• Keine Ergebnisse gefunden

Forecasting Demand for Electricity: Some Methodological Issues and an Analysis

N/A
N/A
Protected

Academic year: 2022

Aktie "Forecasting Demand for Electricity: Some Methodological Issues and an Analysis"

Copied!
63
0
0

Wird geladen.... (Jetzt Volltext ansehen)

Volltext

(1)

Munich Personal RePEc Archive

Forecasting Demand for Electricity:

Some Methodological Issues and an Analysis

Pillai N., Vijayamohanan

Centre for Development Studies, Prasanth Nagar, Ulloor, Trivandrum, Kerala, India

29 May 2008

Online at https://mpra.ub.uni-muenchen.de/8899/

MPRA Paper No. 8899, posted 30 May 2008 06:50 UTC

(2)

! " # $ % %

(3)

&

' " ! " # (

# ) ( * " "+ * #

, * * ) * + )# #

* +

+ ) % - "+ # * . *" / #

# ! " 0 # #

# * # % # " #

" * # *" # *" #

) 1%

(4)

2

34 5 ' " 6 4 7+ # ) 8 / * %

# # * " # ) ( * "

" # )#" # , *

* ) * * % # *

+ + ) % *

* " # # ( *

" # * , # ) % - "+ #

* . *" / # # !

" 0 # # # * # %

)# ) ) " # " * # *"

# *" # ) 1% #

* # % # , (

# * " + ) (" # #

# # * % # #

" +

(! # " %

(5)

9

# * # " * " (

: : # %

# , ; * < # % =

)# # ( # * # # )

( + # ( : #

# # # %

# # : * # + ) # " (

* # #

< # )# # ) " # + #

, 1 * # ( (! ,

0

< # )# # # (! .( 1 ( ,/ )#

) 1 * 1 ) %

# # " (" # # " %

" # # )

" + *" # *# * *

*"+ # *"% # # + # ) +

, "%

- # # # 1 # (! .( 1 ( ,/

" , # # ( # #

# ( # # " % > # "

; * < %

# * " ) ;& <%

(6)

" # # # " (" ,

# ( ( % > ) + # *# # #

" # : # # " ) + ,

" 1" # # ( ( # "

"%

# , *" " * ( * (

# #

< , " 6 5 ( 0

< ( ; * < " 6 5 ( 5 &0

< , " 6 (0

< 1 " 6 ; 5 ( < ? 10

< @ ) # 0

< ;= < * " 6 5 (" %

# # * # *

< 8 * # * * " 6 5 ( * " %

@ ) # * @ : %

(7)

< 8 * " 6 8 ? ; 5 (<0

(< @ : " 6 8 , ; ( <0

)# 8 # ( + . / .(/ # (

%

, + # ( ( + "+ " *

; <+ # * , ( % #

.(/ * # # * ; < # + * #

# * (" # * " * * ; # < * ) #

% A# # # * + *

" ; ( <+ " ) # .( 5 & /+ . / * * #

% , * , + # * # "

* % # * + )# # B " + #

, # 1 % # + # .(/ "

* # ; , < * ) # " % 1 # + "

* ) .1/ " * ( ) :

"% ; 1 6 + ) * %< # * ) # # ( ("

* # .(/ (" # .1/ # + . 5 ( / ;6 "<%

@ ) # # # ( )# # # %

# # # # ( .4/ 0 * : .

6 "/+ # + 8+ . 6 "/% # @ : +

# ) + " + )# # * % A # # @ : + #

* ) # # ( # * " # ) # # *

# * * " " #

+ * ( # # * ( #

(8)

C

" # % # # * # ; * <

* % # # # * #

; < 6 0 # D(D # * # # *

# " + # * # + # * ) # #

% E # , ( # ) *

" *% F # #

* ) # ** ( % #

" + # ) ( %

# ( ( # # , # (

" B 1 ) " + # " " *

"% ( #

+ B + % # "

* " ( , # G - ; *

* * * < %

" * + # * ( B " % =

+ # " + " # #

# " ( # *

% # ) *"

1 (" ( % # *

# # + # (

( * , %

( : ( % > * #

+ # * " ) ) % # )#" # , B

# : ) # * %

# " , " # ( #

% # , # * ( # #

B # ; * < # + " #

% , + # " #

%

(9)

H

I * ; * < # + ) " #

, * *" + #

< * # + ) + %0

(< " ; <+ +

: ( + + %0

< ( " " + * " + %

# ( ) " " (

( # * %

# + ) # # ( 1 + %

# ( # # # ) # # *

# ( % # " *%

" # # " ; # I% 4%< ) *

(" " ; C < # E J ' + )

, * + # * + + + *

; " + CC<% : * # # "

# " C + "

; < # " "+ + #

* # * # # # %

;(< # # # " %

; < # * " ( %

(10)

; < # # * # * " #

, % ' * &+ " # "

" %

F " " # ) # # * ( 1

* " " ) "+ # ; <

( ( " ( * *

B % " D ** ; C < ) # # ( ) )

; < - B # * *

, * # +

;(< # " # ( # %

# ; # I4< # # *

+ ( # I4 = ) %

" D ** + # # # : D #

) " * " # D% 4

# *# * # " " # *#

1 " * # +

# ( ( % 4 # # :

# # + * * # + # (" "+ (

: # *# B " # # (" # +

+ ) ; < ** * (

%

# " # + ** (

" * # * ) # !

# ; " 1 ( * ) # * " * ) *# <% #

* # ( ) # * % #

)# # # ( # # #

" + # * " ( (" * # #

(11)

(" # # ** (

* + % %+ (" # ! % > ) + # # **

( + " + 1 # K84 #

( ( ) # ** * ( # ( +

) # * # # %

# + " B (" #

* (" # ' ) 4 " ; 4< ("

# - " ' *"+ # ' " # " ; ' < ( * # 4

# 4% # # , # # ) (

# , # " % 4 + (

, ( ) # # * " (" # %

# * ! "

" # # "% B

. ! / " * " " (" " *

* % # + #

# ( # # ! ;

# ! <% G ) " * B

(" * * " % #

+ + ( *# *+ ) ) 1 +

( * ) # * " # * ) #

" % I * # + # * (

# 1 # " # ) # , #

" * %

K # # # + # 4 ( * ) # " ( #

# -A " # ) # ) " #

B ) ) % # # #

* # # # " (" # *

(12)

" # * " (

) # ) % G * " " # (

+ # , ) # * ) ( ( *

** * # % # ) # 4 ( #

) # # ( # # 4'E

* # * , % 4 # #

) * # #

+ # ) # # 4 %

E # # * # 4 " # " * # *

# ! + * ; * <+ ) " #

" " % # + # " ( #

# : * # % # ! # #

* / " ( * ) # #

4/ ) # " ** * % = ( # # +

# )# + # # * # # "

(" ( # , # * + % E #

* " # 4 * #

+ " # # * " #

# ( % # * # # #

* " ) # # + ( # * *

% # 4+ )#

* ** * + * # #

( * : * " " # *#

% = # + # ( # # 4 " ( ) " ( % #

4 , # (" ( ) & H + #

* * " # " + *# ( , % # #

*" (" # 4 # &# 4+

9 # &9 + 2&H+ 9 + H C ;-I< "

