Aspects of Mathematical Modelling: Applications in Science, Medicine, Economics and Management

Mathematics and Biosciences in Interaction Managing Editor Wolfgang Alt Division of Theoretical Biology Institute of Mo...

Author: Roger J. Hosking | Roger J. Hosking | Ezio Venturino

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Mathematics and Biosciences in Interaction Managing Editor Wolfgang Alt Division of Theoretical Biology Institute of Molecular and Cellular Botanics University of Bonn Kirschallee 1 D-53115 Bonn e-mail: [email protected]

Editorial Board Fred Adler (Dept. Mathematics, Salt Lake City) Mark Chaplain (Dept. Math. & Computer Sciences, Dundee) Andreas Deutsch (Center for Information Services and High Performance Computing (ZIH), Dresden) Andreas Dress (Shanghai Institutes for Biological Sciences, Shanghai, and Max Planck Institute for Mathematics in the Sciences, Leipzig) David Krakauer (Dept. of Zoology, Oxford) Robert T. Tranquillo (Dept. Chem. Engineering, Minneapolis)

Mathematics and Biosciences in Interaction is devoted to the publication of advanced textbooks, monographs, and multi-authored volumes on mathematical concepts in the biological sciences. It concentrates on truly interdisciplinary research presenting currently LPSRUWDQWELRORJLFDO½HOGVDQGUHOHYDQWPHWKRGVEHLQJGHYHORSHGDQGUH½QHGLQFORVH relation to problems and results relevant for experimental bioscientists. The series aims at publishing not only monographs by individual authors presenting their own results, but welcomes, in particular, volumes arising from collaborations, joint research programs or workshops. These can feature concepts and open problems as a result of such collaborative work, possibly illustrated with computer software providing statistical analyses, simulations or visualizations. The envisaged readership includes researchers and advanced students in applied mathematics – numerical analysis as well as statistics, genetics, cell biology, neurobiology, bioinformatics, biophysics, bio(medical) engineering, biotechnology, evolution and behavioral sciences, theoretical biology, system theory.

Aspects of Mathematical Modelling Applications in Science, Medicine, Economics and Management Roger J. Hosking Ezio Venturino Editors

Birkhäuser Basel · Boston · Berlin

Editors: Roger J. Hosking Universiti Brunei Darussalam Dept. Mathematics BE1410 Gadong Brunei

Ezio Venturino Università di Torino Dipto. Matematica Via Carlo Alberto 10 10123 Torino Italy

Library of Congress Control Number: 2007935882

Bibliographic information published by Die Deutsche Bibliothek 'LH'HXWVFKH%LEOLRWKHNOLVWVWKLVSXEOLFDWLRQLQWKH'HXWVFKH1DWLRQDOELEOLRJUD½H detailed bibliographic data is available in the Internet at . 7KHXVHRIUHJLVWHUHGQDPHVWUDGHPDUNVHWFLQWKLVSXEOLFDWLRQHYHQLIQRWLGHQWL½HG as such, does not imply that they are exempt from the relevant protective laws and regulations or free for general use.

ISBN 978-3-7643-8590-3 Birkhäuser Verlag AG, Basel - Boston - Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of WKHPDWHULDOLVFRQFHUQHGVSHFL½FDOO\WKHULJKWVRIWUDQVODWLRQUHSULQWLQJUHXVHRI LOOXVWUDWLRQVUHFLWDWLRQEURDGFDVWLQJUHSURGXFWLRQRQPLFUR½OPVRULQRWKHUZD\VDQG storage in data banks. For any kind of use permission of the copyright owner must be obtained. © 2008 Birkhäuser Verlag AG, P.O. Box 133, CH-4001 Basel, Switzerland Part of Springer Science+Business Media Printed on acid-free paper produced from chlorine-free pulp. TFC Cover illustration: See page 73. With the friendly permission of Q.J.A. Khan Printed in Germany ISBN 978-3-7643-8590-3

e-ISBN 978-3-7643-8591-0

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www.birkhauser.ch

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" 7) '8 5 )' # ! 7E&8 ") 66=46=,C G/F> 4" = ,>6/J ,2 ,)F= D9 2 2 > C*C ! L "4= C* =)F/= 6/2C+,2>C J20,> ,2 =),42 5 4" ,)F= 5 C ! 5L9 *,> ,> F C4 C* "C C*C ,2 C*,> =),42 C* C=2>,2C >6C,/ 6/2C 2 ,2>C 6CC=2> C*C "4=0 ,2 C* =/J >C) 4" C* ,2G>,42 4" C* C =>,>C2C ,2>C> = =4 C*=4F)* C* ,#F>,42 4" C* ,2>C>9 4C* C* 6/2C 2 ,2>C ,40>>> = C*="4= %2//J ,>C=,FC *404)24F>/J ,2 >6 724C >*4H289 2 42C=>C ,2 =),42 E H,C* ! L 7,2 ,)F= D C ! 5L8 C* C 6/2C 2 C+=>,>C2C ,2>C 6CC=2> 4 24C =4 2 G=J ,2 C,0 724C >*4H289 =,C,42> 4" C* 6CC=2> =>F/C "=40 C*

