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#27Q`2 `mTim`2X q�M; 2i �HX (Rk) /2KQMbi`�i2/ � S61> i?�i i`�Mb7Q`Kb T`2b@bm`2 ~m+im�iBQMb ;2M2`�i2/ #v � E�`K�M pQì2t bi`22iX h?2 �mi?Q`b `2TQì2/�* TQr2` Q7 0.7 nW 7Q` � T`2bbm`2 ~m+im�iBQM Q7 �#Qmi 0.003 bar �i 52HzX h?2T`QiQivT2 r�b 2p�Hm�i2/ �i p2`v HQr T`2bbm`2 p�Hm2bX �MQi?2` ivT2 Q7 2H2+@i`QK�;M2iB+ S61> 7Q` r�i2` bvbi2Kb r�b `2TQì2/ BM (Rj)- r?2`2 i?2 �mi?Q`b/2KQMbi`�i2/ �M 2M2`;v ?�`p2bi2` 7Q` � bvbi2K rBi? T`2bbm`2 ~m+im�iBQMb Q70.0025 bar �i 30Hz- r?B+? b?Qr2/ �* TQr2` Q7 0.4mW �i HQr QmiTmi pQHi�;2U5.5mVVX *�Q 2i �HX (R9) T`QTQb2/ � S61> 7Q` r�i2` /Bbi`B#miBQM bvbi2KbrBi? HQr bi�iB+ T`2bbm`2- i?2B` T`QiQivT2 +QMbBbi2/ Q7 �M �KTHB}2/ KmHiBH�v2`TB2xQ2H2+i`B+ bi�+F rBi? � `2bQM�Mi 7`2[m2M+v �`QmM/ 100HzX h?2 T`QTQb2/2M2`;v ?�`p2bi2` T`Q/m+2/ �M QT2M@+B`+mBi pQHi�;2 Q7 83.6mV 7Q` � T`2bbm`2p�`B�iBQM Q7 0.09 bar �i �#Qmi 93Hz �M/ � bi�iB+ T`2bbm`2 Q7 2.5 barX �Hi?Qm;?i?2`2 Bb �M Q#pBQmb BMi2`2bi BM T`2bbm`2 ~m+im�iBQM BM /Bz2`2Mi 2MpB`QMK2Mib-`2b2�`+? QM S61> 7Q` ?B;? bi�iB+ T`2bbm`2 2MpB`QMK2Mib U2X;X- ?v/`�mHB+ bvb@i2KbV Bb HBKBi2/ iQ i?2 bim/B2b BM (3)- (R8)Ĝ(ky)X

PZTStack

PressureRipple

Fluid-PZTInterface

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RX � BMi2`7�+2 2tTQb2/ iQ i?2 ~mB/ i?�i +QMp2ìb i?2 /vM�KB+ T`2bbm`2 BMiQ� K2+?�MB+�H 7Q`+2X

kX � i`�Mb/m+2` i?�i +QMp2ìb i?2 7Q`+2 BMiQ 2H2+i`B+�H TQr2`X

jX �M BMi2`7�+2 +B`+mBi i?�i `2+iB}2b- `2;mH�i2b- �M/ K�M�;2b i?2 iBK2@p�`vBM; 2M2`;v ;2M2`�i2/ #v i?2 i`�Mb/m+2`X

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8

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e

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1M2`;v i`�Mb/m+2`*QMp2`bBQM Q7 7Q`+2 iQ 2H2+i`B+�H 2M2`;v +�M #2 �+?B2p2/ rBi? 2M2`;v +QMp2ì@2`b bm+? �b TB2xQ2H2+i`B+ �M/ K�;M2iQbi`B+iBp2 /2pB+2bX h?2b2 K�i2`B�Hb +�M+QMp2ì /vM�KB+ bi`2bb BMiQ 2H2+i`B+�H 2M2`;v i?`Qm;? i?2 /B`2+i TB2xQ2H2+i`B+2z2+i �M/ BMp2`b2 K�;M2iQbi`B+iBQM- `2bT2+iBp2HvX AM i?2 +QMi2ti Q7 S61>-TB2xQ2H2+i`B+ /2pB+2b ?�p2 ;�BM2/ KQ`2 �ii2MiBQM /m2 iQ i?2B` bBKTH2` BKTH2@K2Mi�iBQM (j8)X AM 7�+i- TB2xQ2H2+i`B+ bi�+Fb �`2 QM2 Q7 i?2 KQbi `2b2�`+?2//2pB+2b 7Q` 2M2`;v ?�`p2biBM; �TTHB+�iBQMb BMpQHpBM; H�`;2 +QKT`2bbBp2 7Q`+2b-Qz@`2bQM�M+2 2t+Bi�iBQMb- Q` BKT�+i 2p2Mib (3)- (R9)- (je)Ĝ(9d)X

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AM (j8)- i?2 �mi?Q`b +QKT�`2 TB2xQ2H2+i`B+ UTB2xQ+2`�KB+V- bBM;H2 +`vbi�HUSJL@jy%ShV �M/ K�;M2iQbi`B+iBp2 Uǵh2`72MQH@.ǶV bi�+Fb �b b?mMi /�KT2`bXh?2 2tT2`BK2Mi�H K2�bm`2K2Mib b?Qr i?�i bBM;H2 +`vbi�H bi�+Fb Bb i?2 T`2@72``2/ i`�Mb/m+2`- rBi? TB2xQ2H2+i`B+ T`QT2ìB2b- 7Q` 2M2`;v ?�`p2biBM;- 7QHHQr2/#v i?2 TB2xQ+2`�KB+ �M/ H�biHv i?2 K�;M2iQbi`B+iBp2X >Qr2p2`- bBM;H2 +`vbi�Hb

d

�`2 +m``2MiHv MQi �b +QKK2`+B�HHv �p�BH�#H2 �b TB2xQ2H2+i`B+ QM2b- r?B+? +QK@THB+�i2b i?2B` rB/2bT`2�/ �/QTiBQMX

