este me ayudo bastante, espero que a ustedes también

2.
=
=
B D W É Q ] @ J
B D W É Q ] @ J
?46
?46
Numrzds
Numrzds afstrfoufads8
afstrfoufads8
bmltrjfams y bmltrjs
bmltrjfams y bmltrjs
am krdvmada
am krdvmada

4.
=.4. FLQ_JA]BBFÒL
=.4. FLQ_JA]BBFÒL
Cds
Cdstd dcj
td dcjrd sm cd su
rd sm cd supums
pumstj qum `d dtrdb
tj qum `d dtrdbbfòl mhmr
bfòl mhmrbf
bfad pjr `d Qfm
ad pjr `d Qfmrrd sj
rrd sj-
-
orm ul bumr
orm ul bumrpj ré
pj rékf
kfaj pj
aj pjaéd rm
aéd rmprm
prmsml
smltdr
tdrsm pjr uld sj
sm pjr uld sj`d numr
`d numrzd
zd [
[
. Ms
. Mstd
td
numr
numrzd, am
zd, amlj
ljif
ifld
ldad numr
ad numrzd am krd
zd am krd
vm
vmada j pm
ada j pmsj am` bumr
sj am` bumrpj, am
pj, amoéd dp`f
oéd dp`f-
-
bdr
bdrsm ml m`
sm ml m` bml
bml
trj am
trj am krd
krd
vm
vmada
ada am` bumr
am` bumrpj (smb
pj (smbbfòl 2.?). Am cm
bfòl 2.?). Am cmbcj, `d
bcj, `d
Qfm
Qfmrrd mhmr
rrd mhmrbm uld numr
bm uld numrzd sj
zd sjorm bd
orm bdad uld am `ds pdr
ad uld am `ds pdrté
tébu
bu`ds qum bjls
`ds qum bjlstf
tftu
tu-
-
yml d`
yml d` bumr
bumrpj. Ml ms
pj. Ml mstm sml
tm smltf
tfaj, `d db
aj, `d dbbfòl am `d Qfm
bfòl am `d Qfmrrd sj
rrd sjorm ul bumr
orm ul bumrpj
pj
ré
rékf
kfaj am
aj amom rm
om rmprm
prmsml
smltdr
tdrsm pjr ul krdl lø
sm pjr ul krdl løim
imrj am pm
rj am pmqum
qumôds numr
ôds numrzds
zds
afs
afstrf
trfouf
oufads sj
ads sjorm tj
orm tjaj m` bumr
aj m` bumrpj. Rfl mi
pj. Rfl miodr
odrkj, ml ms
kj, ml mstm bd
tm bdpé
pétu
tu`j sm
`j sm
dprml
dprmlam
amrä qum `d tj
rä qum `d tjtd
td`f
`fada am af
ada am afbcds numr
bcds numrzds pm
zds pmqum
qumôds pum
ôds pumam smr rmmi
am smr rmmi-
-
p`d
p`dzd
zdad pjr uld sj
ad pjr uld sj`d numr
`d numrzd mquf
zd mquf
vd
vd`ml
`mltm
tm [
[
. Qdi
. Qdiofæl sm dprml
ofæl sm dprmlam
amrä bò
rä bò-
-
ij am
ij amtmr
tmrif
ifldr m` bml
ldr m` bmltrj am krd
trj am krd
vm
vmada, ms
ada, mstj ms, m` pul
tj ms, m` pultj am dp`f
tj am dp`fbd
bdbfòl
bfòl
am `d rm
am `d rmsu`
su`tdl
tdltm
tm [
[
, pd
, pdrd bumr
rd bumrpjs am vd
pjs am vdrfds njr
rfds njrids.
ids.
Ml `d prf
Ml `d prfim
imrd pdr
rd pdrtm am` bd
tm am` bdpé
pétu
tu`j sm ams
`j sm amsbrf
brfoml bumr
oml bumrpjs of
pjs ofaf
afiml
imlsfj
sfj-
-
ld
ld`ms bj
`ms bjij p`d
ij p`dbds p`d
bds p`dlds y d`di
lds y d`diorms qum ms
orms qum mstäl bjl
täl bjltm
tmlf
lfajs ml ul p`d
ajs ml ul p`d-
-
lj ad
lj adaj. Rm fl
aj. Rm fltrj
trjau
aubml ajs bjl
bml ajs bjlbmp
bmptjs qum ms
tjs qum mstäl iuy rm
täl iuy rm`d
`dbfj
bfjld
ldajs bjl
ajs bjl
`d am
`d amtmr
tmrif
ifld
ldbfòl am` bml
bfòl am` bmltrj am krd
trj am krd
vm
vmada am uld p`d
ada am uld p`dbd j am ul d`di
bd j am ul d`di-
-
orm8 m` bjl
orm8 m` bjlbmp
bmptj am
tj am bml
bml
trjf
trjfam
am am ul ärmd j am uld `é
am ul ärmd j am uld `élmd y m` bjl
lmd y m` bjlbmp
bmptj
tj
am`
am` prf
prf
imr
imr ij
ij
iml
iml
tj
tj am ul ärmd j am uld `é
am ul ärmd j am uld `élmd bjl rms
lmd bjl rmspmb
pmbtj d ul mhm
tj d ul mhm
ad
adaj.
aj.
Qdi
Qdiofæl sm dprml
ofæl sm dprmlam
amrä qum m` bä`
rä qum m` bä`bu
bu`j am` ärmd am uld su
`j am` ärmd am uld supmr
pmrnf
nfbfm am
bfm am
rm
rm
vj
vj`u
`ubfòl j am` vj
bfòl j am` vj`u
`uiml am ul bumr
iml am ul bumrpj am rm
pj am rm
vj
vj`u
`ubfòl ms
bfòl mstä af
tä afrmb
rmbtd
tdiml
iml-
-
tm rm
tm rm`d
`dbfj
bfjld
ldaj bjl
aj bjl `d am
`d amtmr
tmrif
ifld
ldbfòl am` bml
bfòl am` bmltrjf
trjfam am `d `é
am am `d `élmd j am` ärmd
lmd j am` ärmd
utf
utf`f
`fzd
zdajs pd
ajs pdrd km
rd kmlm
lmrdr af
rdr afbcd su
bcd supmr
pmrnf
nfbfm j bumr
bfm j bumrpj am rm
pj am rm
vj
vj`u
`ubfòl (tmj
bfòl (tmjrm
rm-
-
ids am Wdp
ids am Wdppus-Ku`
pus-Ku`af
aflus). Dam
lus). Damiäs, bj
iäs, bjij sm iums
ij sm iumstrd ml `ds smb
trd ml `ds smbbfj
bfjlms
lms
=.3 y =.6, `d am
=.3 y =.6, `d amtmr
tmrif
ifld
ldbfòl am` bml
bfòl am` bmltrjf
trjfam am ul ärmd sfi
am am ul ärmd sfip`f
p`fnf
nfbd m` dlä
bd m` dlä-
-
`f
`fsfs am vf
sfs am vfkds su
kds su
hm
hmtds d bdr
tds d bdrkds afs
kds afstrf
trfouf
oufads y m` bä`
ads y m` bä`bu
bu`j am `ds numr
`j am `ds numrzds mhmr
zds mhmr-
-
bf
bfads sj
ads sjorm su
orm supmr
pmrnf
nfbfms rmb
bfms rmbtdl
tdlku
ku`d
`drms su
rms suimr
imrkf
kfads, bj
ads, bjij bji
ij bjipumr
pumrtds cf
tds cf-
-
aräu
aräu`f
`fbds y pjr
bds y pjrbfj
bfjlms am prm
lms am prmsds.
sds.
D` nf
D` nfld` am` bd
ld` am` bdpé
pétu
tu`j sm dprml
`j sm dprmlam
amrä bò
rä bòij am
ij amtmr
tmrif
ifldr tdl
ldr tdltj m` bml
tj m` bml-
-
trj am krd
trj am krd
vm
vmada am bumr
ada am bumrpjs trf
pjs trfaf
afiml
imlsfj
sfjld
ld`ms bj
`ms bjij m` bml
ij m` bmltrjf
trjfam am ul
am am ul
vj
vj`u
`uiml y `js prf
iml y `js prfim
imrjs ij
rjs ijiml
imltjs am af
tjs am afbcj vj
bcj vj`u
`uiml bjl rms
iml bjl rmspmb
pmbtj
tj d
d
`js p`d
`js p`dljs bjjr
ljs bjjram
amld
ldajs.
ajs.
Ä_MDR
Ä_MDR V
V @ÉLMDR
@ÉLMDR
=.?. BMLQ_J AM K_D^MADA AM ]L B]M_WJ OFAFIMLRFJLD@
=.?. BMLQ_J AM K_D^MADA AM ]L B]M_WJ OFAFIMLRFJLD@
Wd
Wdrd
rd flf
flfbfdr, bjl
bfdr, bjlsf
sfam
amrm uld p`d
rm uld p`dbd p`d
bd p`dld cj
ld cjrf
rfzjl
zjltd` (nf
td` (nfku
kurd =.4). @d p`d
rd =.4). @d p`d-
-
bd pum
bd pumam af
am af
vf
vfafr
afrsm ml
sm ml l
l m`m
m`miml
imltjs pm
tjs pmqum
qumôjs. @ds bjjr
ôjs. @ds bjjram
amld
ldads am` prf
ads am` prf-
-
Nfkurd =.4
Nfkurd =.4 Bmltrj am krdvmada am uld p`dbd.
Bmltrj am krdvmada am uld p`dbd.
x
x
y
y
z
z
K
K
J
J J
J


x
x


y
y
[
[
9
9
∎
∎ [
[
΢
΢I
I y
y 8
8 

x [
x [
9 ΢
9 ΢ x
x ∎
∎[
[
΢
΢I
I x
x 8
8 

y
y [
[
9 ΢
9 ΢ y
y ∎
∎[
[
x
x
y
y
z
z
y
y
x
x
??7
??7
Njtjkrdnéd =.4
Njtjkrdnéd =.4 M` od`dlbm prmbfsj am `js
M` od`dlbm prmbfsj am `js
bjipjlmltms am ul iòvf` rmqufmrm am uld
bjipjlmltms am ul iòvf` rmqufmrm am uld
bjiprmlsfòl am `js bmltrjs am krdvmada y
bjiprmlsfòl am `js bmltrjs am krdvmada y
bmltrjfams, qum sjl `js tòpfbjs prflbfpd`ms am
bmltrjfams, qum sjl `js tòpfbjs prflbfpd`ms am
mstm bdpétu`j.
mstm bdpétu`j.
BDWÉQ]@J
BDWÉQ]@J =
= N]M_XDR
N]M_XDR
AFRQ_FO]FADR8 BMLQ_JFAMR
AFRQ_FO]FADR8 BMLQ_JFAMR
V BMLQ_JR AM K_D^MADA
V BMLQ_JR AM K_D^MADA
=.4
=.4 Fltrjaubbfòl
Fltrjaubbfòl
=.?
=.? Bmltrj am krdvmada am ul bumrpj
Bmltrj am krdvmada am ul bumrpj
ofafimlsfjld`
ofafimlsfjld`
=.2
=.2 Bmltrjfams am ärmds y `élmds
Bmltrjfams am ärmds y `élmds
=.1
=.1 Wrfimrjs ijimltjs am ärmds y
Wrfimrjs ijimltjs am ärmds y
`élmds
`élmds
=.=
=.= W`dbds y d`diorms bjipumstjs
W`dbds y d`diorms bjipumstjs
=.>
=.> Amtmrifldbfòl am bmltrjfams pjr
Amtmrifldbfòl am bmltrjfams pjr
fltmkrdbfòl
fltmkrdbfòl
=.;
=.; Qmjrmids am Wdppus-Ku`aflus
Qmjrmids am Wdppus-Ku`aflus
=.3
=.3 Bdrkds afstrfoufads ml vfkds
Bdrkds afstrfoufads ml vfkds
=.6
=.6 Numrzds sjorm supmrnfbfms
Numrzds sjorm supmrnfbfms
suimrkfads
suimrkfads
=.47
=.47 Bmltrj am krdvmada am ul bumrpj
Bmltrj am krdvmada am ul bumrpj
tr
trfafimlsfjld`. Bmltrjfam am ul
fafimlsfjld`. Bmltrjfam am ul
vj`uiml
vj`uiml
=.44
=.44 Bumrpjs bjipumstjs
Bumrpjs bjipumstjs
=.4?
=.4? Amtmrifldbfòl am bmltrjfams am
Amtmrifldbfòl am bmltrjfams am
vj`øimlms pjr fltmkrdbfòl
vj`øimlms pjr fltmkrdbfòl

5.
??4
??4
=.?. Bmltrj am krdvmada am ul bumrpj
=.?. Bmltrj am krdvmada am ul bumrpj
ofafimlsfjld`
ofafimlsfjld`
x
x
y
y
z
z
J
J 

y
y
9
9
[
[
∎
∎ [
[


x
x
K
K
x
x
y
y
y
y
z
z
J
J
x
x
΢
΢I
I y
y 8
8


x [
x [
9 ΢
9 ΢ x
x ∎
∎[
[
΢
΢I
I x
x 8
8 

y
y[
[
9 ΢
9 ΢ y
y ∎
∎[
[
Nfkurd =.?
Nfkurd =.? Bmltrj am krdvmada am ul d`diorm.
Bmltrj am krdvmada am ul d`diorm.
im
imr
r m`
m`m
miml
imltj sm rm
tj sm rmprm
prmsml
smltdl bjl
tdl bjl x
x4
4 y
y y
y4
4, `ds am` sm
, `ds am` smkul
kulaj m`m
aj m`miml
imltj sm
tj sm
rm
rmprm
prmsml
smltdl bjl
tdl bjl x
x?
? y
y y
y?
?, mt
, mtb. @ds numr
b. @ds numrzds mhmr
zds mhmrbf
bfads pjr `d Qfm
ads pjr `d Qfmrrd sj
rrd sjorm
orm
`js m`m
`js m`miml
imltjs am `d p`d
tjs am `d p`dbd sm
bd smräl rm
räl rmprm
prmsml
smltd
tdads, rms
ads, rmspmb
pmbtf
tf
vd
vdiml
imltm, bjl
tm, bjl


[
[
4
4,
, 

[
[
?
?,
, .
. .
. .
. ,
, 

[
[
l
l. Ms
. Mstds numr
tds numrzds j pm
zds j pmsjs ms
sjs mstäl af
täl afrf
rfkf
kfajs cd
ajs cdbfd m`
bfd m`
bml
bmltrj am `d Qfm
trj am `d Qfmrrd5 sfl mi
rrd5 sfl miodr
odrkj, pd
kj, pdrd tj
rd tjajs `js prj
ajs `js prjpò
pòsf
sftjs präb
tjs präbtf
tfbjs,
bjs,
sm pum
sm pumam su
am supj
pjlmr qum af
lmr qum afbcds numr
bcds numrzds sjl pd
zds sjl pdrd
rd`m
`m`ds. Wjr tdl
`ds. Wjr tdltj, su rm
tj, su rmsu`
su`-
-
tdl
tdltm ms uld sj
tm ms uld sj`d numr
`d numrzd ml `d ifs
zd ml `d ifsid af
id afrmb
rmbbfòl. @d idk
bfòl. @d idklf
lftua
tua [
[ am ms
am ms-
-
td numr
td numrzd sm jo
zd sm jotfm
tfmlm d pdr
lm d pdrtfr am `d su
tfr am `d suid am `ds idk
id am `ds idklf
lftu
tuams am `js pm
ams am `js pmsjs
sjs
am `js m`m
am `js m`miml
imltjs8
tjs8

N
N z
z8
8 [
[ 
 
[
[
4
4 
 
[
[
?
? 
 
 
 
 
 
[
[
l
l
pdrd jotmlmr `ds bjjramldads
pdrd jotmlmr `ds bjjramldads x
x

 y
y y
y

 am` pultj
am` pultj K
K, ajlam amom dp`fbdrsm
, ajlam amom dp`fbdrsm
`d rmsu`tdltm
`d rmsu`tdltm [
[
, sm msbrfom qum `js ijimltjs am
, sm msbrfom qum `js ijimltjs am [
[ bjl rmspmbtj d `js
bjl rmspmbtj d `js
mhms
mhms y
y y
y x
x sjl fkud`ms d `d suid am `js ijimltjs bjrrmspjlafmltms am
sjl fkud`ms d `d suid am `js ijimltjs bjrrmspjlafmltms am
`js pmsjs m`mimltd`ms, mstj ms
`js pmsjs m`mimltd`ms, mstj ms

I
I y
y8
8 x
x

[
[ 
 x
x4
4 
[
[
4
4 
 x
x?
? 
[
[
?
? 
  
   
  x
x l
l 
[
[
l
l

I
I x
x8
8 y
y

[
[ 
 y
y4
4 
[
[
4
4 
 y
y?
? 
[
[
?
? 
  
   
  y
y l
l 
[
[
l
l
(=.4)
(=.4)
Rf dcj
Rf dcjrd sm fl
rd sm flbrm
brmiml
imltd m` lø
td m` løim
imrj am m`m
rj am m`miml
imltjs ml `js bud
tjs ml `js bud`ms sm cd af
`ms sm cd af-
-
vf
vfaf
afaj `d p`d
aj `d p`dbd y sf
bd y sfiu`
iu`tä
tälmd
lmdiml
imltm sm afs
tm sm afsif
iflu
lu
ym m` td
ym m` tdid
idôj am bd
ôj am bdad m`m
ad m`m-
-
iml
imltj sm jo
tj sm jotfm
tfmlml, ml m` `é
lml, ml m` `éif
iftm, `ds sf
tm, `ds sfkufml
kufmltms mx
tms mxprm
prmsfj
sfjlms8
lms8
[
[ 
 
 a[
a[ x
x

[
[ 
 
 x a[
x a[ y
y

[
[ 
 
 y a[
y a[ (=.?)
(=.?)
Mstds mbudbfjlms amnflml m` pmsj
Mstds mbudbfjlms amnflml m` pmsj [
[
y `ds
y `ds bjjramldads
bjjramldads x
x

 y
y y
y

 am` bmltrj
am` bmltrj
am krdvmada
am krdvmada K
K am uld p`dbd p`dld. Rm pumaml amrfvdr `ds ifsids mbud-
am uld p`dbd p`dld. Rm pumaml amrfvdr `ds ifsids mbud-
bfjlms pdrd ul d`diorm qum sm mlbumltrd ml m` p`dlj
bfjlms pdrd ul d`diorm qum sm mlbumltrd ml m` p`dlj xy
xy (nfkurd =.?).
(nfkurd =.?).
Rm josmrvd qum usud`imltm m` bmltrj am krdvmada
Rm josmrvd qum usud`imltm m` bmltrj am krdvmada K
K am ul d`diorm lj
am ul d`diorm lj
mstä `jbd`fzdaj sjorm mstm ø`tfij.
mstä `jbd`fzdaj sjorm mstm ø`tfij.

