Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
,UL ee<br />
hLuittLh WU!it<br />
`|ih 2fff<br />
_|ih4 , @4 WG tih 5ii|<br />
E2fI Lt_ih @ iULL4) LTih@|} _ih @ € i_ i U@}i h@|i hi}4i 5TTLti |@| <br />
|i Uhhi| TihL_ |i 4@h!i| U*i@h} i U@}i h@|i t }ih |@ |i € i_ i U@}i h@|i<br />
E@ `@| |)Ti Lu |h@t@U|Lt 4t| |i 4Li|@h) @|Lh|it i}@}i |L 4@|@ |i € i_<br />
i U@}i h@|i @| |t Uhhi| *ii*q<br />
Mhiu @tih Wu e t |i _L**@h ThUi Lu uLhi} i U@}ic |i |ihi t @ i Uitt tTT*)<br />
Lu _L**@ht @_ @ i Uitt _i4@_ uLh uLhi} i U@}i iUic |L| |ihi|L<br />
|i ThUi Lu uLhi} i U@}i L*_ Uhi@ti E_h@ @ tTT*)_i4@_ _@}h@4 AL<br />
Thii| e uhL4 ht} |L |i 4@h!i| h@|i |i 4Li|@h) @|Lh|it 4t| M) _L**@ht<br />
@_ ti** uLhi} i U@}i<br />
EM OL L*_ |t |h@t@U|L @TTi@h |i UL|h)
C 1<br />
A<br />
1+ $r<br />
C 0<br />
6}hi G<br />
<br />
E@ W4@}i |@| @ }hi@| L@|L t _tULihi_ U ** }hi@|*) Uhi@ti u|hi UL4i<br />
@UhLit@ OL _Lit |i ThL_U|L LTTLh||it ti| tu|q `@| L*_ @TTi<br />
|L ULt4T|L u @UhLit@ __ L| @i @UUitt |L Lh*_ U@T|@* 4@h!i|tq w@Mi* |t<br />
ULt4T|L TL| <br />
Mhiu @tih 5*LTi MiUL4it t|iiTih @t |ihi @hi 4Lhi LTTLh||it uLh u|hi ThL_U<br />
|L Wu |ihi ihi L @UUitt |L Lh*_ U@T|@* 4@h!i|t |i ULt4T|L L*_ tu|<br />
|L@h_t |i u|hi( iUic Thiti| ULt4T|L L*_ *!i*) _iUhi@ti Etii €}hi 2<br />
EM `@| @TTit |L |i @|@h!) h@|i Lu |ihit| @UhLit@q , T*@<br />
Mhiu @tih Ai @|@h!) h@|i htitc @t |i |ihit| h@|i ihi |ihi t L _ithi uLh<br />
|h@_i u|hi }LL_t hi^hit @ }ih h@|i |L hiiU| |i }ih ThL_U|L LTTLh<br />
||it<br />
EU Wu @UhLit@ @t @UUitt |L |i Lh*_ U@T|@* 4@h!i|t @| @TTit |L ThL_U|L @_<br />
ULt4T|Lq , T*@ w@Mi* |i i ULt4T|L TL| <br />
Mhiu @tih @UhLit@ ** ThL_Ui ihi n eo t |@}i| |L |i ThL_U|L *i<br />
At ** L*i 4Lhi u|hi ThL_U|L W| ** |i MLhhL @}@t| |t |L €@Ui<br />
Uhhi| ULt4T|L hhi| ULt4T|L ** Mi }ih |@ T@h| EMc tii €}hi<br />
G<br />
E_ 5TTLti @UhLit@ @t @ *@h}i iULL4) `@| L*_ @TTi |L |i Lh*_ |ihit| h@|i<br />
}i |t _tULih)q<br />
Mhiu @tih Ai Lh*_ |ihit| h@|i L*_ htic MiU@ti @UhLit@ t L _tt@}<br />
At U@tit @ i Uitt Lh*_ _i4@_ uLh Uhhi| ULt4T|Lc tL |i ThUi 4t| hti<br />
