An analytic solution for magnetization distribution in multigrain ferromagnetic materials in an applied magnetic field

Q (D c-h C"D

U.

Cra

0

F3 _{_~~~~~~~~}

A

C]

_Co]

CX C)CH

C

CD H c-h

cr

A

C-h-0

0

cn CD C-r) -h CiO c-h

©

c-CD

0

o I

0

0

oq

_to

C

C)

c~r c-h C-i_H CD CD CD ~A * CD

*

t

'(D CD

~~~~C

_Hr (D C. t". _c~~~~~~~~~- (D'

*

0

N

,

c-CD_H CT] C 02(

9'.

U)

~:

>A.

Cr

t) '

.c1

.

r

tS:.

t:

CD

'

Cr Cr~

C

Cn

Cr

i

C3 CD

M

H

r-

,

0

(1) O CD

o

0

Q

0

0

0

QD

Cr

C' C)_c-.' C PAJ O, H .

l-

Cr5~~~~~~~f

CD

Io -CD OD CD P CD C-th h 0 eCD CD O-(D _{H D} C H -2.

S([-CD C o C

I-o

cen

-

Ct

-~

=~

.

_Ct'

0

o

~,rb

. -e 0

>

CD -h CD C . .

Ct

f-A

CD " H o

0

.

c-h

C

0

C ·

CD o cn

0

C

-0

Q:

c c .CD Ce C, t>

rn

0P

cr

N'

9'

c O c y- c' H O ('1)5 -t H-CD

~

C J ci. Ca .

9'=h

p

~

c'-" 0

₀₀

o

CD q Up 5

~

9 _{~~ 9,~~~CD9'H~~~~C}D N

c-C~~~-

I'

D

~

CCD PU k -,

D

ICC

C

C)

~~:rl

_{EH -}

_{0 0}

C _{CD~ Ca} HO 9, ~~~~~ H

2J 2.

sP

'0 -

0~~~~~~

hr. 0rr ~c- rn

~.0 =

~h1 CD CCa+ CD~~~~~~~~~~~~~~~Ct - a- ID-CD~~~~~~~~~~~~~~~CS CD· g99 tC -c~~~~~-F- H

--9,

(

0

9'

0 Qj0zci P,~ H F - ,D OCa CDc~ . . N. ca CD E CA 0 _. ;_₍ H

o<.

0

P. 9,

tl

P) .-- 0 CD

0

cn H-- CD (7 _-cn cn _, -0.

0

_©

U

I-z p

-o

C')

p-0,

C-F tb Cr c-F-0 0

0

_Cr

_r

O

gp

0 CD

0

g

.

. 0o (D -

0

ci-

_~

21

tHO (D _{C. D'} ~.., .. 0J q ' 0q I--I' -Cr (D C-fc (D H

o

cn_'-'

S.

D

0

,D_cp

0

_D C-t c-F

,

C. 5d

_©

o

©

e-F Ce

©

©

_'11

ol

D N C-F

-c-F

.

t

₀

Q t

_0e

oFQ

~~~1

~

n

_r

~~

CI)~~~U

5

o

o

,3

CD CD CD c" C C

Co

(

ci-o

₀

c- i-z. CC r

o

ci-C

F- -tQ h- _ci-

C

H

HW

_p

cF

(DO

tGq

Ci-Ci)

ct

s. CI)

0

to t o o

to

C

a

00

) C

0 0

0 0

C

uc

CQ oo OD

CA) CAD 0oN)I

~~CD

c~~~~~~~~C

~~~~

0 CD~~~~~~~~~~ CD

Ž2C

C.+ C C+ D PD cI C -k CD® C n E

O

r

t

~~~~~~~:

~~~

g

3

O

:

q

6 o

5

5 CD OC

H

II

cn 0

o

D *

o

C D D

5

o

.r CD

~

zC P C * C + C ,

oCD~

Q O S CD XD

HD

CD

o

C) * P- . CD C

0

* 09 2 ; CD P CD ' _{C H} ® _. CD _{-- cI} q _{~ --} '

₀

C

D

n

C

D

0

C

D

* 0

S

~ Cl) ~ CD H 0 CD H

O0

_-C

-

0

D

.

_0·

c-I-*

CD

7D

cn09

CD

~

0 -0 00 ~CX oD Q

H

C)

P

* 09 1 t~~~~~~~~~~~~~~~C N

* C

D C

D

* I I * I. CC 00 CD -. 0 CD H o

t 2 B

H0 0 (/~_CD C CU CD PD

-"

0 }- C , .

090

_c -* o D * CDA c-I-O

~-I

r

...Jml e

c-C+

0

aq

=:W

PD C C C P P P OP -s- ,J o o

C?

C 0~~~

C-t-

(

o

(

zn

zi PD c cF

₃

Q 0 CD~~~~~C Ci- D ~C - ~' o p (D CD P cn

~~

z - n ci

S t

_o~ w ₀

o$C

CD

H~

~

p

-_o+ P Ca _{c 0} -_{o c P}

cr > t

CD

(D

o

a -F

0

_vH

U -

CD

N

0

P.

-(D '7 CC) o .. CD . C-CD

~ ~

*

-hn

H

o

0

o

c-n CD

0

('

H c-f

o

o

-C) F -CD

0

CD

4.

C)_CD cn

0

CD><P CD PD C

~pD

cn o t

(

i-

pn

H _. O

-0

c

0

o ,_. OP cn Ca -. PD 0-

<2

.

C)+H

_H

m

co

o .

_{0- Po}

'-' C _{H c-} C) 0D

cc'

P'D

.f._{_ Ca CD}

PD O Pt

o .- .- , -. < Ca- 0

®

'

-V 0 OP PD C) D . S

S

c- cn H CD OP O~~a c- - ci-_t

I

S

H Ca _c . B- _{, P 0} -

-.=

c-p -. CD PD ( O H _D C _C 0 CD_t CD CD c < PD CD)

2 2o

o

~

~-

~~

~

0

~~CD

