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Measurement of community and laboratory-generated airborne particulates using a new sampling method


Material Information

Measurement of community and laboratory-generated airborne particulates using a new sampling method
Physical Description:
Farina, Laura
University of South Florida
Place of Publication:
Tampa, Fla
Publication Date:


Subjects / Keywords:
NIOSH methods
Aerosol chamber
Particulate matter
Dissertations, Academic -- Environmental and Occupational Health -- Masters -- USF   ( lcsh )
non-fiction   ( marcgt )


ABSTRACT: This project resulted from an alleged dust problem affecting the residents in a Florida community. The residents claimed that there were elevated dust levels caused by a rock quarry adjacent to their homes. The purpose of this work was to assess total particulate, respirable particulate, and the coarse content of the sampled particles through traditional NIOSH methods, and using a new, real-time instrument known as the EPAM 5000. Data from the EPAM and NIOSH methods were compared to the EPA's particulate matter standards and the OSHA permissible exposure limits for total and respirable dust. Dust levels using the NIOSH methods were below the limit of detection. There were measurable dust levels in all three size fractions (PM10, PM2.5, PM1) for the EPAM. Due to the undetectable levels of the NIOSH method sampling, further sampling in a laboratory environment was conducted in order to compare NIOSH methods with the EPAM 5000 method. The project continued into an aerosol chamber in the USF College of Public Health Breath Lab for further data collection in order to compare results using traditional NIOSH methods with the results obtained from the EPAM 5000. The chamber was associated with a dust generator that released a steady flow of fly ash particulate at a specific revolution per minute (rpm). Each run of data collection sampled approximately 1 m3 of air and persisted for six to seven hours. Four separate runs were conducted, each at a different generation rate of fly ash. There were measurable dust levels using the NIOSH total dust and NIOSH respirable dust methods. There were also measurable dust levels in all three size fractions (PM10, PM2.5, PM1) for the EPAM. The results of all methods were compared. The PM2.5 and PM1 sampling heads of the EPAM 5000 were compared to the NIOSH respirable dust sampling results. The PM10 sampling head of the EPAM was compared to the NIOSH total dust sampling results. NIOSH 0500 concentration results were within 10% of the EPAM PM10 concentration.
Thesis (M.S.P.H.)--University of South Florida, 2010.
Includes bibliographical references.
System Details:
Mode of access: World Wide Web.
System Details:
System requirements: World Wide Web browser and PDF reader.
Statement of Responsibility:
by Laura Farina.
General Note:
Title from PDF of title page.
General Note:
Document formatted into pages; contains X pages.

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:
usfldc doi - E14-SFE0003478
usfldc handle - e14.3478
System ID:

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Full Text
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Farina, Laura.
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Measurement of community and laboratory-generated airborne particulates using a new sampling method
h [electronic resource] /
by Laura Farina.
[Tampa, Fla] :
b University of South Florida,
Title from PDF of title page.
Document formatted into pages; contains X pages.
Thesis (M.S.P.H.)--University of South Florida, 2010.
Includes bibliographical references.
Text (Electronic thesis) in PDF format.
Mode of access: World Wide Web.
System requirements: World Wide Web browser and PDF reader.
3 520
ABSTRACT: This project resulted from an alleged dust problem affecting the residents in a Florida community. The residents claimed that there were elevated dust levels caused by a rock quarry adjacent to their homes. The purpose of this work was to assess total particulate, respirable particulate, and the coarse content of the sampled particles through traditional NIOSH methods, and using a new, real-time instrument known as the EPAM 5000. Data from the EPAM and NIOSH methods were compared to the EPA's particulate matter standards and the OSHA permissible exposure limits for total and respirable dust. Dust levels using the NIOSH methods were below the limit of detection. There were measurable dust levels in all three size fractions (PM10, PM2.5, PM1) for the EPAM. Due to the undetectable levels of the NIOSH method sampling, further sampling in a laboratory environment was conducted in order to compare NIOSH methods with the EPAM 5000 method. The project continued into an aerosol chamber in the USF College of Public Health Breath Lab for further data collection in order to compare results using traditional NIOSH methods with the results obtained from the EPAM 5000. The chamber was associated with a dust generator that released a steady flow of fly ash particulate at a specific revolution per minute (rpm). Each run of data collection sampled approximately 1 m3 of air and persisted for six to seven hours. Four separate runs were conducted, each at a different generation rate of fly ash. There were measurable dust levels using the NIOSH total dust and NIOSH respirable dust methods. There were also measurable dust levels in all three size fractions (PM10, PM2.5, PM1) for the EPAM. The results of all methods were compared. The PM2.5 and PM1 sampling heads of the EPAM 5000 were compared to the NIOSH respirable dust sampling results. The PM10 sampling head of the EPAM was compared to the NIOSH total dust sampling results. NIOSH 0500 concentration results were within 10% of the EPAM PM10 concentration.
Advisor: Steven Mlynarek, Ph.D.
NIOSH methods
Aerosol chamber
Particulate matter
Dissertations, Academic
x Environmental and Occupational Health
t USF Electronic Theses and Dissertations.
4 856


