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Measurement and modeling of oxides of nitrogen from vehicular contributors

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Material Information

Title:
Measurement and modeling of oxides of nitrogen from vehicular contributors
Physical Description:
Book
Language:
English
Creator:
Kenty, Kerstin Lesley
Publisher:
University of South Florida
Place of Publication:
Tampa, Fla
Publication Date:

Subjects

Subjects / Keywords:
NOx
CALINE4
Air pollution
DOAS
NO
Dissertations, Academic -- Chemical Engineering -- Doctoral -- USF   ( lcsh )
Genre:
bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

Notes

Abstract:
ABSTRACT: The focus of this research was the examination of the emission and transformation of nitrogen oxides emitted from vehicles. Measured data for this experiment were collected from May 1 thru May 31, 2002, and were compared to values modeled with CALINE4. CALINE4 is a photochemical and dispersive model used to predict concentrations of NOX (NO+NO2) from line sources. The measurement campaign was coincident with the Bay Regional Atmospheric Chemistry Experiment (BRACE). An ambient air quality monitoring site was constructed adjacent to Gandy Boulevard, in Tampa, FL. When comparisons of measured and modeled NO and NO2 values were made it was found that CALINE4 underpredicted NO2; i.e., underpredicted the conversion of NO, for both daytime and nighttime conditions. Possible causes of this bias were investigated and it was found that the simple kinetic mechanism present in CALINE4 was not sufficient to account for all of the reactions occurring.^ A simulation was run with a more comprehensive NO conversion mechanism and it was found that the reactions containing peroxy radicals affected the conversion rate but were not present in the simple CALINE4 mechanism. The simulation runs suggested that the ratio of radicals to O3 remained nearly constant during the course of the reaction. This pointed to an improved mechanism where the photolytic rate constant in CALINE4 could be replaced with a new constant, keff. This brought theday time calculations within reasonable agreement of the measured values, including an unexpected improvement in nighttime concentrations. Specifically, this modification eliminated the negative fractional bias in calculated daytime NO2 concentrations, moving it from -0.16 to 0.043. The fractional bias in nighttime calculations was improved from -0.17 to -0.036.^ Average hourly traffic counts were then used as inputs to the model to compare to the entire month of May 2002 data and it was found that the daytime fractional bias was improved from -0.27 to -0.06 and the nighttime from -0.35 to -0.24
Thesis:
Dissertation (Ph.D.)--University of South Florida, 2006.
Bibliography:
Includes bibliographical references.
System Details:
System requirements: World Wide Web browser and PDF reader.
System Details:
Mode of access: World Wide Web.
Statement of Responsibility:
by Kerstin Lesley Kenty.
General Note:
Title from PDF of title page.
General Note:
Document formatted into pages; contains 169 pages.
General Note:
Includes vita.

Record Information

Source Institution:
University of South Florida Library
Holding Location:
University of South Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 001921041
oclc - 190859776
usfldc doi - E14-SFE0001874
usfldc handle - e14.1874
System ID:
SFS0026192:00001


This item is only available as the following downloads:


Full Text
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Measurement and modeling of oxides of nitrogen from vehicular contributors
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ABSTRACT: The focus of this research was the examination of the emission and transformation of nitrogen oxides emitted from vehicles. Measured data for this experiment were collected from May 1 thru May 31, 2002, and were compared to values modeled with CALINE4. CALINE4 is a photochemical and dispersive model used to predict concentrations of NOX (NO+NO2) from line sources. The measurement campaign was coincident with the Bay Regional Atmospheric Chemistry Experiment (BRACE). An ambient air quality monitoring site was constructed adjacent to Gandy Boulevard, in Tampa, FL. When comparisons of measured and modeled NO and NO2 values were made it was found that CALINE4 underpredicted NO2; i.e., underpredicted the conversion of NO, for both daytime and nighttime conditions. Possible causes of this bias were investigated and it was found that the simple kinetic mechanism present in CALINE4 was not sufficient to account for all of the reactions occurring.^ A simulation was run with a more comprehensive NO conversion mechanism and it was found that the reactions containing peroxy radicals affected the conversion rate but were not present in the simple CALINE4 mechanism. The simulation runs suggested that the ratio of radicals to O3 remained nearly constant during the course of the reaction. This pointed to an improved mechanism where the photolytic rate constant in CALINE4 could be replaced with a new constant, keff. This brought theday time calculations within reasonable agreement of the measured values, including an unexpected improvement in nighttime concentrations. Specifically, this modification eliminated the negative fractional bias in calculated daytime NO2 concentrations, moving it from -0.16 to 0.043. The fractional bias in nighttime calculations was improved from -0.17 to -0.036.^ Average hourly traffic counts were then used as inputs to the model to compare to the entire month of May 2002 data and it was found that the daytime fractional bias was improved from -0.27 to -0.06 and the nighttime from -0.35 to -0.24
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Dissertation (Ph.D.)--University of South Florida, 2006.
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System requirements: World Wide Web browser and PDF reader.
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;B /*/*Annn%n nnnn#nn"&$nnnn n>$#n n;BB;+n$#nnrn;BB;+n$#nnr*n;B B@+nnnr*n;BB4+ &8Cnnr*n;BB1+n%nnr*n;BB1+n$2 r-nnr*n;BB1+n<# nr*n;BB6+n--rn;BB6?*nnnnnr*n>;BB4?n n@+n/+nnn$/nnnnnnD& -+nD*nn@n2nnn "n+nn/nn2nnnnr n2nnn#*nnn2nnn nr *nn$/n2nnnnrn*nn.nn# n+nn"nrn2nrnn nn$/n *nnr*n;BB4?*/nnn2nnrnn 2n #n2nrnnrrnn*nn,n rnn

