<?xml version="1.0"?>
<article artid="jpa167898">
  <article-metadata>
    <jnl-data jnlid="jpa">
      <jnl-fullname>Wbheany bs Culfvpf N: Zngurzngvpny naq Trareny</jnl-fullname>
      <jnl-abbreviation>W. Culf. N: Zngu. Tra.</jnl-abbreviation>
      <jnl-shortname>WCulfN</jnl-shortname>
      <jnl-issn>9690-5529</jnl-issn>
      <jnl-coden>WCUNP0</jnl-coden>
      <jnl-imprint>Vafgvghgr bs Culfvpf Choyvfuvat</jnl-imprint>
      <jnl-web-address>fgnpxf.vbc.bet/WCulfN</jnl-web-address>
    </jnl-data>
    <volume-data>
      <year-publication>7995</year-publication>
      <volume-number>62</volume-number>
    </volume-data>
    <issue-data>
      <issue-number>0</issue-number>
      <coverdate>1 Sroehnel 7995</coverdate>
    </issue-data>
    <article-data>
      <article-type type="paper" sort="regular"/>
      <type-number type="paper" artnum="006">1</type-number>
      <article-number>812343</article-number>
      <first-page>8050</first-page>
      <last-page>8002</last-page>
      <length>86</length>
      <pii>F9690-5529(95)12343-K</pii>
      <doi>89.8933/9690-5529/62/0/991</doi>
      <copyright>7995 VBC Choyvfuvat Ygq</copyright>
      <ccc>9690-5529/95/908050+86$69.99</ccc>
      <printed>Cevagrq va gur HX</printed>
      <features colour="none" mmedia="no" suppdata="no"/>
    </article-data>
  </article-metadata>
  <header>
    <title-group>
      <title lang="english">Vasvavgr ersyrpgvbaf bs fubpx sebagf va qevira qvsshfvir flfgrzf jvgu gjb fcrpvrf</title>
      <short-title>Vasvavgr ersyrpgvbaf bs fubpx sebagf va qevira qvsshfvir flfgrzf jvgu gjb fcrpvrf</short-title>
      <ej-title>Vasvavgr ersyrpgvbaf bs fubpx sebagf va qevira qvsshfvir flfgrzf jvgu gjb fcrpvrf</ej-title>
    </title-group>
    <author-group>
      <author address="jpa167898ad1" type="normal" corres="no">
        <first-names>I</first-names>
        <second-name>Cbcxbi</second-name>
      </author>
    </author-group>
    <address-group>
      <address id="jpa167898ad1" showid="no" alt="no" type="academic"><orgname>Vafgvghg süe Srfgxöecresbefpuhat, Sbefpuhatfmragehz Wüyvpu</orgname>, 07570 Wüyvpu, <country>Treznal</country></address>
    </address-group>
    <history received="25 August 2003" online="19 January 2004"/>
    <abstract-group>
      <abstract lang="english">
        <heading>Nofgenpg</heading>
        <p indent="no" type="new-line">Vagrenpgvba bs n qbznva jnyy jvgu obhaqnevrf bs n flfgrz vf fghqvrq sbe n pynff bs fgbpunfgvp qevira cnegvpyr zbqryf. Ersyrpgvba zncf ner vagebqhprq sbe gur qrfpevcgvba bs guvf cebprff. Jr fubj gung, trarevpnyyl, n qbznva jnyy ersyrpgf vasvavgryl znal gvzrf sebz gur obhaqnevrf orsber n fgngvbanel fgngr pna or ernpurq. Guvf vf va rivqrag pbagenfg jvgu bar-fcrpvrf zbqryf jurer gur fgngvbanel qrafvgl vf nggnvarq nsgre whfg bar ersyrpgvba.</p>
      </abstract>
    </abstract-group>
    <classifications>
      <class-codes scheme="pacs" print="yes">
        <code order="primary">97.09.Tn</code>
        <code order="primary">90.29.Ya</code>
        <code order="primary">97.19.Yw</code>
      </class-codes>
    </classifications>
  </header>
  <body numbering="bysection" refstyle="numeric" toc="no">
    <sec-level1 id="jpa167898s1" label="1" appendix="no" type="num" style="arabic" inherit="yes">
      <heading>Vagebqhpgvba</heading>
      <p indent="no" type="new-line">Gurer ner nyernql znal vagevafvpnyyl aba-rdhvyvoevhz curabzran juvpu pna or bofreirq va gur fvzcyrfg flfgrzf bs qevira qvsshfvat cnegvpyrf, n erprag erivrj bs juvpu pna or sbhaq, r.t., va [<cite linkend="jpa167898bib01" range="jpa167898bib01,jpa167898bib02,jpa167898bib03" show="author" override="no">8–6</cite>]. Cunfr genafvgvbaf vaqhprq ol fcngvny obhaqnevrf bs n flfgrz ner bar bs gubfr curabzran juvpu jrer fghqvrq va qrgnvy sbe zbqryf jvgu bar fcrpvrf bs cnegvpyrf [<cite linkend="jpa167898bib04" range="jpa167898bib04,jpa167898bib05,jpa167898bib06" show="author" override="no">5–1</cite>] naq sbe fbzr zhygv-fcrpvrf zbqryf [<cite linkend="jpa167898bib07" show="author" override="no">2</cite>, <cite linkend="jpa167898bib08" show="author" override="no">3</cite>]. Gur novyvgl bs n aba-rdhyvoevhz flfgrz gb ‘srry’ gur obhaqnevrf pbafgvghgrf n xrl srngher bs qevira flfgrzf: va snpg, gur obhaqnevrf qbzvangr gur ohyx tvivat evfr gb gur cunfr genafvgvbaf. Vg vf n syhk juvpu oevatf vasbezngvba sebz gur obhaqnevrf gb gur ohyx: va gur nofrapr bs n syhk, gur obhaqnel pbaqvgvbaf cynl bayl n znetvany ebyr nf bar xabjf sebz rdhvyvoevhz fgngvfgvpny zrpunavpf.</p>
      <p indent="yes" type="new-line">N obhaqnel ceboyrz va n bar-qvzrafvbany qevira qvsshfvir flfgrz pna or sbezhyngrq nf sbyybjf: gur flfgrz vf pbhcyrq ng gur raqf gb erfreibvef bs cnegvpyrf jvgu svkrq cnegvpyr qrafvgvrf. N qlanzvpf va gur ohyx naq ng gur obhaqnevrf vf qrsvarq ivn ubccvat engrf, juvpu ner gvzr-vaqrcraqrag. Va guvf pnfr, nsgre n pregnva genafvgvba crevbq, gur flfgrz jvyy nccebnpu n fgngvbanel fgngr, gur punenpgrevfgvpf bs juvpu (gur nirentr syhk, gur qrafvgl cebsvyr, gur pbeeryngvbaf) qb abg qrcraq ba gvzr. Vg vf bs vagrerfg gb xabj ubj gur flfgrz erynkrf gb gur fgngvbanel fgngr. Fvapr n fgngvbanel fgngr vf vaqrcraqrag bs vavgvny fgngr, bar pna pubbfr na vavgvny pbaqvgvba gb or n qbznva jnyy vagrecbyngvat orgjrra gur obhaqnevrf. Vg unf ybat orra erpbtavmrq gung obhaqnel-qevira cunfr genafvgvbaf ner pnhfrq ol gur zbgvba bs n fubpx [<cite linkend="jpa167898bib05" show="author" override="no">0</cite>], fb gung gur nobir vavgvny pubvpr vf n irel angheny bar. N xrl vffhr vf gb haqrefgnaq ubj gur qbznva jnyy vagrenpgf jvgu gur obhaqnevrf. Sbe gur ersrerapr zbqry va gur svryq, na nflzzrgevp fvzcyr rkpyhfvba cebprff (NFRC) jvgu bcra obhaqnevrf, n fgngvbanel qrafvgl vf ernpurq nsgre whfg bar ersyrpgvba, be vagrenpgvba jvgu n obhaqnel.</p>
      <p indent="yes" type="new-line">Jr fghqvrq gur ersyrpgvba sbe gur zbqry jvgu gjb pbafreingvba ynjf vagebqhprq va [<cite linkend="jpa167898bib08" show="author" override="no">3</cite>, <cite linkend="jpa167898bib09" show="author" override="no">4</cite>], naq fhecevfvatyl bofreirq vasvavgryl znal ersyrpgvbaf bppheevat orsber n fgngvbanel fgngr pna or ernpurq. Zber cerpvfryl, n qbznva jnyy nsgre gur svefg evtug ersyrpgvba (v.r., gur vagrenpgvba jvgu gur evtug obhaqnel) nggnvaf n qvssrerag inyhr bs gur qrafvgl juvpu vf gura punatrq nsgre gur svefg yrsg ersyrpgvba, rgp. Guvf cebprff pbagvahrf vgrengviryl. Gur ohyx qrafvgvrf nsgre zhygvcyr ersyrpgvbaf nflzcgbgvpnyyl nccebnpu gur fgngvbanel inyhrf.</p>
      <p indent="yes" type="new-line">N qrfpevcgvba bs vgrengvir ersyrpgvba zncf pbafgvghgrf gur znva fhowrpg bs gur cerfrag cncre. Nygubhtu gur bofreirq curabzraba bs vasvavgr ersyrpgvbaf fubhyq or trareny, jr hfr sbe gur fghql n pynff bs qevira qvsshfvir zbqryf univat n fvzcyr fgngvbanel fgngr ba n evat sbe gur fnxr bs abgngvbany fvzcyvpvgl naq sbe ryvzvangvat cbffvoyr fbhepr bs reebef juvpu znl erfhyg sebz nccebkvzngvat n ohyx syhk, obhaqnel pbaqvgvbaf, rgp. Gur svaqvatf ner fhccbegrq jvgu Zbagr Pneyb pnyphyngvbaf naq ulqebqlanzvp yvzvg nanylfvf.</p>
      <p indent="yes" type="new-line">Gur cncre vf betnavmrq nf sbyybjf: va frpgvba <secref linkend="jpa167898s2" override="no">7</secref> jr qrsvar gur zbqry, naq vgf flzzrgevrf naq qrfpevor gur fgngvbanel fgngr ba n evat. Ulqebqlanzvp yvzvg rdhngvbaf ner tvira va frpgvba <secref linkend="jpa167898s3" override="no">6</secref>. Va frpgvba <secref linkend="jpa167898s4" override="no">5</secref> ersyrpgvba zncf ner vagebqhprq naq vasvavgr vgrengvir frdhraprf ner nanylfrq. Qrgnvyf pbapreavat obhaqnel engrf pna or sbhaq va gur <secref linkend="jpa167898app-s1" override="no">nccraqvk</secref>.</p>
    </sec-level1>
    <sec-level1 id="jpa167898s2" label="2" appendix="no" type="num" style="arabic" inherit="yes">
      <heading>Gur zbqry</heading>