2
C 1<br />
1+ $r<br />
B<br />
A<br />
C 0<br />
6}hi 2G<br />
C 1<br />
1+ $r<br />
C<br />
C 0<br />
6}hi G
EfI Lt_ih |i t4T*i ki)it@ 4L_i* Lu UL4i _i|ih4@|L |i LTi iULL4)<br />
#L4it|U @MtLhT|L |t 4L_i* t }i M)<br />
' n kt qo<br />
E<br />
ihi t t hi@* L|T| EhiU@** |@| ThUit @hi € i_ |i 4L_i*c o t |i hi@* h@|i Lu |ihit|c<br />
@_ k t *itt |@ Li Ai |h@_i M@*@Ui Ei| i TLh|t U@ Mi h||i @t<br />
f ' A 6t n ^<br />
E2<br />
ihi ^ t |i hi@* i U@}i h@|ic @_ A t |i @|LL4Lt |h@_i M@*@Ui<br />
E@ W i^@|L E2 |i igiU| Lu @ U@}i ^ L f t TLt|i `) 4}| i i TiU| |t<br />
|L Mi |hiq Wt |t 4Lhi *!i*) |L Mi |hi |i tLh| h Lh |i *L} hq , T*@<br />
Mhiu @tih W| t *!i*) |L Mi |hi u i TLh|t @_ 4TLh|t @hi tit|i |L |i hi*@|i<br />
ThUic ^ Ai 4Lhi tit|i |L |t ThUi |i 4Lhi *!i*) |i |h@_i M@*@Ui **<br />
htic MiU@ti | ** Lgti| |i Uhi@ti_ ULt| Lu 4TLh|t i |i hi@* i U@}i h@|i<br />
Uhi@tit At igiU| t 4Lhi *!i*) |i *L}ih h MiU@ti i TLh|t @_ 4TLh|t<br />
** @_t| 4Lhi u**) | |4ic *i |i ThUi igiU| t t|@|@iLt<br />
EM Bh@T f @t @ uU|L Lu t OL _Lit |t uU|L tu| u ^ htit Lh u uLhi} UL4i<br />
_iUhi@titq<br />
Mhiu @tih f t @ _iUhi@t} uU|L Lu t c _i |L |i u@U| |@| 4TLh|t hti |<br />
UL4i Wu ^ Uhi@tit |i Uhi tu|t T@h_t Wu uLhi} UL4i htit |i Uhi @*tL<br />
tu|t T@h_t EMiU@ti A htit<br />
EU #i€i t @t 7U #h@ |i 7U Uhi @t @ uU|L Lu t OL L*_ |t uU|L<br />
tu| u |i |ihit| h@|i ui** Lh u }Lih4i| tTi_} Uhi@ti_<br />
Mhiu @tih At t @ TLt|i uU|L Lu UL4ic @_ @t @ |ihUiT| @| n qo<br />
Ai t*LTi Lu |t Uhi t i^@* |L @ Etii €}hi eG<br />
E_ , T*@ ) 7U ' f t |i i^*Mh4 UL_|L uLh |i }LL_t 4@h!i|<br />
Mhiu @tih ,^*Mh4 |i }LL_t 4@h!i| 4i@t |@| UL4i i^@*t @}}hi}@|i<br />
_i4@_c Lh t ' n U n C n f ' n f OiUic t ' f t t| @<br />
i^@*i| @) |L h|i |i UL_|L Ai TL| t |@| |L|@* UL4i U@ Mi tTi|<br />
i|ih L _L4it|U }LL_t E@MtLhT|L Lh uLhi} }LL_t Ei| i TLh|t<br />
Ei 5TTLti |@| @| |i |@* i^*Mh4 |i }LL_t 4@h!i| |@| f : fc M| |@| t t<br />
Mi*L |i u**i4T*L)4i| *ii* Lu L|T| `i @i |L TL*U) t|h4i|tG i Ti_|hi<br />
U@}} @_ i Ti_|hi t|U} Wu i t |L @i u** i4T*L)4i| @_ @ |h@_i<br />
