by Eugene Brigham and Michael Ehrhardt
, ÿ
71839ÿ 1 9ÿ 139ÿ ÿ
ÿÿÿÿ
ÿ
!"#$ÿ
%&'(ÿ)ÿ*+,-(ÿ
ÿ
./01ÿ0340ÿ03151ÿ67ÿ48ÿ/915:4;ÿ<10=118ÿ031ÿ>?@ÿ48AÿBC:06;:1DE3/6E1ÿFC1706/87Gÿ47ÿ7/B1ÿ/Hÿ031ÿ>?@ÿ70401B1807ÿ451ÿC71Aÿ68ÿ
BC:06;:1DE3/6E1ÿFC1706/87Iÿ
J#KÿLM
NÿOJP
Qÿ
ÿ
ÿRSÿTU-VÿWU&XU&+VYUS-ZÿV[(ÿ\*]ÿ&+S^-ÿ'S_(&ÿV[(ÿ\`]ÿ
+ÿ%&'(ÿ
aÿ*+,-(ÿ
b.cdefgÿ%&'(ÿ
ÿ
hÿ%[(ÿ\[+Y&T+SÿUiÿV[(ÿjU+&_ÿT'-Vÿ+,-Uÿa(ÿV[(ÿ\`]ÿ
+ÿ%&'(ÿ
aÿ*+,-(ÿ
b.cdefgÿ*+,-(ÿ
ÿ
kÿ%[(ÿaU+&_ÿUiÿ_Y&(WVU&-ÿY-ÿV[(ÿ[Yl[(-Vÿ&+S^YSlÿaU_mÿYSÿ+ÿWU&XU&+VYUSZÿ+S_ÿV[(ÿW[+Y&T+SÿUiÿV[(ÿaU+&_ÿY-ÿV[(ÿ[Yl[(-Vÿ&+S^YSlÿ
YS_YnY_'+,ÿ%[(ÿ\`]ÿl(S(&+,,mÿoU&^-ÿ'S_(&ÿV[(ÿaU+&_ÿ+S_ÿYV-ÿW[+Y&T+SZÿ+S_ÿV[(ÿaU+&_ÿl(S(&+,,mÿ[+-ÿV[(ÿ+'V[U&YVmÿVUÿ
&(TUn(ÿV[(ÿ\`]ÿ'S_(&ÿW(&V+YSÿWUS_YVYUS-ÿ%[(ÿ\`]Zÿ[Uo(n(&ZÿW+SSUVÿ&(TUn(ÿV[(ÿaU+&_Zÿa'Vÿ[(ÿU&ÿ-[(ÿW+Sÿ(S_(+nU&ÿVUÿ
[+n(ÿV[(ÿaU+&_ÿnUV(_ÿU'Vÿ+S_ÿ+ÿS(oÿaU+&_ÿnUV(_ÿYSÿ-[U',_ÿ+ÿWUSi,YWVÿ+&Y-(ÿRVÿY-ÿXU--Ya,(ÿiU&ÿ+ÿX(&-USÿVUÿ-YT',V+S(U'-,mÿ
-(&n(ÿ+-ÿ\`]ÿ+S_ÿW[+Y&T+SÿUiÿV[(ÿaU+&_ZÿV[U'l[ÿT+SmÿWU&XU&+V(ÿWUSV&U,ÿ(pX(&V-ÿa(,Y(n(ÿYVÿY-ÿa+_ÿVUÿn(-VÿaUV[ÿUiiYW(-ÿYSÿ
V[(ÿ-+T(ÿX(&-USÿ
+ÿ%&'(ÿ
aÿ*+,-(ÿ
b.cdefgÿ%&'(ÿ
ÿ
qÿr+&VS(&-[YX-ÿ+S_ÿX&UX&Y(VU&-[YX-ÿl(S(&+,,mÿ[+n(ÿ+ÿV+pÿ+_n+SV+l(ÿUn(&ÿWU&XU&+VYUS-ÿ
+ÿ%&'(ÿ
aÿ*+,-(ÿ
b.cdefgÿ%&'(ÿ
ÿ
sÿtÿ_Y-+_n+SV+l(ÿUiÿV[(ÿWU&XU&+V(ÿiU&TÿUiÿU&l+SYu+VYUSÿY-ÿV[+VÿWU&XU&+V(ÿ-VUW^[U,_(&-ÿ+&(ÿTU&(ÿ(pXU-(_ÿVUÿX(&-US+,ÿ