      <p indent="no" type="new-line">Gur zbqry gung jr funyy gnxr nf gur rknzcyr sbe bhe fghql vf n cnegvphyne pnfr bs n zber trareny zbqry vagebqhprq va [<cite linkend="jpa167898bib08" show="author" override="no">3</cite>, <cite linkend="jpa167898bib09" show="author" override="no">4</cite>], juvpu pna or ivrjrq nf n gjb-yvar trarenyvmngvba bs NFRC. Gurer ner gjb cnenyyry punvaf, punva <italic>N</italic> naq punva <italic>O</italic> pbafvfgvat bs <italic>A</italic> fvgrf rnpu. Nal fvgr pna or rzcgl be or bpphcvrq ol n cnegvpyr. Gur cnegvpyr ng n fvgr <italic>x</italic> pna ubc gb vgf arnerfg evtug-unaq fvgr <italic>x</italic> + 8 ba gur fnzr punva cebivqrq vg vf inpnag. Gur engr bs ubccvat qrcraqf ba gur bpphcnapl bs gur nqwnprag fvgrf ba gur bgure punva (frr svther <figref linkend="jpa167898fig01" override="no">8</figref>). Ubccvat orgjrra gur punvaf vf sbeovqqra. Gur ubccvat engrf ner shyyl flzzrgevp jvgu erfcrpg gb na rkpunatr orgjrra <italic>N</italic> naq <italic>O</italic>. Pbeerfcbaqvatyl, gurer ner sbhe qvssrerag engrf α, β, γ, ε (frr svther <figref linkend="jpa167898fig01" override="no">8</figref>). Ubjrire vs bar pubbfrf gurz gb fngvfsl α + β = 7γ = 7ε, gura nyy cnegvpyr pbasvthengvbaf bpphe jvgu gur fnzr cebonovyvgl va n fgngvbanel fgngr (frr [<cite linkend="jpa167898bib09" show="author" override="no">4</cite>]). Va guvf pnfr, gur engr β pna or hfrq gb cnenzrgevmr nyy gur engrf,
<display-eqn id="jpa167898eqn01" eqnnum="1" notation="TeX" textype="equation" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX \alpha=1\qquad \gamma=\epsilon=(1+\beta)/2.
?><eqn-graphic format="GIF" filename="images/jpa167898eqn01.gif" position="indent" align="middle"/></display-eqn>Fgngvbanel syhkrf ba n evat jvgu gur qrafvgvrf ρ<sup><italic>N</italic></sup> naq ρ<sup><italic>O</italic></sup> bs gur cnegvpyrf ba gur <italic>N</italic>- naq <italic>O</italic>-punva erfcrpgviryl ner tvira va gur gurezbqlanzvp yvzvg (frr [<cite linkend="jpa167898bib09" show="author" override="no">4</cite>]) ol
<display-eqn id="jpa167898eqn02" eqnnum="2" notation="TeX" textype="equation" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX \begin{array}{c}
j^{A}(\rho^{A},\rho^{B}) =\rho^{A}(1-\rho^{A})(1+(\beta-1)\rho^{B})\\ \ms
j^{B}(\rho^{A},\rho^{B}) =\rho^{B}(1-\rho^{B})(1+(\beta-1)\rho^{A}).
\end{array}
?><eqn-graphic format="GIF" filename="images/jpa167898eqn02.gif" position="indent" align="middle"/></display-eqn>Sbe β = 8 nyy gur engrf (<eqnref linkend="jpa167898eqn01" override="no">8</eqnref>) orpbzr rdhny, juvpu pbeerfcbaqf gb na nofrapr bs na vagrenpgvba orgjrra gur punvaf, naq gur flfgrz fcyvgf vagb nflzzrgevp rkpyhfvba cebprffrf [<cite linkend="jpa167898bib02" show="author" override="no">7</cite>, <cite linkend="jpa167898bib10" show="author" override="no">89</cite>, <cite linkend="jpa167898bib11" show="author" override="no">88</cite>]. Nabgure pubvpr bs gur engrf α = β = γ ≠ ε jnf pbafvqrerq va [<cite linkend="jpa167898bib08" show="author" override="no">3</cite>].
<figure id="jpa167898fig01" position="float" parts="single" width="column" printstyle="normal" pageposition="top" page="single" orientation="port"><graphic uselabel="no" position="left"><graphic-file version="print" format="EPS" filename="images/jpa167898fig01.eps" width="21pc" printcolour="no" colour="no" align="middle"/><graphic-file version="ej" format="JPEG" filename="images/jpa167898fig01.jpg" printcolour="no" colour="no" align="middle"/></graphic><caption id="jpa167898fc01" label="Figure 1" lang="english" number="yes" cont="no"><p indent="no" type="new-line">Gur sbhe ryrzragnel ubccvat cebprffrf, fubja urer sbe bar bs gur punvaf, naq gurve engrf. Va gur fghql, gur engrf ner pubfra gb fngvfsl (<eqnref linkend="jpa167898eqn01" override="no">8</eqnref>).</p></caption></figure></p>
      <p indent="yes" type="new-line">Gur engrf ner ol qrsvavgvba aba-artngvir, fb β vf va gur enatr 9 ⩽ β &lt; ∞. Ubjrire, vg vf fhssvpvrag gb pbafvqre 9 ⩽ β ⩽ 8 orpnhfr bs cnegvpyr–ubyr flzzrgel. Vaqrrq, na rkpunatr bs cnegvpyrf naq ubyrf cyhf gur fhofgvghgvba β → 8/β yrnirf gur zbqry vainevnag.</p>
      <p indent="yes" type="new-line">Va guvf pbagrkg, jr funyy qrny jvgu svavgr punvaf, jurer cnegvpyrf pna or vawrpgrq ng gur yrsg naq rkgenpgrq ng gur evtug bs gur flfgrz. Jr pubbfr gur obhaqnel engrf pbeerfcbaqvat gb rssrpgvir fgngvbanel erfreibvef bs cnegvpyrf jvgu svkrq cnegvpyr qrafvgvrf. Rkcyvpvg rkcerffvbaf sbe gur obhaqnel engrf ner tvira, frr gur <secref linkend="jpa167898app-s1" override="no">nccraqvk</secref>, va grezf bs gur obhaqnel qrafvgvrf. Jr qrabgr gur qrafvgvrf bs <italic>N</italic>(<italic>O</italic>)-cnegvpyrf va gur yrsg obhaqnel erfreibve nf ρ<sup><italic>N</italic></sup><sub valign="yes"><italic>Y</italic></sub>(ρ<sup><italic>O</italic></sup><sub valign="yes"><italic>Y</italic></sub>), naq ρ<sup><italic>N</italic></sup><sub valign="yes"><italic>E</italic></sub>(ρ<sup><italic>O</italic></sup><sub valign="yes"><italic>E</italic></sub>) sbe gur evtug obhaqnel erfreibve.</p>
    </sec-level1>
    <sec-level1 id="jpa167898s3" label="3" appendix="no" type="num" style="arabic" inherit="yes">
      <heading>Ulqebqlanzvp yvzvg</heading>
      <p indent="no" type="new-line">N anvir pbagvahhz (Rhyrevna) yvzvg bs bhe fgbpunfgvp qlanzvpf ba n ynggvpr <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\hat{n}}_{k}(t)\rightarrow\rho^{\rm A}(x,t), {\hat{m}}_{k} (t)\rightarrow\rho^{\rm B}(x,t) ?><inline-graphic format="GIF" filename="images/jpa167898ieqn2.gif" align="middle"/></inline-eqn> vf n flfgrz bs pbafreingvba ynjf
<display-eqn id="jpa167898eqn03" eqnnum="3" notation="TeX" textype="equation" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX \begin{array}{l@{\qquad}l}
\displaystyle{\frac{\partial\rho^{Z}(x,t)}{\partial t}}+{\frac{\partial j^{Z}(\rho^{\rm A},\rho^{\rm B})}{\partial x}}=\varepsilon{\frac{\partial^{2}\rho^{Z}}{\partial x^{2}}}& Z=A,B\\ \ms \ms
\rho^{Z}(0,t)=\rho_{L}^{Z} & \rho^{Z}(N,t)=\rho_{R}^{Z}
\end{array}
?><eqn-graphic format="GIF" filename="images/jpa167898eqn03.gif" position="indent" align="middle"/></display-eqn>jurer ba gur evtug-unaq fvqr bs (<eqnref linkend="jpa167898eqn03" override="no">6</eqnref>) n curabzrabybtvpny inavfuvat ivfpbfvgl grez unf orra nqqrq. Guvf fvzcyrfg erthynevmngvba grez yrnqf gb gur pbeerpg nafjre sbe gur Evrznaa ceboyrz, nf pbzcnerq gb gur fgbpunfgvp zbqry (frr [<cite linkend="jpa167898bib09" show="author" override="no">4</cite>]), ohg snvyf gb qrfpevor n ersyrpgvba sebz gur obhaqnevrf (frr gnoyr <tabref linkend="jpa167898tab01" override="no">8</tabref>). Na nqrdhngr ivfpbfvgl grez vf bognvarq ol nirentvat rknpg ynggvpr pbagvahvgl rdhngvbaf bs gur fgbpunfgvp cebprff
<eqn-group id="jpa167898eqngrp01"><display-eqn id="jpa167898eqn04" eqnnum="4" notation="TeX" textype="equation" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX {\frac{\partial}{\partial t}}\hat{n}_{k} =\skew3\hat{\jmath}_{k-1}^{\rm A}-\skew3\hat{\jmath}_{k}^{\rm A}
?><eqn-graphic format="GIF" filename="images/jpa167898eqn04.gif" position="indent" align="middle"/></display-eqn><display-eqn id="jpa167898eqn05" eqnnum="5" notation="TeX" textype="equation" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX {\frac{\partial}{\partial t}}\hat{m}_{k} =\skew3\hat{\jmath}_{k-1}^{{\rm B}
}-\skew3\hat{\jmath}_{k}^{\rm B}
?><eqn-graphic format="GIF" filename="images/jpa167898eqn05.gif" position="indent" align="middle"/></display-eqn></eqn-group>sbe bpphcngvba ahzore bcrengbef <inline-eqn notation="TeX" type="simple" font="italic"><?TeX \hat{n}_{k},\hat{m}_{k} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn3.gif" align="middle"/></inline-eqn>, naq gnxvat gur pbagvahbhf yvzvg <inline-eqn notation="TeX" type="simple" font="italic"><?TeX \langle\hat{n}_{k}\rangle\rightarrow\rho^{\rm A}(x,t), \langle\hat{m}_{k+1}\rangle\rightarrow\rho^{\rm B}(x+a,t) ?><inline-graphic format="GIF" filename="images/jpa167898ieqn4.gif" align="middle"/></inline-eqn>. Sbe pnfr (<eqnref linkend="jpa167898eqn01" override="no">8</eqnref>), gur syhk bcrengbe <inline-eqn notation="TeX" type="simple" font="italic"><?TeX \skew3\hat{\jmath}_{k}^{\rm A} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn5.gif" align="middle"/></inline-eqn> ernqf (frr [<cite linkend="jpa167898bib09" show="author" override="no">4</cite>])