3L

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-4,2C ,06C 4" 'CC2,2) C,42 4" ,2>C ,#F>,42 42 C* 42 *2 2 )=4HC* 4" C* ,2>C 2C 6/2C ,40>> 42 C* 4C*=9 > ,)F= D >F))>C> ,2 =),42 E C ! 5L C* 0I,0F0 G/F> 4" C* 6/2C ,40>> = ,>C=,FC ,2 H, =2) CH2 L 2 5 /42) C* *4=,K42C/ I,>9 *F> 42 G=) C* 6/2C ,40>> ,2 =),42 E C.> >0//= G/F> C*2 ,2 =),42 5 H*= C* 0I,0F0 6/2C ,40>> ,> /4> C4 59 > C* F=C,42 4" C* ,2>C =6=4FC,42 6=,4 ,2=>> C* 6/2C+ ,2>C ,40>> 4>,//C,42> =,>,2) ,2 =),42 E 4" C* 6=0C= >6 40 =)+ F/= 7"9 ,)F= E C ! ! ! L#8 2 C* G/F> 4" )C G=J /4> C4 K=4 7"9 ,)F= D89 * 0I,0F0 G/F> 4" C* 6/2C ,40>> ,2 =),42 E 40 G2 /=)= C*2 C* 0I,0F0 G/F> 4" C* 6/2C ,40>> 4>,//C,42> ,2 =),42 59 4HG= C* G=) 6/2C ,40>> ! ),G2 J ;FC,42 7EE8 ,> >C,// >0//= ,2 =),42 E C*2 ,2 =),42 5 7"9 ,)F= E89 * =>42 ,> C*C ,2 =),42 E C* 0,2,0F0 6/2C ,40>> G/F ,> />> C*2 C* 0,2,0F0 6/2C ,40>> G/F ,2 =),42 59 >,> ,2 =),42 E C* 6/2C ,40>> C.> ,C> 0,2,0F0 G/F> "4= 0F* /42)= C,0 C*2 ,2 =),42 5 7"9 ,)F= D8 =>F/C,2) ,2 C* C4C/ => 4" C* ! G/F 7"9 ,)F= E89 C ,> 24C/ C*C C* ,#=2 ,2 C* *=C= 4" C* 6/2C+,2>C J20,> 4> 24C 2>>=,/J / C4 >>2C,//J ,#=2C 622,> 4" C* G=) 6/2C ,40>> ! 42 C* F=C,42 4" C* ,2>C =6=4FC,42 6=,4 9 2 "4= I06/ C ! ! ! L#5 C* )=6*> ! 78 ,2 =),42 5 2 =),42 E = G=J /4> C4 * 4C*= 7"9 ,)F= E8 G2 C*4F)* C* F2=/J,2) 6/2C+,2>C J20,> = ,#=2C 724C >*4H289 *F> ,2 =),42 5 C* 4>,//C,42> 4" C* C 6/2C 2 C+=>,>C2C ,2>C ,40>> = =)F/= H*,/ ,2 =),42 E C* 4>,//C,42> = G=J ,==)F/=9 * 4==>642,2) G/F> 4" C* ,#F>,42 2F0= = K=4 ,2 =),42 5 2 =4F2 L9LE ,2 =),42 E C // G/F> 4" C* F=C,42 4" C* ,2>C =6=4FC,42 6=,4 9

% - &&' *G G/46 426CF/ =C,42+,#F>,42 04/ 4" C* C =46 C+ >F>6C,/ >>+ 2 =>+,2>C> C+=>,>C2C ==+,2>C> >J>C0 ,2 4== C4 >,0F/C 0>>,G ,2G>,42 4" C =>,>C2C ,2>C>9 *G >*4H2 C*C C* )=4HC* 2F0=> 2

C=0,2 H*C*= 4= 24C C+=>,>C2C ,2>C> 2 ,2G %/ >4H2 H,C* C =469 * =>F/C> 4C,2 ,06/J C*C C*4=4F)* 0>F=02C> 4F/ //4H F> C4 >C,0C C* /,,/,CJ 4" ,2G>,42 "4= ),G2 C=2>)2, =46 >4H2 ,2 ),G2 )4)=6*,/ =),42 G,K9 4" C* 42>C2C> 2 H*,* 6=0C=,> C* >CF=C,2) "F2C,42/ =>642>> 7;FC,42> 5L 5D8? C* 6=0C=>

2 H*,* = J,/ 4$,2C> 4" C* >F>6C,/ >>+ 2 =>+,2>C> =>6C,G/J 2 =>,>C2C ==+,2>C> C4 C* 6/2C> 7;FC,42> 55 5D8? 2 C* ,2>C 04=C/,CJ =C>

2 7;FC,42> 55 5D8 C4 /F/C C* )=4HC* 2F0=> 2

9 F* 0>F=02C> H4F/ 4" 6=C,F/= ,2C=>C C4 *. C* G/,,CJ 4" C* )=4HC* 2F0=> ,2 )=,F/CF=/ 6=C, 2 "4= ,2G>,42 =,>. >>>>02C>9 4 4F= .24H/) >F* 0>F=02C> *G 24C JC 2 ==, 4FC9