c) Cymbala) Multilayer Stack

b) Ampli�ed Stack

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JQ`2Qp2`- bi�iB+ T`2bbm`2 HBKBib i?2 /2bB;M Q7 S61> BM i2`Kb Q7 i?2 ~mB/@iQ@K2+?�MB+�H BMi2`7�+2X SQr2` BMi2MbBiv Bb K2�bm`2/ �b 2M2`;v T2` �`2�- bm;@;2biBM; i?�i � S61> rBi? � H�`;2` 2tTQb2/ �`2� +�M T`Q/m+2 KQ`2 TQr2` (3)X>Qr2p2`- � H�`;2` BMi2`7�+2 �`2� �HbQ BKTHB2b � ?B;?2` +QKT`2bbBQM 7Q`+2- r?B+?K�v �/p2`b2Hv �z2+i i?2 BMi2`7�+2 �M/ i?2 i`�Mb/m+2`X *QMb2[m2MiHv- bim/B2b?�p2 b?QrM i?2 TQbbB#BHBiv Q7 BKT`QpBM; i?2 T2`7Q`K�M+2 Q7 S61> rBi?Qmi BM@+`2�bBM; i?2 �`2� Q7 i?2 ~mB/@K2+?�MB+�H BMi2`7�+2 #v mbBM; �+QmbiB+ `2bQM�iQ`b(R3)X

kR

6B;m`2 jXR, LQBb2b BM ?v/`�mHB+ bvbi2KbX

jXk 1M2`;v 7Q+mbBM; K2i?Q/b 7Q` T`2bbm`2 ~m+im�iBQMb2M2`;v ?�`p2bi2`b

h?2 T2`7Q`K�M+2 Q7 i?2 S61> +�M #2 BKT`Qp2/ i?`Qm;? �+QmbiB+ `2bQM�iQ`bX� +QKKQM �+QmbiB+ 7Q+mbBM; /2pB+2 Bb i?2 >2HK?QHix `2bQM�iQ` U>_V- r?B+?+�M �KTHB7v T`2bbm`2 ~m+im�iBQMb �i � ;Bp2M 7`2[m2M+vX h?2 >_ +QMbBbib Q7 �M�``Qr M2+F i?�i +QMM2+ib iQ � +�pBiv- �b b?QrM BM 6B;X jXkX

Helmholtz resonator

Mass

ks cr

Cavity

Neck

Mechanical Representation

Z

C

LR

P(t)

neckneck

Zcavity

6B;m`2 jXk, 1H2+i`B+�H `2T`2b2Mi�iBQM Q7 �M �+QmbiB+ >2HK?QHix `2bQM�iQ`

�bbmKBM; i?�i i?2 +?�`�+i2`BbiB+ /BK2MbBQMb Q7 i?2 `2bQM�iQ` �`2 bK�HH2`i?�M i?2 r�p2H2M;i? Q7 i?2 T`2bbm`2 ~m+im�iBQMb UQM i?2 Q`/2` Q7 K2i2`b 7Q`1000HzV- i?2 `2bQM�iQ` +�M #2 KQ/2H2/ #v ǴHmKT2/@2H2K2MiǴ T�`�K2i2`bXh?2 2H2+i`B+�H �M�HQ;v- `2T`2b2Mi2/ �b �M _G* +B`+mBi- Bb b?QrM BM 6B;X jXk (R8)Xh?2 M2+F Q7 i?2 >_ Bb KQ/2H2/ �b �M BM/m+iBp2 2H2K2Mi ULV �M/ i?2 +�pBiv �b

kk

� +�T�+BiQ` UCVX URV Bb i?2 �+QmbiB+ `2bBbi�M+2X h?2 `2bQM�Mi 7`2[m2M+v Q7 i?2bvbi2K- 7Q` HQr +QM+2Mi`�iBQM Q7 �B`- +�M #2 2biBK�i2/ #v (R8)

fres = 1

2π

!""# d2neckc2f

lnecklcavd2cavUjXRV

JQbi Q7 i?2 �+QmbiB+ HQbb2b �`2 `2H�i2/ iQ i?2 M�``Qr M2+F UpBb+Qmb HQbb2bV-/�KTBM; HQbb2b BM i?2 K�i2`B�H �M/ ?v/`�mHB+ ~mB/- �M/ �+QmbiB+ `�/B�iBQMHQbb2b (R8)- (ke)- (d8)- (dd)X 6`QK jXR Bi +�M #2 b22M i?�i i?2 `2bQM�M+2 Q7 >_+�M #2 `2/m+2/ 2Bi?2` #v BM+`2�bBM; i?2 pQHmK2 +�pBiv Ulcavd2cavV- i?2 H2M;i? Q7i?2 M2+F lneck- Q` /2+`2�bBM; i?2 M2+FǶb /B�K2i2` dneckX AM T`�+iB+2- BM+`2�bBM;i?2 pQHmK2 Q7 i?2 +�pBiv Q` i?2 H2M;i? Q7 i?2 M2+F K�v `2bmHi BM �M BM72�bB#HvH�`;2 /2pB+2X PM i?2 Qi?2` ?�M/- /2+`2�bBM; i?2 M2+F /B�K2i2` ?�b � M2;�iBp22z2+i QM i?2 ;�BM (R8)X