,Y+aY,YVY(-ÿYSÿV[(ÿ(n(SVÿUiÿa+S^&'XVWmÿV[+Sÿ+&(ÿYSn(-VU&-ÿYSÿ+ÿVmXYW+,ÿX+&VS(&-[YXÿ
+ÿ%&'(ÿ
aÿ*+,-(ÿ
b.cdefgÿ*+,-(ÿ
ÿ
vÿtSÿ+_n+SV+l(ÿUiÿV[(ÿWU&XU&+V(ÿiU&TÿUiÿU&l+SYu+VYUSÿY-ÿV[+VÿWU&XU&+VYUS-ÿ+&(ÿl(S(&+,,mÿ,(--ÿ[Yl[,mÿ&(l',+V(_ÿV[+Sÿ
X&UX&Y(VU&-[YX-ÿ+S_ÿX+&VS(&-[YX-ÿ
+ÿ%&'(ÿ
aÿ*+,-(ÿ
b.cdefgÿ*+,-(ÿ
ÿ
wÿxUT(ÿX+&VS(&-ÿYSÿ+ÿX+&VS(&-[YXÿT+mÿ[+n(ÿ_Yii(&(SVÿ&Yl[V-ZÿX&YnY,(l(-Zÿ+S_ÿ&(-XUS-YaY,YVY(-ÿV[+SÿUV[(&ÿX+&VS(&-ÿ
+ÿ%&'(ÿ
ÿ 0123ÿ5ÿ
, ÿ
71839ÿ 1 9ÿ 139ÿ ÿ
ÿÿÿÿ
ÿ
!"ÿ
#ÿ
$ÿ
%&'()*+ÿ-.ÿ
ÿ
/ÿÿ
0
"
ÿÿ"1ÿ
2
"ÿ!ÿÿ
3
"ÿ$ÿ"1
"ÿ"ÿ
0$ÿ0.#
ÿ"
4
"ÿ
ÿ-.ÿ
#ÿ
$ÿ
%&'()*+ÿ
$ÿ
ÿ
5ÿ6"ÿ$ÿ
7ÿ1
0ÿ"ÿ"
$ÿ8$ÿ$12ÿ"$"ÿÿ
ÿ2
"$12ÿ"1
ÿÿ
ÿ
2
"ÿ
ÿ-.ÿ
#ÿ
$ÿ
%&'()*+ÿ-.ÿ
ÿ
9ÿÿ0
ÿÿ$"
"ÿ
ÿ22"$12ÿ$ÿ"1
"ÿ7.ÿ!
7ÿ#ÿ42$0ÿ"ÿ2$
ÿ
#
"7ÿÿ"1ÿ#.$$$ÿ$ÿ#
:.2"ÿ
-1$ÿ2#
!ÿ.
0ÿ#ÿ
00ÿÿ7.ÿ!0ÿ
ÿ
2
"ÿ"ÿ2
"ÿ"1ÿ#.$$$ÿ
ÿ-.ÿ
#ÿ
$ÿ
%&'()*+ÿ-.ÿ
ÿ
ÿ6ÿ
ÿ
2
"ÿ
"$ÿ"ÿ#ÿ"
40ÿ
$ÿ
ÿ;ÿ
2
"<ÿ"1ÿ"ÿ
ÿ
0ÿ"1ÿ
2
"ÿ"
4ÿ=<ÿ"$ÿ$"
:1
0$ÿ
ÿ1
ÿ"ÿ2
7ÿ2$
ÿ"
4$ÿÿ"1ÿ!8$ÿ"ÿ
!ÿ
ÿ-.ÿ
#ÿ
$ÿ
%&'()*+ÿ-.ÿ
ÿ
>ÿ6ÿ
ÿ
2
"ÿ
"$ÿ"ÿ#ÿ"
40ÿ
$ÿ
ÿ;ÿ
2
"<ÿ"1ÿ#"1ÿ"ÿ
0ÿ"$ÿ$"
:1
0$ÿ
ÿ
0ÿ
ÿ0
ÿ"
4$ÿ
-1$ÿ2$ÿ
$ÿ2."ÿ"ÿ"1ÿ0
ÿ-
4ÿ?0ÿÿ0ÿ"ÿ
.
ÿ"1ÿ!
"ÿÿ$!
ÿ#.$$$$ÿ
ÿ-.ÿ
#ÿ
$ÿ
%&'()*+ÿ
$ÿ
ÿ
@ÿ6"ÿ$ÿ
7ÿ
$$ÿ42$ÿ"ÿ!ÿ
ÿ
2
"ÿ"1
ÿ
ÿ22"$12ÿ#
.$<ÿ"1ÿ
ÿ22"$12<ÿ4"$ÿ
ÿ0
.!"$ÿ
ÿA.0ÿ
ÿ-.ÿ
#ÿ
$ÿ
%&'()*+ÿ
$ÿ
ÿ
Bÿ-1ÿ!ÿ
2"
ÿ
ÿ!ÿ$ÿ
:
7ÿ"ÿA.<ÿ"1ÿ
"ÿ"1ÿ2#
#
"7ÿ"1
"ÿ"ÿ
ÿ#ÿ
30ÿ
$ÿ
ÿ
2
"ÿ
ÿ-.ÿ
#ÿ
$ÿ
%&'()*+ÿ-.ÿ
ÿ
Cÿÿ0$
0
"
ÿÿ!ÿ
ÿ
2
"ÿ
"1ÿ"1
ÿ
ÿ2
"$12ÿ$ÿ"1
"ÿ"1$ÿ!