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22n1+>/An2+>1n1+>2:n 2920210n-,n1+>01n1+>2:n/+A9n1+>1>n r 29202>Bn8+ n /+:0?n/+B?>nA+2?n/+:11n # 29202/1n-8+ n /+:B9n/+:2BnA+>/n/+:A:n nn%! nrnnrnCn#n1n nnnnnnnnnnnnnn ( 6, $ ( )*r+ 6, $ ( )*r+7 r 1 )*r+ 2/2A221n, n 1+>2?n1+>29n2+20n1+>2?n 2920210n-,n1+>11n1+>1Bn2+/Bn1+>10n r 29202>Bn8+ n /+:A9n/+:A>n2+/:n/+:A:n # 29202/1n-8+ n /+:10n/+:10n2+22n/+:10n


n nnnn ( 6, $ ( )*r+ 6, $ ( )*r+7 r 1 )*r+ 2/2A221n, n 1+>29n1+>/?n2+00n1+>/0n 2920210n-,n1+>1Bn1+>1>n2+20n1+>1Bn r 29202>Bn8+ n /+:A>n/+:A>n2+22n/+:A>n # 29202/1n-8+ n /+:10n/+:29n2+?19n/+:/Bn ( 6, $ ( )*r+ 6, $ ( )*r+7 r 1 )*r+ 2/2A221nr,n1+>/>n1+>1An2+A1n1+>/?n 2920210nr8n/+:1>n/+:AAn2+0:n/+:1?n ( 6, $ ( )*r+ 6, $ ( )*r+7 r 1 )*r+ 2/2A221nr,n1+>1An1+>/n2+>/>n1+>/:n $ 29202>?nr8n/+:22n/+:21n2+//9n/+:2/n


:Bn1+>0n/+0n1+>>9n 3rnA>19:n3r1n1+>221n1+0:1n/+1:n1+>22n 1+>2>>n1+0::An 1+>11:n1+0:A9n 1+>/:9n1+0?1>n 1+>1:0n1+09B0n 1+>209n1+0?2:n 1+>AA:n1+0?1>n 1+>/AAn1+0:9Bn 1+0?0>n1+0:?/n 1+>11n1+0:9Bn 3rnnA>A20n3rAn1+>2Bn1+0?n2+B?>n1+>22n 1+>/A/n1+>2:/n 1+>2A>n1+09??n 1+>1>/n1+090:n 1+090:n1+0:?Bn 1+>2:0n1+0:B/n 1+>/0/n1+>2/:n 1+>/??n1+0?0Bn 1+0?1n1+0?0/n 1+>1:1n1+>22:n nA 0>B99n3r0n1+>1/0n1+0?9Bn/+1An1+>/2n 1+>11n1+>121n 1+>12?n1+>2/1n 1+>ABAn1+>22:n 1+>A09n1+0?1n 1+>1>Bn1+0?:Bn 1+>A99n1+0?/n 1+>120n1+0?/n 1+>A09n1+0?/n 1+>A/Bn1+0?1>n