6.
???
??? Numrzds afstrfoufads8 bmltrjfams y bmltrjs
Numrzds afstrfoufads8 bmltrjfams y bmltrjs
am krdvmada
am krdvmada
=.2. BMLQ_JFAMR AM
=.2. BMLQ_JFAMR AM Ä_MDR
Ä_MDR V @ÉLMDR
V @ÉLMDR
Ml m`
Ml m` bd
bdsj am
sj am uld p`d
uld p`dbd p`d
bd p`dld cj
ld cjij
ijkæ
kælmd am ms
lmd am mspm
pmsjr ulf
sjr ulfnjr
njrim, `d idk
im, `d idk-
-
lf
lftua
tua 
[
[ am` pm
am` pmsj am ul m`m
sj am ul m`miml
imltj am `d p`d
tj am `d p`dbd pum
bd pumam mx
am mxprm
prmsdr
sdrsm bj
sm bjij
ij

[
[ 
 

t
t 

D
D
ajlam
ajlam 
 
 pmsj mspmbénfbj (pmsj pjr ulfada am vj`uiml) am` idtmrfd`
pmsj mspmbénfbj (pmsj pjr ulfada am vj`uiml) am` idtmrfd`
t
t 
 mspmsjr am `d p`dbd
mspmsjr am `d p`dbd


D
D 
 ärmd am` m`mimltj
ärmd am` m`mimltj
Ml njr
Ml njrid sf
id sfif
if`dr, sm pum
`dr, sm pumam mx
am mxprm
prmsdr `d idk
sdr `d idklf
lftua
tua [
[ am` pm
am` pmsj am tj
sj am tjad
ad
`d p`d
`d p`dbd bj
bd bjij
ij
[
[ 
 

tD
tD
ajlam
ajlam D
D ms m` ärmd tjtd` am `d p`dbd.
ms m` ärmd tjtd` am `d p`dbd.
Rf sm mi
Rf sm mip`mdl `ds ulf
p`mdl `ds ulfad
adams am usj bj
ams am usj bjiøl ml Ms
iøl ml Mstd
tdajs ]lf
ajs ]lfajs, sm
ajs, sm
am
amom mx
om mxprm
prmsdr m` pm
sdr m` pmsj ms
sj mspm
pmbé
bénĴ
nĴbj
bj 
 ml `o/nt
ml `o/nt2
2
, m` ms
, m` mspm
pmsjr
sjr t
t ml pfms y `ds
ml pfms y `ds
ärmds
ärmds 

D
D y
y D
D ml pfms bud
ml pfms budard
ardajs. Ml
ajs. Mltjl
tjlbms, sm jo
bms, sm josmr
smr
vd
vd qum
qum 
[
[ y
y [
[
ms
mstd
tdräl mx
räl mxprm
prmsd
sdajs ml `f
ajs ml `fords. Rf sm usdl `ds ulf
ords. Rf sm usdl `ds ulfad
adams am` RF, sm am
ams am` RF, sm amom
om
mx
mxprm
prmsdr d
sdr d 
 ml L/i
ml L/i2
2
,
, d
d t
t ml im
ml imtrjs y d `ds ärmds
trjs y d `ds ärmds 

D
D y
y D
D ml im
ml imtrjs
trjs
bud
budard
ardajs5 ml
ajs5 mltjl
tjlbms, `js pm
bms, `js pmsjs
sjs 
[
[ y
y [
[ ms
mstd
tdräl mx
räl mxprm
prmsd
sdajs ml lmw
ajs ml lmw-
-
tjls.
tjls.†
†
Rf sm sus
Rf sm sustf
tftu
tu
ym
ym d
d 
[
[ y d
y d [
[ ml `ds mbud
ml `ds mbudbfj
bfjlms am ij
lms am ijiml
imltj (=.4) y
tj (=.4) y
sm af
sm af
vf
vfam d tj
am d tjajs `js tær
ajs `js tærif
ifljs ml
ljs mltrm
trm 

t
t, sm jo
, sm jotfm
tfmlm
lm

I
I y
y8
8 x
x


D
D 
 x
x4
4 

D
D4
4 
 x
x?
? 

D
D?
? 
 
 
 
 
 x
x l
l 

D
D l
l

I
I x
x8
8 y
y


D
D 
 y
y4
4 

D
D4
4 
 y
y?
? 

D
D?
?  
   
  
 y
y l
l 

D
D l
l
Rf sm flbrmimltd m` løimrj am m`mimltjs ml `js b
Rf sm flbrmimltd m` løimrj am m`mimltjs ml `js bud`ms sm afvfam m` ärmd
ud`ms sm afvfam m` ärmd
D
D y sfiu`tälmdimltm sm afsifluym m` tdidôj am
y sfiu`tälmdimltm sm afsifluym m` tdidôj am bdad m`mimltj, sm jo-
bdad m`mimltj, sm jo-
tfmlm ml m` `éiftm
tfmlm ml m` `éiftm
x
x


D
D 
 
 x
x aD
aD y
y


D
D 
 
 y
y aD
aD (=.2)
(=.2)
Ms
Mstds mbud
tds mbudbfj
bfjlms am
lms amnf
nflml `ds bjjr
lml `ds bjjram
amld
ldads
ads x
x

 y
y y
y

 am` bml
am` bmltrj am krd
trj am krd
vm
vmada
ada
am uld p`d
am uld p`dbd cj
bd cjij
ijkæ
kælmd. M` pul
lmd. M` pultj bu
tj bu
yds
yds bjjr
bjjram
amld
ldads sj
ads sjl
l x
x

 y
y y
y

 tdi
tdi-
-
ofæl sm bj
ofæl sm bjlj
ljbm bj
bm bjij m`
ij m` bml
bml
trjf
trjfam B am` ärmd D
am B am` ärmd D am `d p`d
am `d p`dbd (nf
bd (nfku
kurd =.2).
rd =.2).
Rf `d p`d
Rf `d p`dbd lj ms cj
bd lj ms cjij
ijkæ
kælmd, ms
lmd, mstds mbud
tds mbudbfj
bfjlms lj sm pum
lms lj sm pumaml utf
aml utf`f
`fzdr pd
zdr pd-
-
rd am
rd amtmr
tmrif
ifldr m` bml
ldr m` bmltrj am krd
trj am krd
vm
vmada am `d p`d
ada am `d p`dbd5 sfl mi
bd5 sfl miodr
odrkj, æs
kj, æstds døl
tds døl
am
amnf
nflml d` bml
lml d` bmltrjf
trjfam am` ärmd.
am am` ärmd.
Ml m` bdsj am ul d`diorm cjijkælmj am smbbfòl trdlsvmrsd` ulf-
Ml m` bdsj am ul d`diorm cjijkælmj am smbbfòl trdlsvmrsd` ulf-
njrim, `d idklftua
njrim, `d idklftua 
[
[ am` pmsj am ul m`mimltj am d`diorm pumam
am` pmsj am ul m`mimltj am d`diorm pumam
mxprmsdrsm bjij
mxprmsdrsm bjij

[
[ 
 
 d
d 

@
@
ajlam
ajlam 
 
 pmsj mspmbénfbj am` idtmrfd`
pmsj mspmbénfbj am` idtmrfd`
d
d 
 ärmd am `d smbbfòl trdlsvmrsd` am` d`diorm
ärmd am `d smbbfòl trdlsvmrsd` am` d`diorm


@
@ 
 `jlkftua am` m`mimltj
`jlkftua am` m`mimltj
†
†
Rm am
Rm amom sm
om smôd
ôd`dr qum ml m` Rfs
`dr qum ml m` Rfstm
tmid Fl
id Fltmr
tmrld
ldbfj
bfjld` am ulf
ld` am ulfad
adams km
ams kmlm
lmrd`
rd`iml
imltm sm bd
tm sm bdrdb
rdbtm
tm-
-
rf
rfzd d ul idtmrfd` ad
zd d ul idtmrfd` adaj pjr su aml
aj pjr su amlsf
sfada
ada 
 (id
(idsd pjr ulf
sd pjr ulfada am vj
ada am vj`u
`uiml) ml `u
iml) ml `ukdr am bd
kdr am bd-
-
rdb
rdbtm
tmrf
rfzdr
zdr`j pjr su pm
`j pjr su pmsj ms
sj mspm
pmbé
bénf
nfbj
bj 

. Ml
. Mltj
tjlbms, m` pm
lbms, m` pmsj ms
sj mspm
pmbé
bénf
nfbj am` id
bj am` idtm
tmrfd` sm pum
rfd` sm pumam
am
jo
jotm
tmlmr d pdr
lmr d pdrtfr am `d rm
tfr am `d rm`d
`dbfòl
bfòl

 
 

k
k
ajl
ajlam
am k
k 
 6.34 i/s
6.34 i/s?
?
.
. Bj
Bjij
ij 
 sm mx
sm mxprm
prmsd ml ek/i
sd ml ek/i2
2
, sm jo
, sm josmr
smr
vd qum
vd qum 
 ms
mstd
tdrä mx
rä mxprm
prmsd
sdaj ml
aj ml
(ek/i
(ek/i2
2
)(i/s
)(i/s?
?
), mstj ms, ml L/i
), mstj ms, ml L/i2
2
.
.

7.
??2
??2
M` bmltrj am krdvmada am ul d`diorm bjflbfam bjl m`
M` bmltrj am krdvmada am ul d`diorm bjflbfam bjl m` bmltrjfam B am
bmltrjfam B am
`d `élmd @
`d `élmd @ qum amnflm `d njrid am` d`diorm (nfkurd =.1). @ds bjjram-
qum amnflm `d njrid am` d`diorm (nfkurd =.1). @ds bjjram-
ldads
ldads x
x

 y
y y
y

 am` bmltrjfam am `d `élmd
am` bmltrjfam am `d `élmd @
@ sm jotfmlml d pdrtfr am `ds mbud-
sm jotfmlml d pdrtfr am `ds mbud-
bfjlms
bfjlms
x
x


@
@ 
 
 x a@
x a@ y
y


@
@ 
 
 y a@
y a@ (=.1)
(=.1)
=.1. W_FIM_JR IJIMLQJR AM Ä_MDR V @ÉLMDR
=.1. W_FIM_JR IJIMLQJR AM Ä_MDR V @ÉLMDR
@d fl
@d fltm
tmkrd`
krd` 
 x aD
x aD ml `ds mbud
ml `ds mbudbfj
bfjlms (=.2) am `d smb
lms (=.2) am `d smbbfòl dl
bfòl dltm
tmrfjr sm bj
rfjr sm bj-
-
lj
ljbm bj
bm bjij m`
ij m` prf
prf
imr ij
imr ij
iml
iml
tj am` ärmd
tj am` ärmd D bjl rms
D bjl rms pmb
pmb
tj d`
tj d` mhm y
mhm y y sm rm
y sm rm-
-
prm
prmsmltd bjl
smltd bjl T
T y
y.
. Ml njr
Ml njrid sf
id sfif
if`dr, `d fl
`dr, `d fltm
tmkrd`
krd` 
 y aD
y aD am
amnf
nflm m`
lm m` prf
prf
imr
imr
ij
ij
iml
iml
tj
tj am D
am D bjl rms
bjl rms pmb
pmb
tj
tj d`
d` mhm x
mhm x y
y sm rm
sm rmprm
prmsml
smltd bjl
td bjl T
T x
x. Dsé sm ms-
. Dsé sm ms-
brf
brfom
om
T
T y
y 
 
 x aD
x aD T
T x
x 
 
 y aD
y aD (=.=)
(=.=)
Rf bji
Rf bjipd
pdrd
rdijs `ds mbud
ijs `ds mbudbfj
bfjlms (=.2) bjl `ds mbud
lms (=.2) bjl `ds mbudbfj
bfjlms (=.=), sm jo
lms (=.=), sm josmr
smr-
-
vd
vd qum
qum `js
`js prf
prfim
imrjs ij
rjs ijiml
imltjs am` ärmd
tjs am` ärmd D
D pum
pumaml smr mx
aml smr mxprm
prmsd
sdajs bj
ajs bj-
-
ij `js prj
ij `js prjaub
aubtjs am` ärmd bjl `ds bjjr
tjs am` ärmd bjl `ds bjjram
amld
ldads am su bml
ads am su bmltrjf
trjfam8
am8
T
T y
y 
 x
x


D
D T
T x
x 
 y
y

D
D (
(=
=.
.>
>)
)
D pdr
D pdrtfr am `ds mbud
tfr am `ds mbudbfj
bfjlms (=.>) sm bjl
lms (=.>) sm bjlb`u
b`u
ym qum `ds
ym qum `ds bjjr
bjjram
amld
ldads am`
ads am`
bml
bmltrjf
trjfam am ul ärmd pum
am am ul ärmd pumaml jo
aml jotm
tmlmr
lmrsm d` af
sm d` af
vf
vfafr `js prf
afr `js prfim
imrjs ij
rjs ijiml
iml-
-
tjs am af
tjs am afbcd ärmd ml
bcd ärmd mltrm m` ärmd ifs
trm m` ärmd ifsid. @js prf
id. @js prfim
imrjs ij
rjs ijiml
imltjs am ul
tjs am ul
ärmd tdi
ärmd tdiofæl sjl øtf
ofæl sjl øtf`ms ml `d im
`ms ml `d imbä
bälf
lfbd am id
bd am idtm
tmrfd
rfd`ms pd
`ms pdrd am
rd amtmr
tmrif
ifldr
ldr
`js ms
`js msnumr
numrzjs am bjr
zjs am bjrtm ml vf
tm ml vfkds su
kds su
hm
hmtds d bdr
tds d bdrkds trdls
kds trdls
vmr
vmrsd
sd`ms. Wjr ø`
`ms. Wjr ø`tf
tfij,
ij,
d pdr
d pdrtfr am `ds mbud
tfr am `ds mbudbfj
bfjlms (=.>) sm jo
lms (=.>) sm josmr
smr
vd qum sf m`
vd qum sf m` bml
bmltrjf
trjfam am ul ärmd
am am ul ärmd
ms
mstä `j
tä `jbd
bd`f
`fzd
zdaj sj
aj sjorm ul mhm bjjr
orm ul mhm bjjram
amld
ldaj, ml
aj, mltjl
tjlbms m` prf
bms m` prfimr ij
imr ijiml
imltj
tj
am` ärmd bjl rms
am` ärmd bjl rmspmb
pmbtj d msm mhm ms fkud` d bm
tj d msm mhm ms fkud` d bmrj. Am id
rj. Am idlm
lmrd fl
rd fl
vmr
vmrsd, sf m`
sd, sf m`
prf
prfimr ij
imr ijiml
imltj am ul ärmd bjl rms
tj am ul ärmd bjl rmspmb
pmbtj d ul mhm bjjr
tj d ul mhm bjjram
amld
ldaj ms fkud`
aj ms fkud`
d bm
d bmrj, ml
rj, mltjl
tjlbms m` bml
bms m` bmltrjf
trjfam am` ärmd ms
am am` ärmd mstä `j
tä `jbd
bd`f
`fzd
zdaj sj
aj sjorm msm mhm.
orm msm mhm.
Rm pum
Rm pumaml utf
aml utf`f
`fzdr rm
zdr rm`d
`dbfj
bfjlms sf
lms sfif
if`d
`drms d pdr
rms d pdrtfr am `ds mbud
tfr am `ds mbudbfj
bfjlms
lms
(=.=) y (=.>) pd
(=.=) y (=.>) pdrd am
rd amnf
nflfr `js prf
lfr `js prfim
imrjs ij
rjs ijiml
imltjs am uld `é
tjs am uld `élmd bjl rms
lmd bjl rms-
-
pmb
pmbtj d `js mhms bjjr
tj d `js mhms bjjram
amld
ldajs y pd
ajs y pdrd mx
rd mxprm
prmsdr af
sdr afbcjs ij
bcjs ijiml
imltjs bj
tjs bjij `js
ij `js
prj
prjaub
aubtjs am `d `jl
tjs am `d `jlkf
kftua
tua @
@ am `d `é
am `d `élmd y `ds bjjr
lmd y `ds bjjram
amld
ldads
ads x
x

 y
y y
y

 am su bml
am su bml-
-
trjf
trjfam.
am.
=.1. Wrfimrjs ijimltjs am ärmds y `élmds
=.1. Wrfimrjs ijimltjs am ärmds y `élmds
J
J x
x
x
x
y
y
y
y
J
J x
x
y
y
D
D
9
9
∎
∎ D
D
΢
΢I
I y
y 8
8 

x D
x D 9 ΢
9 ΢ x
x ∎
∎ D
D
΢
΢I
I x
x 8
8


y D
y D 9 ΢
9 ΢ y
y∎
∎ D
D
B
B


y
y


x
x
x
x
x
x
y
y
y
y
J
J
x
x
y
y
J
J
9
9


y
y


x
x
∎
∎ @
@
@
@
΢
΢I
I y
y 8
8 

x
x@
@ 9 ΢
9 ΢ x
x ∎
∎ @
@
΢
΢I
I x
x 8
8 

y
y@
@ 9 ΢
9 ΢ y
y ∎
∎ @
@
B
B
Nfkurd =.2
Nfkurd =.2 Bmltrjfam am ul ärmd.
Bmltrjfam am ul ärmd. Nfkurd =.1
Nfkurd =.1 Bmltrjfam am uld `élmd.
Bmltrjfam am uld `élmd.