2>C,,/ C =46> 2= >>,G C+=>,>C2C >C 2G>,42

35

,2 4F= 04/ "4= C* 6/2C 2 ,2>C J20,> 62> 42 F2=C,2 ,26FC 6=0C=> C* 04/ 4FC6FC >*4F/ 24C ,2C=6=C > 6=,C,G 4" C* 6/2C+,2>C >J>C0 *G,4F= FC 0F>C ,2C=6=C H,C*,2 C* 42CIC 4" 64>>,/ >2=,4> 4" 646F/C,42 J20,>9 ,C*,2 4F= 426CF/ 66=4* H ,2G>C,)C C* J20,> 4" C* 04/ )=,F/CF=/ >J>C0 ,2 6=0C= >6 H*,* H *G >*4H2 42>,>C> 4" CH4 =),42> ,2 ,)F= 5 H,C* ,#=2C ,2C=,2>, J20,> 5A9 *G >*4H2 C*C G/F> 4" C* 42>C2C> 2 H*,* 6=0C=,> C* #C,G "F2,CJ =C> 4" >>+ =>+ 2 ==+,2>C> =>6C,G/J > =6=>2C ,2 75&8 75@8 >>2C,//J #C C* *=C= 4" C* 622 4" C* G=) 6/2C ,40>> ! ,2 ;FC,42 7EE8 42 C* /2)C* 4" C* ,2>C =6=4FC,42 6=,4 ,2 4C* =),42 5 2 =),42 E 4" C* 6=0C= >6 7"9 ,)F= E89 C *> 2 >*4H2 C*C ,2 C* )2=/ > C* 622 4" "F2,CJ =C 2 =6=>2C J C* "F2C,42 78 !

:

7EA8

H*= ,> C* 646F/C,42 2>,CJ 2 C* "F2C,42 =6=>2C> C* 646F/C,42 2>,CJ >F* C*C */" 4" C* "0/> 2 "=C,/,> D (9 " C* 646F/C,42 2>,CJ ,> *,)* 7,99 8 C*2 2 ,2 C*,> > C* >6C,4+C064=/ J20,> 2 >=, H,C* C* F> 4" 4F= 04/ 75L8 7589 " C* 646F/C,42 2>,CJ ,> /4H 7,99 8 C*2 9 =46= 6/2C+,2>C J20,> *G 2 2/J> ,2 5 5@ 5A 2 ,C ,> 4" ,2C=>C C4 406= C* =>F/C> 4C,2 "=40 >CF,> 4" 4C* /,0,C,2) >>9 758 2 5A H*= H *G "4F2 C*C C* 6/2C+,2>C J20,> =>F/C,2) "=40 2 ,2G>,42 4" C+=>,>C2C ,2>C> 2 242+F2,;F C*=4F)*4FC C* ,2>C =6=4FC,42 6=,49 2 6=C,F/= *4C, CC=C4= 2 C* /,0,C J/ *G 2 >*4H2 C4 4I,>C >4 C*C C* C+6/2C C+=>,>C2C ,2>C >J>C0 02,">C> ,C*= *4C, 4= =)F/= 4>,//C,42> 4" 6/2C 2 ,2>C ,40>> 62,2) F642 C* >6C,/ ,>C=,FC,42> 4" C* 6/2C 2 ,2>C ,40>>9 F= 2/J>,> 4" C* 0>>,G ,2G>,42 4" C+=>,>C2C ,2>C> ==, 4FC H,C* C* 04/ 75L8 758 H*= >*4H C*C C* ,2C=,2>, J20,> 4" C 6/2C 2 C+=>,>C2C ,2>C ,40>> 2 ,C*= 2 ;F,/,=,F0 4= =)F/= 4>,//C,42> H,C* 24 C,2) 4" *4C,,CJ 7C* 40,22C J6F24G I6422C H> 24C 64>,C,G89 2 *4C, J20,> 4 24C 0=) ," C* 2>,CJ 4" C+=>,>C2C ,2>C> ,> *,)* =>F/C,2) ,2 C* 622 9 7E8 4= C* ,>C,2C,42 CH2 C* ,2C=,2>, J20,> ,2 =),42> 5 2 E 4" 6=0C= >6 ,2 ,)F= 5 *> 2 >*4H2 C4 / C4 ,>C,2C,42> CH2 C* 622,> 4" C* G=) 6/2C ,40>> 42 C* F=C,42 4" C* ,2>C =6=4FC,42 6=,4 5&9 2 42C=>C "4= > ,2 04/ 75L8 758 C*> 622,> 2 G=J >,0,/= C4 * 4C*= G,K9 H*2 G/F> 4" C* 42>C2C> 2 H*,* 6=0C=,> C* #C,G "F2,CJ =C> 4" >>+ =>+ 2 ==+,2>C> =>6C,G/J ,2 ;FC,42> 75&8 75@8 = J42 >40 ,2C=G2,2) ,2C=G/ 7"9 ,)F= E89

