United States Environmental Protection Agency, Region 9 

Air Division 

Technical Support Document 

for 

EPA’s Notice of Proposed Rulemaking 

for the 

California State Implementation Plan 

Mojave Desert Air Quality Management District’s 

Rule 1159, Stationary Gas Turbines 

Prepared by: Idalia Perez 

February 2012 
Mojave Desert Air Quality Management District (MDAQMD) 

Submitted Rule 

MDAQMD Rule 1159, Stationary Gas Turbines 

§ Amended: September 28, 2009 

§ Submitted: May 17, 2010 

§ Determined complete: June 8, 2010 

Previous Rule Submittals 

There are no outstanding submittals of Rule 1159. 

SIP-Approved Rule 

§ Adopted: February 22, 1995 

§ Approved by EPA: April 9, 1996 (61 FR 15719) 

Rule Summary 

Rule 1159 regulates emissions of oxides of nitrogen (NOx) and carbon monoxide (CO) from 

non-utility stationary gas turbine systems with ratings equal to or greater than 0.3 MW. 

The emission limits in the Rule are (Section C): 

Emission 

Control Tech. 

Operating 

hours/year 

Rating (MW) NOx limit (ppm) CO limit 

Gas Fuel Liquid Fuel (ppm) 

SCR and 

DLN > 877 > 10 5 25 200 

DLN > 877 2 – 10 25 65 200 

SCR > 877 2 – 10 35 65 200 

DLN > 877 < 2 42 50 250 

SCR or DLN < 877 > 10 25 42 200 

§ 90 ppm NOx for the Southern California Gas Company Turbine Model LM 1500 

§ 225 ppm NOx for Southern California Gas Company Turbine General Electric Model 

Frame 3 

The rule language includes exemptions (Section D). Section D.3 exempts the Southern California 

Gas Company General Electric Model Frame 3 turbine located in Kelso, California from testing 

requirements. Monitoring, administrative and recordkeeping requirements are contained in 

various provisions in Sections E, F, G and H. 

Impact on Emissions

According to the staff report, the District does not expect a reduction in emissions due to the 

implementation of this rule because all existing sources affected by the Rule already comply with 

the emission limits. 

Rule Evaluation Criteria 

We have primarily used the following three criteria to evaluate Rule 1159: 
Rule Stringency Section 172(c)(1) of the Clean Air Act (CAA) requires nonattainment 

areas to implement all reasonably available control measures (RACM), including such 

reductions in emissions from existing sources in the area as may be obtained through the 

adoption, at a minimum, of reasonably available control technology (RACT), as 

expeditiously as practicable. Ozone nonattainment areas classified as moderate or above 

must require RACT for all major sources of NOx. CAA § 182(b)(2) & (f). In addition, 

SIP rules must implement RACM, including RACT, in moderate PM-10 nonattainment 

areas (see CAA sections 189(a)(1)) The MDAQMD regulates an ozone nonattainment 

area classified as Severe-17 for the 1-hour ozone standard and classified as moderate for 

the 8-hour ozone standard (see 40 CFR part 81), thus Rule 1159 must fulfill RACT 

requirements for NOx in the nonattainment area of the District. The MDAQMD also 

regulates a moderate PM-10 nonattainment area, and is therefore subject to the 

requirement under sections 189(a)(1)(C) and 189(e) of the Act to implement RACM for 

control of PM-10 and PM-10 precursor emissions. 

Enforceability CAA section 110(a)(2)(A) requires that regulations submitted to EPA for 

approval into a State Implementation Plan (SIP) must be clear and legally enforceable. 

SIP Revisions CAA section 110(l) prohibits EPA from approving any SIP revision that 

would interfere with any applicable requirement concerning attainment and reasonable 

further progress (RFP) or any other applicable requirement of the CAA. In addition, CAA 

section 193 prohibits the modification of any SIP-approved control requirement in effect 

before November 15, 1990, in a nonattainment area.