;(" # &#+ 2#+ 9#+ #+ # + 4<% # + # ) + (

# * # ) # # ; (

C &C%C -I *" " < + *# ) # )

(13)

&

# *% K ) " # ) * *

* # # " # # : %

! ( # ( ; &#+ 2#+ 9# #< 4

) # % " # 1

? *" B ( # # #

( # # ( " +

; * # * B 1 *

( "<% # 4 # # 9# 4 . ( / ;@

+ C &<0 )# # E ; " #

" < # # 4 . # ( */

;@ + C 2C<% * # * #

# 4 ; # ) ( + , + 9<+ # 4 * E

) 1 * * " # % #

* * ) # 9%C&+ + # >

'> # ! % #

! # , ) ( # * ) # #

% = # # + # ! ) ( #

; * * <% # ( # # *" 9 ("

# " H 9 -I%

( ) 1 * *" * (

*" + # 8' ;8 * * ' *"

*<+ E'' - ''4' ;E 1# ' *" ' " 'G

' " 4 ' <+ -' '' 4+ '8@'-+ % ' *"

; ' <+ E * + # ) = ' I K +

4 # *" ; '='F I4< * "

*" *" " ; + " F% G " <+ ,

( # # ( # 4'E% # # *"+ ) # )

* "+ 1

(14)

2

*" ? * " ( ) ( #

( *" # *" B " ( " )

# , # * # ( B " % # *" # B

# ** * # * " %

# " ( + * *# # #

# # # * # " ; #

( " < # * B #

% # " * ( , #

# * # + # , # "

% > ) + # * #

) 1+ , # # +

% # ( " * # #

+ *" # "+ * ) # # +

* # + + # % #

" %

B # ) #

, # ) " # ( # " + *

# ) " + # (!

% * ** * " *

# : + + )# " (

* " " "+ ) 1+ # (

" ( " * ( " " # *

# # % > ) + # " ) #

* # # *" * ) "

)# # ( # " * % #

# % = , + 9 + # + "+

( # # # "

) ! % 9 # ; + %

(15)

9

"<% # " # ) " 9% & ; +

&%H <% * + # ) " 9%H # ; +

%9 <% ; 4 " + = " 4 + 9 + L % + (

2 %< + # * # + "+ (

# 4 " # ) %

" # # + C%H 0 + ) "

%CC 9%C& "% ;4 ( + H+ 4K+ @K + ( % +

% H H %< * # ; & C H<+ ) , #

)# * ( #

( C% # % # * #

*" ) ;* ( 1

( )< # ! C H ) , H%H

; %&<0 # 9% ; %H<0 = : 2%C ; C% <0 9%9 ; %H<0 "

%& ; 9%&<0 % ; %&<0 2 % ;99% <0 - -

% ; &% <0 4 %H ; % <0 = - % ; %C<0 F =

- %2 ; %H<0 - # " &% ;&% <0 ' - # " 2% ;2% <0 &&%

;& %&<% ; - '+ " = ** * G + J + + "

= %<

# # *" B ( # : )

" : * 1 + # ) # " (

" % # # *" # #

* # ? , " ) #

* + # # * "

, + * % - + # * (

* # " " ( * #

( * " # % # * # #

* # * / (

; < ) 2 %9 0 9 + ) 29% ;

C C + H H + + ) " 9 % + 9 %& + 2 % H

<% # + ( 9 # 4 #

* # * ) ( (" # *

(16)

C H% ) 9 # ( #

( & ( < " *" # *

;I * : - * ' F44 G + 9 +

F44K+ @K + J " H+ % <% K " C% # 2 %9

# ( ; % C%C " <

# *" # # "

; ( %+ % 2 2 <% # ( # * : * + #

# # + * # " 9 )

G % 2&&C9H% + )# # 9 # 0

# # ; < 4 / " ) G % 9 %9 ) # C&% C

# ; ( %+ % C 9<% ) # * # * # '>

" 2C% ) * ( ;-I<

" % # # ( * ** *

( # " # * # # # )# # #

" , " 1 1%

# + # : # # # # *"+

* # ( ** * # *"

# ?4 % # = " ; C9<+ % % >

C <+ G% % # ; C <+ F E ! ; C <+ A E 1 ; C < J% %

1# ; H <+ % % ; H < # #

% % % ; H < " # ** * ) # )

* + * "+

+ # ** ( # *

%

% % / ) 1+ . # B " # "

" * 1 ) " / ; #

# + % ,<+ " ( # 1 % > ) + # "

# # )# # ** * (" #

# " *

, % * # " , " (

(17)

" " * * ** * ( )

% " B + ;

" ) # # ** (" " * ( 1+ C + CC<+ #

(" + # # # ** * *

; # "< 0 ; (

<% * *# ( # " # ** * + (

# + #

) # 1 * ! + " # , # ( 1

" % - + # " * # ( " # *

# ; # * # # #

# # < # # ; # # *

" *" ) # # ( <0 )# * +

# ( # 1 # # # # * * "

% K ( * # * # # #

; *< " # + # *

# # * " + #

* ) # # % # (

( % # + % % / * #

# + # *# # *

" % # * " ) (

" * # * + # * # ; *< * ) #

+ # * + # # " # 1 ) * "

* % - + # K84 # ** (

* ( " # # ( " #

%

, # * *

# % % / (( * #

/ #" ) " + ) # ( . ( / %

# ( ( #"

) * + ( * 1 + . ( / " #

(18)

C

* ) " + )# #

+ ) # %

' # " " " B *% #

" ) " #

% " * "

# ( " # ( ( +

+ # + ( " ) ( * # ; ( #

) ) < # # %

# , + # # ) #

, # 1 ; < C H ) ! 2%&

0 " " % H #

;F 4 + 4K+ @K <% H H + # #

) ) 9% 9 9% & " # "+ %9 % &

"% # * ) # " # ( * *#

( # + "+ #

+ 1 % # * # " #

, ) * ) H% 2 H H & % C

C H+ 1 * * * ) # %&9 +

)# # 1 %&& % #

" ;−<&% % % # ** " ) 1 *

( " 1 ; "< ! ( ;−< %9 0 % %+

* # # " ,

* ( ; < %9 * # # 1

, % # + " " 1

# * # , # # %

# # F 4 4 " , #

* % # * # # "

, *# # # ( # * (

" : * C # )# # # "

% # , # ; & F44< #

(19)

H

) ! C% # ( + %9 ;> #

', ' " 4 + + F44K+ @K + 4 %+ H<%

# ) " %& % & 2 ; # <+ %H

% ; # <+ C% %H HC HH ;92 <%

# " # *# ( *

, , ' * / )%

= , + # #

# % # " #

; # ( C # <

) CC&%2& * % % 9 ; H 4 ' "

E <+ # * * * * "

, G % C9 % C ; + G % %C #< " C% 9 #

; G % &9%H< # " % # 4 + # "

; < C H ) 2%C&

* % C % + # *

, G % C22% ; G % % #< "% #

# ( C # "

# " # " % * + # "

C H ) 9H %C *

% &2%C9 + * * * " , G %

H2&% ; + &% H #< " %2 # ; G %

2 < # " % 4 "+ ( #

" * ( *# * )# # "

# # + , " + )

# , % - + # )#

" ( ) # ) # *+

# ( " # # B )# #

# * , %

# # H + # ( ) + , * )

*#( * ; <% 4 # *# " H& H2+

(20)