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/0 2nnnn2nn@nn2nn#n2n/*nn, 2nrnnr2nnn#n nrnnnr2 n#rnn/*n)rnnnnnrn #nrnnC+nn2nrrnr2nn nnrnn rnn>nnr*n;BB4?*nnnnn2nnnr2nrnr #rnn nnnnnn"&$n*nn82 #+nnnn2 rnrnr#rn2n#rr+nn"&$n nrn2n rnnnn nJn0*6/*nn,nrn2nrr nn:n2#+nnnnn nnnnr nnnn>nnr*n;BB4?*%rr+n$/nn2nrC*nn"&$nn2nrnr2 n nnnnrn*nn.nnn# +nr n2nrrn2nn"nr*nn nnn"nr nnnrrnnn2nr n2nn 2n0*64nn0*=Bn2nnrnnrrn nn*nn,n nn"nrn2nnnnn nrnnn*nn3n2 rnnn"&$nn2nnrrn n2nn" rnnnnnrn# rnn>nnr* ;BB4?*

PAGE 33

/; $#nn2-n>;BB;+;BB;+;BB@?nnnn" &$nn" $n!#rn nn>"$! ?n rnnn>%?*nnn 2nn"&$n2nC+nrnn&r*n nn%D?*$#nn2-n>;BB;+;BB;+;BB@?nrnn#n nrn2 n%$#nn2-n;BB;+;BB;+;BB@?*$#nn2-n>;BB;+n;BB;+n;BB@?n#n/n nn2nrrnrnrnn Jn0*=Ann0*=6n#n2n+ 2#+n#nn#rnn2nn n2nnrn nnn2n*

PAGE 34

// $#nnr*n>;BB@?nnnn$/nrnrn#n2rrn2nn2 nn> nJn0*B1?*nn,nn"&$nnnn$/nn/&@nnnnnnn *nn,n2n2nn nnrnnnnn*$#nn2-n>;BB;+n;BB;?nnnn"& $nn nnnrn2rrn2nnn>D?n *nn2nrn2 rnnnrn#rn+nr nnrn nnnnnD+n-2nn nnn rnn#rnnnnrrnn Dnrn* %nnC+nnrnn>nn n2n?n2n Jn0*1A n0*1=+nnrn Jn0*;6nn0*;/nnn&rn Jn0*1@nn0*1=*nn, rrCnnnCnnrnnn nrn rnnnnnn#r n2nnn"& $nnnDnn>6*4nn4*A:n=*@nn@*6n n n&@nnn+ #r?*nn,nDnnn"&$nr-nn nrn r*nn,nnnnn nn2 nnnrnnnnn nrnnnn;&/nrn&nnnnrrCnnn $#nn2-n>;BB@?nnnn2nn n2nn# rnnnn"&$n2nnC*nn!nnn n2n 2nn#n+nnnnnnn n2nn#nr

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/@ nnnn*nn8nn2n nnn#nnnn rnnrnnn2nn#*nn, nnnCnrn nrnn2nnnnnn*%nnr*n>;BB1?nnn#nnn"&$n nnn r+n3r*nn.nn8n>n?nn n2nrnnr rnn"&$n*nn #r+nrnn 8n2 #rr*nn,nnnrr2nnn nnnn8* --rn>;BB6?nn"&$n2nnn nn@n-n2 nn*nn,nnnnnn2n nrnnn "&$nn2nrn2nnnn *nn,nn n2nnrnr#rn2nnn/0Lnn nrnn2 #nn> nJn0*61?nn2nnrnr#rn2nrnn/0Ln nr nnrn> nJn0*/1?* rrnn2nnnnnn nr2nnn#n ;/nnrn*nn$rnrnnn2n nrnn rnnn0*B=n2nnrnn0*BBn nnn#rnn0*6n* ,nrnnnrnnn0*6nnnn nnnr nnn"&$n*nn3n2nnn nnnn2 rnnnnrnrnn2nrnn 2nnn >%nnr*n;BB1?*