:$ÿ"ÿ!ÿ0
.
"ÿÿ"1ÿ!8$ÿ
$"$ÿ"ÿ"
$ÿ"1ÿ$12ÿ"$"$ÿ
ÿ-.ÿ
ÿ 0123ÿ5ÿ
, 7ÿ
91 3ÿ 1ÿ 13ÿ ÿ
ÿÿÿ
ÿ
ÿ!
"#$ÿ
%ÿ
&ÿ
'()*+,-ÿ
&ÿ
ÿ
/ÿ"
0"ÿ
&ÿ
ÿ1
$ÿ#
2&ÿ$ÿ
&ÿ
ÿ$3ÿ
#ÿ$ÿ
&ÿ
1$
ÿ43&ÿ&ÿ%
5&ÿ1
$&6ÿ&$237&ÿ
ÿ
$ÿ&5%8$ÿ$ÿ1&
ÿ
%$&ÿ
ÿ$3ÿ
#ÿ"&ÿ%
251$ÿ
7ÿ
&ÿ%
5&ÿ$ÿ&ÿ
&ÿ$ÿ$
&
ÿ&3
&ÿ
ÿ&$2ÿ$3
ÿ
1
$&31ÿ$&$&ÿ
ÿ45ÿ
%ÿ
&ÿ
'()*+,-ÿ45ÿ
ÿ
9ÿ:ÿ7ÿ$ÿ#
;#0ÿ$&ÿ&3
37&6ÿ
5<ÿ
ÿ
#6&ÿ#
"#$ÿ#5&$ÿ
$$#1$ÿ$ÿ#
;#0ÿ$3ÿ&$2ÿ1ÿÿ$3ÿ
"ÿ5<ÿÿ$3ÿ&$26&ÿ=$&ÿ
5=ÿ
ÿ45ÿ
%ÿ
&ÿ
'()*+,-ÿ45ÿ
ÿ
>ÿ:
ÿ#
"#$ÿ1
$&ÿÿ
ÿ#
ÿ7&"7ÿ$ÿ#
;#0ÿ$3ÿ
#6&ÿ;1$7ÿ1
$&ÿ
ÿ$3ÿ5$ÿ?
<ÿ$3&ÿÿ
&ÿ#
;#0ÿ$3ÿ&$237&6ÿ
$3ÿ
&ÿ
ÿ$3ÿ5$ÿ?
ÿ
ÿ45ÿ
%ÿ
&ÿ
'()*+,-ÿ
&ÿ
ÿ
@ÿ:ÿ7ÿ$ÿ#
;#0ÿ$&ÿ&3
37&6ÿ
5<ÿ
ÿ
#6&ÿ#
"#$ÿ#5&$ÿ
$$#1$ÿ$ÿ#
;#0ÿ$3ÿ;1$7ÿABCÿ
ÿ45ÿ
%ÿ
&ÿ
'()*+,-ÿ
&ÿ
ÿ
DEÿ:ÿ7ÿ$ÿ#
;#0ÿ$&ÿ&3
37&6ÿ
5<ÿ
ÿ
#6&ÿ#
"#$ÿ#5&$ÿ
$$#1$ÿ$ÿ#
;#0ÿ$3ÿ&$2ÿ1ÿÿ
ÿ
&1
ÿ$
"$ÿ7
$ÿ
ÿ45ÿ
%ÿ
&ÿ
'()*+,-ÿ
&ÿ
ÿ
Dÿ&ÿ
ÿ&5$ÿ
ÿ
ÿ&
7
&ÿ5"ÿ75"ÿ$3ÿ1
&$ÿ7
7<ÿ$3ÿ3
&ÿ%ÿ
ÿ&$"ÿ15&3ÿ$ÿ#1ÿ%5&&&ÿ
$3&ÿ
ÿ45ÿ
%ÿ
&ÿ
'()*+,-ÿ45ÿ
ÿ
DDÿ43ÿ
ÿ#
?ÿ$?1&ÿ
ÿ5$3
ÿ%5&&&ÿ%3
ÿÿ;
#1ÿ&ÿ3ÿ;5$&ÿ17ÿ
#
$ÿ$3
$ÿ$3?ÿ
2ÿ&ÿ$ÿ$ÿ%
2&ÿ
7ÿ$ÿ&$237&ÿ:$ÿ&ÿ"
ÿ$ÿ17ÿ&53ÿ
#
$ÿ$ÿ%
2&<ÿ%5$ÿ$ÿ&ÿ$ÿ"
ÿ$ÿ
17ÿ$ÿ$ÿ&$237&ÿ%
5&ÿ$3?ÿ
ÿ$3ÿ&ÿ
ÿ$3ÿ
#<ÿ$ÿ5$&7&ÿ
ÿ45ÿ
%ÿ
&ÿ
'()*+,-ÿ
&ÿ
ÿ 0123ÿ5ÿ