) # * # ( # ; <% G * *#

) # B " # # # * )

# *+ * # ) % G

* # ( * " # *# " B ( %

# # * ( ( + #

( ! * " ( (

+ )# # ( ( *% K #

# )# + #

# # * (

% # # # " B # * (

(" # * ) # # (

# # # *% # ( !

# ;A E 1+ C 2<% # #

+ # (" # * * 1

# # ( 1 % # (

) # # # # ( " %

A # # # # #" # : # ) # ;

< ) 1 # ) #

) " # ? % # # ) # (

* # ( # ) " % > ) +

) # " # # # ; " #

< * ; 0 #

* # ) # * " #

# ( " # " <+ " ( "

* ( % # # # ) " #

# # # ( " + %+

)# # % # * ) # )

* " ( (" # * ) # ( ; <

# " # ) ; % %+ "

<+ # ( ) # ) % ;4 %

% + H H H&0 > ; C < # (

(21)

&

%< # + #

# * ; 1 ) < # " * /

% # " ( * ) # # " *"

; " 1 ) ; A< < #

( ) # ) % > ) + # ) "

) ; *"< ) # ( "% K # ( +

+ "+ + ) #

" ( % - + ( ; <

# ; < * *" + "

# + ( " #

" "0 # + # # # + )# #

* # , # " % # " #

* % * ) * ) " , (

" # * ) # ; # # "

+ % %+ ; <+ <%

# * ) H& H2+ #

+ + 8 # ( # #

, + ( * " ;

<+ ( # > '> " . # / ; * + ( +

+ %< # % # * " " * "

" # 4 / > '> * # # )

# * ) # # # ( # ** * + # * ) #

* ( # # % # + +

# "%

" " # , # ) " * #

( ) # ) # * ; H H&<+ # )

; H& H2<+ # ! # "

) " "% # ) #

# (" * # # ( "

# + ( # * # " % #

+ ) # # # #

(22)

&

+ ( ) # " * + )# # ( (" ) *

# # * ) )# # #

. / # * * ) # * (

%

# .@ ( / * #

# @ # ** * ) # # # * *

* " " #

% F ( # # * # ;

( < # " # # * ; G

' + <% # *# # ) # * # # )

* ) H& H2+ *" #

; # 8 * < #

* ) # ( + * # *# " #

; <% " # *

# # + + * ;( ) # #

<% # + # ** * + )# # * ) ,

% H % * + " ; <

# C% 9 % # ( # # .# : / ;* ) #

< . / ;* ) # "+ % %+ * ) # <

* ) # ( # * ) # * %

;F # + )# . / # * ) #

%< # * ) # " ; % %+ +

) A < # )

( 1 * ;

* " " < # *"

* % F )+ ( ) ) # )

) ( " # * ) * %

A , # # #

( ∆ ∆ + )# ∆ + " ∆ <

# ; < # ( ( # %

(23)

&&

F , ) 1 # * * ) # # ∆ ∆ # ) #

# * ) # * % #

# ; # # #

< " ( ) " 0 # ) + ) ! ( "

# # # * # # # "

# # 1 # #

+ ( ) # * ) * % # # !

; < (

)#

! " # ∆ ∆

$ %% & '($ () %% ''* '(

+ + ,

# # ) # *" #

" , * ; % %+ < (

% A # #

( + )# )

* + # * ) # #

) # * % > ( # ! ) "

* ) # + # * ) # ∆ ∆ #

* ) # # ! %

F ) # ) # # ( + * # *

H H& # + H& H2+ )

% A ) # *

* * * ;- .- < +

+ # ( ) ** +

(24)

&2

** , " ( + )#

( # " . , / (" % (

α β / + # / * , + (

": . , / (" * * * *

* ; G - < % # ( * #

α β

φ

0

θ

0 η + )# η " "

( ; < ;)# <+

φ θ

" #

* ; G< * * ;- < 0 # ( 1)

# ; , + 0 0$ $+ % # (

" , # # # ( ,

* + , # #

# ( , "+ 1 " # (

; E , J 1 + C + # + + 0 - 1 1 A# ) *# +

CH+ # % 0 " 1 G ( + H + # % & <%

# ( 1 ) * # * " +

# * ; < ; , +

< ) # )# # * # # *# ( ( " # #

) " % K " # * #

4 * + ( " * + *

) " , 1 ) * ( # %

- + # ( " ) # *

# " # % @ ! 1 * * 0

# * ( 9 H

" ( # ! ( + * ! " " #

2 " % > + # * * * *% + #

+ # + * + * " (

; * , # * * ( , <%

) ( # # # *" ( " #

(25)

&9

% = * * *+ * )

( %

* # * # , ( "+ ( B " *

* " # ( % "

1 * " ) 1 1 ) )# # )# ,

1 " ( ( 1 ) # % *

+ # " * : )#" " * " <

) * B ( ; < <

" ; <+ < # 1 # " "

# " * ; *%+ # # * ( <+ <

* # * # " ( ; %*%+

) # ) * <+ < # , * ( + #

) # + "+ %+ " ( " % "

+ 1 ) " ; < ; <% * +

* ( 1 * # 1 1 *

) # , %

I " " % # * " #

) # # * # # % = " * +

# : + # # # # % # (

# # # B + " ) 1+

* + # , / B +

# ( ) %

A ) # " # # ,

;-1< ) ; * ) ;-A<< # " C H C H

# ) 1 # , , % G (

# * " + % %+ + +

" # *# " H& H2% > ) + #

(26)

&

* " * # ( ) ( + ) 1 #

#+ ! , # * #

# % ;A # # * ) # + " (

# ( # # %< ( # 2 3

# * ) # # # % #

, " ( ( # ) " *

+ )# # # ** ( ;-1 ! -1+ #

" ( < , # # % A # # # #

( # + ( # *

# # + # ) " # 1 #

% # + * " * # #

( #+ B ;.-34<+

( ;- 4<+ ( * ;- 4<+ #

B " ;5 < * ) # 2 %

.-34 # B # # B ( ) #

# %- 4 ! # # # ( ) #

) + )# - 4* - 4 * % ' "+ # # + #

( ( # %

5 " # .-34 #

# , % * (" # #

.-34 # # B # B #

# + # # ) ) " ( ) % 5 6 + #

# # % 5 6 +

# # # + # # # ) % # 5

2 + ( ;0 <+ ;6 <+

; <+ ) # 0 6 % # 0

" + # , )# # # #

# # % A# ( # # 5 +

) ) # ( 0 # : * % # 6 #

( " # # * ( " # ( "%

(27)

&

6 * + # # # ( " )# #

# ) + + )# # B ( % )

) # ( " ( ) # ) % # #

" + % %+ # * *

* ( # ( % 4 (

, " ) # + #

( % + * " # " 5 M + #

( B " # 2 0 6 6 + 6 %

F )+ ( # # # *# " * #

# + ! .$+ 7 ; ( <% # .8

/ # ( ( # * "

# 8 6 %9 86 % + * 0 ( # #

% = # * " ; ( < # 1 + #

19 &+ * " * % # 19

( # * B ** ( +

# # * ;( # * # <+

) #19 &% # # 1 #

# ( * # * 19 # #

% # # * +1 #

( − %& C+ # ( )# # # #

% 9 * % > ) ! # #" #

+ # # 2 3 # %

4 "+ # * # * + # 6− % C9+ #

( * " ( %

> ) + # # ) + , + # A

" )+ * # % #

, ( ( # * # (" * # *

( # *# " % A# # ) #

( ( ) # * + " 1 " # #

*#( * ) ) % = " * + ; "

