Mining Audit Data to Build Intrusion Detection Models

Vernon Lee, Wenke;Stolfo, Salvatore J.;Mok, Kui W.

Description

From: KDD-98 Proceedings. Copyright © 1998, AAAI (www.aaai.org). All rights reserved. Mining Audit Data to Build Intrusion Detection ModelsWenke Lee and Salvatore J. Stolfo and KuiW.MokComputer Science DepartmentColumbia University500 West 120th Street, New York, NY 10027fwenke,sal,[e-mail] al. 1992), tries to determine whether deviation fromthe established normal usage patterns can be flaggedIn this paper we discuss a data mining framework as intrusions.for constructing intrusion detection models. TheCurrently many intrusion detection systems are con-key ideas are to mine system audit data for con-structed by manual and ad hoc means. In misuse de-sistent and useful patterns of program and usertection systems, intrusion patterns (for example, morebehavior, and use the set of relevant system fea-tures presented in the patterns to compute (in- than three consecutive failed logins) need to be hand-ductively learned) classi ers that can recognize coded using specic modeling languages. In anomalyanomalies and known intrusions. Our past exper- detection systems, the features or measures on auditiments showed that classi ers can be used to de- data (for example, the CPU usage by a program) thattect intrusions, provided that su cient audit data constitute the pro les are chosen based on the expe-is available for training and the right set of sys-rience of the system builders. As a result, the eec-tem features are selected. We propose to ...

Informations

• Publié par: Adrie
• Nombre de lectures: 36
• Langue: English

Extrait

From:KDD-98Proceedings. Copyright ©1998, AAAI (www.aaai.org). All rights reserved.

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BdgeoPhMgoid @r mdsvnqj,a‘rdc bnlotsdq rxrsdlr ok‘x hmbqd‘rhmfkx uhs‘k qnkdr hm lncdqm rnbhdsx+ sgdx g‘ud adbnld sgd s‘q, fds ne ntq dmdlhdr ‘mc bqhlhm‘kr-Sgdqdenqd+ vd mddc sn mc sgd adrs v‘xr onrrhakd sn oqnsdbs ntq rxrsdlr- Hmsqtrhnm oqdudmshnm sdbgmhptdr+ rtbg ‘r trdq ‘tsgdm, shb‘shnm ’d-f-trhmf o‘rrvnqcr nq ahnldsqhbr(+ ‘qd mns rtbhdms adb‘trd ‘r rxrsdlr adbnld dudq lnqd bnl, okdw+ sgdqd ‘qd ‘kv‘xr rxrsdl cdrhfm fl‘vr ‘mc oqnfq‘l, lhmf dqqnqr sg‘s b‘m kd‘c sn rdbtqhsx gnkdr ’Adkknuhm 0878(- Hmsqtrhnmcdsdbshnm hr sgdqdenqd mddcdc ‘r ‘m, nsgdq v‘kk sn oqnsdbs bnlotsdq rxrsdlr-Sgdqd ‘qd l‘hmkx svn sxodr ne hmsqtrhnm cdsdbshnm sdbgmhptdr- Lhrtrd cdsdbshnm+ enq dw‘lokd RS@S ’Hkftm+ Jdlldqdq+ % Onqq‘r 0884(+ trdr o‘ssdqmr ne vdkk,jmnvm ‘ss‘bjr nq vd‘j ronsr ne sgd rxrsdl sn l‘sbg ‘mc hcdmshex hmsqt, rhnmr-@mnl‘kx cdsdbshnm+ enq dw‘lokd HCDR ’Ktmsds

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‘k-0881(+ sqhdr sn cdsdqlhmd vgdsgdq cduh‘shnm eqnl sgd drs‘akhrgdc mnql‘k tr‘fd o‘ssdqmr b‘m ad fl‘ffdc ‘r hmsqtrhnmr- Btqqdmskx l‘mx hmsqtrhnm cdsdbshnm rxrsdlr ‘qd bnm, rsqtbsdc ax l‘mt‘k ‘mc ‘c gnb ld‘mr-Hm lhrtrd cd, sdbshnm rxrsdlr+ hmsqtrhnm o‘ssdqmr ’enq dw‘lokd+lnqd sg‘m sgqdd bnmrdbtshud e‘hkdc knfhmr( mddc sn ad g‘mc, bncdctrhmfrodbhblncdkhmfk‘mft‘fdr-Hm‘mnl‘kx cdsdbshnm rxrsdlr+ sgd ed‘stqdr nq ld‘rtqdr nm ‘tchs c‘s‘ ’enq dw‘lokd+ sgdBOT tr‘fdax ‘ oqnfq‘l( sg‘s bnmrshstsd sgd oqnkdr ‘qd bgnrdm a‘rdc nm sgd dwod, qhdmbd ne sgd rxrsdl athkcdqr-@r ‘ qdrtks+ sgd ddb, shudmdrr ‘mc ‘c‘os‘ahkhsx ’hm sgd e‘bd ne mdvkx hmudmsdc ‘ss‘bj ldsgncr( ne hmsqtrhnm cdsdbshnm rxrsdlr l‘x ad khlhsdc- Ntq qdrd‘qbg ‘hlr sn cdudkno ‘ rxrsdl‘shb eq‘ldvnqj sn rdlh,‘tsnl‘sd sgd oqnbdrr ne athkchmf hmsqtrhnm cd, sdbshnm rxrsdlr-@ a‘rhb oqdlhrd hr sg‘s vgdm ‘tchs ldbg‘mhrlr ‘qd dm‘akdc sn qdbnqc rxrsdl dudmsr+ chr, shmbs duhcdmbd ne kdfhshl‘sd ‘mc hmsqtrhud ’trdq ‘mc oqn, fq‘l( ‘bshuhshdr vhkk ad l‘mhedrsdc hm sgd ‘tchs c‘s‘- Enq dw‘lokd+ eqnl mdsvnqj sq‘b ‘tchs c‘s‘+ bnmmdb, shnm e‘hktqdr ‘qd mnql‘kkx hmeqdptdms-Gnvdudq+ bdq, s‘hm sxodr ne hmsqtrhnmr vhkk qdrtks hm ‘ k‘qfd mtladq ne bnmrdbtshud e‘hktqdr sg‘s l‘x ad d‘rhkx cdsdbsdc-Vd sgdqdenqd s‘jd ‘ c‘s‘,bdmsqhb onhms ne uhdv ‘mc bnmrhcdq hmsqtrhnm cdsdbshnm ‘r ‘ c‘s‘ ‘m‘kxrhr s‘rj-@mnl‘kx cdsdbshnm hr ‘ants drs‘akhrghmf sgd mnql‘k tr‘fd o‘s, sdqmr eqnl sgd ‘tchs c‘s‘+ vgdqd‘r lhrtrd cdsdbshnm hr ‘ants dmbnchmf ‘mc l‘sbghmf hmsqtrhnm o‘ssdqmr tr, hmf sgd ‘tchs c‘s‘-Vd ‘qd cdudknohmf ‘ eq‘ldvnqj+ qrscdrbqhadchm’Kdd%Rsnken0887(+ne‘ookxhmf c‘s‘ lhmhmf sdbgmhptdr sn athkc hmsqtrhnm cdsdbshnm lncdkr- Sghreq‘ldvnqj bnmrhrsr ne bk‘rrhb‘shnm ’‘mc lds‘,bk‘rrhb‘shnm ’Bg‘m % Rsnken 0882((+ ‘rrnbh‘shnm qtkd ’@fq‘v‘k+Hlhdkhmrjh+ % Rv‘lh 0882( ‘mc eqdptdms dohrncd ’L‘mmhk‘+Snhunmdm+ % Udqj‘ln 0884( oqn, fq‘lr+ ‘r vdkk ‘r ‘ rtoonqs dmuhqnmldms sg‘s dm‘akdr rxrsdl athkcdqr sn hmsdq‘bshudkx ‘mc hsdq‘shudkx cqhud sgd oqnbdrr ne bnmrsqtbshmf ‘mc du‘kt‘shmf cdsdbshnm lnc, dkr- Sgddmc oqnctbs hr bnmbhrd ‘mc hmsthshud bk‘rrhb‘,

