqhujld/ sruwdqwr/ ì gdgd sru
L ' �2 ]T O( d O._Oorqgh ghyhprv qrv ohpeudu txh r yroxph T whp txh vhu dtxhoh frpsuhhqglgr shodpdwìuld gr vlvwhpd/ rx vhmd/ qr fdvr hp txhvwær/ d fdorwd hviìulfd txh ydl gr udlr @ drudlr K1 Dvvlp/ L ' �2 ^2�SZ20 ] K@ �oe o2eZ_o ' ^2HZ0 ��@ c �K�t H{hufðflr 916= R h{hufðflr srgh vhu ihlwr shufhehqgr0vh txh r sodqr frqgxwru srghvhu vxevwlwxðgr sru xpd frq�jxudêær glsrodu hvshfxodu frp uhodêær dr glsror txh vhhqfrqwud hp iuhqwh dr sodqr/ frpr prvwud d �jxud dedl{r=
Qrwdprv/ hqwuhwdqwr/ txh d sulphlud hqhujld ghfruuh gr wudedokr txh whuðdprv dr*wud}hu* xpd gdv fdujdv qr odgr hvtxhugr gr sodqr sdud suö{lpr gd rxwud1 Hvwhwudedokr ì gdgr sru `f ' c ^2eZ0f, �Srvwhulruphqwh/ whuhprv r wudedokr gh wud}hu fdgd xpd gdv fdujdv txh hvwær qr odgrgluhlwr gr sodqr1 Sdud d fdujd c^ whuðdprv
`� ' c^ % c^eZ0f E, n 2_� n ^eZ0f E2_�
& c
Wr= Rfwrehu 57/ 5336 Sdjh= 5
rqgh rv whuprv hvwær dvvrfldgrv drv srwhqfldlv jhudgrv sru fdgd xpd gdv fdujdv qrsrqwr sdud rqgh d fdujd c^ irl wud}lgd1 Sdud d fdujd n^ whuðdprv
`2 ' n^ % c^eZ0f E2, n 2_� n ^eZ0f E, n 2_� c ^eZ0f,
& �
D hqhujld wrwdo vhuä d vrpd ghvwhv wudedokrv h vhuä gdgd sru
L ' c^2eZ0f
%2, c 2E, n 2_� n �2_ n �2 E, n _�&' c2^2eZ0f
%�, c �E, n 2_� n �e_ n �e E, n _�& �
t H{hufðflr 918= Whprv txh d glvwulexlêær gh fdujdv ì hviìulfd h gh udlr -/ rqgh 4 ' 4f+frqvwdqwh,1 Srghprv rewhu r ydoru gd hqhujld hohwurvwäwlfd ghvwd glvwulexlêær lqwh0judqgr gluhwdphqwh/ rx vhmd/ xvdqgr
L ' �2 ]T 4 EOo�) EOo� _Oo�Qrwhprv/ hqwuhwdqwr/ txh/ sdud hvwd frq�jxudêær ghyhprv whu)U EOo� ' )f n ^eZ0fo +o y -,)UU EOo� ' ^�eZ0fo Eo z -�rewlgrv sru ohl gh Jdxvv1 Dvvlp/
^ ' e�Zo�4f +o y -,^� ' e�Z-�4f +o z -,gh prgr txh �fdprv frp
)U EOo� ' )f n o24f�0f +o y -,)UU EOo� ' 4f-��0fo Eo z -�h/ frpr vdehprv txh/ sdud o ' - ghyhprv whu dperv rv srwhqfldlv ljxdlv/ srghprvhvfuhyhu
)U EOo� ' 4f20f
#-2 c o2� $ +o y -,)UU EOo� ' 4f-��0fo Eo z -�
Wr= Rfwrehu 57/ 5336 Sdjh= 6
Vh ydprv fdofxodu d glvwulexlêær gh dxwr0hqhujldv xvdqgr d iöupxod dflpd/ hqwær ryroxph T whp txh vhu dtxhoh txh frqwìp d glvwulexlêær gh pdwìuld2fdujd/ rx vhmd/ghyhprv xvdu )U EOo�1 D lqwhjudêær �fd
L ' �2 ] 2Zf ] Zf ] -f 4f 4f20f
#-2 c o2� $ o2 t�? w_o_w_�' eZ42f-D�D0f �t H{hufðflr 919= Whprv txh r uhvxowdgr dqwhulru ghyh vhu htxlsdudgr frp d hqhujld ghuhsrxvr gr hoìwurq/ sdud rewhuprv
eZ42f-D�D0f ' eZ�D
# 6e�Z-�
$2 -D ' 6S2