(28)

&C

& " 9 " <+ # # ,

# ( ) # % A# * * #

* # # #

( ) # + ** * # # ( # 1 "

# + )# # ( #

, 1 " ( " # + #

* # # #

# * % # ( #

%

# + ) # # ) *

* + . , # (

+ )# . . / # #

; * < % # + ! .$ 7 #

" # )+ # 19/ &+ # *# # #

, + ) # . + # #

# ( "+ ) ( * * C "% > ) +

+ )# # ( " # % + #

( " # # * +

(" , * # # ; # <% #

# # )# # ) ( )%

= # + ) # ( #

B ;.-34<+ ( ;- 4<+

( * ;- 4<+ ) # B " ;5 < *

) # 2 ( ;0 <+ ;6 <+

; <% E" # + # #

* # " * * ? ( "+ ) # " )5 + * ) #

: 0 : 6 % + #

, + # . # " # )

0 + # , # # ) 5

# # *# ! .$ 7 * # + #

(29)

&H

* # * # * " ; ( <

" # # ; , < +

) # " ) 5 + ( # # (

+ , + 0 : )# 6 + 2 + "

"% * # " + # + # * # (

# * + * # ( %

4 "+ # # " *" ; < * #

" ; ;-I<< C H C H #

) 1 # * ( &% # *# # ( +

# , "%

G ( ( # # ( ) # # # " ("

) # * ) # *% * ) # " * #

# * ! # *# 1

+ " , , + # " #

( # 4 % > #

* # ! # ) #

# % # # *" , # * #

) # # *" ,

# ) ; <% # ) 1 " #

*" # ) 1 # .( / # *

% K # # ! ) + #

)# ( # ( . - *%

! " # $

# " ; < ( ; < # *

; C H H H&< ( # *# " * ) # "

(30)

&

)($,':' ,;$:

:,*:: ',$$<

.$ =,')('> 34. '*, '> 7 );',:*:>

19 =,)=*)>

.-34 (',=*> 5 =,=:(*>

)# * ( 1 + 34. * + 19

( A +.-34 B + 5 # B "

% # ) 19 #

% > ) + # ) " # *

# , 0 # )# ( * ( #

* # 0 . - %

* H& H2 C H+ " # 4 * )

, C% 9 % # ) " *

# # * # * ) # (

* # % # # # #

# ( ;∆ ?∆F< # ( + * ) #

( %C29 %

F )+ # ; % & < # # * )

" # * + # *

* # ( #

)# # * # ! + + % # ) #

H& H2+ # " # ) *# + # ; % %+ <

(" C % -I # " ; H H&+

(" 99% -I H H <+ )# # ( (

# + # (" # * *# + ( ) #

" # ( + # " +

# # ( ( 2 2C% -I% 4 "+ C H+ # " #

"+ # *" # # ( &H% -I+ * #

( + # CC %&2 -I%

(31)

2

# )# + * # * H H& # !

H& H2+ )# ) # # ( + * #

) * #

:',<;( $,=:=

=,*:: ;=,=')

.$ =,'('> 34. ));,':;> 7 ); ,$$>

19 =, ;(:>

.-34 )$(,;):> 5 =,=)<)>

# * # + ) "

. - ;/<% E # , #

# + ) #

( " # . - = $

# % # +

/ −

φ

0

θ

0−

θ

$0$ 6

)#

φ

. +

θ θ

$ - 6

% #

4 +

φ

=,(')> ),: '>

4 +

θ

=,$<=> ,*) >

4 +

θ

$ =,:($> <,$ >

.$ =,(:;> 34. $*,*::> 7 *(,$*(>

19 ,'<=<>

χ

$ ) <= (,:)>

(32)

2

.-34 $ , ''> 5 =, ((:,

#

θ θ

$ - $ # * *

#

θ θ

$ (" # B

θ

$

θ

< >

θ

$

θ

< >

− <

θ

$ < ,

4 "+ #

φ φ

$ . $ ) # #

* * # - $ % # " #

. $ " )# - $ +

( "+ - % " "% ;=

. + # " " − <

φ

< %< #

. - = $ ( " # %

* * # . - ( * * # 1 *+ * #

.* /+ (" # 1 * " . / #

, ( # # % E" + #

" *+ # * : +

# # # #

# + # ) # * ( # # #

# ( : % + # #" # :

* * ; ) : <

! ; # * <+ # ;

) < # ( ) # # &

;34< # ; & ;31<<%

B " (" # # B ; # #" #

# # )# + % %+ # " ) # # # <% 4

#

χ

$ * # ; ( * # #

(33)

2&

B ) *# (" # ( <+ (

( " %

= # ( . - = $ + #

( ) ) # # ± $ 34 #

χ

$ # 2C * ;9

* 2 < H% 2+ * # ( ) #

% ; %29< # ( + # # #

)# %

# α β −

φ

0

θ

0 −

θ

$0$ 6 %

# # " * ( )

−<<(),;=$ $,) *: −=,''( 0 −=,$ $ 0−=,:); 0$ 6

−=,=$' :,=< $,<(< ,<*= ),:';

.$ =,''(> 34. )), =:> 7 :;(',<)>

19 $,=*''>

χ

$ < <= (,(*>

.-34 $<,:=(> 5 =,= $',

# . - ( " # # " )

χ

$

;) # "< # B "% #

( : ) # # * + * # )#

# # % # , ; ( < #

; 7< % CH # H# *+ ) ) # # $34 + #

34 # ( * % H% # # # ;−

% & C< " # ; <31; % 9<%

# ( * # ( #

% # #" # + #

; 7< ( ) # # ; ( <

(34)

22

( , # ( ) # # $ 34

# % # 7 # ( # *

; # , ( # 7( * %2 9 # # + ) #34

6 % H<+ * * # # # %

> # B + ) ( *

%

F # # # # * "%

E # # .-34 # 5 # (" # ) # 0.-34

2&H% ; # ( * < &9% ; # 0 . - <+

5 % 29 % 2%

A # # # ) # #

; < H H ; # # C H

"<% # ( H # #

; < * ) # * ; H& H2 C H<+ % %+ % H

* % # ; < H& H2

( 2 ( # 0 # ) + (" C H+ ( "

( # ;* ) * ( % %<+ * (

# * , # %

# # ) # ; < " *# "

( ) # # 4 0 , + C H+ ! ; 99 % 9 -I<

( C%& # # 4 * ; CC -I< & + ( % 2

;& % 9 -I ? & CC -I<0 )# ) # # 9# 4+ C

H ! ( ( ) # 4 ; &H -I< #

& ( && ) ; # # 4 2&H 9 -I<% + # ) + (

# ) # # * ) #

C%29 + # C% 9 + #

) B # # 4 + * ) # C% 2 +

B # 9# 4 ) % # ( # #

*

(35)

29

# ( # ( )# #

0 H& H2+ # E # ( * # (

) % * C H H H&+ # ( #

) " # * * , * ) # %

+ )# # H& H2 C H+ # * ) # )