jXj 1M2`;v >�`p2biBM; pB� JmHiBH�v2` SB2xQ2H2+i`B+ai�+Fb

SB2xQ2H2+i`B+ /2pB+2b �`2 bK�`i K�i2`B�Hb i?�i +�M +QMp2`i K2+?�MB+�H 2M2`;vBMiQ 2H2+i`B+�H 2M2`;v i?`Qm;? i?2 /B`2+i TB2xQ2H2+i`B+ 2z2+iX SB2xQ2H2+i`B+BivBb i?2 2H2+i`B+ +?�`;2 i?�i �++mKmH�i2b BM bQK2 bQHB/ K�i2`B�HbX AM +`vbi�HHBM2K�i2`B�Hb rBi?Qmi BMp2`bBQM bvKK2i`v- 7Q` 2t�KTH2- i?2 TB2xQ2H2+i`B+ 2z2+i�`Bb2b 7`QK i?2 HBM2�` 2H2+i`QK2+?�MB+�H BMi2`�+iBQM #2ir22M K2+?�MB+�H �M/2H2+i`B+�H bi�i2bX h?Bb T`Q+2bb Bb `2p2`bB#H2- r?B+? K2�Mb i?�i B7 � K�i2`B�H2t?B#Bib i?2 /B`2+i TB2xQ2H2+i`B+ 2z2+i- Bi �HbQ 2t?B#Bib i?2 `2p2`b2 TB2xQ2H2+i`B+2z2+i (93)- (8j)- (d3)X 6Q` 2t�KTH2- H2�/ xB`+QM�i2 iBi�MBi2 USwhV K�i2`B�HbT`Q/m+2 TB2xQ2H2+i`B+Biv r?2M i?2B` bi`m+im`2 Bb /27Q`K2/- �M/ pB+2 p2`b�XSB2xQ2H2+i`B+ bi�+Fb �`2 Q7i2M mb2/ �b �+im�iQ`b BM bK�HH /2~2+iBQMb- ?B;? 7Q`+2b�M/ ?B;? T`2+BbBQMX

� KmHiBH�v2` TB2xQ2H2+i`B+ bi�+F Bb � /2pB+2 +QKTQb2/ Q7 i?BM H�v2`b Q7 SwhK�i2`B�HX h?2 bi�+F ;2M2`�i2b 2H2+i`B+�H 2M2`;v �b � `2bmHi Q7 �M �TTHB2/ 7Q`+2XAM T`BM+BTH2- �M 2H2+i`B+ +m``2Mi Bb ;2M2`�i2/ �b � `2bmHi Q7 i?2 /Bbim`#2/ +?�`;2#�H�M+2 r?2M bm#D2+i2/ iQ �M 2ti2`M�H bi`2bbX AM `2+2Mi v2�`b- i?2b2 /2pB+2b?�p2 7QmM/ �TTHB+�iBQM BM 2M2`;v ?�`p2biBM; b+2M�`BQb r?2`2 Qi?2` TQTmH�`Swh bi`m+im`2b U2X;X- +�MiBH2p2`bV +�MMQi #2 mb2/X *QKT�`2/ iQ +�MiBH2p2`b-TB2xQ2H2+i`B+ bi�+Fb +�M rBi?bi�M/ ?B;?2` +QKT`2bbBQM 7Q`+2b rBi?Qmi #`2�FBM;�M/ Qz2` #2ii2` Qz@`2bQM�M+2 2M2`;v ?�`p2biBM; +�T�#BHBiB2bX 6Q` TB2xQ2H2+@i`B+ /2pB+2b mb2/ 7Q` 2M2`;v ?�`p2biBM;- i?2`2 Bb � bT2+B}+ TQH�` �tBb i?�i/2i2`KBM2b ?Qr i?2 bvbi2K rQ`FbX SB2xQ2H2+i`B+ bi�+Fb QT2`�i2 BM Ǵjj@KQ/2Ǵ-r?B+? K2�Mb i?�i i?2 7Q`+2 Bb �TTHB2/ BM i?2 /B`2+iBQM Q7 i?2 TQHBM; Q7 i?2TB2xQ2H2+i`B+X 6B;X jXjX

kj

6B;m`2 jXj, SB2xQ2H2+i`B+ ;2M2`�iQ` KQ/2bX

h?2 TB2xQ2H2+i`B+ bi�+F Bb i?2 T�`�HH2H +QK#BM�iBQM Q7 KmHiBTH2 H�v2`b Q7TB2xQ2H2+i`B+ K�i2`B�HX h?2 ;2M2`�i2/ +?�`;2 BM 2�+? TB2xQ2H2+i`B+ TH�i2 BM`2bTQMb2 iQ � 7Q`+2 Bb

Q = d33F UjXkV

r?2`2 d33 Bb i?2 2z2+iBp2 TB2xQ2H2+i`B+ +Q2{+B2Mi BM i?2 33 /B`2+iBQM �M/F Bb i?2 7Q`+2Xh?2 +?�`;2 ;2M2`�i2/ BM i?2 bi�+F +�M #2 2biBK�i2/ #v

Qstack = nd33F UjXjV

r?2`2 d33 Bb i?2 2z2+iBp2 TB2xQ2H2+i`B+ +Q2{+B2Mi Q7 � bBM;H2 H�v2` �M/ M Bbi?2 MmK#2` Q7 H�v2`bX h?2 2[mBp�H2Mi TB2xQ2H2+i`B+ +Q2{+B2Mi Q7 � TB2xQ2H2+i`B+bi�+F +�M #2 2biBK�i2/ #v

d∗33 = cnd33 UjX9V

r?2`2 c < 1 Bb /2i2`KBM2/ #v i?2 +QMbi`m+iBQM �M/ T`QT2`iB2b Q7 i?2 bi�+FXc Bb /2T2M/2Mi QM i?2 +QM};m`�iBQM �M/ +QMbi`m+iBQM Q7 i?2 bi�+F rBi? ivTB+�H`2TQ`i2/ BM i?2 `�M;2 Q7 dyW iQ N8W (98)X

AM i?2 b�K2 K�MM2`- i?2 +�T�+Bi�M+2 Q7 i?2 bi�+F Bb i?2 +QK#BM�iBQM Q7i?2 +�T�+Bi�M+2 Q7 2�+? H�v2`X

Cstack = nεrε0At

UjX8V

ε0 �M/ εr �`2 p�+mmK �M/ `2H�iBp2 T2`KBiiBpBiv Q7 i?2 K�i2`B�H- `2bT2+iBp2HvXA �M/ t �`2 i?2 �`2� �M/ i?B+FM2bb Q7 i?2 TB2xQ2H2+i`B+ H�v2`X 6Q` Qz@`2bQM�M+2

k9

QT2`�iBQM- i?2 QT2M@+B`+mBi pQHi�;2 Bb Q#i�BM2/ #v i?2 pQHi�;2 +?�`;2 `2H�iBQM(98)- (dN)

v(t) = Q(t)Cstack

= nd33F (t)Cstack

UjXeV

AM 2bb2M+2- iBK2@/2T2M/2Mi pQHi�;2 Bb ;2M2`�i2/ #v i?2 +?�M;2 Q7 +?�`;2BM i?2 bi�+F �b i?2 `2bmHi Q7 �M �TTHB2/ 7Q`+2X

h?2 ;2M2`�i2/ 2H2+i`B+�H TQr2`- 7Q` � bBMmbQB/�H 7Q`+2- +�M #2 2biBK�i2/ #v(98)

