! % $ "# &' $ ( )( $ & $ # ( # * * * * + $ # ,% , # $ - # $ # . $ % $ % % / 0 # $ # , & $ ( .( 1 ' ' 2 $ ' $ ( 2 % 1 5 $ , % 22 3 2 $ , 4 % +( ' * + * + * + # , 6 $ $ % % 6 % % )( 7 6 8 = & ∧ (% 9 % 7 $ $ $ .( % : 1 $ # & # ( ) # $ 2 $ % $ 8 )( 2 , # % ' (; ' 2 % $ # ' 4 1 # − 1 $ 1 = # = ' ' $ % = τ # τ % τ τ τ ' & 8 $ 8 ( ( ' • < 1 < = & < + < ∧ <( − τ <= • * & < + < ∧ <( τ & < + < ∧ <( σ ) 4 < 8 <# # 4 < ⊥ == # < 66 <∧ < % + <∧ < ' # # = − # = = )% ' $ < ⊥ <? B# * ( • −A − ? = @% ) # < =σ% ' % < 66 8 < 8 < =σ% + * $ < <= + < τ < 66 << < ⊥ σ ? = >% # 4 < ? = −A % = )# < 66 ? @% − − − % 3 % ≈ σ% < % 1 = & + ∧ (− τ < & + <=σ& + ∧ ( $ ρ == & = < + ρ% # C # , $ =σ& + ∧ ( + • ' ' = + < < ? = −A % − # ? % + =σ& + ∧ (% ( 2 # − =− D ( .( F ( 4 7& • ( ' 2 ' % ' = σ + ∧ ⋅ + σ > & 66 σ = ⋅ + & ∧ (⋅ + & ∧ (⋅ ( = ⋅ λ C = <+ = + = −∇ ⋅ + = − # $ σ > = ' • = ' + + + & ∧ # $ & λ ∧ (⋅ = & ∧ (⋅ ) 0 7 λ = ( % 8 # ' • $ F = ⋅ = # • * % B F = ' λ ⋅ 4 & ∧ (⋅ # % =− λ ∧ ⋅ + λ =− ⋅ δ =− > ∧ =− ⋅ φ λ∧ =− =− ⋅ φ % E * # =− φ # φ = φ • * =− φ % 1 + & (' = ∧ & ( ;4 G 8 % & ( # ' # = + B F 4 8 == $ # > =% $ <= φ λ φ > =# ' * φ < =% + & (' + + & (> = ∧ 2 2 & =− & (> $ ( =− φ # # # # # 9 H 2 # # # % # = =( 1 5( I # = + =− φ $ & >=% : ' ' 1 = −∇ − & # ( $ 2 % ∂ ∂ A • ' + ' 2 =σ& + ∧ ( 1 ⋅ σ > = # −∇ ⋅ + ' • $ ' =− • − ∂ ⋅ ∂ + = ( ∧ ⋅ ) 0 = * * + += & , % : ∂ % ∂ % ; 1 G # 2 $ 1 5 F = − ' ∂ ⋅ ∂ = + + # 1 G % # % : • B F ' = − > =− • ' ' ) = − = =+ ' ∂ ⋅ ∂ φ ∂ ⋅ ∂ $ # 1 4 =− $ G % 1 # ⋅ =− ∇∧ ⋅ % 1 φ = µ= & (%π % 2 # &( & ) 0 J % 8 =% φ# ( >= % ( $ ' =− ∂ + ∂ ∧ # G 2 % =− φ & (% # E( • φ = =− ' 1 φ =− # # 1 1 2 $ % • 0 1φ #8 − φ = > 8 = 1 1φ # = $ &φ − φ ( # $ % ( $ 8 * * 1 ' 0 G8 F # 4% , $ # # 1 2 1 . / ' # # % ) 1 $# $ 4 $ 1 0 1 # # # $ % 8 $ # # # G 1 + 8# 2 $ % 1 =σ& + ∧ ( = −∇ − ∇∧ ! =− ∂ ∂ ∂ ∂ " )( 1 % K .( 1 ( 1 ' % ) 1 φ1 # <=% + # % ' # $ 1% φ1 # $ $ ) 1 $ $ > =# % # φ 1 < =# (F # φ # =− φ > =# % = % ∧ F + % 7 # > ! * 7 "# 2 4 1 5 !# )( L ( $ % ( 1 ω ω% D ' =− φ =− 'N ' + + ≈− φ= ⋅ = = ω φ & ( ω% ω% (. • ) 4 * + =− ; 4 = =% $ # % # * ' + C • * , ≠= 4 % B $ 1 ' ! $ + + $ = = ' * - − % # (=− % % = " = % ω + =− O =− % − % • B $ ' δ$ = # + = = %∆ % % " C + % # & O + + % θ =# +# # % O & 4 # ( # = −# δ$ = −δ$ % M C δ$ = + C 1/ φ=− & = "# ( % • . ' C 8 $ % & P ( .