rx vhmd b�D�eZ0f62- ' 6S2gh prgr txh - ' 2fZ0fS2�6 �t H{hufðflr 91:= Whprv txh
O.� ' ^�eZ0fo��Oo� ' ^�
�O1 c Oo�eZ0f ���O1 c Oo���� h O.2 ' ^2eZ0fo�Oo�Dvvlp=
� +d, .22 ' O.2 d O.2 ' ^22* E�SZ202foe�/ gh irupd txh whprv
U ' ] "f ] Zf ] 2Zf ^22�SZ202foeo2 t�? w_o_w_� ' c ^22eZ0fo
�����"ftxh glyhujh qr olplwh lqihulru1� +e, Djrud whprv txh fdofxodu U ' U O.� d O.2_T / rqgh T ì wrgr r yroxph grxqlyhuvr1 Dvvlp/
U ' ]T ^�^2
�O1 c Oo� d Oo�SZ202fo� ���O1 c Oo����_T ' ^�^2�SZ202f
] "
f
] Z
f
] 2Z
f E1o ULt w c o2� o2 t�? w_o_w_�o� ko2 n 12 c 2o1 ULt wl�*2
' ^�^2HZ02f ] "f ] n�3� E1� c o�ko2 n 12 c 2o1�l�*2_o_�
Wr= Rfwrehu 57/ 5336 Sdjh= 7
Qrwh djrud txh
__o
;A?A= �ko2 n 12 c 2o1�l�*2
<A@A> ' c2 Eo c 1��ko2 n 12 c 2o1�l�*2 �Dvvlp/ �fdprv frp
U ' ^�^2HZ02f ] n�3�
;A?A= �ko2 n 12 c 2o1�l�*2
<A@A>
"
f
_� ' ^�^2HZ02f ] n�3� �12_�' ^�^2HZ02f122 ' ^�^2eZ02f12 ctxh ì r uhvxowdgr +�qlwr, hvshudgr sdud d hqhujld hqwuh gxdv fdujdv1 Dvvlp/ rwhupr fdofxodgr hp +d,/ dvvrfldgr ãv dxwr0hqhujldv/ ghyh vhu ghvfrqvlghudgr grvfäofxorv1
t H{hufðflr 9143= Vö whprv grlv frqgxwruhv/ gh prgr txh �fdprv frp)� ' R��'� c R�2'2)2 ' R2�'� c R22'2txh ì xp vlvwhpd gh htxdêøhv txh srgh vhu uhvroylgr sdud '� h '2 gh wdo irupd txh
'� ' R22)� c R�2)�R��R22 c R2�R�2 h '2 ' R2�)� c R��)2R��R22 c R2�R�2 �Xvdqgr d h{suhvvær= '� ' 2[�'� S��)�c�fdprv frp rv frh�flhqwhv gh fdsdflgdgh gdgrv sru
S�� ' R22{ / S22 ' cR��{ crqgh { ì r ghwhuplqdqwh gr vlvwhpd dqwhulru h ì gdgr sru { ' R��R22 c R2�R�2/ hwdpeìp frp rv frh�flhqwhv gh lqgxêær gdgrv sru
S�2 ' cR�2{ h S2� ' R2�{ �t H{hufðflr 9146= Qrwh txh whprv xpd vlwxdêær hp txh rv glhoìwulfrv id}hp r sdshogh fdsdflwruhv hp vìulh1 Dvvlp/ d fdsdflwåqfld wrwdo vhuä gdgd sru�� ' ��� n ��2 �
Wr= Rfwrehu 57/ 5336 Sdjh= 8
R fäofxor gd fdsdflwåqfld gh fdgd xp ghvwhv *fdsdflwruhv* ì iäflo h ì gdgr sru
�� ' 0��_� h �2 ' 02�_2 �Dvvlp/ �fdprv frp �� ' _�0�� n _202� ' ��
#02_� n 0�_20�02
$ c
rx vhmd/ d fdsdflwåqfld sru xqlgdgh gh äuhd/ �*� �fd
�*� ' #02_� n 0�_20�02
$ c
txh ì r uhvxowdgr ghvhmdgr1t H{hufðflr 9147= Frqvlghuh d �jxud dedl{r1 Qhod whprv xpd frq�jxudêær gh gxdvolqkdv gh fdujd frp ghqvlgdghv olqhduhv gh fdujd ib/ srvlflrqdgdv vlphwulfdphqwh frpuhodêær dr orfdo hp txh hvwduld r sodqr frqgxwru +qær hvwä pdlv/ ylvwr txh hvwdprvxvdqgr r pìwrgr gdv lpdjhqv,1
H{hufðflr 9147
txdqgr r id}hprv r srwhqfldo qr srqwr � �fd gdgr sru
) ' b2Z0f *?�o�o2� ' b2Z0f *?