M@*@Ui i^@* |L 3ihLc @| t |i @TThLTh@|i @tt}4i| Lu t|h4i|t |L |@h}i|tq<br />
`) _Lit | 4@||ihq<br />
Mhiu @tih `i tL*_ ti i Ti_|hi U@}} |L tu| 7 U _Lc Tih@Tt M)<br />
Uhi@t} }Lih4i| tTi_} Lh U||} o At L*_ h@ti UL4i M| U@ti i|<br />
i TLh|t |L _iUhi@ti `i tL*_ |i ti i Ti_|hi t|U} EU@}it A Lh ^<br />
|L tu| f T@h_t Etii €}hi D iU@ti |@**) f : f i UL*_ }i| @@)<br />
| |i LTTLt|i @tt}4i| |t U@tic M| }iih@* | L*_ Mi ThLM*i4@|U<br />
Ai L*) hi@tL | t L| |t U@ti t |@| uLh ML| |@h}i|t i ii_ |L h@ti t <br />
e
T<br />
+ φq<br />
S-I<br />
0<br />
− A+<br />
βr<br />
NX<br />
6}hi eG<br />
5TTLtic Liihc |@| |@**) f f Ai 4ThL} |i |h@_i M@*@Ui L*_<br />
4Li t u@h|ih uhL4 u** i4T*L)4i| W |@| U@ti i ii_ |L ti |i TL*U) | |i<br />
UL4T@h@|i @_@|@}i |L |i |@h}i|c @_ i Ti_|hi t|U} @t @ UL4T@h@|i<br />
@_@|@}i | hitTiU| |L |i |h@_i M@*@Ui<br />
e EfI Lt_ih @ U*Lti_ iULL4) LTih@|} _ih |i }L*_ t|@_@h_ 5TTLti |@| |@**)<br />
|i ThUi *ii* t *L}h i^*Mh4 L tTTLti |@| @ i _tULih) Lu }L*_ LUUht<br />
E| |i UL|h)c tL |@| |i ULt| Lu ThL_U} }L*_ t *Lih<br />
E@ `@| @TTit |L |i ThUi *ii* Ehi*@|i |L |i ThUi Lu }L*_ |i i i^*Mh4q<br />
Mhiu @tih Ai i i^*Mh4 L*_ @i @ }ih ThUi *ii* hi*@|i |L }L*_c @t<br />
|i t|LU! Lu }L*_ L*_ Mi }ih 5ii €}hi S ihi |i Uhi@ti_ ThL_U|L Lu<br />
}L*_ EuhL4 f |L U@tit |i t|LU! |L hti @_ |i hi*@|i ThUi Lu }L*_ |L u@**<br />
EM L tTTLti |@| |i iULL4) t LTi @*)3i |i igiU|t Lu |i }L*_ _tULih) E@}@<br />
@tt4i | t @ _L4it|U _tULih) `@| @TTit |L |i ThUi *ii* Ehi*@|i |L |i ThUi<br />
Lu }L*_q `** |i ThUi *ii* U@}i 4Lhi Lh *itt |@ T@h| E@q , T*@<br />
Mhiu @tih BL*_ tTT*) @}@ ** Uhi@ti |i ThUi *ii* hi*@|i |L }L*_ | Lh<br />
}ih _L4it|U ThUi *ii* 4@!it t *itt UL4Ti||i Lh*_ 4@h!i|t At **<br />
U@ti Lh |h@_i M@*@Ui |L _i|ihLh@|i @_ }L*_ |L L L| Lu |i UL|h) At<br />
** Lgti| |i Uhi@ti }L*_ |L tL4i i |i| OiUic |i i^*Mh4 |i ThUi<br />
*ii* ** L| hti @t 4U 5L4i Lu |i }L*_ t ti_ @MhL@_ |t U@ti W T@h|<br />
E@ |i hti Lh ThUi *ii* _iTi_t L |i |L|@* Uhi@ti }L*_ UL4T@hi_ |<br />
|i _L4it|U _i4@_ uLh }L*_ W |i LTi iULL4) | t |i Lh*_ _i4@_ uLh }L*_<br />