8.
??1
??1 Numrzds afstrfoufads8 bmltrjfams y bmltrjs
Numrzds afstrfoufads8 bmltrjfams y bmltrjs
am krdvmada
am krdvmada
Rm af
Rm afbm qum ul ärmd
bm qum ul ärmd D
D ms
ms sf
sf
iæ
iæ
trf
trfbd bjl rms
bd bjl rms
pmb
pmb
tj d ul mhm
tj d ul mhm OO
OO
 sf pd
sf pd-
-
rd tj
rd tjaj pul
aj pultj
tj W
W am` ärmd mxfs
am` ärmd mxfstm ul pul
tm ul pultj
tj W
W
 am msd ifs
am msd ifsid ärmd td` qum
id ärmd td` qum
`d `é
`d `élmd
lmd WW
WW
 smd pmr
smd pmrpml
pmlaf
afbu
bu`dr d
`dr d OO
OO
 y af
y afbcd `é
bcd `élmd ms
lmd mstä af
tä af
vf
vfaf
afad ml ajs
ad ml ajs
pdr
pdrtms fkud
tms fkud`ms pjr m` mhm ml bums
`ms pjr m` mhm ml bumstfòl (nĴ
tfòl (nĴku
kurd =.=
rd =.=d
d). Rm af
). Rm afbm qum uld `é
bm qum uld `é-
-
lmd
lmd @
@ ms sf
ms sfiæ
iætrf
trfbd bjl rms
bd bjl rmspmb
pmbtj d ul mhm
tj d ul mhm OO
OO
 sf sd
sf sdtfs
tfsnd
ndbm bjl
bm bjlaf
afbfj
bfjlms
lms
sf
sfif
if`d
`drms. Budl
rms. Budlaj ul ärmd
aj ul ärmd D
D j uld `é
j uld `élmd
lmd @
@ pj
pjsmm ul mhm am sf
smm ul mhm am sfim
imtréd
tréd
OO
OO
, su prf
, su prfimr ij
imr ijiml
imltj bjl rms
tj bjl rmspmb
pmbtj d
tj d OO
OO
 ms fkud` d bm
ms fkud` d bmrj y su bml
rj y su bml-
-
trjf
trjfam ms
am mstä `j
tä `jbd
bd`f
`fzd
zdaj sj
aj sjorm af
orm afbcj mhm. Wjr mhmi
bcj mhm. Wjr mhmip`j, ml m` bd
p`j, ml m` bdsj am` ärmd
sj am` ärmd
D
D am `d nf
am `d nfku
kurd =.=
rd =.=
o
o, `d bud` ms sf
, `d bud` ms sfiæ
iætrfbd bjl rms
trfbd bjl rmspmb
pmbtj d` mhm
tj d` mhm y
y, sm jo
, sm josmr
smr-
-
vd
vd qum pd
qum pdrd bd
rd bdad m`m
ad m`miml
imltj am ärmd
tj am ärmd aD
aD am dos
am dosbf
bfsd
sd x
x mxfs
mxfstm ul m`m
tm ul m`miml
iml-
-
tj am ärmd
tj am ärmd aD
aD
 qum tfm
qum tfmlm `d ifs
lm `d ifsid su
id supmr
pmrnf
nfbfm y bu
bfm y bu
yd
yd dos
dosbf
bfsd ms
sd ms 

x
x. Rm
. Rm
bjl
bjlb`u
b`u
ym
ym qum `d
qum `d fl
fltm
tmkrd` ml `d prf
krd` ml `d prfim
imrd am `ds mbud
rd am `ds mbudbfj
bfjlms (=.=) ms fkud`
lms (=.=) ms fkud`
d bm
d bmrj y, pjr tdl
rj y, pjr tdltj, sm tfm
tj, sm tfmlm qum
lm qum T
T y
y 
 7. Qdi
7. Qdiofæl sm bjl
ofæl sm bjlb`u
b`u
ym d
ym d pdr
pdrtfr
tfr
am `d prf
am `d prfim
imrd am `ds rm
rd am `ds rm`d
`dbfj
bfjlms (=.2) qum
lms (=.2) qum x
x

 
 7. Wjr bjl
7. Wjr bjlsf
sfkufml
kufmltm, sf ul
tm, sf ul
ärmd
ärmd D
D j uld `é
j uld `élmd
lmd @
@ pj
pjsmml ul mhm am sf
smml ul mhm am sfim
imtréd, su bml
tréd, su bmltrjf
trjfam
am B
B ms
mstä `j
tä `j-
-
bd
bd`f
`fzd
zdaj sj
aj sjorm af
orm afbcj mhm.
bcj mhm.
Dam
Damiäs, sm am
iäs, sm amom sm
om smôd
ôd`dr qum sf ul ärmd j uld `é
`dr qum sf ul ärmd j uld `élmd pj
lmd pjsmm ajs mhms
smm ajs mhms
am sf
am sfim
imtréd, su bml
tréd, su bmltrjf
trjfam
am B
B am
amom ms
om mstdr `j
tdr `jbd
bd`f
`fzd
zdaj ml `d fl
aj ml `d fltmr
tmrsmb
smbbfòl am
bfòl am
msjs ajs mhms (nf
msjs ajs mhms (nfku
kurd =.>). Ms
rd =.>). Mstd prj
td prjpfm
pfmada pmr
ada pmrif
iftm am
tm amtmr
tmrif
ifldr am fl
ldr am flim
im-
-
afd
afdtj m` bml
tj m` bmltrjf
trjfam am ärmds bj
am am ärmds bjij bér
ij bérbu
bu`js, m`fp
`js, m`fpsms, bud
sms, budard
ardajs, rmb
ajs, rmbtäl
täl-
-
ku
ku`js, trfälku
`js, trfälku`js mquf
`js mquf`ä
`ätm
tmrjs u jtrds nf
rjs u jtrds nfku
kurds sf
rds sfiæ
iætrf
trfbds, dsé bj
bds, dsé bjij m` bml
ij m` bml-
-
trjf
trjfam am `élmds qum tfm
am am `élmds qum tfmlml `d njr
lml `d njrid am `d bfr
id am `d bfrbul
bulnm
nmrml
rmlbfd am ul bér
bfd am ul bérbu
bu`j,
`j,
m` pm
m` pmré
réim
imtrj am ul bud
trj am ul budard
ardaj, ml
aj, mltrm jtrjs.
trm jtrjs.
Nfkurd =.>
Nfkurd =.>
Nfkurd =.;
Nfkurd =.;
Nfkurd =.=
Nfkurd =.=
Rm af
Rm afbm qum ul ärmd
bm qum ul ärmd D
D ms
ms sf
sf
iæ
iæ
trf
trfbd bjl rms
bd bjl rms
pmb
pmb
tj
tj d
d ul
ul bml
bml
trj
trj J
J sf
sf
pd
pdrd bd
rd bdad m`m
ad m`miml
imltj am ärmd
tj am ärmd aD
aD am bjjr
am bjjram
amld
ldads
ads x
x y
y y
y mxfs
mxfstm ul m`m
tm ul m`miml
iml-
-
tj am ärmd
tj am ärmd aD
aD
 am fkud` su
am fkud` supmr
pmrnf
nfbfm bjl bjjr
bfm bjl bjjram
amld
ldads
ads 

x
x y
y 

y
y (nf
(nfku
kurd
rd
=.;). Ml
=.;). Mltjl
tjlbms, sm bjl
bms, sm bjlb`u
b`u
ym qum
ym qum di
diods fl
ods fltm
tmkrd
krd`ms ml `ds mbud
`ms ml `ds mbudbfj
bfjlms (=.=)
lms (=.=)
sjl fkud
sjl fkud`ms d bm
`ms d bmrj y qum
rj y qum T
T x
x 
 T
T y
y 
 7. Qdi
7. Qdiofæl, d pdr
ofæl, d pdrtfr am `ds mbud
tfr am `ds mbud-
-
bfj
bfjlms (=.2), sm bjl
lms (=.2), sm bjlb`u
b`u
ym
ym qum
qum x
x

 
 y
y

 
 7, ms
7, mstj ms, qum m` bml
tj ms, qum m` bmltrjf
trjfam am`
am am`
ärmd bjfl
ärmd bjflbf
bfam bjl su bml
am bjl su bmltrj am sf
trj am sfim
imtréd
tréd J
J. Ml njr
. Ml njrid dlä
id dlä`j
`jkd, sf uld `é
kd, sf uld `é-
-
lmd pj
lmd pjsmm ul bml
smm ul bmltrj am sf
trj am sfim
imtréd
tréd J
J, m` bml
, m` bmltrjf
trjfam am `d `é
am am `d `élmd bjfl
lmd bjflbf
bfaf
afrä
rä
bjl m` bml
bjl m` bmltrj
trj J
J.
.
Rm am
Rm amom sm
om smôd
ôd`dr qum uld nf
`dr qum uld nfku
kurd bjl ul bml
rd bjl ul bmltrj am sf
trj am sfim
imtréd lj lm
tréd lj lm-
-
bm
bmsd
sdrfd
rfdiml
imltm pj
tm pjsmm ul mhm am sf
smm ul mhm am sfim
imtréd (nf
tréd (nfku
kurd =.;) y qum uld nf
rd =.;) y qum uld nfku
kurd bjl
rd bjl
ajs mhms am sf
ajs mhms am sfim
imtréd lj lm
tréd lj lmbm
bmsd
sdrfd
rfdiml
imltm tfm
tm tfmlm ul bml
lm ul bmltrj am sf
trj am sfim
imtréd (nf
tréd (nf-
-
ku
kurd =.>
rd =.>d
d). Rfl mi
). Rfl miodr
odrkj, sf uld nf
kj, sf uld nfku
kurd pj
rd pjsmm ajs mhms am sf
smm ajs mhms am sfim
imtréd qum
tréd qum
sjl pmrpml
sjl pmrpmlaf
afbu
bu`d
`drms ml
rms mltrm sé, m` pul
trm sé, m` pultj am fl
tj am fltmr
tmrsmb
smbbfòl am af
bfòl am afbcjs mhms
bcjs mhms
ms ul bmltrj am sf
ms ul bmltrj am sfim
imtréd (nf
tréd (nfku
kurd =.>
rd =.>
o
o).
).
@d am
@d amtmr
tmrif
ifld
ldbfòl am `js bml
bfòl am `js bmltrjf
trjfams am ärmds dsf
ams am ärmds dsfiæ
iætrf
trfbds y am `é
bds y am `é-
-
lmds y ärmds qum pj
lmds y ärmds qum pjsmml ul sj
smml ul sj`j mhm am sf
`j mhm am sfim
imtréd sm ms
tréd sm mstu
tuafd
afdrä ml `ds smb
rä ml `ds smb-
-
bfj
bfjlms =.> y =.;. Ml `ds nf
lms =.> y =.;. Ml `ds nfku
kurds =.3D y =.3O sm iums
rds =.3D y =.3O sm iumstrdl `js bml
trdl `js bmltrjf
trjfams
ams
am njr
am njrids bjiulms am ärmds y am `élmds.
ids bjiulms am ärmds y am `élmds.
B
B
B
B
O
O
O
O'
'
O
O
O
O'
'
A
A
A
A'
'
A
A'
'
A
A
d
d)
) o
o)
)
x
x
x
x
y
y
J
J
B
B
D
D
‒
‒
x
x
aD
aD
aD
aD'
'
W
W
W
W'
'
O
O'
'
d
d)
)
o
o)
)
O
O
x
x
y
y
J
J
D
D aD
aD
a
aD
D'
'
x
x
y
y
‒
‒ y
y
‒
‒ x
x

9.
Nfkurd =.3D
Nfkurd =.3D Bmltrjfams am ärmds bjiulms.
Bmltrjfams am ärmds bjiulms.


x
x
J
J B
B
r
r
Njrid
Njrid Ärmd
Ärmd


x
x


x
x


x
x


y
y


y
y
Ärmd trfdlku`dr
Ärmd trfdlku`dr
]l budrtj am ärmd
]l budrtj am ärmd
bfrbu`dr
bfrbu`dr
Ärmd smifbfrbu`dr
Ärmd smifbfrbu`dr
]l budrtj am ärmd
]l budrtj am ärmd
m`éptfbd
m`éptfbd
Ärmd
Ärmd
smifm`éptfbd
smifm`éptfbd
Ärmd
Ärmd
smifpdrdoò`fbd
smifpdrdoò`fbd
Ärmd pdrdoò`fbd
Ärmd pdrdoò`fbd
Mlhutdpdrdoò`fbd
Mlhutdpdrdoò`fbd
Mlhutd kmlmrd`
Mlhutd kmlmrd`
Rmbtjrbfrbu`dr
Rmbtjrbfrbu`dr
B
B
B
B
B
B


y
y


y
y
B
B
B
B


x
x


x
x
B
B
B
B


y
y


y
y
c
c
2
2
oc
oc
?
?
o
o
?
?
o
o
?
?
1
1r
r
1
1r
r
2
2d
d
1
1
2
2d
d
3
3
2
2c
c
=
=
2
2c
c
47
47
?
?dc
dc
2
2
2
2c
c
=
=
1
1dc
dc
2
2
dc
dc
2
2
1
1
o
o
1
1
1
1r
r
?
?
?
?
1
1
o
o
1
1
1
1d
d
J
J
J
J
J
J
J
J
J
J
J
J
J
J
J
J
r
r
c
c
7
7
d
d
d
d
d
d
d
d
d
d
o
o
y
y 9
9 ex
ex?
?
c
c
c
c
l
l + 4
+ 4
l
l + ?
+ ?
d
d l
l + 4
+ 4
1
1
l
l + ?
+ ?
c
c dc
dc
l
l + 4
+ 4
B
B
7
7
7
7
7
7


x
x


y
y
y
y 9
9 ex
ex l
l
c
c
B
B
2
2δ
δ
?
?r
r
sml
sml δ
δ
r
r
?
?
δ
δ
2
2

2
2

2
2

2
2

2
2
2
2

r
r
?
?


r
r
?
?


do
do


do
do




??=
??=
=.1. Wrfimrjs ijimltjs am ärmds y `élmds
=.1. Wrfimrjs ijimltjs am ärmds y `élmds

10.
??>
??> Numrzds afstrfoufads8 bmltrjfams y bmltrjs
Numrzds afstrfoufads8 bmltrjfams y bmltrjs
am krdvmada
am krdvmada
=.=. W@DBDR V D@DIO_MR BJIW]MRQJR
=.=. W@DBDR V D@DIO_MR BJIW]MRQJR
Ml iubcjs bdsjs, uld p`dbd p`dld pumam
Ml iubcjs bdsjs, uld p`dbd p`dld pumam afvfafrsm ml rmbtälku`js, trfäl-
afvfafrsm ml rmbtälku`js, trfäl-
ku`js u jtrds am `ds njrids bjiulms ijstrdads ml `d nfkurd =.3D. @d
ku`js u jtrds am `ds njrids bjiulms ijstrdads ml `d nfkurd =.3D. @d
dosbfsd
dosbfsd S
S

 am su bmltrj am krdvmada
am su bmltrj am krdvmada K
K pumam amtmrifldrsm d pdrtfr am
pumam amtmrifldrsm d pdrtfr am
`ds dosbfsds
`ds dosbfsds x
x

4
4,
, x
x

?
?, . . . ,
, . . . , x
x

 l
l am `js bmltrjs am krdvmada am `ds afnmrmltms
am `js bmltrjs am krdvmada am `ds afnmrmltms
pdrtms qum bjlstftuyml `d p`dbd, mxprmsdlaj qum m` ijimltj am` pmsj
pdrtms qum bjlstftuyml `d p`dbd, mxprmsdlaj qum m` ijimltj am` pmsj
am tjad `d p`dbd bjl rmspmbtj d` mhm
am tjad `d p`dbd bjl rmspmbtj d` mhm y
y ms fkud` d `d suid am `js ij-
ms fkud` d `d suid am `js ij-
imltjs am `js pmsjs am `ds afnmrmltms pdrtms bjl rmspmbtj d msm ifsij
imltjs am `js pmsjs am `ds afnmrmltms pdrtms bjl rmspmbtj d msm ifsij
mhm (nfkurd =.6). @d jramldad
mhm (nfkurd =.6). @d jramldad V
V

 am` bmltrj am krdvmada am `d p`dbd sm
am` bmltrj am krdvmada am `d p`dbd sm
mlbumltrd am uld njrid sfif`dr, fkud`dlaj ijimltjs bjl rmspmbtj d`
mlbumltrd am uld njrid sfif`dr, fkud`dlaj ijimltjs bjl rmspmbtj d`
mhm
mhm x.
x. Dsé, sm msbrfom
Dsé, sm msbrfom

I
I y
y8
8 S
S

 (
([
[
4
4 
 [
[
?
? 
  
   
  [
[
l
l)
) 
 x
x

4
4[
[
4
4 
 x
x

?
?[
[
?
? 
  
   
  x
x

 l
l[
[
l
l

I
I x
x8
8 V
V

 (
([
[
4
4 
 [
[
?
? 
  
   
  [
[
l
l)
) 
 y
y

4
4[
[
4
4 
 y
y

?
?[
[
?
? 
  
   
  y
y

 l
l[
[
l
l


x
x


y
y
r
r
sml
sml d
d
d
d
?
?r
r

 



?
?r
r
?
?r
r
?
?

 r
r

 r
r
Njrid
Njrid
]l budrtj am drbj
]l budrtj am drbj
bfrbu`dr
bfrbu`dr
Drbj smifbfrbu`dr
Drbj smifbfrbu`dr
Drbj am bérbu`j
Drbj am bérbu`j
@jlkftua
@jlkftua
7
7
?
?d
dr
r
7
7
J
J
J
J
J
J
B
B
B
B
r
r
r
r
B
B


x
x


y
y


x
x
d
d
d
d
9
9
x
x
y
y
z
z
x
x
y
y
z
z
J
J
K
K


S
S


V
V
[
[4
4 [
[?
?
[
[2
2
K
K4
4
K
K?
?
K
K2
2
΢
΢ [
[
΢
΢I
I y
y 8
8 

S
S ΢
΢
[
[
9 ΢
9 ΢


x
x [
[
΢
΢I
I x
x
8
8 

V
V ΢
΢
[
[
9 ΢
9 ΢


y [
y [
J
J
Nfkurd =.6
Nfkurd =.6 Bmltrj am krdvmada am uld p`dbd bjipumstd.
Bmltrj am krdvmada am uld p`dbd bjipumstd.
Nfkurd =.3O
Nfkurd =.3O Bmltrjfams am njrids bjiulms am `élmds.
Bmltrjfams am njrids bjiulms am `élmds.