PAC =√2πfCPV2rms UjXdV

jX9 SQr2` *QM/BiBQMBM;

6B;m`2 jX9, *B`+mBi KQ/2H Q7 � Qz@`2bQM�M+2 TB2xQ2H2+i`B+ bi�+F 2M2`;v ?�`@p2bi2`

� TB2xQ2H2+i`B+ i`�Mb/m+2` bm#D2+i2/ iQ � iBK2@p�`vBM; K2+?�MB+�H 2t+Bi�@iBQM +�M #2 2H2+i`B+�HHv KQ/2H2/ �b � +m``2Mi bQm`+2 BM T�`�HH2H iQ � +�T�+BiQ`�M/ � `2bBbiQ` �b b22M BM };m`2 jX9 (98)X h?2 `2bBbi�M+2 Bb �M�HQ;Qmb iQ i?2 HQbb7�+iQ` Q7 i?2 K�i2`B�H (3y) �M/ Cp Bb i?2 +�T�+Bi�M+2 Q7 i?2 bi�+FX �bbmKBM;� bBMmbQB/�H 2t+Bi�iBQM- i?2 +m``2Mi ;2M2`�i2/ +�M #2 2biBK�i2/ �++Q`/BM; iQ(98) #v

Ip = ωd∗33Fcos(ωt) UjX3V6Q` � bi�+F +QMM2+i2/ iQ � `2bBbiBp2 HQ�/ i?2 K�tBKmK /2HBp2`2/ 2H2+i`B+�H

TQr2` Bb (98)

PL = πfCpV2rms UjXNV

hQ #2 �#H2 iQ mb2 i?2 TQr2` ;2M2`�i2/ #v i?2 TB2xQ2H2+i`B+ bi�+F- i?2 iBK2@p�`vBM; pQHi�;2 ;2M2`�i2/ #v i?2 bi�+F Kmbi #2 `2+iB}2/X 6Q` � bBMmbQB/�H2t+Bi�iBQM- i?2 iQi�H �KQmMi Q7 +?�`;2 ;2M2`�i2/ #v TB2xQ2H2+i`B+ bi�+F 2p2`v?�H7 +v+H2 Bb

Qstack = 2CpVp UjXRyV

k8

h?2 +mKmH�iBp2 +?�`;2 i?�i +�M #2 /2HBp2`2/ iQ �M 2H2+i`B+ HQ�/ /2T2M/b QMi?2 `2+iB}2` +B`+mBiX 6Q` i?2 +�b2 Q7 i?2 7mHH@r�p2 #`B/;2 `2+iB}2`- i?2 QT2`�iBQMBb b?QrM BM };m`2 jX8X

6B;m`2 jX8, q�p27Q`Kb Q7 i?2 QT2`�iBQM Q7 i?2 7mHH@r�p2 #`B/;2 `2+iB}2`

*QMbB/2`BM; ?�H7 +v+H2 Q7 QT2`�iBQM- i?2 BMM2` +�T�+Bi�M+2 Q7 i?2 bi�+F Bb+?�`;2/ mT iQ VDC +2VD #27Q`2 i?2 #`B/;2 `2+iB}2` +�M +QM/m+iX h?2 �KQmMiQ7 +?�`;2 HQbi /m`BM; i?Bb T`Q+2bb U`2T`2b2Mi2/ �b i?2 r?Bi2 TQ`iBQM Q7 i?2r�p27Q`K Q7 Ip BM };m`2 jX8V +�M #2 /2i2`KBM2/ #v

Qlost = 2(VDC + 2VD)Cp UjXRRVh?2 `2+iB}2/ TQr2` +�M #2 +�H+mH�i2/ �b i?2 /Bz2`2M+2 #2ir22M i?2 iQi�H

+?�`;2 �M/ i?2 +?�`;2 HQbb BM i?2 BMM2` +�T�+Bi�M+2 (e8)- i?Bb `2bmHib BM

PDC = 2fVDC(Qstack −Qlost) = 2CpfVDC(2Vp − 2(VDC + 2VD)) UjXRkV

6BM/BM; i?2 K�tBKmK TQr2`- QM2 +�M }M/ i?2 QTiBK�H pQHi�;2 7Q` TQr2`i`�Mb72` �b

[FBR] V optDC = Vp

2− VD UjXRjV

PM2 Q7 i?2 K�BM /`�r#�+Fb Q7 i?2 7mHH@r�p2 #`B/;2 �b � TQr2` +QM/BiBQMBM;+B`+mBi Bb i?�i i?2 QT2M +B`+mBi Q7 i?2 i`�Mb/m+2` Kmbi #2 �i H2�bi Vp > 2VD-r?B+? HBKBib i?2 QT2`�iBM; `�M;2X �HbQ- BM T`�+iBb2- i?2 QmiTmi pQHi�;2 Kmbi#2 Km+? ?B;?2` i?�M 2VD iQ #2 bmBi�#H2 7Q` TQr2`BM; 2H2+i`QMB+ /2pB+2bX

h?mb- iQ BM+`2�b2 i?2 TQr2` ;2M2`�iBQM Q7 � TB2xQ2H2+i`B+ bi�+F /Bz2`2Mii2+?MB[m2b iQ `2/m+2 Qlost Kmbi #2 mb2/X 6Q` BMbi�M+2- T�bbBp2 i2+?MB[m2b bm+?�b b?mMi BM/m+iQ` (Rd) Q` +B`+mBi i2+?MB[m2b bm+? �b bvM+?`QMBx2/ brBi+?BM;