( C C 4 θ ' Ω & ' ' # &$ $ () 4 • • # * % ( & % 4 > # $ 8 , 7 G8 $ *$ % $ # 18 $ $ % # $ ( θ = ω% ' • ; * ' φ ' = φ # $ φ = φ 1 +φ & % ( * # % ) #φ=' 'N φ= = ' ) # + &ω − Ω ( + = φ= = ω − Ω &! $ = φ= & (+ "( & ( * ' + % $ = =− $ ω= J = 1 = ϕ # & + ϕ( & + ( = −φ= % = • * & & C ; (' () # =' ' #∆ = ' $ = −φ= & ( & ∂φ ∂θ θ φ=' * ∧ &θ − Ω ( 1 ∂φ = −φ= ∂θ &θ − Ω ( 5 C 4 ( < #∆ >= × &φ= ( <) = − φ= − =− & φ= ( = − φ= + + < #∆ > Q ω *8* $ $ < #∆ > ω (F • ' • % • # >= # $ ω & Q ( *8* & ( =< # ∆ > − # + ω * == < #∆ > Ω > > > * ω # ># # < #= #= < # < # > 2 8 2 % 2 % 1 2 % 2 > 8 < #∆ >< # # ω <= # ω $ ω # G 8 =% ω $ > ω# 2 G 8 $ ; 8 % # 8 #= > # & $ ω 2 % >=( #= < # < # # % 2 E( $ ' θ =ω ≠ • $ % ∆θ = # ∆ − # • B * 2 & (θ &θ $ & (' < θ >= ω * $ < θ >( = ω & (' & ( ω $ $ (( 2 ( >> ( $ θ • ' %∆ ω =< # ∆ > − # • ; ω 8 ω ==# ' #= > # $ % A( . 2 >=# 9 7 ' 22 ) = # Ω% = 2 = # Ω # = ) G 1 = = 22 Ω # = ( % , + 1 = Ω% = # # * % F (+ $ 2 & & ( $ 2 # $ $ $ 2 ( ( • * P 8 F # = ' * = 8 ω% $ : % % $ ' # 4 ) # G F 2 $ # &$ (# G % • * F 7 $ * ; F # ) F ' F % $ % % % C & 7 8 ; $ F ( , # % F & ( ! )( 2 ( • ' : 8 = =− • ' * ' ' 2 φ 7 2 = = =− &! "( + φ =− φ % * 4 % ( • ' =σ& + ∧ ( • C 1/ IF ∂ ∇∧ = − # ∂ (C 4 Γ 1 Γ ⋅ =− φ $ R * * & # ( $ $ 2 $ # ' = & + ∧ ( 4 C 1/ IF 4 ∇∧ =− E ∂ ∂ .( B J ' ' 8= J % 2 $ () 4 % 4 * * $ , $ % ( >4 8 +& % ∂ ' # ∇∧ =− ∂ %+ = & #θ/ # &/ # ( 4 # 4 ' 4 θ % = µ= ) 0 ( 4 & % % ' ' + + 4 ⋅ = ∇∧ ⋅ π % % = − µ= = − µ= 1 = − ∂ ⋅ ∂ π% θ % E( 6 − 6 ' = λ )% # # ∆ = λ) )% = λ%) ) − µ = ) = − λµ = ) ) A 6 ) # ∆ = − λµ = =− E − 6 µ= λ + % ∆θ = # ∆ # θ =− > E µ= λ µ= λ θ =− ) = =# θ = = = 0 → +∞ # θ = ω " µ= λ ω" = ' = =% % $ 8 =% ( $ $ $ S + θ , θQ - 2 + • ' * ) + G8# + , # 2 % ω= + 8$ 4 4 $ 1# + $ 7% 7 ' * ' + +== & 4 F % $ + % ( 4# φ % θ −θ Q =− # φ = ×π % × = φ= &θ − θ Q ( N φ= = π ) # = φ= &θ Q−ω= ( ) 7 ⋅ = ⋅ = ∧ ⋅ + = ) # % Q = & θ Q% Qθ ∧ θ Q− & (⋅ % Q + = Q & θ% θ ∧ & (⋅ ω= 1 = φ= &θ Q−ω= ( % * + % ∆θ Q = # % &B # G ∧ (( ⋅ =& % ∧ ∧& % =− %% % $ ∂φ # = ∂θ Q * C $ 1 ( & & (( ⋅ & # # = − φ= ' * $ 1$ θ %∆ ' ϕ= ω Q+ω Q = ω= N ω Q = θ Q % ω Q = ω= ( − − 6τ ) Nτ = %∆ φ= + G8 4 % ) 2 # ==# > > * 1 +&# +&# # ' = ∧ + # = & % ∧& + 8 8+ Q 1 $ , 1 φ # % # 4 2 # ω Q = ω= # $ → =# % $ $ , % 1 8 . = % ∆θ Qθ Q & = = % ∆θ Q ( P = ' %∆ + & ω= 8+ =# +# # $ = − # = − φ= + 8 + ,# # #+ = −# #+ Q ( K = =# + = # × ω= = − φ=ω= ' $ • + # $ = 5 θ = θ Q= = ) = =# > =# +∞ ∆θ = = $ $ + # θ ' ∆θ Q ' = φ= &θ Q−θ ( # # % ∆θ Q " = + ) % ∆θ Q = φ= φ= &θ − θ Q ( &∆θ − ∆θ Q ( % θQ" = = % θQ" ≠ = # # ' > θQ" # ∆θ Q # %%T + N ∆θ = ∆θ Q . $ =$ % +( C $ & (= ' ' = (F & = − (% : % # ' + = E = = µ= =− φ = −µ= = µ= = = E (C + D ) ' 4 $ & # + ' + ' − % = = =% + % = #E % + = $ = ' = 2 = (% % E % = E Q = *8* = E () + = ' • C • C = + ' = E # % − E + = N $ (> =− = = = − = E = U $ ( • + ; ( = • R ( < ( σ → +∞ % 9 V W ' % # ( < E# AW # $ $ M $ # 9 . AW = − C $ % $ ( = #DW 'D # D° 1 M O & > < > > & # 8 $ 8 8 % # , ( =− # = + ( = µ= ∧ # + = = C • * 2 $ 1 % > # 1 & Q *8* $ ( =(= (= − 2 ( . .= ( = " &. ( . B &) * > & (; = / ) 1 % # 1 : 2 & $ ( 1( , 1 8 % & ( & ( $ 2 # 2 % 8 % ( • X + & • > 2 8 F I ( % ; # 2 2 8 . I & ( ? µ % T = # ! $ $ $ 2 "$ , % $ % &B $ . ># . > ( () • • • B ; > V % & 1 ( • ' $ % Y > G 2 &U(# 8 , 2 ' = =− + + $ φ =− % φ1 =− φ1 # Q $ % U(# # $ φ =φ 1 + 2 ' *8* 7 8 ==Z% F( ' $ & * * # $ % φ= , (> + % • φ = =− 1 φ= # # Q & *8* =− & • &= + & ∧ (⋅ ) & & > &= • C $ ' + O &+ &= )$ = • (− − 6τ ) #τ= ; =− ' • &= # (− &=− − 6τ )< = . + (> + == 22 • ==− ' φ % # $ φ = φ 1 +φ =φ 1 + =− & + *8* =− &+ − 8 = = # & = =# = = 8 = =+ # & = = + =− & • Q C &= &+ • + = &= − & &= & − # . + + & 22 # ( == &ω (( = &= − ( = = (> % ' &= 2 # Q *8* $ + & L( . 2 ( / ω & ' = =− # % ) = =# 8 8 % σ = +∞ ( &' () ω = ω= # $ 4 $ & 7( 7 ' $ % # $ $ = % ( + 8 +&# % ∆θ = # = = φ= & G 8 $ 1$ # Y ( ( ' == + = =− ∧ + # )$ = # = + + ⋅ # =σ& + ∧ (# # =− ω ' = = ) Q − ∧ − Qω =− ω & ω = φ=ω Q= + φ=ω = = + # θ *8* + φ=ω = = + $ E( ; ' Y + 1 φ= + = + 1 == %∆ − 6τ = Nτ = + φ= %∆ #ω + = ' ω= 8 = =+ # + φ=ω= = = # =− = φ=ω= & = =+ ( = = # ω & = =+ ( = = % % A( @ φ= %∆ ω = ω + &ω= − ω ( ω= )$ ω = φ= + + ' ω= ω $ %∆ − 6τ ω S ω 9( ., ' 4 & # (= & # ( $ $ ' 8 8 4 & # 7 # =− = & + ∧ (% E ( ' ∇⋅ C 1/ • >4 # ' & # ( 4 & %) S 8 = − φ= )$ & # (= & # ( # ∂ ⋅ ∂ =− % F 4# 1 # φ ×π % Q= & ) θ ( & Q# ( × π% Q = ∂ ∂ %' C 1/ ⋅ =− $ B 4 &' • + = =# ∇ ∧ N 4 4 ( × π % = −π % # =− θ ( G • + = & + ∧ ( 4 − θ θ+ θ = > = − Q = + − & G θ ∧ = & = *8* # − θ =− θ θ+ θ =− − − &== • ' $ = $ = = )$ )$ # 1 # = = + & =# ( = & =# ( + 0 • ) = =# $ = =# = G θ= = # = = # θ= = = % & = #=( # &= = = % A • > 1 Y $ $ 5 $ $ # & $ = (8 # (@ σ∆ = % =θ ' σ∆ > = % =θ = ∆σ ∆ = E( ; = ∆ = = π ∆φ , 2 & 1 ( 1