B?2n3r>n1+>220n1+09?n2+>?n1+>22n 1+>2>?n1+0?2>n 1+0?:An1+0?n 1+>/1Bn1+09:?n 1+>2A:n1+0?2>n 1+0?99n1+0?n 1+0?01n1+09:?n 1+>/A/n1+09:?n 1+>2An1+09:?n 1+>290n1+09:?n nA 0>B99n3rBn1+09AAn1+0??1n2+09n1+0?2n 1+0B:>n1+>2A1n 1+0B:>n1+0?2>n 1+09B?n1+09:0n 1+0?2>n1+0?9/n 1+09:0n1+09B0n 1+0::Bn1+0?2?n 1+0?An1+0?>/n 1+09>0n1+>22:n 1+091An1+09:?n nnnnnnnnnnn


n n % nnrnrnCn2+0n8n n ( ( )*r+ ( )*r+7 6,1 )*r+ #29202/1n3r/n1+>02n1+00A2n0+2An1+09?n 1+0002n 1+0>/2n 1+0>A2n 1+0A12n 1+0A02n 1+0A22n 1+01A2n 1+01B2n 1+0A?2n nA 0>B?2n3r1n1+0?9An1+099/n2+A1n1+0?>n 1+>2:0n1+0?2>n 1+0?>An1+0?0/n 1+>2B/n1+0?1>n 1+>22:n1+0?2>n 1+0?:Bn1+0?2>n 1+0?B9n1+0?/:n 1+0?:9n1+0?1>n 1+0?A>n1+0?11n 1+0?9/n1+09?2n nA 0>B99n3rAn1+>10/n1+09B0n/+>?n1+0?>n 1+>12?n1+0:B9n 1+>/22n1+091Bn 1+>/A/n1+0:/2n 1+>2?>n1+0:/>n 1+>1//n1+0B92n 1+>/B9n1+0:>/n 1+>/:An1+0:1>n 1+>2:0n1+0::>n 1+>2:?n1+0B92n


B99n3r0n1+0?B9n1+>//AAn2+>?>n1+>29n 1+0?0Bn1+>1/0n 1+>20>n1+>/n 1+>21>n1+>/0/n 1+>2:Bn1+>/A/n 1+0?09n1+>2/1n 1+0?/:n1+>21An 1+>2A9n1+>1A/n 1+>2?>n1+>1B0n 1+0?B9n1+>19>n nA 0>B9:n3r>n1+>2?Bn1+09?1n2+09?n1+>2/n 1+>/0An1+0?:Bn 1+>2B2n1+0?9An 1+>210n1+0??0n 1+>/1An1+0?21n 1+>2:Bn1+09?Bn 1+>29Bn1+>2/:n 1+>2/?n1+>221n 1+>2A>n1+0?BAn 1+>/22n1+0?/1n nA 0>B99n3rBn1+>/AAn1+>/?n2+/>:n1+>2Bn 1+09/9n1+>/B1n 1+>/B1n1+0?A>n 1+>/B:n1+>1BAn 1+>/B?n1+099/n 1+>2>An1+>//Bn 1+>1//n1+>/:>n 1+09>0n1+>/2:n 1+0::9n1+>29An 1+>2:0n1+0?22n nn


?n3r/n1+>AB2n1+>/B2n2+A91n1+>A0n 1+>002n1+>A12n 1+>0B2n1+>1>2n 1+>A:2n1+>0A2n 1+>1?2n1+>1:2n 1+>AB2n1+>A?2n 1+>0:2n1+>A?2n 1+>AB2n1+>102n 1+>0:2n1+>A02n 1+>1?2n1+>//2n nA 0>B?/n3r1n1+>/1Bn1+0B>>n/+222n1+0?2n 1+>//Bn1+0::Bn 1+>//n1+090:n 1+>/1Bn1+0:/>n 1+0?/2n1+09?>n 1+>2B0n1+09/Bn 1+0?0n1+092/n 1+0?0/n1+0:1>n 1+>2/0n1+090:n 1+0?12n1+0B?2n nA 0>B9:n3rAn1+0??/n1+0B:2n/+B>n1+09>n 1+>/1/n1+0B?2n 1+>2/1n1+0>:Bn 1+>//2n1+0B:1n 1+>290n1+0BB>n 1+>2/:n1+0B?1n 1+>/:9n1+0:A1n 1+>21An1+0>>/n 1+>202n1+0B21n 1+>219n1+0B//n