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/4 ,rn;nCnnnn9nn nn& $nnrnnnn*,rn;*nn$nn8rn#n$n 3rn<+n+ n+nrnnn< n* < r $#n2->;BB;+n;BB;+;BB@? @ %< n;n nJn0*BA n/n nJn0*B1 $nrrnn;ALr2nn%< $#n2->;BB;+n;BB;+;BB@? %< n;n Jn0*BA$nn /*Annn%< $#n2->;BB;+n;BB;+;BB@? / %< n;n nJn0*=A n/n Jn0*=6 $#n2->;BB;+n;BB;+;BB@? $ / %< nJn0*B1/&@nnnn#* %< nnr*>;BB4? / rnJn0*B/4 nnr*>;BB4? @ "nnJn0*==@KG& 0*04/ --r>;BB6? @ R/0Ln n J 0*B16H/0Ln n Jn0*/1 .nrnnn2nr2nRnn/0L* %nnr*;BB1 8nJn0*B=$rnrn n $#n2->;BB;+n;BB;+;BB@? .CD n;n J0*1A n/n J0*1= nnrnnnnnnnnnnrrrrCn*

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/A ,rn;*n>? < r $#n2->;BB;+n;BB;+;BB@? ,rD n;n nJn0*;6 n/n nJn0*;/ $nCn* $#n2->;BB;+n;BB;+;BB@? &FrD n;n Jn0*1@ n/n Jn0*1= $nCn* nnr*>;BB4? rnJn0*6// nnr*>;BB4? $ / "nrnJn0*644n 0*=B4 rnn r+nrn2n#nn"rnrn /*/*1n2nnn3n2nn3 ,nrnnn"&$nnrrn-2 *nn3n 2n2nn#nnnnn2#r* nn3 rnnnnnrnnn n* /*/*6nn nnnn,nnnrnnrnnn n>?nnn nnnnnn*nnnn n +nnnn#nnnnn n//0nn>8rr nr*n;BB;?*nn,nnnn#nrnn nrnnnrnn nnnnnn#rnnnn #*nn,+n nnrnnnnnn2n n*nn

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/1 nnnnn2nr#r(n+nnnn nnrnnn #*nn$r+nnrnnrnn n#nn #rnnnnnnrn>n ?*nn nnr#rn>"?nrnnnn2n n*n%+nr +n2nnnnnrnnnr rnnn& nnrnnrrn*nn,nnr nnnrn*nn, nnrrn$ nn;BB=?*nDnnn2nn rn#n nnrnnnn2#rn>$rn n n;BB=?* ,nnnnnnnnn nnrn rr*nn,nrn2rrnn+nn n&nn 2#rn>$nnn;BB=?*n rr+nnnnnn#n2nn nnrn nrnnnrnnn> nr*n;B=4?*

PAGE 39

/6rrrr+ +rrr+ +n /*@nn$+n$+nn/*@*;nn$nn$nnnnn+n/n>nKn/nJnF?nnG >8@G84 K?*nnnnnn+nnnn n *nnnn-nr+nnn rnrnn 2nnnnnn*nn,n nnnnn-n nnrn+nnnn$+nnn2n n* nnnF+n2nnrnnn* ,nnnnnrn2nn nnnr& n2nr*nn,n,n.nnnnn n* /*@*/nnnnCnn/+n2nnnCnnnn>8@?*n%n 8@nnnnnnnnnn nnrr nrnnnnnnnnrn nnnnr*nn/nrCnn2#rnrnn4/4n+n2nn nnr*nn, rnnnnnnS+n2nnSnnn nrnnn nn@*nn,n@nnnnn2nnnn/*nnn,nnrr nnnnr2n>$rnn n;BB =?(

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/= rr++ +r++ +rr = {} = + n r + r = -nnnnrrnnnnn#rn nnrCn nnn@nrr+nnn/nn/*nn' / ?=nn;0 &@ n &; /n >n?0+@00 nJn1*0nn;0 &@4 +nnJn/*@ +@00 nJn0+nnJn0 @ nrr &; n &; @ ;*=nn;0 &;4 @ nrr &; n &; 4 n>n?0+@00 nJn1*/nn;0 &@0 +nnJn@*/ +@00 nJn1*/nn;0 &@0 +nnJn;*@ @ nrr &; n &; (nn/ nn4 +nnrr2nrnnnr( n )n,nnnnnn0+@00 +nn0+ +nnnnnnnnrn/n>$rn n;BB=?*