ke

i2+?MB[m2b- r?B+? �BK iQ `2/m+2 i?2 +?�`;2 HQbb BM i?2 BMi2`M�H +�T�+Bi�M+2 Q7i?2 bi�+F (eR)- (e8)Ĝ(eN)- (3R)X

kd

.Bb+mbbBQM

AM i?Bb b2+iBQM- Bbbm2b `2H�i2/ iQ i?2 T`2bbm`2 ~m+im�iBQM 2M2`;v ?�`p2bi2` �`2/Bb+mbb2/ #�b2/ QM i?2 `2bmHib T`2b2Mi2/ BM i?2 T�T2`bX h?2 /Bb+mbbBQM 7Q+mb2bQM i?2 }M/BM;b- +QMi`B#miBQMb �M/ HBKBi�iBQMb Q7 i?2 rQ`F T`2b2Mi2/X h?Bbb2+iBQM Bb /BpB/2/ BMiQ b2p2`�H bm#b2+iBQMb /2�HBM; rBi? p�`BQmb bim/B2b �M/+QKTQM2Mib Q7 i?2 ?�`p2bi2`- K�BMHv i?2 2tT2`BK2Mi�H �TT�`�imb- �+QmbiB+`2bQM�iQ`- ~mB/@iQ@K2+?�MB+�H BMi2`7�+2- TB2xQ2H2+i`B+ bi�+F- 2M2`;v +QM/BiBQM@BM;- �M/ bvbi2K BMi2;`�iBQMX

9XR 1tT2`BK2Mi�H �TT�`�imb

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(9e) aX �/?BF�`B- JX AX 6`Bbr2HH- �M/ .X CX AMK�M- ǳSB2xQ2H2+i`B+ 2M2`;v?�`p2biBM; 7`QK #`Q�/#�M/ `�M/QK pB#`�iBQMb-Ǵ aK�ì J�i2`X ai`m+iX-pQHX R3- MQX RR- TX RR8 yy8- a2TX kyyNX

(9d) sX q�M;- wX a?B- CX q�M;- �M/ >X sB�M;- ǳ� bi�+F@#�b2/ ~2t@+QKT`2bbBp2 TB2xQ2H2+i`B+ 2M2`;v ?�`p2biBM; +2HH 7Q` H�`;2 [m�bB@bi�iB+HQ�/b-Ǵ aK�ì J�i2`X ai`m+iX- pQHX k8- MQX 8- TX y88 yy8- J�`X kyReX

(93) *X *Qp�+B �M/ �X :QMi2�M- ǳSB2xQ2H2+i`B+ 2M2`;v ?�`p2biBM; bQHmiBQMb,� `2pB2r-Ǵ a2MbQ`b- pQHX ky- MQX Rk- TX j8Rk- CmMX kyky- BbbM, R9k9@3kkyX

(9N) qX *?2M- uX q�M;- �M/ qX .2M;- ǳ.27Q`K�#H2 7Q`+2 �KTHB}+�iBQM7`�K2 T`QKQiBM; TB2xQ2H2+i`B+ bi�+F 2M2`;v ?�`p2biBM;, S�`�K2i`B+KQ/2H- 2tT2`BK2Mib �M/ 2M2`;v �M�HvbBb-Ǵ CQm`M�H Q7 AMi2HHB;2Mi J�@i2`B�H avbi2Kb �M/ ai`m+im`2b- pQHX k3- MQX d- TTX 3kdĜ3je- CmHX kyReX

9k

(8y) aX q2M �M/ ZX sm- ǳ.2bB;M Q7 � irQ@bi�;2 7Q`+2 �KTHB}+�iBQM 7`�K2 7Q`TB2xQ2H2+i`B+ 2M2`;v ?�`p2biBM;-Ǵ BM kyRd A111 AMi2`M�iBQM�H *QM72`2M+2QM *v#2`M2iB+b �M/ AMi2HHB;2Mi avbi2Kb- *Aa kyRd �M/ A111 *QM72`2M+2QM _Q#QiB+b- �miQK�iBQM �M/ J2+?�i`QMB+b- _�J kyRd @ S`Q+22/BM;b-kyR3- Bb#M, Nd3R8j3ejRj88X

(8R) JX 1p�Mb- EX �r- �M/ GX h�M;- ǳGQr 7`2[m2M+v 2M2`;v ?�`p2biBM; mbBM;� 7Q`+2 �KTHB}2/ TB2xQ2H2+i`B+ bi�+F-Ǵ BM A111f�aJ1 �AJ- kyRd- Bb#M,Nd3R8yNy8NN3yX

(8k) a?m#BM *?2M- GB`QM; q�M;- q�MHm w?Qm- SX Jmb;`�p2- hB�M@"BM; sm-�M/ G2B wmQ- ǳPTiBK�H /2bB;M Q7 7Q`+2 K�;MB}+�iBQM 7`�K2 Q7 � TB2xQ2H2+@i`B+ bi�+F 2M2`;v ?�`p2bi2`-Ǵ S`Q+22/BM;b Q7 i?2 aSA1- pQHX N9j8- TTX RĜRR- kyR8- BbbM, RNNed8esX

(8j) JX a�7�2B- >X �X aQ/�MQ- �M/ aX _X �MiQM- ǳ� `2pB2r Q7 2M2`;v ?�`p2bi@BM; mbBM; TB2xQ2H2+i`B+ K�i2`B�Hb, ai�i2@Q7@i?2@�`i � /2+�/2 H�i2` Ukyy3ĜkyR3V-Ǵ aK�`i J�i2`X ai`m+iX- pQHX k3- MQX RR- TX RRj yyR- P+iX kyRNX

(89) CX S�HQb��`B- JX G2BMQM2M- CX >�MMm- CX CmmiB- �M/ >X C�MimM2M- ǳ1M@2`;v ?�`p2biBM; rBi? � +vK#�H ivT2 TB2xQ2H2+i`B+ i`�Mb/m+2` 7`QK HQr 7`2@[m2M+v +QKT`2bbBQM-Ǵ CQm`M�H Q7 1H2+i`Q+2`�KB+b- pQHX k3- MQX 9- TTX kR9ĜkRN- J�`X kyRkX