3E

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$( "+)#.+#" J27-7A2GA 251B A7AB3G 3 GGAG.K 2G,5 $5A M2.3.3+ 7ABBJA N32.B .3K51K.3+ 5271.G ,J23 7,NB.515+N; 3 G,.B 2511.3+ 77A5, G, 7,NB.515+.1 BNBG2 .B BJ.K. .3G5 3J2A 5$ 1.30 .3GAG.3+ BJJ3.GB GA2 >527AG23GB?; 3 +3A1 , 527AG23G L.11 53G.3 B.3+1 7,NB.1 53BG.GJ3G BJ, B 155 AA5B7.31 )J. 89 5A G.BBJ 3 .3GABG.G.1 )J.; 5LKA 73.3+ 53 G, 251@B 5271M.GN +.K3 53BG.GJ3G 2N 77A .3 25A G,3 53 527AG23G 5$ G, 251; N32.B .3 , 527AG23G .B B7.' N 1J27 G.2-733G $J3G.53B +.K.3+ 527AG23G1 7ABBJAB L,.1 .3A23G1 ,3+B .3 )5LB 3 527AG23G1 K51J2B A 5G.3 N BB5.G.3+ AB.BG3 3 5271.3 7A2GAB L.G, /3G 527AG23GB; 3 7AG.J1A .3GAG.53 GL3 /3G BJJ3.GB .B BBJ2 G5 G0 71 G G, .3GA$B 5$ G, 251@B 527AG23GB; 7G.1 AB51JG.53 .B 1.2.G N G, 3J2A 5$ '3 527AG23GB JG 251B 5$ G,.B GN7 L.G, K3 A1G.K1N B211 3J2A 5$ 527AG23GB 5$G3 7A5J M113G +A23G L.G, 1.3.1 G; J27-7A2GA 251B ,K 3 JB G5 BGJN .3GAA3.1 7ABBJA $5A 25A G,3 IPP NAB; 5LKA L.G, $L M7G.53B 7AK.5JB 251B ,K 57G ABGA.G.53B 035L3 B G, >11." 53A5 5GA.3? G5 AJ 5271M.GN; , 11.- 53A5 $A2L5A0 53B.AB G, .3GAA3.1 BNBG2 G5 5271G1N 315B L.G,.3 G, .3GAA3.1 KJ1G L,., .B BBJ2 G5 A.+.; B7.' .3)5L 5$ 155 G5 G, .3GAA3.1 AGA.B 7A5K.B $5A.3+ $5A G, BNBG2 3 5JG)5L $A52 G, J+J1A J1 .B BBJ2 G5 .3BG3G35JB1N =JG G5 G,.B .3)5L; ,B ABGA.G.53B N.1 15B BNBG2 L.G, 53BG3G G5G1 K51J2; GA.G1N .3GAA3.1 251B ,K 7A5J 3J2A 5$ .275AG3G ABJ1GB G,G .11J2.3G G, 2,3.B2B 5$ .3GAA3.1 7ABBJA /JBG23GB .3 B.GJG.53B .3K51K.3+ 5G, 35A21 3 7G,57,NB.515+N; 5LKA G, .1.GN 5$ G,B 15B-BNBG2 251B G5 .35A75AG G, .3)J3 5$ .275AG3G MGAA3.1 $G5AB 53 .3GAA3.1 7ABBJA N32.B .B 1A1N 1.2.G; 5A M271 G, .275AG3G J%A.3+ %GB 5$ G, B7.31 B7 53 .3GAA3.1 7ABBJA 335G .AG1N .31J; JA.3+ G, 'ABG $L ,5JAB 5A NB 5$ B7 ).+,G 511G.53 5$ BN27G52B ! .31J.3+ ,, K52.G.3+ 3JB 1G,A+N 3 +BGA. .B52$5AG ! 5$G3 $$GB 2/5A.GN 5$ AL 22AB; 1G,5J+, K.3 BJ++BGB G,G B52 5$ G,B BN27G52B A $5A2 5$ 25G.53 B.03BB BB5.G L.G, G, $J3G.53.3+ 5$ G, KBG.J1A 3 B3B5AN BNBG2B JA.3+ M75BJA G5 2.A5+AK.GN 3K.A5323GB 5G,A 5BAK BN27G52B .%A .3 B.+3.'3G LNB $A52 GAABGA.1 23.$BGG.53B 5$ 25G.53 B.03BB 8 9; ,.1 .B A5J+,1N 5.3.3G L.G, G, .3.G.G.53 5$ 25G.53 BN27G52B .3 2.A5+AK.GN A 1N; ,N .3K51K G.K AG,A G,3 7BB.K , 25G.53B 3 5 35G .3K51K 51 BLGB B1.KG.53 $.1 7115A 5A 5L1 JA+3N; 1B5 J31.0 BN27G52B .3 2.A5+AK.GN A JBJ11N BB5.G L.G, ,, 3 K52.G.3+ G3B G5 BJ3 L.G,5JG .3.G.1 AG,.3+ 5A 3JB; G ,B 3 ,N75G,B.B E G,G 1KG .3GAA3.1 7ABBJA 8 9 2N 71N A51 .3 G, K15723G 5$ B52 5$ G, 5K BN27G52B .3 2.A5+AK.GN;