" % H % # # ( , ! #

# . / ) # . / % %+ ( "

+ # # + 1 +

# ( % # + # * ) #

# ( # ( # ; < C% 9

% # # * # # +

+ ) # ) + # ( * )

# * # H& H2%

* # + )# # ( * ) % H

+ " * ) C% 9 ; *

" # # * <% @ # +

# ( ) ) * ) # ; %

< + # # # * ) ;C% 9<×; % < ? ; % H< 6

% % % * + ) # #

# # ∆ ∆ + )# ( #

+ * ) * # " % % % % #

+ * ) % CC % %+ #

# # * ) " # * +

# + * # #

# ( % # ( #

" # ) * # ;) # ( 1 <

$)<,$* ,*(';

:,:*) :=, ='

.$ =,''($> 34. $= ,==<> 7 $$:)$,;<>

(36)

2 19 =,))'=>

.-34 ';,=)'> 5 =,= :$>

# # " * ) . - = $

+ ) # # ) *

4 +

φ

=,;*)> *,)=:>

4 +

θ

=,$<=> ,* *>

4 +

θ

$ =,:'=> <,$;(>

.$ =,*='> 34. =(,)$<> 7 )$,;:)>

19 ,'; :>

χ

$ ) <= ',=<>

.-34 =$,*;:> 5 =,$*(),

# " * ( )

'=,: * ,( ;; −=,*=; 0 −=,$ ; 0−=,:*= 0$ 6

$,)$$ '=,<;' *,:= ,:=: <,=$

.$ =,''':> 34. =(,(;> 7 ((*$,()>

19 $,=$ <>

χ

$ < <= (,<$>

.-34 = ,()> 5 =,==*(>

. + −=,==*;;> 4 + 31 ;,) >

- ? + + @ # 7 =, ') (# !>

34 =, :(>

- ? + + @ # 7 =,)== ;# >

34 =, :(,

(37)

2

F # ( ( # 34. + ) # #

% # # )# #" # #

% # # ( ) #

# # ) # # ! %

# ( H * ) #

* ; < ;(" <% # # 9#

4 * C H ; &H -I< " C

; H % -I< # " + ;2 9 H -I<+ " 9H

; 2 &%& -I<% ' "+ #

) ; ) # # + + ( + # #

) # ( < " ( 1 # ) # .

1 / % * * ) *# # ) + ) #

) *# # 1 %

&! " #

F , ) 1 # * # , ;-1<% # *

# # * # # " # # * ) # -1 "

# " # *+ * + H + -1 # " *

1 # # *+ # # , # !

+ )# " (! ) % * + -1

# * , * ) # % + )#

# * + % % E # * ) # -1 ( # #

+ * " *-1 " % # + # ( # * ) #

-1(" # .# : / * ) # ;* ) # < ) ) ("

# " * . / * ) # ;* ) # -1 -1 <% #

* # # : # " )

-1 "% > ) # ( * -1 ) # %

E ) ) ( ( . - + * -1 + *

" * . - # # # + #

) ( %

(38)

2C

* + )# * ) % % %+ -1 *

, * ) # % % E # + % H * ) #

# # ; % < × ; % H< ? ; % < 6 %C * ) # -1 *

+ # % % # ; %C < * ) # )

# # -1 * + # #

* ; < + ) # ∆-1∆ +

* ) %92H % % # # ) + *

+ # # -1 # + * ( ) ;) #

( 1 <

-1 :=,$:; =,<<'

;,=; <$,;*=

.$ =,'(*> 34. $<,:;)> 7 ($=,*<*>

19 =,;=<=>

.-34 $),:;=> 5 =,=$'(,

# # + # -1

* + # ( + # + ) *# (" #

( * ) * % # -1 #

; < ( + , + H& H2 ( 2H%

-A * # H&2%& -A% # " + # ( + -1 ("

! & -A # " + )# H H&+ (" CC%H -A

H H % # -1 C H & % -A * #

CH %H -A%

F ) *# ) # # " B

# + * * * ; G-<% 8

" 1 # 1 ) H& H2+ #

, ( # " + *

-A+ ) # * ; < ( # " +

(39)

2H

G- & % # ) # * " × %& 6

H -A B H& H2+ * # # ( "+ #

# + * " % -A%

# ( " # # ) " # ( "

# " * " # * #

* 11 #" ) ! C CC+ # "

( ) # # " *+

* * * , ) # * B # % =

C H+ ) # & G-+ # " B + * # ( " +

# 1 * & -A+

2 -A+ * " CC %H -A% F # # "

) ( ) # , CH %H -A # " + )# #

) # *# . ( / *"+ * *

# *" # " % ; # ( ) +

(" * + * + %+ ) ( # ( )%<

# + * # -1 #

! -1 + " # ) * # ) #

-1 $',;$= =,<**

<,*;) **,=:(

.$ =,'''> 34. $;,:':> 7 ) )<',:>

19 =,<;;<>

.-34 $:,')(> 5 =,= :,

# * ) # + # #

. - = $ + " # , * # = =

# ) # % # #

/ −

φ

0

θ

0−

θ

$0$ 6

(40)

2

)#

φ

. +

θ θ

$ - 6 )# %

#

4 +

φ

=,:;(> :,*:$>

4 +

θ

=,$)'> $,=(*>

4 +

θ

$ =,*:;> ;,)<:>

.$ =,;:<> 34. :,;: > 7 $:,:))>

19 $,=$':>

χ

$ ) <= ,=:>

.-34 <,(<( > 5 =,)=*),

# " # # + # ) # B

+ + # # )# +

* # * . , ( /%

# . - = $ # ) ( ) # #

# -1 # + # #

-1 $:,);; =,<(=( −=,:') 0 −=,,$$( 0−=,*:$ 0$6

$,;=* $=,*=' :,(<; ,' : ;, )*

.$ =,''':> 34. :,(<$> 7 $ :=:,*$>

19 $,=**=>

χ

$ < <= =,( >

.-34 <,( '> 5 =,==;:$>

# . - ( " # # # %

# # # ; % < " : ) #

# ; <31;&%2C2<0 # 7+ # , (

(41)

9

( * %&2 # # * ;34 6 % H<+ # 7+ # , (

( * %&9 # ;34 6 % H<% ( + # " ) # B

) # " # B "% # 34. ; & %

# %H9& # 0 . - < #

; & % 2H.-34 + 5 # 9%H

.-34 % # 0 . - < ( %

# -1 # -1 + ) # #

; < H H )% # (

H * ) # * ) # * + % %+

% H % % * % # 1 * " ( )

# ( -1 # 4 % = # " C H H +

-1 ; -A< & 9 % + 0 )# # 9# 4

; (" # 4 < & 9+ % > ) + # ) *

# + # 9# 4 * # 0 )# # & (

# + & + ( HC % K # # # + #

# 4 ; (" # E < #

" , + & 9 ; -A<

2 C% + 9&& %C+ 9 %&+ 9H %C+ & %&+ 9C %& H29% + # # 4

2 &+ 9&& + 9 + 9H + 2 + 9HH+ H % F # +

# -1 0 . - + # "

* # . / 0

# , # 4 %

F , ) ( * -1 # -1 #

( + * ) * # #

# ; % < ) # * % A #

# " ) * ) * #

* # # ) # (

) * ) # % + # )

(" % % % * % ( #

* ) # -1 ) # 1 #

(42)