(88) �X C�bBK- :X u2bM2`- >X q�M;- �X a�7�`B- �X J�?2`- �M/ "X "�bBHv-ǳG�#Q`�iQ`v i2biBM; �M/ MmK2`B+�H bBKmH�iBQM Q7 TB2xQ2H2+i`B+ 2M2`;v?�`p2bi2` 7Q` `Q�/r�v �TTHB+�iBQMb-Ǵ �TTHB2/ 1M2`;v- pQHX kk9- TTX 9j3Ĝ99d- �m;X kyR3X

(8e) >X w?�Q- CX GBM;- �M/ CX ul- ǳ� +QKT�`�iBp2 �M�HvbBb Q7 TB2xQ2H2+i`B+i`�Mb/m+2`b 7Q` ?�`p2biBM; 2M2`;v 7`QK �bT?�Hi T�p2K2Mi-Ǵ CQm`M�H Q7i?2 *2`�KB+ aQ+B2iv Q7 C�T�M- pQHX Rky- MQX R9y9- TTX jRdĜjkj- kyRkX

(8d) uX *�Q- �X a?�- wX GBm- CX GB- �M/ qX CB�M;- ǳ1M2`;v QmiTmi Q7 TB2xQ2H2+@i`B+ i`�Mb/m+2`b �M/ T�p2K2Mib mM/2` bBKmH�i2/ i`�{+ HQ�/-Ǵ CQm`M�HQ7 *H2�M2` S`Q/m+iBQM- pQHX kdN- TX Rkj 8y3- C�MX kykRX

(83) uX Em�M;- �X .�MB2Hb- �M/ JX w?m- ǳ� b�M/rB+?2/ TB2xQ2H2+i`B+ i`�Mb@/m+2` rBi? ~2t 2M/@+�Tb 7Q` 2M2`;v ?�`p2biBM; BM H�`;2 7Q`+2 2MpB`QM@K2Mib-Ǵ CQm`M�H Q7 S?vbB+b ., �TTHB2/ S?vbB+b- pQHX 8y- MQX j9- TX j98 8yR-�m;X kyRdX

(8N) sX GB- JX :mQ- �M/ aX .QM;- ǳ� ~2t@+QKT`2bbBp2@KQ/2 TB2xQ2H2+i`B+i`�Mb/m+2` 7Q` K2+?�MB+�H pB#`�iBQMfbi`�BM 2M2`;v ?�`p2biBM;-Ǵ A111h`�Mb�+iBQMb QM lHi`�bQMB+b- 62``Q2H2+i`B+b �M/ 6`2[m2M+v *QMi`QH-pQHX 83- MQX 9- TTX eN3Ĝdyj- �T`X kyRRX

(ey) wX CX *?2r- hX _m�M- �M/ JX w?m- ǳSQr2` K�M�;2K2Mi +B`+mBi 7Q` rB`2@H2bb b2MbQ` MQ/2b TQr2`2/ #v 2M2`;v ?�`p2biBM;, PM i?2 bvM2`;v Q7 ?�`@p2bi2` �M/ HQ�/-Ǵ A111 h`�Mb�+iBQMb QM SQr2` 1H2+i`QMB+b- pQHX j9-MQX N- TTX 3edRĜ3e3R- kyRNX

9j

(eR) aX *?�K�MB�M- �X Jm?i�`Q;Hm- �M/ >X EmH�?- ǳ� b2H7@�/�TiBM;bvM+?`QMBx2/@brBi+? BMi2`7�+2 +B`+mBi 7Q` TB2xQ2H2+i`B+ 2M2`;v ?�`@p2bi2`b-Ǵ A111 h`�Mb�+iBQMb QM SQr2` 1H2+i`QMB+b- pQHX j8- MQX R-TTX NyRĜNRk- C�MX kykyX

(ek) wX CX *?2r �M/ JX w?m- ǳ�/�TiBp2 K�tBKmK TQr2` TQBMi }M/BM; mbBM;/B`2+i pQ+fk i`�+FBM; K2i?Q/ rBi? KB+`Qr�ii TQr2` +QMbmKTiBQM 7Q`2M2`;v ?�`p2biBM;-Ǵ A111 h`�Mb�+iBQMb QM SQr2` 1H2+i`QMB+b- pQHX jj-MQX N- TTX 3Re9Ĝ3Rdj- kyR3X

(ej) ěě- ǳ�/�TiBp2 b2H7@+QM};m`�#H2 `2+iB}2` 7Q` 2ti2M/2/ QT2`�iBM; `�M;2Q7 TB2xQ2H2+i`B+ 2M2`;v ?�`p2biBM;-Ǵ A111 h`�Mb�+iBQMb QM AM/mbi`B�H1H2+i`QMB+b- pQHX ed- MQX 9- TTX jkedĜjkde- kykyX

(e9) CX GB�M; �M/ qX@>X GB�Q- ǳAKT`Qp2/ /2bB;M �M/ �M�HvbBb Q7 b2H7@TQr2`2/bvM+?`QMBx2/ brBi+? BMi2`7�+2 +B`+mBi 7Q` TB2xQ2H2+i`B+ 2M2`;v ?�`p2biBM;bvbi2Kb-Ǵ A111 h`�MbX AM/X 1H2+i`QM- pQHX 8N- MQX 9- TTX RN8yĜRNey- �T`XkyRkX

(e8) uX EX _�K�/�bb �M/ �X SX *?�M/`�F�b�M- ǳ�M 2{+B2Mi TB2xQ2H2+i`B+2M2`;v ?�`p2biBM; BMi2`7�+2 +B`+mBi mbBM; � #B�b@~BT `2+iB}2` �M/ b?�`2/BM/m+iQ`-Ǵ BM A111 CX aQHB/@ai�i2 *B`+mBib- kyRyX

