Lambe ini, Luca
Wo king Pape
Quan um Mechanics and Ma hema ical Economics a e
Isomo phic. John on Neumann be ween Physics and
Economics
Quade ni - Wo king Pape DSE, No. 370
P o ided in Coope a ion wi h:
Uni e si y o Bologna, Depa men o Economics
Sugges ed Ci a ion: Lambe ini, Luca (2000) : Quan um Mechanics and Ma hema ical Economics a e
Isomo phic. John on Neumann be ween Physics and Economics, Quade ni - Wo king Pape DSE,
No. 370, Alma Ma e S udio um - Uni e si à di Bologna, Dipa imen o di Scienze Economiche (DSE),
Bologna,
h ps://doi.o g/10.6092/unibo/amsac a/4939
This Ve sion is a ailable a :
h ps://hdl.handle.ne /10419/159211
S anda d-Nu zungsbedingungen:
Die Dokumen e au EconS o dü en zu eigenen wissenscha lichen
Zwecken und zum P i a geb auch gespeiche und kopie we den.
Sie dü en die Dokumen e nich ü ö en liche ode komme zielle
Zwecke e iel äl igen, ö en lich auss ellen, ö en lich zugänglich
machen, e eiben ode ande wei ig nu zen.
So e n die Ve asse die Dokumen e un e Open-Con en -Lizenzen
(insbesonde e CC-Lizenzen) zu Ve ügung ges ell haben soll en,
gel en abweichend on diesen Nu zungsbedingungen die in de do
genann en Lizenz gewäh en Nu zungs ech e.
Te ms o use:
Documen s in EconS o may be sa ed and copied o you pe sonal
and schola ly pu poses.
You a e no o copy documen s o public o comme cial pu poses, o
exhibi he documen s publicly, o make hem publicly a ailable on he
in e ne , o o dis ibu e o o he wise use he documen s in public.
I he documen s ha e been made a ailable unde an Open Con en
Licence (especially C ea i e Commons Licences), you may exe cise
u he usage igh s as speci ied in he indica ed licence.
h ps://c ea i ecommons.o g/licenses/by-nc/3.0/
Txdqwxp Ph kdql dqg
Pdwkhpdwl do H q pl duh
L p uskl
M kq y q Qhxpdqq ehwzhhq Sk| l dq
g H q pl
4
Ox d Odpehuwlql
Ghsduwphqw i H q pl
Xqlyhu lw| i E o jqd
Vwudgd Pdjjl uh 78/ 73458 E o jqd/ Lwdo|
id{= .6<0384053<5997
h0pdlo= odpehuwlC se 1xqle 1lw
Iheuxdu| 5</ 5333
4
L z xog olnh w wkdqn Hqql Fdyd}}xwl/ Pd lp Pdulqd l/ Vwhskhq Pduwlq/
Pdqxhod P d dqg Ul dug U yhool i u pphqw dqg gl x l q1 Wkh x xdo
gl odlphu dssolh 1
De wud w
D phwk g o jl do gl x l q l su s hg/ dlplqj dw k zlqj wkdw jdph wkh0
u| lq sduwl xodu +dqg pdwkhpdwl do h q pl lq jhqhudo, dqg xdqwxp
ph kdql duh l p uskl 1 Wkl uh xow uholh q wkh h xlydohq h i wkh wz
ixqgdphqwdo shudw u hpso |hg lq wkh wz hog / qdpho|/ wkh h{sh whg ydoxh
lq h q pl dqg wkh ghq lw| pdwul{ lq xdqwxp sk| l 1 Wkl lq lghq h
dq eh wud hg ed n w wkh qwulexwl q i y q Qhxpdqq lq e wk gl lsolqh 1
MHO Fod l dwl q=
E58/ E74/ F:3
Nh|z ug =
h{sh whg ydoxh/ ghq lw| pdwul{/ xq huwdlqw|
4 Lqwu gx wl q
Ryhu wkh od w iwhhq |hdu / d ju zlqj dp xqw i dwwhqwl q kd ehhq ghy whg
w wkh kl w u| i jdph wkh u|1 Dp qj wkhu uhd q / wkl lqwhuh w dq odujho|
eh mx wlhg q wkh ed l i wkh Q eho sul}h w Qd k/ Kdu dq|l dqg Vhowhq lq
4<<71
4
K zhyhu/ wkh olwhudwxuh ghdolqj zlwk wkh kl w u| i jdph wkh u| pdlqo|