.3 .A5+AK.GN

I6H

3 BKA1 BN27G52B BJ, B ,, 3 BJ3 K52.G.3+ BGA53+1N AB21 G,5B BB5.G L.G, 3.+3 .3GAA3.1 ,N7AG3B.53; JAG,A G, $G G,G G, 53BG 5$ G,B BN27G52B 5JAB A1N .3 ).+,G BJ++BGB G,G G,N 2N A1G G5 G, L11-5J23G )J. B,.$G G,G +.3B G 1J3, 3 53G.3JB $5A 77A5M.2G1N 6P ,5JAB .3G5 ).+,G; JA.3+ G,.B 7A.5 GL3 6(PP21 3 IPPP21 5$ )J. 2N B,.$G $A52 G, 15LA G5 G, J77A 5N L.G, 4P: 5$ G,.B B,.$G G0.3+ 71 L.G,.3 G, 'ABG GL5 3 ,1$ ,5JAB II; 3GA1 K35JB 7ABBJA 1B5 ABB .3 2.A5+AK.GN 1G,5J+, G, B.B $5A G,.B '3.3+ .B 2BJA G $A52 53 BGA53JG 5KA 4-,5JA 7A.5 6; ,.B 77A 2715NB 2G,2G.1 251 5$ 1J27-7A2GA GN7 G,G ,B 3 K157 IP G5 BGJN G, %GB 5$ 2.A5+AK.GN 3 .GB +A5J3-B 1.3.1 315+JB 53 .3GAA3.1 7ABBJA 8 9; , 11." 53A5 5GA.3 ,B 3 AK50 .3 G,.B 251; N 2.3+ G, .3GAA3.1 BNBG2 .3 L,51-5N 7,NB.515+N B 5775B G5 53'3.3+ .G L.G,.3 G, A3.1 KJ1G G, 7AB3G 251 115LB 53B.BG3G .31JB.53 5$ G, B,.$G 5$ 7,1. )J. $A52 G, 15LA G5 G, J77A 5N 5BAK .3 2.A5+AK.GN; , A.5KBJ1A %GB 5$ 2.A5+AK.GN A 5$G3 B.2J1G N +A5J3B , 5L3 G.1G 89 7A5JAB; 1.3.1 G M.BGB $5A .3GAA3.1 7ABBJA 8 9 JA.3+ B,5AG-GA2 , 5L3 G.1G 6H 3 527A.B53B GL3 G,.B G 3 G, ABJ1GB 5$ B.2J1G.53B ,K 3 JB G5 K1.G G, 7AB3G 251; 11 5$ G, 7AG..73GB M75B G5 ,5JAB 5$ G, ( +A 7A5JAB .3 * A75AG ,, 3 5G,A 2.1 BN27G52B; 5LKA 1.GG1 5AAB753.3+ G M.BGB $5A @B JA.3+ 153+-GA2 M75BJA G5 .G,A 5A 2.A5+AK.GN; , ,, 3 3JB BJ%A N BGA53JGB .3 2.A5+AK.GN A 35G A75AG N G,5B M75B G5 MG3 ( 5A E +A .3 6* 6( L,A B,.$G 5$ 7,1. )J. B.2.1A G5 G,G .3 2.A5+AK.GN .B B7J1G G5 5JA; ,A .B G,JB B52 =JBG.53 5JG G, MG3G G5 L,., 153+-GA2 %G.K1N B.2J1GB G, AB753B 5$ G5 2.A5+AK.GN; 1G,5J+, G, 7AB3G B.2J1G.53B 7A5K. .3B.+,GB .3G5 G, 75BB.1 A.5KBJ1A %GB 5$ 153+-GA2 G, 7A.2AN $5JB 5$ G,.B 2511.3+ %5AG .B BGJN 5$ JB1 A1G.53B,.7B GL3 2.A5+AK.GN %GB 3 .3GAA3.1 7ABBJAB; G.2J1. 53B.A L.11 .31J 2.A5+AK.GN-.3J ,3+B .3 AGA.1 7ABBJA 3GA1 K35JB 7ABBJA 3 155 5115. 5B25G. 7ABBJA; A52 G,.B 31NB.B 1K1B 5$ .3GAA3.1 7ABBJA 2N =J3G.' L.G, AB7G G5 75G3G.1 ,3+B .3 G, A.5KBJ1A BNBG2 J G5 2.A5+AK.GN; BJ1GB 5$ G,.B BGJN BJ++BG G,G G, J7LA )J. B,.$GB .3 2.A5+AK.GN 3 BB5.G ,3+B .3 G, A.5KBJ1A BNBG2 335G N G,2B1KB 1KG .3GAA3.1 7ABBJA G5 1K1B BB5.G L.G, 3.+3 .3GAA3.1 ,N7AG3B.53; .B $5J3 G5 J3%G N G, M7G ,3+B .3 AGA.1 7ABBJA 3 G5 ,3+ .3 7A111 L.G, 3GA1 K35JB 7ABBJA; 25AG .3AB .B 7A.G J G5 G, M7G A57 .3 5115. 5B25G. 7ABBJA .3 2.A5+AK.GN; 5LKA K3 L.G, 11 5$ G,B BG.2J1. 52.3 .3 2.A5+AK.GN .B 7A.G G5 1BB G,3 G,G 7A.G $5A 153+-GA2 3 .G 2N K3 1BB G,3 M7A.3 53 AG, .3 G, BJ7.3 75B.G.53; 53B=J3G1N .$ 3.+3 .3GAA3.1 ,N7AG3B.53 5B K157 .3 B7

I6*

; ; 0.3 3 ; ; GK3B

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I6(

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I6E

; ; 0.3 3 ; ; GK3B

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869

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I6D

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849

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I6

; ; 0.3 3 ; ; GK3B

BG 5$ 5J71 1+A. =JG.53B; 31NB.B 5$ G,B BGN BGG B51JG.53B .B G, 7A.3.71 $5JB 5$ G,.B 77A; 11 5$ G, B.2J1G.53B 7A$5A2 ,A .3K51K G, B51JG.53 5$ =JG.53 849; JB 5$ G, 5271M.GN 5$ 15B $5A2 B51JG.53B LA 5G.3 L.G, G, . 5$ G, 2G,2G.1 B5$GLA 70+ G,2G.; $5A 31NO.3+ ,3+B $A52 B BGG J G5 KA.5JB BG.2J1. .G .B 3BBAN G5 77A5M.2G 35A21 23 K1JB $5A 11 733G 3 .3733G KA.1B B L11 B 5G.3 B1 K1JB $5A 251 7A2GAB BJ, B )J..GN '1GAG.53 3 A)G.53 5&.3GB; ,3KA 75BB.1 G,B BGAG.3+ K1JB ,K 3 5G.3 $A52 K.11 1.3.1 G; 5LKA .3 G, B 5$ 5G,A KA.1B 3 7A2GAB BJ, B G, '1GAG.53 5&.3G 3 G, B BGG 7ABBJAB 3 .G .B 3BBAN G5 BG.2G B 3 B1 K1JB $A52 251 1.AG.53 B.2J1G.53B N ,.K.3+ 53B.BG3N GL3 251 7A.G.53B 3 1.3.11N 5BAK BGN-BGG ABJ1GB 5$ 53BG3G-AG .3$JB.53B; 53BG3G-AG .3$JB.53 7A5JAB A B.2J1G N .35A75AG.3+ 3 .3$JB.53 GA2 .3G5 =JG.53 849; ,.B 1.AG.53 7A5BB .B 7AB3G .3 $J11 G.1 .3 IP; 3.G.1 3 1.AG K1JB JB .3 G, 3J2A.1 B.2J1G.53B A +.K3 .3 1 6;