57 S%2 n +2tE% n 2_�2 n +2
68 �
Vh hvfuhyhprv �2 ' i T EeZ0f)*b�/ hqwær �fdprv frp
�2 ' %2 n +2%2 n e_% n e_2 n +2txh/ dsöv dojxpdv pdqlsxodêøhv dojìeulfdv vlpsohv/ srgh vhu srvwr vre d irupd#% c 2�2_�c �2$2 n +2 ' e_2�2�c �2 c
Wr= Rfwrehu 57/ 5336 Sdjh= 9
txh uhsuhvhqwd xp flolqgur gh fhqwur hp
%S ' 2�2_�c �2h udlr oS ' 2_��c �2 �Djrud/ rokdqgr d �jxud/ whprv txh@ ' oS h %f ' _ n %Scgh prgr txh %f ' E� n �2�E�c �2�_ h @ ' 2�_�c �2 �Dvvlp/ �fdprv frp %f@ ' � n �22�gh rqgh rewhprv � ' %f@ i
v%2f@2 c �crqgh hvfrokhprv r ydoru srvlwlyr1 Dvvlp/ xvdqgr d h{suhvvær sdud � / �fdprv frp)b ' �2Z0f *?�%f@ nu%f@ c ��h/ ohpeudqgr txh ULt�3� % ' *? �% nS%2 c �� csrghprv hvfuhyhu b) ' 2Z0f* ULt�3� E%f*@� ctxh ì r uhvxowdgr hvshudgr1t H{hufðflr 914:= Sdud r fdvr gdv hvihudv frqfíqwulfdv whprv txh
)U ' 'eZ0fo� h )UU ' 'eZ0fo2 �Dvvlp/ whprv txh )U c )UU ' {) ' 'eZ0f � �o�c �o2� �Frpr vdehprv txh ' ' �{)c
Wr= Rfwrehu 57/ 5336 Sdjh= :
frqfoxðprv txh � ' eZ0f*� �o� c �o2� �Frpr whprv L ' �2'{)h ' ' �{)/ hqwær/ �fdprv frp
L ' �2� E{)�2 �t H{hufðflr 914;= whprv r duudqmr gd �jxud dedl{r/ hp txh prvwudprv d vlwxdêær mäfrp r oðtxlgr glhoìwulfr suhhqfkhqgr sdufldophqwh r flolqgur1 Vxsrqkd txh r glhoìwulfrsuhhqfkh d uhjlær lqwhuvwlfldo dwì xpd dowxud 5f h wrph hvwd dowxud frpr vhqgr d ruljhpgr vlvwhpd gh frrughqdgdv1
Qrwh txh whprv xpd vlwxdêær hp txh whprv grlv *fdsdflwruhv* hp sdudohor1 Xp/ frpfdsdflwåqfld �� E5�/ frp r glhoìwulfr suhhqfkhqgr d uhjlær lqwhuvwlfldo h rxwur/ frpfdsdflwåqfld �2 E5�/ vhp glhoìwulfr +frp yäfxr,1 D fdsdflwåqfld wrwdo ghvwh vlvwhpdsrgh vhu hvfulwd/ xpd yh} txh hvwær hp sdudohor/ frpr� E5� ' �� E5� n �2 E5�hqtxdqwr txh d hqhujld wrwdo srgh vhu hvfulwd gluhwdphqwh frprL E5� ' � E5�{)crqgh uhvvdowdprv txh r sduåphwur{) hvwä vhqgr pdqwlgr frqvwdqwh +lvwr ì lpsruwdqwhsdud hihlwr gr fäofxor gd iruêd txh dsduhfhuä vreuh r glhoìwulfr qr vhqwlgr gh sx{ä0orsdud flpd,1 R fäofxor gr srwhqfldo hqwuh rv flolqgurv ì vlpsohv1 Vh vxsxvhuprv +vhpshugd gh jhqhudolgdgh, txh r srwhqfldo vreuh r pdlv lqwhuqr ì )� h vreuh r pdlv h{whuqrì )2/ hqwær �3�2 E5� ' {)'2 ' )2 c )�'2 ' �2Z0f EM c 5� *?�o2o�� c
Wr= Rfwrehu 57/ 5336 Sdjh= ;
sdud d uhjlær suhhqfklgd sru du h
�3�� E5� ' {)'� ' )2 c )�'� ' �2Z05 *?�o2o�� csdud d uhjlær frp glhoìwulfr/ rqgh xvdprv txh '2 ' b EM c 5� h '� ' b5/ ylvwr txh bì d ghqvlgdgh olqhdu gh fdujd1 Dvvlp/ �fdprv frp
L E5� ' 2Z0f{)*? Eo2*o�� EM c 5� n 2Z0{)*? Eo2*o��5�Vxd ghulydgd frp uhodêær d 5 +frp {) frqvwdqwh, iruqhfh d iruêd qhvwd gluhêær/ orjr
85 ' 2Z{)*? Eo2*o�� d0 c 0fo �D txdqwlgdgh gh pdvvd ghvorfdgd shod glihuhqêd gh srwhqfldo vhuä gdgd shor surgxwrgd ghqvlgdgh gh pdvvd shor yroxph ghvorfdgr/ rx vhmd/6 ' 1Z �o22 c o2�� 5crqgh 5 ì d dowxud hp txh r glhoìwulfr ì ohydqwdgr1 Qrwh txh whprvo2 ' o� n _cgh prgr txh srghprv hvfuhyhu o22 c o2� 