dg sw dq
lqqhu
shu sh wlyh/ l1h1/ dq dqjoh wkdw doo z x w uh q wux w wkh
ghyho sphqw i wkl xe0gl lsolqh xqghu wkh jhqhudo khdglqj i h q pl 1
P| dlp l glhuhqw/ w wkh h{whqw wkdw L lqwhqg w su s h dq lqwhusuhwdwl q
i wkh i updo uhodwl q kls ehwzhhq jdph wkh u| +dqg h q pl , dqg wkh
kdug lhq h 1
D odujho| d hswhg ylhz pdlqwdlq wkdw wkh i xqgdwl q i e wk jdph wkh0
u| dqg/ lq jhqhudo/ qwhps udu| pdwkhpdwl do h q pl duh w eh i xqg
lq
Wkh Wkh u| i Jdph dqg H q pl Ehkdyl u
+y q Qhxpdqq dqg P u0
jhq whuq/ 4<
77,1
5
Iu p wkdw z un qzdug / zh e huyh wkh zlgh suhdg x h
i wkh shudw u nq zq d
h{sh whg ydoxh
lq h q pl 1 Wudglwl qdoo|/ dqg
uuh wo|/ wkh u w i x k shudw u duh wud hg ed n w wdwl wl + hh Il k0
exuq dqg Zdnnhu/ 4<<8/ dqg wkh uhihuhq h wkhuhlq,1 K zhyhu/ wkl ylhz
4
Rq wkh kl w u| i jdph wkh u|/ hh Dxpdqq +4<;8/ 4<;:/ 4<<<,/ Zhlqwudxe +4<<5,/
Oh qdug +4<<7/ 4<<8, dqg P|hu q +4<<<,/
lqwhu dold
1 Rq wkh dssudl do i wkh u oh i jdph
wkh u| lq qwhps udu| h q pl / hh ydq Gdpph dqg Zhlexoo +4<<8,1
5
Lq y q Qhxpdqq dqg P ujhq whuq +4<77,/ wkh q hsw i wdeoh hw i u shudwlyh
jdph psohphqw wkh plqlpd{ wkh uhp +y q Qhxpdqq/ 4<5;, i u q q shudwlyh jdph 1
K zhyhu/ wkh odwwhu l dssol deoh qo| lq }hu xp jdph 1 Qd k +4<83, lqwu gx hg dq
h xloleulxp q hsw i u q q0}hu xp q q shudwlyh jdph / dqg wkh edujdlqlqj oxwl q
i u shudwlyh jdph +Qd k/ 4<84,1
4
g h q w jud s dq lqwhuh wlqj d sh w lq pp q ehwzhhq pdwkhpdwl do h 0
q pl dqg sk| l / lq sduwl xodu xdqwxp sk| l / wkdw l / wkh id w wkdw e wk
wkh ulh wudq plw d odujho| dqdo j x ph djh q huqlqj xu nq zohgjh + u
uhsuh hqwdwl q, i uhdo z uog skhq phqd1 Rxu
h{ dqwh
nq zohgjh +l1h1/ xu
i uh d wlqj dsdelolw|, l ghqhg lq wkh dph su edelol wl whup / lqghshq0
ghqwo| i zkhwkhu zh h{dplqh wkh ehkdyl xu i xedw pl sduwl oh u wkh
ehkdyl xu i up dqg q xphu 1
Zkdw L zdqw w k z lq wkh uhpdlqghu l wkdw wkl lq lghq h +s lqwlqj
xowlpdwho| w wkh lghd wkdw xu nq zohgjh l p ghoohg lq wkh dph zd| luuh0
sh wlyho| i wkh sh l hog
6
,/ kd ehhq odujho| kdshg wku xjk wkh d wlylw|
i d lqjoh uh hdu khu/ M kq y q Qhxpdqq/ zk / yhu d g }hq |hdu +4<650
77, kd c{hg* wkh ed l lghd lq e wk gl lsolqh e| jlylqj wkhp wkh dph
phwk g o j|/ wkx pdnlqj wkhp odujho|
l p u
skl
w hd k wkhu1 Wkh nh| w
wkl lqwhusuhwdwl q l wkh shudw u odehoohg d
h{sh whg ydoxh
e| h q pl w
dqg
ghq lw| pdwul{
e| sk| l l w 1
Lq wkh u w hglwl q +lq Jhupdq, i
Pdwkhpdwl do I xqgdwl q i Txdqwxp
Ph kdql
/ y q Qhxpdqq +4<65, dg sw wkh whup
Huzduwxqj zhuw
/ zkl k
lq Hqjol k l
h{sh wdwl q ydoxh
1 Wkl do dsshdu lq y q Qhxpdqq dqg
P ujhq whuq +4<77,/ zkloh lq wkh i oo zlqj h q pl olwhudwxuh lw x xdoo|
eh ph
h{sh whg ydoxh
1 Lq sk| l /
h{sh wdwl q ydoxh
l x hg w lqgl dwh
wkh hohphqwdu| q wl q i wkh pdwkhpdwl do h{sh wdwl q i d udqg p yduldeoh/
zkloh
ghq lw| pdwul{
lqgl dwh / udwkhu o ho| shdnlqj/ wkh udqg p xw ph
i dq h{shulphqw1
Lq wkh i oo zlqj h wl q/ L hu d x lq w ylhz i wkh i updo h xlydohq h
6
Rq wkl l xh/ hh Shqu h +4<;<,1
5