~~~~c-~~Ca

.

o-

_C

ul g H- I O B 0 oD p- -N- ci

--.

c- - ₀ H ₀

9

°

_~~~~7 PDD CD Ca

~~~~~~~~~~0

CD CD~~~~~~~~~~C ( D

$=

C+o n

C D _CD ( >₀

PD

~ c- _0~~~0H c-C+ (D~~~~~~~~~C (D o oq H XD CD .Ca

-

(D-.

0

~CD~t

Ca PDC0

C) ~~~~

0

C)

H~~~~C 0 CD PD C ) H~~~~~

SO

Ca D P D 0H

C

0D *~~~~

z

0

C~~~~~~C

o

0

on

AL

0

~~~~~~~~

CD~~~~~~~~~Co QC D53~~~~~~~C -. Q t-C-., _{CD D}

S

₀ J-CD CD M H-t CD

0

Cr M C-t CD , C

~~~~~ P

CD P CD

5

CD

~<

CD~

o

SD

c~~~~~~~~--lSi-.

E.P

CD I CD II~~~~~~~~-_H+

_~

_{J Cr D c} 0 CD D CD

D

C-.

~~

CD CD~~~C CD C CD

~~~~~

~~~~

~~

5~~~CD-CD

~

) I~ Cr

S

+ c- Cr-~

S

. Cr

Pp~~~~~~~~~~~r~~C

_®~~~~~~

CD c-I-

~CD

S

~~~~~

~~~

~

CD C O~~q c -I t CD P C+

c-I-o

CD

c~n

N~c

0

H MD CD CD CD

~vCD

c~c:N

o

p

P-1 j CD CD CD G CD C0q CD $CD_O

_p~

c+

cn,

CL CD Cr -H- _OCD

Po

H CD p. e e c- -cn

z

b 0n 4 -,^L t;:

o

o

ci C) cD C HD H c-+ cn pDr

0

c- -- H

S

CD

B

o

_{0 ~ -}a, ~. o.~-.. _{P -. c-- CD}ow CD P c-P C D _cD~~~~~~~~~(R° CD j

o

cP

_®

_0~

_®

_~

ci-

_~.~"i

c

.

-

0

-S

0 X -C D . C D CF

S

0

[~J

_" 0 D

C/)

, - -

DC c-F - C DH O'q ~' F'- C,, PD _CD o X . CD CD ° CD CD

~~

0~~ "'

0

~-"

0n CD c- C 0 C~~~~~~~~-e- c' CD _~~ 0 PD~ c~~~~~~~~CCD

oD

CD -. C) CD

~~~

PD

~~~~-

Ci D

c-

--H CD CDQ- CD -

N

,-.

_JR

1•

~~

- ,

c-

~P

H

Q-.

-CD CD 0

CD

~~~~~

H'

CDI

C-r CD CD D 0 0 ~ 'C0CD c-- CC.0

PDD

CD

-

D CD

~~

PD CD 0

H~~C

"

CD

₀

cn

ZD

PD C

(DW~

~"~' 0 C/+ 0

o

S

Po H S

g(2-C)

H P - 0

* JR

-. CD~ _Y -~ - k 0q. c--c-t- 9 CD D C) o o 0 CD _{O (D}C JR 0 PD 0 C)

O

CD 5C+ 0 cn c-I

O

-,

9o

..

Q

-k

0

P+ O 0 - ₀ -. H 5" _c-F

S

P_Cd

0

"

-F-PD 0

'

S. 5 .~ Cr -b-CD < C -1 c-F o CY) O C S) S - CD (D c-F

0

(D CD

F

_C* N

-,

CD

o

cn C)_('D c"

-Ft PD

o

i..

CD --P'D ci-t Crq c-I-+ c-+-\ S c-I-09_CD S_.D o CD CD JR 0_P'D c-F

0

S CD I

o

c--o

0S (D 0

0

P'D cr c-k H..~ 04

©~~~~~ tQ

~"CD

0%CDH (D

~

t

~

~

~

C

5

H II -. Ht < D8 _0~~~~~~~~ ~

8-~~oZCD

CD~~~~~C o-i D _{PD tQ}H o. q CD ND C

I~~~~~~~~~~~~~~~~t

jj~~

-~C

+

+

+.

I.

~~~~~~~~~~~~~~~~~~~o

~-~ ~ ~ ~ ~

~~l-~~~~~~~~~

_d

o

₀ CD CD Cr CD~~~~~~~~~~~C CD3H

cn

00

o

crq

-~~~~a Cr Crt

~

N~F

_

C.

C)

CD O-q c-i- _CD

C"

~ ~~ ~

- 7' aq0 -~ c< CDJC

c/) Qq Crf 0 ci-ccn CD' c-" ,_ _09~~~N H $

~~~~t

P

0

- c:~ E _H .I _H

p

ND | C-. oQ H' m c-

-ti'

NL Cl c-h CD orq 5CD O c-CD (1) C op ( 11 0 PD N o

PDC

c-i CD _Cr

0

S. c-ho II D CD c-f- c-h-ho PD c-h

0

C ..-. ,.- -ND

c-0

w

0

c-h F-CD p

_-.

ho PD p c-n 0

m

1) c-o ('D

¢-h-0

P)_N cD CD Cr C+ PD CD Cr

z

0-op C-l

+ + 8

I~

~ I,

o t

~

o

±

±>..~~~~~~~~~~~~~~.a

f)

P

~'

2 / H .' d))

H

CD

as

CD .-. c-h 5-

_I

_>

8 o

_t

( _cD~~~~~~CH P'D . D 2.'q I _CiD~~~~~C

0

a , H Nto Lo

o

o4

₀

ll c-+

.

oc-l_PD

©

c- I-PD Cl C--

₀

H o

₀

C+ CD~ op Il N CL Cr~ ,0

NDI

±

Co

2.'

Cr ND

0

ND

-F

p

Co

P

Co

2.'