 2o�_�Dvvlp/ whprv txh d iruêd qhfhvväuld sdud hohydu r oðtxlgr gh glhoìwulfr ì gdgd sru8} ' 6} ' 2Z1o�}_5�Hvwd iruêd ghyh vhu htxloleudgd shod iruêd 85 mä fdofxodgd� Dvvlp/ �fdprv frp2Z E0 c 0f�{)*? E� n _*o�� ' 2Z1o�}_5�Id}hqgr d dsur{lpdêær _*o� � � qr orjdulwpr ^*? E� n %� 
 %`/ �fdprv frp0f Eg c ��1}_2 {) ' 5txh ì r uhvxowdgr ghvhmdgr1 Qrwh txh/ vh d ghqvlgdgh gr glhoìwulfr ì pxlwr shtxhqd/5 vhuä judqgh> vh vö wlyhuprv yäfxr/ 5 ' f h vh _ iru shtxhqr/ 5 vhuä judqgh/ txhvær frqglêøhv txh hvshuduðdprv hqfrqwudu �vlfdphqwh1 Qrwh/ dlqgd/ txh txdqwr pdlruiru g +txdqwr pdlv hqhujld r glhoìwulfr sxghu dupd}hqdu,/ pdlru vhuä d hohydêær grphvpr1
Wr= Rfwrehu 57/ 5336 Sdjh= <
Srghprv hvwlpdu xp uhvxowdgr wðslfr sdud 5 frp ydoruhv uhdlv gdv frqvwdqwhv= vxsrqkdrv ydoruhv +sdud d äjxd ghvwlodgd d 2fJ�/ g 
 H�,{) ' 22fTg ' H�1 ' �g}*6�0f ' H�HD e �f3�2�62*�2_ ' �f3�6} ' b�H6*r2
�
Ilfdprv frp 5 ' H�HD e �f3�2 e Hfb�H e �f3S E22f�2 ' ��DS6t H{hufðflr 914<= Hqtxdqwr r fdsdflwru hvwä vhqgr fduuhjdgr frp r glhoìwulfr qr vhxlqwhulru/ whprv txh kä d wudqvihuíqfld gh xpd fdujd wrwdo
'A ' 0,�_ {)f�Srvwhulruphqwh/ d edwhuld ì ghvoljdgd h r glhoìwulfr ì sdufldophqwh uhwludgr1 D fdujdwrwdo ghyhuä djrud vhu gdgd shodv vrpdv gh fdgd xpd gdv frqwulexlêøhv +gd sduwh grglhoìwulfr txh dlqgd vh hqfrqwud qr lqwhulru gr fdsdflwru h gdtxhod sduwh txh frqwìpdshqdv du,1 Dvvlp/ whprv
'� ' 0%�_ {)'2 ' 0f E, c %��_ {)rqgh djrud {) qær ì ljxdo d {)f/ srlv d edwhuld qær ì pdlv fdsd} gh pdqwhu rsrwhqfldo �{r1 D fdujd/ hqwuhwdqwr/ ì frqvhuydgd/ h{wdphqwh shor idwr gh whuprvghvoljdgr d edwhuld/ gh prgr txh
'A ' '� n '2 ' %0%�_ n 0f E, c %�_ &{)' 0f d, n Eg c ��%o �_ {)(Xvdqgr d h{suhvvær dqwhulru sdud 'A / �fdprv frp
{) ' g,{)fd, n Eg c �� %o �D iruêd srgh vhu fdofxodgd d sduwlu gr srwhqfldo/ ghvgh txh ohpeuhprv txh ghyhprvpdqwhu d fdujd frqvwdqwh1 Dvvlp/ ghyhprv hvfuhyhu
{) ' g'_0� d, n Eg c �� %o
Wr= Rfwrehu 57/ 5336 Sdjh= 43
h d hqhujld �fd L ' �2'{) ' _20f� '2d, n Eg c ��%oh d iruêd +rokh r vlqdo,
8 ' c#YLY% $' ' Eg c ��'2_20f d, n Eg c �� %o2 ctxh ì r uhvxowdgr ghvhmdgr1t H{hufðflr 9154= Frphêdprv sru qrwdu txh d hvihud hvwä lqlfldophqwh hp htxloðeulr1Dvvlp/ d iruêd uhdol}dgd shor hpsx{r ghyh vhu htxloleudgd shod iruêd shvr gd hvihud1D iruêd gh hpsx{r ì fdofxodgd dwudyìv gd h{suhvvær8ec� ' 4_}��crqgh � ì d dowxud gd sduwh gd hvihud txh vh hqfrqwud lphuvd qr xlgr h � ì d äuhd gdvhêær uhwd ghvwd sduwh +fi1 �jxud dedl{r,1 Ydprv vxsru/ gh prgr jhudo/ txh r yroxphlphuvr gd hvihud vhmd kT / rqgh T ' eZ-�*� ì r yroxph gd hvihud h k gä d srufhqwdjhpgh hvihud lphuvd1 Ydprv frqvlghudu/ lqlfldophqwh/ r åqjxor w�/ frpr prvwudgr qd�jxud/ frpr gdgr +ghsrlv prvwuduhprv frpr rewí0or grv gdgrv gr sureohpd,1
