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WARNATZ, MAAS & DIBBLE (2006) -Combustion - Physical and Chemical Fundamentals, Modeling and Simulation

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Prévia do material em texto

J. Warnatz · U. Maas · R.W. Dibble 
Combustion
J. Warnatz · U. Maas · R.W. Dibble 
Combustion
Physical and Chemical Fundamentals,
Modeling and Simulation, Experiments,
Pollutant Formation
4th Edition
With 227 Figures and 22 Tables
Prof. Dr. Dr. h.c. Jürgen Warnatz
Universität Heidelberg
Interdisziplinäres Zentrum 
für Wissenschaftliches Rechnen
Im Neuenheimer Feld 368
D-69120 Heidelberg, Germany
Prof. Dr. Robert W. Dibble
University of California
Dept. of Mechanical Engineering
Etcheverry Hall
94720 Berkeley, CA, USA
ISBN-10 3-540-25992-9 4th ed. Springer Berlin Heidelberg New York
ISBN-13 978-3-540-25992-3 4th ed. Springer Berlin Heidelberg New York 
This work is subject to copyright. All rights are reserved, whether the whole or part of the material 
is concerned, specifi cally the rights of translation, reprinting, reuse of illustrations, recitation, broad-
casting, reproduction on microfi lm or in other ways, and storage in data banks. Duplication of this 
publication or parts thereof is permitted only under the provisions of the German Copyright Law of 
September 9, 1965, in its current version, and permission for use must always be obtained from Sprin-
ger. Violations are liable to prosecution under German Copyright Law.
Springer is a part of Springer Science+Business Media
springer.com
© Springer-Verlag Berlin Heidelberg 1996, 1999, 2001, and 2006
Printed in Germany
The use of general descriptive names, registered names, trademarks, etc. in this publication does not 
imply, even in the absence of a specifi c statement, that such names are exempt from the relevant pro-
tective laws and regulations and therefore free for general use.
Typesetting: Digital data supplied by data
Final processing: PTP-Berlin Protago-TEX-Production GmbH, Berlin (www.ptp-berlin.com)
Cover-Design: medionet AG, Berlin 
Printed on acid-free paper 62/3141/Yu – 5 4 3 2 1 0
Library of Congress Control Number: 2006927345
Prof. Dr. Ulrich Maas
Universität Karlsruhe (TH)
Institut für Technische Thermodynamik
Kaiserstr. 12
D-76128 Karlsruhe, Germany
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3Rk �C�E1e�g^l,gl^1` RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR LkL
3Rh �C�E1e�1CJ,@g@1` RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR Lk:
3R: �1F`@g@n@gqe�F�Cq`@` RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR Lkb
3R9 �p1^,@`1` RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR Lk3
0 ��.+/�:?�1/3:".+F"!?�-�."; RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR LkG
GRL �JlFg1^8CJoe�JFN^1E@p1/e�C�E1`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR LkG
GRk 
�E@F�^e�1ge�JFN^1E@p1/e�C�E1`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR Lhh
GRh �JFN^1E@p1/e�C�E1`e�@g>e��`ge�>1E@`g^qeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR Lh9
GR: �p1^,@`1` RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR Lh3
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2I 	(/+@+1/?�:1�";;"; RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR L:L
LsRL �1E1FJn\`e�F�Cq`@`eJ8e�>1^E�Ce�pNCJ`@JF`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRReL:k
LsRk �^�FB?��E1F1g`B@@\`e�F�Cq`@`eJ8e�>1^E�Ce�pNCJ`@JF` RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR L:h
LsRh �lgJ@;F@g@JF-e
;F@g@JFe
@E@g` RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR L:9
LsR: �lgJ@;F@g@JF-e
;F@g@JF?�1C�qe�@E1eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR L:3
LsR9 
F/l,1/e
;F@g@JF.e�@F@ElEe
;F@g@JFe�F1^;@1` RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR L:G