11.
??;
??;
=.=. W`dbds y d`diorms bjipumstjs
=.=. W`dbds y d`diorms bjipumstjs
9
9
x
x
y
y
J
J
B
B


S
S


V
V
D
D4
4
D
D2
2
D
D?
?
B
B4
4 B
B?
?
B
B2
2
΢
΢ D
D
T
T y
y 9
9


S
S ΢
΢
D
D 9 ΢
9 ΢


x
x D
D
T
T x
x
9
9


V
V ΢
΢
D
D 9 ΢
9 ΢


y D
y D
x
x
y
y
J
J
Nfkurd =.47
Nfkurd =.47 Bmltrjfam am ul ärmd bjipumstd.
Bmltrjfam am ul ärmd bjipumstd.
x
x
y
y
z
z
x
x
y
y


x
x4
4


x
x?
?


xD
xD


x
x
[
[4
4
[
[?
?
[
[2
2
D
D4
4
D
D4
4 Rmifbérbu`j
Rmifbérbu`j
D
D?
? _mbtälku`j
_mbtälku`j
bjip`mtj
bjip`mtj
D
D2
2 Dkuhmrj
Dkuhmrj
bfrbu`dr
bfrbu`dr
D
D?
? D
D2
2
+
+
‒
‒
D
D


x
x2
2


x
x4
4


x
x2
2


x
x?
?
+
+
+
+
‒
‒
+
+ +
+
‒
‒
‒
‒
Nfkurd =.44
Nfkurd =.44
j ml njrid bjlamlsdad,
j ml njrid bjlamlsdad,
S
S

 
[
[ 
 
 x
x

[
[ V
V

 
[
[ 
 
 y
y

[
[ (=.;)
(=.;)
Mstds mbudbfjlms sm pumaml rmsj`vmr pdrd `ds bjjramldads
Mstds mbudbfjlms sm pumaml rmsj`vmr pdrd `ds bjjramldads S
S

 y
y V
V

 am`
am`
bmltrj am krdvmada am `d p`dbd.
bmltrj am krdvmada am `d p`dbd.
Rf `d p`d
Rf `d p`dbd ms cj
bd ms cjij
ijkæ
kælmd y am ms
lmd y am mspm
pmsjr ulf
sjr ulfnjr
njrim, m` bml
im, m` bmltrj am krd
trj am krd-
-
vm
vmada bjfl
ada bjflbf
bfam bjl m` bml
am bjl m` bmltrjf
trjfam
am B
B am su ärmd. @d dos
am su ärmd. @d dosbf
bfsd
sd S
S

 am` bml
am` bmltrjf
trjf-
-
am am` ärmd pum
am am` ärmd pumam am
am amtmr
tmrif
ifldr
ldrsm jo
sm josmr
smr
vdl
vdlaj qum m` prf
aj qum m` prfimr ij
imr ijiml
imltj
tj
T
T y
y am` ärmd bji
am` ärmd bjipums
pumstd bjl rms
td bjl rmspmb
pmbtj d` mhm
tj d` mhm y
y pum
pumam mx
am mxprm
prmsdr
sdrsm bj
sm bjij m`
ij m`
prj
prjaub
aubtj am
tj am S
S

 bjl m` ärmd tj
bjl m` ärmd tjtd` y bj
td` y bjij `d su
ij `d suid am `js prf
id am `js prfim
imrjs ij
rjs ij-
-
iml
imltjs am `ds ärmds m`m
tjs am `ds ärmds m`miml
imltd
td`ms bjl rms
`ms bjl rmspmb
pmbtj d` mhm
tj d` mhm y
y (nf
(nfku
kurd =.47). @d
rd =.47). @d
jr
jram
amld
ldad
ad V
V

 am` bml
am` bmltrjf
trjfam sm ml
am sm mlbuml
bumltrd am njr
trd am njrid sf
id sfif
if`dr, bjl
`dr, bjlsf
sfam
amrdl
rdlaj
aj
m` prf
m` prfimr ij
imr ijiml
imltj
tj T
T x
x am` ärmd bji
am` ärmd bjipums
pumstd. Dsé, sm tfm
td. Dsé, sm tfmlm
lm
T
T y
y 
 S
S

 (
(
D
D4
4 
 D
D?
? 
  
   
  D
D l
l)
) 
 x
x

4
4
D
D4
4 
 x
x

?
?
D
D?
? 
 
 
 
 
 x
x


l
l
D
D l
l
T
T x
x 
 V
V

 (
(
D
D4
4 
 D
D?
? 
  
   
  D
D l
l)
) 
 y
y

4
4
D
D4
4 
 y
y

?
?
D
D?
? 
 
 
 
 
 y
y

 l
l
D
D l
l
j ml njrid bjlamlsdad,
j ml njrid bjlamlsdad,
T
T y
y 
 S
S

 

D
D 
 
 x
x


D
D T
T x
x 
 V
V

 

D
D 
 
 y
y


D
D (=.3)
(=.3)
Mstds mbudbfjlms prjpjrbfjldl `js prfimrjs ijimltjs am` ärmd bji-
Mstds mbudbfjlms prjpjrbfjldl `js prfimrjs ijimltjs am` ärmd bji-
pumstd j pumaml utf`fzdrsm pdrd jotmlmr `ds bjjramldads
pumstd j pumaml utf`fzdrsm pdrd jotmlmr `ds bjjramldads S
S

 y
y V
V

 am su
am su
bmltrjfam.
bmltrjfam.
Rm am
Rm amom tm
om tmlmr buf
lmr bufad
adaj am dsfk
aj am dsfkldr
ldr`m m` sfk
`m m` sfklj dprj
lj dprjpfd
pfdaj d` ij
aj d` ijiml
iml-
-
tj am bd
tj am bdad ärmd. @js prf
ad ärmd. @js prfim
imrjs ij
rjs ijiml
imltjs am ärmds, d` fkud` qum `js ij
tjs am ärmds, d` fkud` qum `js ij-
-
iml
imltjs am `ds numr
tjs am `ds numrzds, pum
zds, pumaml smr pj
aml smr pjsf
sftf
tf
vjs
vjs j
j lm
lmkd
kdtf
tf
vjs.
vjs. Wjr
Wjr mhmi
mhmip`j,
p`j,
ul ärmd bu
ul ärmd bu
yj
yj bml
bmltrjf
trjfam ms
am mstä `j
tä `jbd
bd`f
`fzd
zdaj d `d fz
aj d `d fzqufmr
qufmrad am` mhm
ad am` mhm y
y tml
tmlarä
arä
ul prf
ul prfimr ij
imr ijiml
imltj lm
tj lmkd
kdtf
tf
vj bjl rms
vj bjl rmspmb
pmbtj d af
tj d afbcj mhm. Dam
bcj mhm. Damiäs d` ärmd
iäs d` ärmd
am ul dku
am ul dku
hm
hmrj sm `m am
rj sm `m amom dsfk
om dsfkldr ul sfk
ldr ul sfklj lm
lj lmkd
kdtf
tf
vj
vj (nĴ
(nĴku
kurd =.44).
rd =.44).
Am idlmrd sfif`dr, ml iubcjs bdsjs ms pjsfo`m amtmrifldr m` bml-
Am idlmrd sfif`dr, ml iubcjs bdsjs ms pjsfo`m amtmrifldr m` bml-
trj am krdvmada am ul d`diorm bjipumstj j m` bmltrjfam am uld `élmd
trj am krdvmada am ul d`diorm bjipumstj j m` bmltrjfam am uld `élmd
bjipumstd afvfafmlaj d` d`diorm j d `d `élmd ml m`mimltjs iäs sfi-
bjipumstd afvfafmlaj d` d`diorm j d `d `élmd ml m`mimltjs iäs sfi-
p`ms (vædsm prjo`mid rmsum`tj =.?).
p`ms (vædsm prjo`mid rmsum`tj =.?).

12.
W_JO@MID _MR]M@QJ =.4
W_JO@MID _MR]M@QJ =.4
Wdrd m` ärmd p`dld ijstrdad ml `d nfkurd, amtmriflm8
Wdrd m` ärmd p`dld ijstrdad ml `d nfkurd, amtmriflm8 d
d) `js prfimrjs ij-
) `js prfimrjs ij-
imltjs bjl rmspmbtj d `js mhms
imltjs bjl rmspmbtj d `js mhms x
x y
y y
y,
, y
y o
o) `d uofbdbfòl am su bmltrjfam.
) `d uofbdbfòl am su bmltrjfam.
RJ@]BFÒL
RJ@]BFÒL
Bjipjlmltms am` ärmd.
Bjipjlmltms am` ärmd. M` ärmd sm jotfmlm bjl `d suid am ul rmb-
M` ärmd sm jotfmlm bjl `d suid am ul rmb-
tälku`j, ul trfälku`j y ul smifbérbu`j y amspuæs sm rmstd ul bérbu`j. ]tf-
tälku`j, ul trfälku`j y ul smifbérbu`j y amspuæs sm rmstd ul bérbu`j. ]tf-
`fzdlaj `js mhms bjjramldajs ijstrdajs, sm amtmrifldl m` ärmd y `ds bjjram-
`fzdlaj `js mhms bjjramldajs ijstrdajs, sm amtmrifldl m` ärmd y `ds bjjram-
ldads am` bmltrjfam pdrd bdad uld am `ds ärmds bjipjlmltms y `umkj sm
ldads am` bmltrjfam pdrd bdad uld am `ds ärmds bjipjlmltms y `umkj sm
fltrjaubml ml `d tdo`d qum dpdrmbm ml `d pdrtm flnmrfjr. M` ärmd am` bérbu`j
fltrjaubml ml `d tdo`d qum dpdrmbm ml `d pdrtm flnmrfjr. M` ärmd am` bérbu`j
sm flafbd bjij lmkdtfvd pumstj qum amom rmstdrsm am `ds
sm flafbd bjij lmkdtfvd pumstj qum amom rmstdrsm am `ds amiäs ärmds. Lòtmsm
amiäs ärmds. Lòtmsm
qum `d bjjramldad
qum `d bjjramldad y
y

 am` bmltrjfam am` trfälku`j ms lmkdtfvd pdrd `js mhms
am` bmltrjfam am` trfälku`j ms lmkdtfvd pdrd `js mhms
ijstrdajs. @js prfimrjs ijimltjs am `ds ärmds bjipjlmltms bjl rmspmbtj
ijstrdajs. @js prfimrjs ijimltjs am `ds ärmds bjipjlmltms bjl rmspmbtj
d `js mhms bjjramldajs sm bd`bu`dl y sm fltrjaubml ml `d tdo`d.
d `js mhms bjjramldajs sm bd`bu`dl y sm fltrjaubml ml `d tdo`d.
??3
??3
d
d)
) Wrfimrjs ijim
Wrfimrjs ijimltjs am
ltjs am` ärmd
` ärmd.
. Bjl `ds mbudbfjlms (=.3), sm msbrfom
Bjl `ds mbudbfjlms (=.3), sm msbrfom
T
T x
x 
 
 y
y


D
D 
 =7>.?
=7>.? 
 47
472
2
ii
ii2
2
T
T x
x 
 =7>
=7> 
 47
472
2
ii
ii2
2
T
T y
y 
 
 x
x


D
D 
 ;=;.;
;=;.; 
 47
472
2
ii
ii2
2
T
T y
y 
 ;=3
;=3 
 47
472
2
ii
ii2
2
o
o)
) ]ofbdbfòl am` bmltrjfam
]ofbdbfòl am` bmltrjfam.
. Rf sm sustftuyml `js vd`jrms adajs ml `d
Rf sm sustftuyml `js vd`jrms adajs ml `d
tdo`d, amltrj am `ds mbudbfjlms qum amnflml m` bmltrjfam am ul ärmd bji-
tdo`d, amltrj am `ds mbudbfjlms qum amnflml m` bmltrjfam am ul ärmd bji-
pumstd sm jotfmlm
pumstd sm jotfmlm
S
S

 
 D
D 
 
 x
x


D
D8
8 S
S

 (42.3?3
(42.3?3 
 47
472
2
ii
ii?
?
)
) 
 ;=;.;
;=;.; 
 47
472
2
ii
ii2
2
S
S

 
 =1.3 ii
=1.3 ii
V
V

 
 D
D 
 
 y
y


D
D8
8 V
V

 (42.3?3
(42.3?3 
 47
472
2
ii
ii?
?
)
) 
 =7>.?
=7>.? 
 47
472
2
ii
ii2
2
V
V

 
 2>.> ii
2>.> ii
Bjipjlmltm
Bjipjlmltm D
D, ii
, ii?
?
x
x

, ii
, ii y
y

, ii
, ii x
x

D
D, ii
, ii2
2
y
y

D
D, ii
, ii2
2
_
_m
mb
bt
tä
äl
lk
ku
u`
`j
j (
(4
4?
?7
7)
)(
(3
37
7)
) 
 6.>
6.> 
 47
472
2
>
>7
7 1
17
7 
=;>
=;> 
 47
472
2

231
231 
 47
472
2
Qrfälku`j
Qrfälku`j 

4
4
?
?

(4?7)(>7)
(4?7)(>7) 
 2.>
2.> 
 47
472
2
17
17 
?7
?7 
411
411 
 47
472
2

;?
;? 
 47
472
2
Rmifbérbu`j
Rmifbérbu`j 

4
4
?
?



(>7)
(>7)?
?

 =.>==
=.>== 
 47
472
2
>
>7
7 4
47
7=
=.
.1
1>
> 
226.2
226.2 
 47
472
2

=6>.1
=6>.1 
 47
472
2
Bérbu`j
Bérbu`j 


(17)
(17)?
?

 
=.7?;
=.7?; 
 47
472
2
>
>7
7 3
37
7 
274.>
274.> 
 47
472
2

17?.?
17?.? 
 47
472
2

 D
D 
 42.3?3
42.3?3 
 47
472
2

 x
x


D
D 
 
;=;.;
;=;.; 
 47
472
2

 y
y


D
D 
 
=7>.?
=7>.? 
 47
472
2
y
y
x
x
37 ii
37 ii
>7 ii
>7 ii
>7 ii
>7 ii
17 ii
17 ii
4?7ii
4?7ii
y
y
x
x
B
B
S
S
9 =1.3 ii
9 =1.3 ii
V
V
9
9 2>.> ii
2>.> ii
y
y y
y
x
x
37 ii
37 ii
>7 ii
>7 ii
r
r
4
4 9 >7 ii
9 >7 ii
r
r
?
? 917 ii
917 ii
4?7ii
4?7ii
x
x x
x x
x x
x
y
y y
y y
y
9
9 +
+ +
+ Z
Z
17 ii
17 ii
17 ii
17 ii
‒?7 ii
‒?7 ii
9
9 ?=.1> ii
?=.1> ii
1
1r
r
4
4
2
2 r
r
4
4 9
9 >7 ii
>7 ii
r
r
?
? 9
9 17 ii
17 ii
>7 ii
>7 ii
>7 ii
>7 ii
>7 ii
>7 ii
37 ii
37 ii 47=.1> ii
47=.1> ii 37 ii
37 ii



13.
W_JO@MID _MR]M@QJ =.?
W_JO@MID _MR]M@QJ =.?
@d nfkurd ijstrdad mstä cmbcd d pdrtfr am ul pmadzj am d`diorm am`kdaj y
@d nfkurd ijstrdad mstä cmbcd d pdrtfr am ul pmadzj am d`diorm am`kdaj y
cjijkælmj. Amtmriflm `d uofbdbfòl am su bmltrj am krdvmada.
cjijkælmj. Amtmriflm `d uofbdbfòl am su bmltrj am krdvmada.
RJ@]BFÒL
RJ@]BFÒL
Bj
Bjij `d nf
ij `d nfku
kurd ms
rd mstä cm
tä cmbcd am ul d`di
bcd am ul d`diorm cj
orm cjij
ijkæ
kælmj, su bml
lmj, su bmltrj am krd
trj am krd
vm
vm-
-
ada bjfl
ada bjflbf
bfam bjl m` bml
am bjl m` bmltrjf
trjfam am `d `é
am am `d `élmd bj
lmd bjrrms
rrmspjl
pjlafml
afmltm. Wjr tdl
tm. Wjr tdltj, sm am
tj, sm am-
-
tmr
tmrif
ifld
ldrä af
rä afbcj bml
bcj bmltrjf
trjfam. Rf sm sm
am. Rf sm sm`mb
`mbbfj
bfjldl `js mhms ijs
ldl `js mhms ijstrd
trdajs, bjl jrf
ajs, bjl jrfkml
kml
ml
ml D
D, sm am
, sm amtmr
tmrif
ifldl `ds bjjr
ldl `ds bjjram
amld
ldads am` bml
ads am` bmltrjf
trjfam am bd
am am bdad smk
ad smkiml
imltj am `é
tj am `é-
-
lmd y sm bd`
lmd y sm bd`bu
bu`dl `js prf
`dl `js prfim
imrjs ij
rjs ijiml
imltjs bjl rms
tjs bjl rmspmb
pmbtj d `js mhms bjjr
tj d `js mhms bjjram
amld
ld-
-
ajs.
ajs.
Rmkimltj
Rmkimltj @
@, fl.
, fl. x
x

, fl.
, fl. y
y

, fl.
, fl. x
x

@
@, fl
, fl?
?
y
y

@
@, fl
, fl?
?
DO
DO ?
?1
1 4
4?
? 7
7 ?
?3
33
3 7
7
OB
OB ?
?>
> 4
4?
? =
= 2
24
4?
? 4
42
27
7
BD
BD 4
47
7 7
7 =
= 7
7 =
=7
7

 @
@ 
 >7
>7 
 x
x


@
@ 
 >77
>77 
 y
y


@
@ 
 437
437
Bjl `d sustftubfòl am `js vd`jrms jotmlfajs ml `d tdo`d, ml `ds mbudbfjlms qum
Bjl `d sustftubfòl am `js vd`jrms jotmlfajs ml `d tdo`d, ml `ds mbudbfjlms qum
amnĴlml m` bmltrjfam am uld `élmd bjipumstd, sm jotfmlm
amnĴlml m` bmltrjfam am uld `élmd bjipumstd, sm jotfmlm
S
S

 
 @
@ 
 
 x
x


@
@8
8 S
S

 (>7 fl.)
(>7 fl.) 
 >77 fl
>77 fl?
?
S
S

 
 47 fl.
47 fl.
V
V

 
 @
@ 
 
 y
y


@
@8
8 V
V

 (>7 fl.)
(>7 fl.) 
 437 fl
437 fl?
?
V
V

 
 4
42 fl.
2 fl.
??6
??6
?
?
>
>
f
f
l
l
.
.
47 fl.
47 fl.
?1 fl.
?1 fl.
B
B
O
O
D
D
47 fl.
47 fl.
4? fl.
4? fl.
= fl.
= fl.
?1 fl.
?1 fl.
B
B
y
y
x
x
O
O
D
D
?
?
>
>
f
f
l
l
.
.