Guidance and policy documents that we used to define specific enforceability, RACT and 

RACM requirements include the following: 

§ Issues Relating to VOC Regulation, Cutpoints, Deficiencies, and Deviations (the “Blue 

Book”), US EPA, OAQPS (May 25, 1988). 

§ Guidance Document for Correcting Common VOC and Other Rule Deficiencies, EPA 

Region IX (August 21, 2001, the “Little Bluebook”). 

§ State Implementation Plans; General Preamble for the Implementation of Title I of the 

Clean Air Act Amendments of 1990, 57 FR 13498 (April 16, 1992); 57 FR 18070 (April 

28, 1992). 

§ State Implementation Plans; Nitrogen Oxides Supplement to the General Preamble for 

the Implementation of Title I of the Clean Air Act Amendments of 1990 (the “NOX

Supplement to the General Preamble”), US EPA, 57 FR 55620 (November 25, 1992). 

§ State Implementation Plans for Serious PM-10 Nonattainment Areas, and Attainment 

Date Waivers for PM-10 Nonattainment Areas Generally; Addendum to the General 

Preamble for the Implementation of Title I of the Clean Air Act Amendments of 1990, 59 

FR 41998 (August 16, 1994).

§ PM-10 Guideline Document, US EPA 452/R-93-008 (April 1993).

§ Alternative Control Technology Document, NOx Emissions from Stationary Gas 

Turbines, US EPA, 453/R-93-007 (January 1993)

http://www.epa.gov/ttncatc1/dir1/gasturb.pdf
§ Determination of Reasonably Available Control Technology and Best Available Retrofit 

Control Technology for the Control of Oxides of Nitrogen from Stationary Gas Turbines, 

California Air Resources Board (May 18, 1992) 

http://www.arb.ca.gov/research/apr/reports/l3092.pdf

§ Status Report on NOx Controls for Gas Turbines, Cement Kilns, Boilers, and Internal 

Combustion Engines; Northeast States for Coordinated Air Use Management 

(NESCAUM, December 2000) http://www.nescaum.org/documents/nox-2000.pdf

Evaluation of Rule Stringency 

According to the staff report, five turbines in the District are subject to this rule. Of the five 

units, only one of them (Southern California Gas, Adelanto) is located in the current ozone 

nonattainment area and is thus required to meet RACT for NOx if it is a major source per CAA § 

182(f). This unit is an 11 MW natural gas fueled Jet Derivative Engine, Model GE LM 1500 that 

drives a 3 stage natural gas compressor with nominal 15,000 shaft horsepower. This turbine was 

placed in service in the early 1970’s and the facility has no viable cogeneration applications. 

We believe Rule 1159 implements RACT for units in the current nonattainment area for reasons 

including: 

- The 1993 ACT provides technical information including control techniques and 

achievable controlled NOx emission levels from stationary gas turbines. Rule 1159 

requirements are in alignment with levels of controls that the ACT shows are 

achievable. 

- Rule 1159 requirements are the same as those determined o be RACT in the 1993 

ARB RACT/BARCT determination. 

- The limits in the rule are consistent with what the 2000 report by NESCAUM 

determined to be feasible for retrofit installations. 

- Although the limit for the existing unit is on the high end of the spectrum, we believe 

this is appropriate given the age and location of the unit. 

Since no CTG has been issued recently for this activity, we do not have clear national guidance 

defining presumptive RACT. However, we believe the analysis summarized above sufficiently 

demonstrates that Rule 1159 implements RACT. 

CAA §172(c)(1) requires nonattainment areas to implement all reasonably available control 

measures, including such reductions in emissions from existing sources in the area as may be 

obtained through the adoption, at a minimum, of RACT, as expeditiously as practicable. Gas 

turbines emit NOx, which is a precursor to both PM and ozone. Therefore, MDAQMD must 

implement RACM for turbines if those measures will advance attainment of the National 

Ambient Air Quality Standard (NAAQS) for PM10 or ozone, when considered collectively with 

other reasonable measures. Additional control measures may be required pursuant to CAA 

§172(c)(1) if both: (1) additional measures are reasonably available; and (2) these additional 

reasonably available measures will advance attainment in the area when considered collectively. 