Cr

0

I I CoD_r ND

I

C. Co -3-_{+ I}

--

-

4o

HS Q Cr Co ,---~-h I ND 0n

+

r.') C

+

--ot

o 31S~C

+

Co

+

-0-0

(P v C*D C-+F c--h

0

C-i) CD)

1.

o '

S

o

o o ~0 CO

~

- Ci 2 0n z > 1 CD

U)

X -sQ cnh o.

-

-CD~~~~C

vF

O

~~~~~~~~0

_{0 .}

nw

o~~~~~

C, ~ · H

O~~~- C ) .-hc ) - 3 O r S P

CD

_et

c-+

~

* H to *~~~~~' H · cn

;

C-D 0 C'DD 9

~~~

CD c+~~~~C--- c D CD

0

t

S

CD

0

0

0

HC

H

o

D7 , w '

0

~ ~

-

,

D CD c~~C

_*

.

_-,

_t

_C

H

o

(D

o

t

cn _ND~~~~~CUc, c-C.

to

CD CD~~~~~C H_N) to f, CU (I ¢I

o

.

CD

Cr-0

CD H I-.,c-k

c"-tic')

o

_W

o₀₎ cF -. Cl Co rC J) O C/i) , ' a-. 0

0

H CD (D~~~~~C II II II c-F-("D bO D' ·3 ' -.-. ( E~~~~~~~~~~1 i-~

t~~

r. *

H

Ci c-

I-t-H'

_~CD

_o~,I

7

a

~~~CD

HL 11 o

0

CD CD iCi P

C

c-F a₁ N) - >

+

-+

b) p

>Co

1- / H 1., -N t

cI-1 I -4 tS I ;~ N1 I to NN

N

~~

NDI~r

Co^

soC

a

8 >

S

~ ~

|

a

S~~~~C

H Ir-s(D

cc

3 ( I I I H

o-,

CD Cr - HF (D

0

CD CD, PD D D

_o

0 OR

o-0

0

PD CD_Ci) cnf

±

0

NO cn -2 C I to~~~C c, _ND~~~~C ND _{Qb 2~}n Co I I.

Z

NDI

2

>

0

('

±

o, o

±~~~~

_P

Co"'

_{~~~~~~~~~~~~~~~~~~~~~I}

0

';

L'Co-?

DI

,.. . o.. CD CD c-+-Oq II 11 P

C-.

g,

0

-CD

. .

P-ci)

on

,- f-N) I , I

+

-

C

Coo

ra ~ _.-. r

o~~C

_{+ I}

a+

tQ

~

8

A

0 NDce

a

+

_a-

Q!

_{Cr r~(i)} ~ C ND cn c

a

_CO

2)

-:r I, CD Cr D cn

II

cn

₂

o

-©.

rX

0

~U

_o.

Cr cn c-F

+

CD

0

11 II c~ rD L"'O

+

±

P ~+_*Cor

~Q

₈

a-c) N) +

a

o

N)

P

- a-a- Co

8±+

aI) ND-fr"L C-1

HI o C 0 CD CD CDF F CD C a c -- o II CD CD~~~~~~C CD H

o

C+O H c Cn CDC)

_.

_.

enCD

-0

r

O

S

00~~~ _{1 H F} II -0I

5

gn en -S% CD . C -Cs-(1) o D

en

tD go H

~~~~

~~

ND

S

b~ Cc S

S

~

©D

H

CD

o

c7qCD_D S

0

Qq_CD

_o

(D

0

m en CD

.0

cF₆ Sj CD n cn

0

c-

C-0

z

0

tn

c-0

en PD en Ft

0

c-A Crq en -ND) S-_. crq cF o 0 o-. cn 0

r-zn .0'

.)

(1) PD P S -CD H CD 4.L en II cn (D

-.

I Q I H t o_C)

0

N U\) Cq I 11 CD I

+

1n f Hc I

I

_-2

Ia

N

to C Cq C )

0

0 l ND cn- Q NDIF-i -2 N b C~

I

t t1?

₊

/

_+o -HS + 1. QtS + I

a-

C3

en en CD CD C C) oq o H c-F C CD C FtoH PD

o

ZPD P) 0 c--- CD

4

CD 0 CD Pn _4. e₀ CD > ( c-F CD

o

1,

c-

oq 03 PD QQC c--- c, - () o C -. -F C PD~ CO

+

C-CD PD 5--_c-F 5_,. 5_PD

o

cF c-- 5-.-PD c-oP c-CD_H (D CF C)

0

cD

5.

ND

-N) H-Cn ND

H-~00

-[I H _{'~~fl g} CD CD _{(D C} l CD ₀ CD D ND

~D-CD

o

C

CD

_I0

too M Ca~~~~~~~~~c

0

0

cn

~~~~~~C

_{Mi Dt}

c-.

I

~

s_

-

~

H

M

CD~~~~~~~~~~~~~~~~~~~~~C

cn~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-

c-tojk-~~

n

0

~0-

Ca DC

+-

_t

_{,, I}

P)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~P

+

o

_{II' CI-} CaZ;::

~ _CD

_{_}

~~~~~~~~oo

_{PD PD CD Ca~~~~~~~~~~~~~~~~C} C0 tQ

•

ottkol

₅

c-h

±Q 1-, _{ND CD}

~

+

"

+~

to2

CD

~

~

~

~

~

-

+

+

N'cra

-to~~~~

~

_c-h

S

_0eD 4 " c-t~~~~~~~~~~~~~ .