,( !. +#" !+#* ,($( #0" + + *!. +#"* ,5AG GA2 .B B.2J1G N .3GA5J.3+ 3+G.K 3+1 .3 =JG.53 849; .G.5311N 1.3.11N 5BAK ,3+B .3 3GA1 KBJ1A 7ABBJAB A .35A75AG .3G5 3 .3 G,.B =JG.53; ,B ABJ1GB A G,3 527A G5 G, 1.3.1 5BAKG.53B 5$ G05K 3 ,BGJ0,.3 $5A K35JB B.3JB 7ABBJA 3 G, 5BAKG.53B 5$ JAG,N 6H $5A .3GAA3.1 7ABBJA; , K1JB 5$ 3 A7AB3G.3+ G, +AK.GN-.3J ,NA5BGG. $5A MAG N G, 51J23 5$ )J. GL3 G, 3GA1 3 .3GAA3.1 527AG23GB A B 53 G, .BG3 GL3 G, A.+,G GA.J2 3 G, B 5$ G, A.3 .3+ I ; 2 ; ,.B ABJ1GB .3 # # II IHI 22+; 3 1.3.1 BGJ.B BGN-BGG AB753B LB 2BJA $GA BKA1 2.3JGB; ,A$5A 155 5115. 5B25G. 7ABBJA .B BBJ2 G5 A2.3 J3,3+ JA.3+ G, JAA3G B.2J1G.53B; JAG,A25A G, /J+J1A K.3 7ABBJAB 7A5K. N G05K 3 ,BGJ0,.3 A 53B.A G5 .3.G.K 5$ G, K35JB-B.3JB 527AG23G 7ABBJA B G, 7G,LN GL3 G,B 527AG23GB B,5J1 A2.3 J3ABGA.G JA.3+ BJ7.3 3 , 5L3 G.1GB; JA.3+ MG3 155 5115. 5B25G. 7ABBJA A57B 6( L,., .3 GJA3 1GAB G, 35A21 $5AB .3K51K .3 )J. '1GAG.53 G G, AA1 7.11AN 1K1; ,JB 153+ GA2 .B B.2J1G .3 233A B.2.1A G5 B,5AG-GA2 M7G G,G 155 5115. 5B25G. 7ABBJA A57B N H;H 22+ $GA * ,5JAB 5$ E +A 6(; ,.B .B .35A75AG .3G5 G, 251 N BGG.3+ # H H .3 =JG.53 849; 3 G,.B B 35 1.3.1 G M.BGB $5A G, .3GAA3.1 AB753B;

.3 .A5+AK.GN

I64

(#1#& ( &#-1 5&4. 4. #( 1! (4'-#& .#'4&1#)(. BN251

BGAG.3+ K1J

J3.GB

BA.7G.53

4I;P I;P H*;6(*E D; I (;* 66;I 66;I 66;P 6PH(;P 6PH(;P ;*ID P;I44( P;6I H P;6I H P P;I44( 6PH*;(D6I P;HIP4 P;6PE4 6 P;PEE( EE;(P 8 9

22+ 22+ 22+ 22+ 22+ 22+ 22+ 22+ 21F2.3 21F2.3 21F2.3 21F2.3 21F2.3 21F2.3 21F2.3 21F2.3 21F2.3 21F2.3 21F2.3 353 821F2.39F22+ 821F2.39F22+ 821F2.39F22+

3GA1 AGAN 7ABBJA .3GAA3.1 AGAN 7ABBJA 7.11AN 7ABBJA K35JB B.3JB 7ABBJA 3GA1 K.3 7ABBJA K3GA.J1A 7ABBJA A.3 7ABBJA MGA-K3GA.J1A 7ABBJA AA1 155 )5L 8AGA.B9 AA1 155 )5L 87.11A.B9 G5G1 $5A2G.53 AG $5A2G.53 $A52 ,5A5. 71MJB 5G,A $5A2G.53 '1GAG.53 A5BB 155 A.3 AA.A 3G )5L GL3 K3GA.1 3 A.3 GA3B23G1 )5L 155 )5L $A52 7.11A.B G5 B.3JBB B5A7G.53 .3G5 G, K35JB B.3JBB MGAA3.1 B5A7G.53 155-A.3 AA.A A)G.53 5&.3G 155-A.3 AA.A '1GAG.53 5&.3G )J..GN GL3 K3GA.J1A 3 A.3 11 5G,A )J..G.B