In separate rulemakings, EPA will take action on the State’s RACM demonstration for ozone and 

PM10 based on an evaluation of the control measures submitted as a whole and their overall 

potential to advance the applicable attainment dates in the District. See 40 CFR §§ 51.1010, 

51.912(d). 
Evaluation of Enforceability 

Per §110(a) of the Act, SIP rules must be enforceable. Some of the criteria essential in practically 

enforceable rules include clear statements of applicability, specificity of the standard that must 

be met, explicit statements of compliance time frames, explicit statements of the size of exempt 

units and the length of time of exempt periods, and inclusion of record keeping requirements. We 

believe the submitted rule adequately fulfills most of the relevant criteria identified above. 

Specifically, the rule: 

• is generally clear and has clear applicability; 

• includes adequate recordkeeping and other compliance provisions; 

• has testing and compliance timeframes. 

Nonetheless, Section D.3 includes language that undermines enforceability. 

Specifically, Section D.3 exempts the Southern California Gas Company General Electric Model 

Frame 3 turbine located in Kelso, California from testing requirements. The District submitted 

additional information (attached) indicating that it is economically infeasible for source tests to 

be conducted at this facility. We believe that the unit can be tested using a previous version of 

EPA Method 20. Method 20 was amended on May 15, 2006 (71 FR 28082). The previous 

version of Method can be found in CFRs up to the 2006 version. As explained in EPA’s 

proposed action (68 FR 58838), Method 20 was only amended to remove the testing duplication 

between Method 20 and not because the method was deemed ineffective. This method allows for 

testing at the exhaust point of the turbine, before dilution and the stack. This circumvents the 

issues that the facility claims as a justification for why it is not feasible to source test this unit. 

Evaluation of CAA § 110(l) and 193 

The submitted rule has more stringent emission limits than the version that is currently SIPapproved, thus strengthening the requirements of the SIP. Therefore, we propose to determine 

that a approval of the submittal would comply with CAA sections 110(l) and 193 because (1) the 

proposed SIP revision would not interfere with the on-going process for ensuring that 

requirements for RFP and attainment of the NAAQS are met, and (2) the submitted SIP revision 

is more stringent than the existing SIP requirements. 

Rule Deficiency 

Section D.3 exempts the Southern California Gas Company General Electric Model Frame 3 

turbine located in Kelso, California from testing requirements. 

Suggested Rule Improvement 

Although not currently basis for rule disapproval, EPA recommends that the MDAQMD 

strengthen the NOx emission limits or cap the hours of operations for the following units: 

• Southern California Gas Company Turbine Model LM 1500 

• Southern California Gas Company Turbine General Electric Model Frame 3 

For example, Imperial Valley APCD Rule 400.1 and Antelope Valley AQMD Rule 1134 exempt 

certain turbines that cannot be retrofitted cost effectively from emission limits, but limit the 

number of hours they are operated per year to less than 400 and 200 hours, respectively. 

Recommendation 
EPA staff recommends a limited approval and limited disapproval of MDAQMD Rule 1159 

under CAA sections 110(k)(3) and 301(a). 

Other References 

1. Submitted Rule 1159, adopted on September 28, 2009 

2. Staff Report, dated January 1, 2010 

3. SIP approved Rule 1159, adopted on February 22, 1995 

4. EPA Method 20, version previous to the May 15, 2006 amendment 










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1⁄2±21⁄2a2 ̈Æø ̈·±2 3aø­ ́Æa3a2 ̈ Æø21a  ̈ ̧ø ̈ ·­ 

­°a1⁄2·o·ao o±Æ øooa1⁄2 ̈ao ­± ́Æ1⁄2a 1⁄2ø ̈a1±Æ·a­ ·2  ̈ ̧a 

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3aø­ ́Æa3a2 ̈ ­ß­ ̈a3 ø2o  ̈ ̧a μ2±©2 1⁄2±2Û