9

% # ) # # -1

* * ) # % % # * * * ) # % CC

% % # ∆-1∆ + 0 # * ) # #

# # -1 # + # #

! -1 * % # ( 1 # ) *

#

-1 ', )= =,<':=

,=; $=$,*(=

.$ =,'''> 34. < , :<> 7 < $ , =>

19 =,$<<:>

.-34 <=, )*> 5 =, :,

# ( %

# # " # . - $

= $ % # +

/ −

φ

0−

φ

$0$

θ

0−

θ

$0$ 6

)#

φ φ

$ . +

θ θ

$ - + 6

)# % #

4 +

φ

=,* ;> <,):(>

4 +

φ

$ =, ) > $,**)>

4 +

θ

=,$*)> ,'(=>

4 +

θ

$ =,;'<> :,$''>

.$ =,*'*> 34. (,;;)> 7 )(,)*>

(43)

9&

19 ,'=)$>

χ

$ < )' =,::>

.-34 *,<$; > 5 =,,$$$(,

# " # # + # ) # B

+ + # # )# +

* # * . , ( /%

# + "

-1 −$=),=*( =,:$=< −=,< * 0−=,:<$ 0$ −=,<(=0

−=,< < )*,()' $,=;: $,<(: $,<;)

−=,<$( 0$ 6

$,;''

.$ =,'''(> 34. (,=')> 7 < =* ,<)>

19 $,=$;$>

χ

$ : )' , :>

.-34 ;,;<)> 5 =,==<;)>

. + −=,=)':> + 31 $,;;;>

- ? + + @ # 7 =,$;; =# !>

34 =, ;=>

- ? + + @ # 7 =,$ = )# > 34

=, ;=,

# ( # # 34. # ; ) # #

< # *# " * % # * # 1 * # )#

# # + # B "% # # -1

( % # , ) # #

+ # ( H # * ) #

% + # * ; <

;(" <% A # # 9# 4 ! C H ;& 9

(44)

92

-A< " % 9H &%& -A # " +

& ; & 9 -A<+ " 29% ; H %& -A<% #

-1 (" # & -A C H #

! # ( -1 % = # + )+

# " B # , #

; ( < 1 * C H+ * *

9 -A & G-+ HH -A+ * # ( "

% * # # * ! # )

+ " # 1 " # # " # (

% # # # . "/ , +

) ) ! ( # ) # * "

* %

" + # ( ( : * # ( 0

) # ) # ( ; * # <

* "% > ) + * # # (

( " # # ( "% # *

# 1 * # # # B "+ # .* /+

# % - + # # ( # #

* # % K # # # + * # #

( ( # ) " + )# # ) ( )%

'# ()

# ** * + .( /+ # + *" ,

# " " # # +

# # 1 # %

4'E H * + :%+ + + 8 "+ > '>

"+ ( *# *+ * + ) ) 1 + 0 C H+

) " # ( % A 1

" # 9 . # / * # * * +

(45)

99

( *# *+ ) ) 1 + % (

+ # 9 %

K " # #

; < ( # % # + * #

# ( # # ( % E ) ) ( "

#

<

C H+ # ( C # (

*" # 4'E+ ( 9 *"

+ 2 %9 + 9 %

; <% C C + # * # # ( +

+ + ) " C + 9%2+ H%H & %9 %

# * " * # # # * ) # # ) " * "

# * # # % ' *" ; < #

* ) * % % % * +

# ) # * ) # # ( %C

%C + # * ) # % C

"% # # *

" # # ( # # .# : / ; < # . / ;

"+ < * ) # ( # * ) # %

' " ( # ; + < )

# # + + * * *"

% #

* ) * ; * *

"< # %

# ; H H&< ( ; <

# ( # *# " * * ( )

(46)

9

−;*,<' =,<)$;

−',* ( )*,* (

.$ =,'(;> 34. *,<:$> 7 <$$,;*>

19 =, '(*>

.-34 ;,;)'> 5 =,=)'',

# * ) * % % % #

" * # B ( # % ∆ ∆

# + # * ) #

C%C % % * + )# # # #

# ( # * # ! +

( # % # ( # ": * #

# # F # #

. - = % # ( + ) # ( 1 +

< ,:;< =,:;<< −=,''*( 0 −=,;=:( 0 6

=,<' $$,(= : ,=$: <,:;=

.$ =,'''<> 34. =,=)';> 7 $=**',)'>

19 $,= >

χ

$ ) ); <,<(>

.-34 =,=)*<> 5 =,==)=<>

. + =,==$ ':> 4 + 31 =,==;)=<>

- ? + + @ # 7 =,$; '# !>

34 =, ;<>

- ? + + @ # 7 =,) $# > 34

=, ;<,

# # # : 7 7 ) # #

* % # * ) # # ) # B #

(47)

9

B "% ! # # ; <

* ) # %C9 # # : %

<

# + )# ( # ! ( # ( :

# 4'E+ ( # ( + 1

H% # + % # + %&

# C H% C C + # * # ) &&%&+ 2% + % +

%& "% * ) # # + #

* " # )#

# # ( # # # : # * ) #

# * ) # % + +

# * # %

# ; 9 H H&< # * ( )

−$$,<)* =,;' )

−),)$: ',;;=

.$ =,';=> 34. =,($<> 7 )(;,:=*>

19 =,<')=>

.-34 =, ;(> 5 =,=<:$,

# # / *"

# ) " * ; , HC HH+ )# (" ( 9 -I

H HC< 9 0 + (" ( & -I H

-I * (" 9 -I # , " % * H& H2 9 + * )

* %9 % > ) + # * #

# * ) # ) ! ( " (

# " + # * ) # " # 2 "

; C H<% * # " # + *

(48)

9C

* * ) # C% + # # *

# ) # " ! % * # * + # *# ; H& H2

H <+ # * ) % % %+ #

# # # % = # #

* ( + # ∆ ∆ + #

* * ) # C% 2 + )# # #

# # % # !

# * # # (

": * # # 0 . - ) 1 ( #

) * ;) # ( 1 <

*,;=( =,* $< −=,''=: 0 6

=,*)( $),::: ;=,:<=

.$ =,''(> 34. =,=:*$> 7 ; '*,$($>

19 ,')($>

χ

$ $ ) (,$(>

.-34 =,=:<:> 5 =,==<(;>

. + =,==*($)> + 31 =,=='(<>

- ? + + @ # 7 =,))' :#

:# !> 34 =, **>

- ? + + @ # 7 =,) # > 34

=, **,

< 8

# 8 # 4'E " %C #

( + %C # *" + H%9

# + & % # C H% C C + #

# ) " 2% + % + 2% + % % ' # *# # "

# *# * ) # * # # # ( + #

(49)

9H

# " " * 0 )

" A +

" *

; <%

# ; H H&< # # (

$=,$)( =,==::

),*;( $$,= *

.$ =,':(> 34. $,==*> 7 <(<,*$(>

19 =,;< <>

.-34 ,<<(> 5 =,=< ',

# # # ; < * ) #

C%& % %+ # ∆ ∆ " * * ) #

2%C + ) # )# # ) ! #

% # ! # # ( ": 0 #

# ( ; < * # * *

) . - = = % #

<,<: =,);' −=,'':* 0 6

=,$); ) ,')) <=,:=;

.$ =,''<> 34. =,=;:*> 7 )=:<,''>

19 $,=<;:>

χ

$ $ ); :,($>

.-34 =,=;)=> 5 =,==:(=>

. + =,==$= > + 31 =,= =*>

- ? + + @ # 7 =,$($ ) !>

34 =, ;<>

(50)

9

- ? + + @ # 7 =,$$( '# > 34

=, ;<,

< > N '>

A # ! % 2 # ( # 4'E 9%2

# + # > N '> 1 & #

*" + " 2 # C H0 # *

# C C ) % 9+ &H% + % + & %9 "% A# #

# + # # % " *

" # # 1 #

# % 4 * "+ # *# # " + 1 # + 1

* ) # # ( ; %& < # #

; % <+ # * ) # ) # # ) " ( # #

+ # # 8 " # ) !