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/B r + +rr+ + %nn#n+n-/nn-4nnnnn-;nn'/+ nnrnrn>nr?*/*@*@n,nr-rn?nrn2n8+nnnnnrn n>H;0Ln n?+n@nrn>$rnn n;BB=?*nnnn ,nr-rnrnnn2nnnn n#nn r-9nn+nnn8nrnn@nrnn2nn ;;nn;/*nn!n;/nnnn+n nnrnn;0Ln n*n)n nnnr-rnr*nnnnnnr-nnn rnn -+nnnrnnnn>R8?n nnnn# nn>8@?nnn>8/?nnn+nnnnn2-n&8 *nn,rr+n,n8nnnnr-nnn nnn nn#rrnnnr#nn n>$rnn ;BB=?*

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@0++ +rrn ,nr-rnrnnnnPrnnr#rQ n2n/n nn>$rnn n;BB=?+nn rnnr-rn rn><9/?+n2nnn;@* ,nr-rnnrnnn2nnnn nr-nrn>< ?n /nn2nnn;4*nn,nnnn n2nn<9/rn>$rnn n;BB=?*,nnnr-nrnnnrn nnn2 nn>#rrnn?*nn)rnrnrnnn #nnnnn+nnrnr-n r&/n >n;A?nnn8/n>?nrrnnnrn nnn>$rnn n;BB= ?* ,nnnnn;Ann2n nnn/nn8+ n2nnn;1*,nnnnnnnn8/nnrnrnn nn8nrn>$rnn n;BB=?*rrnrr+ ++ +rrnrrrr+ +r

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@; /*@*4nnn,2nnn+n rnnr*n>;BB0?nn$n n8n>;BB6?+ nnnnnn nn+n2n'/nC*n rnnr*n>;BB0?nnnnn nrnnnn@*nn,nnrnnnnn nr+nnr nnnnnn@n2*nn,nn nnnrnnrnrr nnrnnn +n2nnnnn* rrnnnnnn2nnn n@nrnn@n /( )rnnnnn#rnnn nnnr+ rnrnnrn>#nr2?+nnn2 nrnr >$?nnnnnnn@nrnnnrnn* ,nn+n2nr2+n2rnnn nnn r*rrrr+ +

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@/rrr+ +rr +rr + ,nnnnnnnnnn nnnn;= 2rnnn>7nnr*n;BB;?+nnn rnnn2-n$& +n#nn$&/n+n-nnnnr*nn n?nn8@$8//*nn8@nrn2rrnnnnnn2 @+nn2rrn8@$8/nr*n,n8@$8/nrn2rrn-rn n2nnn;B*,n8@$nrn2rnnnCnn8@$/*nn,nn2rn +nn2nnn/0+nnn8@nr*nn,n8@nr 2rnrrnn8@/+nnnr*nn 8@/n2rnnnnnn rnnr*n;BB0?*n,nnn nn8/nnn/*@n;0&;/n@nr&;nn&;n>2rnnr*n;BB0?* ,nnrnnnrnn2rn#n nnnn n#nnnn8Fnr*nn,nn2rnnnF+

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@@ nnnn+nnnnnrnr +nnnnnr *nn rrnr+nr-nnnn,n.n +nnnn n2nnnnnrn*nn,n nnnnnr nnnnnr nr*n;B=A?*nn "rr+nnrnnrn2rnn nnnnn2 /+nnnrn2nnn2nnn;4* $nn8n>;BB6?nrnrnnnn nnn#r *nnn,nnrrn#nn nnnn nKn/nnnnnn#rnnn>8n n$n;BB1?* ,nnrrnn2n/n2rnnnnn#r nrCnnn>nr*n;B=4:nnn n;BB4:n r*n;B=1?n*,nnnnrrnn nnnn n0*/;;01n+n2nnnn2n2rnnnn n*nn" -J;*4A;0&Bn&/n&;nn/B=nn>-nnr*n;BB1?nnrnn nn nrnnnn#nn0*@n n&;+n2#+ rnrn2n#nn2n0*6n n@*/nn&;*nn, nnnrnn2n Cr+n-2nn nrn>nnr*n;B=/?n+nnrnn n8G&/n#r+