14.
W_JO@MID _MR]M@QJ =.2
W_JO@MID _MR]M@QJ =.2
]ld odrrd smifbfrbu`dr ulfnjrim am pmsj
]ld odrrd smifbfrbu`dr ulfnjrim am pmsj [
[
y rdafj
y rdafj r
r mstä ulfad d ul pmrlj
mstä ulfad d ul pmrlj
ml
ml D
D y amsbdlsd bjltrd
y amsbdlsd bjltrd uld supmrnfbfm sfl
uld supmrnfbfm sfl nrfbbfòl ml
nrfbbfòl ml O
O. Amtmriflm `ds rmdb-
. Amtmriflm `ds rmdb-
bfjlms ml
bfjlms ml D
D y
y O
O.
.
RJ@]BFÒL
RJ@]BFÒL
Afdkrdid am bumrpj `form.
Afdkrdid am bumrpj `form. Rm afouhd ul afdkrdid am bumrpj `form
Rm afouhd ul afdkrdid am bumrpj `form
am `d odrrd. @ds numrzds qum dbtødl sjorm `d odrrd sjl su pmsj
am `d odrrd. @ds numrzds qum dbtødl sjorm `d odrrd sjl su pmsj [
[
, m` bud` mstä
, m` bud` mstä
dp`fbdaj ml m` bmltrj am krdvmada
dp`fbdaj ml m` bmltrj am krdvmada K
K (buyd pjsfbfòl sm jotfmlm d pdrtfr am `d
(buyd pjsfbfòl sm jotfmlm d pdrtfr am `d
nfkurd =.3O)5 uld rmdbbfòl ml
nfkurd =.3O)5 uld rmdbbfòl ml D
D, rmprmsmltdad pjr sus bjipjlmltms
, rmprmsmltdad pjr sus bjipjlmltms D
D
x
x y
y D
D
y
y
y uld
y uld rmdbbfòl cjrfzjltd`
rmdbbfòl cjrfzjltd` ml
ml O
O.
.
Mbudbfjlms am mquf`forfj
Mbudbfjlms am mquf`forfj

`
`
I
I D
D 
 78
78 O
O(?
(?r
r
)
) 
 [
[
 
 7
7
O
O 
 
 O
O 
 y
y
y
y



N
N x
x 
 78
78 D
D x
x 
 O
O 
 7
7
D
D
x
x 
 
O
O 
 
 D
D
x
x 
 z
z


x
x

N
N y
y 
 78
78 D
D y
y 
 [
[ 
 7
7 D
D
y
y 
 [
[
x
x
Ruidlaj `ds ajs bjipjlmltms am `d rmdbbfòl ml
Ruidlaj `ds ajs bjipjlmltms am `d rmdbbfòl ml D
D8
8
D
D 

[
[ ?
?


 
?
?

4
4
?
?
D
D 
 [
[
4
4 


4
4
?
?
tdl
tdl 
 
 
 
 
 
 tdl
tdl
4
4


@ds rmspumstds tdiofæl pumaml mxprmsdrsm bjij sfkum8
@ds rmspumstds tdiofæl pumaml mxprmsdrsm bjij sfkum8
D
D 
 4.716
4.716[
[ o
o;?.2·
;?.2· O
O 
 7.243
7.243[
[ y
y
?
?r
r




[
[


[
[



[
[




4
4




?
?
[
[




[
[




[
[




?27
?27
D
D
O
O
J
J
r
r
K
K
O
O
D
D x
x
D
D
D
D y
y
[
[
O
O
?
?r
r
?
?r
r


D
D y
y
9
9 [
[
d
d
D
D x
x
9
9
[
[


D
D
[
[





15.
_ M R J @ ] B F Ò L A M W _ J O @ M I D R
_ M R J @ ] B F Ò L A M W _ J O @ M I D R
M L N J _ I D F L A M W M L A F M L Q M
M L N J _ I D F L A M W M L A F M L Q M
Ml ms
Ml mstd `mb
td `mbbfòl sm am
bfòl sm amsd
sdrrj
rrj``d
``drjl `ds mbud
rjl `ds mbudbfj
bfjlms km
lms kmlm
lmrd
rd`ms pd
`ms pdrd `j
rd `jbd
bd`f
`fzdr `js bml
zdr `js bmltrjs am
trjs am
krd
krd
vm
vmada am bumr
ada am bumrpjs of
pjs ofaf
afiml
imlsfj
sfjld
ld`ms y d`di
`ms y d`diorms Umbud
orms Umbudbfjlms (=.?)Y y `js bml
bfjlms (=.?)Y y `js bmltrjf
trjfams am
ams am
ärmds p`d
ärmds p`dlds Umbud
lds Umbudbfj
bfjlms (=.2)Y y am `élmds Umbud
lms (=.2)Y y am `élmds Umbudbfj
bfjlms (=.1)Y. Ml `js prj
lms (=.1)Y. Ml `js prjo`m
o`mids qum sm
ids qum sm
prm
prmsml
smltdl d bjl
tdl d bjltf
tflud
ludbfòl, sm am
bfòl, sm amom
omräl `j
räl `jbd
bd`f
`fzdr `js bml
zdr `js bmltrjf
trjfams am ärmds bji
ams am ärmds bjipums
pumstds y `é
tds y `é-
-
lmds j tml
lmds j tmlaräl qum am
aräl qum amtmr
tmrif
ifldr
ldrsm `js prf
sm `js prfim
imrjs ij
rjs ijiml
imltjs am` ärmd am p`d
tjs am` ärmd am p`dbds bji
bds bjipums
pums-
-
tds Umbud
tds Umbudbfj
bfjlms (=.3)Y.
lms (=.3)Y.
4
4.
. @
@j
jbd
bd`f
`f
zd
zdbfòl am bml
bfòl am bml
trjf
trjf
ams am
ams am ärmds bji
ärmds bji
pums
pums
tds y
tds y `é
`é
lmds.
lmds. @js prj
@js prjo`m
o`mids rm
ids rm-
-
sum`
sum`tjs =.4 y =.? f`us
tjs =.4 y =.? f`ustrdl m` prj
trdl m` prjbm
bmaf
afifml
ifmltj qum am
tj qum amom sm
om smkufr
kufrsm d` rm
sm d` rmsj`
sj ̀vmr prj
vmr prjo`m
o`mids am
ids am
ms
mstm tf
tm tfpj. Rfl mi
pj. Rfl miodr
odrkj, cdy bfmr
kj, cdy bfmrtjs pul
tjs pultjs qum sm am
tjs qum sm amoml ml
oml mlnd
ndtf
tfzdr.
zdr.
d
d)
) M` prf
M` prfimr pd
imr pdsj ml `d sj
sj ml `d sj`u
`ubfòl am
bfòl amom smr am
om smr ambf
bfafr bò
afr bòij bjls
ij bjlstrufr m` ärmd j `d `é
trufr m` ärmd j `d `élmd
lmd
ad
adad, d pdr
ad, d pdrtfr am `ds njr
tfr am `ds njrids bj
ids bjiu
iulms am `d nf
lms am `d nfku
kurd =.3. Rm am
rd =.3. Rm amom rm
om rmbj
bjlj
ljbmr qum, ml m` bd
bmr qum, ml m` bd-
-
sj am ärmds p`d
sj am ärmds p`dlds, uld njr
lds, uld njrid ml pdr
id ml pdrtf
tfbu
bu`dr sm pum
`dr sm pumam bjls
am bjlstrufr am vd
trufr am vdrfds id
rfds idlm
lmrds. Dam
rds. Dam-
-
iäs, ijs
iäs, ijstrdr `ds af
trdr `ds afnm
nmrml
rmltms bji
tms bjipj
pjlml
lmltms (bj
tms (bjij sm cd
ij sm cdbm ml m` prj
bm ml m` prjo`m
o`mid rm
id rmsum`
sum`tj =.4)
tj =.4)
dyu
dyuad
adrä d ms
rä d mstd
tdo`m
o`mbmr bj
bmr bjrrmb
rrmbtd
tdiml
imltm sus bml
tm sus bmltrjf
trjfams y sus ärmds j `jl
ams y sus ärmds j `jlkf
kftu
tuams. Lj am
ams. Lj amom
om
j`
j ̀vf
vfadr
adrsm qum, pd
sm qum, pdrd jo
rd jotm
tmlmr `d njr
lmr `d njrid am
id amsmd
smdad, ms pj
ad, ms pjsf
sfo`m rms
o`m rmstdr j su
tdr j suidr ärmds.
idr ärmds.
o
o)
) Rm rm
Rm rmbj
bjifml
ifmlad qum pd
ad qum pdrd bd
rd bdad prj
ad prjo`m
o`mid sm bjls
id sm bjlstru
tru
yd uld td
yd uld tdo`d qum bjl
o`d qum bjltml
tmlkd `ds
kd `ds
ärmds j `ds `jl
ärmds j `ds `jlkf
kftu
tuams y `ds bjjr
ams y `ds bjjram
amld
ldads rms
ads rmspmb
pmbtf
tf
vds
vds am
am sus
sus bml
bmltrjf
trjfams. Ms msml
ams. Ms msmlbfd` rm
bfd` rm-
-
bjr
bjradr qum `ds ärmds qum sjl ‐rm
adr qum `ds ärmds qum sjl ‐rmij
ij
vf
vfads’ (pjr mhmi
ads’ (pjr mhmip`j `js dku
p`j `js dku
hm
hmrjs) sm tj
rjs) sm tjidl bj
idl bjij lm
ij lm-
-
kd
kdtf
tf
vds. Dam
vds. Damiäs sm am
iäs sm amom fl
om flb`ufr m` sfk
b`ufr m` sfklj am `ds bjjr
lj am `ds bjjram
amld
ldads lm
ads lmkd
kdtf
tf
vds. Wjr
vds. Wjr tdl
tdltj, sfmi
tj, sfmi-
-
prm am
prm amom jo
om josmr
smr
vdr
vdrsm `d uof
sm `d uofbd
bdbfòl am` jrf
bfòl am` jrfkml am `js mhms bjjr
kml am `js mhms bjjram
amld
ldajs.
ajs.
b
b)
) Budlaj smd pjsfo`m, sm amoml utf`fzdr bjlsfamrdbfjlms am sfimtréd Usmbbfòl =.1Y
Budlaj smd pjsfo`m, sm amoml utf`fzdr bjlsfamrdbfjlms am sfimtréd Usmbbfòl =.1Y
pdrd amtmrifldr bjl idyjr ndbf`fada `d uofbdbfòl am ul bmltrjfam.
pdrd amtmrifldr bjl idyjr ndbf`fada `d uofbdbfòl am ul bmltrjfam.
a
a)
) Ml `ds nòriu`ds am `d nfkurd =.3 pdrd m` smbtjr bfrbu`dr y pdrd m` drbj am` bérbu`j,
Ml `ds nòriu`ds am `d nfkurd =.3 pdrd m` smbtjr bfrbu`dr y pdrd m` drbj am` bérbu`j,
m` älku`j sfmiprm amom smr mxprmsdaj ml rdafdlms.
m` älku`j sfmiprm amom smr mxprmsdaj ml rdafdlms.
?.
?. Bä`
Bä`bu
bu`j am `js prf
`j am `js prf
im
im
rjs ij
rjs ij
iml
iml
tjs am
tjs am ul
ul ärmd.
ärmd. @js prj
@js prjbm
bmaf
afifml
ifmltjs pd
tjs pdrd uof
rd uof-
-
bdr m` bml
bdr m` bmltrjf
trjfam am ul ärmd y pd
am am ul ärmd y pdrd am
rd amtmr
tmrif
ifldr `js prf
ldr `js prfim
imrjs ij
rjs ijiml
imltjs am ul ärmd sjl
tjs am ul ärmd sjl
sf
sfif
if`d
`drms5 sfl mi
rms5 sfl miodr
odrkj, pd
kj, pdrd bd`
rd bd`bu
bu`dr ms
`dr mstjs ø`
tjs ø`tf
tfijs lj ms lm
ijs lj ms lmbm
bmsd
sdrfj am
rfj amtmr
tmrif
ifldr m` ärmd
ldr m` ärmd
tj
tjtd`. Dam
td`. Damiäs, bj
iäs, bjij sm sm
ij sm smôd
ôd`ò ml `d smb
`ò ml `d smbbfòl =.1, sm am
bfòl =.1, sm amom rm
om rmbj
bjlj
ljbmr qum m` prf
bmr qum m` prfimr ij
imr ij-
-
iml
imltj am ul ärmd bjl rms
tj am ul ärmd bjl rmspmb
pmbtj d ul mhm bml
tj d ul mhm bmltrjf
trjfad` ms fkud` d bm
ad` ms fkud` d bmrj.
rj.
2
2.
. _
_m
m
sj
sj`u
`ubfòl am prj
bfòl am prj
o`m
o`m
ids qum
ids qum fl
fl
vj
vj`u
`ubrdl d` bml
brdl d` bml
trj am krd
trj am krd
vm
vm
ada.
ada. Ml `js prj
Ml `js prj-
-
o`m
o`mids qum sm prm
ids qum sm prmsml
smltdl d bjl
tdl d bjltf
tflud
ludbfòl sm bjl
bfòl sm bjlsf
sfam
amrd qum `js bumr
rd qum `js bumrpjs sjl cj
pjs sjl cjij
ijkæ
kælmjs5
lmjs5
pjr tdl
pjr tdltj, sus bml
tj, sus bmltrjs am krd
trjs am krd
vm
vmada bjfl
ada bjflbf
bfaml bjl sus bml
aml bjl sus bmltrjf
trjfams. Dam
ams. Damiäs, budl
iäs, budlaj ul
aj ul
bumr
bumrpj qum ms
pj qum mstä sus
tä suspml
pmlaf
afaj am ul sj
aj am ul sj`j pmr
`j pmrlj ms
lj mstä ml mquf
tä ml mquf`f
`forfj, m` pmr
orfj, m` pmrlj y m` bml
lj y m` bmltrj
trj
am krd
am krd
vm
vmada am` bumr
ada am` bumrpj am
pj amoml ms
oml mstdr `j
tdr `jbd
bd`f
`fzd
zdajs sj
ajs sjorm `d ifs
orm `d ifsid `é
id `élmd vmr
lmd vmrtf
tfbd`.
bd`.
Wuafmrd pdrmbmr qum iubcjs am `js prjo`mids ml mstd `mbbfòl tfmlml pjbj qum vmr bjl
Wuafmrd pdrmbmr qum iubcjs am `js prjo`mids ml mstd `mbbfòl tfmlml pjbj qum vmr bjl
m` mstuafj am `d imbälfbd. Rfl miodrkj, smr bdpdz am `jbd`fzdr m` bmltrjfam am njrids
m` mstuafj am `d imbälfbd. Rfl miodrkj, smr bdpdz am `jbd`fzdr m` bmltrjfam am njrids
bjipumstds smrä msmlbfd` ml vdrfjs tòpfbjs qum sm mstuafdräl iäs dam`dltm.
bjipumstds smrä msmlbfd` ml vdrfjs tòpfbjs qum sm mstuafdräl iäs dam`dltm.
?24
?24

16.
?2?
?2?
Wrjo`mids
Wrjo`mids
=.4 d =.6
=.4 d =.6 @jbd`fbm m` bmltrjfam
@jbd`fbm m` bmltrjfam am` ärmd p`dld
am` ärmd p`dld qum sm iumstrd m
qum sm iumstrd ml bdad
l bdad
nfkurd.
nfkurd.
y
y
x
x
27 ii
27 ii
277 ii
277 ii
?17 ii
?17 ii
27 ii
27 ii
y
y
x
x
?
?7
7 i
ii
i 2
27
7 i
ii
i
2> ii
2> ii
?1 ii
?1 ii
x
x
y
y
4
4?
? f
fl
l.
. ?
?4
4 f
fl
l.
.
4= fl.
4= fl.
y
y
> fl.
> fl.
> fl.
> fl.
> fl.
> fl.
> fl.
> fl.
2 fl.
2 fl.
x
x
x
x
y
y
r
r
9 1 fl.
9 1 fl.
3 fl.
3 fl.
4? fl.
4? fl.
3 fl.
3 fl.
> fl.
> fl.
x
x
y
y
4?7 ii
4?7 ii
r
r 9 ;= ii
9 ;= ii
x
x
y
y
r
r 9 23 fl.
9 23 fl.
4> fl.
4> fl.
?7 fl.
?7 fl.
x
x
y
y
27 fl.
27 fl.
27 fl.
27 fl.
r
r 9 4= fl.
9 4= fl.
?7 fl.
?7 fl.
x
x
y
y
>7 ii
>7 ii
>7 ii
>7 ii
Nfkurd W=.4
Nfkurd W=.4 N
Nf
fk
ku
ur
rd
d W
W=
=.
.?
? N
Nf
fk
ku
ur
rd
d W
W=
=.
.2
2
Nfkurd W=.1
Nfkurd W=.1 N
Nf
fk
ku
ur
rd
d W
W=
=.
.=
= N
Nf
fk
ku
ur
rd
d W
W=
=.
.>
>
Nfkurd
Nfkurd W=.;
W=.; Nfkurd
Nfkurd W=.3
W=.3 Nfkurd W=.6
Nfkurd W=.6