LsRc �N�^Be
;F@g@JF RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR L9h
LsRb �1gJF�g@JF` RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR L9b
LsR3 �p1^,@`1` RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR Lch
22 �1E*�".3":�@C:"?�F+!�@+1/ ?�/(+/"?�/1�, RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR Lc9
LLRL �lF/�E1Fg�Ce�>1FJE1F�e@Fe�ggJe�F;@F1` RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR Lc9
LLRk �p@/�g@JFe�ge
Fg1^E1/@�g1e�1EN1^�gl^1` RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR Lc3
LLRh 
Jo?�1EN1^�gl^1e�p@/�g@JFeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR LcG
LLR: 
;F@g@JFe�^J,1``1`e@Fe�1,@N^J,�g@F;e�F;@F1`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR Lbh
LLR:RL �FJ,Be��E�;1`e@Fe�ggJe�F;@F1` RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR Lbh
LLR:Rk 
;F@g@JFe@Fe�@1`1Ce�F;@F1` RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR Lb:
LLR:Rh �>1e	��
e�JF,1Ng RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR Lb9
LLR:R: �>1e�
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e�JF,1Ng RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR Lbb
LLR9 �p1^,@`1` RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR Lb3
2B �)"?��D+":*�@1,";*�8C�@+1/;?%1:?�):""*�+."/;+1/�-?�"��@+/(?�-1E?RRRR LbG
LkRL �>1e�JF`1^n�g@JFe�Ul�g@JF` RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR LbG
LkRLRL �n1^�CCe��``e�JF`1^n�g@JF RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRReL3s
LkRLRk �N1,@1`e��``e�JF`1^n�g@JF RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRReL3L
LkRLRh �JE1FglEe�JF`1^n�g@JF RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRReL3L
LkRLR: �F1^;qe�JF`1^n�g@JF RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRReL3k
LkRk �>1e�EN@^@,�Ce
�o` RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR L3h
LkRkRL �1ogJF\`e
�oeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR L3h
LkRkRk �Jl^@1^\`e
�oeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR L3:
LkRkRh �@,B\`e
�oe�F/e�>1^E�Ce�@88l`@JFeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR L3:
LkRkR: ��C,lC�g@JFeJ8eg>1e�^�F`NJ^ge�J188@,@1Fg`e8^JEe�JC1,lC�^e��^�E1g1^`eRRRRRRRR L39
LkRh �p1^,@`1` RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR L39
2A �C:�C-"/@?�"��@+/(?�-1E; RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR L3b
LhRL �JE1e�lF/�E1Fg�Ce�>1FJE1F� RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR L3b
LhRk �@^1,ge�lE1^@,�Ce�@ElC�g@JF RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR L3G
LhRh�JF,1Ng`e8J^e�l^&lC1F,1e�J/1C@F;-e�@E1?e�F/e��n^1?�n1^�;@F; RRRRRRRRRR LGk
LhR: �1qFJC/`?�n1^�;1/e��n@1^?�gJB1`eO����Pe�Ul�g@JF` RRRRRRRRRRRRRRRRRRRRRRRRRRRRRR LG:
LhR9 �l^&lC1F,1e�J/1C` RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR LGc
LhRc �1�Fe�1�,g@JFe��g1` RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR kss
LhRb �JF,1Ng`e8J^e�l^&lC1F,1e�J/1C@F;-e�^J&�&@C@gqe�1F`@gqe�lF,g@JF`eRRRRRRRRRRRRR ksk
LhR3 �//q?�^1�B?�Ne�J/1C`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR ksc
LhRG �l^&lC1Fge�,�C1`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR ksb
LhRLs 
�^;1?�//qe�@ElC�g@JFeO
��PeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR ksG
LhRLL �p1^,@`1`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR kLL
��&C1eJ8e�JFg1Fg`
� ��&C1eJ8e�JFg1Fg`
2' �C:�C-"/@?�1/3:".+F"!?�-�.";eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR kLh
L:RL �JFN^1E@p1/e�C�E1`eo@g>e�Ul@C@&^@lEe�>1E@`g^qeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR kL:
L:Rk �@F@g1?��g1e�>1E@`g^qe@Fe�JFN^1E@p1/e�C�E1`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRkLb
L:Rh �C�E1e�pg@F,g@JFeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR kkL
L:R: ���?�@ElC�g@JF`eJ8e�l^&lC1Fge�JF?�^1E@p1/e�C�E1`e�`@F;e�e�JFg1?