1⁄2a2 ̈Æø ̈·±2 ±o  ̈ ̧a 1⁄2ø¥·æÆø ̈·±2 1ø­Ú 
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øo ̈aÆ ø ­ ̈ø ̈ao °aÆ·±o ±o ±°aÆø ̈·±2 o ́Æ·21 

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±Æ øo¶ ́­ ̈3a2 ̈  ̈±±μ °¥ø1⁄2a ø2o  ̈ ̧a ·2° ́ ̈ 1⁄2±2Û

1⁄2a2 ̈Æø ̈·±2 ø ̈  ̈ ̧a  ̈·3a ±o  ̈ ̧a 3aø­ ́Æa3a2 ̈­ 

©ø­ ¶aÆ±Ú 

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 ̈ ̧a μ2±©2 1⁄2±21⁄2a2 ̈Æø ̈·±2 ±o  ̈ ̧a 1⁄2ø¥·æÆø ̈·±2 

1ø­ øo ̈aÆ ø ­ ̈ø ̈ao °aÆ·±o ±o ±°aÆø ̈·±2 o ́Æ·21 

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±Æ øo¶ ́­ ̈3a2 ̈  ̈±±μ °¥ø1⁄2a ø2o  ̈ ̧a ·2° ́ ̈ ø ̈ 

 ̈ ̧a  ̈·3a ±o  ̈ ̧a 3aø­ ́Æa3a2 ̈­ ©ø­ ø  ̧·1 ̧Û 

¥aTMa¥ TMø¥ ́aÚ 

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°±2a2 ̈ ·2  ̈ ̧a ­ø3°¥a 1ø­Ù ± ̈ ̧aÆ  ̈ ̧ø2  ̈ ̧a 1ø­ 

1⁄2±3°±2a2 ̈ æa·21 3aø­ ́ÆaoÚ 

ÌÚ ”aø­ ́Æa3a2 ̈ Õß­ ̈a3 –aÆo±Æ3ø21⁄2a Õ°a1⁄2·o·1⁄2øÛ

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ÌÚÓ ×2 ̈aÆoaÆa21⁄2a Œa­°±2­aÚ ‘a­­  ̈ ̧ø2 oÓ 

°aÆ1⁄2a2 ̈ ±o  ̈ ̧a ­°ø2 TMø¥ ́aÚ 

ÌÚÌ Œa­°±2­a Ã·3aÚ “± 1Æaø ̈aÆ  ̈ ̧ø2 Ìð 

­a1⁄2±2o­Ú 

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­°ø2 TMø¥ ́a ±TMaÆ  ̈ ̧a °aÆ·±o ±o aø1⁄2 ̧  ̈a­ ̈ Æ ́2Ú 

ÌÚÎ ›ø¥·æÆø ̈·±2 ‹Æ·o ̈Ú ‘a­­  ̈ ̧ø2 oÓ °aÆ1⁄2a2 ̈ 

±o  ̈ ̧a ­°ø2 TMø¥ ́a ±TMaÆ  ̈ ̧a °aÆ·±o ±o aø1⁄2 ̧  ̈a­ ̈ 

Æ ́2Ú 

ÏÚ fl°°øÆø ̈ ́­ ø2o Œaø1a2 ̈­ 

ÏÚÔ ”aø­ ́Æa3a2 ̈ Õß­ ̈a3Ú À­a ø2ß 3aø­Û

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a®°a1⁄2 ̈ao  ̈± 3aa ̈  ̈ ̧a ­°a1⁄2·o·1⁄2ø ̈·±2­ ·2  ̈ ̧·­ 

3a ̈ ̧±oÚ fl ­1⁄2 ̧a3ø ̈·1⁄2 ±o ø2 ø1⁄21⁄2a° ̈øæ¥a 3aø­Û

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a­­a2 ̈·ø¥ 1⁄2±3°±2a2 ̈­ ±o  ̈ ̧a 3aø­ ́Æa3a2 ̈ 