|@| t Uh|U@*<br />
EU 5TTLti |@| |i 4Li|@h) @|Lh|it |t iULL4) @|i_ |L Thii| |i ThUi<br />
4Li4i|t |@| )L _ihi_ T@h| EM `@| TL*Uit 4}| |i) Thti |L @UUL4T*t<br />
|tq Wu |i) @_ihi |L |i }L*_ t|@_@h_ ** |iti TL*Uit Lh! |i *L} hq , T*@<br />
D
T1 + φ q<br />
SI 0<br />
T<br />
+ φq<br />
SI 1<br />
0<br />
− A + r<br />
0 β<br />
Y F<br />
NX 1<br />
NX 0<br />
− A + r<br />
1 β<br />
6}hi DG<br />
PG<br />
P<br />
⎛ PG<br />
⎞<br />
⎜ ⎟<br />
⎝ P ⎠<br />
0<br />
D<br />
N<br />
+ D<br />
M<br />
PG<br />
P<br />
⎛ PG<br />
h<br />
⎜<br />
⎝ P<br />
0 ,<br />
y ⎞<br />
y ⎟<br />
f ⎠<br />
shift due to gold<br />
discovery<br />
⎛<br />
h<br />
P G<br />
⎜<br />
⎝ P<br />
1 ,<br />
y ⎞<br />
y ⎟<br />
f ⎠<br />
⎛ PG<br />
⎞<br />
⎜ ⎟<br />
⎝ P ⎠<br />
*<br />
δf<br />
⎛ P<br />
⎜<br />
⎝ P<br />
G ,<br />
y ⎞<br />
⎟<br />
⎠<br />
G 0 G* G g1 g* g2 g<br />
6}hi SG<br />
S
Mhiu @tih AL Thii| |i _L4it|U ThUi *ii* uhL4 |@**) Uhi@t} t i@t)G |i<br />
@|Lh|it UL*_ Uhi@ti |i _i4@_ uLh 4Li|@h) }L*_ M) Uhi@t} |i hitihi<br />
h@|L At L*_ Lgti| |i hti |i }L*_ t|LU!c *i@} |L|@* 4Li) t|LU! @u<br />
uiU|i_ iU@ti |i hi*@|i ThUi Lu }L*_ _Lit L| u@** |i }L*_ t|LU! ** UL|i<br />
|L Uhi@ti @_ |i @|Lh|it 4t| UL|i |L |}|i 4Li|@h) TL*U) | | t<br />
ui@tM*i @t i !iiT @UU4*@|} }L*_<br />
E_ L tTTLti |@| t|i@_ Lu @ }L*_ _tULih) |ihi @t @ i L}iLt Uhi@ti hi@*<br />
UL4i |i iULL4) `@| @TTit |L |i _i4@_ uLh }L*_q `@| @TTit |L |i<br />
ThUi *ii* Ehi*@|i |L |i ThUi Lu }L*_ |i LTi iULL4) ihtL Lu |i 4L_i*q `@|<br />
@TTit |L hit|Lhi i^*Mh4q Wu |i @_t|4i| |L i^*Mh4 |@!it |4i ) 4}|<br />
|i }L*_ t|@_@h_ Mi t|hittu*q , T*@<br />
Mhiu @tih Ai _i4@_ uLh }L*_ Uhi@tit | }i }L*_ t|LU!t |i hi*@|i ThUi<br />
Lu }L*_ Uhi@tit Ai u@** |i ThUi *ii* 4@!it t 4Lhi UL4Ti||i h i|<br />
i TLh|t Uhi@ti @_ }L*_ t|LU!t htic hit|Lh} |i hi*@|i ThUi Lu }L*_ |L |t |@*<br />
*ii* Wu |t @_t|4i| |@!it @ *L} |4i |i i ** @i @ u@**} ThUi *ii* <br />
|i |ih4 At UL*_ U@ti _i@|L@h) Thitthit @_ hiUittL Wu |i @_t|4i|<br />
t t*L TL*U)4@!iht 4@) t |L @U| MiuLhi |i @|L4@|U @_t|4i| |@!it T*@Ui<br />
.