(ee) .X :mvQK�` �M/ JX G�HH�ì- ǳ_2+2Mi T`Q;`2bb BM TB2xQ2H2+i`B+ +QMp2`bBQM�M/ 2M2`;v ?�`p2biBM; mbBM; MQMHBM2�` 2H2+i`QMB+ BMi2`7�+2b �M/ Bbbm2b BMbK�HH b+�H2 BKTH2K2Mi�iBQM-Ǵ JB+`QK�+?BM2b- pQHX k- TTX kd9ĜkN9- .2+XkyRRX

(ed) AX *X GB2M- uX *X a?m- qX CX qm- aX JX a?Bm- �M/ >X *X GBM- ǳ_2pBbBi Q7b2`B2b@aa>A rBi? +QKT�`BbQMb iQ Qi?2` BMi2`7�+BM; +B`+mBib BM TB2xQ2H2+@i`B+ 2M2`;v ?�`p2biBM;-Ǵ aK�ì J�i2`B�Hb �M/ ai`m+im`2b- pQHX RN- MQX Rk-TX Rk8 yyN- P+iX kyRyX

(e3) *X *?2M- "X w?�Q- �M/ CX GB�M;- ǳ_2pBbBi Q7 bvM+?`QMBx2/ 2H2+i`B++?�`;2 2ti`�+iBQM Ua1*1V BM TB2xQ2H2+i`B+ 2M2`;v ?�`p2biBM; #v mbBM;BKT2/�M+2 KQ/2HBM;-Ǵ aK�ì J�i2`B�Hb �M/ ai`m+im`2b- pQHX k3- MQX Ry-TX Ry8 y8j- a2TX kyRNX

(eN) GX :�`#mBQ- JX G�HH�ì- .X :mvQK�`- *X _B+?�`/- �M/ .X �m/B;B2`- ǳJ2@+?�MB+�H 2M2`;v ?�`p2bi2` rBi? mHi`�HQr i?`2b?QH/ `2+iB}+�iBQM #�b2/ QMbb?B MQMHBM2�` i2+?MB[m2-Ǵ AM/mbi`B�H 1H2+i`QMB+b- A111 h`�Mb�+iBQMb QM-pQHX 8e- TTX Ry93ĜRy8e- J�v kyyNX

(dy) wX CX *?2r- hX _m�M- �M/ JX w?m- ǳai`�BM 2M2`;v ?�`p2biBM; TQr2`2/rB`2H2bb b2MbQ` bvbi2K mbBM; �/�TiBp2 �M/ 2M2`;v@�r�`2 BMi2`7�+2 7Q`2M?�M+2/ T2`7Q`K�M+2-Ǵ A111 h`�Mb�+iBQMb QM AM/mbi`B�H AM7Q`K�iB+b-pQHX Rj- MQX e- TTX jyyeĜjyRe- kyRdX

99

(dR) 6X CX a+?r�ìx- 1X �X aFQr- �X 1ìm`F- �M/ EX �X *mM27�`2- ǳ1M2`;v?�`p2biBM; 7`QK �+QmbiB+ }2H/b 7Q` b2H7@TQr2`2/ b2MbQ`b BM TmKT2/ ~mB/bvbi2Kb-Ǵ BM a2MbQ`b �M/ aK�ì ai`m+im`2b h2+?MQHQ;B2b 7Q` *BpBH- J2@+?�MB+�H- �M/ �2`QbT�+2 avbi2Kb kyRd- CX SX GvM+?- 1/X- aSA1- �T`XkyRdX

(dk) JX 6X hQQi?K�M- 1X hBM;- 1X aFQr- �M/ EX �X *mM27�`2- ǳJmHiB7mM+@iBQM�H b2H7@TQr2`2/ ?v/`�mHB+ bvbi2K b2MbQ` MQ/2-Ǵ BM aSA1 aX aX- kyR3-Bb#M, Nd3R8RyeReNkNX

(dj) EX 1/;2- ǳ.2bB;MBM; [mB2i2` ?v/`�mHB+ bvbi2Kb @ bQK2 `2+2Mi /2p2HQT@K2Mib �M/ +QMi`B#miBQMb UBMpBi2/ F2vMQi2 T�T2`V-Ǵ 1M;HBb?- 9i? C>SaAMi2`M�iBQM�H avKTQbBmK QM 6HmB/ SQr2` c *QM72`2M+2 /�i2, yR@RR@RNNN-LQpX RNNN- TTX jĜkdX

(d9) >X PìrB;- ǳ1tT2`BK2Mi�H �M/ �M�HviB+�H pB#`�iBQM �M�HvbBb BM ~mB/TQr2` bvbi2Kb-Ǵ AMi2`M�iBQM�H CQm`M�H Q7 aQHB/b �M/ ai`m+im`2b- pQHX 9k-MQX kR- TTX 83kRĜ83jy- kyy8- S�*�J oAAA aS1*A�G Aaal1- BbbM, yyky@de3jX

(d8) GX EBMbH2`- GX EBMbH2`- �X 6`2v- �X *QTT2Mb- �M/ CX a�M/2`b- 6mM/�K2M@i�Hb Q7 �+QmbiB+bX qBH2v- kyyy- Bb#M, Nd3y9dR39d3NkX

(de) aX JQQ`2- ǳ� `2pB2r Q7 MQBb2 �M/ pB#`�iBQM BM ~mB/@}HH2/ TBT2 bvbi2Kb-ǴBM a2+QM/ �mbi`�H�bB�M �+QmbiX aQ+X *QM7X- kyReX

(dd) aX >Q`QrBix- hX LBb?B/�- GX *�ii�72bi�- �M/ JX a?2TH�F- ǳ*?�`�+i2`B@x�iBQM Q7 � +QKTHB�Mi@#�+FTH�i2 >2HK?QHix `2bQM�iQ` 7Q` �M 2H2+i`QK2@+?�MB+�H �+QmbiB+ HBM2`-Ǵ AMiX CX �2`Q�+Qmbi- pQHX R- MQX k- TTX R3jĜky8-kyyN- BbbM, R9d8@9dksX