,(-( )#)/+2 *!. +#"* .3 G,A .B +AGA )J. B,.$G LN $A52 G, 733G 1.2B .3 2.A5+AK.GN G,3 .3 I6 2.A5+AK.GN B.2J1G.53B A 7A$5A2 N 1GA.3+ 155 71B2 5115. 5B25G. 7ABBJAB G5 +AGA MG3G G,3 G,G 5BAK JA.3+ ,-5L3 G.1G; $ G, 155 5115. 5B25G. 7ABBJA A57B H;H 22+ 6( L.G, 3 PP 21 AJG.53 .3 733G 1.2 K51J2 6* JA.3+ .G .B BG.2G $A52 G, G 5$ * 6* G,G 3 6 PP 21 AJG.53 .3 733G 1.2 K51J2 I6 JA.3+ 2.A5+AK.GN B,5J1 ABJ1G .3 71B2 5115. 5B25G. 7ABBJA A57 5$ 35 25A G,3 E;H 22+; , 1.2.G 25J3G 5$ G K.11 $5A ,J23B .3 2.A5+AK.GN BJ++BGB G,G 23 3GA1 AGAN 7ABBJA A2.3B J3,3+ 8* BGA53JGB9 I 3 G,G 3GA1 K35JB 7ABBJA A57B G5 5JG P 22+ 853 BGA53JG9 6; ,B ,3+B A .35A75AG .3G5 G, 251 N BGG.3+ # P # 3 # E H .3 =JG.53 849; +.3 .3 G,.B B 35 1.3.1 G M.BGB $5A G, .3GAA3.1 AB753B;

IIP

; ; 0.3 3 ; ; GK3B

,(,( ##)" ))) " !)#)/+2 ,A .B 35 G K.11 $5A G, AB753B 5$ ,1G,N 155-A.3 AA.A G5 .22AB.53 .3 2.A5+AK.GN 3K.A5323G; , .3G+A.GN 5$ G, 155-A.3 AA.A .B A1G G5 G, G.+,G3BB 5$ G, /J3G.53B GL3 /3G 35G,1.1 11B .3 G, L11B 5$ G, .3GAA3.1 7.11AN KBB1B; KA1 527533GB 53GA.JG G5 2.3G.3.3+ G, G.+,G3BB 5$ G,B /J3G.53B 53 AG,; 2/5A A51 .B AG.31N 71N N ,B.53 GL3 G, 35G,1.1 11B 3 G,.B 527533G L.11 35G %G N 1GAG.53B .3 +AK.GN; 5LKA +AK.GG.531 J315.3+ 5$ 5N G.BBJB 3 )J.B 53 5$ G, 25BG 7AKB.K ,3+B JB N 2.A5+AK.GN 3K.A5323G 2N ,K 3 .1.GN G5 1GA G, .3G+A.GN 5$ G, 155-A.3 AA.A; M75BJA G5 ,.+,A 1K1B 5$ A.G.53 .3 B7 N53 G, B,.1 5$ G, AG,@B G25B7,A 2N 1B5 %G G, 35A21 K51J2B 5$ G, 35G,1.1 11B .3 LN G,G L.11 AJ G.+,G3BB; 2BJA 5$ G.+,G3BB 2N 5G.3 N M2.3.3+ G, MG3G 5$ G, 5KA17 A+.53 3 G, B7 GL3 G, 35G,1.1 11B .3 G, L11B 5$ G, AA1 7.11AN KBB1B; J G5 G, A.+..GN 5$ G, 7.11AN B23G 22A3 G, 7.11AN K51J2 A2.3B 3A1N 53BG3G 3 ,3 G, MG3G 5$ G, 5KA17 A+.53 L.11 1B5 A2.3 3A1N 53BG3G K3 .3 G, $ 5$ .3AB 7.11AN 7ABBJA; 0N 527533G 5$ G, G.+,G3BB 5$ G,.B /J3G.53 .B G,A$5A G, B7 GL3 5KA177.3+ 11B; ,.B B7 L.11 GA2 G, /J3G.53 +7; 3 35A21 +AK.GN 15BJA 5$ G, /J3G.53 +7 .B 2.3G.3 G,A5J+, G, /5.3G G.53 5$ G, .3GA.5A 7.11AN 7ABBJA 3 G, MGA31 .3GABG.G.1 )J. 7ABBJA L,., J+23G ,B.53 5$ G, 35G,1.1 11B; 3 GA2B 5$ 7ABBJAB .3 G, 251 G, 7ABBJA G,G GB G5 07 G, +7 15B 3 LA.GG3 B G, BJ2 # < L,A .B G, .3GABG.G.1 )J. 7ABBJA 5$ G, A.3 3 .B G, .3GAA3.1 7.11AN 7ABBJA; .3 G, A.3 .B 25BG1N )J. .G .B 71 5$ GA3B2.GG.3+ ,NA5BGG. 7ABBJA G5 G, 7.11A.B; ,JB .3 35A21 +AK.GN ,NA5BGG. $5AB G G5 J+23G ; ,.B J+23GG.53 .B 7.G .3 G, G57 .11JBGAG.53 5$ .+JA I; 5LKA .3 2.A5+AK.GN 35 BJ, ,NA5BGG. 7ABBJA .B 7AB3G 3 B5 G,.B J+23GG.53 .B A25K; ,.B .3 GJA3 AJB 3 B 7.G N G, 5GG52 .11JBGAG.53 .3 .+JA I G, G.+,G3BB 5$ G, /J3G.53B 2N AJ; ,.B AB53.3+ .B 53B.BG3G L.G, 5BAKG.53B G,G $5A +3A1 7.11AN-G.BBJ AA.AB .3 G, ABG 5$ G, 5N 2J, 25A )J. M.GB G, 1+ G.BBJB .3 GJ1 2.A5+AK.GN 53.G.53B B 5775B G5 .G,A G, BJ7.3 5A ,-5L3 G.1G 89 75B.G.53B .3 +A5J3-B M7A.23GB II; N53 5L AG, A.G G, 7A5GG.53 5$ G, AG,@B G25B7,A +.3BG A.G.53 .B 35 153+A K.11 3 7A5GG.K 2,3.B2B BJ, B .3AB B,.1.3+ A 3BBAN .3 5AA G5 7A5GG AL 22AB .3 B7 +.3BG KAB A.G.53 %GB; K3 L.G, JAA3G 5J3GA2BJAB 53B.A1 53A3 BG.11 A2.3B 5JG A.G.53 ,1G, .BBJB;