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@4 nnrnnnnrnr-*n n,nnr nnnrnnnnnn n#nnn /nrnnnnnr*n .nnn+nnnnn nnn #nnnn/+n2n2nnnnn;@&;1n#*nn, rnrnnnnn2rrnrnn2 nn# nnnnrnrnnn Cnnn/* /*4nn$n!nr/*4*;n3nnn$nn$n!n r rrnn2nnrnrnnr rnnn nn2nrnnnnnnn* nnnr nnnn+nnrn#nn# rnn n#nn2n*nn,nrnn rrnrrnr nnrn>$!?*nn,nrnnn nnn2 rnrnnrnnn2nr r* $!nrrnn+nnrnn nnr +nn+nrn#n#n rn>n n/00/?*n82#+n#nnrnnn nrnrnr 2-nnrrnn>nnn/ 00/?*nn nn rnrrnrnr+n2n+n2 2n

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@A rnnnn#rn>rrnnr*n;B6=+n$ nnn/00;?* rnn#nnDnnrnr n>! r+n222**#?*nnnnrn#n nn>+ /+nF?+nnrnrnrnnnnnn nn 3!4*nn3!4nnnDnrnnn 22n nnnrnnrn# rn>$nnn/00;+ .n;B=B+;B=4?*nn nnnrrnr nrnn 2n+n2n+n+nr#n +nn+n rnnnnnnrnrn nn >.n;B=B?*nn82#+nnrn#rnn Dnrn nrnnr#nnn nn* /*4*/nn$n!nrn8nnnnn2-nnrnrn+ n$n>;B@/?n#r nrn2nr*nn$9nrnnnr nnrn nnnnnn2nrn# nnnnrn >$nnn/00;?*nn+n,n>;B60?n nnrnnr 2nrnnn4AUn>$nnn/00;? *nnrn>;B6@?nrr2+

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@1 2nn,9nrn2nnn& rn2n n4AU>$nnn/00;?*nnrn#nn rnnrn2 nn;AU*nn%nn+nn>;B6/?n#rnnrnn n2nr 2nrn>$nnn/00;?*nn82#+n2n nrnn nnn*nn%nnrn2+n n$n>;B@/?n --rnnr*n>;B=/?nnnr+nnnr n2nnrn2*nn%nnnnrn2nnrn n>$nn /00;+n!rn;BBA?*nnrn>;B6@?nn#nnr nnnnrnr nrn>$nnn/00;?+nn!rn>;B BA?nn rrnnrnnnrn nrnnrn>$ nn/00;?*nnnn rn>;B=B?n#rn nrnnrn nrnnnnDrnn$rn *nn!nnn 2rrnnnnrnr2*$n>;B@/?nnnnnrnnn nn* 8#n#nnn,rn>;B;A?nn;B //?nrnn nnnrnnnnn n+ ,r9nrnnnnnnn rnn2 n2nrnn#+nrnn n#r* rr+n2nnnnr+nn,rn rnnn 2nrnn+nrrnnnrn n>!rn;BBA?*nn$

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@6 c p= -+ + rr r r r r c p=rr r #nnnnnnn nn nnDnn*nn%+n$n rnn#nnnr *nn,nn2nnnn2nrn2n r*nn$ rnnnrnn#nnnnn nnnn nrn>;B@/?*nn,nrnnO9nn rrn#nn$n2( nn)n nnnnn@+nEnnnnnn&;n&;+n++Cn nnnnn+nnn2nnnn&;+n n 'nn>#rn2n;nn/?+nnn+ +Cnnn rnnnnnn*$n#rnnnnnnnrn nnnn rn+nnnnnnnrn rnnrr2nnn #nCnnnnrr*nn3n2nrn nnn nrn2n#nnnnnrnr nnrnn nrnnnnrn*nn,nn2n nnn

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@= c jps s r r rr=n/;nn//nn2n#*nn,nrnn 2rrnnn# nnn>$n;B@/?*$9n2-nrnnn2nnn n2rnn nrn#rnnn*nn$nr nnnnn100nnnn+nnn nnn2r #n2nn#n*,n>;B60?n#rnnrnnnrn nn nrn2*nn,n2nnnn$ 9n>;B@/?nrn >n//?*nn,nnnnnrn2nn2nnn rnnnnn/@n>r2?*)n nnnnn@+nEnnnnnnnn>n&;n&;?+ Cnnnn#nnn2nnnCn nn+nnnn2 nnn&;+nn8nnnrnnn*nn3nnnn nn Crnn+n +nnnn>nn,nnn$ r?nnnnnnnnn nnn' nnnnrrnnnn n* rn>;B6@?nn,9n>;B60?nnn rn2nnnn2 n>$nnn/00;?*nnrn#n nrnn