17.
?22
?22
Wrjo`mids
Wrjo`mids
=.47 d =.4=
=.47 d =.4= @jbd`fbm m` bmltrjfam am` ärmd p`dld qum sm iumstrd ml
@jbd`fbm m` bmltrjfam am` ärmd p`dld qum sm iumstrd ml
bdad nfkurd.
bdad nfkurd.
=.4>
=.4> Amtmriflm `d bjjramldad
Amtmriflm `d bjjramldad y
y am` bmltrjfam am` ärmd sjiormdad ml
am` bmltrjfam am` ärmd sjiormdad ml
tærifljs am
tærifljs am r
r
4
4,
, r
r
?
? y
y δ
δ
.
.
=.4;
=.4; Amiumstrm qum sf
Amiumstrm qum sf r
r
4
4 tfmlam d
tfmlam d r
r
?
?, `d `jbd`fzdbfòl am su bmltrjfam
, `d `jbd`fzdbfòl am su bmltrjfam
tfmlam d smr fkud` d` bmltrjfam am ul drbj bfrbu`dr am rdafj (
tfmlam d smr fkud` d` bmltrjfam am ul drbj bfrbu`dr am rdafj (r
r
4
4 +
+ r
r
?
?)/?.
)/?.
=.43
=.43 Wdrd m` ärmd ijstrdad, amtmriflm `d rm`dbfòl
Wdrd m` ärmd ijstrdad, amtmriflm `d rm`dbfòl d
d
/
/
o
o td` qum
td` qum x
x

 
 y
y

.
.
=.46
=.46 Wdrd m` ärmd smifdlu`dr am` prjo`mid =.44, amtmriflm `d rm`dbfòl
Wdrd m` ärmd smifdlu`dr am` prjo`mid =.44, amtmriflm `d rm`dbfòl
r
r
?
?
/
/
r
r
4
4 td` qum
td` qum y
y

 
 2
2r
r
4
4
/1.
/1.
x
x
y
y
Rmifm`fpsm
Rmifm`fpsm
;7 ii
;7 ii
?> ii
?> ii
1
1;
; i
ii
i 1
1;
; i
ii
i
x
x
y
y
r
r
?
?
94? fl.
94? fl. r
r
4
4
9 3 fl.
9 3 fl.
Wdräoj`d
Wdräoj`d
^ærtfbm
^ærtfbm
=7 ii
=7 ii
4= ii
4= ii
37 ii
37 ii
y
y
x
x
x
x
y
y
r
r
x
x 9
9 ey
ey?
?
?7 ii
?7 ii ?7 ii
?7 ii
27 ii
27 ii
x
x 9
9 ey
ey?
?
x
x
y
y 9
9 ex
ex?
?
y
y
?7 fl.
?7 fl.
?7 fl.
?7 fl.
x
x
y
y
^ærtfbm
^ærtfbm
Wdräoj`d
Wdräoj`d
;= ii
;= ii
>7 ii
>7 ii
>7 ii
>7 ii
x
x
y
y
δ
δ δ
δ
r
r
4
4 r
r
?
?
x
x
y
y
y
y 9
9 ex
ex?
?
d
d
o
o
N
Nf
fk
ku
ur
rd
d W
W=
=.
.4
47
7 N
Nf
fk
ku
ur
rd
d W
W=
=.
.4
44
4 N
Nf
fk
ku
ur
rd
d W
W=
=.
.4
4?
?
Nfkurd
Nfkurd W=.42
W=.42
Nfkurd W=.4> y W=.4;
Nfkurd W=.4> y W=.4;
Nfkurd W=.43
Nfkurd W=.43
N
Nf
fk
ku
ur
rd
d W
W=
=.
.4
41
1 N
Nf
fk
ku
ur
rd
d W=.4=
W=.4=

18.
=.?7
=.?7 ]ld vfkd bjipumstd sm bjlstruym mipmrldlaj budtrj p`dbds d
]ld vfkd bjipumstd sm bjlstruym mipmrldlaj budtrj p`dbds d
budtrj älku`js am >7
budtrj älku`js am >7 
 >7
>7 
 4? ii, bjij sm iumstrd ml `d nfkurd. @js pmr-
4? ii, bjij sm iumstrd ml `d nfkurd. @js pmr-
ljs mstäl fkud`imltm mspdbfdajs d `j `drkj am `d vfkd, `d bud` sjstfmlm uld
ljs mstäl fkud`imltm mspdbfdajs d `j `drkj am `d vfkd, `d bud` sjstfmlm uld
bdrkd vmrtfbd`. Bjij sm amiumstrd ml `d imbälfbd am idtmrfd`ms, `ds numrzds
bdrkd vmrtfbd`. Bjij sm amiumstrd ml `d imbälfbd am idtmrfd`ms, `ds numrzds
bjrtdltms mhmrbfads sjorm `js pmrljs ml
bjrtdltms mhmrbfads sjorm `js pmrljs ml D
D y
y O
O sjl prjpjrbfjld`ms d `js prf-
sjl prjpjrbfjld`ms d `js prf-
imrjs ijimltjs rmspmbtj am` mhm bmltrjfad`
imrjs ijimltjs rmspmbtj am` mhm bmltrjfad` x
x am `ds ärmds sjiormdads am
am `ds ärmds sjiormdads am
rjhj qum sm iumstrdl, rmspmbtfvdimltm, ml `ds pdrtms
rjhj qum sm iumstrdl, rmspmbtfvdimltm, ml `ds pdrtms d
d y
y o
o am `d nfkurd. Rf sm
am `d nfkurd. Rf sm
sdom qum `d numrzd mhmrbfad sjorm m` pmrlj ml
sdom qum `d numrzd mhmrbfad sjorm m` pmrlj ml D
D ms am ?37 L, amtmriflm `d
ms am ?37 L, amtmriflm `d
numrzd mhmrbfad sjorm m` pmrlj ml
numrzd mhmrbfad sjorm m` pmrlj ml O
O.
.
?21
?21 Numrzds afstrfoufads8 bmltrjfams y bmltrjs
Numrzds afstrfoufads8 bmltrjfams y bmltrjs
am krdvmada
am krdvmada
=.?4 y =.??
=.?4 y =.?? M` mhm cjrfzjltd`
M` mhm cjrfzjltd` x
x sm trdzd d trdvæs am` bmltrjfam
sm trdzd d trdvæs am` bmltrjfam B
B y af-
y af-
vfam d`
vfam d` ärmd ijstrdad
ärmd ijstrdad ml ajs
ml ajs ärmds bjipjlmltms
ärmds bjipjlmltms D
D4
4 y
y D
D?
?. Amtmriflm m` prf-
. Amtmriflm m` prf-
imr ijimltj am bdad ärmd bjipjlmltm rmspmbtj am` mhm
imr ijimltj am bdad ärmd bjipjlmltm rmspmbtj am` mhm x
x, y mxp`fqum `js
, y mxp`fqum `js
rmsu`tdajs jotmlfajs.
rmsu`tdajs jotmlfajs.
277 ii
277 ii
4? ii
4? ii 4? ii
4? ii
4? ii
4? ii
4? ii
4? ii
>7 ii
>7 ii
>7 ii
>7 ii
D
D
B
B B
B
x
x x
x
O
O
d
d)
) o
o)
)
1=7 ii
1=7 ii
x
x
y
y
B
B
D
D4
4
D
D?
?
1.= fl.
1.= fl.
1.= fl.
1.= fl.
;.= fl.
;.= fl.
x
x
y
y
B
B
D
D4
4
D
D?
?
7.;= fl.
7.;= fl.
7.;= fl.
7.;= fl.
4.=7 fl.
4.=7 fl.
4.=7 fl.
4.=7 fl.
?.77 fl.
?.77 fl.
?.77 fl.
?.77 fl.
1.77 fl.
1.77 fl.
?.77 fl.
?.77 fl.
4.=7 fl.
4.=7 fl.
Nfkurd W=.?7
Nfkurd W=.?7
Nfkurd W=.?4
Nfkurd W=.?4
Nfkurd W=.??
Nfkurd W=.??

19.
=.?2
=.?2 M` prfimr ijimltj rmspmbtj am` mhm
M` prfimr ijimltj rmspmbtj am` mhm x
x am` ärmd sjiormdad qum
am` ärmd sjiormdad qum
sm iumstrd ml `d nfkurd sm rmprmsmltd bjl
sm iumstrd ml `d nfkurd sm rmprmsmltd bjl T
T x
x.
. d
d) Mxprmsm
) Mxprmsm T
T x
x ml tærifljs am
ml tærifljs am
o
o,
, b
b y
y `d afstdlbfd
`d afstdlbfd y
y amsam `d odsm am` ärmd sjiormdad cdstd m` mhm
amsam `d odsm am` ärmd sjiormdad cdstd m` mhm x
x.
. o
o) Am-
) Am-
tmriflm m` vd`jr am
tmriflm m` vd`jr am y
y pdrd m` bud`
pdrd m` bud` T
T x
x ms iäxfij y mlbumltrm afbcj vd`jr iä-
ms iäxfij y mlbumltrm afbcj vd`jr iä-
xfij.
xfij.
?2=
?2=
Wrjo`mids
Wrjo`mids
=.?1 d =.?;
=.?1 d =.?; ]l d`diorm am`kdaj y cjijkælmj sm ajo`d pdrd njridr
]l d`diorm am`kdaj y cjijkælmj sm ajo`d pdrd njridr
m` pmréimtrj am `ds nfkurds qum sm flafbdl d bjltfludbfòl. @jbd`fbm m` bmltrj
m` pmréimtrj am `ds nfkurds qum sm flafbdl d bjltfludbfòl. @jbd`fbm m` bmltrj
am krdvmada am `d nfkurd njridad bjl m` d`diorm.
am krdvmada am `d nfkurd njridad bjl m` d`diorm.
=.?1
=.?1 Nfkurd W=.4.
Nfkurd W=.4.
=.?=
=.?= Nfkurd W=.?.
Nfkurd W=.?.
=.?>
=.?> Nfkurd W=.2.
Nfkurd W=.2.
=.?;
=.?; Nfkurd W=.;.
Nfkurd W=.;.
=.?3
=.?3 ]ld odrrd bfrbu`dr ulfnjrim bjl 3 `o am pmsj y 47 fl. am rdafj
]ld odrrd bfrbu`dr ulfnjrim bjl 3 `o am pmsj y 47 fl. am rdafj
sm ulm d ul pdsdajr ml
sm ulm d ul pdsdajr ml B
B y
y d`
d` bdo`m
bdo`m DO
DO. Amtmriflm
. Amtmriflm d
d) `d tmlsfòl ml m` bd-
) `d tmlsfòl ml m` bd-
o`m,
o`m, o
o) `d rmdbbfòl ml
) `d rmdbbfòl ml B
B.
.
=.?6
=.?6 M` m`mimltj
M` m`mimltj DOBAM
DOBAM njrid pdrtm am ul iòvf` y sm cfzj d pdrtfr
njrid pdrtm am ul iòvf` y sm cfzj d pdrtfr
am uld sj`d pfmzd am tuomréd am d`uiflfj. Rf sm sdom qum m` m`mimltj mstä
am uld sj`d pfmzd am tuomréd am d`uiflfj. Rf sm sdom qum m` m`mimltj mstä
dpjydaj ml
dpjydaj ml B
B y qum
y qum `
` 
 ? i, amtmriflm `d afstdlbfd
? i, amtmriflm `d afstdlbfd a
a am idlmrd qum `d pjr-
am idlmrd qum `d pjr-
bfòl
bfòl OBA
OBA am` m`mimltj pmridlmzbd cjrfzjltd`.
am` m`mimltj pmridlmzbd cjrfzjltd`.
=.27
=.27 M` m`mimltj
M` m`mimltj DOBAM
DOBAM njrid pdrtm am ul iòvf` y sm cfzj d pdrtfr
njrid pdrtm am ul iòvf` y sm cfzj d pdrtfr
am uld sj`d pfmzd am tuomréd am d`uiflfj. Rf sm sdom qum m` m`mimltj mstä
am uld sj`d pfmzd am tuomréd am d`uiflfj. Rf sm sdom qum m` m`mimltj mstä
dpjydaj ml
dpjydaj ml B
B y
y qum
qum a
a ms fkud` d 7.=7 i, amtmriflm `d `jlkftua
ms fkud` d 7.=7 i, amtmriflm `d `jlkftua `
` am` ordzj
am` ordzj
AM
AM td` qum mstd pjrbfòl am` m`mimltj pmridlmzbd cjrfzjltd`.
td` qum mstd pjrbfòl am` m`mimltj pmridlmzbd cjrfzjltd`.
x
x
y
y
o
o
b
b
y
y
b
b
B
B
O
O
r
r
B
B
D
D
D
D
O
O B
B A
A
M
M
4.=7 i
4.=7 i
a
a
7.;= i
7.;= i
`
`
==
==·
·
==
==·
·
Nfkurd
Nfkurd W=.?2
W=.?2
Nfkurd W=.?3
Nfkurd W=.?3
Nfkurd W=.?6 y W=.27
Nfkurd W=.?6 y W=.27

20.
?2>
?2> Numrzds afstrfoufads8 bmltrjfams y bmltrjs
Numrzds afstrfoufads8 bmltrjfams y bmltrjs
am krdvmada
am krdvmada
=.24
=.24 M` d`diorm cjijkælmj
M` d`diorm cjijkælmj DOB
DOB mstä ajo`daj ml ul drbj smifbfrbu-
mstä ajo`daj ml ul drbj smifbfrbu-
`dr y uld smbbfòl rmbtd bjij sm iumstrd ml `d nfkurd, damiäs sm mlbumltrd
`dr y uld smbbfòl rmbtd bjij sm iumstrd ml `d nfkurd, damiäs sm mlbumltrd
ulfaj d uld drtfbu`dbfòl ml
ulfaj d uld drtfbu`dbfòl ml D
D. Amtmriflm m` vd`jr am
. Amtmriflm m` vd`jr am γ
γ td` qum m` d`diorm sm
td` qum m` d`diorm sm
mlbumltrm ml mquf`forfj ml `d pjsfbfòl flafbdad.
mlbumltrm ml mquf`forfj ml `d pjsfbfòl flafbdad.
=.2?
=.2? Amtmriflm `d afstdlbfd
Amtmriflm `d afstdlbfd c
c td` qum m` bmltrjfam am` ärmd
td` qum m` bmltrjfam am` ärmd sjiormdad
sjiormdad
mstæ tdl `mhjs bjij smd pjsfo`m am `d `élmd
mstæ tdl `mhjs bjij smd pjsfo`m am `d `élmd OO
OO
, budlaj
, budlaj d
d)
) e
e 
 7.47 y
7.47 y o
o)
) e
e 

7.37.
7.37.
=.22
=.22 Rf sm sdom qum `d afstdlbfd
Rf sm sdom qum `d afstdlbfd c
c sm sm`mbbfjlò pdrd idxfifzdr `d afs-
sm sm`mbbfjlò pdrd idxfifzdr `d afs-
tdlbfd
tdlbfd y
y

 amsam `d `élmd
amsam `d `élmd OO
OO
 cdstd m` bmltrjfam am` ärmd sjiormdad, amiums-
cdstd m` bmltrjfam am` ärmd sjiormdad, amiums-
trm qum
trm qum y
y

 
 ?
?c
c
/2
/2
=.>. AMQM_IFLDBFÒL AM BMLQ_JFAMR WJ_ FLQMK_DBFÒL
=.>. AMQM_IFLDBFÒL AM BMLQ_JFAMR WJ_ FLQMK_DBFÒL
M` bml
M` bmltrjf
trjfam am ul ärmd `f
am am ul ärmd `fif
iftd
tdad pjr bur
ad pjr bur
vds
vds dld
dld`é
`étf
tfbds (ms
bds (mstj ms, bur
tj ms, bur
vds
vds
am
amnf
nflf
lfads pjr mbud
ads pjr mbudbfj
bfjlms d`
lms d`km
kmordf
ordfbds) pjr `j km
bds) pjr `j kmlm
lmrd` sm am
rd` sm amtmr
tmrif
ifld mvd
ld mvd-
-
`udl
`udlaj `ds fl
aj `ds fltm
tmkrd
krd`ms qum dpd
`ms qum dpdrm
rmbml ml `ds mbud
bml ml `ds mbudbfj
bfjlms (=.2) am `d smb
lms (=.2) am `d smb-
-
bfòl =.28
bfòl =.28
x
x


D
D 
 
 x aD
x aD y
y


D
D 
 
 y
y aD
aD (=.2)
(=.2)
Rf m` m`mimltj am ärmd
Rf m` m`mimltj am ärmd aD
aD ms ul pmqumôj rmbtälku`j am `dajs
ms ul pmqumôj rmbtälku`j am `dajs ax
ax y
y ay
ay,
,
`d mvd`udbfòl am bdad uld am mstds fltmkrd`ms rmqufmrm uld
`d mvd`udbfòl am bdad uld am mstds fltmkrd`ms rmqufmrm uld fltmkrdbfòl
fltmkrdbfòl
ajo`m
ajo`m bjl rmspmbtj d
bjl rmspmbtj d x
x y
y y
y . Qdiofæl ms lmbmsdrfd uld fltmkrdbfòl ajo`m
. Qdiofæl ms lmbmsdrfd uld fltmkrdbfòl ajo`m
sf sm usdl bjjramldads pj`drms pdrd `ds bud`ms
sf sm usdl bjjramldads pj`drms pdrd `ds bud`ms aD
aD ms ul m`mimltj am
ms ul m`mimltj am
`dajs
`dajs ar
ar y
y r
r a
a
.
.
Rfl miodrkj, ml `d idyjréd am `js bdsjs ms pjsfo`m amtmrifldr `ds
Rfl miodrkj, ml `d idyjréd am `js bdsjs ms pjsfo`m amtmrifldr `ds
bjjramldads am` bmltrjfam am ul ärmd bjl uld sj`d fltmkrdbfòl. Mstj
bjjramldads am` bmltrjfam am ul ärmd bjl uld sj`d fltmkrdbfòl. Mstj
sm `jkrd sm`mbbfjldlaj d
sm `jkrd sm`mbbfjldlaj d aD
aD bjij ul rmbtälku`j j tfrd am`kdad j bjij
bjij ul rmbtälku`j j tfrd am`kdad j bjij
ul smbtjr bfrbu`dr am`kdaj (nĴkurd =.4?)5 m` bmltrjfam am ul rmbtälku`j
ul smbtjr bfrbu`dr am`kdaj (nĴkurd =.4?)5 m` bmltrjfam am ul rmbtälku`j
am`kdaj mstä `jbd`fzdaj ml su bmltrj y m` bmltrjfam am ul smbtjr am`-
am`kdaj mstä `jbd`fzdaj ml su bmltrj y m` bmltrjfam am ul smbtjr am`-
kdaj mstä `jbd`fzdaj d uld afstdlbfd am
kdaj mstä `jbd`fzdaj d uld afstdlbfd am 