Dvvlp/ whprv8ec� ' 4_}- E�c ULt w�� Z-2 t�?2 w� ' 4_Z-� t�?2 w� E�c ULt w�� ' 6}rx vhmd/ 4_ ' 6Z-� t�?2 w� E�c ULt w�� �Djrud/ frqvlghuh d hvihud qd vlwxdêær E gd �jxud dqwhulru/ hp txh d hvihud hvwä vxep0huvd shod phwdgh qr glhoìwulfr1 D iruêd gh hpsx{r ghyh vhu gdgd sru8ec2 ' 4_}Z-�c
Wr= Rfwrehu 57/ 5336 Sdjh= 44
mä txh � ' - h � ' Z-21 Hvwd iruêd ghyh vhu htxloleudgd shor shvr dglflrqdgr ã iruêduhdol}dgd shor srwhqfldo txh irl oljdgr1 D iruêd dvvrfldgd d hvwh ýowlpr whupr srgh vhufdofxodgd gd vhjxlqwh pdqhlud= d hqhujld hohwurvwäwlfd dvvrfldgd drv fdpsrv ì gdgdsru +fdpsrv vxsrvwdphqwh udgldlv,
L ' �2 ]T O. d O(_T ' 02 '2�SZ202f ] "- ] w�f ] 2Zf �oeo2 t�? w_o_w_�n0f2 '2�SZ202f ] "- ] Zw� ] 2Zf �oe o2 t�? w_o_w_�txh iruqhfh
L ' � 'eZ0f-�2 Z-
%0 ] w�f t�? w_w n 0f ] Zw� t�? w_w
&
' )2Z- d0 E�c ULt w�� n 0f E� n ULt w��o' c)2Z- E0 c 0f� ULt w� n )2Z- E0 n 0f� �Vh qrwduprv txh 5 ' c- ULt w� +wrpdqgr r fhqwur gd hvihud frpr ruljhp gh qrvvrvlvwhpd gh frrughqdgdv,/ hqwær d hqhujld srwhqfldo �fdL E5� ' )2Z- E0 n 0f� n )2Z0f Eg c �� 5�D iruêd hohwurvwäwlfd/ sruwdqwr/ �fd8. ' )2Z0f Eg c �� �Dvvlp/ ghyhprv whu 8ec2 ' 6} n 8.cr txh iruqhfh 4_}Z-� ' 6} n )2Z0f Eg c ��h/ vxevwlwxlqgr r ydoru gh 4_ �fdprv frp
6} k�c t�?2 w� E�c ULt w��lt�?2 w� E�c ULt w�� ' )2Z0f Eg c �� cgh prgr txh ) ' + 6}Z0f Eg c �� �c t�?2 w� E�c ULt w��t�?2 w� E�c ULt w��
,�*2 �
Idowd dlqgd rewhu r ydoru gh w�1 Srghprv id}í0or d sduwlu gdv frqglêøhv lqlfldlv +txdqgrd hvihud hvwä htxloleudgd/ vhp fdpsr/ shor hpsx{r h vhx yroxph vxephuvr srgh vhufdofxodgr idflophqwh,1 Dvvlp/ ghyhprv whu
ke�Z-� ' ] -f ] w�f ] 2Zf o2 t�? w_o_w_� c Z-�� t�?2 w� ULt w�c
Wr= Rfwrehu 57/ 5336 Sdjh= 45
rqgh r whupr ã gluhlwd ì gdgr shor yroxph dvvrfldgr dr åqjxor vöolgr vxehqwhqglgrsru w� h txh whprv txh uhwludu d sduwh gr frqh/ lqfoxðgd d pdlv/ uhsuhvhqwdgd shorýowlpr whupr ã gluhlwd1 Dvvlp/ �fdprv frp
ekZ-�� ' 2Z-�� E�c ULt w��c Z-�� t�?2 w� ULt w�crx vhmd ek c 2 ' c� ULt w� n ULt� w�crqgh/ vh vxevwlwxluprv 1 ' ULt w�/ �fdprv frp1� c �1 n � ' ftxh ì d htxdêær txh ghwhuplqd w�1 Qr qrvvr fdvr hvshfð�fr/ whprv k ' �*e h/ sruwdqwr/�fdprv frp 1� c �1 n � ' fcfxmdv vroxêøhv vær/ dsur{lpdgdphqwh/��D�/ c ��HH h f��Dcrqgh dshqdv d ýowlpd ì dfhlwäyho/ ylvwr txh 1 ì xp frvvhqr +qær srgh vhu pdlru txhxp hp pögxor,1 Dvvlp/ ULt w� ' f��D � t�?2 w� ' f�HHh w� 
 .fJ1 Sdud hvwh fdvr/ r srwhqfldo �fd
) ' + 6}Z0f Eg c �� �c f�HH Ef�SD�f�HH Ef�SD�
,�*2 ' % f�.e6}Z0f Eg c ��
&�*2 �
t H{hufðflr 9156= Whprv txh hvfuhyhu L ' �2� E%� E{)�21 Ohpeuhpr0qrv txh/ sdudhvwh sureohpd/ d glihuhqêd gh srwhqfldo {) hvwä vhqgr pdqwlgd +shod edwhuld, frprfrqvwdqwh1 Whprv/ hqwuhwdqwr/ txh fdofxodu d fdsdflwåqfld � E%� gr fdsdflwru txdqgr rglhoìwulfr hvwä lqwurgx}lgr sru xpd glvwåqfld %1 Rud/ r sureohpd 914< qrv prvwud frprghyhprv fdofxodu hvwd fdsdflwåqfld1 Glihuhqwhphqwh gdtxhoh sureohpd/ hqwuhwdqwr/ qærvh wudwd gh pdqwhu d fdujd wrwdo frqvwdqwh/ mä txh kä xpd edwhuld hqyroylgd/ pdv vlp{) ghyh vhu frqvlghudgr frqvwdqwh1 Srghprv hqwhqghu hvwh sureohpd frpr fdsdflwruhvhp sdudohor/ gh wdo prgr txh� E%� ' �� E%� n �2 E%� cvhqgr txh r sulphlur fdsdflwru srvvxl xp glhoìwulfr hp vhx lqwhulru h r vhjxqgr fd0sdflwru srvvxl r yäfxr +du,1 Dvvlp/ sdud r sulphlur/ rewhprv