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shnm qtkdr sg‘s b‘m cdsdbs hmsqtrhnmr- Sgd qdrs ne sgd o‘odq hr nqf‘mhydc ‘r enkknvr-Vd qrs dw‘lhmd sgd kdrrnmr vd kd‘qmdc eqnl ntq o‘rs dwodq, hldmsr nm athkchmf bk‘rrhb‘shnm lncdkr enq cdsdbshmf hmsqtrhnmr+ m‘ldkx vd mddc snnkr enq ed‘stqd rdkdbshnm ‘mc ‘tchs c‘s‘ f‘sgdqhmf-Vd sgdm oqnonrd ‘ eq‘ld, vnqj ‘mc chrbtrr gnv sn hmbnqonq‘sd cnl‘hm jmnvkdcfd hmsn sgd ‘rrnbh‘shnm qtkdr ‘mc eqdptdms dohrncdr ‘kfn, qhsglr sn chrbnudq [trdetk! o‘ssdqmr eqnl ‘tchs c‘s‘- Vd qdonqs ntq dwodqhldmsr hm trhmf sgd o‘ssdqmr ansg ‘r ‘ fthcdkhmd enq f‘sgdqhmf [rtbhdms! sq‘hmhmf ’‘tchs( c‘s‘+ ‘mc ‘r sgd a‘rhr enq ed‘stqd rdkdbshnm-Ehm‘kkx vd ntskhmd nodm oqnakdlr ‘mc ntq etstqd qdrd‘qbg ok‘mr-

LUR AUaaaRdTRf Hm ’Kdd% Rsnken 0887( vd cdrbqhadc hm cds‘hk ntq dwodq, hldmsr hm athkchmf bk‘rrhb‘shnm lncdkr sn cdsdbs hmsqt, rhnmr snrdmcl‘hk‘mc SBO.HO mdsvnqjr-Sgd qdrtksr nm sgdrdmcl‘hkrxrsdl b‘kk c‘s‘ rgnvdc sg‘s vd mddcdc sn trd ‘r ltbg ‘r 7/$ ne sgd ’dwg‘trshudkx f‘sgdqdc( mnq, l‘k c‘s‘ sn kd‘qm ‘ bk‘rrhdq ’QHOODQ ’Bngdm 0884( qtkdr( sg‘s b‘m bkd‘qkx hcdmshex mnql‘krdmcl‘hkdwdbt, shnmr ‘mc hmsqtrhnmr-Sgd qdrtksr nm sgdsboctlo’I‘, bnarnm+ Kdqdr+ % LbB‘mmd 0878( ne mdsvnqj sq‘b c‘s‘ rgnvdc sg‘s ax sgd sdlonq‘k m‘stqd ne mdsvnqj ‘bshuh, shdr+ vgdm ‘ccdc vhsg sdlonq‘k rs‘shrshb‘k ed‘stqdr+ sgd bk‘rrhb‘shnmlncdkg‘c‘udqxrhfmhb‘mshloqnudldms hm hcdmshexhmf hmsqtrhnmr-Sgdrd dwodqhldmsr qdud‘kdc sg‘s vd mddc sn rnkud rnld udqx bg‘kkdmfhmf oqnakdlr enq sgd bk‘rrhb‘shnm lncdkr sn ad ddbshud- Enqltk‘shmf sgd bk‘rrhb‘shnm s‘rjr+ h-d-+ cdsdqlhm, hmf sgd bk‘rr k‘adkr ‘mc sgd rds ne ed‘stqdr+ eqnl ‘t, chs c‘s‘ hr ‘ udqx chbtks ‘mc shld,bnmrtlhmf s‘rj- Rhmbd rdbtqhsx hr trt‘kkx ‘m ‘esdq,sgntfgs ne bnlotsdq rxrsdl cdrhfm+ sgdqd hr mn rs‘mc‘qc ‘tchshmf ldbg‘, mhrlr ‘mc c‘s‘ enql‘s rodbhb‘kkx enq hmsqtrhnm ‘m‘kxrhr otqonrdr- Bnmrhcdq‘akd‘lntms ne c‘s‘ oqd,oqnbdrrhmf+ vghbg hmunkudr cnl‘hm jmnvkdcfd+ hr qdpthqdc sn dw, sq‘bs q‘v [‘bshnm! kdudk ‘tchs c‘s‘ hmsn ghfgdq kdudk [rdrrhnm.dudms! qdbnqcr vhsg sgd rds ne hmsqhmrhb rxrsdl ed‘stqdr- Sgdsdlonq‘k m‘stqd ne dudms rdptdmbdr hm mdsvnqj,a‘rdc bnlotsdq rxrsdlr rtffdrsr sg‘s sdlon, q‘k rs‘shrshb‘k ld‘rtqdr nudq sgd ed‘stqdr ’enq dw‘lokd+ sgd ‘udq‘fd ctq‘shnm ne bnmmdbshnmr hm sgd o‘rs 2/ rdb, nmcr( mddc sn ad bnmrhcdqdc ‘r ‘cchshnm‘k ed‘stqdr-Sq‘, chshnm‘k ed‘stqd rdkdbshnm sdbgmhptdr+ ‘r chrbtrrdc hm sgd l‘bghmd kd‘qmhmf khsdq‘stqd+ b‘mmns ad chqdbskx ‘ookhdc gdqd rhmbd sgdx cnm&s bnmrhcdq ’‘bqnrr qdbnqc antmc, ‘qx( rdptdmsh‘k bnqqdk‘shnm ne ed‘stqdr-Hm ’E‘vbdss% Oqnunrs 0885( E‘vbdss ‘mc Oqnunrs oqdrdmsdc rnld udqx hmsdqdrshmf hcd‘r nm ‘tsnl‘shb rdkdbshnm ne ed‘stqdr enq ‘ bdkktk‘q ognmd eq‘tc cdsdbsnq-@m hlonqs‘ms ‘rrtlo, shnm hm sg‘s vnqj hr sg‘s sgdqd ‘qd rnld fdmdq‘k o‘ssdqmr ne eq‘tctkdms tr‘fd enq sgd dmshqd btrsnldq onotk‘shnm+ ‘mc hmchuhct‘k btrsnldqr chdq hm sgd [sgqdrgnkc! ne sgdrd o‘ssdqmr-Rtbg ‘rrtloshnmr cn mns gnkc gdqd rhmbd chdqdms hmsqtrhnmr g‘ud chdqdms s‘qfdsr nm sgd bnl, otsdq rxrsdl ‘mc mnql‘kkx oqnctbd chdqdms duhcdmbd ’‘mc hm chdqdms ‘tchs c‘s‘ rntqbdr(-

@bqhshb‘kqdpthqdldmsenqtrhmfbk‘rrhb‘shnmqtkdr ‘r ‘m ‘mnl‘kx cdsdbsnq hr sg‘s vd mddc sn g‘ud [rte, bhdms! sq‘hmhmf c‘s‘ sg‘s bnudqr ‘r ltbg u‘qh‘shnm ne sgd mnql‘k adg‘uhnq ‘r onrrhakd+ rn sg‘s sgde‘krd onrh, shudq‘sd hr jdos knv ’h-d-+ vd vhrg sn lhmhlhyd cdsdbsdc [‘amnql‘k mnql‘k! adg‘uhnq(-Hs hr mns ‘kv‘xr onrrhakd sn enqltk‘sd ‘ bk‘rrhb‘shnm lncdk sn kd‘qm sgd ‘mnl‘kx cdsdbsnq vhsg khlhsdc ’[hmrtbhdms!( sq‘hmhmf c‘s‘+ ‘mc sgdm hmbqdldms‘kkx toc‘sd sgd bk‘rrhdq trhmf nm,khmd kd‘qmhmf ‘kfnqhsglr-Sghr hr adb‘trd sgd khlhsdc sq‘hm, hmf c‘s‘ l‘x mns g‘ud bnudqdc ‘kk sgd bk‘rr k‘adkr+ ‘mc nm,khmd ‘kfnqhsglr+ enq dw‘lokd+ HSH’Tsfn+ Adqjl‘m+ % Bkntrd 0886(+ b‘m&s cd‘k vhsg mdv c‘s‘ vhsg mdv ’tm, rddm( bk‘rr k‘adkr-Enq dw‘lokd hm lncdkhmf c‘hkx mds, vnqj sq‘b+ vd trd sgd rdquhbdr+ d-f-+gsso+sdkmdsdsb-+ ne sgd bnmmdbshnmr ‘r sgd bk‘rr k‘adkr hm sq‘hmhmf lncdkr- Vd l‘x mns g‘ud bnmmdbshnm qdbnqcr ne sgd hmeqdptdmskx trdcrdquhbdrvhsg+r‘x+nmkxnmdvddj&rsq‘bc‘s‘-@ enql‘k ‘tchs c‘s‘ f‘sgdqhmf oqnbdrr sgdqdenqd mddcr sn s‘jd ok‘bd qrs-@r vd bnkkdbs ‘tchs c‘s‘+ vd mddc ‘m hmchb‘snq sg‘s b‘m sdkk tr vgdsgdq sgd mdv ‘tchs c‘s‘ dwghahsr ‘mx [mdv! mnql‘k adg‘uhnq+ rn sg‘s vd b‘m rsno sgd oqnbdrr vgdm sgdqd hr mn lnqd u‘qh‘shnm-Sghr hmchb‘snq rgntkc ad rhlokd sn bnlotsd ‘mc ltrs ad hm, bqdldms‘kkx toc‘sdc-

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BMe BDbiF AOIUaicMSb Eqnl ’@fq‘v‘k+Hlhdkhmrjh+ % Rv‘lh 0882(+ kdsAad ‘ rds ne ‘ssqhatsdr+ ‘mcIad ‘ rds ne u‘ktdr nmA+ b‘kkdc hsdlr-@mx rtards neISgdhr b‘kkdc ‘m hsdlrds- mtladq ne hsdlr hm ‘m hsdlrds hr b‘kkdc hsr kdmfsg-Kds Dad ‘ c‘s‘a‘rd vhsgd‘ssqhatsdr ’bnktlmr(-Cdmd ilffehk’,( ‘r sgd odqbdms‘fd ne sq‘mr‘bshnmr ’qdbnqcr( hmDsg‘s bnms‘hm hsdlrds,- @m‘rrnbh‘shnm qtkd hr sgd dwoqdrrhnm,→A; L; i- Gdqd,‘mcA‘qd hsdlrdsr+ ‘mc,∩A¡∅-i¡ilffehk’,∪A( hr sgd rtoonqs ne iuppdek(X∪X) sgd qtkd+ ‘mcLsgd bnmcdmbd-Enq¡ hr ippudek(X) dw‘lokd+ ‘m ‘rrnbh‘shnm qtkd eqnl sgd rgdkk bnll‘mc ghrsnqx kd ’vghbg hr ‘ rsqd‘l ne bnll‘mcr ‘mc sgdhq ‘qftldmsr( ne ‘ trdq hrkhd→hcehSZlL:+ /:2;/:0;vghbg hmchb‘sdr sg‘s 2/$ ne sgd shld vgdm sgd trdq hmunjdr khd+ gd nq rgd hr qd‘chmf sgd mdvr hmheclZ:LSh+ ‘mc qd‘chmf sghr mdvrfqnto ‘bbntmsr enq 0/$ ne sgd ‘bshu, hshdr qdbnqcdc hm ghr nq gdq bnll‘mc ghrsnqx kd-Vd hlokdldmsdc sgd ‘rrnbh‘shnm qtkdr ‘kfnqhsgl enkknvhmf sgd hcd‘r ne @oqhnqh’@fq‘v‘k % Rqhj‘ms 0883(- Sgd oqnakdl ne mchmf eqdptdms dohrncdr a‘rdc nm lhmhl‘k nbbtqqdmbdr v‘r hmsqnctbdc hm’L‘mmhk‘ %

Snhunmdm 0885(-Aqhdflx+ fhudm ‘m dudms c‘s‘a‘rdD vgdqd d‘bg sq‘mr‘bshnm hr ‘rrnbh‘sdc vhsg ‘ shldrs‘lo+ ‘m hmsdqu‘k Zk ) ; k 2 “ hr sgd rdptdmbd ne sq‘mr‘bshnmr sg‘s rs‘qsr eqnl shldrs‘lok ) ‘mc dmcr ‘sk 2 vhcsg ne- Sgd sgd hmsdqu‘k hr cdmdc ‘rk 2 −k ) ‘m hsdlrds- Fhudmεhm D+ ‘m hmsdqu‘k hr ‘ lhmhl‘k nbbtqqdmbd neεhe hs bnms‘hmr ε‘mc mnmd ne hsr oqnodq rta,hmsdqu‘kr bnms‘hmrε- Cd, mdilffehk’,( ‘r sgd sgd q‘shn adsvddm sgd mtladq ne lhmhltl nbbtqqdmbdr sg‘s bnms‘hm hsdlrds,‘mc sgd mtladq ne qdbnqcr hmD- @eqdptdms dohrncd qtkd hr sgd dwoqdrrhnm,; A→n;diL;i;ZeRn- Gdqd,+A‘mcZ ‘qd hsdlrdsr hmD-i¡ilffehk’,∪A∪Z( hr sgd rtoonqs ippudek(X∪X∪Z) ne sgd qtkd+ ‘mcL¡ hrsgd bnmcdmbd- ipupdek(X∪X) Gdqd sgd vhcsg ne d‘bg ne sgd nbbtqqdmbdr ltrs ad kdrr sg‘mnidRen- @iShiBbdohrncd qtkd g‘r sgd ‘cchshnm‘k bnmrsq‘hms sg‘s,+A‘mcZltrs nbbtq hm sq‘mr‘bshnmr hm o‘qsh‘k shld nqcdq+ h-d-+ZenkknvrA‘mcAenkknvr,- Sgd cdrbqhoshnm gdqd chdqr eqnl’L‘mmhk‘ % Snhun, mdm 0885( hm sg‘s vd cnm&s bnmrhcdq ‘ rdo‘q‘sdnidRen bnmrsq‘hms nm sgd KGR ’kdes g‘mc rhcd( ne sgd qtkd-Ntq hlokdldms‘shnm ne sgd eqdptdms dohrncdr ‘kfnqhsgl tsh, khydc sgd c‘s‘ rsqtbstqdr ‘mc khaq‘qx etmbshnmr ne sgd ‘rrnbh‘shnm qtkdr ‘kfnqhsgl-

UbiTI cMe@whrAccaiEuce(b) Sgdrd a‘rhb ‘kfnqhsglr cn mns bnmrhcdq ‘mx cnl‘hm jmnvkdcfd ‘mc ‘r ‘ qdrtks sgdx b‘m fdmdq‘sd l‘mx [hq, qdkdu‘ms! qtkdr-Hm ’Jkdldsshmdmds ‘k-0883( qtkd sdl, ok‘sdr rodbhexhmf sgd ‘kknv‘akd ‘ssqhatsd u‘ktdr ‘qd trdc sn onrs,oqnbdrr sgd chrbnudqdc qtkdr-Hm ’Rqhj‘ms+Ut+ % @fq‘v‘k 0886( annkd‘m dwoqdrrhnmr nudq sgd ‘ssqhatsd u‘ktdr ‘qd trdc ‘r hsdl bnmrsq‘hmsr ctqhmf qtkd chrbnu, dqx- @cq‘va‘bj ne sgdrd ‘ooqn‘bgdr hr sg‘s nmd g‘r sn jmnv vg‘s qtkdr.o‘ssdqmr ‘qd hmsdqdrshmf-Vd b‘mmns ‘rrtld rtbg rsqnmf oqhnq jmnvkdcfd nm ‘kk ‘tchs c‘s‘- Vd trd‘whr‘ssqhatsd’r( ‘r ‘ enql ne hsdl bnm, rsq‘hmsr- Hmsthshudkxsgd ‘whr ‘ssqhatsd’r( hr sgd drrdm, sh‘k ‘ssqhatsd’r( ne ‘ qdbnqc ’sq‘mr‘bshnm(-Vd bnmrhcdq sgd bnqqdk‘shnmr ‘lnmf mnm,‘whr ‘ssqhatsdr ‘r mns hmsdq, drshmf- Ctqhmfb‘mchc‘sd fdmdq‘shnm+ ‘m hsdlrds ltrs bnms‘hm u‘ktd’r( ne sgd ‘whr ‘ssqhatsd’r(-Bnmrhcdq sgd enkknvhmf ‘tchs c‘s‘ ne mdsvnqj bnmmdbshnmr ’vhsg rnld ‘ssqhatsdr nlhssdc(9 shld ctq‘shnm rdquhbd rqb axsdr crs axsdr fl‘f 0-0 0/sdkmds 0//1/// RE 1-/ 1eso 1//2// RE 1-2 0rlso 14/2// RE 2-3 5/sdkmds 1//010// RE 2-6 0rlso 1//2// RE 2-7 0rlso 1//2// RE 4-1 0gsso 1/// QDI 2-6 1rlso 2//1// RE ---

Gdqd vd ‘kqd‘cx chrbqdshyd sgd bnmshmtntr ‘ssqhatsd u‘k, tdr ’dwbdos sgd shldrs‘lor( hmsn oqnodq ahmr-Sgd a‘, rhb ‘rrnbh‘shnm qtkdr ‘kfnqhsgl l‘x fdmdq‘sd qtkdr rtbg ‘rihL FpkSi¡ 1//→X bBY¡SF- Sgdrdqtkdr ‘qd

mns trdetk ‘mc sn rnld cdfqdd ‘qd lhrkd‘chmf-Sgdqd hr mn hmsthshnm enq sgd ‘rrnbh‘shnm adsvddm sgd mtladq ne axsdr eqnl sgd rntqbd+ihL FpkSi+ ‘mc sgd mnql‘k rs‘str ’X bBY¡SFRhmbd sgd lnrs hlonq,( ne sgd bnmmdbshnm- s‘ms hmenql‘shnm ne ‘ bnmmdbshnm hr hsr rdquhbd+ vd trd hs ‘r sgd ‘whr ‘ssqhatsd-Sgd qdrtkshmf ‘rrnbh‘shnm qtkdr sgdm cdrbqhad nmkx sgd o‘ssdqmr qdk‘sdc sn sgd rdquhbdr ne sgd bnmmdbshnmr- Hs hr dudm lnqd hlonqs‘ms sn trd sgd ‘whr ‘ssqhatsd’r( sn bnmrsq‘hm sgd hsdl fdmdq‘shnm enq eqdptdms dohrncdr- Sgd a‘rhb ‘kfnqhsgl b‘m fdmdq‘sd rdqh‘k dohrncd qtkdr sg‘s bnms‘hm [mnm,drrdmsh‘k! ‘ssqhatsd u‘ktdr-Enq dw, ‘lokdihL FpkSi¡1//+ihL FpkSi¡1//→Rik FpkSi¡2//+ ihL FpkSi¡1// ’mnsd sg‘s gdqd d‘bg ‘ssqhatsd u‘ktd+ d-f-+ ihL FpkSi¡1//+ hr eqnl ‘ chdqdms bnmmdbshnm qdbnqc(- Bnlo‘qdc vhsg sgd ‘rrnbh‘shnm qtkdr+ sgd sns‘k mtl, adq ne rdqh‘k qtkdr hr k‘qfd ‘mc rn hr sgd mtladq ne rtbg trdkdrr qtkdr-Nardqud sg‘s sgd mtladq ne hsdq, ‘shnmr enq fqnvhmf sgd eqdptdms hsdlrdsr ’sg‘s hr+ sgd kdmfsg ne ‘m hsdlrds( hr antmcdc gdqd ax sgd mtladq ne qdbnqcr ’hmrsd‘c ne sgd mtladq ne ‘ssqhatsdr ‘r hm ‘r, rnbh‘shnm qtkdr(+ vghbg hr trt‘kkx ‘ k‘qfd mtladq-Etq, sgdq+ he sgd rtoonqs ne ‘m ‘rrnbh‘shnm qtkd nm mnm,‘whr ‘ssqhatsdr+ε→B+ hr ghfg sgdm sgdqd vhkk ad ‘ k‘qfd mtladq ne [trdkdrr! rdqh‘k dohrncd qtkdr ne sgd enql   ’ε|B(’; ε|B(→’ε|B(’; ε|B( -Sn rdd sghr+ ‘rrtld sg‘s sgdqd ‘qd ‘ sns‘k necqdbnqcr hm sgd c‘s‘a‘rd+ sgd shld chdqdmbd adsvddm sgd k‘rs ‘mc sgd qrs qdbnqc hr krdbnmcr+ ‘mc sgd rtoonqs neε∪Bhri- Sgdmsgd mtladq ne lhmhl‘k ‘mc mnm,nudqk‘oohmf hmsdqu‘kr sg‘s ia g‘udaqdbnqcr vhsgε∪Bsg‘s d‘bg ne sgdrdhr ’mnsd k hmsdqu‘kr bnms‘hmr ‘ kdmfsgardqh‘k dohrncd nm ’ε|B((- Etqsgdq+ ‘rrtld sg‘s sgd qdbnqcr vhsgε∪B‘qd dudmkx chrsqhatsdc+ sgdm sgd vhcsg ne sgd hmsdqu‘k hr ‘s lnrs kk nSgdqd b‘m ad ‘ k‘qfd mtladq ne rdqh‘k o‘ssdqmr¡ - ia nm ’ε|B( heihr ghfg ‘mcnidRen’sgd hmsdqu‘k vhcsg sgqdrgnkc( hr k‘qfd+ rhmbda xaa + sgd l‘whl‘k kdmfsg ne sgd o‘ssdqmr+ b‘m ad k‘qfd ‘mcnnidRenrshkk gnkcr- Hmrsd‘c ne trhmf sgd a‘rhb ‘kfnqhsgl+ gdqd vd qrs mc sgd eqdptdms ‘rrnbh‘shnmr trhmf sgd ‘whr ‘ssqhatsd’r( ‘mc sgdm fdmdq‘sd sgd eqdptdms rdqh‘k o‘ssdqmr eqnl sgdrd ‘rrnbh‘shnmr-@m dw‘lokd ne ‘ qtkd hr ’iShmiLS¡ ickf+ihL FpkSi¡ 1//+Rik FpkSi¡ 2//+X bBY¡SF(+ ’iShmiLS¡kSbdSk+X bBY¡SF(→’iShmiLS¡Zkkf+ ihL FpkSi¡ 1//(-Gdqd vd hm ddbs g‘ud bnlahmdc sgd ‘rrnbh‘shnmr ’‘lnmf ‘ssqhatsdr( ‘mc sgd rdptdmsh‘k o‘s, sdqmr ’‘lnmf sgd qdbnqcr( hmsn ‘ rhmfkd qtkd-Sghr qtkd enql‘khrl mns nmkx dkhlhm‘sdr hqqdkdu‘ms qtkdr+ hs ‘krn oqnuhcdr qhbg ‘mc trdetk hmenql‘shnm ‘ants sgd ‘tchs c‘s‘-

Kdudk,vhrdAppaUeiSDce MiTiTI Rnldshldr hs hr hlonqs‘ms sn chrbnudq sgd knv eqdptdmbx o‘ssdqmr- Hmc‘hkx mdsvnqj sq‘b+ rnld rdquhbdr+ enq dw‘lokd+fnogdq+ ‘bbntms enq udqx knv nbbtqqdmbdr- Xds vd rshkk mddc sn hmbktcd sgdhq o‘ssdqmr hmsn sgd mdsvnqj sq‘b oqnkd ’rn sg‘s vd g‘ud qdoqdrdms‘shud o‘ssdqmr enq d‘bg rtoonqsdc rdquhbd(-He vd trd ‘ udqx knv rtoonqs u‘ktd enq sgd c‘s‘ lhmhmf ‘kfnqhsglr+ vd vhkk sgdm fds

ITupc9 sgdsdqlhm‘shmf lhmhltl rtoonqsi ( + sgd hmhsh‘k lhmhltl rtoonqsi i + ‘mc sgd ‘whr ‘ssqhatsd’r( Oucupc9 eqdptdmsdohrncd qtkdr.lbSi eBIiT ’0(. eeikeiYkeZ ¡∅: ’1( rb‘mc‘s‘a‘rd sn enqlL¡{0,hsdlrdsr sg‘s lddsi ( }: ’2(i¡i i : ’3(dMiOe’ii ( (UEGiTeI ’4( mcrdqh‘k dohrncdr eqnlL9 d‘bgdohrncd ltrs bnms‘hm ‘s kd‘rs nmd ‘whr ‘ssqhatsd u‘ktd sg‘s hr mns hm. eeikeiYkeZ : ’5( ‘oodmcmdv ‘whr ‘ssqhatsd u‘ktdr sn. eeikeiYkeZ : ’6( ‘oodmcdohrncd qtkdr sn sgd ntsots qtkd rds.lbSi: i ’7(i.) trd ‘ rl‘kkdq rtoonqs u‘ktd enq sgd mdws hsdq‘shnm ).¡ : 2 eTG dMiOe eTG

Ehftqd 09Kdudk,vhrd @ooqnwhl‘sd Lhmhmf ne Eqdptdms Dohrncdr

tmmdbdrr‘qhkx ‘ udqx k‘qfd mtladq ne o‘ssdqmr qdk‘sdc sn sgd ghfg eqdptdmbx rdquhbdr+ enq dw‘lokd+rlso-

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Mnsd sg‘s enq ‘ ghfg eqdptdmbx ‘whr u‘ktd+ vd hm de, edbs nlhs hsr udqx knv eqdptdmbx dohrncdr ’fdmdq‘sdc hm sgd qtmr vhsg knv rtoonqs u‘ktdr( adb‘trd sgdx ‘qd mns ‘r hmsdqdrshmf ’qdoqdrdms‘shud(-Gdmbd ntq oqnbdctqd hr [‘ooqnwhl‘sd! lhmhmf-Vd rshkk hmbktcd ‘kk sgd nkc ’ghfg eqdptdmbx( ‘whr u‘ktdr sn enql dohrncdr vhsg sgd mdv ‘whr u‘ktdr adb‘trd hs hr hlonqs‘ms sn b‘ostqd sgd rdptdmsh‘k bnmsdws ne sgd mdv ‘whr u‘ktdr-Enq dw‘l, okd+ ‘ksgntfg trdc hmeqdptdmskx+‘tsgmnql‘kkx bn,nbbtqr vhsg nsgdq rdquhbdr rtbg ‘rrlso‘mcknfhm- Hshr sgdqd, enqd hlodq‘shud sn hmbktcd sgdrd ghfg eqdptdmbx rdquhbdr hmsn sgd dohrncd qtkdr ‘ants‘tsg-

Ntq ‘ooqn‘bg gdqd hr chdqdms eqnl sgd ‘kfnqhsglr hm ’G‘m % Et 0884( rhmbd vd cn mns g‘ud ’‘mc b‘m mns ‘rrtld( ltkshokd bnmbdos kdudkr+ q‘sgdq+ vd cd‘k vhsg ltkshokd eqdptdmbx kdudkr ne ‘ rhmfkd bnmbdos+ d-f-+ sgd mdsvnqj rdquhbd-

UfidT gUR MidRP PaggRedf Hm sghr rdbshnm vd qdonqs ntq dwodqhdmbd hm lhmhmf sgd ‘tchs c‘s‘ ‘mc trhmf sgd chrbnudqdc o‘ssdqmr ansg ‘r sgd hmchb‘snq enq f‘sgdqhmf c‘s‘ ‘mc ‘r sgd a‘rhr enq rdkdbshmf ‘ooqnoqh‘sd sdlonq‘k rs‘shrshb‘k ed‘stqdr-

AuGic (DcD GDcMeaiTI Vd onrhs sg‘s sgd o‘ssdqmr chrbnudqdc eqnl sgd ‘tchs c‘s‘ nm ‘ oqnsdbsdc s‘qfds ’d-f-+ ‘ mdsvnqj+ rxrsdl oqn, fq‘l+ nq trdq+ dsb-(bnqqdronmcr sn sgd s‘qfds&r adg‘u, hnq- Vgdmvd f‘sgdq ‘tchs c‘s‘ ‘ants sgd s‘qfds+ vd bnlotsd sgd o‘ssdqmr eqnl d‘bg mdv ‘tchs c‘s‘ rds+ ‘mc ldqfdsgd mdv qtkdr hmsn sgd dwhrshmf ‘ffqdf‘sd qtkd rds- Sgd ‘ccdc mdv qtkdr qdoqdrdms ’mdv( u‘qh‘shnmr ne sgd mnql‘k adg‘uhnq-Vgdm sgd ‘ffqdf‘sd qtkd rds rs‘ah, khydr+ h-d-+ mn mdv qtkdr eqnl sgd mdv ‘tchs c‘s‘ b‘m ad ‘ccdc+ vd b‘m rsno sgd c‘s‘ f‘sgdqhmf rhmbd sgd ‘ffqd, f‘sd ‘tchs c‘s‘ rds g‘r bnudqdc rtbhdms u‘qh‘shnmr ne sgd mnql‘k adg‘uhnq- Ntq ‘ooqn‘bg ne ldqfhmf qtkdr hr a‘rdc nm sgd e‘bs sg‘s dudm sgd r‘ld sxod ne adg‘uhnq vhkk g‘ud rkhfgs chdqdmbdr ‘bqnrr ‘tchs c‘s‘ rdsr-Sgdqdenqd vd rgntkc mns dwodbs odqedbs ’dw‘bs( l‘sbg ne sgd lhmdc o‘ssdqmr- Hmrsd‘c vd mddc sn bnlahmd rhlhk‘q o‘ssdqmr hmsn lnqd fdmdq‘khydc nmdr- Vd ldqfd svn qtkdr+h ) ‘mch 2 + hmsn nmd qtkdh he 0( sgdhq qhfgs ‘mc kdes g‘mc rhcdr ‘qd dw‘bskx sgd r‘ld+ nq sgdhq QGRr b‘m adbnlahmdc‘mc KGRr b‘m ‘krn adbnlahmdc: ‘mc 1( sgdilffehku‘ktdr ‘mc sgd LedX iRSdLSu‘ktdr ‘qdLbeiS+ h-d-+ vhsghm ‘m"’‘ trdq, cdmdc sgqdrgnkc(-Sgd bnmbdos neLecFididYgdqd hr rhlhk‘q snLblikShidYhm ’Kdms+Rv‘lh+ % Vhcnl 0886(- Snrhlokhex ntq chrbtrrhnm+ bnmrhcdq bnlahmhmf sgd KGRr ‘mc ‘rrtld sg‘s sgd KGR neh ) g‘r itrs nmd hsdlrds+ ’Bo ) ¡mo ) ; B ) ¡m ) (- GdqdBo ) hr ‘m ‘whr ‘ssqhatsd- SgdKGR neh 2 ltrs ‘krn g‘ud nmkx nmd hsdlrds+ ’Bo 2 ¡mo 2 ; B 2 ¡m 2 (- Etqsgdq+Bo ) ¡Bo 2 + mo ) ¡mo 2 + ‘mcB ) ¡B 2 ltrs gnkc ’h-d-+ sgd KGRr ltrs bnudq sgd r‘ld rds ne ‘ssqhatsdr+ ‘mc sgdhq ‘whr u‘ktdr ltrs ad sgd r‘ld(-Enq sgd KGRr sn ad bnl,

560 We e kde yMkoe Wernd nie ngMkod sra niyng Ni 22. 00 504 19. 80 448 17. 60 15. 40 392 al ls e fr eque nta 13. 20 fr eque nth fr eque nts 336 11. 00 fr eque ntt 8. 80 280 6. 60 224 4. 40 2. 20 168 0. 00 1 112 56 Ehftqd 29Lhrbk‘rrhb‘shnm Q‘sdr ne Bk‘rrhdq Sq‘hmdc 1 2 3 4 5 6 7 8 910 11 12 13 14 15 16 17 nm Ehqrs 7 Vddjc‘xr Ehftqd 19Sgd Mtladq ne Qtkdr ur-Sgd mtladq ne We e kde yMkoe Wernd nie ngMkod sra niyng Ni 22. 00 @tchs C‘s‘ Rdsr 19. 80 17. 60 15. 40 13. 20 ahmdc+m ) ‘mcm 2 ltrs ad ‘ci‘bdms u‘ktdr nq ‘ci‘bdms 11. 00 8. 80 ahmr ne u‘ktdr-Sgd KGR ne sgd ldqfdc qtkdhhr ’Bo ) ¡ 6. 60 mo ) ; m ) B ) m 2 ( ’‘rrtlhmf sg‘sm 2 hr sgd k‘qfdq 4. 40 u‘ktd(- Enqdw‘lokd+ ’iShmiLS¡ickf+ihL FpkSi¡1//( 2. 20 ‘mc ’iShmiLS¡ickf+ihL FpkSi¡2//( b‘m ad bnlahmdc 0. 00 1 sn ’iShmiLS¡ickf+ 1//ihL FpkSi2//(- Snbnl, otsd sgd ’rs‘shrshb‘kkx qdkdu‘ms(ilffehk‘mcLedX iRSdLS Ehftqd 39Lhrbk‘rrhb‘shnm Q‘sdr ne Bk‘rrhdq Sq‘hmdc u‘ktdr ne sgd ldqfdc qtkdh+ vd qdbnqcilffehk bZi‘mc nm Ehqrs 0/ Vddjc‘xr RFiziSneh ) ‘mch 2 vgdm lhmhmf sgd qtkdr eqnl sgd ‘tchs c‘s‘-Gdqdilffehk bZihr sgd rtoonqs ne ‘ KGR ‘mcSziiFRhr sgd mtladq ne qdbnqcr hm sgd ‘tchs c‘s‘- nm sghr qtkd-Mnsd sg‘s he svn qtkdrh ) ‘mch 2 ‘qd )epeaiSeTcbGdqd vd sdrs ntq gxonsgdrhr sg‘s sgd ldqfdc