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@B () () ()() n n n nn n q p q scqqscqq scqqscqq rr r r rrr= + n r + n r ++- nrnnnnrn2 nnn;AUn2nr* ,nrn()nEnnrnn+nnn2n+nnn rnn> #nr?+n8nn+n nnnrnnn#nr >nnrnn2n?nn +Cnnn2n #nrnnnnCn+n#r*nn,nr nnn2 n,n>;B60?nrnnrn2nrnn 10U+n2#+nn rn2nnrnnr*nn%n2n 2n;AUnn10Un nnnrnn;AUnnnnn nn* 3n;B6/+nn#rnnrnnrn nrn>$n n/00;?*nnnn#n#nnnn nn2n nrrnrn2nr+nnn22n nn;0n-nnr nnnrrn2nrrn2nnnrr 2nn&2n2n nrrnrn2n&nnn&2n nr*nn,+nn+ 2+nP#nnn2n2nnnnn nnnrnn #nnnn#nnnnnrn nrPn>

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40 " =n r ++ n r -r r r rrr r r rpssss s ;B6/?*n%nnnnnnr& nnn nnrnnnnnrn nnrnnnn+ nnrnnrnnnnDn rrn>&? nnnnnr*nn 9nrnn2 r2nnn/A()nEnnnrnnnnn&@:n T+n InnnCrnn#r n+n#r+nnnn nnnn nrnr:nInnnnrnn:n8nn rnnnn:nn nnnn2nnnGnnnn nrnnnrn >nnn/00/?*n,nDnn nnn# nnnnn+nnn rrn>;B 1/?*nn3nnn nn#rnrnnn nnnn nnrnn#nnrnn n*nnnr nnn+n2#+nnn2rrn n >n;B6/?*nn$n2n$9nn>;B@/?n2-+n--rnnr*nn> ;B=/?nnnn# nnrnnrnnrn2*nn, n2nnn#nnn2nnn$ 9nrn>$nn

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4; /00;?*nn82#+n!rn>;BBA?nnnnnn rn2nnn nnn2nnnrnrnn n*nn!r9nrn #rn2nn;AUn2nr*nn!r9nrn2n nnn2-nnr >;B6@?nnn$9n2-n>;B@/?nnnrn nnnnrnr *!r9n>;BBA?n2-nnnn2nrn2n n;AUnnn2n nnrnnn2nnnnrrn nn*nnn 2nrn+nnrrr+nnrn Or2n9n>!rn;BBA?* ,nnn!r9n2-nnnnCnn rnnn nnnnnnrn*nn!r 9nrnn rrnnrnnnrn nrnnrn>$ nn/00;?*nn r9n>;B=B?nrnr#nnnrn nrnn rn>nnn/00/+n$nnn/0 0;?*nn,n2nn rnn#nnnnnnnr nnn rn>$nnn/00;?*nnn,nnr nnnrn2n#r nrrnnn2nnnn>nn rn;B=B?*nn,nrnr nn2-nn-n>;B6=?nnn nnnnn2rn>nnn/00/?*nn,nnn rnrnn2nn /1*nn)n nnnrn2nn2nnn2n +nJnn Kn0+n2n0nnn-n>;B6=?nrnn2nn nnn

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4/ () () "" "= n r + + n r -n r + ++ n r r r r r r r r r rpss s s qcq s qcq s nnnnnnnnnnnnnnnnnnnnnnnnnnnn r n2n:nn0nnrnn>80nJn8nKn8+n8nnrn?n'n >nn rn;B=B+nnnn/00/?*nn$n>;BBB?nrnnnn r n>;B=B?nnn nr+n3+nnnnnrnn n#nn*nnn $nnn#nnnnn nrnn #*nnnrn#nnnnn nrnrnn nnrnnrn#*nn$rnrn -nnnnrn nn> nn$n;BBB?*

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4@ /*4*/*;nDn$rn!nnnnnnnrrnn2nn2 nnDn$rn n>-n;B66+;B66?*nn,nn2nrrnnD rnn P#nn#rnnn! n83D8)TnrQn> -n;B66?*nnDr n2nnn#nn! nn;B61nnn83D8) Tnrn n2n#rnn#rnn2nr n#*nn,nn nrnnnn#rnnnr+n nn<)T&/n>< nr*n/00/+n;B6=?*nn;B6=?nr*nnnrnn2n#r nnnn rn&nrnnrn> !-nn8n;B6B? nn&nnrnnnn rnnr >!-+nnnr*nn;B6B?*nn!-nn;B=@?n nrnnr nrnnnn& nrn+ nnDnrnnnnn> n3rn!2 nn2nrn?*.nnnrnnnnn+n nnr#nnn2 rn#r+nnnnnn nnnrrn rn*nn3nnnn2nnnn2 nrn2n#n nrnnnnn*nnn nnnn nrn#rn>**+n$nn8n;BB6?+n rnn>**+n