Sc-h

_o M M t~ to ~ = MCtoCt to

M) Q ) z2

$

A .

cn cnw r

p I- o cb~~~~c c-k_{- nj- _CD}

CDK

0

ii~~

CD U C; C) ~ p ~ ₁~ CC)n_p

o

C

p-.

o

0 v-. L. c1 CD O I I x, + t o D $ -O

r,

O

gq

p

-. >

-

,-'

U)

,- ,

p

I

.

c~~

~~~~~~~~~-t'

-, _("Dp (D

-Dr) c1-1 CD

_o

CD

c--t--CD p -] U -(D 0 0 CD I CD CD o cn c--.

o

< =. . C .~ CD o

-'

H1 C O > C 8

+

a

z

I

S

a

%6.-ta

+ +

+

+

tQ

0-Co C) i--En (D

C-h-0

c.-h c-h Ci) -G-11 C7)

+

+

-0-

_tu

+

+

-0-+

0- N--6.,O bO

II Ii~~~~~I

11

a

1 a l l ½ -- t-E bO~ b~ o b

.,

Q .. p-

o

rZ

Q H H H

0-

)

0

-)

N

)

H'o 0 CS l -i - c 0-,

ot

_{°j C} H 0 O H _C-- 1K)

~ ~

. ,,% .

CD C-t CD C .

o

pL _CD Of -> N _D

I '-z-,j t

c-h~~~~~~~7 cn = + Or C"

_W

C- D

₊

C*

₍

CD bl o 9 o _I-I' Q~0

a

85 $E > 11~~C II II

-5-

_II oo [K) U) C+-_.11 crq

o

cnh CD CD - c--CD C) o I.Il (D S. S

0

S Or)

II II

aaa+

-

-g

_z 8

Y

_a

I

± -' ½ ±o C+

½o

G

z'

-o j cn CD 0_CD

©

c-CD o'q

₀

h) c-n I CD

©

C+ 0

_.

c-'

©

(CD

-0

CD c'-h

0

CO

+

s-

a~~-G

_S

,

a

+

.- ,--,^o

"~

+

/

+

II

+k

+

+S

+

H ,- H IQ

c-<H

PD crq_{PD C} C+ z c-o

CD

o

0 PD c -- c-h C+

-o

o

=

c-

--PD) _h} ch_O D CD o

o

C/O C4

0

-' PD F -o'

-CO C- c- C-I- crq h-(T) X (D CO

0

o

CO h-0 -G-P) ~a t3) CD CO

0D C0 CD H L>

_I

P®

0

0 D 0 _ _ j D CD Q C+ _{- H--} H DCH -- at 0 _{0 CDP}

~

; H: H j CD (D Cl) _{P (}

_CD0

at CD at

~~

_{cn CD a D} C m ::Z

~C.

_H ' _{g~~~~~~~~~~~ 0}

~

C

_Ct l ) -,

c

n

a

0

a

CD -~~~~~~~D C) C

CD-

CD

_P

_H -

S-.

_P O' (D

_I.-

_-P

C-

_n

d) _H

a

CD CD CD

_~C

H C CD H at _at :: O -

0

C

0-tjCl ) _{0: ' D} CD q -. CD7 a CD -. _P~

~~D

_CD PD

a z

_H

₂

0 Cl)

~7

0 at0 5CD CD 0~~~~~~~C , _{.Q H} CD at~

~~~~

CD at PD c- -n- CD CD~~~~~~~~~~~~DC

'

D

O p

o

0

-

_{C D}

_{C-- C 1}

n

_{P D}

_Z

a t a t . H CD C- D CD

PD 0

0

D

0

. 0 CD CD It at C D CD CDq CD PDD_Cl..

o

cn C) 0 PD CL

0

tsL.

c-(D 0 0 o. _{H ,} at_. C'D

o

C D o IH_0" :. CD

I

o

O ₀

Z

CD C -. °, CD cn H O atH H 0

cn

0

-PD

D

PDZ

0

b

O* 0~~~~HZ O

_o

PD

_MO

cr _{0 , 0}> _CD H Q~~~Q (D (D

P:D '

z, c at -; . C D CD CD + (D PD CD CD Cl HD 0 CD -0 atD Cl) at az t CD PD *: CD Hc PDr0" '0 PD CD '-"- (

a

p - C D C-q cn cn C-

c

o~~

_CD CD P _CDD CD _{PD 0} C CD CD

0

0 C/ t ' PD _cn0 a

(1 ) ,,

_a+

DC

CD

_PD

₀

HCnC c

.

PD

.

CD

'-"

_{CD 0}

0 H PD 0 2 H

aHC

_{D S}

cr

Ci) (D cn CD

-,

CD PD CD oq (D CD

_(')

Gq

_B,

M"I o_, CD PD CD H cn 0-1,

0

P) 0) P... P

cnn

H (D

C-C

0

Perturbed Angle (degreesj '-4

~*

'- CD to -0 X

~o F

('

(D e on . -o _{O, D}

PC>

t

-o

°CD "--* O C CC

.

O I

0

CD cn cn CD U) _CD < CD

₂

C) CDD _

.

.

,F

0 O C+ 0-- CD 0 D

'-'

CD

·--

t -

c--

-C 0r ,

0

C

CD

oq (DO D

'0"

o

(1) C o c C C-+ CD 00 CR n X C.T H m C CD ; 0 °D C < P

~CD

D D CD °~ m m ~ m

3

3 O _{cn P-} r _cQ J.- P., g CD I.~ o g< F) Co C C s H CtC CD CD j 0 CD O C D C D o 3 CD Z

_0D

t vF o t _ c D + CD N

~

c CD Ct) c (D Cr

S

C ~'

0

-

C

R

z r X m

~~~~~~O

2 D U) co 9~ CD C CD CD

CP

0 D0 -. _{D H} - . C * D

U

0

_~

_Ct CRt

U)

~~~~~~~~o

CD CD 0 U C c-k

0

~~

_C) M 0 K0

0

0~~

o

C

¢

D

ot~CD0

P-,~ r 0 CD _CD D _U) CD _CD CtF CD

S

P: HD CtF CD H+ CD P CR C-.

pC

0

(

CD C-t ~, _ CD C CD CD U)CD-

CD-CD

0

_~

'qCt

0

Z

C C 0 C ~ . o-c CD CD -' cF , sH c/']

o

C U)

Do

CD e) '"'-x-0 CD cn

~cR

Ct -n:

0

-- H CD

CD

. C pPD

~ cP

O09

CD p O H 00

0 D

~ oq p.