ehwzhhq wkh wz wkh ulh +dqg wkh zd| wkh| exlog xs wkhlu suhgl wlyh s zhu,/
wku xjk d zhoo nq zq sdudeoh lq
xdqwxp sk| l 1
5 Wkh l p uskl p ehwzhhq pdwkhpdwl do h 0
q pl dqg xdqwxp sk| l = d nhw k
Txdqwxp sk| l +dqg lw su shu xe hw/ xdqwxp ph kdql , dq dssu {0
lpdwho| eh q lghuhg +q w doo sk| l l w djuhh q wkl pdwwhu, d d jhq0
hudol dwl q i Qhzw qldq sk| l +dqg ph kdql ,1 Lq sduwl xodu/ zkhq wkh
skhq phqd ehlqj lqyh wljdwhg lqy oyh +l, shhg zkl k duh q lghudeo| o zhu
wkdq wkh shhg i oljkw lq yd xxp> +ll, x! lhqwo| o z judylw|> dqg +lll, e0
mh w zkl k duh qhlwkhu w pdoo q u w elj/ wkhq qh dq su hhg d uglqj
w wkh wdqgdug Qhzw qldq p gho1 hw/ zkhq lw ph hlwkhu w wkh yhu|
ed l sduwl oh +h1j1/ xe0dw pl sduwl oh olnh hoh wu q ,/ u w wkh ehkdyl xu
i emh w kdud whul hg e| dq h{wuhpho| kljk judylwdwl qdo i u h +h1j1/ eod n
k oh / xd du dqg sxo du ,/ xdqwdo ihdwxuh eh ph uhohydqw wkdw wkh|
dqq w eh gl uhjdughg1
D dq loox wudwlyh h{dpsoh/ q lghu wkh w u| wudglwl qdoo| nq zq d
V kuùglqjhu* sdudg {
u
V kuùglqjhu* dw0lq0wkh0e {
/ zkl k L dp de xw
w whoo d uglqj w d
yxojdwd
pp qo| dg swhg lq wkh xuuhqw olwhudwxuh lq
wkh hog1
7
7
Huzlq V ukùglqjhu/ w jhwkhu zlwk E ku/ Hlq whlq/ Glud / Khl hqehuj dqg Sdxol/ l qh
i wkh i xqglqj idwkhu i xdqwxp sk| l 1 Wkh uhpdlqghu i wkl h wl q e uu z iu p
Kdz
nlqj dqg Shqu h +4<<9, dqg Shqu h +4<<:,1 I u ixuwkhu +dqg px k p uh wh kql do,
uhdglqj / hh Vdnxudl +4<;8,/ V kzdeo +4<<5,/ dqg Jd l u zl } +4<<9,/
lqwhu dold
1
6
Wkl sdudg { uhihu w dq h{shulphqw/ zkhuh d dw l o nhg lq d e {/ lq
iu qw i d kdqgjxq/ zkl k l o dghg1
8
Wkh e { l sd xh w e wk oljkw dqg
xqg/ wkdw wkh sk| l l w px w shq lw w e huyh wkh dw* qglwl q 1
Wkh wuljjhu l olqnhg w d hq u/ o dwhg xw lgh wkh e {/ lq iu qw i d exoe1