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44 nr*n/00;?+nnn>**+n--n nr*nn/00;+nnnr* /00/+nr2n/00A?*/*4*/*/nDn$rn!rnnnnnnnn n!-nn8n>;B6B? n!-nnr*nn>;B6B?*nnnrnnnn nrr2* Dnnnnn$nn n;B6Annn# nnr+n3*nnnrnn@A/n#r+n# nn+nn-+nn// #rn>#rnn@00nn?+n2nnrnn# rnn=0n-n&;*nn, ;0n-n-nnnrnnn&n *nn,nn2 n#n;6nnnnn*nn,nr nnn> nnrnnn#r?n2nA41/n nn+nn;@A1n nrnnn>!-nn8n;B6B?* n2nnn/+nrrnnrnr n2nrnn 2nn2nnnnnnnnn-n> !-nnr*n;B6B?* )nnn/0nn2nnnn nnn n*nn)nn2nrnnn (n;*A+n4*4nn;0*44n >n?*nnrnnnrrn2nn nn@*,n2 nnnnn1n8Cnn2n;nn1n>n n/+@?*nn, n2nrnrnnnnnn n>!nr*n;B6B?*

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4A nnnnnn2nn nnnn #n#r*nn)nn;1n-nn//n#rn2n# nnn-nn$%1nn*nn,n2nrnnn2+n2nn r nrn#nnnn#rn nnn*nn% rnr+nn-n#n@0n+n2nrCn n$%1nn %n/*nDn$rn!n,-n*nn,rrn2n2nnnnrnn#rn-nnrnnrn*nn%n@nrnnrn2 %nnn!-nnr*>;B6B?*

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41 %n@*nrrn,2nrnnDn$r n!*nn,nn nnn2nrnnnn;*/+n 4*4nn;0*44nnnn*nn$% 1 rn2nrnnnn0*An>n2?+n@*An nB*An*nn%nnn!nr*n>;B6B?* #n*nn,nrnCn2n@0n*nn$%1nrn2nrCn nnr&rnnn2nr nn >!-nnr*nn;B6B?*nn$%1nrn2nrnnnnn0*A+n@*AnnB *A *-n>;B66?n2nnnrnnn nn *nn%+n2nnn2nnnr2nn 2n

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46 nn*nn-nrnnnn2 nn2rrn#r 2n2nnnnnnn2rrn nPn-*Qnn rn-n2nnnDn$rn!nn n#rn#r rnnrnn2n*nn,nn nnnrn* 82#+nnn22n+nn#nnn2 nnn nnnr*nn-nnnn nrnrn nnr*-nrnrnn2nrnnnnn *nn%+ -nnn2n;00nnnnnnr nnnn nrnn+nnnnr2n2n nnn2nr -n#nnr2nnrnn>; B66?* /*4*@n rrn$rnrnnrnnnnnn nnrn nnnrn*nnnrnnn rr &Dnn rnr*nnnnrnnnnn2 nnrnn rrn2rrn#n2nnnnn n#rnn nnnn;nnA+n2n;nnrn nAnnr*nn)n nnnnn2nnrnnn nnnnn rnnnnrr*nn82#+nnnn nnrnn nnnnnnnnn2rrn-+n +nn2nrnn

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A= # = -+ -+ n r r rrrr r r r r rpss sss 22+nnrnnnrrn nnr&r n2nDnr+n2nnn/6 ( 2nnnnrnn+nnn2n+n nn CnnnCr n#rnDn2nn+n #r:nn8nn nn>.n;B=4+n;B=B+n;BB/?* nnnrnn+nnn#n nn&r* ,n&rnnnnrnrnn2n rnr* <2nnn2nrnnn nnn&r+ nnnnnnn2nnrn n*nn%n rn&rnnrnn nnCnnn nnnrnn>.n;B=4+n;B=B+n;BB/?*n #nn2+nnCnnnnnr nn*nn$ n=*nn,nnnnCnnnn nn#nn2 rn@nnnn*nn rrnnr nn#rn2-n nnnnnrn@nnCrr*nn rnr >#rn?nnrnrn>#rnn nn?nn nn#nn2nn+nn 2nn nn>.n;B=4+n;B=B+nnnr*n;B =;+n!-nn<