­ß­ ̈a3 øÆa oa­1⁄2Æ·æao æa¥±©Ê 
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±Æ aØ ́·TMø¥a2 ̈Ù ±°a2Ûa2oaoÙ ­ ̈Æø·1 ̧ ̈  ̈ ́æa ±o 

­ ́oo·1⁄2·a2 ̈ ¥a21 ̈ ̧  ̈±  ̈ÆøTMaÆ­a  ̈ ̧a ­ø3°¥a 

°±·2 ̈­Ú 

ÏÚÔÚÓ Õø3°¥a ‘·2aÚ ÿaø ̈ao  ̄‚ÁÎ p› ̃ ­ ̈ø·2Û

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ø2ø¥ß¶aÆ­Ú 

ÏÚÔÚÌ ›ø¥·æÆø ̈·±2 ø¥TMa fl­­a3æ¥ßÚ fl  ̈ ̧ÆaaÛ 

©øß TMø¥TMa ø­­a3æ¥ß  ̈± o·Æa1⁄2 ̈  ̈ ̧a ¶aÆ± ø2o 

1⁄2ø¥·æÆø ̈·±2 1ø­a­  ̈±  ̈ ̧a ­ø3°¥a 1⁄2±2o· ̈·±2aÆø2o  ̈±  ̈ ̧a ø2ø¥ß¶aÆ­Ú Ã ̧a 1⁄2ø¥·æÆø ̈·±2 TMø¥TMa 

ø­­a3æ¥ß ­ ̧ø¥¥ æa 1⁄2ø°øæ¥a ±o æ¥±1⁄2μ·21  ̈ ̧a 

­ø3°¥a 1ø­ o¥±© ø2o ±o ·2 ̈Æ±o ́1⁄2·21 1⁄2ø¥·æÆøÛ

 ̈·±2 1ø­a­  ̈±  ̈ ̧a 3aø­ ́Æa3a2 ̈ ­ß­ ̈a3 © ̧a2 

·2  ̈ ̧a 1⁄2ø¥·æÆø ̈·±2 3±oaÚ 

ÏÚÔÚÏ “—Ó  ̈± “— ›±2TMaÆ ̈aÆÚ Ã ̧ø ̈ °±Æ ̈·±2 ±o 

 ̈ ̧a ­ß­ ̈a3  ̈ ̧ø ̈ 1⁄2±2TMaÆ ̈­  ̈ ̧a 2· ̈Æ±1a2 o·±®Û

·oa  ̄“—Ó ̃ ·2  ̈ ̧a ­ø3°¥a 1ø­  ̈± 2· ̈Æ±1a2 ±®·oa 

 ̄“— ̃Ú Õ±3a ø2ø¥ß¶aÆ­ øÆa oa­·12ao  ̈± 3aø­Û

 ́Æa “—» ø­ “—Ó ±2 ø ©a ̈ æø­·­ ø2o 1⁄2ø2 æa 

 ́­ao ©· ̈ ̧± ́ ̈ ø2 “—Ó  ̈± “— 1⁄2±2TMaÆ ̈aÆ ±Æ ø 

3±·­ ̈ ́Æa Æa3±TMø¥  ̈Æø° °Æ±TM·oao  ̈ ̧a ­ø3°¥a 

¥·2a  ̈±  ̈ ̧a ø2ø¥ß¶aÆ ·­  ̧aø ̈ao  ̄‚ÁÎ p› ̃  ̈±  ̈ ̧a 

·2¥a ̈ ±o  ̈ ̧a ø2ø¥ß¶aÆÚ ×2 øoo· ̈·±2Ù ø2 “—Ó  ̈± 

“— 1⁄2±2TMaÆ ̈aÆ ·­ 2± ̈ 2a1⁄2a­­øÆß ·o  ̈ ̧a “—Ó °±ÆÛ

 ̈·±2 ±o  ̈ ̧a a® ̧ø ́­ ̈ 1ø­ ·­ ¥a­­  ̈ ̧ø2 Î °aÆ1⁄2a2 ̈ 

±o  ̈ ̧a  ̈± ̈ø¥ “—» 1⁄2±21⁄2a2 ̈Æø ̈·±2Ú fl­ ø 1 ́·oaÛ

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·o  ̈ ̧a 1ø­  ̈ ́Ææ·2a ·­ ±°aÆø ̈ao ø ̈ Áð °aÆ1⁄2a2 ̈ ±Æ 