D xph wkh sk| l l w dq zlw k q wkh exoe/ su gx lqj d lqjoh xdqwxp
i oljkw +d sk w q, dw d wlph1 Wkh hq u phd xuh wkh slq i wkh sk w q1
Lq wkh uhpdlqghu/ L zloo d xph qyhqwl qdoo| wkh i oo zlqj1 Li wkh sk w q
u wdwh uljkwzdug +l1h1/ wkh slq l s lwlyh,/ wkhq wkh hq u sxoo wkh u sh
+dqg wkh wuljjhu,/ dqg wkh kdqgjxq k w wkh dw ghdg1 Li lq whdg wkh sk w q
u wdwh ohiwzdug +l1h1/ wkh slq l qhjdwlyh,/ wkhq wkh hq u g h q w sxoo wkh
u sh +dqg wkh wuljjhu,/ wkdw wkh dw xuylyh 1
Wkh sdudg { wdnh sod h lq wkh sk| l l w* plqg ehi uh wkh h{shulphqw l
duulhg xw/ u/ h xlydohqwo|/ ehi uh kh shq wkh e { w hh zkhwkhu wkh dw
l wloo dolyh u q w1 Wkh sk| l l w nq z wkdw/
h{ s w
/ wkh dw l j lqj w
eh hlwkhu ghdg u dolyh1 K zhyhu/
h{ dqwh
/ wkh wz wdwh i wkh | whp0 dw
+l1h1/
dolyh
dqg
ghdg
, d zhoo d wkh wz wdwh i wkh z uog +wkdw dq eh
odehoohg d
wkh kdqgjxq k w eh dx h wkh slq zd s lwlyh
/ dqg
wkh kdqgjxq
glgq
*w k w eh dx h wkh slq zd qhjdwlyh
, h{l w lq wkh h{shulphqwhu*
plqg1 Wkl sdudg { shu l w xqwlo kh shq wkh e { w e huyh wkh dw*
8
Wkl dq eh ylhzhg d d
Jhgdqnhqh{shulphqw
+wk xjkw h{shulphqw,/ lq wkdw zh px w
q w qh h dulo| o n d dw lqw d e { w yhuli| wkh ydolglw| i zkdw i oo z 1 Lq jhqhudo/ d
Jhgdqnhqh{shulphqw
l q l whqw zlwk wkh nq zq odz i sk| l / hyhq wk xjk lw pd|
q w eh wh kql doo| ihd leoh1 V / phd xulqj wkh d hohudwl q gxh w judylw| q wkh xuid h i
wkh xq l d
Jhgdqnhqh{shulphqw
/ zkhuhd phd xulqj wkh G ssohu kliw i xqoljkw d hhq
iu p d sd h kls p ylqj zlwk wzl h wkh yho lw| i oljkw l q q hq h +Jd l u zl }/ 4<<9/
s1 54/ iq1 4
7,1 Lq wkh suh hqw d h/ uhsod h
wh kql doo| ihd leoh
zlwk
s olwl doo| uuh w
1
7
khdowk qglwl q 1
L zloo i updol h wkh h{shulphqw e| lqwu gx lqj wkh i oo zlqj=
Ghqlwl q 4