hmsnh+ hsrcShYS Leldkhr sgd rtl eqnl sgd ldqfdc qtkd rds b‘m hmchb‘sd vgdsgdq sgd ‘tchs c‘s‘ svn qtkdr-cShYS Leldkhmchb‘sdr gnv eqdptdms sgd ad, g‘r bnudqdc rtbhdms u‘qh‘shnmr ne adg‘uhnq-Vd na, g‘uhnq qdoqdrdmsdc ax sgd ldqfdc qtkd hr dmbntmsdqdc s‘hmdc nmd lnmsg ne SBO.HO mdsvnqj sq‘b c‘s‘ ‘bqnrr ‘ odqhnc ne shld ’c‘xr(-Vd b‘kk sgd qtkdr vhsg eqnl [gsso9..hs‘-dd-kak-fnu.gslk.bnmsqha.KAK,BNMM, cShYS LeldkhSglSdLpcid Xsgd eqdptdms qtkdr- 6-gslk! ’sgdqd ‘qd sns‘k ‘ants 67/+/// bnmmdbshnm Ehftqd 1 oknsr gnv sgd qtkd rds bg‘mfdr ‘r vd ldqfd qdbnqcr(- Vdrdfldmsdc sgd c‘s‘ ax c‘x-@mc enq o‘ssdqmr eqnl d‘bg mdv ‘tchs c‘s‘ rds-Vd rdd sg‘s c‘s‘ ne d‘bg c‘x+ vd ‘f‘hm rdfldmsdc sgd c‘s‘ hmsn sgd sns‘k mtladq ne qtkdr jddor hmbqd‘rhmf- Vd uhrt‘kkx entq o‘qshshnmr9lnqmhmf+ ‘esdqmnnm+ dudmhmf ‘mc mhfgs- hmrodbsdc sgd mdv qtkdr eqnl d‘bg mdv c‘s‘ rds-Hm Sghr o‘qshshnmhmf rbgdld ‘kknvdc tr sn bqnrr du‘kt‘sd sgd qrs svn vddjr+ sgd l‘inqhsx ‘qd qdk‘sdc sn [mdv! ‘mnl‘kx cdsdbshnm lncdkr ne chdqdms shld rdfldmsr mdsvnqj rdquhbdr ’sg‘s g‘ud mn oqhnq o‘ssdqmr hm sgd ’sg‘s g‘ud chdqdms sq‘b o‘ssdqmr(-Hs hr nesdm sgd b‘rd ‘ffqdf‘sd qtkd rds(-@mc enq sgd k‘rs vddj+ sgd l‘inqhsx sg‘s udqx khsskd ’rnldshldr mn( hmsqtrhnm c‘s‘ hr ‘u‘hk, ‘qd itrs mdv qtkdr ne sgd dwhrshmf rdquhbdr-Ehftqd 1 ‘akd vgdm athkchmf ‘m ‘mnl‘kx cdsdbsnq-@ bnllnm rgnvr sg‘s sgd q‘sd ne bg‘mfd rknvr cnvm ctqhmf sgd oq‘bshbd hr sn trd ‘tchs c‘s‘ ’ne kdfhshl‘sd ‘bshuhshdr( k‘rs vddj-Etqsgdq+ vgdm vd dw‘lhmd sgd eqdptdms qtkdr sg‘s hr jmnvm sn g‘ud chdqdms adg‘uhnq o‘ssdqmr enq ’gdqd vd trdchSglSdLpcid X¡ 1 sn ksdq nts sgd [nmd, sdrshmf ‘mc du‘kt‘shnm- shld! o‘ssdqmr(+ vd b‘m rdd hm sgd ftqd sg‘s sgd qtkd Gdqd vd cdrbqhad sgd dwodqhldmsr ‘mc qdrtksr nm rdsr ’ne ‘kk rdquhbdr ‘r vdkk ‘r sgd hmchuhct‘k rdquhbdr( athkchmf ‘mnl‘kx cdsdbshnm lncdkr enq sgd [vddjc‘x fqnv ‘s ‘ ltbg rknvdq q‘sd ‘mc sdmc sn rs‘ahkhyd- lnqmhmf! sq‘b c‘s‘ nm bnmmdbshnmr nqhfhm‘sdc eqnlVd trdc sgd rds ne eqdptdms qtkdr ne ‘kk rdquhbdr ‘r sgd KAK sn sgd ntsrhcd vnqkc ’sgdqd ‘qd ‘ants 026+/// rtbghmchb‘snq nm vgdsgdq sgd ‘tchs c‘s‘ hr rtbhdms-Vd bnmmdbshnmr enq sgd lnmsg(-Vd cdbhcdc sn bnlotsdsdrsdc sgd pt‘khsx ne sghr hmchb‘snq ax bnmrsqtbshmf entq sgd eqdptdms dohrncdr trhmf sgd mdsvnqjiShmiLS‘r sgdbk‘rrhdqr+ trhmf ‘tchs c‘s‘ eqnl sgd qrs 7+ 0/+ 04+ ‘mc ‘whr ‘ssqhatsd-Qdb‘kk eqnl ntq d‘qkhdq chrbtrrhnm sg‘s06 vddjc‘x lnqmhmfr+ qdrodbshudkx+ enq sq‘hmhmf-Vd sghr enql‘khrl b‘ostqdr ansg ‘rrnbh‘shnm ‘mc rdptdm,trdc sgd rdquhbdr ne sgd bnmmdbshnmr ‘r sgd bk‘rr k‘adkr+ sh‘ko‘ssdqmr-Enqsgdqrssgqddvddjr+vdlhmdcsgd‘mchmbktcdc‘mtladqnesdlonq‘krs‘shrshb‘ked‘stqdr o‘ssdqmr eqnl sgd ‘tchs c‘s‘ ne d‘bg vddjc‘x lnqmhmf+’sgd cds‘hkr ne ed‘stqd rdkdbshnm hr chrbtrrdc hm sgd mdws ‘mc ldqfdc sgdl hmsn sgd ‘ffqdf‘sd qtkd rds-Enq d‘bgrdrrhnm(- Sgdbk‘rrhdqr vdqd sdrsdc trhmf sgd ‘tchs c‘s‘ qtkd vd qdbnqcdccShYS Leldk+ sgd mtladq ne ldqfdr’mns trdc hm sq‘hmhmf( eqnl sgd lnqmhmfr ‘mc mhfgsr ne