* ) # " # B ) )

# * O # *# + *" * # *#

B + (" # 4 * E + ( * %

> # * ) * * # %

+ ) ! # # %

A# + ) + ( > '> * )

% 2 + # (" C% H % %

I * # + + + ( * ) % H %

%+ # # * ) ; % H<× ;C% H<?; % 2< 6 C% % %+

# &%H& % # #

# %

# ( + * # ; H H&<

# ; H& H2 C H< # + )# ":

* # ( ; < * + # "

(51)

" ( # . - = % #

"

(,<( =, <;: −=,'*) 0 −=,:' 0 6

:,$;; ) ,)*) <',*)) <,(*$

.$ =,''=$> 34. =,=*=*> 7 $ (,); >

19 $,=::$>

χ

$ ) ); ),'<>

.-34 =,=;;(> 5 =,==<: >

. + =,==$)'> + 31 =,= )>

- ? + + @ # 7 =,$'$ !>

34 =, ;<>

- ? + + @ # 7 =, *< (# > 34

=, ;<,

< K #

* + ( *# *+ ) ) 1 + ; ) ) "

C H< . # / # % A # %2 # (

%& # + # #

*" ( C%9 # C H% #

* # C C ) " 2%C+ C%2+ H% % %

* # %& # ( %9

+ * 9%9 %

C H% # C C * # ) 2% + H%H+ &%& 2%

"% " # ; < #

; < ) # + ( # # " * # )#

# + * ) * % " *

" ; < # 1 # )#

(52)

% * + # # # ( * " > N '> "

# ) # * " ; ( # #

# < ; <+ # *#

" ; ( # < * * % # * ) *

* # # %

# ; 9 H H&< # * ("

$:,$(< =,== :(

',;:: ;, <)

.$ =,;'*> 34. )=,)<=> 7 )*,*)(>

19 =,)(')>

.-34 $(,<''> 5 =,=*$$,

* # (" C%HC % %+

* + # # # % #

∆ ∆ # ) * * ) # %92 0 #

! # * #

% # # #

* # * # ( ; < # # (

) " . - = = % # + "

;,'$ =,$(') −=,''=; 0 6

=,<:$ $',<$; $),'<

.$ =,''(> 34. =,=(==> 7 $'(,=)*>

19 ,';;$>

χ

$ $ ) ',)<>

.-34 =,=*;$> 5 =,==;<;>

(53)

&

. + =,==*$)> + 31 =,= )(>

- ? + + @ # 7 =,$*: $# !>

34 =, **>

- ? + + @ # 7 =,)=; ) !> 34

=, **,

# ; H H C H< # ; H + *

# + + * ) # < # #

.( / # ) # # % # # #

# # / # ;# "

< # > '> ( : * " # )#

% E" & 9 + # # * %

# ( # # ) # 2C% # #

# > '> " ;) # 2 % # < ("

+ + # * ) * # )#

2%H % % * + # ! 9% % %

> ) + # ; # *# # (

+ # * ) * %& % % # > '>

%C % % # + > '>

, # & 2 9+ " ( , % # *

" > '> " # ) #

+ )# " # # /

, %

# ( 1 # # ( # ** *

# * ( ) # # %

4 ** * ( % # 4 *

E / ;4 E< ( + " +

( # 4 E/ > '> "+ ( *

# *# * ) # + (

+ )# # # + # #

+ # + # (

(54)

2

% (! # " # #

# , # " # #

" P * * " ( #

# # P # * + ** #+

# + # ) , "+

%

(55)

9

!

" #$%&$' ##'&##

( ) * + ! , - . /

' !% G& = A

C& % 9% H % H& HH% %C

9 % &%99 ( " &%2C QQ

& % 9 2%C

4 ' "

E L

% 9 H% ' % 9 %

G "

F " ;χ&< 41 ) 4

% 2 ; %C& 9< % 2% 2 %

* ;=< >

" ;=<

G > ;=< G'4' ;=<

% 9 55 %2 %C

; < ; %& 9H< ; % &<

&0 ) * + ! , /

' !% G& = A

% H& 9 % 9 % CC CC2%C %2 C

% C2 9&% & ( " 2%92CQ

4 ' "

E L

% H &% ' & % % 9

G "

F " ;χ&< 41 ) 4

%99 ; %9H 9< % &% & % 2

* ;=< > " ;=< G > ;=< G'4' ;=<

%29 % 9 % 2%&H

; < ; % 2< ; < ; <

0 ) * + ! , /

' !% G& = A

H % 9 2%C %H 29H% & % C

H % & H% C ( " 2% QQ

4 ' "

E L

% 9% ' C % &C % C2

G "

F " ;χ&< 41 ) 4

2%2 ; % HC < % H 2%& C &%&

* ;=< > " ;=< G > ;=< G'4' ;=<

2 % 2 % &% H%2H

; < ; % < ; < ; <

(56)

1& ! ,1 + 2 $/ ) * + ! , /

' !% G& = A

C%& 2% C % C2 9C % %9HC

% 2C 2 % 2

4 ' "

E L

% % C % C9 % C

G

"

F " ;χ&< 41 ) 4

&% H ; %2 9 < %& 2% & 2CC% 9

* ;=< > " ;=< G > ;=< G'4' ;=<

5 5 &% 5

; % H9 <

$ & & 3 + ! ,4 &* /

' !% G& = A

%& %&& % HC 2 HC% %H2C

$( % H % ( # % 22

( " % 9 Q

4 ' "

E L

% 29 %22' 9 % 2 % C

G "

F " ;χ&< 41 ) 4

C% ; % &< %2HC % & % 9

* ;=< > "

;=<

G > ;=< G'4' ;=<

C%& %H& &%CH % C

; % < ; % &< ; % 2 < ; % 2&<

5 0 & 3 + ! , /

' !% G& = A

%&2 &%&9 % 2 2&C%9 %HC2

$( % C C&% ( # %9 9

( " %&

4 ' "

E L

% % ' 9 % & % H

G "

F " ;χ&< 41 ) 4

%2C ; % 2 < %9 &% 9 % C

* ;=< > " ;=< G > ;=< G'4' ;=<

%9 %& %22 %2

; %&2&&< ; %H C2< ; %HHC&< ; % 2 <

(57)

% 0 6 , / ) * + ! , /

' !% G& = A

H2% % % HC % 2 %H

% C %& ( " % 9 Q

G; < % 9 %9

4 ' "

E L

% 29 9% ' % 2 % C

G "