B?2n3r0n1+09A/n1+00>1n/+>/?n1+0B0n 1+092/n1+000:n 1+091/n1+00?2n 1+09?2n1+00>Bn 1+0:9Bn1+000:n 1+090An1+00>?n 1+092Bn1+001?n 1+09ABn1+0000n 1+091/n1+00B0n 1+09>?n1+00A0n 3rnA>A20n3r>n1+>2/?n1+0??:n2+A>An1+>/2n 1+0990n1+0?:Bn 1+>/:>n1+0?:Bn 1+>1B/n1+>2AAn 1+>A0Bn1+>2>2n 1+>/9An1+>2?Bn 1+>/AAn1+0?9?n 1+>1/0n1+>/??n 1+0?A:n1+0???n 1+>199n1+>1A:n 3rnnA>19:n3rBn1+0?/2n1+>219n2+299n1+0??n 1+09B0n1+090An 1+>2:?n1+0??:n 1+09?Bn1+091An 1+>/2>n1+>/>0n 1+>290n1+09?>n 1+0:?9n1+>2A9n 1+0?12n1+>221n 1+>1//n1+>2:An 1+>/B9n1+0?B/n nnn


?n3r/n1+0??2n1+0912n2+:>>n1+0?>n 1+>2/2n1+0?A2n 1+>2A2n1+09:2n 1+>202n1+0?12n 1+>222n1+0::2n 1+>2?2n1+0?>2n 1+>212n1+0?22n 1+>/>2n1+0:B2n 1+>2B2n1+0::2n 1+>2/2n1+0912n 3rnA>A2Bn3r1n1+>2B?n1+>/1/n/+0/Bn1+0?0n 1+>1//n1+0?>2n 1+0909n1+>209n 1+>2/1n1+>2B0n 1+>1B:n1+>210n 1+>11:n1+10??n 1+>111n1+>20>n 1+>1A:n1+090:n 1+>/:9n1+>2?1n 1+0?A1n1+0?>Bn 3rnA>19:n3rAn1+0?22n1+09?2n2+92?n1+09:n 1+>2/:n1+09>0n 1+0?22n1+0:BBn 1+0?A1n1+0B?>n 1+>/2:n1+0B22n 1+>2>>n1+0?:Bn 1+09B0n1+0?2?n 1+>2A>n1+0>:/n 1+>20?n1+0B:2n 1+09AAn1+0:0/n


B?2n3r0n1+099/n1+0:>:n/+29:n1+0:9n 1+099?n1+0BB2n 1+0?/>n1+0B0>n 1+099/n1+0B1>n 1+0?9An1+0B>2n 1+>2/1n1+0B1>n 1+0?20n1+0B12n 1+0?BAn1+0BA>n 1+099/n1+0BA2n 1+0990n1+0BA:n nA0>?/ n 3r>n1+>/01n1+0?9/n2+>B/n1+>/2n 1+>/92n1+>2/0n 1+>/?An1+>221n 1+>/9An1+0??:n 1+>/?>n1+0?:Bn 1+>/:>n1+0??1n 1+>/22n1+>/A9n 1+>/>1n1+>//:n 1+>1A>n1+0?B/n 1+>/19n1+>2?0n nnA 0>B9:n3rBn1+>12/n1+09B?n/+1/:n1+0?>n 1+>/:An1+0:>>n 1+>2>>n1+090:n 1+>2>2n1+0:?/n 1+>/A/n1+0::/n 1+>2/?n1+0:?/n 1+>/AAn1+091Bn 1+>2/:n1+0:A2n 1+>/1Bn1+090Bn 1+>/A9n1+0:B/n nnnnn


n :/n n $#4Tnr(n$nr&88$r,4&n r,&8


2n2+2/:n2+20/n 2+2A0n2+2//n 2+22Bn2+2/9n 2+//?n2+//9n 2+2A:n2+/22n2+2>Bn2+/>2n $.! 2+/B1n2+10An $ 2+20Bn2+2>Bn2+2/9n2+20?n 2+221n2+21An 2+//?n2+/2>n nnnnnnnnn % 11


n :An n $#4Tn#(n&n-&8,&8.n8$,nCnr&4,.n 48n n



n n n











n n nn






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n n nn

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n ?9n n $#4Tn$(nr&4,.n48n4n$D48&$,nr& #4,4&n n