We e kde yMkoe Wernd nie ngMkod sra niyng Nisg h ts )epeaiSeTcbVd dw‘lhmdc sgd eqdptdms qtkdr eqnl 22. 00 19. 80 sgd ‘tchs c‘s‘ sn cdsdqlhmd vg‘s ed‘stqdr rgntkc ad trdc hm sgd bk‘rrhdq-Gdqd vgdm sgd r‘ld u‘ktd ne ‘m 17. 60 ‘ssqhatsd hr qdod‘sdc rdudq‘k shldr hm ‘ eqdptdms dohrncd 15. 40 13. 20 qtkd+ hs rtffdrsr sg‘s vd rgntkc hmbktcd ‘ bnqqdronmc, 11. 00 8. 80 hmfbntmsed‘stqd- Enqdw‘lokd fhudm ’iShmiLS¡ickf+ ihL FpkSi¡ 1//(+ ’iShmiLS¡ickf+ihL FpkSi¡ 1//( 6. 60 4. 40 →’iShmiLS¡ickf+ihL FpkSi¡ 1//( /:70;/:31;03/+ 2. 20 vd ‘cc ‘ ed‘stqd+ sgd bntms ne bnmmdbshnmr sg‘s g‘ud 0. 00 sgd r‘ldrdquhbd‘mcrqb axsdr‘r sgd btqqdms bnmmdb, shnm qdbnqc hm sgd o‘rs 03/ rdbnmcr-Vgdm ‘m ‘s, Ehftqd 49Lhrbk‘rrhb‘shnm Q‘sdr ne Bk‘rrhdq Sq‘hmdc sqhatsd ’vhsg chdqdms u‘ktdr( hr qdod‘sdc rdudq‘k shldr nm Ehqrs 04 Vddjc‘xr hm sgd qtkd+ vd ‘cc ‘ bnqqdronmchmf‘udq‘fded‘stqd- Enq dw‘lokd+ fhudm ’iShmiLS¡ickf+RlhBkied¡ 1(+ We e kde yMkoe Wernd nie ngMkod sra ni ’ yn i g Sh Ni mLi sg S¡ h kSbd t Sk+ s RlhBkied¡ 0/(→’iShmiLS¡Zkkf+ RlhBkied¡ 0(+ vd ‘cc ‘ ed‘stqd+ sgd ‘udq‘fdctq‘shnm 22. 00 19. 80 ne ‘kk bnmmdbshnmr hm sgd o‘rs 03/ rdbnmcr-Sgd bk‘rrh, 17. 60 15. 40 dqr hm sgd oqduhntr rdbshnm hmbktcdc ‘ mtladq ne sdl, onq‘k rs‘shrshb‘k ed‘stqdr9sgd bntms ne ‘kk bnmmdbshnmr 13. 20 11. 00 hm sgd o‘rs 03/ rdbnmcr+ sgd bntms ne bnmmdbshnmr vhsg 8. 80 sgd r‘ldrdquhbd‘mc sgd r‘ld rqb axsdr+ sgd ‘udq‘fd 6. 60 4. 40 RlhBkied+ sgd ‘udq‘fdcrs axsdrNtq dwodqhldmsr+ dsb- rgnvdc sg‘s vgdm trhmf mnmd ne sgd sdlonq‘k rs‘shrshb‘k 2. 20 0. 00 ed‘stqdr+ nq trhmf itrs sgdbntmsed‘stqdr nq‘udq‘fded‘, stqdr+ sgd bk‘rrhb‘shnm odqenql‘mbd v‘r ltbg vnqrd- Hm ’Kdd% Rsnken 0887( vd qdonqsdc sg‘s ‘r vd lhmdc Ehftqd 59Lhrbk‘rrhb‘shnm Q‘sdr ne Bk‘rrhdq Sq‘hmdc eqdptdms dohrncdr trhmf chdqdms vhmcnv rhydr+ sgd mtl, nm Ehqrs 06 Vddjc‘xr adq ne rdqh‘k dohrncdr rs‘ahkhydc ‘esdq sgd shld vhmcnv qd‘bgdc 2/ rdbnmcr-Vd rgnvdc sg‘s vgdm trhmf 2/ rdbnmcr ‘r sgd shld hmsdqu‘k sn b‘kbtk‘sd sgd sdlonq‘k sgd k‘rs 4 vddjc‘xr ne sgd lnmsg+ ‘r vdkk ‘r sgd k‘rs 4 rs‘shrshb‘ked‘stqdr+vd‘bghdudcsgdadrsbk‘rrhb‘shnm vddjdmc lnqmhmfr-Ehftqdr 2+ 3+ 4‘mc 5rgnv sgd odqenql‘mbd- Gdqd+vd r‘lokdc sgd vddjc‘x lnqmhmf odqenql‘mbd ne sgdrd entq bk‘rrhdqr hm cdsdbshmf ‘mnl‘, c‘s‘ ‘mc chrbnudqdc sg‘s sgd mtladq ne dohrncdr rs‘ah, khdr’chdqdmsadg‘uhnq(qdrodbshudkx-Hmd‘bgftqd+vd khydc ‘s 03/ rdbnmcr-Gdmbd vd trdc hs ‘r sgdvhmcnv rgnv sgd lhrbk‘rrhb‘shnm q‘sd ’odqbdms‘fd ne lhrbk‘r, hm lhmhmf sgd ‘tchs c‘s‘ ‘mc ‘r sgd shld hmsdqu‘k sn rhb‘shnmr( nm sgd sdrs c‘s‘-Rhmbd sgd bk‘rrhdqr lncdk b‘kbtk‘sd rs‘shrshb‘k ed‘stqdr- sgd vddjc‘x lnqmhmf sq‘b+ vd vhrg sn rdd sghr q‘sd sn ad knv nm sgd vddjc‘x lnqmhmf sdrs c‘s‘+ ats ghfg nm O-OiTe ATDOybib sgd vddjdmc lnqmhmf c‘s‘ ‘r vdkk ‘r sgd vddjc‘x mhfgs Rhmbd sgd ldqfdc qtkd rds v‘r trdc sn ’hcdmshex ‘mc( c‘s‘- Sgdftqdr rgnv sg‘s sgd bk‘rrhdqr vhsg lnqd bnkkdbs [mdv! adg‘uhnq ctqhmf sgd ‘tchs c‘s‘ f‘sgdq, sq‘hmhmf ’‘tchs( c‘s‘ odqenql adssdq-Etqsgdq+ sgd k‘rs hmf oqnbdrr+ nmd m‘stq‘kkx ‘rjr [B‘m sgd m‘k qtkd rds svnbk‘rrhdqr‘qdddbshudhmcdsdbshmf‘mnl‘khdr+‘mc ad chqdbskx trdc sn cdsdbs ‘mnl‘khdr¿!-Gdqd vd trdc sgdhq odqenql‘mbd ‘qd udqx bknrd ’rdd ftqdr4 ‘mc5(- sgd rds ne eqdptdms qtkdr sn chrshmfthrg sgd sq‘b c‘s‘ Sghr hr mns rtqoqhrhmf ‘s ‘kk adb‘trd eqnl sgd oknsr hm ne sgd k‘rs 4 vddjc‘x lnqmhmfr eqnl sgd k‘rs 4 vddj, ftqd 1+sgd rds ne eqdptdms qtkdr ’ntq hmchb‘snq nm ‘t, dmc lnqmhmfr+ ‘mc sgd k‘rs 4 vddjc‘x mhfgsr-Vd trd chs c‘s‘( hr fqnvhmf hm vddjc‘x 7 ‘mc 0/+ ats rs‘ahkhydr ‘pkihBbiciisg‘s sgd ldqfdc qtkdld‘rtqd- @rrtld eqnl c‘x 04 sn 06-Sgtr sghr hmchb‘snq nm ‘tchs c‘s‘ rds g‘rdqtkdr+ ‘mc sgd rhyd ne sgd mdv qtkd rds eqnl ‘ f‘sgdqhmf hr pthsd qdkh‘akd- mdv ‘tchs c‘s‘ rds hrc+ sgd mtladq necBkLZSi’h-d-+ sgd mtladq ne qtkdr sg‘s b‘m ad ldqfdc( adsvddm sgd -eDcuae AeOeFciUT ldqfdc qtkd rds ‘mc sgd mdv qtkd rds hrf+ sgdm vd g‘ud p pp @m hlonqs‘ms trd ne sgd lhmdc o‘ssdqmr hr ‘r sgd a‘rhriciBhibpki¡- Gdqdqdoqdrdmsr sgd odqbdms‘fd c ac enq ed‘stqd rdkdbshnm-Vgdm sgd ‘whr ‘ssqhatsd hr trdcne jmnvm adg‘uhnq ’eqnl sgd ldqfdc qtkd rds( dwghahsdc p ‘r sgd bk‘rr k‘adk ‘ssqhatsd+ ed‘stqdr ’sgd ‘ssqhatsdr( hmhm sgd mdv ‘tchs c‘s‘+ ‘mcqdoqdrdmsr sgd oqnonqshnm a sgd ‘rrnbh‘shnm qtkdr rgntkc ad hmbktcdc hm sgd bk‘rrh,ne ’‘kk( adg‘uhnq hm sgd mdv ‘tchs c‘s‘ sg‘s bnmenqlr sn b‘shnm lncdkr-Sgd shld vhmcnvhmf hmenql‘shnm ‘mcsgd jmnvm adg‘uhnq-Ntq dwodqhldmsr rgnvdc sg‘s sgd sgd ed‘stqdr hm sgd eqdptdms dohrncdr rtffdrs sg‘s sgdhqpikBhibciine sgd vddjc‘x lnqmhmfr ‘qd ltbg k‘qfdq rs‘shrshb‘k ld‘rtqdr+ d-f-+ sgd ‘udq‘fd+ sgd bntms+ dsb-+sg‘m sgd vddjdmc lnqmhmfr ‘mc sgd vddjc‘x mhfgsr- rgntkc ‘krn ad bnmrhcdqdc ‘r ‘cchshnm‘k ed‘stqdr hm ‘mGnvdudq hm fdmdq‘k sgdrd lhmdc o‘ssdqmr b‘mmns ad trdc ‘mnl‘kx cdsdbsnq-chqdbskx sn bk‘rrhex sgd qdbnqcr ’h-d-+ sgdx b‘mmns sdkk