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1@rrr + = + n + + = + rrr + = + rr rnnn2n#rnnnnn nn>. ;B=4+n;B=B?*/*A*1n/nnn3!4 nnnrnDnrnrn n# +nnn/+nrnrn+n@nrn n*n,nrnnnn nnnn #nnnnnnn nnn nnrnnn*nnn,n nnn#r nnn@nnnnr#rnr&rnnnn + nnrnn#nn/nnn>.n;BB/?*nnn,+ #nn#nnnrnrn2 n3!4* 3!4nnnrnnnnn 6nnB+n 2nr2nnn/Bnn@;(2nnnnrrnnn nnnnnnrn>. ;B=4+n;B=B+n;BB/?*

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14 nnrnnn@0nn rnn nnn/nnnnnnnnrr n#nn2*nn3rnrnnn nnnB/*ALn n6*ALn/+nn*nn3!4nnnn rnnnrrnrnnn@00n n22n>. ;B=4+n;B=B+n;BB/?*"2nnnnrnnC nnn+ /nn@nn#rnnn*nn.nnn rrnnrrnnnnn nn nnnrnr+nnrnnrnn nr nnnrnn2nnr*nn% nrn +nrnnn#rnn# nnrnr /n*n,nrnnnnnn n& #r+nrnnnnn*nn% n#nr& n+n3!4nnnnrn /n* ,nnnn#nnr&n#rn *nn.nn nnnnn&#n+n3!4n 'nr-n nnrnnnnrn/nnnnnC nrnnnrnnn n*nnn+n n#nnnnn2nn& #n >.n;B=4+n;B=B+n;BB/?*

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1A 3nnnnnnn3!4nnn rn#rn2n nnrrnnrnnnn #rnnn* %nrn##nnnnrrrn2n +n nnnn+nn#rnnnn nrn nrnrnnn#*nn nnnrn *nn,nnnnrnnrnn nnr+n2 n>.n;BB/?*3nnnnnrnnrnnnn rrrn2n+ nrnnn>.n;BB/?*nn

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16 $nnn$nnnrr n( N,nnnnnrn2nn,n.n nnn rn-n#nnnnrrnrn2 nn.
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1= nnrn>nnrnnrn;* /n-rnnn?* ,nnnrnrnrCnnnnn nnn n,n.+n-nnrnrnnn nrn #n-n#rn+n2rnrr2nn-n nnr2 n* nnnn2nn2nnnn nn *nnnnnnnDn.r#*nnnn nnn n!#rn nnn8rrn n>D ?*nn rrnnnnDnnn rn+n/+n+ @+nn$/*nnnnn.
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1B @*/n3@*/*;nDn$n33nnnDn$nnrnn n$n<8?n n+nn2rrnnn+n2nr nn*nnrrn 2nnnnrnrn>#r?nnrn nn +n2#n nrn-nnnnr+nn nr&&r #nrnnnrnr*nnnnn nrnr nnnnnrn nnn nrnn ;0nn;;*

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6; 2nn;/nnrn#nn#nnn;A +n/00/*nn%n7n/&6 nn2nnnrnnnrnrr rnnn#n2n/00*An*nn8n nnn 2nrn/*An*nn,n$nnrnn rr*nn$ nnr-nnr+n2rnnn nrr* +n/+n$/+nC+nn@nnrrnnr*nn,rnn+& r+n2#+nnnrr*nn, +nnn nnnnnnnnnr-nn nn2rrn n#rrnnrnnn*nn%nn r+n nrn2n/;;n+n2nrnnrn nnnn>nnnnnrrnrC ?nnnn 2rn-nnnnn#nnn n2nr* ,rn4nrnnrrnnnnn n* ,rn4*nnnnDnnnn$n nnrn,* Dnn, n>? nn>?40,r+n+n&r/0Cn> @ ?@0 $rnn>$ / ?/0 nn> / ?/0 .C 10

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6A = rnrnnnnrnnn nnnr nnnrrnnnrn+nn nnnnn nnnnnrrnn#nn#n nnn>**+ rn?nnnr2n#nnrnn>* *+nrn ?*,nrnrnnnrnnn@ @( )nnnnnrn>?+nnnn nn rn>?+nnnnrnnnrnrrn>?nnnnnrn >?*nn3rr+nnrnnrn nnr nnnnnnnnr nnnnn nn*nn.n#nnnnn#rnnnnrn# 2n*nnn#nnnnr nnnr nnCnnrn*nn,nnr n2nn2 nCnn*nn3$,nrnn n2 n2n#rr*nn)n3$,nrnn2n n#rr+nn nn#rrn2n*nn,nrrnr nrnn nnn.*

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6= @*/*4nDn)n3nn2nnnnDn.+nn!# rn,r nnnnnrrn nnnnn .
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