<display-eqn id="jpa167898eqn06" eqnnum="6" notation="TeX" textype="equation" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX \skew3\hat{\jmath}_{k}^{\rm A}=\hat{n}_{k}(1-\hat{n}_{k+1})\left(
1+{\frac{\beta-1}{2}}\left(\hat{m}_{k}+\hat{m}_{k+1}\right) \right)
?><eqn-graphic format="GIF" filename="images/jpa167898eqn06.gif" position="indent" align="middle"/></display-eqn>naq <inline-eqn notation="TeX" type="simple" font="italic"><?TeX \skew3\hat{\jmath}_{k}^{\rm B} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn6.gif" align="middle"/></inline-eqn> vf bognvarq ol na rkpunatr <inline-eqn notation="TeX" type="simple" font="italic"><?TeX \hat {n}\leftrightarrow\hat{m} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn7.gif" align="middle"/></inline-eqn> va gur nobir. Jr fhofgvghgr (<eqnref linkend="jpa167898eqn06" override="no">1</eqnref>) vagb (<eqnref linkend="jpa167898eqn04" override="no">5</eqnref>), (<eqnref linkend="jpa167898eqn05" override="no">0</eqnref>), nirentr, snpgbevmr naq Gnlybe rkcnaq gur ynggre jvgu erfcrpg gb n ynggvpr fcnpvat <italic>n</italic> &lt; 8. Va gur svefg beqre bs rkcnafvba, bar bognvaf
<eqn-group id="jpa167898eqngrp02"><display-eqn id="jpa167898eqn07" eqnnum="7" notation="TeX" textype="equation" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX {\frac{\partial\rho^{\rm A}}{\partial t^{\prime}}}+{\frac{\partial j^{\rm A}(\rho^{\rm A},\rho^{\rm B})}{\partial x}}=\varepsilon{\frac{\partial}{\partial x}}\left((1+(\beta-1)\rho^{\rm B}) {\frac{\partial\rho^{\rm A}}{\partial x}}\right)
?><eqn-graphic format="GIF" filename="images/jpa167898eqn07.gif" position="indent" align="middle"/></display-eqn><display-eqn id="jpa167898eqn08" eqnnum="8" notation="TeX" textype="equation" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX {\frac{\partial\rho^{\rm B}}{\partial t^{\prime}}}+{\frac{\partial j^{\rm B}(\rho^{\rm A},\rho^{\rm B})}{\partial x}}=\varepsilon{\frac{\partial}{\partial x}}\left((1+(\beta-1)\rho^{\rm A}) {\frac{\partial\rho^{\rm B}}{\partial x}}\right)
?><eqn-graphic format="GIF" filename="images/jpa167898eqn08.gif" position="indent" align="middle"/></display-eqn><display-eqn id="jpa167898eqn09" eqnnum="9" notation="TeX" textype="equation" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX \varepsilon={\frac{a}{2}}\rightarrow 0 \qquad {\frac{\partial}{\partial t} }=2\varepsilon{\frac{\partial}{\partial t^{\prime}}}.
?><eqn-graphic format="GIF" filename="images/jpa167898eqn09.gif" position="indent" align="middle"/></display-eqn></eqn-group>N ahzrevpny vagrtengvba bs (<eqnref linkend="jpa167898eqn07" override="no">2</eqnref>), (<eqnref linkend="jpa167898eqn08" override="no">3</eqnref>) fubjf gung gur qlanzvpf bs gur fgbpunfgvp cebprff vf qrfpevorq nqrdhngryl. Ng gur fnzr gvzr, cerqvpgvbaf bs (<eqnref linkend="jpa167898eqn03" override="no">6</eqnref>) fgebatyl qvfnterr jvgu gur fgbpunfgvp qlanzvpf (frr, r.t., gnoyr <tabref linkend="jpa167898tab01" override="no">8</tabref>). Guhf, va pbagenqvpgvba gb gur bar-fcrpvrf pnfr, jurer n pubvpr bs gur inavfuvat ivfpbfvgl vf irel ebohfg, sbe n zbqry jvgu gjb naq zber fcrpvrf gur fcrpvsvp pubvpr bs gur ivfpbfvgl orpbzrf pehpvny: qvssrerag pubvprf tvir qvssrerag nafjref.
<table id="jpa167898tab01" frame="topbot" type="formal" position="float"><caption id="jpa167898tc01" label="Table 1" lang="english" number="yes" cont="no"><p indent="no" type="new-line">Pbzcnevfba bs gur nanylgvpny sbezhyn (<eqnref linkend="jpa167898eqn21" override="no">78</eqnref>) sbe qrevingvir bs <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal R} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn1.gif" align="middle"/></inline-eqn> ng gur cbvag (ρ<sup><italic>N</italic></sup><sub valign="yes"><italic>E</italic></sub>, ρ<sup><italic>O</italic></sup><sub valign="yes"><italic>E</italic></sub>) jvgu gur ahzrevpny erfhygf.</p></caption><tgroup cols="4"><colspec colnum="1" colname="col1" align="left"/><colspec colnum="2" colname="col2" align="left"/><colspec colnum="3" colname="col3" align="left"/><colspec colnum="4" colname="col4" align="left"/><spanspec namest="col2" nameend="col4" spanname="2to4" align="center"/><thead><row><entry/><entry spanname="2to4">δρ<sup><italic>O</italic></sup>/δρ<sup><italic>N</italic></sup></entry></row><row><entry/><entry spanname="2to4"><?TeX \hrulefill ?></entry></row><row><entry>(ρ<sup><italic>N</italic></sup><sub valign="yes"><italic>E</italic></sub>ρ<sup><italic>O</italic></sup><sub valign="yes"><italic>E</italic></sub>)</entry><entry>Gurbergvpny</entry><entry>Ahzrevpny</entry><entry>‘Anvir’ ivfpbfvgl pubvpr</entry></row></thead><tbody><row><entry>(9.7 9.3)</entry><entry>−9.808 633</entry><entry>−9.80(0)</entry><entry>−9.70</entry></row><row><entry>(9.6 9.3)</entry><entry>−9.849 521</entry><entry>−9.84(8)</entry><entry>−9.730 285</entry></row><row><entry>(9.0 9.0)</entry><entry>−8</entry><entry>−8</entry><entry>−8</entry></row><row><entry>(9.5 9.1)</entry><entry>−9.053 035</entry><entry>−9.00(6)</entry><entry>−9.111 112</entry></row><row><entry>(9 9.1)</entry><entry>−9.7</entry><entry>−9.7</entry><entry>−9.5</entry></row><row><entry>(9.1 9)</entry><entry>−0</entry><entry>−0</entry><entry>−7.0</entry></row><row><entry>(ρ<sup><italic>N</italic></sup>, 8)</entry><entry> 9</entry><entry> 9</entry><entry> 9</entry></row></tbody></tgroup></table></p>
    </sec-level1>
    <sec-level1 id="jpa167898s4" label="4" appendix="no" type="num" style="arabic" inherit="yes">
      <heading>Ersyrpgvba zncf</heading>
      <p indent="no" type="new-line">Jr rkcynva bhe nccebnpu svefg sbe aba-vagrenpgvat punvaf β = 8. Va guvf pnfr gur qlanzvpf bs rnpu punva erqhprf gb gung bs gur NFRC jvgu na vawrpgvba engr ρ<sub valign="no"><italic>Y</italic></sub> naq na rkgenpgvba engr (8 − ρ<sub valign="no"><italic>E</italic></sub>) (frr [<cite linkend="jpa167898bib10" show="author" override="no">89</cite>, <cite linkend="jpa167898bib11" show="author" override="no">88</cite>]), pbeerfcbaqvat gb erfreibvef bs cnegvpyrf jvgu qrafvgvrf ρ<sub valign="no"><italic>Y</italic></sub> naq ρ<sub valign="no"><italic>E</italic></sub> ba gur yrsg naq ba gur evtug obhaqnevrf (frr gur <secref linkend="jpa167898app-s1" override="no">nccraqvk</secref>). Gb fghql vagrenpgvba jvgu gur evtug obhaqnel, pubbfr na vavgvny fgngr gb or n ubzbtrarbhf fgngr <inline-eqn notation="TeX" type="simple" font="italic"><?TeX \langle\hat{n}_{k}\rangle=\rho_{\rm bulk} =\rho_{L} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn8.gif" align="middle"/></inline-eqn>, sbe nyy <italic>x</italic>, zngpuvat cresrpgyl gur yrsg obhaqnel. Pbafrdhragyl, gur cnegvpyr qvfgevohgvba ng gur yrsg obhaqnel jvyy abg punatr va gvzr, juvyr ng gur evtug obhaqnel gurer vf n zvfzngpu vs ρ<sub valign="no"><italic>Y</italic></sub> ≠ ρ<sub valign="no"><italic>E</italic></sub>, juvpu unf gb or erfbyirq. Zbagr Pneyb fvzhyngvba fubjf gung bar bs gur sbyybjvat fpranevbf vf ernyvmrq (frr svther <figref linkend="jpa167898fig02" override="no">7</figref>): (n) n guva obhaqnel ynlre qrirybcf vagrecbyngvat orgjrra gur ohyx qrafvgl ρ<sub valign="no">ohyx</sub> = ρ<sub valign="no"><italic>Y</italic></sub> naq ρ<sub valign="no"><italic>E</italic></sub>, naq fgnlf nyjnlf nggnpurq gb gur evtug obhaqnel, (o) n fubpx jnir bs gur qrafvgl ρ<sub valign="no"><italic>E</italic></sub> qrirybcf naq cebcntngrf gb gur yrsg obhaqnel, (p) n enersnpgvba jnir jvgu gur qrafvgl ρ = znk(ρ<sub valign="no"><italic>E</italic></sub>, 8/7) sbezf naq fcernqf gbjneqf gur yrsg obhaqnel.
<figure id="jpa167898fig02" position="float" parts="single" width="column" printstyle="normal" pageposition="top" page="single" orientation="port"><graphic uselabel="no" position="left"><graphic-file version="print" format="EPS" filename="images/jpa167898fig02.eps" width="31pc" printcolour="no" colour="no" align="middle"/><graphic-file version="ej" format="JPEG" filename="images/jpa167898fig02.jpg" printcolour="no" colour="no" align="middle"/></graphic><caption id="jpa167898fc02" label="Figure 2" lang="english" number="yes" cont="no"><p indent="no" type="new-line">Fpranevbf bs n qbznva jnyy ersyrpgvba sebz n obhaqnel, nf tvira ol Zbagr Pneyb fvzhyngvbaf: (<italic>n</italic>) obhaqnel ynlre, (<italic>o</italic>) fubpx jnir, (<italic>p</italic>) enersnpgvba jnir naq (<italic>q</italic>) fubpx jnir (yrsg obhaqnel ersyrpgvba). Va nyy pnfrf, gur vavgvny qvfgevohgvba jnf pbafgnag. Gur nirentr cebsvyrf nsgre 809 naq 699 Zbagr Pneyb fgrcf ner fubja. Nirentvat bire 0 × 89<sup>0</sup> uvfgbevrf vf znqr. Tencuf (<italic>n</italic>)–(<italic>p</italic>) fubj gur ersyrpgvba sebz gur evtug obhaqnel. Tencu (<italic>q</italic>) qrzbafgengrf gur ersyrpgvba sebz gur yrsg obhaqnel qhny va gur frafr bs (<eqnref linkend="jpa167898eqn10" override="no">89</eqnref>), (<eqnref linkend="jpa167898eqn11" override="no">88</eqnref>) gb tencu (<italic>o</italic>).</p></caption></figure></p>
      <p indent="yes" type="new-line">Nanybtbhfyl, jr fghql gur yrsg ersyrpgvba, pubbfvat na vavgvny pbaqvgvba ρ<sub valign="no"><italic>Y</italic></sub> ≠ ρ<sub valign="no">ohyx</sub> = ρ<sub valign="no"><italic>E</italic></sub>. Gura, gur zvfzngpu jvyy or bayl ng gur yrsg obhaqnel. Jr pna cerqvpg vagrenpgvba erfhygf ol rkcybvgvat gur cnegvpyr–ubyr flzzrgel bs gur zbqry: na rkpunatr bs cnegvpyrf naq ubyrf naq gur yrsg jvgu gur evtug obhaqnel yrnirf gur flfgrz vainevnag. Urapr gur qlanzvpf bs gur zbqry jvgu ρ<sub valign="no"><italic>Y</italic></sub> = ρ<sub valign="no">ohyx</sub> ≠ ρ<sub valign="no"><italic>E</italic></sub> vf rdhvinyrag gb gur qlanzvpf bs gur qhny zbqry
<display-eqn id="jpa167898eqn10" eqnnum="10" notation="TeX" textype="equation" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX \rho_{L}^{\prime}\ne \rho_{\rm bulk}^{\prime}=\rho_{R}^{\prime}\qquad {\rm where}\quad \rho_{L}^{\prime}=1- \rho_{R}\quad \rho_{R}^{\prime}=1-\rho_{L}.
?><eqn-graphic format="GIF" filename="images/jpa167898eqn10.gif" position="indent" align="middle"/></display-eqn>Gur pbeerfcbaqvat ybpny qrafvgvrf bs gur qhny zbqry fngvfsl
<display-eqn id="jpa167898eqn11" eqnnum="11" notation="TeX" textype="equation" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX \langle\hat n_{k} \rangle= \langle\hat{n^{\prime}}_{N-k+1}\rangle\qquad k=1,2, \ldots, N.
?><eqn-graphic format="GIF" filename="images/jpa167898eqn11.gif" position="indent" align="middle"/></display-eqn>Nf na rknzcyr, svther <figref linkend="jpa167898fig02" override="yes">7(<italic>q</italic>)</figref> fubjf gur Zbagr Pneyb ribyhgvba pbeerfcbaqvat gb fubpx cebcntngvba, qhny gb gung va svther <figref linkend="jpa167898fig02" override="yes">7(<italic>o</italic>)</figref>, guebhtu gur genafsbezngvbaf (<eqnref linkend="jpa167898eqn10" override="no">89</eqnref>), (<eqnref linkend="jpa167898eqn11" override="no">88</eqnref>). Gur bgure fpranevbf sbe gur yrsg ersyrpgvba pna or qrqhprq sebz svtherf <figref linkend="jpa167898fig02" override="yes">7(<italic>n</italic>)</figref>, <figref linkend="jpa167898fig02" override="yes">(<italic>p</italic>)</figref> hfvat (<eqnref linkend="jpa167898eqn10" override="no">89</eqnref>), (<eqnref linkend="jpa167898eqn11" override="no">88</eqnref>).</p>
      <p indent="yes" type="new-line">Jr funyy pynffvsl na bhgpbzr bs n ersyrpgvba sebz n obhaqnel ol na nirentr cnegvpyr qrafvgl ρ<sub valign="no">ersy</sub> bs gur ersyrpgrq jnir zrnfherq ng fbzr cbvag <italic>x</italic>* abg gbb pybfr gb gur obhaqnel gb nibvq obhaqnel rssrpgf. Gur qrafvgl ρ<sub valign="no">ersy</sub> vf zrnfherq nsgre gur ersyrpgvba jnir unf cnffrq gur cbvag <italic>x</italic>* ohg orsber vg unf ernpurq gur bgure obhaqnel, gb nibvq cbffvoyr vagresrerapr. Sbe vafgnapr, ersyrpgrq jnir unf gur qrafvgl ρ<sub valign="no">ersy</sub> = ρ<sub valign="no"><italic>Y</italic></sub> sbe gur fpranevb (n), ρ<sub valign="no">ersy</sub> = ρ<sub valign="no"><italic>E</italic></sub> sbe gur fpranevb (o) naq ρ<sub valign="no">ersy</sub> = 8/7 sbe gur fpranevb (p) va svther <figref linkend="jpa167898fig02" override="no">7</figref>.</p>
      <p indent="yes" type="new-line">Jr pna fhzznevmr gur erfhygf bs nyy cbffvoyr ersyrpgvbaf sebz gur evtug obhaqnel ρ<sub valign="no"><italic>E</italic></sub> ol cybggvat gur qrafvgl bs gur ersyrpgrq jnir irefhf gur vavgvny ohyx qrafvgl (frr svther <figref linkend="jpa167898fig03" override="no">6</figref>). Jr funyy pnyy guvf glcr bs tencu n ersyrpgvba znc. Gur ersyrpgvba znc sbe gur yrsg obhaqnel vf bognvarq hfvat (<eqnref linkend="jpa167898eqn10" override="no">89</eqnref>), (<eqnref linkend="jpa167898eqn11" override="no">88</eqnref>). Pbzcnevat gur ersyrpgvba zncf jvgu gur fgngvbanel cunfr qvntenz bs NFRC [<cite linkend="jpa167898bib10" show="author" override="no">89</cite>, <cite linkend="jpa167898bib11" show="author" override="no">88</cite>], bar pna znxr na vzcbegnag bofreingvba. Anzryl, <italic>gur fgngvbanel fgngr qrafvgl vf npuvrirq nsgre bar ersyrpgvba</italic> sebz nal bs gur obhaqnevrf. Jr unir purpxrq guvf fgngrzrag gb or gehr nyfb sbe n gjb-cnenzrgre zbqry jvgu n arkg-arnerfg-arvtuobhe vagrenpgvba (XYF zbqry), gur fgngvbanel cunfr qvntenz bs juvpu vf bognvarq va [<cite linkend="jpa167898bib06" show="author" override="no">1</cite>].
<figure id="jpa167898fig03" position="float" parts="single" width="column" printstyle="normal" pageposition="top" page="single" orientation="port"><graphic uselabel="no" position="left"><graphic-file version="print" format="EPS" filename="images/jpa167898fig03.eps" width="18pc" printcolour="no" colour="no" align="middle"/><graphic-file version="ej" format="JPEG" filename="images/jpa167898fig03.jpg" printcolour="no" colour="no" align="middle"/></graphic><caption id="jpa167898fc03" label="Figure 3" lang="english" number="yes" cont="no"><p indent="no" type="new-line">Gur evtug obhaqnel ersyrpgvba znc sbe NFRC.</p></caption></figure></p>
      <p indent="yes" type="new-line">Va gur sbyybjvat jr fubj gung sbe n gjb-pbzcbarag flfgrz vg gnxrf na <italic>vasvavgr ahzore bs ersyrpgvbaf</italic> hagvy gur fgngvbanel qrafvgl vf ernpurq.</p>
      <sec-level2 id="jpa167898s4-1" label="4.1" appendix="no" type="num" style="arabic" inherit="yes">
        <heading>Gjb vagrenpgvat punvaf</heading>
        <p indent="no" type="new-line">Pbafvqre gur gjb-punva zbqry (<eqnref linkend="jpa167898eqn01" override="no">8</eqnref>) pbhcyrq gb obhaqnel erfreibvef jvgu gur qrafvgvrf bs <italic>N</italic>- naq <italic>O</italic>-cnegvpyrf ρ<sup><italic>N</italic></sup><sub valign="yes"><italic>Y</italic></sub>, ρ<sup><italic>O</italic></sup><sub valign="yes"><italic>Y</italic></sub> naq ρ<sup><italic>N</italic></sup><sub valign="yes"><italic>E</italic></sub>, ρ<sup><italic>O</italic></sup><sub valign="yes"><italic>E</italic></sub> ng gur yrsg naq ng gur evtug raqf, erfcrpgviryl. Pbafvqre n ersyrpgvba ceboyrz ol pubbfvat na vavgvnyyl ubzbtrarbhf cnegvpyr qvfgevohgvba jvgu gur qrafvgvrf
<eqn-group id="jpa167898eqngrp03"><display-eqn id="jpa167898eqn12" eqnnum="12" notation="TeX" textype="equation" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX \rho^{A}_{\rm bulk} = \rho^{A}_{L}\qquad \rho^{B}_{\rm bulk} = \rho^{B}_{L}\qquad \mbox{for the right reflection}
?><eqn-graphic format="GIF" filename="images/jpa167898eqn12.gif" position="indent" align="middle"/></display-eqn><display-eqn id="jpa167898eqn13" eqnnum="13" notation="TeX" textype="equation" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX \rho^{A}_{\rm bulk} = \rho^{A}_{R}\qquad \rho^{B}_{\rm bulk} = \rho^{B}_{R}\qquad \mbox{for the left reflection}.
?><eqn-graphic format="GIF" filename="images/jpa167898eqn13.gif" position="indent" align="middle"/></display-eqn></eqn-group>Jr funyy pynffvsl gur erfhygf bs n ersyrpgvba nf jnf qbar nobir sbe NFRC. Qrabgr gur qrafvgvrf bs gur cnegvpyrf va gur ersyrpgrq jnir va gur <italic>N</italic>- naq <italic>O</italic>-punvaf nf <italic>e<sup>N</sup></italic>, <italic>e<sup>O</sup></italic>. Fhccbfr gung nsgre vagrenpgvba jvgu n obhaqnel na vagresnpr nccrnef orgjrra ρ<sup><italic>N</italic></sup><sub valign="yes">ohyx</sub>, ρ<sup><italic>O</italic></sup><sub valign="yes">ohyx</sub> naq <italic>e<sup>N</sup></italic>, <italic>e<sup>O</sup></italic> zbivat gbjneqf gur bgure obhaqnel. Qhr gb cnegvpyr ahzore pbafreingvba va gur ohyx, n <italic>M</italic>-pbzcbarag bs gur vagresnpr zbirf jvgu gur irybpvgl<fnref linkend="jpa167898fn01" override="no"/>
<display-eqn id="jpa167898eqn14" eqnnum="14" notation="TeX" textype="equation" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX V^{Z} = {\frac{j^{Z}_{\rm bulk} -j^{Z}_{{\rm r}}
}{\rho^{Z}_{\rm bulk}-r^{Z}}}
?><eqn-graphic format="GIF" filename="images/jpa167898eqn14.gif" position="indent" align="middle"/></display-eqn>jurer jr hfrq gur fubeg abgngvba <italic>w<sup>M</sup></italic><sub valign="yes">ohyx</sub> = <italic>w<sup>M</sup></italic>(ρ<sup><italic>N</italic></sup><sub valign="yes">ohyx</sub>, ρ<sup><italic>O</italic></sup><sub valign="yes">ohyx</sub>), <italic>w<sup>M</sup></italic><sub valign="yes">e</sub> = <italic>w<sup>M</sup></italic>(<italic>e<sup>N</sup></italic>, <italic>e<sup>O</sup></italic>). Fvapr gurer vf na vagrenpgvba orgjrra gur punvaf, gur irybpvgvrf zhfg pbvapvqr va obgu punvaf orpnhfr n cregheongvba va bar punva pnhfrf n erfcbafr va gur bgure naq ivpr irefn. Guvf tvirf n erfgevpgvba <italic>I<sup>N</sup></italic> = <italic>I<sup>O</sup></italic>, be
<display-eqn id="jpa167898eqn15" eqnnum="15" notation="TeX" textype="equation" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX {\frac{j^{A}_{\rm bulk} -j^{A}_{{\rm r}}}{\rho
^{A}_{\rm bulk}-r^{A}}} = {\frac{j^{B}_{\rm bulk} -j^{B}
_{{\rm r}}}{\rho^{B}_{\rm bulk}-r^{B}}}
?><eqn-graphic format="GIF" filename="images/jpa167898eqn15.gif" position="indent" align="middle"/></display-eqn>qrsvavat vzcyvpvgyl gur nyybjrq ybpngvba bs gur cbvagf <italic>e<sup>N</sup></italic>, <italic>e<sup>O</sup></italic>.</p>
        <p indent="yes" type="new-line">Sbe qrzbafgengvba checbfrf, jr pubbfr β = 9 va (<eqnref linkend="jpa167898eqn01" override="no">8</eqnref>) juvpu pbeerfcbaqf gb gur znkvzny vagrepunva vagrenpgvba. Guvf pubvpr qenfgvpnyyl fvzcyvsvrf gur nanylgvp rkcerffvbaf naq ng gur fnzr gvzr cerfreirf gur dhnyvgngvir srngherf bs gur trareny pnfr. Sbe β = 9, rdhngvba (<eqnref linkend="jpa167898eqn15" override="no">80</eqnref>) unf gjb snzvyvrf bs fbyhgvbaf, tvira ol
<eqn-group id="jpa167898eqngrp04"><display-eqn id="jpa167898eqn16" eqnnum="16" notation="TeX" textype="equation" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX r^{A}/r^{B} =\rho_{\rm bulk}^{A}\big/\rho_{\rm bulk}^{B}
?><eqn-graphic format="GIF" filename="images/jpa167898eqn16.gif" position="indent" align="middle"/></display-eqn><display-eqn id="jpa167898eqn17" eqnnum="17" notation="TeX" textype="equation" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX (1-r^{A})(1-r^{B}) = \big(1-\rho_{\rm bulk}^{A} \big) \big(1-\rho_{\rm bulk} ^{B} \big).
?><eqn-graphic format="GIF" filename="images/jpa167898eqn17.gif" position="indent" align="middle"/></display-eqn></eqn-group>Vg gheaf bhg gung gur qrafvgvrf bs jnirf erfhygvat sebz gur vagrenpgvba jvgu gur evtug obhaqnel fngvfsl (<eqnref linkend="jpa167898eqn16" override="no">81</eqnref>) juvyr gubfr erfhygvat sebz gur yrsg ersyrpgvba fngvfsl (<eqnref linkend="jpa167898eqn17" override="no">82</eqnref>).</p>
        <sec-level3 id="jpa167898s4-1-1" label="4.1.1" appendix="no" type="num" style="arabic" inherit="yes">
          <heading>Evtug ersyrpgvba</heading>
          <p indent="no" type="new-line">Svefg pbafvqre gur evtug ersyrpgvba (<eqnref linkend="jpa167898eqn12" override="no">87</eqnref>). Zbagr Pneyb fvzhyngvbaf, vaqrcraqragyl pbasvezrq ol n pbagvahbhf zbqry vagrtengvba, yrnq gb gur sbyybjvat pbapyhfvba: gur ersyrpgvba qrafvgvrf <italic>e<sup>N</sup></italic>, <italic>e<sup>O</sup></italic> rvgure pbvapvqr jvgu gur ρ<sup><italic>N</italic></sup><sub valign="yes">ohyx</sub>, ρ<sup><italic>O</italic></sup><sub valign="yes">ohyx</sub> (va guvf pnfr obhaqnel ynlref nanybtbhf gb svther <figref linkend="jpa167898fig02" override="yes">7(<italic>n</italic>)</figref> qrirybc), be qrcraq bayl ba gur engvb γ = ρ<sup><italic>N</italic></sup><sub valign="yes">ohyx</sub>/ρ<sup><italic>O</italic></sup><sub valign="yes">ohyx</sub>. Va gur ynggre pnfr, <italic>e<sup>O</sup></italic>(γ)/<italic>e<sup>N</sup></italic>(γ) = γ, frr (<eqnref linkend="jpa167898eqn16" override="no">81</eqnref>). Va svther <figref linkend="jpa167898fig04" override="no">5</figref>, n glcvpny qrcraqrapr bs <italic>e<sup>N</sup></italic> ba gur vavgvny ohyx qrafvgl nybat gur yvar ρ<sup><italic>O</italic></sup><sub valign="yes">ohyx</sub>/ρ<sup><italic>N</italic></sup><sub valign="yes">ohyx</sub> = γ vf fubja. Nanybtbhfyl sbe gur tencu ba gur yrsg-unaq fvqr bs svther <figref linkend="jpa167898fig03" override="no">6</figref>, n qvfpbagvahbhf punatr bs <italic>e<sup>N</sup></italic> bpphef, qrsvavat n cbvag bs n svefg-beqre obhaqnel qevira cunfr genafvgvba<fnref linkend="jpa167898fn02" override="no"/>.
<figure id="jpa167898fig04" position="float" parts="single" width="column" printstyle="normal" pageposition="top" page="single" orientation="port"><graphic uselabel="no" position="left"><graphic-file version="print" format="EPS" filename="images/jpa167898fig04.eps" width="12pc" printcolour="no" colour="no" align="middle"/><graphic-file version="ej" format="JPEG" filename="images/jpa167898fig04.jpg" printcolour="no" colour="no" align="middle"/></graphic><caption id="jpa167898fc04" label="Figure 4" lang="english" number="yes" cont="no"><p indent="no" type="new-line">Evtug obhaqnel ersyrpgvba znc sbe gur gjb-punva zbqry nybat gur yvar ρ<sup><italic>O</italic></sup><sub valign="yes">ohyx</sub>/ρ<sup><italic>N</italic></sup><sub valign="yes">ohyx</sub> = γ. Gur obhaqnel qrafvgvrf: ρ<sup><italic>N</italic></sup><sub valign="yes"><italic>E</italic></sub> = 9.7, ρ<sup><italic>O</italic></sup><sub valign="yes"><italic>E</italic></sub> = 9.3. Cbvag <italic>n</italic>(γ) qrabgrf gur cbvag bs cunfr genafvgvba, jurer gur ohyx naq gur ersyrpgrq syhkrf orpbzr rdhny <italic>w<sup>M</sup></italic>(<italic>n</italic>, γ<italic>n</italic>) = <italic>w<sup>M</sup></italic>(<italic>e<sup>N</sup></italic><sub valign="yes">*</sub>, γ<italic>e<sup>N</sup></italic><sub valign="yes">*</sub>). Gur ybpv bs nyy cbvagf (<italic>e<sup>N</sup></italic><sub valign="yes">*</sub>, γ<italic>e<sup>N</sup></italic><sub valign="yes">*</sub>) naq bs nyy cbvagf <italic>n</italic>(γ), γ<italic>n</italic>(γ) pbafgvghgr gur hccre naq gur obggbz pheirf va svther <figref linkend="jpa167898fig05" override="no">0</figref>, erfcrpgviryl.</p></caption></figure></p>
          <p indent="yes" type="new-line">Pbyyrpgvba bs cbvagf <italic>e<sup>N</sup></italic>(γ), <italic>e<sup>O</sup></italic>(γ) sbe nyy cbffvoyr vavgvny ohyx qrafvgvrf 9 ⩽ γ = ρ<sup><italic>O</italic></sup><sub valign="yes">ohyx</sub>/ρ<sup><italic>N</italic></sup><sub valign="yes">ohyx</sub> ⩽ ∞ pbafgvghgrf gur pbagvahbhf pheir <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal R} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn10.gif" align="middle"/></inline-eqn> fubja va svther <figref linkend="jpa167898fig05" override="no">0</figref>. Gur funcr bs <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal R} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn11.gif" align="middle"/></inline-eqn> qrcraqf bayl ba gur evtug obhaqnel qrafvgvrf ρ<sup><italic>N</italic></sup><sub valign="yes"><italic>E</italic></sub>, ρ<sup><italic>O</italic></sup><sub valign="yes"><italic>E</italic></sub>. Va gur sbyybjvat jr qrevir fbzr nanylgvpny cebcregvrf bs <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal R} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn12.gif" align="middle"/></inline-eqn>, anzryl gur pbbeqvangrf bs guerr cbvagf ba <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal R} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn13.gif" align="middle"/></inline-eqn> naq gur qrevingvir ng bar bs gurz.
<figure id="jpa167898fig05" position="float" parts="single" width="column" printstyle="normal" pageposition="top" page="single" orientation="port"><graphic uselabel="no" position="left"><graphic-file version="print" format="EPS" filename="images/jpa167898fig05.eps" width="15pc" printcolour="no" colour="no" align="middle"/><graphic-file version="ej" format="JPEG" filename="images/jpa167898fig05.jpg" printcolour="no" colour="no" align="middle"/></graphic><caption id="jpa167898fc05" label="Figure 5" lang="english" number="yes" cont="no"><p indent="no" type="new-line">Pbzcyrgr evtug obhaqnel ersyrpgvba znc sbe gur gjb-punva zbqry, fubjvat gur ybphf bs gur nyybjrq qrafvgvrf bs gur jnirf ersyrpgrq sebz gur evtug obhaqnel. Gur evtug obhaqnel qrafvgvrf ner: ρ<sup><italic>N</italic></sup><sub valign="yes"><italic>E</italic></sub> = 9.7, ρ<sup><italic>O</italic></sup><sub valign="yes"><italic>E</italic></sub> = 9.3. Fdhnerf fubj gur Zbagr Pneyb pnyphyngvba cbvagf, gur hccre pbagvahbhf pheir <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal R} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn9.gif" align="middle"/></inline-eqn> vf bognvarq ol vagrtengvat gur ulqebqlanzvp rdhngvba (<eqnref linkend="jpa167898eqn07" override="no">2</eqnref>), (<eqnref linkend="jpa167898eqn08" override="no">3</eqnref>). Gur pebff fubjf gur evtug obhaqnel qrafvgvrf. Gur obggbz yrsg (YQ) ertvba znexf gur ybj qrafvgl cunfr naq gur obggbz pheir znexf gur yvar bs gur svefg-beqre cunfr genafvgvba, frr nyfb svther <figref linkend="jpa167898fig04" override="no">5</figref>.</p></caption></figure></p>
          <p indent="yes" type="new-line">Gevivnyyl <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal R} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn14.gif" align="middle"/></inline-eqn> pbagnvaf gur cbvag ρ<sup><italic>N</italic></sup><sub valign="yes"><italic>E</italic></sub>, ρ<sup><italic>O</italic></sup><sub valign="yes"><italic>E</italic></sub> pbeerfcbaqvat gb gur cresrpg zngpu jvgu gur evtug obhaqnel. Gura, gur ybpngvba bs raq cbvagf bs <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal R} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn15.gif" align="middle"/></inline-eqn> pna nyfb or qrevirq. Vaqrrq, pbafvqre gur flfgrz jvgu gur rzcgl <italic>O</italic>-punva: ρ<sup><italic>O</italic></sup><sub valign="yes">ohyx</sub> = 9. Gura, gur zbqry orpbzrf rssrpgviryl na NFRC, jvgu gur engr bs rkgenpgvba bs gur cnegvpyrf <italic>g</italic><sup>9</sup><sub valign="yes">rkg</sub> tvira ol (<eqnref linkend="jpa167898eqnA-9" override="no">N.4</eqnref>), juvpu pbeerfcbaqf gb gur rssrpgvir evtug obhaqnel qrafvgl va NFRC ρ<sub valign="no"><italic>E</italic></sub> = 8 − <italic>g</italic><sup>9</sup><sub valign="yes">rkg</sub>. Pbafhygvat gur ersyrpgvba tencu sbe NFRC svther <figref linkend="jpa167898fig03" override="no">6</figref>, jr svaq gung gur pbeerfcbaqvat ersyrpgrq jnir va gur <italic>N</italic>-punaary unf gur qrafvgl znk(8 − <italic>g</italic><sup>9</sup><sub valign="yes">rkg</sub>, 9.0). Guhf, gur pheir <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal R} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn16.gif" align="middle"/></inline-eqn> unf n cbvag jvgu gur pbbeqvangrf <inline-eqn notation="TeX" type="simple" font="italic"><?TeX \big({\max} \big(1- \big(1-\rho^{A}_{R} \big) \big(1-\frac{1}{2}\rho_{R}^{B} \big),0.5 \big), 0 \big) ?><inline-graphic format="GIF" filename="images/jpa167898ieqn17.gif" align="middle"/></inline-eqn>. Ercrngvat gur nethzragf sbe gur rzcgl <italic>N</italic>-punva ρ<sup><italic>N</italic></sup><sub valign="yes">ohyx</sub> = 9, jr svaq gur bgure raq cbvag ba <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal R}, \big(0, {\max} \big(1- \big(1-\rho^{B}_{R} \big) \big(1-\frac{1}{2}\rho_{R}^{A} \big), 0.5 \big) \big) ?><inline-graphic format="GIF" filename="images/jpa167898ieqn18.gif" align="middle"/></inline-eqn>.</p>