3±Æa ±o °aøμ ¥±øo 1⁄2ø°ø1⁄2· ̈ßÚ fl 1⁄2±2TMaÆ ̈aÆ ·­ 

2a1⁄2a­­øÆß  ́2oaÆ ¥±©aÆ ¥±øo 1⁄2±2o· ̈·±2­Ú 

ÏÚÔÚÎ ”±·­ ̈ ́Æa Œa3±TMø¥ ÃÆø°Ú fl ÆaoÆ·1Û

aÆø ̈±ÆÛ ̈ß°a 1⁄2±2oa2­aÆ ±Æ ± ̈ ̧aÆ  ̈ß°a oaTM·1⁄2a 

oa­·12ao  ̈± 1⁄2±2 ̈·2 ́± ́­¥ß Æa3±TMa 1⁄2±2oa2­ø ̈a 

oÆ±3  ̈ ̧a ­ø3°¥a 1ø­ © ̧·¥a 3ø·2 ̈ø·2·21 3·2·Û

3ø¥ 1⁄2±2 ̈ø1⁄2 ̈ æa ̈©aa2 ø2ß 1⁄2±2oa2­ø ̈a ø2o  ̈ ̧a 

­ø3°¥a 1ø­Ú Ã ̧a 3±·­ ̈ ́Æa Æa3±TMø¥  ̈Æø° ·­ 

2± ̈ 2a1⁄2a­­øÆß o±Æ ø2ø¥ß¶aÆ­  ̈ ̧ø ̈ 1⁄2ø2 3aø­ ́Æa 

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ø2ø¥ß¶aÆ­Ù  ̄ø ̃  ̧aø ̈  ̈ ̧a ­ø3°¥a ¥·2a  ́°  ̈±  ̈ ̧a 

·2¥a ̈ ±o  ̈ ̧a ø2ø¥ß¶aÆ­Ù  ̄æ ̃ oa ̈aÆ3·2a  ̈ ̧a 

3±·­ ̈ ́Æa 1⁄2±2 ̈a2 ̈  ́­·21 3a ̈ ̧±o­ ­ ́æ¶a1⁄2 ̈  ̈± 

 ̈ ̧a ø°°Æ±TMø¥ ±o  ̈ ̧a flo3·2·­ ̈Æø ̈±ÆÙ ø2o  ̄1⁄2 ̃ 

1⁄2±ÆÆa1⁄2 ̈  ̈ ̧a “—» ø2o o·¥ ́a2 ̈ 1⁄2±21⁄2a2 ̈Æø ̈·±2­ 

 ̈± ø oÆß æø­·­Ú 

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­°a1⁄2·o·ao ·2 ¤–fl ”a ̈ ̧±o ÎÂ  ̧±©aTMaÆÙ ø2 ± ́ ̈Û 

±oÛ­ ̈ø1⁄2μ o·¥ ̈aÆ ·­ Æa1⁄2±33a2oao © ̧a2  ̈ ̧a 

­ ̈ø1⁄2μ 1ø­  ̈a3°aÆø ̈ ́Æa a®1⁄2aao­ ÓÎð  ̈± Ìðð p›Ú 

ÏÚÔÚÈ Õø3°¥a – ́3°Ú fl 2±2Æaø1⁄2 ̈·TMa ¥aøμÛ 

oÆaa ­ø3°¥a ° ́3°  ̈± ° ́¥¥  ̈ ̧a ­ø3°¥a 1ø­ 

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­°ø2 TMø¥ ́aÚ 

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­°ø2 TMø¥ ́aÚ 

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 ̈ ̧ø2 ðÚÓÎ °aÆ1⁄2a2 ̈ ±o  ̈ ̧a ­°ø2 TMø¥ ́aÚ fl3æ·a2 ̈ 