F " ;χ&< 41 ) 4

9%H ; % < %229 %HC & %9

* ;=< > " ;=< G > ;=< G'4' ;=<

% H%CH 2% 9 2%2

; % &< ; % C< ; % < ; % 9 C<

' ( 6 , / ) ) + ! , - . /

' !% G& = A

9 2% %H % H &%9C % &

% & % ( " &% H Q

& % 9%C&

G; < %C 9%

4 ' "

E L

% 2 % ' 2 % 2 % C

G "

F " ;χ&< 41 ) 4

%29 ; % 29< %9H %2 &2 %2C

* ;=< > " ;=< G > ;=< G'4' ;=<

%C 55 9% 2% C

; % C< ; % < ; % 2 <

# & 6 , / ) + ! , /

' !% G& = A

%& 2 % 9 % 2 & &C%2 %C

% H &%H& ( " %H

G; < %C H % 9

4 ' "

E L

% 9 % 2' 2 % & % H

G "

41 ) 4

F " ;χ&<

% ; % C9< % 2% % C

* ;=< > " ;=< G > ;=< G'4' ;=<

%2 2 %& & %

%2

; %& < ; % CC< ; % < ; % 2&<

(58)

C

2 " 7 , & 8 6 / + ! , - /

' !% G& = A

%2 &% % 2 & &C%2 %C

% 2 &%& ( # %HHC

$( %C H % 9 ( " %H

4 ' "

E L

% 9 % 2' 2 % & % H

G "

41 ) 4

F " ;χ&<

% ; % C9< % 2% % C

* ;=< > " ;=< G > ;=< G'4' ;=<

%CC %& & &%2

%2

; %& < ; % &< ; % < ; % H&<

F

% QD DQQD * "%

&% 5 6 ( B

2% 55 6 * ,

9% = * ( 1 # * %

% 6 ' " # 4 ;- I <

% !% G B 6 ! G B 0

C% 6 # B "

H% 6 F *

% E 6 E 0 L 6 L

% 6

% G; < 6 ' *

&% ( " 6 J ;= < "

2% G > ;=< 6 * > " ;=< ; * <

9% G'4' ;=< 6 G * 4 ;=<

(59)

H

&3

" #52&5 ##'&##

+ !, /

' !% G& = A

& % %&2 % 2 H % %2

* % C H% 2 ( " % Q

$ % &C 9%&2

+, 2 % 2 &%2

4 ' "

E L

% &9 % 9' 9 % & % H

G "

F " ;χ&< 41 ) 4

9% ; % H< % 9%H2 % 9

* ;=< > " ;=< G > ;=< G'4' ;=<

2% H &% 9 %992 2%99

; % &22< ; % 29 < ; %H 9 < ; % 929<

+ !, - - /

' !% G& = A

%&2C %&C % & %& % 2

* % H2 & % ( " &% QQ

$ % 2 9%C

+, %2 H 2%&

4 ' "

E L

% % 2' 2 % & % H

G "

F " ;χ&< 41 ) 4

% ; % 9H< % 9H &%&& % CC

* ;=< > " ;=< G > ;=< G'4' ;=<

% H % %C %

; % < ; % &< ; % &< ; % & <

(60)

+ !, - /

' !% G& = A

& % & % & % 9 %H2 %

* %HC C% & ( " %H2CQ

$ % C %2C

+, H%&HC %9

2 % H &%C

4 ' "

E L

% && C% 9' % %

G "

F " ;χ&< 41 ) 4

&2&%2& ; % < %&& % C2%9C

* ;=< > " ;=< G > ;=< G'4' ;=<

2%99 2% 2 % %9 C

; % 9C< ; % & < ; %2H& < ; % 2C2<

) + !, 9 - ") - - /

' !% G& = A

9% & %C2 % &2% %C9H

F % 9 % 2 ( " &% QQ

% 9% C

G %& &%&

% 9 % &

4 '

"

E L

% &% ' 2 % & % H

G "

- 4 41 ) JE

F "

2% C' H % C2 % &%9 % &

; %C& <

* ;=< > " ;=< G > ;=< G'4' ;=<

9%HH %C % C%C

; % &2< ; % 92 < ; %9 < ; % C<

(61)

$ + !, - - - /

' !% G& = A

% 9 % % 9 9C %CC %2C

* %2 2%9 ( # &%CHH

$ %2 &%H2 ( " %99

+, %& C &%

$( % 2C 9%

4 ' "

E L

% 9 2% ' 2 % %

G "

F " ;χ&< 41 ) 4

% % ; %92C < % 2%& %

* ;=< > " ;=< G > ;=< G'4' ;=<

&%CC %9 % 9 % &

; % CC9< ; %HC H< ; % H22< ; % & <

F

% QD DQQD * "%

&% 6 ' " # 4 ;- I <

2% F 6 F ( ' "

9% 6 4 ; H H <

% G 6 * ;G < ; H H& <

% = * ( 1 # * %

(62)

9)

% E ! + F ; C < % + 4

4 4 + + % % E * # %+ %

&% E ,+ @% '% % J 1 + @% -% ; C < + + >

"+ 4 = %

2% @ ; C9<+ # G # = "

%

9% @ ; CC< , % - $

) . * - / 0 . 112(&33&+ 4 *

E + = (%+ # # ++ + %

% > + % % ; HC < - + K, I "

%

% G ' + ; < % , %

(4 + 5 + - ,

+ 11 + <%

C% 8 :+ # ; CC< . * # *"+ #

: # 1 , /+ A % F # ; %<; CC< % H2

9%

H% - 1 1 + 4% A# ) *# + 4% % ; CH< -

+ + A "+ F ) R 1%

% F # + A % ; %< ; CC< % -

% + F # > + %

(63)

&

% # + G% % ; C < %

+ + . * ( # + F ) R 1%

% 1#+ J" % ; H < % + +

* + @ + F ) # %

&% + % % ; H < %

5 + ( + + * ( # *

"+ F ) # %

2% F% L ! " # ;& < +

5 - 6 7 A 1 * F % 2 &+

4 + # # + + %

9% " 1+ G% 4% G ( + % 8% ; H <

+ & %+ - @ ) > %

% G "+ " F% ; <8 +

" # * 4 9%% : + E *

# ?? " "% *% ? ( ? S # 9 & 2%

% " + 8% % ; C < D # " "D+ ;

% + L % + F % + ;4 *<%

C% " + 8% % ; CC< D # *" "

D+ A % F # ; %< ; CC<%

H% A E 1 ; C < - ) +

A E 1 " 4 "+ F ( %

Referenzen

ÄHNLICHE DOKUMENTE

Centre for Development Studies, Prasath Nagar, Ulloor, Trivandrum, Kerala, India. 1

Centre for Development Studies, Prasanth Nagar, Ulloor, Trivandrum, Kerala, India. 1

Centre for Development Studies, Prasanth Nagar, Ulloor, Trivandrum, Kerala, India. 27

Centre for Development Studies, Prasanth Nagar, Ulloor, Trivandrum, Kerala, India. 5

Centre for Development Studies, Prasanth Nagar, Ulloor, Trivandrum, Kerala, India. 25

Centre for Development Studies, Prasanth Nagar, Ulloor, Trivandrum, Kerala, India. 4

Centre for Development Studies, Prasanth Nagar, Ulloor, Trivandrum, Kerala, India. 26

Centre for Development Studies, Prasantha Nagar, Ulloor, Thiruvananthapuram, Kerala. 27