(d3) 6X L�`Bi� �M/ JX 6Qt- � _2pB2r QM SB2xQ2H2+i`B+- J�;M2iQbi`B+iBp2- �M/J�;M2iQ2H2+i`B+ J�i2`B�Hb �M/ .2pB+2 h2+?MQHQ;B2b 7Q` 1M2`;v >�`p2bi@BM; �TTHB+�iBQMb- kyR3X

(dN) hX "X sm- 1X CX aBQ+?B- CX >X E�M;- GX wmQ- qX w?Qm- sX h�M;- �M/ sXCB�M;- ǳ� TB2xQ2H2+i`B+ Swh +2`�KB+ KmHiBH�v2` bi�+F 7Q` 2M2`;v ?�`p2bi@BM; mM/2` /vM�KB+ 7Q`+2b-Ǵ BM �aJ1 .1h*- kyRR- Bb#M, Nd3ydNR389d38X

(3y) CX GB�M;- >X aX@>X *?mM;- �M/ qX@>X GB�Q- ǳ.B2H2+i`B+ HQbb �;�BMbiTB2xQ2H2+i`B+ TQr2` ?�`p2biBM;-Ǵ aK�ì J�i2`X ai`m+iX- pQHX kj- MQX N-TX yNk yyR- CmHX kyR9X

(3R) uX *X a?m- AX *X GB2M- �M/ qX CX qm- ǳ�M BKT`Qp2/ �M�HvbBb Q7 i?2aa>A BMi2`7�+2 BM TB2xQ2H2+i`B+ 2M2`;v ?�`p2biBM;-Ǵ aK�ì J�i2`X ai`m+iX-pQHX Re- MQX e- TTX kk8jĜkke9- P+iX kyydX

(3k) wX qm �M/ ZX sm- ǳ.2bB;M �M/ /2p2HQTK2Mi Q7 � RR2H irQ@/B`2+iBQM�H2M2`;v ?�`p2bi2` rBi? bBM;H2 TB2xQ2H2+i`B+ bi�+F-Ǵ A111 h`�MbX AM/X 1H2+@i`QM- pQHX e3- MQX k- TTX RkNyĜRkN3- kykyX

98

(3j) >X sB�Q- >X ZB2- �M/ *X _X "Qr2M- ǳJQ/2HHBM; Q7 i?2 +B`+mH�` 2/;2@+H�KT2/ BMi2`7�+2 Q7 � ?v/`�mHB+ T`2bbm`2 2M2`;v ?�`p2bi2` iQ /2i2`KBM2TQr2`- 2{+B2M+v �M/ #�M/rB/i?-Ǵ J2+?�MB+�H avbi2Kb �M/ aB;M�H S`Q@+2bbBM;- pQHX R9e- TX Ryd yRj- kykR- BbbM, y333@jkdyX

(39) wX qm �M/ ZX sm- ǳ.2bB;M �M/ i2biBM; Q7 � RR2H #B/B`2+iBQM�H 2M2`;v ?�`@p2bi2` rBi? bBM;H2 TB2xQ2H2+i`B+ bi�+F-Ǵ J2+?�MB+�H avbi2Kb �M/ aB;M�HS`Q+2bbBM;- kyRN- BbbM, RyNeRkReX

(38) qX w?Qm- hX "X sm- �M/ GX wmQ- ǳ1M2`;v /2HBp2`v 7`QK TB2xQ2H2+i`B+?�`p2bi2` iQ `2bBbiBp2 HQ�/-Ǵ BM JPoA* kyR9 @ Rki? AMi2`M�iBQM�H *QM@72`2M+2 QM JQiBQM �M/ oB#`�iBQM *QMi`QH- kyR9X

(3e) CX >- �X /2 "Q2`- _X GQ2M/2`bHQQi- �M/ >X J- ǳSQr2` ?�`p2biBM; BM �?2HB+QTi2` `QiQ` mbBM; � TB2xQ bi�+F BM i?2 H�; /�KT2`-Ǵ CX AMi2HX J�iXavbiX ai`X- pQHX k9- CmMX kyRkX

(3d) .X oX .X 1M/2- "X "Qb- qX �X :`Q2M- �M/ GX .Q`iK�Mb- ǳGB72iBK2 Q7TB2xQ+2`�KB+ KmHiBH�v2` �+im�iQ`b, AMi2`TH�v Q7 K�i2`B�H T`QT2`iB2b �M/�+im�iQ` /2bB;M-Ǵ CQm`M�H Q7 1H2+i`Q+2`�KB+b- pQHX kk- TTX RejĜRdy- kyyNX

(33) S?vbBF AMbi`mK2Mi2 USAV :K#>- _2HB�#BHBiv �M/ HB72iBK2 Q7 KmHiBH�v2`TB2xQ �+im�iQ`b- PMHBM2- �++2bb2/, kyky@y8@ye- kyyNX

(3N) JX �H;m2`Ʀ- "X *?2M;- 6X :mBm- JX _22+2- JX SQQH2- �M/ LX �H7Q`/-ǳ.2;`�/�iBQM Q7 i?2 /jj TB2xQ2H2+i`B+ +Q2{+B2Mi 7Q` Txi +2`�KB+b mM/2`bi�iB+ �M/ +v+HB+ +QKT`2bbBp2 HQ�/BM;-Ǵ CQm`M�H Q7 i?2 1m`QT2�M *2`�KB+aQ+B2iv- pQHX kR- MQX Ry- TTX R9jdĜR99y- kyyR- BbbM, yN88@kkRNX

(Ny) >X sB�Q- >X ZB2- �M/ *X _X "Qr2M- ǳJQ/2HHBM; Q7 i?2 +B`+mH�` 2/;2@+H�KT2/ BMi2`7�+2 Q7 � ?v/`�mHB+ T`2bbm`2 2M2`;v ?�`p2bi2` iQ /2i2`KBM2TQr2`- 2{+B2M+v �M/ #�M/rB/i?-Ǵ J2+?�MB+�H avbi2Kb �M/ aB;M�H S`Q@+2bbBM;- pQHX R9e- TX Ryd yRj- kykR- BbbM, y333@jkdyX

9e

javier aranda final[33]

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