Perturbed Angle (degrees)

m

co 8 FR

h-I m

CD

~CD

(D 0 CD CD cn + Cf H 0 -o tCD

_o

~CD

I * C * CD c-j

0

0

o C D cD 0 <

~~

jq 0

~~~~~CD

Q7' C o C.

0

PD H

CD~~C

~

D P oCD C D

q

~0

mColDiD-PD~ ½C

PDt

CD (D

(P

0

Q Co) K)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Cf

t0 C PD D 0 H Co CD H : CD PD CDQ 0 0D

crq

C-' o H Q C ,- Co

~~~~~~~

P~~D CoF CD

~~~~~~~~~D

C - - C

~~~~~~~~~~C+

PD PD -P P H H

P)

CtC

0

o D . CD - 9i C < C-'4 P

~

PD-Q

-'

-

,

P

o

D

0D

_~ ' o CD

C

CD

o' D CD Co

4:

₀

CDPDCDj Co cn 0 H ~ CD C- CD C C DH CD

~~~~~~~~~~(

cn C_

oq

_®

_CD

_D~~~~~~~~~~c

_--.

_{C_~~~~~+.'}

_D

0 c'- CD CF O C+ CD C o-- oD _{(D CD ~~~~~~~~J}

~7

_{n ~~~~~~:s~~}J.

~.~~~~~IT I= N

13

='Z0 (D C~~~~~~~- -CD _tQ

CD~

_{C D} CC F" CD o .

~~.'

~ ~ ~

Q CD Co

0

0

> s O

a

(-<

~.

H

x

D H

g ~~

o t _CD

o '

c2 89 Co z

4'

CD _{*-. C} f-N) C -- O 0i- C 0 CD

r

_-

~o

0

_C Q- (C PD P , D

SCD

o~

·

_~~~

.

_~

_0~~

_~~~~~~~--

p

t

i3l

o

~~~~~~~CD

Co

~~~~~~~~

Ft~~~~ N) H4j 0o cD

o

.

CD

SQ

·

CD

o

_o

00 cZ n C+ C+_. CD C CD

--Co C) C _oP cx o O'3 c) C C 03 ' -. O o o C

P

S

09 CD c--09

U

Obq CD i-t i -o PD CD

0

cn (-} cm ib '+ (PD C+- c-o- _Coc-F

N

C) Con c~n _Co $ H

-0

Ci-O 0 c ll

-9

Q o C) j 0 Co o.

Co

0

,--, .. _ cn-C Co

030

,' --4 00 I

S

- PD

00r

o (-D (.-CT) D, NO ( b

o

c-F' i. .'b "D Cd Co

~-

C)

-0

0

_cn o

o

it-i

Co o CD C))< C. c-

S

oo o

09

oPD C N) 0_CD I PD PD

N

_I e r D tD O (C H PD 0 PD i-i o PH a. H. Ct o CD H. I , C cr _ Co ~'_PDC.' C) C

i

₀

o

i D I

_{C C}

{D

_D

PD o = t i-CD o

_o

O

P)

₀

H c-C}

-9

C)

c-F Co Cl

(.D

iD m ('D o _CD 00_{(t CD} CD 4'1 Cb 7 Co ₎

₀

o O0 Jo

_o

_o

c-(D 0_c-F. C--l 0 i 0 0 Cg c c-FO -s

0

( Co PD 09 0--d md 0 0 Oq p lz

Tol

0

aq

oc

z

(D

z

md 0 x ND

1

H CD c4-© t cn c CDCD ED H ~ In 0 CD (D * C or Up H

11hz

CD _'-' 5C _{~- '-} D_II - p) 5^ * P) 00 CD _(/2o i,- I= 11 H 1H H 11 P

OD a ' 0

-*

a

m

- r- t

H

H

H

P.-iiII II 11 11-- -3 ' 11 C 0

*

o

I

r

+

x

C. 11

x

I~

-. I-+L >1 C/2H3 11 11 M tT1 II W 14 CD En_&z

a

el+

_a

_H

CD

0

- - ,.. 11001

B-~

_.&-

_p

B

>4

~.

₂

-p

>4

H

Ca p >4 t. 17i-

,-m

rd

r

CD

X

B g~~

,_.m

1 ltN t l

_~~~~~

_a

_cn::

O-0

cn _.

o~~

o~~

(/ Qrs

0

CD

0-0

rt

t

0

O4

r-

-

=:1

C 8 _ CD CD2 Ov >

OtQ

'C CD

q

CD p

C-X- t 0

^0

_{(DW(D CD C}C_

b9

CD CD S CD LA _{Cn C} - = D C O_{W CD}

tc9

D CD n - C

X X

~

3 _- I -.

H

CD

_H

.

0

L-CD_l w ./

~-+

C-+ CD En

:

H±t.~

-r cn > _ m~c CD r, _..| C D k)

_p

.

t-. p

II I e--. a + -I I D C CD C

~~ rtt.-

oo~~~~~~C

II ~ '

0 0

L~. . _~.~~C0 L4 0 ~,

CD~]C

CDQ C.

Ho

_CDa _ CD

-CD

_<rCD C- 0 '~CD g Eh ° O

cq

p CD n O Ca C 0 s q

CD

ra

t )C

D

r

t- ll

~:'CD

p 11 P t

.o II °

o

0

cD

_c

ii >

C)

a

O.-

=

ci

_Ca~~~

-

~C

. :C CL Ca

-0

r

G

p0 ,o

S

CD

BrB

CD 1 W C

o

_{t 0}(~

₀

p

S. Ca

o

B -t

0

t

.

x

L. t- / I ~r /--I 1~- . _l

HHH

oUo

ratsinr r B

mm

0 0

o

>

o

-.

~tI

,,

0

bo" bO

r

St

o

3

o

z

C) t--l CD c) CD Ca In1

6: 2

_- .

tq

_: 0

H

' 0 0 0

C~t =IA

-CD _CDrCDCD

-t

0

0

o D

0

-Ca C r.~ Si

!3

CND P. -. CD

w5

ZCwXA CD + s CD pC c + DaC f-*p' P CD _. I

A

-H _ p 1-HF

H

m CD_ CD CD Co Pz CD CD CD CD Pz

p

t112>_Hcn PD CD

-Co CD Co M I1

z

~3

CD CD CD P >3 CD CD Pz P

P

lift

r r-

CD _3 eD CD !!P) 1 CD A P* 60 00 trCD m C N)

a'

P

CD CD_CD

4-a

Ut_CD

P

H

CD P

H

CD P CD f-tCC) lI P CD w ' t CL PQ CD * Pz Co f-f. CD P) .P?

H

Pz >3 CD P) P

p

HH

o H HD

H

rr

,CD C 0C" 11 11 P1 °I o

a

t .Z._

la °CL cn

a CD

CD HCD C CD ef

rl,

CD Co CD

a

Co 1

_z

CD_Pz CD rf_. p f-. P)

3

CD ef

p

P P cn

-L

P CD rt PA CD CD

P

CD CD Pz P) r--cn 11 Co Cr

0<

CD Co CD CL_ef. CD

-H

a'

_D f-CD

P

c~~~~-

M

i

2;=

: P

M 17 O 7 t#

CD

~DO

CD

aC

z

PS

¼

HE

0-- CDD

-

CD

CD ~ ~ ~

rZCD

~

C

~ ~ n ACD~

~Dp

CD

z

CD

P

C cn m

0>-

Q

CD fl~~~~~~~C P " P~~~~~~c

uo

.'o

t

CD

5

CD _Ca PD A

r-p

Ca cn P .

>-

r)

E n

-.

C) CD Pz >3CD

P

CD PD

_p

lid cr

0

0

_.

P

-0-A Pz CD C)

r

Pw CDC P _ CD CD W CD CU c CD r-A

EA

0

p a

o

_CD= CD CD CD

X X

HH o-. L".

P

5

.

C

D

. n i *

CD

-

C

'"

'

<

_Y.,

~

at

CD H P

, +

a'"' PC D <C_WCDa

r-I-5<

CD PP

Ca%

Ca M VXO CD CD

- crr

Pz

CD

H

P p-P C-I2 pI 4W

C)

S

tjCD

₀

_-A CD Q C CD _ CD tCD

_H

CD CD CD CD p P_

QS,

rLCD 0.'a (- P p

_w

l

_Pz

Co

a

v

Fp

CD

~J-

C+ rII H9 C CD Co

t

.

tQ p

_H

CD F

H

CD CD

F

SD

=

I

+

,,

F,,

PN-C Pr C N- '

_a.'

~~

p *

' ..

X

.

CD

-ins

_-.

_a'=r

r p _.D

, r

44 CD P P Pz

5-

_a'

_p

D X P

H X HH Ht

X<

H

et"

X

I1 _cn ' ~ P) _{,_} I I

₀

II11

_>

1 N r + '

P- *

'

S

CD-=.g

P P t

C;D

^'

cn C CD C) w el.,

r>

I _ rL) CL

X x

_CD C4 0101 II i

i !

tI',O

XC1

D O

0

'-*

01

l

II

c c ¼ m

r

r~

r

II ~ I

_~ II -

..

ICD

,';"~

t

,"_

c

7 zi

'

;

v

-'~

a r PD a p '.z e + n.F _CA CD

~a

Z

F t . HP~~~~C

+

p 3 z

cr p

_g

_

X

H P

cr -CD _r