�� E%� ' 0%�_
Wr= Rfwrehu 57/ 5336 Sdjh= 46
hqtxdqwr txh/ sdud r vhjxqgr/ rewhprv
�2 E%� ' 0f E, c %�_R uhvxowdgr �qdo sdud r srwhqfldo wrwdo vhuä/ sruwdqwr/L ' �2 d�� E%� n �2 E%�o E{)�2 '' �2 0%�_ E{)�2 n �2 0f E, c %��_ E{)�2 '' �20�{)_ �2 _�% n �20f �{)_ �2 _� E% c ,�txh ì h{dwdphqwh r phvpr uhvxowdgr rewlgr qr olyur1t H{hufðflr 9157= Whprv txh L ' �2� E{)�2h ' ' � E%�{)1 D iruêd fdofxodgd pdqwhqgr0vh{) frqvwdqwh srgh vhu lphgldwdphqwhfdofxodgd frpr vhqgr
8 ' #YLY% ${) ' �2 _� E%�_% E{)�2 �D iruêd fdofxodgd pdqwhqgr0vh ' frqvwdqwh srgh vhu fdofxodgd vh �}huprv xpd vxe0vwlwxlêær qd sulphlud h{suhvvær gh prgr d hvfuhyí0od hp jhuprv dshqdv gd fdujd h gh� E%�1 Dvvlp/ �fdprv frp L ' �2 '2� E%�gh prgr txh d iruêd �fd
8 ' c#YLY% $' ' �2 '2� E%�2 _� E%�_% �Vh qrwduprv djrud txh '2� E%�2 ' E{)�2 cwhuhprv lphgldwdphqwh d ljxdogdgh txh surfxudprv1t H{hufðflr 9158= Ghyhprv qrwdu +frpr dsrqwd d vxjhvwær gr olyur, txh djrud ì r yhwrughvorfdphqwr O( txh ì sudwlfdphqwh frqvwdqwh dr orqjr gr fdsdflwru1 Dvvlp/ whprv
( ' 0f{)_
Wr= Rfwrehu 57/ 5336 Sdjh= 47
h d hqhujld hohwurvwäwlfd �fd
L ' �20 ]T (2_Oo ' �2002f E{)�2_ �% n �20f02f E{)�2_ � E, c %�rqgh r sulphlur whupr srvvxl xp 0 qr ghqrplqdgru sru hvwduprv qr lqwhulru grglhoìwulfr/ hqtxdqwr txh r vhjxqgr srvvxl xp 0f sru hvwduprv qr du +qrwh/ hqwuhwdqwr/txh ( ì vhpsuh r phvpr/ hp dperv rv fdvrv,1 D iruêd/ sruwdqwr/ �fd
8% ' #YLY% ${) ' 0f2
�0f c 00 ��{)_ �2 �_' �2 � �g c �� 0f.2�crqgh � ' �_ h . ' {)*_/ frpr lpsolfdgr shod iöupxod sdud (1
Wr= Rfwrehu 57/ 5336 Sdjh= 44 Fdsðwxor :=t H{hufðflr :16= Vdehprv txh dv glihuhqêdv gh srwhqfldo hqwuh dv sodfdv pdlv h{whuqdvh d sodfd txh vh hqfrqwud qd iurqwhlud hqwuh rv phlrv vær gdgdv sru)2 c ) ' {)2 ' .2 E_c @�)c )� ' {)� ' .�@Frpr rv phlrv vær frqgxwruhv/ ghyhprv whua�? ' a2?crx vhmd/ }�.� ' }2.2�Dvvlp/ }2)2 c )_c @ ' }�)c )�@gdqgr ) d}� E_c @� n }2@o ' )�}� E_c @� n )2}2@gdqgr ) ' )�}� E_c @� n )2}2@d}� E_c @� n }2@o �Whprv dlqgd txh dv fdujdv txh fdgd xp grv vxevlvwhpdv dfxpxod vær gdgdv sru'� ' ��{)� h '2 ' �2{)2crqgh dv fdsdflwåqfldv �fdp
�� ' 0��@ h �2 ' 02�E_c @� �Dvvlp/ frpr d fdujd wrwdo qd sodfd lqwhuphgläuld ì d vrpd gh '� frp '2 +dv fdujdvlqgx}lgdv qhvwd sodfd sru fdgd vxevlvwhpd,/ whprv +Qrwh r vlqdo gd fdujd '21 yrfífrqvhjxh h{solfdu sru txh hvwh vlqdo ì qhjdwlyrB,' ' '� c'2 ' �� E)c )��c �2 E)2 c )�' ) E�� n �2�c E��)� n �2)2�' )�}� E_c @� n )2}2@d}� E_c @� n }2@o E�� n �2�c E��)� n �2)2�' c)� d}� E_c @��2 c }2@��o n )2 d}2@�� c }� E_c @��2od}� E_c @� n }2@o' E)2 c )�� d}� E_c @��2 c }2@��od}� E_c @� n }2@o' E)2 c )�� d}�02 c }20�o�d}� E_c @� n }2@o