.3 .A5+AK.GN

II6

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3G M7A.23GB 53 AG, N BOON3B0. 6P 66 .3K51K.3+ 11 7,53 A.G.53 253BGAG G, 75G3G.1 %G G,G M75BJA G5 K3 B211 25J3GB 5$ A.G.53 .3 B7 3 ,K 53 G, 155-A.3 AA.A; ,N A75AG G,G G, 25.1 7,53 A.G.53 G.KG 353-G,A21 GA3B.3G ,3+B .3 G, 7A5G.3 M7ABB.53 1K1B 5$ ,B7ID 3 7H .3 ,J23 35G,1.1 11B; G .B ,N75G,B.B .3 6P G,G G.KG.53 5$ ,B7ID 2N JB 3 .3AB .3 155-A.3 AA.A 7A2.1.GN G,A5J+, BG.1.BG.53 5$ 35G,1.1 11 BGABB 'AB; 3AB 7A5G.3 G.K.GN 2N K3 JB G, 35G,1.1 11B G,2B1KB G5 B,A.30 " 1BB3.3+ G,.A K51J2 L.3.3+ G, /J3G.53 +7 3 AJ.3+ G, 5KA17 A+.53;

III

; ; 0.3 3 ; ; GK3B

53B=J3G1N A.G.53 M75BJA .3 B7 77AB 71 5$ KAB1N .27G.3+ G, .3G+A.GN 5$ G, 155 A.3 AA.A;

$ +AK.GG.531 J315.3+ M75BJA G5 .3AB A.G.53 N53 5L AG, A.G 5A B52 5G,A $GJA 5$ 2.A5+AK.GN 3K.A5323G .3JB B1.+,G ,3+B .3 G, 155-A.3 AA.A L.G, GA1.3+" 3.B 251 $5A G, )5L G, '1GAG.53 5&.3G 3 G, A)G.53 5&.3G .3 869 3 /JBG G5 A)G G,B ,3+B; 3 7AG.J1A AB .3 G, G.+,G3BB 5$ G, 155-A.3 AA.A J G5 ,3+ $A52 G, AG,-5J3 BJ7.3 75B.G.53 G5 2.A5+AK.GN 2N 2511 N 3 .3AB .3 G, '1GAG.53 5&.3G 3 AB .3 G, A)G.53 5&.3G; 3 7A$5A2.3+ G, B.2J1G.53B =JG.53 849 .B B51K $5A G, BGN-BGG 7ABBJAB 3 .3 GA2B 5$ 3 G, G.1G 3+1 ; ,B A BA. .3 GA2B 5$ ,3+B $A52 G, B BGG N #

#

8 9 P HD 8 9 P 4P B.389 86P9

#

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8 9 P HD 8 9 P 4P B.389 8669

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86I9

,B =JG.53B $5A2 G, B.B $5A 5G, 8 # P9 3 2.A5+AK.GN 8 # P9 B.2J1G.53 ABJ1GB; G B,5J1 35G G,G J G5 G, BGA.G A+J1G.53 5$ AA1 155 )5L .3 G,.B 251 G, 7ABBJA ,3+B 5K A J3%G N ,3+B .3 3GA1 AGAN 7ABBJA; 3 G, 25A 15AG 251 .3 4 L,A 1A+ ,3+B .3 3GA1 AGAN 7ABBJA A M7G G,.B 2N 35G G, B; 5LKA B.3 3GA1 AGAN 7ABBJA A2.3B A1G.K1N 53BG3G .3 B,5AG GA2 6D 153+GA2 6* 3 2.A5+AK.GN I G,A .B 35 3 G5 .35A75AG BJ, 1A+ ,3+B .3G5 G,B B.2J1G.53B;

( !. +#" )*. +* 1.G.53 5$ G, 2G,2G.1 251 .B 3BBAN $5A .G 3 53B.BG3G1N JB G5 B.2J1G G, %GB 5$ 153+-GA2 3 2.A5+AK.GN 3K.A5323GB L,A 1.3.1 G .B J3K.11 $5A 527A.B53; 3 G, 7AB3G L5A0 251 K1.G.53 .B 7A5K. N 527A.B53 5$ G, 251@B 7A.G.53B $5A B,5AG-GA2 3 1.3.1 G; ($( #)++)! #0" + + , ABJ1GB 5$ B,5AG-GA2 B.2J1G.53B B L11 B 1.3.1 ABJ1GB A +.K3 .3 1 I G03 $A52 IP L,A ,3+B $A52 G, B BGG A .B71N; A 8 9 # 8 9 8 9; ,.B 77A5, .B 57G G5 5225G .%A3B .3 G, B BGG K1JB GL3 G, 251 3 1.3.1 G; 1B5 .3 G,.B G1 A7AB3GB 5G, 3 B G,B .%A3B A .3G.1 .3 B,5AG-GA2 ,-5L3 G.1G B.2J1G.53B; 3 G, A5L 5AAB753.3+

.3 .A5+AK.GN

IIH

4''-#. 1 -)' 1%)5 ( !.14%!#( ( 4-1!7 *2 ( ')& -.4&1., -..4-. - #( '' ( ( &. - #( -., # E

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II*

; ; 0.3 3 ; ; GK3B

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