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n1?+?0n$n2An B;/1;2? n /A(/> n n?/+1nB0+Bn1?+?0nEnA>nn B;/1;2? n />(22 n -n??+An>B+B?n1?+?0nEnA>nn B;/9;2? n 9(0? n n92+9n?2+>n1?+?Bn$n2An B;/9;2? n ?(21 n -n9A+:n9/+An1?+?Bn$n2An B;/9;2? n /0(29 n -n?:+0n>/+1:n1?+?BnEnA>n B;/9;2? n /0(11 n n/22+/n0?+:n1?+?BnEnA>n B;/?;2? n 9(0A n -n9A+>nB?+9n1?+?0nn2n B;/?;2? n ?(22 n n9A+>n:/+1n1?+?0nn2n B;/?;2? n /0(/2 n -n?A+1nB/+:n1?+?0nEnA>n B;/?;2? n /0(1A n n/2/+1n>0+Bn1?+?0nEn A>nn nn B;10;2? n 9(>2 n rn:>+Bn>B+9n1?+:9nEn2An B;10;2? n /0(/2 n rn99+:n>/+An1?+:9nEn>:n B;1>;2? n 9(A1 n rn:9+0nB1+0n1?+9BnEn2An B;1>;2? n /A(19 n rn91+?n>9+:n1?+9BnEn>:n nnNnnnnnn ++ nnnn nn

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n /22n n $#4Tn (n$T,$#$#n4&"nr"-$8n#,n n