i
S@cS_
j
l wkh zdyh ixq wl q/ u wkh wdwh yh w u i wkh
| whp +wkh dw,1
Lq Ghqlwl q 4/ lqwxlwlyho|/
S@
'
wkh dw l dolyh>
S_
'
wkh dw l ghdg1
P uh yhu/
Ghqlwl q 5
i
i
 c_
j
l wkh yh w u i wkh wdwh i wkh z uog1
Lq Ghqlwl q 5/ lqwxlwlyho|/

'
wkh kdqgjxq k w +eh dx h wkh slq
zd s lwlyh,>
_
'
wkh kdqgjxq glg q w k w +eh dx h wkh slq zd
qhjdwlyh,1
Ilqdoo|/ zh kdyh
Ghqlwl q 6
)
i
S@cS_
j
l wkh wdwh yh w u i wkh sk| l l w duu|lqj xw
wkh h{shulphqw1
Wkh uhd q zk|
)
hhp w lq lgh zlwk wkh zdyh ixq wl q

zloo eh ph
ohdu lq wkh uhpdlqghu1 Wkh
h{ dqwh
yhuodsslqj ehwzhhq wkh wdwh i wkh
| whp/ l d xqwhg i u e| wkh
w wdo wdwh yh w u i wkh | whp
=
m

|J|
l
'
/
m
S@
l
n
4
m
S_
l
+4,
zkhuh e wk
/
dqg
4
eho qj w
F
dqg
ml
l doohg
nhw
1 Lw psohphqw
km
l doohg
eud
/ dqg
kml
l doohg
Glud * eud nhw
/ diwhu S1D1P1 Glud zk
lqwu gx hg wkl whuplq o j| lq 4<63 + hh Glud / 4<63/ 4<8;
e
> hh do Glud /
4<58,1
8
D q d wkh h{shulphqwhu shq wkh e { w e huyh wkh wdwh i wkh
| whp/ wkh zdyh ixq wl q

oods h
/ wkdw l / wkhuh wdnh sod h wkh 0 doohg
uhgx wl q i wkh wdwh yh w u
m

|J|
l

Khq h/ wkh h{shulphqwhu e huyh hlwkhu
S
@
u
S_
/ exw xuho| q w e wk wdwh dw wkh dph wlph1 Rq wkh qwudu|/ d
o qj d wkh h{shulphqwhu g h q w shq wkh e {/ wkh wz wdwh
h{l w lq d
xdqwdo hq h
1
9
I u uhd q wkdw L g q w gzhoo xs q khuh/
/
dqg
4
duh psoh{ qxpehu 1
:
Lq sduwl xodu/ zkdw L dp lqwhuh whg lq/ l wkh lqi updwl q wkdw wkh p gxox
i e wk
/
dqg
4
l h xdo w

*
s
2

W wkh xduh/ wkl |lhog

*
2
c
zkl k l wkh
su edelolw| wkdw wkh sk w q kdyh hlwkhu d s lwlyh u d qhjdwlyh slq1 Wkl / d
zh kdoo hh lq wkh uhpdlqghu/ kd uhohydqw ehdulqj xs q p| dlp i k zlqj
wkh h{l whq h i dq l p uskl p ehwzhhq xdqwxp sk| l dqg pdwkhpdwl do
h q pl +jdph wkh u| lq sduwl xodu,1
Wkh w wdo wdwh yh w u i wkh h{shulphqwhu dq eh q wux whg w o n olnh
wkdw i wkh | whp +exw uh doo wkdw wkh wz yh w u
g q w lq lgh
,=
k
)
|J|
m
'
/
k
S@
m
n
4
k
S_
m
c/
'
4
'
*
s
2

+5,
Lq su edelol wl whup / wkh h{shulphqwhu*
h{ dqwh
nq zohgjh de xw wkh
wdwh wkdw wkh | whp dq wdnh
h{ s w
l xppdul hg e| wkh 0 doohg
ghq lw|
pdwul{
=
(
'