~~~CD

CD

~

r

-D CD CD,

'* '5

-r

^~

CD 11 -111

m

₊ 11 M p 7-1 G 11 CD 0 Ca

a

m o

r

_t

_H

tt M

m

_o

t3

t O

.

t u I

nil

p p

II

e-!-[,.3

r

GTE r

4

-

m

v lO + P- + l

I

: : t

I,

CDZ~Z

rt

-C-,.

P.

+

+

-9-

r

9-CDF CD

r+~

COCD ₍₁

_HA

CE _

-

_p

CDP f'*

CD

_pT CD

-CL

QZ CD CD

Xm

CD CD CD C.+

-_[3

p._

z ri

'r-3

Oi

HI ZC2.

H

ZH ' H

I t

tl

CD CD

+

*

_v

_~~~~

_l::r'

54~~~~~~~~~~" ' _r-

CL

1)i_CL CD

Lj

C.' e-¶3

r

_o

t

3 o

='40

_Io r+i CD

H

_{11 .}

_X~~~

><H'

_{pz +}

mHHW

_{11t-- 11 1T} CD ' D

fri

H

_%WZ

*

q -CD

CL

rL

V

~7-- L CL CD

II

·

,~~~~~~---

"n lar'

I

V CD CD

>

. CD

Io

9--, zr

Mm

m

HH H L3 _L. F3fr_{B.- x}

5 5

11

cn I I I

C-i C-i

t!3- .' !iF"I,

O CD gDNT ) P

-v_

-G _

P

C CD C *

Lu

t

rt r

tut tutu o t. ". X: 11 11 C 1

4 4

'

H

-

H

e-D C N ) -~ ~ ~ ~ ~

-II

4-

+- N) +

-CD

+

-j D

~

_CD C

fi

c_

CD

5-

2,

CD P

P

C A H 'XCD vC F D CD N) r- N)

C DP

C

eCD CD~ Ca tz tQ i ) %LCD PL

4

CD -CD CD

t

H

-.

CD C r4> P_

H

CD

N]

)

P.

P)

S

"11 tt

-qH

-.

_{43 m:}

o p

0F-X9 QS tr ZIH te H r A + CD CDf O c- _-r

_n.