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n n n %! n4&"n2B22n8nCn8n2+1n 0 (; : )+ (; : )+ % : )+ )+ r % )r+ 1 2 )*r+ % 3 )+ % 3 )+ % : )+ nr& )*+ nr& )/*+ 3r1n2+2/A0/ n 2+2/A>A n 2+222/1n2+222//n022n1+>2n???+1B9n/+22n2+//2n2+//2n/ /2n 3rAn2+2/A1? n 2+2/A01 n 2+222/An2+222/1n022n1+>2n/222+1An/+22n2+/12n2+/12n/ 12n 3r0n2+2/A2> n 2+2/A1n2+222/>n2+222/0n022n1+>/n/22>+1>n/+2/n2+/02n 2+/A?n/A?n 3r>n2+2/A11 n 2+2/AA0 n 2+222/1n2+222//n022n1+>2n??9+>A9n/+22n2+//2n2+//2n/ /2n 3rBn2+2/1B9 n 2+2/199 n 2+22212n2+222/?n022n1+0?n??>+1/Bn/+22n2+/?2n2+/?/n/ ?/n -)n/ n 2+2/1B9 n 2+2/1B? n 2+2222/n n %n2+/A0n/A0n -)n1 n 2+2/1:: n 2+2/1:: n 2+22222n n n#%n 2+2A0nA0n -)nA n 2+2/>2A n 2+2/>2: n 2+22220n n rDn1>+A2n1>+A2n -)n0 n 2+2/A?n2+2/A9? n 2+2222/ n n rn>n>n -)n> n 2+2//?A n 2+2//9? n 2+22220 n n n 2+2222Bn n n2+//2n//2n n n %n2+2222/n n nnnnnnnnnn /2/n
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n n n %" 4&"n2>22n,nCn8n2+1n 0 (; : )+ (; : )+ % : )+ )+ r % )r+ 1 2 )*r+ % 3 )+ % 3 )+ % : )+ nr& )*+ nr& )/*+ /n2+2/AA1 n 2+2/A>1n2+22212n2+222/?n022nA+A9n/A>A+9An/+A>n2+/?2 n2+/02An/02n 1n2+2/1?B n 2+2/A/>n2+222/?n2+222/9n022nA+01n/AB:+91n/+A:n2+/92 n2+/A/Bn/A1n An2+2/A1> n 2+2/A09n2+2221An2+22211n022nA+A?n/A>0+2/n/+A>n2+112 n2+/B1>n/B1n 0n2+2/AB/ n 2+2/A:Bn2+222/>n2+222/0n022nA+1?n/A/0+B1n/+A/n2+/02 n2+/2B>n/2Bn >n2+2/A/A n 2+2/AAAn2+22212n2+222/?n022nA+A0n/AAB+99n/+A0n2+/?2 n2+/01/n/01n Bn2+2/A1? n 2+2/A0:n2+222/9n2+222/:n022nA+/9n/1:1+99n/+1:n2+/:2 n2+/AABn/A0n :n 2+2/A10 n 2+2/A01n2+222/9n2+222/:n022nA+A2n/A1/+/0n/+A1n2+/:2 n2+/19:n/1?n 9n2+2//9> n 2+2/129n2+2221An2+22211n022nA+A9n/A>A+>Bn/+A>n2+112 n2+/B1>n/BAn ?n2+2/>1B n 2+2/>0/n2+222/>n2+222/0n022nA+A0n/AA:+1?n/+A0n2+/02 n2+/20:n/2>n -)n/ n 2+2/1B9 n 2+2/1B?n2+2222/n % n 2+/A>n/A>n -)n1 n 2+2/1:: n 2+2/1::n2+22222n n#%n 2+21/n1/n -)nA n 2+2/>2A n 2+2/>2:n2+22220n rDn/>+1>2n/>+1>n -)n0 n 2+2/A?n2+2/A9?n2+2222/n rn?n?n -)n> n 2+2//?A n 2+2//9?n2+22220n n2+2222Bn n2+/2>n/2>n % n 2+2222/ n n /21n
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n n n %# n4&"n2B22n8nCn8n2+0n 0 (; : )+ (; : )+ % : )+ )+ r % )r+ 1 2 )*r+ % 3 )+ % 3 )+ % : )+ nr& )*+ nr& )/*+ 3r/n2+2/1:? n 2+2/1?B n 2+222/:n2+222/>n022n 1+0?n ??>+B2n/+22n2+/>2n2+/>/n/>/n 3r1n2+2//?