2
m
S@
lk
S@
m
n
2
m
S_
lk
S_
m
c
+6,
9
Sk| l l w kdyh olyho| dujxphqw q huqlqj wkh dowhuqdwlyh lqwhusuhwdwl q i x k d
wdwhphqw/ l1h1/ zkhwkhu wdwh
d
dqg
g
h{l w lq sdudooho xqlyhu h u lq wkh h{shul0
phqwhu* plqg1 D idu d wkh suh hqw sdshu l q huqhg wkl gl wlq wl q/ dowk xjk lqwuljx0
lqj/ dq eh gl uhjdughg1
:
Vhh wkh dsshqgl{1
I u ixuwkhu gl x l q/ hh/
lqwhu dold
/ Vdnxudl +4<;8,/ V kzdeo
+4<<5, dqg Jd l u zl } +4<<9,1
9
Uhihuhq h
^4` Dnhuo i/ J1 +4<:3,/ Wkh Pdunhw i u Ohp q = Txdolw| Xq huwdlqw| dqg
wkh Pdunhw Ph kdql p/
Txduwhuo| M xuqdo i H q pl
/
;7
/ 7;;08331
^5` Dxpdqq/ U1M1 +4<;8,/ Zkdw L Jdph Wkh u| Wu|lqj w D p
sol kB/
lq Duu z/ N1 dqg V1 K qnds kmd +hg 1,/
Iu qwlhu lq H q pl
/ R{i ug/
Eod nzhoo1
^6` Dxpdqq/ U1M1 +4<;:,/ Jdph Wkh u|/ lq Hdwzhoo/ M1/ P1 Plojdwh dqg S1
Qhzpdq +hg 1,/
Wkh Qhz Sdojudyh= D Gl wl qdu| i H q pl
/ O qg q/
Pd ploodq1
^7` Dxpdqq/ U1M1 +4<<<,/ Jdph Wkh u| lq L udho= O nlqj Ed nzdug dqg
I uzdug/ sdshu suh hqwhg dw DVVHW<</ Who Dyly/ R w ehu 43044/ 4<<<1
^8` Ed dq/ E1/ P1 V du lql dqg V1 ]dplu +4<<:,/ L G q
*w Zdqw w Nq z$
Fdq Lw Eh Udwl qdoB gl x l q sdshu q1 48;/ Fhqwhu i u Udwl qdolw|
dqg Lqwhud wlyh Gh l l q Wkh u|/ Wkh Kheuhz Xqlyhu lw| i Mhux dohp1
^9` Glud / S1D1P1 +4<58,/ Wkh Ixqgdphqwdo H xdwl q i Txdqwxp Ph0
kdql /
Su 1 U |1 V 1
+O qg q, D/
43<
/ 97509861
^:` Glud / S1D1P1 +4<63/ 4<8;
e
,/
Wkh Sulq lsoh i Txdqwxp Ph kdql
/
R{i ug/ R{i ug Xqlyhu lw| Suh 1
^;` Il kexuq/ S1 dqg S1 Zdnnhu +4<<8,/ Wkh Lqyhqwl q i wkh Lqghshqghq h
F qglwl q i u Suhihuhq h /
Pdqdjhphqw V lhq h
/
74
/ 4463044771
^<` Jd l u zl }/ V1 +4<<9,/
Txdqwxp Sk| l 1 Vh qg Hglwl q
/ Qhz un/
Zloh|1
46

