h}moh yroehT mutnauQ ehT fo setalutsoP

:

-

. -

.

.

. regnidorhcS niwrE

. scinahceM evaW

- - grebnesieH renreW

cariD.M.A.P . scinahceM xirtaM mutnauQ citsivitaleR

. arbeglA

.scinahceM mutnauQ -

- . setalutsop

: .

.

. yroehT mutnauQ ehT fo setalutsoP -

. .

. .

: -- noitcnuF evaW dna metsyS eht fo etatS

.

etatS noitcnuF evaW noitcnuF

.

.

)t,z,y,x ( . . ( )

noitcartsbA lacitamehtaM yranoitatS

etatS noitcnuF evaW etatS yranoitatS

. . ( ) *

ytilibaborP x .

. x x

xd + x ) - ( xd

xelpmoC

) ) - ( (.

) - ( xd*

: laeR

) - ( . ) - (

: )zdydxd = d( d z , y , x d * ) - (

.

d ) - ( ecapslla

= *

noitidnoC noitazilamroN ) - ( .

dezilamroN ) - ( noitcnuF evaW

devaheB_lleW

: :deulaV-elgniS -

. :suounitnoC -

.

. :etiniF -

.

)

(.

(. )

. etiniF ( )

. n..... , , , teS etelpmoC

"" " " " "

. d

ecapslla =

d j i )-(

ecapslla = ij

noitidnoC ytilanogohtrO" " .

.

: ( )-( )dezilamroN i

( )-( )lanogohtrO .tes lamronohtrO

= i=j

== ijjiji d ij

fo noitaterpretnI

. .

. . nroB .

)I ytisnetnI( .)( etutilpmA

I ( - )

. ( h )

. )d(

) (

(. d ) d

(I d ) I

.

. .

.

. ( ) . .

( ) .

: --

selbavresbO dna srotarepO lacinahceM mutnauQ

rotarepO lacinahceM mutnauQ noitimreH raenil

.

:

. .

( ) . noitimreH *** ffdffd = ) - ( elbatpeccA f, f

laeR

.

. .

.

( ) : .

: : . -qd qP -

= hid hh

.z y x q

m

. x s/m v

vm / = xT ) - (

: xP

m P

mTmv

x

== xxd xP

hid

) - (

x

x

xdd

mT

xdid

xdid

mT

h

hh

=

=

x ) - ( ) - ( ) - (

v m .

xT () x

. y ) - (

. z

:

z

y

mzT

myT

==

h

h

+

+=

=++

xyz

mxyzT

TTTT

h

) - (

m h = T

+

+

xyz

) - ( .

. E ,ygrenE latoT

notlimaH V + T = E ) - (

T noitauqE notlimaH . V

. H =+ HTV ) - (

V . ) - ( T ( noitisop )

. V ) - (

m H

h =+

. ( -)

. (: -) rq rQ xk / xk / r / qq r / qq

vM x xd hid

vm / m h

stnemerusaeM fO yroehT mutnauQ

.

. )selbavresbO( seitreporP prahS -

(. )

.

: . eulaV etulosbA

. selbavresbO prahs-noN -

.

.

naeM . eulaV egarevA eulaV

. : --

selbavresbO fo seulaV etulosbA

:

ia ii = ) - ( )i( i

. .

.

. .

) - ( .

.

.

. - ( )

( .) H E = ) - (

.

: ) - ( =

VE +

m

) - ( h

noitauqE evaW regnidorhcS .

smetsys lacitnedI

. noitubirtsiD

- ( . : . ) ( (

eulaV egarevA noitubirtsiD ( )

. ( ) ( ) ( )

: (. ) ( )

.

: -- snoitcnuF fo noitanibmoC raeniL

noitimreH

i . .

noitisoprepuS

. i

noitanibmoc raeniL

i ) - ( i

= Ci . i iC

. . xq = g

noitisoprepuS noitcnuF eniS

xd d

xkie . xd/d

[: ] [: ]

.

a i .

= a ii k....., = i ) - ( a

. k teS etarenegeD .

i ) - ( k

i = Ci

=

) - ( , ) - ( ) - (

) - ( ) - ( . a : . i

==

=

=

=

=

=

=

=

aCa

Ca

C

C

i

k

ii

i

k

ii

i

k

ii

k

iii

: : --

seulaV noitatcepxE

.