?
?
2
2

r
r d pdrtfr am su værtfbm (bjij
d pdrtfr am su værtfbm (bjij
ml m` bdsj am ul trfälku`j). Mltjlbms, `ds bjjramldads am` bmltrjfam
ml m` bdsj am ul trfälku`j). Mltjlbms, `ds bjjramldads am` bmltrjfam
am` ärmd ml bjlsfamrdbfòl sm jotfmlml mxprmsdlaj qum m` prfimr ij-
am` ärmd ml bjlsfamrdbfòl sm jotfmlml mxprmsdlaj qum m` prfimr ij-
imltj am` ärmd tjtd` bjl rmspmbtj d bdad ulj am `js mhms bjjramldajs
imltj am` ärmd tjtd` bjl rmspmbtj d bdad ulj am `js mhms bjjramldajs
ms fkud` d `d suid (j fltmkrd`) am `js ijimltjs bjrrmspjlafmltms am
ms fkud` d `d suid (j fltmkrd`) am `js ijimltjs bjrrmspjlafmltms am
`js m`mimltjs am` ärmd. _mprmsmltdlaj bjl
`js m`mimltjs am` ärmd. _mprmsmltdlaj bjl x
x

m`
m` y
y y
y

m`
m` `ds bjjramldads am`
`ds bjjramldads am`
bmltrjfam am` m`mimltj
bmltrjfam am` m`mimltj aD
aD, sm msbrfom
, sm msbrfom
T
T y
y 
 x
x


D
D 
 
 x
x

m`
m` aD
aD
T
T x
x 
 y
y


D
D 
 
 y
y

m`
m` aD
aD
(=.6)
(=.6)
D
D
O
O
B
B
r
r
q
q
r
r
O
O O
O'
'
o
o
e
eo
o
d
d
c
c
Nfkurd
Nfkurd W=.24
W=.24
Nfkurd W=.2? y W=.22
Nfkurd W=.2? y W=.22

21.
?2;
?2;
=.>. Amtmrifldbfòl am bmltrjfams
=.>. Amtmrifldbfòl am bmltrjfams
pjr fltmkrdbfòl
pjr fltmkrdbfòl


x
xm`
m`
9
9 x
x


y
ym`
m`
9
9 y
y
/?
/?
aD
aD 9
9 yax
yax
b
b)
)


y
ym`
m`
9
9 y
y
aD
aD 9
9 (
(d
d ‒
‒ x
x)
) ay
ay
o
o)
)


x
xm`
m`
9
9 d + x
d + x
?
?
d
d)
)


x
xm`
m`
9
9 ?
?r
r
2
2


y
ym`
m`
9
9 ?
?r
r
2
2
aD
aD 9
9 4
4
?
?
bjs
bjsγ
γ
sml
sml γ
γ
r
r
?
?
a
aγ
γ


x
xm`
m`


y
ym`
m`


x
xm`
m` 

x
xm`
m`


y
ym`
m`


y
ym`
m`
x
x
d
d
y
y
x
x
y
y
x
x
x
x x
x
y
y y
y
y
y
J
J J
J J
J
ax
ax
ay
ay
W
W(
(
x
x,
, y
y)
)
W
W(
(
x
x,
, y
y)
)
r
r
γ
γ
?
?r
r
2
2
W
W(
( ,
, r
r
)
)
γ
γ
Rf m` ärmd
Rf m` ärmd D
D lj sm bjljbm døl, æstd tdiofæl pumam bd`bu`drsm d pdrtfr
lj sm bjljbm døl, æstd tdiofæl pumam bd`bu`drsm d pdrtfr
am mstjs m`mimltjs.
am mstjs m`mimltjs.
@ds bjjr
@ds bjjram
amld
ldads
ads x
x

m`
m` y
y y
y

m`
m` am` bml
am` bmltrjf
trjfam am` m`m
am am` m`miml
imltj am` ärmd
tj am` ärmd aD
aD
am
amoml mx
oml mxprm
prmsdr
sdrsm ml tær
sm ml tærif
ifljs am `ds bjjr
ljs am `ds bjjram
amld
ldads am ul pul
ads am ul pultj `j
tj `jbd
bd`f
`f-
-
zd
zdaj sj
aj sjorm `d bur
orm `d bur
vd qum `f
vd qum `fif
iftd d` ärmd ml bjl
td d` ärmd ml bjlsf
sfam
amrd
rdbfòl. Dam
bfòl. Damiäs, m` ärmd
iäs, m` ärmd
am` m`m
am` m`miml
imltj
tj aD
aD am
amom mx
om mxprm
prmsdr
sdrsm ml tær
sm ml tærif
ifljs am `ds bjjr
ljs am `ds bjjram
amld
ldads am
ads am
af
afbcj pul
bcj pultj y am `js af
tj y am `js afnm
nmrml
rmlbfd
bfd`ms dprj
`ms dprjpfd
pfdajs. Ms
ajs. Mstj sm cd cm
tj sm cd cmbcj
bcj
ml `d nf
ml `d nfku
kurd =.4? pd
rd =.4? pdrd trms tf
rd trms tfpjs bj
pjs bjiu
iulms am m`m
lms am m`miml
imltjs5 `d pjr
tjs5 `d pjrbfòl
bfòl
am bér
am bérbu
bu`j am `d pdr
`j am `d pdrtm
tm b
b am
amom utf
om utf`f
`fzdr
zdrsm budl
sm budlaj `d
aj `d mbud
mbudbfòl am
bfòl am `d bur
`d bur vd
vd
qum `f
qum `fif
iftd d` ärmd ms
td d` ärmd mstæ ad
tæ adad ml bjjr
ad ml bjjram
amld
ldads pj
ads pj`d
`drms. Am
rms. Amoml sus
oml sustf
tftufr
tufr-
-
sm `ds mx
sm `ds mxprm
prmsfj
sfjlms dprj
lms dprjpfd
pfdads ml `ds nòr
ads ml `ds nòriu
iu`ds (=.6) y am
`ds (=.6) y amom utf
om utf`f
`fzdr
zdrsm `d
sm `d
mbud
mbudbfòl am `d bur
bfòl am `d bur
vd qum `f
vd qum `fif
iftd d` ärmd pd
td d` ärmd pdrd mx
rd mxprm
prmsdr d uld am `ds bjjr
sdr d uld am `ds bjjr-
-
am
amld
ldads ml tær
ads ml tærif
ifljs am `d jtrd. Am ms
ljs am `d jtrd. Am mstd njr
td njrid, sm rm
id, sm rmau
aubm d uld sj
bm d uld sj`d
`d
fl
fltm
tmkrd
krdbfòl. ]ld vmz qum sm cd am
bfòl. ]ld vmz qum sm cd amtmr
tmrif
ifld
ldaj m` ärmd y cdl sf
aj m` ärmd y cdl sfaj mvd
aj mvd`ud
`ud-
-
ads `ds fl
ads `ds fltm
tmkrd
krd`ms ml `ds mbud
`ms ml `ds mbudbfj
bfjlms (=.6), ms
lms (=.6), mstds mbud
tds mbudbfj
bfjlms pum
lms pumaml rm
aml rm-
-
sj`
sj ̀vmr
vmrsm pd
sm pdrd `ds bjjr
rd `ds bjjram
amld
ldads
ads x
x

 y
y y
y

 am` bml
am` bmltrjf
trjfam am` ärmd.
am am` ärmd.
Budl
Budlaj uld `é
aj uld `élmd ms
lmd mstä am
tä amnĴ
nĴlf
lfad pjr uld mbud
ad pjr uld mbudbfòl d`
bfòl d`km
kmordf
ordfbd, pum
bd, pum-
-
am am
am amtmr
tmrif
ifldr
ldrsm su bml
sm su bmltrjf
trjfam d` mvd
am d` mvd`udr `ds fl
`udr `ds fltm
tmkrd
krd`ms qum dpd
`ms qum dpdrm
rmbml ml
bml ml
`ds mbud
`ds mbudbfj
bfjlms (=.1) am `d smb
lms (=.1) am `d smbbfòl =.28
bfòl =.28
x
x


@
@ 
 
 x
x a@
a@ y
y


@
@ 
 
 y
y a@
a@ (=.1)
(=.1)
M` af
M` afnm
nmrml
rmlbfd` am `jl
bfd` am `jlkf
kftua
tua a@
a@ am
amom rmmi
om rmmip`d
p`dzdr
zdrsm pjr uld am `ds sf
sm pjr uld am `ds sfkufml
kufml-
-
tm mx
tm mxprm
prmsfj
sfjlms, am
lms, ampml
pmlafml
afmlaj am buä` bjjr
aj am buä` bjjram
amld
ldad
ad x
x,
, y
y j
j 
 sm sm
sm sm`mb
`mbbfj
bfj-
-
lm bj
lm bjij `d vd
ij `d vdrfd
rfdo`m fl
o`m flam
ampml
pmlafml
afmltm ml `d mbud
tm ml `d mbudbfòl utf
bfòl utf`f
`fzd
zdad pd
ad pdrd am
rd amnf
nf-
-
lfr `d `élmd (ms
lfr `d `élmd (mstds mx
tds mxprm
prmsfj
sfjlms pum
lms pumaml am
aml amrf
rf
vdr
vdrsm bjl m` usj am` tmj
sm bjl m` usj am` tmjrm
rmid
id
am Wf
am Wftäkj
täkjrds)8
rds)8
a@
a@ 
 
 4
4 





 
?
?

ay a@
ay a@ 
 

4
4 





 
?
?

ay
ay
a@
a@ 
 

r
r
?
?






 
?
?

a
a

ay
ay


ax
ax
ay
ay


ax
ax
ar
ar


a
a

Nfkurd =.4?
Nfkurd =.4? Bmltrjfams y ärmds am m`mimltjs afnmrmlbfd`ms.
Bmltrjfams y ärmds am m`mimltjs afnmrmlbfd`ms.

22.
?23
?23 Numrzds afstrfoufads8 bmltrjfams y bmltrjs
Numrzds afstrfoufads8 bmltrjfams y bmltrjs
am krdvmada
am krdvmada
Amspuæs am qum sm cd utf`fzdaj `d mbudbfòl am `d `élmd pdrd mxprmsdr
Amspuæs am qum sm cd utf`fzdaj `d mbudbfòl am `d `élmd pdrd mxprmsdr
uld am `ds bjjramldads ml tærifljs am `d jtrd, sm pumam ``mvdr d bdoj
uld am `ds bjjramldads ml tærifljs am `d jtrd, sm pumam ``mvdr d bdoj
`d fltmkrdbfòl y sm pumaml rmsj`vmr `ds mbudbfjlms (=.1) pdrd `ds bjjr-
`d fltmkrdbfòl y sm pumaml rmsj`vmr `ds mbudbfjlms (=.1) pdrd `ds bjjr-
amldads
amldads x
x

 y
y y
y

 am` bmltrjfam am `d `élmd.
am` bmltrjfam am `d `élmd.
=.;.
=.;. QMJ_MIDR
QMJ_MIDR AM W
AM WDWW]R-K]@AFL]R
DWW]R-K]@AFL]R
Ms
Mstjs tmj
tjs tmjrm
rmids num
ids numrjl njr
rjl njriu
iu`d
`dajs prf
ajs prfim
imrj pjr m` kmò
rj pjr m` kmòim
imtrd krfm
trd krfmkj Wdp
kj Wdp-
-
pus au
pus aurdl
rdltm m` sf
tm m` sfk`j
k`j FFF
FFF ams
amspuæs am Brfs
puæs am Brfstj y num
tj y numrjl rm
rjl rmp`dl
p`dltmd
tmdajs pjs
ajs pjstm
tm-
-
rfjr
rfjriml
imltm pjr m` id
tm pjr m` idtm
tmiä
iätf
tfbj suf
bj sufzj Ku`
zj Ku`af
aflus j Ku`
lus j Ku`afl (4=;;-4>12), sm
afl (4=;;-4>12), sm
rm
rmnfm
nfmrml d su
rml d supm
pmrnf
rnfbfms y bumr
bfms y bumrpjs am rm
pjs am rm
vj
vj`u
`ubfòl.
bfòl.
]ld
]ld su
su
pmr
pmr
nf
nfbfm am rm
bfm am rm
vj
vj`u
`ubfòl
bfòl sm km
sm kmlm
lmrd im
rd imafdl
afdltm `d rj
tm `d rjtd
tdbfòl am uld
bfòl am uld
bur
bur
vd
vd p`d
p`dld bjl rms
ld bjl rmspmb
pmbtj d ul mhm nĴ
tj d ul mhm nĴ
hj.
hj. Wjr
Wjr mhmi
mhmip`j (nf
p`j (nfku
kurd =.42), sm
rd =.42), sm
D
D
O
O
B
B
D
D B
B
O
O
Msnmrd
Msnmrd Bjlj
Bjlj
D
D B
B
Qjrjfam
Qjrjfam
pum
pumam jotmlmr `d supmrnfbfm am uld msnmrd rjtdlaj ul drbj smifbfrbu-
am jotmlmr `d supmrnfbfm am uld msnmrd rjtdlaj ul drbj smifbfrbu-
`dr
`dr DOB
DOB bjl rmspmbtj d` afäimtrj
bjl rmspmbtj d` afäimtrj DB
DB5 sm pumam prjaubfr `d supmrnfbfm
5 sm pumam prjaubfr `d supmrnfbfm
am ul bjlj rjtdlaj uld `élmd rmbtd
am ul bjlj rjtdlaj uld `élmd rmbtd DO
DO bjl rmspmbtj d ul mhm
bjl rmspmbtj d ul mhm DB
DB y sm
y sm
pumam kmlmrdr `d supmrnfbfm am ul tjrjfam j dlf``j rjtdlaj `d bfrbul-
pumam kmlmrdr `d supmrnfbfm am ul tjrjfam j dlf``j rjtdlaj `d bfrbul-
nmrmlbfd am ul bérbu`j bjl rmspmbtj d ul mhm qum lj fltmrsmbd d afbcd
nmrmlbfd am ul bérbu`j bjl rmspmbtj d ul mhm qum lj fltmrsmbd d afbcd
bfrbulnmrmlbfd. ]l
bfrbulnmrmlbfd. ]l bumrpj am rmvj`ubfòl
bumrpj am rmvj`ubfòl sm kmlmrd imafdltm `d rjtdbfòl
sm kmlmrd imafdltm `d rjtdbfòl
am ul ärmd p`dld d`rmamajr am ul mhm nĴhj. Bjij sm iumstrd ml `d nĴkurd
am ul ärmd p`dld d`rmamajr am ul mhm nĴhj. Bjij sm iumstrd ml `d nĴkurd
=.41, sm pumam kmlmrdr uld msnmrd, ul bjlj y ul tjrjfam rjtdlaj `d
=.41, sm pumam kmlmrdr uld msnmrd, ul bjlj y ul tjrjfam rjtdlaj `d
njrid dprjpfdad bjl rmspmbtj d` mhm qum sm flafbd.
njrid dprjpfdad bjl rmspmbtj d` mhm qum sm flafbd.
Msnmrd
Msnmrd Bjlj
Bjlj Qjrjfam
Qjrjfam
QMJ
QMJ_M
_MID F.
ID F. M` ärmd am uld su
M` ärmd am uld su
pmr
pmr
nf
nfbfm am rm
bfm am rm
vj
vj`u
`ubfòl ms fkud` d
bfòl ms fkud` d
`d `jl
`d `jl
kf
kf
tua
tua am
am `d
`d bur
bur
vd
vd km
km
lm
lmrd
rd
trfz
trfz iu`
iu ̀tf
tf
p`f
p`fbd
bdad pjr `d afs
ad pjr `d afs
tdl
tdlbfd rm
bfd rmbj
bj-
-
rrf
rrfad pjr m` bml
ad pjr m` bml
trjf
trjfam am af
am am afbcd bur
bcd bur
vd d`
vd d` ij
ij
iml
iml
tj am
tj am km
km
lm
lmrdr `d su
rdr `d su
pmr
pmr-
-
nf
nfbfm.
bfm.
Amijstrdbfòl.
Amijstrdbfòl. Bjlsfaærmsm ul m`mimltj
Bjlsfaærmsm ul m`mimltj a@
a@ am `d `élmd
am `d `élmd @
@ (nfkurd
(nfkurd
=.4=) qum rjtd d`rmamajr am` mhm
=.4=) qum rjtd d`rmamajr am` mhm x
x. M` ärmd
. M` ärmd aD
aD kmlmrdad pjr m` m`mimltj
kmlmrdad pjr m` m`mimltj
a@
a@ ms fkud` d ?
ms fkud` d ?

y
y a@
a@. Wjr tdltj, m` ärmd tjtd` kmlmrdad pjr
. Wjr tdltj, m` ärmd tjtd` kmlmrdad pjr @
@ ms
ms D
D 


 ?
?

y
y a@
a@. Ml `d smbbfòl =.2 sm mlbjltrò qum `d fltmkrd`
. Ml `d smbbfòl =.2 sm mlbjltrò qum `d fltmkrd` 
 y a@
y a@ ms fkud`
ms fkud`
d
d y
y


@
@, pjr tdltj, sm tfmlm
, pjr tdltj, sm tfmlm
D
D 
 ?
?

y
y


@
@ (=.47)
(=.47)
Nfkurd =.42
Nfkurd =.42
Nfkurd =.41
Nfkurd =.41
Njtjkrdnéd =.?
Njtjkrdnéd =.? Qjajs `js tdlqums am
Qjajs `js tdlqums am
d`idbmldifmltj qum sm iumstrdl ml `d njtjkrdnéd
d`idbmldifmltj qum sm iumstrdl ml `d njtjkrdnéd
sjl bumrpjs am rmvj`ubfòl. Wjr tdltj, `ds ärmds
sjl bumrpjs am rmvj`ubfòl. Wjr tdltj, `ds ärmds
am sus supmrnfbfms y sus vj`øimlms pumaml
am sus supmrnfbfms y sus vj`øimlms pumaml
amtmrifldrsm bjl `js tmjrmids am Wdppus-
amtmrifldrsm bjl `js tmjrmids am Wdppus-
Ku`aflus.
Ku`aflus.