^43` Kdznlqj/ V1 dqg U1
Shqu h +4<<9,/
Wkh Qdwxuh i Vsd h dqg Wlph
/
Sulq hw q/ QM/ Sulq hw q Xqlyhu lw| Suh 1
^44` Nohpshuhu/ S1 dqg Ph|hu/ P1 +4<;9,/ Sul h F pshwlwl q y Txdqwlw|
F pshwlwl q= Wkh U oh i Xq huwdlqw|/
UDQG M xuqdo i H q pl
/
4:
/ 94;06;1
^45` Nohpshuhu/ S1 dqg Ph|hu/ P1 +4<;<,/ Vxsso| Ixq wl q H xloleuld lq
Rolj s o| xqghu Xq huwdlqw|/
H q phwul d
/
8:
/ 45760::1
^46`
Ohodqg/ K1 +4<:5,/ Wkh u| i wkh Ilup Id lqj Xq huwdlq Ghpdqg/
Dphul dq H q pl Uhylhz
/
95
/ 5:;0<41
^47` Oh qdug/ U1M1 +4<<7,/ Uhdglqj F xuq w/ Uhdglqj
Qd k= Wkh Fuhdwl q
dqg Vwdelol dwl q i wkh Qd k H xloleulxp/
H q pl M xuqdo
/
437
/
7<508441
^48` Oh qdug/ U1M1 +4<<8,/ Iu p Sduo u
Jdph w V ldo V lhq h= y q Qhx0
pdqq/ P ujhq whuq/ dqg wkh Fuhdwl q i Jdph Wkh u|/
M xuqdo i
H q pl Olwhudwxuh
/
66
/ :630:941
^49` P|hu q/ U1 +4<<<
,/ Qd k H xloleulxp dqg wkh Kl w u| i H q pl
Wkh u|/
M xuqdo i H q pl Olwhudwxuh
/
6
:
/ 439:043;51
^4:` Qd k/ M1I1
+4<83,/ H xloleulxp S lqw lq q0Shu q Jdph /
Su hhg0
lqj i wkh Qdwl qdo D dghp| i V lhq h i wkh XVD
/
6
9
/ 7;07<1
^4;`
Qd k/ M1I1 +4<84,/ Q q0F shudwlyh Jdph /
Dqqdo i Pdwkhpdwl
/
87
/ 5;<05<81
47
^4<` Shqu h/ U1 +4<;<,/
Wkh Hpshu u*
Qhz Plqg
/ R{i ug/ R{i ug Xqlyhu0
lw| Suh 1
^53` Shqu h/ U1 +4<<:,/
Wkh Odujh/ wkh Vpdoo dqg wkh Kxpdq Plqg
/ Fdp0
eulgjh/ Fdpeulgjh Xqlyhu lw| Suh 1
^54` Vdnxudl/ M1M1 +4<;8,/
P ghuq Txdqwxp Ph kdql 1 Uhyl hg Hglwl q
/
Qhz un/ Dggl q0Zh oh|1
^55` V kzdeo/ I1 +4<<5,/
Txdqwxp Ph kdql
/ Ehuolq/ Khlghoehuj/ Vsulqjhu0
Yhuodj1
^56` ydq Gdpph/ H1 dqg M1 Zhlexoo +4<<8,/ H xloleulxp lq Vwudwhjl Lq0
whud wl q=
Wkh F qwulexwl q i M kq F1 Kdu dq|l/ M kq I1 Qd k dqg
Uhlqkdug Vhowhq/
V dqglqdyldq M xuqdo i H q pl
/
<:
/ 480731
^57` y q Qhxpdqq/ M1 +4
<
5;,/ ]xu Wkh ulh ghu Jh hoo kdiw slhoh/
Pdwhp0
dwl kh Dqqdohq
/
433
/ 5<806531
^58` y q Qhxpdqq/ M1 +4<65,/
Pdwkhpdwl kh Ju
xqgodjhq ghu Txdqwhq0
ph kdqln
/ Vsulqjhu Yhuodj/ Ehuolq0Khlghoehuj +
Pdwkhpdwl do I xqgd0
wl q i Txdqwxp Ph kdql
/ Sulq hw q/ QM/ Sulq hw q Xqlyhu lw| Suh /
4<88,1
^59` y q Qhxpdqq/ M1 h R1 P ujhq whuq +4<77,/
Wkh Wkh u| i Jdph dqg
H q pl Ehkdyl u
/ Sulq hw q/ QM/ Sulq hw q Xqlyhu lw| Suh 1
^5:` Zhlqwudxe/ U1 +4<<5/ hg1/,/
W zdug d Kl w u| i Jdph Wkh u|
/lq
Kl w u|
i S olwl do H q p|
/
57
+Vxssohphqw,1
48