) - (

=

d

d* a

*

meroeht eulaV naeM ( * = d )

* ad ) - (

> < ) - ( . eulaV noitatcepxE

.

aa

aadad

a()d**

*

=

> a

. egarevA emiT

.

i iC = . i

) - ( =

C d

a(C) (C)d

i*i

i

ii*

ii

= a iii i

aCad

aCa

i*ii

i

i

ii*i

i

i

i i ) - (

i

aCa i

dethgieW > a

: snoitcnuF evaW tnednepeD -emiT

tnednepeD-emiT H(q,t) ) - (

td h= id(q,t)

)t,q ( H .t

. .

ypocsortceps tnednepeD_emiT

) ( anemonehP .

.

. )ot( ot , )t(

H ) ( . t )t(

t

. . ) - ( noitatcepxE

- -

: :

. )- ( . :

. .

fo noitcudeR

. noitcnuF evaW ehT

.

etinifeD ) - ( H E =

E(q,t)

td ) - ( h= id(q,t)

)t,q(

= (q,t)eBtEi/h ) - (

: . )t,q(

B ) - ( - ( q = B .

. esahP() pxe ) h/ tEi ) - (

.) - (

: - skrameR yratnemelpmoC

. .

.

.

-- elpicnirP ytniatrecnU grebnesieH dna noitisop repuS

noitanibmoC raeniL

i :

teS etarenegeD i - .

.

noitisoprepuS

ecnerefretnI evitcurtsnoC tnatluseR . tnemecrofnieR

. P

( -) . ( - ) .

. i : ( -) i -

ecnerefretnI evitcurtseD

: esahP-nI

( -) . noitazilacoL

x , xd + x

( -) xd

. . P

P

.

i : ( -) .

suoenatlumiS

elpicnirP ytniatrecnU grebnesieH

.yratnemelpmoC . .

: = .h x P

) - ( x , P

( . x ) .

-- srotarepO fo ytreporP noitimreH eht fo ecnatropmI

naitimreH

laeR .

) - ( ... , , :

. : . *

a = * *a = *

( ) *

: * a = a * = *

**a = * *a = *

d * a = d * d * *a = d *

)*a - a( = d * - d *

. *a = a

a .

: .

. i , j j i

= d j i

i ia = i

j ja = j

d ji )ja- ia( = d i j - d j i

= d j i ) ja - ia (

) ja - ia (

j i = d ji .

-- noitatoN tekcarB cariD

.

I . . | I < *i > I |

= > I | I j | I m | | n < = > n | | m m | | m < = > a m | | *m < = > a <

.

-- setatS fo noitacificepS

:

.

. x ]xP , x [ ...,b ,a >.....b ,a |

. ..., B, A a A >.....,b, a |

. .... b B

==

Bb

Aa

( ) B A

:

. etummoc

A , B a, b = ABBA ) - (

A , B B A ) - ( . .

:-

,

. :

a = : b =

aa == bb ==

: ()(baab) ==

: :-

rotatummoC ] xp ,x [ :

x )x(f ] [

= -i. x f )x(`

)x(fxdx xp )x(f =.x id

h

h

)x(f )x( ` f ] [

hh

hhh

h

h

[x,p] =i = i )x(f

=i-(fx ))x( + i(fx )x( + i)x(f

[x,p] )x(f = (xp - px)x(f) = -ifx[ )x(` + ])x(f

x )x(fxdpx )x(f = -id

x

''xxx

x

.

x- , x x -

/)/a( = N . a )xa-(pxe N = )x( . x )x( . )x(

. : ( k ) uk + u = -

. lanogohtro u ,u ( u ,u s s = d u u ( u ,u

. A k , j -

. k< |A| = >j . k , j

.A : : -

V xdd

m H

. V h =+ .... , , = n xnie = n ; ( )

= n H ( ( xP ) x (

= n : -

= f ( ( k ) xk- = f (

[: ]

: r/qq = f ( ( .) x , r . f

m ,m - Rb - Ra = V

. R b , a l.

. x - : ( -

) ,-( )x-(pxe ; ) ,( xe ; ) ,( xa nis : (

) ,( x/ ; ) ,( )x - ( nat : -

=

=

=

=

nn

nn

Sb

Sa;

SS

n

n

nn

n

mnm

SSab

SSab

= =

= =

=

=

. -

*** ABxdABxd =

. N -

. | N| . )N( . L -

P P x r = L r . r

.L

: