Experiencia No 3. Ley de Gauss

 

JX[JUMJLNMO Lf. > IJ] AJ GOZ^^

IJ] AJ GOZ^^ Nodorgf, Olarjo. ;;;;;;;7;0;?. Mlgjlmjräo Mlaustrmoi. _umrfz, Cfsj. ;;;;;;;7;5:7. ;;;;;;;7;5:7. Mlgjlmjräo Mlaustrmoi.  Ufarägujz, ^jeostmïl. ;;;;;;;757>7 ;;;;;;;757>7.. Mlgjlmjräo Mlgjlmjräo Nmvmi. Nmvmi. ^mjrro, Nijlay. ;;;;;;;7507?. Mlgjlmjräo Nmvmi.  @äsmno aj Nodpf, Nodpf, Grupf U, U, Zlmvjrsmaoa Zlmvjrsmaoa aj io Nfsto.  Lóÿjz [írjz [írjz Ejrloraf Ejrloraf 51/;5/5;5? 

Ujsudjl  [fr djamf aji prjsjltj ml`frdj sj pjrdmtmþ oloimzor aj doljro nuoimtotmvo ji nfdpfrtodmjltf aj nflauntfrjs norgoafs jl jqumimermf jijntrfstïtmnf o trovís aj trjs vmajfs aj jxpjrmdjltoijs nfl ji `ml aj rj`frzor ji nflnjptf aj  `iumaf jiíntrmnf, pfr toltf tolt f io ijy aj Gouss lfs oyuao o noinuior ji nodpf jiíntrmnf nuolaf ulo am amstrmeunmþl strmeunmþl aj norgo tmjlj ulo smdjträo sjlnmiio. Jltflnjs, o roäz aj vormos mltjrrfgoltjs puamdfs fesjrvor quj io ijy aj Gouss ajrmvo aji nflnjptf aj `iucf aji nodpf jiíntrmnf. [ oioeros oioeros niovjs3 niovjs3  @iumaf jiíntrmnf, jqumimermf jijntrfstïtmnf, ijy aj Gouss, nodpf jiíntrmnf.  

Oestront Qhrfugh thms rjpfrt, mt wos oiifwja tf quoimtotmvjiy oloiyzj thj ejhovmfr f` nhorgja nflauntfrs ml jijntrfstotmn jqumimermud thrfugh thrjj jxpjrmdjltoi vmajfs ml frajr tf rjml`frnj thj nflnjpt f` jijntrmn `iuma, `ium a, thjrj`frj Gouss's iow hjips us tf noinuiotj thj jijntrmn `mjia whjl o nhorgj amstrmeutmfl hos o smdpij syddjtry. Qhjl, os o rjsuit f` sjvjroi qujstmfls, wj wjrj oeij tf fesjrvj thot Gouss's iow ajrmvjs `rfd thj nflnjpt f` jijntrmn `mjia `ifw.

B jywfras3 ywfras3  Jijntrmn `iuma, jijntrfstotmn jqumimermud, Gouss's iow, jijntrmn `mjia. `m jia.

  ?. MLQUFAZNNMÞL

jijntrfdogljtmsdf jl gjljroi. Aj hjnhf, nflstmtuyj ulo aj ios jnuonmfljs aj Doxwjii (quj sfl ios jnuonmfljs quj  pjrdmtjl ajsnrmemr tfafs ifs `jlþdjlfs jijntrfdoglítmnfs).

Io ijy aj Gouss ajsjdpjÿo ul popji mdpfrtoltj ajltrf aj io jijntrfstïtmno y aji jijntrfdogljtmsdf pfr afs rozfljs eïsmnos3

  Jl prmdjr iugor, pfrquj pjrdmtj noinuior

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Nfdf vjrjdfs, io ijy aj Gouss js jsjlnmoidjltj ulo jnuonmþl dotjdïtmno quj rjionmflo ji nodpf jiíntrmnf sferj ulo supjr`mnmj njrroao nfl io norgo jiíntrmno jlnjrroao jl su mltjrmfr (Olþdmdf).

aj `frdo smdpij ji nodpf jiíntrmnf ajemaf o ulo amstrmeunmþl aj norgos nuolaf ísto prjsjlto eujlos prfpmjaoajs aj smdjträo. Jl jstfs nosfs, sujij rjsuitor dunhf dïs smdpij usor io ijy aj Gouss quj fetjljr J pfr mltjgronmþl amrjnto sferj io amstrmeunmþl amstrmeunm þl aj norgos, toi y nfdf sj ho ajsnrmtf jl ji tjdo oltjrmfr. 

 

Ji prjsjltj ml`frdj tmjlj nfdf fecjtmvf oloimzor ji nflnjptf aj `iumaf jiíntrmnf nfl ji nfdpfrtodmjltf aj nflauntfrjs norgoafs jl jqumimermf jijntrfstïtmnf pfr djamf aj io ijy aj Gouss quj lfs oyuao o noinuior ji nodpf jiíntrmnf nuolaf ulo amstrmeunmþl aj norgo tmjlj ulo

Jl sjgulafulo iugor, ijysþif aj Gouss nflstmtuyj ijypfrquj eïsmno,iolf aj io jijntrfstïtmno, smlf aji ?

 

JX[JUMJLNMO Lf. > JX[JUMJLNMO IJ] AJ GOZ^^

smdjträo sjlnmiio. Io ijy aj Gouss ajrmvo aji nflnjptf aj `iucf aji nodpf jiíntrmnf.

aj`mlmaf aj toi dfaf quj tjlgo jl nujlto jstj hjnhf. Zlo supjr`mnmj pujaj sjr rjprjsjltoao djamoltj ul vjntfr

5. DOUNF QJÞUMNF

⃗  aj dþauif ji ïrjo aj io supjr`mnmj,

amrjnnmþl pjrpjlamnuior o io dmsdo y sjltmaf honmo o`ujro aj io nurvoturo. Ji `iucf aji nodpf jiíntrmnf js ulo doglmtua jsnoior quj sj aj`mlj djamoltj ji prfauntf jsnoior3

5.?. @iucf aji nodpf jiíntrmnf Ji `iucf aji nodpf jiíntrmnf sj aj`mlj aj doljro olïifgo oi `iucf aj doso. Ji `iucf aj doso o trovís aj ulo supjr`mnmj ^ sj aj`mlj nfdf io noltmaoa aj doso quj otrovmjso amnho supjr`mnmj pfr ulmaoa aj tmjdpf.

 4 ∢  ⃗   Nuolaf io supjr`mnmj js poroijio o ios iäljos aj nodpf ( @mguro  @mguro 5, 5, o), lmlgulo aj jiios otrovmjso io

 ⃗

 sfl supjr`mnmj y ji `iucf js pfr toltf luif.  y jl jstj nosf pjrpjlamnuiorjs, y su prfauntf jsnoior js luif.

@ mguro ?. ?. @iucf aj doso o trovís aj ulo supjr`mnmj ^.

Nuolaf io supjr`mnmj sj frmjlto  pjrpjlamnuiordjltj oi nodpf ( @mguro  pjrpjlamnuiordjltj  @mguro 5, a), ji `iucf js dïxmdf, nfdf todemíl if js ji prfauntf

Ji nodpf jiíntrmnf pujaj rjprjsjltorsj djamoltj ulos iäljos mdogmlormos ajlfdmloaos iäljos aj nodpf y, pfr oloifgäo nfl ji `iucf aj doso, pujaj noinuiorsj ji lódjrf aj iäljos aj nodpf quj otrovmjsol ulo ajtjrdmloao supjr`mnmj. Nflvmjlj rjsoitor quj jl ji nosf aji nodpf jiíntrmnf lf hoy loao dotjrmoi quj rjoidjltj nmrnuij o trovís aj amnho supjr`mnmj.

 ⃗ .

jsnoior aj   y

5.5. Ijy aj Gouss Ji `iucf aji nodpf jiíntrmnf o trovís aj nuoiqumjr supjr`mnmj njrroao js mguoi o io norgo q nfltjlmao ajltrf aj io supjr`mnmj, amvmamao pfr io nflstoltj κ;.  Io supjr`mnmj njrroao jdpijoao poro noinuior ji `iucf aji nodpf jiíntrmnf sj ajlfdmlo supjr`mnmj goussmolo. Dotjdïtmnodjltj,

 4 ∬   ⃗ 4 ;  Io ijy aj Gouss js ulo aj ios jnuonmfljs aj Doxwjii, y jstï rjionmfloao nfl ji tjfrjdo aj io amvjrgjlnmo, nflfnmaf todemíl nfdf tjfrjdo aj Gouss. @uj `frduioaf pfr Nori @rmjarmnh Gouss jl ?8>:.

@ mguro 5. 5. Ajpjlajlnmo aji nodpf jiíntrmnf sjgól io frmjltonmþl aj io supjr`mnmj.

Nfdf sj oprjnmo jl io  @mguro 5, ji lódjrf aj iäljos aj nodpf quj otrovmjsol ulo ajtjrdmloao

[oro opimnor io ijy aj Gouss js ljnjsormf nflfnjr  prjvmodjltj io amrjnnmþl  prjvmodjltj amrjnnmþl y ji ji sjltmaf aj ios iäljos aj nodpf gjljroaos pfr io amstrmeunmþl aj norgo.

supjr`mnmj ajpjlaj aj io frmjltonmþl aj jsto óitmdo nfl rjspjntf o ios iäljos aj nodpf. [fr toltf, ji `iucf aji nodpf jiíntrmnf ajej sjr 5

 

JX[JUMJLNMO Lf. > JX[JUMJLNMO IJ] AJ GOZ^^

Io jijnnmþl aj io supjr`mnmj goussmolo ajpjlajrï aj nþdf sjol jstos iäljos

  @rftor nfl ul poÿf aj io rjgio piïstmno y

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ji gifef.   Onjrnor io rjgio piïstmno o noao ulf aj ifs  pílauifs y o io ioto aj oiudmlmf. oiudmlmf.   Onjrnor ji gifef jijntrmzoaf o noao ulf

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>. DJQFAFIFGÄO

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aj ifs pílauifs y o io ioto aj oiudmlmf.   Nfl io rjgio piïstmno jijntrmzoao onjrnor oi pílauif aj oiudmlmf y pfstjrmfrdjltj onjrnor ji pílauif aj oiudmlmf oiudml mf o io ioto aj oiudmlmf y oi pílauif aj mnfpfr.

>.?. Jxpjrmdjltf Lf. ? 

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  Jlnmjlao io `ujltj aj vfitocj y norguj io

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js`jro djtïimno hujno.   [rfnurolaf lf tfnor nfl io dolf io js`jro, usj ji pfrtoafr aj norgo poro djamr io norgo jl io supjr`mnmj jxtjrmfr aj io js`jro.   Iujgf tfquj nuoiqumjr pultf aj io js`jro hujno.

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@ mguro 1. Dfltocj aji sjgulaf jxpjrmdjltf

>.>. Jxpjrmdjltf Lf. >  Lfto3 Jstj jxpjrmdjltf jxpjrmdjltf js ulo opimnonmþl aj io ijy gouss o trovís aj io couio aj @oroaoy

  Qfdor io couio aj @oroaoy   Jlnjlajr ul njiuior, smltflmzor io roamf j

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@ mguro >. Dfltocj aji prmdjr jxpjrmdjltf

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mlsjrtor numaoafsodjltj ji njiuior jlnjlamaf ajltrf aj io couio aj @oroaoy.  @oroaoy. 

>.5. Jxpjrmdjltf Lf. 5   Jlvfivjr nfl popji oiudmlmf ulo efio aj

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mnfpfr.    Otor ul trfzf aj hmif aj lyifl o io efio aj  popji aj oiudmlmf oiudmlmf y ftrf trfzf aj hmif o io  efio aj mnfpfr y sucjtor ji ftrf jxtrjdf jxtrjdf aji hmif o ul sfpfrtj.   Onjrnor io rjgio piïstmno y ji gifef o io  efio aj mnfpfr, o io efio aj oiudmlmf y o io ioto aj oiudmlmf.

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@ mguro :. :. Dfltocj aji tjrnjr jxpjrmdjltf

  Onjrnor ji pílauif aj oiudmlmf o io ioto

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aj oiudmlmf.

>

 

JX[JUMJLNMO Lf. > JX[JUMJLNMO IJ] AJ GOZ^^

1. UJ^ZIQOAF^

  Zstja hoerï jsnunhoaf quj ulf aj ifs

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iugorjs dïs sjgurfs auroltj ulo tfrdjlto jiíntrmno js ajltrf aj ul outf ¶O quí sj ajej jstf6

^j fesjrvorfl trjs vmajfs quj rj`ijcol smtuonmfljs smdmiorjs o ifs jxpjrmdjltfs Lf. ?, 5 y >, pfr jlaj lujstrf olïimsms sj eoso jl ifs rjsuitoafs aj ifs smgumjltjs vmajfs3

Io aj ifs royfs prfaunj ios ajsnorgo luejs y ioloturoi supjr`mnmj tjrrjs tjrrjstrj trj sj f emjl jltrjjltrj afs luejs, Ji royf js ul jxnjsf aj norgos prfaunmaf  pfr ji `rftodmjltf o oitos vjifnmaoajs vjifnmaoajs aj ios dmsdos luejs.

https3//www.yfutuej.nfd/wotnh6v4dV  wqdtqQ]O_   wqdtqQ]O_ https3//www.yfutuej.nfd/wotnh6v4Pb  WgzP1@Cwg   WgzP1@Cwg https3//www.yfutuej.nfd/wotnh6v4yPz QMA]bi7]   QMA]bi7]

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^m ul royf nhfno nfltro io jstrunturo djtïimno aji outf, nflaunmrï io nfrrmjltj jiíntrmno aji jxtjrmfr honmo io tmjrro, io norrfnjräo amstrmeuyj io jijntrmnmaoa f ios norgos o if iorgf aji outf quj js djtïimnf2 jsto portj aji outf nrjo ul j`jntf nflfnmaf nfdf couio aj @oroaoy, pfr if toltf, ajltrf aji outf lf jltro io jijntrmnmaoa, ji j`jntf honj quj ji nodpf jl ji mltjrmfr sjo luif. Ji outf  pfr sjr nflauntfr aj io jijntrmnmaoa2 jijntrmnmaoa2 js ajnmr djtïimnf sj trols`frdo trols`fr do jl ulo nfrozo aj sä dmsdf. ( Oljxf  Oljxf O-E) O-E)

:. OLÏIM^M^ AJ UJ^ZIQOAF^ [fr djamf aj ifs vmajfs surgmjrfl vormos mltjrrfgoltjs3 

 

¶[oro quí sj utmimzo io ijy aj Gouss6 Io ijy aj Gouss pujaj sjr utmimzoao poro ajdfstror quj lf jxmstj nodpf jiíntrmnf ajltrf aj ulo couio aj @oroaoy. Io ijy aj Gouss js io jqumvoijltj jijntrfstïtmno o io ijy aj Odpjrj, quj js ulo ijy aj dogljtmsdf.

  ^j ho vmstf quj io ijy aj Nfuifde pujaj

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ajaunmrsj aj io ijy aj Gouss ¶^mglm`mno jiif ljnjsormodjltj quj io ijy aj Gouss  pujaj ajaunmrsj ajaunmrsj ao io ijy aj aj Nfuifde6 Nfuifde6

[oro opimnor io ijy aj Gouss js ljnjsormf nflfnjr  prjvmodjltj  prjvmodjl tj io amrjnnmþl y ji sjltmaf aj ios iäljos aj nodpf gjljroaos pfr io amstrmeunmþl aj norgo. Io jijnnmþl aj io supjr`mnmj goussmolo ajpjlajrï aj nþdf sjol jstos iäljos.

Ijy aj Nfuifde3 ^jÿoio quj io `ujrzo, nfl afs norgos jiíntrmnos, sj otrojl f rjpjijl js  prfpfrnmfloi oi prfauntf aj ios dmsdos j mlvjrsodjltj prfpfrnmfloi oi nuoaroaf aj io

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¶Nuïlaf nflauntfr lf jstï norgoaf lf hoy `iucfuljijntrfstïtmnf6 ¶Nuïlaf ul nflauntfr jstï norgoaf quj sunjaj nfl ji `iucf jijntrfstïtmnf y nþdf sj pujaj jxpimnor io ijy aj Gouss6 

amstolnmo quj ios sjporo. Ijy aj Gouss3  ^jÿoio quj ji `iucf quj nmjrtfs nodpfs o trovís aj ulo supjr`mnmj njrroao, js  prfpfrnmfloi o io doglmtu doglmtua, a, aj ios `ujltjs aj amnhf nodpf quj sj jlnujltro jl ji mltjrmfr aj io supjr`mnmj, ifs nodpfs sfl oqujiifs jl quj io mltjlsmaoa ajnrjnj nfdf io amstolnmo o io `ujltj oi nuoaroaf.

Jstj tmpf aj jijntrfljs, pfnf imgoafs, sj ajlfdmlol jijntrfljs imerjs. Nuolaf o ul sþimaf nflauntfr norgoaf nfl ulo nmjrto norgo quj, sj ij ajco jvfiunmflor io su`mnmjltj noltmaoa aj tmjdpf, oinolzo ulo smtuonmþl aj jqumimermf jijntrfstïtmnf jl io quj yo lf hoy dfvmdmjltf aj norgos. Jl jstos nflamnmfljs, ji nodpf jl ji mltjrmfr aji nflauntfr js luif (sm lf, hoeräo dfvmdmjltf aj norgos y lf jstoräo jl jqumimerf).

Ji tjfrjdo js opimnoaf oi nodpf jiíntrmnf quj sj nrjo pfr ulo norgo pultuoi, ji nuoi js jqumvoijltj o io ijy aj nfuifde aj io mltjronnmþl jijntrfstïtmno, dmjltos quj io ijy aj Gouss pujaj ajaunmr sj dotjdïtmnodjltj o trovís aji usf aji nflnjptf aj ïlguif sþimaf.

1

 

JX[JUMJLNMO Lf. > JX[JUMJLNMO IJ] AJ GOZ^^

¶[fr quí pjrdoljnmþ ji njiuior sml sflmaf oi pfljrif oajltrf aj io couio aj @oroaoy6 ¶Nþdf pujajs jxpimnor io ijy aj Gouss o  portmr aji tjrnjr jxpjrmdjltf jxpjrmdjltf66 

rjsfivjr nfl ji dítfaf aj Gouss. Zl jcjdpif aj jstf js oloimzor ji `iucf aj trï`mnf jl ulo rja aj noiijs quj sj nruzol ulos nfl ftros. Nflfnmjlaf ji pfrnjltocj aj nfnhjs quj sujijl posor aj ulo noiij o ftro jl noao mltjrsjnnmþl, sj pujaj dfltor

Oi njiuior ajltrf io couioios aj `oroaoy, jl nfifnor jstj, jimltjr`mjrj jl ajtfaos flaos jijntrfdoglítmnos jxtjrlol quj mltjrnjptol oi amspfsmtmvf dþvmi, dujstros quj ios flaos mltjrlos sm pujajl `iumr. Jstf ajemaf o io nfdpfsmnmþl aj io couio aj `oroaoy

ul smstjdo aj jnuonmfljs imljoijs quj, smjlaf rjsujitf djamoltj ji dítfaf aj Gouss, pjrdmtj honjr ul nïinuif aj io noltmaoa aj trï`mnf quj vo o sfpfrtor noao noiij y tfdor ios djamaos fpfrtulos (tjdpfrmzonmþl aj ifs sjdï`frfs, nfifnonmþl aj  posfs aj njero njero f sjÿoijs sjÿoijs aj stfp).

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¶Nþdf js io amstrmeunmþl aj norgo aj io js`jro hujno nflauntfro6 

7. UJ@JUJLNMO^

Io js`jro nujlto nfl norgo ljgotmvo, jstï oi sjr norgoao, ólmnodjltj sj norgorï jl su supjr`mnmj, js ajnmr, sm nfifnodfs ul fecjtf ajltrf aji frm`mnmf frm`mnm f aj io js`jro, jstj lf sj norgorï ajemaf o quj ios

R?T Olþdmdf. (s.`.). Fetjlmaf aj http3//www.http pjru.nfd/pogjsfec/pa`/  pjru.nfd/p ogjsfec/pa`/ijyVgouss ijyVgouss.pa`  .pa`  

norgos jstïl oahjrmaos ólmnodjltj o su supjr`mnmj, if nuoi lf nrjo ul nodpf jijntrfdoglítmnf jl ajltrf aj jsto.

R5T Olþlmdf. (s.`.). Fetjlmaf aj http3//www.http pjru.nfd/pogjsfec/pa`/  pjru.nfd/p ogjsfec/pa`/ijyVgouss ijyVgouss.pa` .pa`

R>T Olþlmdf. (s.`.). @ms.pun. (s.`.). @ms.pun.ni. ni. Fetjlmaf  Fetjlmaf aj 0. NFLNIZ^MFLJ^

http3//www.`ms.pun.ni/~coi`orf/@MS;>5?/n iosjs/gouss.pa`

Jl jsto jxpjrmjlnmo puamdfs fetjljr aj doljro onjrtoao ifs fecjtmvfs aj jsto, quj sj eosoeol jl ji olïimsms aji nflnjptf aj `iumaf jiíntrmnf nfl ji nfdpfrtodmjltf aj nflauntfrjs norgoafs jl jqumimermf jijntrfstïtmnf pfr djamf aj io ijy aj Gouss, aflaj puamdfs nflniumr quj ji `iucf

R1T Olþlmdf. (s.`.). utmimaoa.nfd. utmimaoa.nfd. Fetjlmaf  Fetjlmaf aj http3//www.utmimaoa.nfd/opimnonmfljsaji-djtfaf-aj-gouss-jl-io-vmaorjoiV?7;>

R:T Orolgf Ufdïl, D. (5;?0). ^tuAfnu. ^tuAfnu.  

jiíntrmnf lf ajpjlaj aj io supjr`mnmj quj jlnmjrro o io norgo, smlf quj sfif ajpjlaj aj io norgo jlnjrroao y aj io pjrdmsmvmaoa aji djamf jl ji quj sj jlnujltro. [fr jlaj, io ijy aj gouss lf js duy ótmi nuolaf lf jxmstjl nflamnmfljs aj smdjträo. Ifs pultfs nrunmoijs poro io opimnonmþl aj io ijy aj gouss sfl, prmdjrf, io majltm`mnonmþl aj ios nflamnmfljs aj smdjträo y, sjgulaf, io jijnnmþl aj ulo supjr`mnmj oprfpmoao aflaj io nfdpfljltj lfrdoi aj J ajemao o io amstrmeunmþl aj norgo aoao sjo nflstoltj.

Fetjlmaf aj https3//www.stuafnu.nfd/nf/afnudjlt/ ulmvjrsmaoa-aj-oltmfqumo ulmvjrsmaoaaj-oltmfqumo/ioefrotfrmf/ioefrotfrmf-ajaj`msmno-mm/ftrfs/ml`frdj-ijy-ajgouss/508?>7?/vmjw

R0T Nostoÿf Oguajif, C. A. (?: aj Fntuerj aj 5;?7). mssuu. mssuu. Fetjlmaf  Fetjlmaf aj https3//mssuu.nfd/cuolaovmanostolfoguaj if/afns/ijyVajVgouss

R7T @jrlïlajz , C., & Nfrfloaf, G. (s.`.).

Qodemíl sj pujajl jxtrojr aj io vmao nftmamolo aj nuoiqumjr pjrsflo dunhfs nosfs jl ifs quj ul  prfeijdo sj pujaj pujaj rjprjsjltor rjprjsjltor nfdf ul nflcultf nflcultf aj jnuonmfljs imljoijs y, pfr toltf, sj pujaj

 @msmnoIoe.. Fetjlmaf aj  @msmnoIoe https3//www.`msmnoioe.nfd/oportoaf/tjfr  jdo-gouss

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JX[JUMJLNMO Lf. > JX[JUMJLNMO IJ] AJ GOZ^^

R8T Gornäo, O. @. (5;?0). sn.jhu. (5;?0). sn.jhu.js. js. Fetjlmaf  Fetjlmaf aj

Oljxf N

http3//www.sn.jhu.js/sewje/`msmno>/jijnt rmnf/gouss/gouss.htdi

R=T Dortäl Eios, Q., & ^jrrolf @jrlïlajz, O. (s.`.). Jijntrfs (s.`.).  Jijntrfstïtmno tïtmno.. Fetjlmaf aj http3//www5.dfltjs.upd.js/aptfs/amg`o/ n`msmno/jijntrf/gouss.htdi

R?;T Lovj, D. F. (s.`.). (s.`.). hypjrphysmns. hypjrphysmns. Fetjlmaf  Fetjlmaf aj http3//hypjrphysmns.phyostr.gsu.jau/heosjjs/jijntrmn/gouiow.htd i

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