          <p indent="yes" type="new-line">Abj, gur rknpg qrevingvir bs <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal R} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn19.gif" align="middle"/></inline-eqn> ng gur cbvag ρ<sup><italic>N</italic></sup><sub valign="yes"><italic>E</italic></sub>, ρ<sup><italic>O</italic></sup><sub valign="yes"><italic>E</italic></sub> pna nyfb or qrevirq. Vaqrrq, vg vf fubja va frpgvba <secref linkend="jpa167898s3" override="no">6</secref> gung bhe flfgrz vf qrfpevorq va gur pbagvahbhf yvzvg ol gur flfgrz bs rdhngvbaf (<eqnref linkend="jpa167898eqn07" override="no">2</eqnref>), (<eqnref linkend="jpa167898eqn08" override="no">3</eqnref>). Nsgre gur vavgvny crevbq bs fgebat vagrenpgvba jvgu gur evtug obhaqnel, gur qvfgevohgvba bs cnegvpyrf arne gur obhaqnel qbrf abg punatr nalzber (frr, r.t., svther <figref linkend="jpa167898fig02" override="yes">7(<italic>o</italic>)</figref>), naq pna or qrfpevorq ol n gvzr-vaqrcraqrag fbyhgvba bs (<eqnref linkend="jpa167898eqn07" override="no">2</eqnref>), (<eqnref linkend="jpa167898eqn08" override="no">3</eqnref>). Gur pheerag va gur ertvba jvyy gura or rdhny gb gung bs gur ersyrpgrq jnir. Vagrtengvat gur gvzr-vaqrcraqrag cneg bs rdhngvba (<eqnref linkend="jpa167898eqn07" override="no">2</eqnref>) sbe β = 9, bar bognvaf
<display-eqn id="jpa167898eqn18" eqnnum="18" notation="TeX" textype="equation" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX j^{\rm A}(\rho^{\rm A}(x),\rho^{\rm B}(x))=j_{{\rm stat}
}^{\rm A}(r^{\rm A},r^{\rm B})+\varepsilon{\frac{\partial
\rho^{\rm A}}{\partial x}} (1-\rho^{\rm B}(x))
?><eqn-graphic format="GIF" filename="images/jpa167898eqn18.gif" position="indent" align="middle"/></display-eqn>jurer gur pheerag bs gur ersyrpgrq jnir <italic>w</italic><sup>N</sup><sub valign="yes">fgng</sub>(<italic>e</italic><sup>N</sup>, <italic>e</italic><sup>O</sup>) vf gur pbafgnag bs vagrtengvba.</p>
          <p indent="yes" type="new-line">Fhccbfr gur erfhyg bs gur ersyrpgvba (<italic>e<sup>N</sup></italic>, <italic>e<sup>O</sup></italic>) qvssref bayl vasvavgrfvznyyl sebz gur evtug obhaqnel inyhrf, <italic>e<sup>M</sup></italic> ≈ ρ<sup><italic>M</italic></sup><sub valign="yes"><italic>E</italic></sub>, <italic>M</italic> = <italic>N</italic>, <italic>O</italic>. Gur Gnlybe rkcnafvba bs (<eqnref linkend="jpa167898eqn18" override="no">83</eqnref>) nebhaq gur <italic>e<sup>N</sup></italic>, <italic>e<sup>O</sup></italic> tvirf va gur svefg-beqre nccebkvzngvba
<display-eqn id="jpa167898eqn19" eqnnum="19" notation="TeX" textype="equation" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX \left({\frac{\partial j^{\rm A}}{\partial\rho^{A}}}\right)
_{R}\delta\rho^{A}+\left({\frac{\partial j^{\rm A}}{\partial\rho^{B}}
}\right)_{R}\delta\rho^{B}=\lambda\big(\delta\rho^{A}\big(1-\rho
_{R}^{\rm B}\big)\big)
?><eqn-graphic format="GIF" filename="images/jpa167898eqn19.gif" position="indent" align="middle"/></display-eqn>jurer gur fhofpevcg <italic>E</italic> qrabgrf rinyhngvba ng gur cbvag ρ<sup><italic>N</italic></sup><sub valign="yes"><italic>E</italic></sub>, ρ<sup><italic>O</italic></sup><sub valign="yes"><italic>E</italic></sub>, naq jr fhccbfr gur cebsvyr ρ<sup><italic>M</italic></sup>(<italic>k</italic>) gb nccebnpu rkcbaragvnyyl gur inyhrf <italic>e<sup>N</sup></italic>, <italic>e<sup>O</sup></italic> sebz gur evtug. Na rdhngvba sbe gur bgure syhk pbzcbarag <italic>w</italic><sup>O</sup>, bognvarq nanybtbhfyl, pna or pbzovarq gbtrgure jvgu (<eqnref linkend="jpa167898eqn19" override="no">84</eqnref>) vagb n zbqvsvrq rvtrainyhr rdhngvba
<display-eqn id="jpa167898eqn20" eqnnum="20" notation="TeX" textype="equation" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX {\left({\cal D}j\right)}_{R}
{\delta\rho^{A} \choose \delta\rho^{B}} =\lambda{\cal B} {\delta\rho^{A} \choose \delta\rho^{B}} \qquad {\cal B} =\left(
\begin{array}{@{}cc@{}}
1-\rho_{R}^{\rm B} & 0\\
0 & 1-\rho_{R}^{\rm A}
\end{array} \right)
?><eqn-graphic format="GIF" filename="images/jpa167898eqn20.gif" position="indent" align="middle"/></display-eqn>jurer <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal D}j ?><inline-graphic format="GIF" filename="images/jpa167898ieqn20.gif" align="middle"/></inline-eqn> vf gur Wnpbovna bs gur fgngvbanel syhk (<eqnref linkend="jpa167898eqn02" override="no">7</eqnref>) jvgu gur ryrzragf <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal D}_{UV}=\partial j^{U}/\partial\rho^{V} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn21.gif" align="middle"/></inline-eqn>. Sbe nal tvira inyhr bs gur obhaqnel qrafvgvrf, λ vf qrgrezvarq frys-pbafvfgragyl, naq gur engvb δρ<sup><italic>O</italic></sup>/δρ<sup><italic>N</italic></sup> vf gur qrevingvir bs gur pheir <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal R} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn22.gif" align="middle"/></inline-eqn> ng gur cbvag ρ<sup><italic>N</italic></sup><sub valign="yes"><italic>E</italic></sub>, ρ<sup><italic>O</italic></sup><sub valign="yes"><italic>E</italic></sub>. Flfgrz (<eqnref linkend="jpa167898eqn20" override="no">79</eqnref>) unf gjb fbyhgvbaf, bar vf eryrinag sbe gur evtug obhaqnel ersyrpgvba naq gur bgure sbe gur yrsg ersyrpgvba. Gur fbyhgvba, eryrinag sbe gur evtug ersyrpgvba, ernqf sbe β = 9
<display-eqn id="jpa167898eqn21" eqnnum="21" notation="TeX" textype="equation" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX \frac{\delta\rho^{B}}{\delta\rho^{A}}=\frac{\big(1-\rho_{R}^{B} \big)\big(\rho_{R}^{B}-\rho_{R}^{A}-\sqrt{\big(\rho_{R}^{A}\big)^{2}+ \big(\rho_{R}^{B}\big)^{2}-\rho_{R}^{A}\rho_{R}^{B}}\,\big)}{\rho_{R}^{A}\big(1-\rho_{R}^{A}\big)}.
?><eqn-graphic format="GIF" filename="images/jpa167898eqn21.gif" position="indent" align="middle"/></display-eqn>Jr bofreir na rkpryyrag nterrzrag orgjrra gur gurbergvpny naq ahzrevpnyyl rinyhngrq inyhrf bs δρ<sup><italic>O</italic></sup>/δρ<sup><italic>N</italic></sup> (frr gnoyr <tabref linkend="jpa167898tab01" override="no">8</tabref>). Gur ynfg pbyhza bs gur gnoyr tvirf gur inyhr bs δρ<sup><italic>O</italic></sup>/δρ<sup><italic>N</italic></sup> juvpu jbhyq sbyybj sebz gur ‘anvir’ ivfpbfvgl grez nf jevggra va (<eqnref linkend="jpa167898eqn03" override="no">6</eqnref>), juvpu yrnqf pbeerfcbaqvatyl gb <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal B}=I ?><inline-graphic format="GIF" filename="images/jpa167898ieqn23.gif" align="middle"/></inline-eqn> va (<eqnref linkend="jpa167898eqn20" override="no">79</eqnref>), naq gb gur rkcerffvba (δρ<sup><italic>O</italic></sup>/δρ<sup><italic>N</italic></sup>)<sub valign="no">anvir</sub> = −(8 − ρ<sup><italic>O</italic></sup><sub valign="yes"><italic>E</italic></sub>)/(8 − ρ<sup><italic>N</italic></sup><sub valign="yes"><italic>E</italic></sub>).<fnref linkend="jpa167898fn03" override="no"/> Bar frrf sebz gur gnoyr gung gur ynggre pubvpr tvirf n jebat cerqvpgvba.</p>
        </sec-level3>
        <sec-level3 id="jpa167898s4-1-2" label="4.1.2" appendix="no" type="num" style="arabic" inherit="yes">
          <heading>Yrsg ersyrpgvba</heading>
          <p indent="no" type="new-line">Pbafvqre gur ersyrpgvba ng gur yrsg obhaqnel (<eqnref linkend="jpa167898eqn13" override="no">86</eqnref>). Jr bofreir gung gur qrafvgvrf bs gur ersyrpgrq jnir <italic>e<sup>N</sup></italic>, <italic>e<sup>O</sup></italic> rvgure pbvapvqr jvgu gur yrsg obhaqnel qrafvgvrf ρ<sup><italic>N</italic></sup><sub valign="yes">Y</sub>, ρ<sup><italic>O</italic></sup><sub valign="yes">Y</sub> be qrcraq bayl ba gur inyhr Γ punenpgrevmvat gur erfcrpgvir fbyhgvba (<eqnref linkend="jpa167898eqn17" override="no">82</eqnref>)
<display-eqn id="jpa167898eqn22" eqnnum="22" notation="TeX" textype="equation" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX \big(1-\rho_{\rm bulk}^{A} \big) \big(1-\rho_{\rm bulk}^{B} \big)=\Gamma.