/ n 2+2/12B n 2+222/>n2+222/An022n1+>2n??9+29n/+22n2+/A2n2+/A2n/A 2n 3rAn2+2/19/ n 2+2/1?: n 2+222/Bn2+222/0n022n1+0?n??:+?Bn/+22n2+/02n2+/02n/0 2n 3r0n2+2//?9 n 2+2/1/? n 2+2221/n2+222/?n022n1+>/n/22A+29n/+22n2+/?2n2+/9?n/ 9?n 3r>n2+2/1B1 n 2+2/19/ n 2+222/?n2+222/:n022n1+>2n/222+B2n/+22n2+/:2n2+/:2n/ :2n 3rBn2+2/1// n 2+2/1AB n 2+2221>n2+2221An022n1+>/n/221+09n/+22n2+1A2n2+11?n1 1?n -)n/ n 2+2/1:A n 2+2/19/ n 2+22229n n %n2+/B9n/B9n -)n1 n 2+2/1B/ n 2+2/1B9 n 2+2222:n n n#%n 2+2A:nA:n -)nA n 2+2/1A0 n 2+2/1A/ n 2+2222A n n rDn1/+:?>n1/+:?n -)n0 n 2+2/1B? n 2+2/1:n2+2222/n n rnBnBn -)n> n 2+2/1:: n 2+2/1:B n 2+2222/ n n 2: n 2+2/>2B n 2+2222/ n n n2+/A2n/A2n -)n: n 2+2/A9? n 2+2/A?/ n 2+22221n n -)n9 n 2+2//9? n 2+2//?0 n 2+2222>n n -)n? n 2+2//?> n 2+2//?> n 2+22222n n n n %n2+22221n n nnnnnn /2An
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n n n %$ 4&"n2>22n,nCn8n2+0n 0 (; : )+ (; : )+ % : )+ )+ r % )r+ 1 2 )*r+ % 3 )+ % 3 )+ % : )+ nr& )*+ nr& )/*+ /n2+2/1B1 n 2+2/1??n2+222A:n2+222ABn022nA+A9n/A>A+9An/+A>n2+AB2 n2+1BBn1BBn 1n2+2/A/? n 2+2/A0:n2+22219n2+2221:n022nA+01n/AB:+91n/+A:n2+1:2 n2+/?:n/?:n An2+2//91 n 2+2/1/An2+222A/n2+222A2n022nA+A?n/A>0+2/n/+A>n2+A22 n2+111n111n 0n2+2/A2> n 2+2/AA1n2+2221:n2+2221Bn022nA+1?n/A/0+B1n/+A/n2+1B2 n2+/?9n/?9n >n2+2//?n2+2/1/0n2+22210n2+2221An022nA+A0n/AAB+99n/ +A0n2+1A2n2+/:1n/:1n Bn2+2/199 n 2+2/A/0n2+2221Bn2+2221>n022nA+/9n/1:1+99n/+1:n2+1>2 n2+/?Bn/?Bn :n 2+2/0B? n 2+2/099n2+222/?n2+222/9n022nA+A2n/A1/+/0n/+A1n2+/92 n2+/ABn/ABn 9n2+2/021 n 2+2/0An2+22219n2+2221:n022nA+A9n/A>A+>Bn/+A>n2+1:2n 2+/??n/??n ?n2+2/A/9 n 2+2/A0:n2+2221?n2+22219n022nA+A0n/AA:+1?n/+A0n2+192 n2+12?n12?n -)n/ n 2+2/1B? n 2+2/1:n2+2222/n % n 2+122n122n -)n1 n 2+2/1:: n 2+2/1:Bn2+2222/n n#%n 2+2A>nA>n -)nA n 2+2/>2: n 2+2/>2Bn2+2222/n rDn/:+>29n/:+>/n -)n0 n 2+2/A9? n 2+2/A?/n2+22221n rn?n?n -)n> n 2+2//9? n 2+2//?0n2+2222>n n 2+2//?>n2+22222n n2+/ABn/ABn % n 2+2222/ n nnnn /20n
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n n n % n4&"n2B22n8nCn8n2+9n 0 (; : )+ (; : )+ % : )+ )+ r % )r+ 1 2 )*r+ % 3 )+ % 3 )+ % : )+ nr& )*+ nr& )/*+ 3r/n2+2/1B> n 2+2/19B n 2+2221/n2+2221/n022n 1+>An /2/A+B2n/+2/n2+1/n2+1/2n1/2n 3r1n2+2/19: n 2+2/A/0 n 2+2221:n2+2221:n022n1+0?n??B+29n/+22n2+1:n2+1:0n1:0 n 3rAn2+2/AB/ n 2+2/A9B n 2+2221>n2+2221>n022n1+0?n??0+/1n2+??n2+1>n2+1>0n1>0 n 3r0n2+2/1A9 n 2+2/1B? n 2+222A/n2+222A/n022n1+0Bn?9>+B0n2+??n2+A/n2+A/:nA/: n 3r>n2+2/1?: n 2+2/A10 n 2+2221:n2+2221:n022n1+>/n/220+22n/+22n2+1:n2+1:/n1: /n 3rBn2+2/1:n2+2/1?? n 2+2221?n2+2221?n022n1+>2n???+B9n/+22n2+1?n2+1?An1?A n -)n/ n 2+2/19/ n 2+2/1:? n 2+22221 n n %n2+1:2n1:2n -)n1 n 2+2/1:n2+2/1BA n 2+2222: n n n#%n 2+2ABnABn -)nA n 2+2/1>9 n 2+2/1>/ n 2+2222: n n rDn/A+>29n/A+>/n -)n0 n 2+2//0> n 2+2//>A n 2+22229n n rnBnBn -)n> n 2+2//:A n 2+2//:> n 2+22221n n 2? n 2+2/>2? n 2+22222n n -+n/2n2+2/A99 n 2+2/A9? n 2+2222/n n -+n//n2+2//?0 n 2+2//?? n 2+2222>n n -+n/1n2+2//?B n 2+2//?> n 2+2222/ n n n n %n2+22222n nn /2>n