ø·Æ 3øß æa  ́­ao o±Æ  ̈ ̧a “—» ¶aÆ± 1ø­Ú 

ÏÚÏ ‹·¥ ́a2 ̈ ›ø¥·æÆø ̈·±2 Ÿø­a­Ú 

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ø·Æ ø ̈ ÓðÚÁ °aÆ1⁄2a2 ̈ —Ó ø­  ̈ ̧a  ̧·1 ̧Û¥aTMa¥ —Ó 1ø­Ú 

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°aÆ1⁄2a2 ̈ —Ó ·2 2· ̈Æ±1a2 o±Æ  ̈ ̧a 3·oÛ¥aTMa¥ 1ø­Ù 

ø2o  ́­a ° ́Æ·o·ao 2· ̈Æ±1a2 o±Æ  ̈ ̧a ¶aÆ± 1ø­Ú 

ÏÚÏÚÓ ⁄±Æ ›—Ó 1⁄2ø¥·æÆø ̈·±2 1ø­a­Ù  ́­a ø 1ø­ 

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ø 1ø­ 1⁄2±21⁄2a2 ̈Æø ̈·±2 æa ̈©aa2 Ó ø2o Î °aÆ1⁄2a2 ̈ 

›—Ó ·2 ø·Æ o±Æ  ̈ ̧a 3·oÛ¥aTMa¥ 1⁄2ø¥·æÆø ̈·±2 1ø­Ù 

ø2o  ́­a ° ́Æ·o·ao ø·Æ  ̄‰Ôðð °°3 ›—Ó ̃ ø­  ̈ ̧a 

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ÎÚ ”aø­ ́Æa3a2 ̈ Õß­ ̈a3 –aÆo±Æ3ø21⁄2a Ãa­ ̈ –Æ±1⁄2aÛ

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±o  ̈ ̧a  ̧·1 ̧a­ ̈ °aøμ TMø¥ ́aÙ  ̈ ̧a ­ß­ ̈a3 ·­ 2± ̈ 

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3øß æa  ́­ao ©· ̈ ̧ ø°°Æ±TMø¥ ±o  ̈ ̧a flo3·2·­Û

 ̈Æø ̈±ÆÚ 

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°Æ±TMø¥ ±o  ̈ ̧a flo3·2·­ ̈Æø ̈±ÆÚ 

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o ́1⁄2 ̈­Ù  ̈ ̧a 2 ́3æaÆ ±o ­ø3°¥a °±·2 ̈­ 3 ́­ ̈ æa 

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 ̈·±2 ±o ÃÆøTMaÆ­a –±·2 ̈­Ú flo ̈aÆ  ̈ ̧a 2 ́3æaÆ ±o 

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ø2o æa1·2 ­ø3°¥·21Ú Ã ̧a 3·2·3 ́3 ­ø3°¥·21 

 ̈·3a ø ̈ aø1⁄2 ̧ °±·2 ̈ ­ ̧ø¥¥ æa Ô 3·2 ́ ̈a °¥ ́­  ̈ ̧a 

øTMaÆø1a ­ß­ ̈a3 Æa­°±2­a  ̈·3aÚ ‹a ̈aÆ3·2a 

 ̈ ̧a øTMaÆø1a ­ ̈aøoßÛ­ ̈ø ̈a 1⁄2±21⁄2a2 ̈Æø ̈·±2 ±o 

o·¥ ́a2 ̈ ø ̈ aø1⁄2 ̧ °±·2 ̈ ø2o Æa1⁄2±Æo  ̈ ̧a oø ̈ø ±2 

⁄·1 ́Æa ÓðäÍÚ 

ÍÚÔÚÓÚÏ Õa¥a1⁄2 ̈·±2 ±o ¤3·­­·±2 Ãa­ ̈ Õø3Û

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Œ¤›Ãfl“ŸÀ‘flŒ ÕÃfl›’Õ

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“±Ú ±o  ̈ÆøTMaÆ­a °±·2 ̈­Ê 

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