23.
ajl
ajlam ?
am ?

y
y

 ms `d afs
ms `d afstdl
tdlbfd rm
bfd rmbj
bjrrf
rrfad pjr m` bml
ad pjr m` bmltrjf
trjfam am
am am @
@ (nf
(nfku
kurd =.4=).
rd =.4=).
Rm
Rm am
amom
om sm
smôd
ôd`dr qum `d bur
`dr qum `d bur
vd km
vd kmlm
lmrd
rdtrfz lj am
trfz lj amom bru
om bruzdr m`
zdr m` mhm sj
mhm sjorm m`
orm m`
bud` rj
bud` rjtd5 sf `j cf
td5 sf `j cfbfm
bfmrd, `ds ajs smb
rd, `ds ajs smbbfj
bfjlms, uld d bd
lms, uld d bdad `d
ad `daj am` mhm, km
aj am` mhm, kmlm
lm-
-
rd
rdrédl ärmds qum tml
rédl ärmds qum tmlarédl sfk
arédl sfkljs jpums
ljs jpumstjs y m` tmj
tjs y m` tmjrm
rmid lj pj
id lj pjaréd dp`f
aréd dp`f-
-
bdr
bdrsm.
sm.
QMJ_MID FF.
QMJ_MID FF. M` vj`uiml am ul bumrpj am rmvj`ubfòl ms fkud` d`
M` vj`uiml am ul bumrpj am rmvj`ubfòl ms fkud` d`
ärmd kmlmrdtrfz iu`tfp`fbdad pjr `d afstdlbfd rmbjrrfad pjr m` bmltrjfam
ärmd kmlmrdtrfz iu`tfp`fbdad pjr `d afstdlbfd rmbjrrfad pjr m` bmltrjfam
am` ärmd d` ijimltj am kmlmrdr m` bumrpj.
am` ärmd d` ijimltj am kmlmrdr m` bumrpj.
Amijstrdbfòl.
Amijstrdbfòl. Bjlsfaærmsm ul m`mimltj
Bjlsfaærmsm ul m`mimltj aD
aD am` ärmd
am` ärmd D
D, m` bud` sm
, m` bud` sm
rjtd bjl rmspmbtj d` mhm
rjtd bjl rmspmbtj d` mhm x
x (nfkurd =.4>). M` vj`uiml
(nfkurd =.4>). M` vj`uiml a^
a^ kmlmrdaj pjr
kmlmrdaj pjr
?26
?26
=.;. Qmjrmids am Wdppus-Ku`aflus
=.;. Qmjrmids am Wdppus-Ku`aflus
y
y
x
x
a^
a^
aD
aD
y
y
x
x
D
D
B
B
?
? y
y


x
x x
x
a@
a@
aD
aD
B
B
@
@


y
y
y
y
?
? 

y
y


Nfk
Nfkurd
urd =.4
=.4=
=
Nfk
Nfkurd
urd =.4
=.4>
>
m` m`mimltj
m` m`mimltj aD
aD ms fkud` d ?
ms fkud` d ?

y
y aD
aD. Wjr tdltj, m` vj`uiml tjtd` kmlmr-
. Wjr tdltj, m` vj`uiml tjtd` kmlmr-
daj pjr
daj pjr D
D ms
ms ^
^ 
 
 ?
?

y
y aD
aD y
y, pumstj
, pumstj qum `d
qum `d fltmkrd`
fltmkrd` 
 y
y aD
aD ms fkud` d
ms fkud` d
y
y


D
D (smbbfòl =.2), sm tfmlm
(smbbfòl =.2), sm tfmlm
^
^ 
 ?
?

y
y


D
D (=.44)
(=.44)
ajl
ajlam
am ?
?

y
y

 ms `d afs
ms `d afstdl
tdlbfd rm
bfd rmbj
bjrrf
rrfad pjr m` bml
ad pjr m` bmltrjf
trjfam am
am am D
D. Ms fi
. Ms fipjr
pjr-
-
tdl
tdltm sm
tm smôd
ôd`dr qum m` tmj
`dr qum m` tmjrm
rmid lj pum
id lj pumam dp`f
am dp`fbdr
bdrsm sf m` mhm am rj
sm sf m` mhm am rjtd
tdbfòl
bfòl
fl
fltmr
tmrsm
smbd d` ärmd km
bd d` ärmd kmlm
lmrd
rdtrfz.
trfz.
@js tmj
@js tmjrm
rmids am Wdp
ids am Wdppus-Ku`
pus-Ku`af
aflus prj
lus prjpjr
pjrbfj
bfjldl uld njr
ldl uld njrid sml
id smlbf
bf-
-
``d am bd`
``d am bd`bu
bu`dr `ds ärmds am su
`dr `ds ärmds am supmr
pmrnf
nfbfms am rm
bfms am rm
vj
vj`u
`ubfòl y `js vj
bfòl y `js vj`ø
`øim
imlms
lms
am bumr
am bumrpjs am rm
pjs am rm
vj
vj`u
`ubfòl. Ml njr
bfòl. Ml njrid fl
id fl
vmr
vmrsd, ms
sd, mstjs tmj
tjs tmjrm
rmids sm mi
ids sm mip`mdl
p`mdl
pd
pdrd am
rd amtmr
tmrif
ifldr m` bml
ldr m` bmltrjf
trjfam am uld bur
am am uld bur
vd
vd p`d
p`dld budl
ld budlaj m` ärmd am `d
aj m` ärmd am `d
su
supmr
pmrnĴ
nĴbfm km
bfm kmlm
lmrd
rdad pjr `d bur
ad pjr `d bur
vd ms bj
vd ms bjlj
ljbf
bfad j pd
ad j pdrd am
rd amtmr
tmrif
ifldr m` bml
ldr m` bml-
-
trjf
trjfam am ul ärmd p`d
am am ul ärmd p`dld budl
ld budlaj m` vj
aj m` vj`u
`uiml am` bumr
iml am` bumrpj km
pj kmlm
lmrd
rdaj pjr
aj pjr
m` ärmd ms bj
m` ärmd ms bjlj
ljbf
bfaj (væd
aj (vædsm m` prj
sm m` prjo`m
o`mid rm
id rmsum`
sum`tj =.3).
tj =.3).

24.
W_JO@MID _MR]M@QJ =.1
W_JO@MID _MR]M@QJ =.1
Amtmriflm pjr fltmkrdbfòl afrmbtd `d `jbd`fzdbfòl am` bmltrjfam am uld ml-
Amtmriflm pjr fltmkrdbfòl afrmbtd `d `jbd`fzdbfòl am` bmltrjfam am uld ml-
hutd pdrdoò`fbd.
hutd pdrdoò`fbd.
RJ@]BFÒL
RJ@]BFÒL
Amtmrifldbfòl am `d bjlstdltm
Amtmrifldbfòl am `d bjlstdltm e.
e. M` vd`jr am
M` vd`jr am e
e sm amtmrifld sustf-
sm amtmrifld sustf-
tuymlaj
tuymlaj x
x 
 d
d y
y y
y 
 o
o ml `d mbudbfòl adad. Rm
ml `d mbudbfòl adad. Rm tfmlm
tfmlm o
o 
 ed
ed?
?
j
j e
e 
 o
o
d
d?
?
. Wjr
. Wjr
tdltj, `d mbudbfòl am `d burvd ms
tdltj, `d mbudbfòl am `d burvd ms
y
y 
 x
x?
?
j
j x
x 
 y
y4
4
?
?
M`mimltj afnmrmlbfd` vmrtfbd`.
M`mimltj afnmrmlbfd` vmrtfbd`. Rm sm`mbbfjld m` m`mimltj afnmrml-
Rm sm`mbbfjld m` m`mimltj afnmrml-
bfd` ijstrdaj y sm amtmrifld m` ärmd tjtd` am `d nfkurd.
bfd` ijstrdaj y sm amtmrifld m` ärmd tjtd` am `d nfkurd.
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M` prfimr ijimltj am` m`mimltj afnmrmlbfd` bjl rmspmbtj d` mhm
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y ms
ms x
x
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pmbtj d` mhm
pmbtj d` mhm x
x ms
ms y
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M`m
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imltj af
tj afnm
nmrml
rmlbfd` cj
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rfzjl
zjltd`
td`.
. Rm pum
Rm pumaml jo
aml jotm
tmlmr `js ifs
lmr `js ifsijs rm
ijs rm-
-
su`
su`td
tdajs bjl
ajs bjlsf
sfam
amrdl
rdlaj ul m`m
aj ul m`miml
imltj cj
tj cjrf
rfzjl
zjltd`. @js prf
td`. @js prfim
imrjs ij
rjs ijiml
imltjs am`
tjs am`
ärmd sjl
ärmd sjl
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Wdrd amtmrifldr
Wdrd amtmrifldr x
x
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y y
y
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, `ds mxprmsfjlms jotmlfads sm sustftuyml lumvdimltm
, `ds mxprmsfjlms jotmlfads sm sustftuyml lumvdimltm
ml `ds mbudbfjlms qum amnflml m` bmltrjfam am` ärmd.
ml `ds mbudbfjlms qum amnflml m` bmltrjfam am` ärmd.
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25.
W_JO@MID _MR]M@QJ =.=
W_JO@MID _MR]M@QJ =.=
Amtmriflm `d uofbdbfòl am` bmltrjfam am` drbj ijstrdaj.
Amtmriflm `d uofbdbfòl am` bmltrjfam am` drbj ijstrdaj.
RJ@]BFÒL
RJ@]BFÒL
Bj
Bjij m` dr
ij m` drbj ms sf
bj ms sfiæ
iætrf
trfbj bjl rms
bj bjl rmspmb
pmbtj d` mhm
tj d` mhm x
x,
, y
y

 
 7. Rm sm
7. Rm sm`mb
`mbbfj
bfjld ul m`m
ld ul m`m-
-
iml
imltj af
tj afnm
nmrml
rmlbfd`, bj
bfd`, bjij sm iums
ij sm iumstrd ml `d nf
trd ml `d nfku
kurd, y sm am
rd, y sm amtmr
tmrif
ifld `d `jl
ld `d `jlkf
kftua
tua
am` dr
am` drbj pjr fl
bj pjr fltm
tmkrd
krdbfòl.
bfòl.
@
@ 
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r a
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M` prfimr ijimltj am` drbj bjl rmspmbtj d` mhm
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y ms
ms
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y 
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sm
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W_JO@MID _MR]M@QJ =.>
W_JO@MID _MR]M@QJ =.>
Am
Amtmr
tmrif
iflm m` ärmd am `d su
lm m` ärmd am `d supmr
pmrnf
nfbfm am rm
bfm am rm
vj
vj`u
`ubfòl ijs
bfòl ijstrd
trdad ml `d nf
ad ml `d nfku
kurd, `d
rd, `d
bud` sm jo
bud` sm jotfm
tfmlm rj
lm rjtdl
tdlaj ul budr
aj ul budrtj am dr
tj am drbj bfr
bj bfrbu
bu`dr bjl rms
`dr bjl rmspmb
pmbtj d ul mhm vmr
tj d ul mhm vmr-
-
tf
tfbd`.
bd`.
RJ@]BFÒL
RJ@]BFÒL
Am dbumraj bjl m` tmjrmid F am Wdppus-Ku`aflus, m` ärmd kmlmrdad ms fkud`
Am dbumraj bjl m` tmjrmid F am Wdppus-Ku`aflus, m` ärmd kmlmrdad ms fkud`
d` prjaubtj am `d `jlkftua am` drbj y `d afstdlbfd rmbjrrfad pjr su bmltrjfam.
d` prjaubtj am `d `jlkftua am` drbj y `d afstdlbfd rmbjrrfad pjr su bmltrjfam.
_mnfrfælajsm d `d nfkurd =.3O, sm tfmlm qum
_mnfrfælajsm d `d nfkurd =.3O, sm tfmlm qum
x
x
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26.
W_JO@MID _MR]M@QJ =.;
W_JO@MID _MR]M@QJ =.;
M` afä
M` afäim
imtrj mx
trj mxtm
tmrfjr am uld pj
rfjr am uld pj`md ms 7.3 i y `d smb
`md ms 7.3 i y `d smbbfòl trdls
bfòl trdls
vmr
vmrsd` am su bj
sd` am su bj-
-
rj
rjld ms bj
ld ms bjij sm iums
ij sm iumstrd ml `d nf
trd ml `d nfku
kurd. Rm sd
rd. Rm sdom qum `d pj
om qum `d pj`md ms
`md mstä cm
tä cmbcd am dbm
bcd am dbm-
-
rj y qum `d aml
rj y qum `d amlsf
sfada am af
ada am afbcj id
bcj idtm
tmrfd` ms
rfd` ms 
 
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;.3= 
 47
472
2
ek/i
ek/i2
2
, am
, amtmr
tmrif
iflm
lm
`d id
`d idsd y m` pm
sd y m` pmsj am `d bj
sj am `d bjrj
rjld.
ld.
RJ@]BFÒL
RJ@]BFÒL
M` vj
M` vj`u
`uiml am `d bj
iml am `d bjrj
rjld sm pum
ld sm pumam ml
am mlbjl
bjltrdr bjl m` tmj
trdr bjl m` tmjrm
rmid FF am Wdp
id FF am Wdppus-
pus-
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aflus, m` bud` ms
lus, m` bud` mstd
tdo`m
o`mbm qum m` vj
bm qum m` vj`u
`uiml ms fkud` d` prj
iml ms fkud` d` prjaub
aubtj am` ärmd am
tj am` ärmd am
`d smb
`d smbbfòl trdls
bfòl trdls
vmr
vmrsd` ad
sd` adad pjr `d afs
ad pjr `d afstdl
tdlbfd rm
bfd rmbj
bjrrf
rrfad pjr su bml
ad pjr su bmltrjf
trjfam ml uld
am ml uld
rm
rm
vj
vj`u
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bfòl bjip`m
p`mtd. Rfl mi
td. Rfl miodr
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kj, m` vj`u
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iml sm pumam am
am amtmr
tmrif
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ldr iäs nä-
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bf`
bf`iml
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tm sf sm josmr
smr
vd qum `d smb
vd qum `d smbbfòl trdls
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vmrsd` sm pum
sd` sm pumam trdls
am trdlsnjr
njridr d pdr
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tfr am` rmb
tfr am` rmbtäl
tälku
ku`j F, bu
`j F, bu
yd ärmd ms pj
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sftf
tf
vd y am` rmb
vd y am` rmbtäl
tälku
ku`j FF, bu
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yd ärmd ms lm
yd ärmd ms lm-
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kd
kdtf
tf
vd.
vd.
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pj
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B
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ik 
 (>7.7 ek)(6.34 i/s
(>7.7 ek)(6.34 i/s?
?
)
) 
 =36 ek
=36 ek 
 i/s
i/s?
?
[
[ 
 =36 L
=36 L
?1?
?1?
W_JO@MID _MR]M@QJ =.3
W_JO@MID _MR]M@QJ =.3
Bjl `js tmj
Bjl `js tmjrm
rmids am Wdp
ids am Wdppus-Ku`
pus-Ku`af
aflus, am
lus, amtmr
tmrif
iflm8
lm8 d
d) m` bml
) m` bmltrjf
trjfam am ul ärmd
am am ul ärmd
sm
smif
ifbfr
bfrbu
bu`dr y
`dr y o
o) m` bml
) m` bmltrjf
trjfam am ul dr
am am ul drbj sm
bj smif
ifbfr
bfrbu
bu`dr. Rm am
`dr. Rm amom rm
om rmbjr
bjradr qum
adr qum
m` vj
m` vj`u
`uiml y m` ärmd su
iml y m` ärmd supmr
pmrnf
nfbfd` am uld ms
bfd` am uld msnm
nmrd sjl, rms
rd sjl, rmspmb
pmbtf
tf
vd
vdiml
imltm,
tm, 
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RJ@]BFÒL
RJ@]BFÒL
M` vj`uiml am uld msnmrd ms fkud` d` prjaubtj am` ärmd am ul smifbérbu`j y
M` vj`uiml am uld msnmrd ms fkud` d` prjaubtj am` ärmd am ul smifbérbu`j y
`d afstdlbfd rmbjrrfad pjr m` bmltrjfam am` smifbérbu`j ml uld rmvj`ubfòl
`d afstdlbfd rmbjrrfad pjr m` bmltrjfam am` smifbérbu`j ml uld rmvj`ubfòl
d`rmamajr am` mhm
d`rmamajr am` mhm x
x.
.
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Am `d ifsid njrid, m` ärmd supmrnfbfd` am uld msnmrd ms fkud` d` prjaubtj am
Am `d ifsid njrid, m` ärmd supmrnfbfd` am uld msnmrd ms fkud` d` prjaubtj am
`d `jlkftua am` smifbérbu`j kmlmrdtrfz pjr `d afstdlbfd rmbjrrfad pjr su bml-
`d `jlkftua am` smifbérbu`j kmlmrdtrfz pjr `d afstdlbfd rmbjrrfad pjr su bml-
trjfam ml uld rmvj`ubfòl.
trjfam ml uld rmvj`ubfòl.
D
D 
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r
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7 i
ii
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7 i
ii
i
>7 ii
>7 ii
27 ii
27 ii
177 ii
177 ii
477 ii
477 ii
Z
Z
477 ii
477 ii >7 ii
>7 ii
=7 ii
=7 ii 27 ii
27 ii
B
BFF
FF
B
BF
F FF
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F
F
2
2;
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= i
ii
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