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n n n % 4&"n2>22n,nCn8n2+9n 0 (; : )+ (; : )+ % : )+ )+ r % )r+ 1 2 )*r+ % 3 )+ % 3 )+ % : )+ nr& )*+ nr& )/*+ /n2+2/A>9 n 2+2/02Bn2+22209n2+22209n022nA+A9n/A>A+9An/+A>n2+0:: n2+A>1nA>1n 1n2+2/11n2+2/1BBn2+2220Bn2+2220Bn022nA+01n/AB:+91n/ +A:n2+0>:n2+AA0nAA0n An2+2/AAA n 2+2/A:Bn2+2220An2+2220An022nA+A?n/A>0+2/n/+A>n2+01: n2+A/>nA/>n 0n2+2/1Bn2+2/A2Bn2+2220Bn2+2220Bn022nA+1?n/A/0+B1n/ +A/n2+0>:n2+A0:nA0:n >n2+2/A91 n 2+2/01:n2+2220>n2+2220>n022nA+A0n/AAB+99n/+A0n2+00: n2+AA0nAA0n Bn2+2/A11 n 2+2/AB1n2+22202n2+22202n022nA+/9n/1:1+99n/+1:n2+A?: n2+A/1nA/1n :n 2+2/1BB n 2+2/A/0n2+22209n2+22209n022nA+A2n/A1/+/0n/+A1n2+0:: n2+AB/nAB/n 9n2+2/A>B n 2+2/02/n2+2220>n2+2220>n022nA+A9n/A>A+>Bn/+A>n2+00: n2+AA2nAA2n ?n2+2/1A? n 2+2/19/n2+22201n2+22201n022nA+A0n/AA:+1?n/+A0n2+0/: n2+A/1nA/1n -)n/ n 2+2/1:/ n 2+2/1:n2+2222/n % n 2+AAAnAAAn -)n1 n 2+2/1:9 n 2+2/1:Bn2+22221n n#%n 2+2/9n/9n -)nA n 2+2/>2? n 2+2/>2?n2+22222n rDn>+02n>+02n -)n0 n 2+2/A99 n 2+2/A9?n2+2222/n rn?n?n -)n> n 2+2//?0 n 2+2//??n2+2222>n n2+2222/n n2+A/1nA/1n % n 2+22222 n nnnn /2Bn
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n n n % 4&"n2>22n,nCn8n/+Bn 0 (; : )+ (; : )+ % : )+ )+ r % )r+ 1 2 )*r+ % 3 )+ % 3 )+ % : )+ nr& )*+ nr& )/*+ /n2+2/11B n 2+2/A>1n2+22/1Bn2+22/1:n022nA+A9n/A>A+9An/+A>n/+1B> n2+?A0n?A0n 1n2+2/199 n 2+2/0//n2+22/1An2+22/10n022nA+01n/AB:+91n/+A:n/+1A> n2+?2An?2An An2+2/191 n 2+2/020n2+22/11n2+22/1An022nA+A?n/A>0+2/n/+A>n/+11> n2+?2>n?2>n 0n2+2/A11 n 2+2/029n2+2229Bn2+2229:n022nA+1?n/A/0+B1n/+A/n2+9B> n2+B>9nB>9n >n2+2/1// n 2+2/A1?n2+22//9n2+22//?n022nA+A0n/AAB+99n/+A0n/+/9> n2+99Bn99Bn Bn2+2/1?/ n 2+2/020n2+22//An2+22//0n022nA+/9n/1:1+99n/+1:n/+/A> n2+9?1n9?1n :n 2+2/191 n 2+2/A?Bn2+22//0n2+22//>n022nA+A2n/A1/+/0n/+A1n/+/0> n2+9B:n9B:n 9n2+2/A>1 n 2+2/0B:n2+22//>n2+22//Bn022nA+A9n/A>A+>Bn/+A>n/+/>> n2+9>An9>An ?n2+2/AB1 n 2+2/0::n2+22//>n2+22//Bn022nA+A0n/AA:+1?n/+A0n/+/>> n2+9B0n9B0n -)n/ n 2+2/1:n2+2/1:n2+22222n % n 2+9B1n9B1n -)n1 n 2+2/1:B n 2+2/1:9n2+22221n n#%n 2+29/n9/n -)nA n 2+2/>2? n 2+2/>/n2+2222/n rDn?+A01n?+A0n -)n0 n 2+2/A9? n 2+2/A99n2+2222/n rn?n?n -)n> n 2+2//?? n 2+2//?Bn2+2222An n 2+2//?An2+22221n n2+B>9nB>9n % n 2+2222/ n /29n
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