_P*

Pa'

CDP

CD z- p Lu_{. f} _Lr-_FL P CD

± 0

x

11 N + . I~j cn

H

XHRHX

'VCD'

P *

CD c CD~

r

P

Pa'

luCD ; r _ CD

0

L.. II₁₁ tlj

0

x

F3 D N)

I TI

o

t

nI

H Hfl

H CD

Z

CD Co C

,-p

6-q

₄

0

li

_-qo

Z

p

C1-A CQ F

cr

p C -A co 1 Co,X-

_N)

,-.

*

CD tCo_{_F}

H

CQ

.

CD

_p

i:.

c

O

t U

'IdtrMtr

0SEE

t'd

(-

n

CD )-- |I

04

0 0

CrC'

P) CQ) cn tZjLo

0

z

-3

PD CD

p

¶3 CDP

-p

_C) m

Q-Z4o

_p

-A - 4-CD II .

Ow

n

CCDZ ,co CD CDa r.,o

.,.,-.3 Q

.t

.:1.., C C..Dt CD Cr' t:o

.

qs~~t

_*

CD

p

-A

tz

-o'

C CD_0C

¶_

CD

p

-A r HH

--Co

CD CA CD J-A CD p o

wwt

Mlt l

000~4

00

H H H H~~~~~~~.''

:~ CZ Z ZL-,

z z z V

r H D C CD Fq C

Co~

zz

C:1.

c

.+

0

C>

C

:Z

...., cL *

p

Q-I

17'~~~o"

CD

rr

CD co _{_.} * w ,_] .-- ' D CDO

,r'j

4""'

- C to

.

P'"b t"'. X¢w Ii,. i:::

H

z

Ct

.-]

p

¶1 _)

.

CD CD _p N)

H

rH X

H Z

Zo ©

2 ~.

o o

r r--

|~

^

0

CD Co C C C

_

a',

P

+ I D

x~~

CD _{X r+}

-~~~~

X

H3

0

A A C Cr C CD P

~

10p CD P- f-_w H Czmr

~3

ii

Z

6

' CD p

*

o cn 1-N

0.

CD -p

0.

(1

_r

D --C-t

-.-t-tl

r

CD C-r I -l CD

*

1-A

0

Co

p

CD -A

5

-l

n

,- e--_Zy CD _Cl)

~

Q Co

A

?

rn CD

+

t

-3mp CD -A p p; :-t_

Ol

O tzq CD CD XA

P

t

J

4

OZ

6

"

CD C

tn

_WC~ CCD Co

Q:0

CD

PL

-3 r+. cn P_{_} I .

r

Wt'

m

N

C)

-A-0 -A-0

ZZ cn " c H I!

6

_z

o-*

Cr P2

+

CD p

-.-x c~

₊

X -CD

p

*

0

Co

+

t'lt.

4

_,

Cz

H H

°~

r-

M

0

6-/ J ="r C p C)

_p

CD_pF

tiXJ

t-CrQ~

!!

o

*

-F r p) S CD

-'

p N-CD pz

N-*

Co pn

(<z

o

*CI

*

t i

tl

_bO Xn

*

k) Atl CQ_{^ q} x we > cn

~

_X

_>C*z _

En

PtQ .-Ca II CD C P)

*

0

CD p o"

_*

0

Ca_p ±z X xD p oiz

CD

O

-H 3 2

ODQ

z

9

C)

C S

a'

mD 2

~-p

CD

pn

XL

ttlt-H

CD Co CD N) cr_CX ! -CD_p

*

0 C p

11d 1 ~ 1-1 11 II II I CD C

0

0L

t rr

o

CD

,"' II

" '

O. (E, o n =~ O o .. _ .- ..

ot~

0

O ] O_CD CD CDP

_H

t c

tCD_-.

0

~C

'> CD CD CD C CD c CDa

r-'

r

9-3 -- o-3 O11 co

o

I0

0

₀

z-Atp

ra

tQ

r:

CD CDC

a

* I Ca _

,, u' 91 o o

CaS oB

C -. CD Icf9_{) cD} 0 S2. Ca

0

r.~

0

Ca

cn

>4~ >4 > St

P

>4 O

-P

. Il

>4

X

-m

t-

4

r

._

Q

o _t~~~~~CZ=Zt. cl It lid

C)

,

of

0

H

H

_C a

S

_',

_Z"

ci

_o

tQi

0

H

z

0

,--" 4J CD D CL CD

_C'

Enb

o- t

. .

cr 0

gtd

0- 0

)

o o-o

PCD CD CD

O

CD

•

0 tIQ

-o

~n

0

Ca

S

0

CD CD Ca

0

0

C:

.--v

C2'

_p

CD I:%

p

(A Ca4 P CD t

i-3

Pi ,-n .j P4

H

CA Pt CD

_p

CD P

p

ZP5CD

~I

PL

_ V I __> CD -' CD ±

$~CD

C CD + PD C -. I s p -C

p

CD

*

PJ Hz H $<) CD O En 5C A CeD t CF En p NCD CD CD 13

* F

tQS

cZ~

0 ± CD

-CD

pCa

+

P-~

CD t4C CD X) F <e p a H

~

CD

3

*

cn Hn -t

H

'l P X w CD 14

t'tj r

z in 0l~r P-A.

M "

,

11' 11 Lii

H

_2l

₄

_{i -A}

H

₄

X X

H H

J- . " 4 tz -G CD CD r-En X

x

-A ql>4 >4 t- -.. En Un~q En - - r* 11 m

w

I.

-o

=

o CD En SI.. >4

P

CD En En

0

CD Pz CD

P

CD CD CD En

,0

En

,j

o

~ I1

r-0

Cw

CD Pz En CD .Lu ,-Lu_Pz

H

CD CD P CD Pz CD P) P

C () CD CD CD

~3

CD _ CL CD CD CD p p) J *En ).A

o

_0~~:r 0

ET.

C"'

b,.)