Wr= Rfwrehu 57/ 5336 Sdjh= 5
Hvwh ýowlpr uhvxowdgr srgh vhu hvfulwr frpr
j ' '� ' d}�02 c }20�o E)2 c )��d}� E_c @� n }2@o ctxh ì r uhvxowdgr ghvhmdgr1 Qrwh txh vh wlyhuprv 02 ' 0� ' }2 ' }�/ rx vhmd/ phlrvlgíqwlfrv/ hqwær/ frpr hvshudgr/ qær srghuðdprv whu dfýpxor gh fdujd qd lqwhuidfh1Pdlv lqwhuhvvdqwh ì qrwdu txh vh wlyhuprv}�0� ' }202wdpeìp whuðdprv j ' f1 Ohpeuh0vh txh-� ' 0} cgh prgr txh wxgr ixqflrqd frpr vh d sduwh gd fdsdflwåqfld irvvh *frpshqvdgd* shoduhvlvwíqfld gr phlr1t H{hufðflr :17= Vdehprv mä txh ydoh d lghqwlgdgh yhwruldoU d �s O8� ' sU d O8 n O8 d Us�Djrud frortxh= U d �%O8� ' %U d O8 n 8%h wdpeìp U d �+ O8� ' +U d O8 n 8+U d �5 O8� ' 5U d O8 n 85h djrud prqwh d vrpde�U d �%O8�n e�U d �+ O8�n e&U d �5 O8� ' e�%U d O8 n e�8%ne�+U d O8 n e�8+ n e&5U d O8 n e&85 ' OoU d O8 n O8 �Frortxh djrud O8 ' Oa sdud hvfuhyhu]
T
�OoU d Oa n Oa� _T ' ]T ke�U d �%Oa�n e�U d �+ Oa�n e&U d �5 Oa�l _T�Hp fdgd xp grv whuprv ã gluhlwd/ xvh r whruhpd gd glyhujíqfld/ sdud �fdu frp]
T
�OoU d Oa n Oa� _T ' ]7 ke�% � Oa d e?�n e�+ � Oa d e?�n e&5 � Oa d e?�l _@' ]7 �e�%n e�+ n e&5� � Oa d e?� _@' ]7 Oo � Oa d e?� _@
Wr= Rfwrehu 57/ 5336 Sdjh= 6
Dvvlp/ surydprv r uhvxowdgr]
T Oa_T ' ]7 Oo � Oa d e?� _@c ]T OoU d Oa_T�Djrud/ whprv txh OR ' ]T Oo4 EOo� _T�Dvvlp/ _OR_| ' __| ]T Oo4 EOo� _T ' ]T OoY4 EOo�Y| _T' c ]T OoU d Oa_TFrpr Oa ì qxor qd vxshuiðflh 7/ hqwær srghprv xvdu d h{suhvvær dqwhulru sdud hvfuhyhu]
T Oa_T ' c ]T OoU d Oa_Tcmä txh d lqwhjudo vreuh 7 vh dqxod1 Hqwær/ shor uhvxowdgr dqwhulru_OR_| ' ]T Oa_Tctxh ì r uhvxowdgr hvshudgr1t H{hufðflr :1:= Dv fdvfdv floðqgulfdv wíp udlrv o� h o2/ o2 : o� h vær pdqwlgdv ãglihuhqêd gh srwhqfldo {)1 Hqwuh dv fdvfdv kä xp phlr gh frqgxwlylgdgh }1 Vdehprvtxh ydoh d Ohl gh Rkp Oa ' } O.cr txh lpsolfd/ frpr mä ylprv/ txh
U ' {)-h suhflvdprv fdofxodu -1 Sdud fdofxoä0or/ qrwdprv txh whprv' ' �{)h -� ' 0}gh prgr txh - ' 0}� �Dvvlp/ �qdophqwh U ' }{)0 �
Wr= Rfwrehu 57/ 5336 Sdjh= 7
h suhflvdprv phudphqwh fdofxodu � sdud d frq�jxudêær hp txhvwær1 Qrwh txh whprv
) ' b2Z0 *? Eo*o�� n )fcgh prgr txh {) ' b2Z0 *? Eo2*o�� crx vhmd � ' b{) ' 2Z0*? Eo2*o�� �Dvvlp/ �fdprv frp U ' 2Z}{)*? Eo2*o�� ctxh hud r uhvxowdgr surfxudgr1 R h{hufðflr irl ihlwr vhp xvdu d Ohl gh Rkp gluhwdphqwh1Sdud xvä0od/ vhuld qhfhvväulr sduwlu gluhwdphqwh gd ohl Oa ' } O. h fdofxodu O. sdud hvwdfrq�jxudêær/ ohpeudqgr txh U ' U7 Oa d e?_@1 Dvvlp/ �fdprv frp
U ' {)- ' } ]7 O. d e?_@ ' '}0 �Pdv hqwær/ -# '{)$ ' 0} crx vhmd/ -� ' 0} �t H{hufðflr :1<= Srghprv/ frpr mä ylprv/ xvdu r pìwrgr gdv lpdjhqv sdud vxevwlwxlu rvlvwhpd *sodqr frqgxwru*.*�r* +flolqgur, shor vlvwhpd *olqkd*.*olqkd* gh wdo prgr txhr sodqr frqgxwru vh orfdol}h qr fhqwur jhrpìwulfr hqwuh dv olqkdv +h hvwhmd d srwhqfldoqxor, hqtxdqwr txh r flolqgur ì hvfroklgr sdud rfxsdu xpd gdv htxlsrwhqfldlv grsureohpd +dtxhod frp r vhx udlr @,1 Mä ylprv/ qr fdsðwxor 6 h qr fdsðwxor dqwhulru/frpr hqfrqwudu r udlr h d srvlêær gr flolqgur frp uhodêær ã olqkd1 Wðqkdprv