��^CJe�1g>J/ RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRekk:
L:R9 �p1^,@`1`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRkkc
2& �C:�C-"/@?�:".+F"!?�-�.";eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRkkb
L9RL �C�``@8@,�g@JFeJ8e�l^&lC1Fge�^1E@p1/e�C�E1` RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR kkb
L9Rk �C�E1C1ge�J/1C`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR khs
L9RkRL �C�E1C1ge�J/1CC@F;e�`@F;e�e�1�,g@JFe�^J;^1``e��^@�&C1eRRRRRRRRRRRRRRRRRRRRRRR khL
L9RkRk �C�E1C1ge�J/1CC@F;e�`@F;e�e
1n1C?�1ge�1g>J/ RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR khk
L9Rh �l^&lC1Fge�C�E1e�1CJ,@gqeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRkhh
L9R: �C�E1e�pg@F,g@JFeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRkh9
L9R9 �g>1^e�J/1C`eJ8e�l^&lC1Fge�^1E@p1/e�JE&l`g@JFeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRkhb
L9Rc �p1^,@`1`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRkh3
2> �1.�C;@+1/?1%?�+8C+!?�/!?�1-+!?�C"-;eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR khG
LcRL �^JNC1ge�JE&l`g@JFeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR khG
LcRLRL �JE&l`g@JFeJ8e�@F;C1e�^JNC1g`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR k:s
LcRLRk �JE&l`g@JFeJ8e�^JNC1ge�^JlN`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR k::
LcRk �N^�qe�JE&l`g@JFeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR k:c
LcRkRL �J^E�g@JFeJ8e�N^�q`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR k:c
LcRkRk �N^�qe�JE&l`g@JFe�J/1`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR k:b
LcRkRh �g�g@`g@,�Ce�1`,^@Ng@JFeJ8e�N^�q`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR k:G
LcRkR: �J/1C@F;eJ8e�l^&lC1Fge�N^�qe�JE&l`g@JFeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRk9k
LcRkR9 �C�E1C1g?�qN1e�J/1C`e8J^e�N^�qe�JE&l`g@JFeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR k9h
LcRh �J�Ce�JE&l`g@JFeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR k99
LcRhRL �q^JCq`@`eJ8ee�J�CeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR k99
LcRhRk �l^F@F;eJ8e�JC�g@C1e�JENJlF/`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR k9c
LcRhRh �l^F@F;eJ8eg>1e�JB1eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR k9c
LcRhR: �J�Ce��`@8@,�g@JFeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR k9b
LcR: �p1^,@`1`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRk93
2= �1:.�@+1/?1%?�+@:+�?�F+!";eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR k9G
LbRL �>1^E�Ce��eO�1C/Jn@,>e��P RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR k9G
LbRk �^JENge��eO�1F@EJ^1e��PeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR kck
LbRh ��e�1F1^�g1/en@�e�@g^Jl`e�p@/1eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR kc9
LbR: �JFn1^`@JFeJ8e�l1Ce�@g^J;1Fe@FgJe�� RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR kc9
LbR9 ��e�1/l,g@JFe&qe�JE&l`g@JFe�J/@8@,�g@JF` RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR kcb
LbRc ��g�Cqg@,e�JE&l`g@JF RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRkbL
LbRb ��e�1/l,g@JFe&qe�J`g?�JE&l`g@JFe�^J,1``1`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR kbk
LbR3 �p1^,@`1`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRekb9
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��&C1eJ8e�JFg1Fg`
2# �1:.�@+1/?1%?�G!:1��:�1/;?�/!?�11@ RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRekbb
L3RL �F&l^Fge	q/^J,�^&JF`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRekbb
L3RLRL �C�E1e�pg@F,g@JFe�l1egJe�g^�@FeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRekb3
L3RLRk �C�E1e�pg@F,g@JFe�ge��CC`e�F/e@Fe��N`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRekb3
L3Rk �J^E�g@JFeJ8e�JCq,q,C@,e�^JE�g@,e	q/^J,�^&JF`eO��	P RRRRRRRRRRRRRRRRRRRRRRRRRRek3s
L3Rh �>1e�>1FJE1FJCJ;qeJ8e�JJge�J^E�g@JFeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRk3h
L3R: �J/1CC@F;e�F/e�@ElC�g@JFeJ8e�JJge�J^E�g@JFeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRek3b
L3R9 �p1^,@`1`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRkGc
20 �%%"�@;?1%?�1.�C;@+1/?�:1�";;";?1/?@)"?�@.1;3)":"eRRRRRRRRRRRRRRRRRRRRRRRRRRRRekGb
LGRL �>1e�g^l,gl^1eJ8eg>1e�gEJ`N>1^1eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRekGb
LGRLRL �^1``l^1e@Feg>1e�gEJ`N>1^1eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRkGb
LGRLRk �1EN1^�gl^1e�F/e�C�``@8@,�g@JFeJ8e�JEN�^gE1Fg`e@Feg>1e�gEJ`N>1^1eRRRRRRRekGG
LGRLRh �JENJ`@g@JFeJ8eg>1e�gEJ`N>1^1eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRehss
LGRkR �>1e�gEJ`N>1^1e�`e�e�>JgJ,>1E@,�Ce�q`g1EeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRehss
LGRkRL 
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�oeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRhss
LGRkRk �g1^F?�JCCE1^e�Ul�g@JFeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRehsL
LGRkRh �J^E�g@JFeJ8e�>JgJ,>1E@,�Ce
�q1^`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRehsk
LGRh 
F,JE@F;e�lFe��/@�g@JF.e�>JgJ,>1E@,�Ce�^@E�^qe�^J,1``1`eRRRRRRRRRRRRRRRRRRRRRRehsh
LGR:R �>q`@,�Ce�^J,1``1`e@Feg>1e�gEJ`N>1^1eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRehs9
LGR:RL �JF`1^n�g@JFeJ8eg>1e��``eJ8e�N1,@1`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRehs9
LGR:Rk �JF`1^n�g@JFeJ8e�F1^;qeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRehsc
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