~ ~

C

,-8

("D CD CD CD '-D> " m,, "CD CD >e co C.)__, rD

5

"

C

'D D_{X ,} CD

0

,---,El

0 _"

("D. U4 ("$ t"'Do _. · ,,,, ,,,._ ITI

0

1eV 11 O.-A r-+ 0 cn r-11

r'

t

M m 3 ii x x 11 11 4:

b-=" ~a ~. =

,,,

t'"' r-

-a

A.>

~. t_ " " D _ CD ~ ~ ~ ~ D '. i. 17 - rl-I,,,..'d oCD

ril

N-g

-CD z cn t

CL

CD) CD s En En F A

H

Xt<H H

><

H3 %ti1 CD

_/

CD

*

CD P)

- C

P.'v

CD pCD Ca_.5 CDr

rim

t~ o o-3 pd

x

-.

11 11

+ 0

cQ " E

r- r

MH

i. . X4 X 11j 4.

.

r

I'

CD H- CD CD PD P P

_

p

P.' P.' CCD

~

_CDP

CD CDx CPD CDN + H PCD 0 a

_CD

O

_CD Pbs C D Pz CD

p

Pz

p4

CD'

It ._

zid

_ ._Q. CD -q CD P-. t~ m

H

til

1

a 't

o

H

93

H

IIIII

,,rA +

±9o

Pp

_rX

*

₈

--,

:o C ^ U. P

ap

~'~

CD

cr

_C

X

_-.

_ A. P

pa

¶5 CD 1 - CD 1 CD '- * -..

a'

CD P P.l

r.

Vm; -- P

pa

Ca ¶5

~e

m

XCD CD I

I-~ X

_{-J _} CD CP .

Pa'

Po

Ir

>< H Rt mX

_cn~~~~c

_~CD

_t

i1

_{t,_s}

_X

En~~~~~~~~~~~~~~~i

CD CD

r '

+

+0

... - I > 5 rcr_D

na

I ¢_.D -L CD X w -1-3 F3-l" II II I I

r

t

O EA

Z

A

-Im

+

u

+

I i CoDo C4 D cn trt

44

CD .D1 CD _./ ~ ¢ p.. CD

Ir

_CE~~~~ECD

+ t

C CD IM E -

S

t A

m 0r_{CD C} 'CD OPz

..

CD CD , .

t

rt"

©

HH

t

I fII H W P o 0' .

:caI

D

1

I-~~+

o

CD+

,, ,,

.,

'-'.

*..

or

r-i, CD

PD

c t

qS o PL CD C,,

I)

H3 H H

_O0OO

H3 P' CQ Co Co X

CooU

zz

Ca

ZZZZ~

_gLrLC

>

wL ii

g t

r

II

ffi

4~ - t

o

C 0 CD CD P) CD

_

-- P = _CD ++

>0''

CD

t:

>

m _ P::o

1:-I

~ ~

og

"

I

H

><H H H

CD

5~

>

5

: *

PD tQ

+r-C -. =:> CD C 0_CN :CD [3

P

- X

_Pz

C_ D ¶5 H3 1 II

!

!

CD CDH+C

'~

C

,,>

^o>w

F

CDr+

~- ~r1,,~ 0 _ v C

r* P -*

C'

Pa"

pa

C" _CD +C' C" p _l ? CD _CD~~~~~CCDp CA F -~~~~~U CD J C

CD

C

U~~~~~U

a

mr'

rL.

c-n

r

nil ~ II

am

Q 1 O4 w

Q

g

co

CD Z C p "CA

~rlp

i.

ItC CD Dp HX Vpz

r

CD

0

lid0U CD 14CaH

_{*, CD}

p 0 0 C _{C CD} CL~~~~~C 10

_;m

_Zp

-

H

H

>

~~~~CD

CD p) t- t CQ3 3 >1 MI trI A

o

z

I

O

t

I'lz

-n D -)

C>

CD C _{gD .}: CD

_FC )

-_"

r

o3q 11

0

r_ 1-s D gal. +n II

©

0

1 % c:r C p I X CD

-

f-17-t

1 O

HA

Z

CD CD HCD > CD -r-L CD t

0--*

?

rC)

H

0 0

r

CDZZ

0H0

CD CD

Sz

-

-o

zs

H0j

CQn C CD F3 cn CD

p)

CD Sz

Q(t

t: t -Q

0

HHO

.,, C/' ~

z~

D

CO O ¶.Z1. CD V C D XCD

0

a

*

_> CD

p

I,

*

ICo CD p Co

0"

I K?

2

CQ

p

.-C s"' 4 C CD Ca

cn

K3

_*

CD

.

-::l

_-*

CD p

,-.

-,-]

CD p tuj En t-q

O

Co

rCo CD

\.,-]

,L _ p * > °Z (1) CL

*

CD Co CD Q 2 >4 t + S 0p _ o CX m v~~C X X

e17'

~'CD-pCCD

IN)

_H

CD CD > *

0

Co p CD F X Qj---] A

.

o

~~~~~ CD CD

~CD

C0

0

ca

ca ca

CL

r

_

w w p

+

cD _{p) X~~}_a o _{C C} 0 a ' 'l

~.-1rtot

CDHC) CD L ICD , .Lc

CD j

cn

-_{o C}p o C Co X + 2O p p PL CD

p

t

r O m

+lro-,

0

-

cQ CD

..

.

93,9

1CDH +CD s , Sz

-0

a'

c

_I CDC.. -CLi

0 o

*

Co

old CQ

c

₊

_CD

p

ca,

q-+

o"

+

x

CD _F

p

*

o

Ca

-+

Cofl.'HX

x t 1

II

r

0

HZ

tT ,

1

~

A

0

ca

;z

CA OCDD * ca 00

_*

_{CD '}

I P C..v CDC p w

+

CD

p

*

-t

0

p)

e-

4

t

eli C

HZ

OH

cnQ

C

*

#N X *Co Co -.

U

*

eli

x

tQ IN)

*

Co U IQ C tiN CD IN, CD PL >

*

0

_!o C

p

_o-' ca

P-ca

H

z