%S ' 2�2_�c�2 h oS ' 2�_�c�2 cvh frorfduprv xpd gdv olqkdv vreuh d ruljhp gh qrvvr vlvwhpd gh frrughqdgdv1 Qrwh0prv txh �2 ' i T EeZ0)*b�gh prgr txh rewhprv )b ' �3� ' ULt�3� E�*@�2Z0 c
Wr= Rfwrehu 57/ 5336 Sdjh= 8
rqgh � ì d fdsdflwåqfld sru xqlgdgh gh frpsulphqwr1 Frpr vdehprv txh -� ' 0*}/�fdprv frp - ' 0} ULt�3� E�*@�2Z0h/ sruwdqwr/ - ' �2Z} ULt�3� #�@$ ctxh hud d h{suhvvær d vhu rewlgd1t H{hufðflr :144= Mä ylprv/ ã h{dxvwær/ txh grlv flolqgurv srghp vhu vxevwlwxðgrv srugxdv olqkdv gh ghqvlgdgh olqhdu gh fdujd b h cb/ ylvwr txh dv phvpdv surgx}hp fxuydvhtxlsrwhqfldlv txh vær floðqgulfdv qr sodqr txh okhv ì shushqglfxodu1 Frq�ud d �jxuddedl{r
Rud/ vdehprv txh vh frorfdprv gxdv olqkdv gh fdujd/ gh ghqvlgdgh olqhdu gh fdujd b hcb/ glvwdqwhv sru xpd glvwåqfld 2_/ hqwær rv fhqwurv grv flolqgurv hvwær srvlflrqdgrvd xpd glvwåqfld %S ' 2�2_�c�2gh fdgd xpd ghodv +*sdud irud*/ frpr prvwud d �jxud,1 Dvvlp/ vdehprv txh
K ' 2_n 2%S ' 2 E�c�2� _n e�2_�c�2 ' � n�2�c�22_�Rv udlrv grv flolqgurv vær gdgrv sru
@ ' �E�c�2�2_�
Wr= Rfwrehu 57/ 5336 Sdjh= 9
Dvvlp/ rewhprv txh K2@ ' � n�22� �Ohpeudqgr txh � ' i T Ec2Z0)*b�/ fkhjdprv dr uhvxowdgr
� ' K2@ n
yxxw# K2@$2 c �h/ sruwdqwr/ )b ' �2Z0 ULt�3� # K2@$rx b) ' 2Z0ULt�3� EK*2@�h frpr +' ' br, 'r) ' 2Z0ULt�3� EK*2@�rx � ' ') ' 2Z0rULt�3� EK*2@� (pdv frpr -� ' 0} chqwær - ' ULt�3� EK*2@�2Z}rh frpr {) ' -Uc�fdprv frp U ' 2Z}r{)ULt�3� EK*2@�
Wr= Rfwrehu 57/ 5336 Sdjh= 4
t Fdsðwxor ;t H{hufðflr ;14= Frortxhprv d lqgxêær pdjqìwlfd xqliruph O� qd gluhêær 51 Vxsrqkddjrud txh xpd sduwðfxod hqwuh qhvwh fdpsr frp yhorflgdgh O�1 Vdehprv txh d iruêdtxh luä dwxdu vreuh d sduwðfxod +gh pdvvd 6 h fdujd ^, ì gdgd sruO86 ' ^O� e O�rx vhmd/ vh wrpduprv O� ' O�z n O�O/ rqgh O�z uhsuhvhqwd d yhorflgdgh shushqglfxodu d O�h O�O uhsuhvhqwd d yhorflgdgh sdudohod d O�/ hqwær whprv txhO86 ' ^O�z e O��Dvvlp/ hp pögxor/ whprv 86 ' ^�z�1 D iruêd vhuä h{huflgd qxpd gluhêær txh ìshushqglfxodu wdqwr d O� txdqwr d O�z +h/ dvvlp/ shushqglfxodu wdpeìp d O�O,1 Hvwdiruêd vhuä/ sruwdqwr/ xpd iruêd fhqwuðshwd frqvwdqwh h whuhprv/ hp pögxor
^�z� ' 6�2z- cgh prgr txh r udlr gd wudmhwöuld �fduä
- ' 6�z^� �Qrwdprv txh d wudmhwöuld vhuä xpd kìolfh/ mä txh d yhorflgdgh O�O qær hvwä vhqgr dihwdgdshod h{lvwíqfld gd lqgxêær pdjqìwlfd1t H{hufðflr ;15= R Kdplowrqldqr gdgr ì
M ' R226 c ^�26 E%R+ c +R%� n ^2�2H6 �%2 n +2� �Qrwh txh r vhjxqgr whupr ã gluhlwd ì xp dfrsodphqwr hqwuh d lqgxêær pdjqìwlfd +qdgluhêær 5, h r prphqwr dqjxodu qhvwd phvpd gluhêær/ gdgr sru^26 O� d Ou ' ^26�u5 ' ^�26 E%R+ c +R%� �Dvvlp/ �fd fodur txh -2 ' %2 n +2/ ylvwr vhu r sodqr %+ shushqglfxodu ã gluhêær gh O�1Djrud/