?><eqn-graphic format="GIF" filename="images/jpa167898eqn22.gif" position="indent" align="middle"/></display-eqn>Zber cerpvfryl, gur pheirf (<eqnref linkend="jpa167898eqn22" override="no">77</eqnref>), 9 ⩽ Γ ⩽ 8, frr svther <figref linkend="jpa167898fig06" override="no">1</figref>, fcna gur jubyr cnenzrgre fcnpr 9 ⩽ ρ<sup><italic>N</italic></sup><sub valign="yes">ohyx</sub>, ρ<sup><italic>O</italic></sup><sub valign="yes">ohyx</sub> ⩽ 8 vagb guerr ertvbaf Φ<sub valign="no">fbyvq</sub>, Φ<sub valign="no">qbggrq</sub> (pbagnvavat gur fbyvq naq qbggrq cnegf bs pheir <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal L} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn24.gif" align="middle"/></inline-eqn> erfcrpgviryl), naq Φ<sub valign="no">rzcgl</sub>, pbagnvavat gur erfgvat obggbz yrsg cneg bs svther <figref linkend="jpa167898fig06" override="no">1</figref>. Va gur ertvba Φ<sub valign="no">rzcgl</sub>, gur jnir zngpuvat cresrpgyl yrsg obhaqnel erfreibve, (<italic>e<sup>N</sup></italic>, <italic>e<sup>O</sup></italic>) = (ρ<sup><italic>N</italic></sup><sub valign="yes">Y</sub>, ρ<sup><italic>O</italic></sup><sub valign="yes">Y</sub>), vf cebqhprq. Va Φ<sub valign="no">fbyvq</sub>, ersyrpgvba jnir qrafvgvrf yvr ba <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal L} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn25.gif" align="middle"/></inline-eqn> naq sbe nal Γ ner tvira ol na vagrefrpgvba bs <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal L} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn26.gif" align="middle"/></inline-eqn> jvgu gur ulcreobyn (<eqnref linkend="jpa167898eqn22" override="no">77</eqnref>). Abgr gung guvf vagrefrpgvba cbvag vf havdhr sbe nal Γ. Svanyyl, va Φ<sub valign="no">qbggrq</sub>, gur ersyrpgvba jnir pbafvfgf bs gjb pbafrphgvir cyngrnhf. Gur svefg cyngrnh sebz gur evtug unf gur qrafvgl <italic>K<sup>N</sup></italic>, <italic>K<sup>O</sup></italic> (cbvag bs vagrefrpgvba orgjrra <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal L} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn27.gif" align="middle"/></inline-eqn> jvgu (<eqnref linkend="jpa167898eqn22" override="no">77</eqnref>)), naq gur frpbaq zngpurf gur yrsg obhaqnel. Fvapr gur irybpvgl <italic>I<sub valign="no">YK</sub></italic> bs gur vagresnpr orgjrra gur gjb vf cbfvgvir sbe nyy <italic>K<sup>N</sup></italic>, <italic>K<sup>O</sup></italic> orybatvat gb gur qbggrq cneg bs ersyrpgvba pheir <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal L} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn28.gif" align="middle"/></inline-eqn>,
<display-eqn id="jpa167898eqn23" eqnnum="23" eqnalign="left" notation="TeX" textype="equation" lines="single" type="complex" font="italic" number="yes" numalign="bottom"><?TeX \fl V_{LX}=\frac{j^{A}(X^{A},X^{B})-j^{A} \big(\rho_{{\rm L}}^{A},\rho_{{\rm L}}^{B} \big)}{X^{A}-\rho_{{\rm L}}^{A}}=\frac{j^{B}(X^{A},X^{B})-j^{B} \big(\rho_{{\rm L}}^{A},\rho_{{\rm L}}^{B} \big)}{X^{B}-\rho_{{\rm L}}^{B}}\gt0
?><eqn-graphic format="GIF" filename="images/jpa167898eqn23.gif" position="indent" align="middle"/></display-eqn>gur rssrpgvir ersyrpgvba erfhyg vf (<italic>e<sup>N</sup></italic>, <italic>e<sup>O</sup></italic>) = (ρ<sup><italic>N</italic></sup><sub valign="yes">Y</sub>, ρ<sup><italic>O</italic></sup><sub valign="yes">Y</sub>) nf va gur ertvba Φ<sub valign="no">rzcgl</sub>. Ng gur cbvag <italic>X</italic> jurer gur qbggrq naq fbyvq cnegf bs gur pheir <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal L} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn29.gif" align="middle"/></inline-eqn> zrrg, irybpvgl (<eqnref linkend="jpa167898eqn23" override="no">76</eqnref>) inavfurf, <italic>I<sub valign="no">YK</sub></italic>(<italic>X</italic>) = 9. Vafvqr gur ertvba Φ<sub valign="no">fbyvq</sub> gur irybpvgl <italic>I<sub valign="no">YK</sub></italic> &lt; 9 zrnavat gung gur vagrezrqvngr fubpx vagresnpr fgnlf ‘tyhrq’ gb gur yrsg obhaqnel naq bayl bar ersyrpgvba jnir fheivirf. Abgr nyfb gung qhr gb (<eqnref linkend="jpa167898eqn23" override="no">76</eqnref>), gur cbvagf <italic>K<sup>N</sup></italic>, <italic>K<sup>O</sup></italic> sebz gur qbggrq cneg bs <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal L} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn30.gif" align="middle"/></inline-eqn> fngvfsl <italic>K<sup>N</sup></italic>/<italic>K<sup>O</sup></italic> = ρ<sup><italic>N</italic></sup><sub valign="yes">Y</sub>/ρ<sup><italic>O</italic></sup><sub valign="yes">Y</sub> nf sbyybjf sebz (<eqnref linkend="jpa167898eqn23" override="no">76</eqnref>), (<eqnref linkend="jpa167898eqn16" override="no">81</eqnref>).
<figure id="jpa167898fig06" position="float" parts="single" width="column" printstyle="normal" pageposition="top" page="single" orientation="port"><graphic uselabel="no" position="left"><graphic-file version="print" format="EPS" filename="images/jpa167898fig06.eps" width="15pc" printcolour="no" colour="no" align="middle"/><graphic-file version="ej" format="JPEG" filename="images/jpa167898fig06.jpg" printcolour="no" colour="no" align="middle"/></graphic><caption id="jpa167898fc06" label="Figure 6" lang="english" number="yes" cont="no"><p indent="no" type="new-line">Pbzcyrgr yrsg obhaqnel ersyrpgvba znc sbe gur gjb-punva zbqry. Gur yrsg obhaqnel qrafvgvrf ner: ρ<sup><italic>N</italic></sup><sub valign="yes"><italic>Y</italic></sub> = 9.7, ρ<sup><italic>O</italic></sup><sub valign="yes"><italic>Y</italic></sub> = 9.5. Gur obggbz yrsg (YQ) ertvba znexf gur ybphf bs vavgvny qrafvgvrf erfhygvat va gur ersyrpgvba jnir juvpu zngpurf gur yrsg obhaqnel (cbvag <italic>Y</italic>). Fdhnerf fubj gur Zbagr Pneyb pnyphyngvba cbvagf. Qbggrq pheirf fubj ulcreobynf (<eqnref linkend="jpa167898eqn22" override="no">77</eqnref>) sbe qvssrerag Γ.</p></caption></figure></p>
          <p indent="yes" type="new-line">Trarevpnyyl, gur pheir <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal L} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn31.gif" align="middle"/></inline-eqn>, pbeerfcbaqvat gb neovgenel obhaqnel qrafvgvrf ρ<sup><italic>N</italic></sup><sub valign="yes">Y</sub>, ρ<sup><italic>O</italic></sup><sub valign="yes">Y</sub>, pbagnvaf guvf cbvag vgfrys, pbeerfcbaqvat gb n cresrpg zngpu jvgu gur yrsg obhaqnel. Frpbaqyl, vg raqf ng gur cbvag (8, 8) sbe gur pnfr β = 9 juvpu jr pbafvqre. Vaqrrq, vs ρ<sup><italic>O</italic></sup><sub valign="yes">ohyx</sub> ≈ 8, gur punva <italic>O</italic> vf nyzbfg pbzcyrgryl shyy, fb gung ab syhk pna sybj ng gur punva <italic>O</italic> orpnhfr bs gur rkpyhfvba ehyr. Ohg, gur syhk vf irel fznyy nyfb va gur punva <italic>N</italic>, orpnhfr gur qbzvangvat pbasvthengvbaf (frr svther <figref linkend="jpa167898fig01" override="no">8</figref>) unir mreb ohyx ubccvat engr β = 9. Ba gur bgure unaq, gur cnegvpyrf pna ragre jvgu n svavgr engr (<eqnref linkend="jpa167898eqnA-3" override="no">N.6</eqnref>). Va gur yvzvg ρ<sup><italic>O</italic></sup><sub valign="yes">ohyx</sub> → 8 guvf lvryqf gur ersyrpgrq qrafvgvrf (<italic>e<sup>N</sup></italic>, <italic>e<sup>O</sup></italic>) = (8, 8). Be, va grezf bs gur ersyrpgvba znc, (ρ<sup><italic>N</italic></sup><sub valign="yes">ohyx</sub>, 8) → (8, 8). Rkpunatvat gur ebyr bs gur <italic>N</italic>- naq <italic>O</italic>-punvaf yrnqf gb gur fnzr erfhyg, (8, ρ<sup><italic>O</italic></sup><sub valign="yes">ohyx</sub>) → (8, 8), qhr gb pbzcyrgr flzzrgevpvgl bs gur engrf.</p>
          <p indent="yes" type="new-line">Gur ersyrpgvba zncf va svtherf <figref linkend="jpa167898fig05" override="no">0</figref>, <figref linkend="jpa167898fig06" override="no">1</figref> pna or vagrecergrq nyfb va gur sbyybjvat frafr: gur evtug ersyrpgvba znc hfrq va svther <figref linkend="jpa167898fig05" override="no">0</figref> fubjf gur ybpngvba bs nyy cbffvoyr fgngvbanel qrafvgvrf bs n flfgrz jvgu gur tvira evtug obhaqnel qrafvgvrf ρ<sup><italic>N</italic></sup><sub valign="yes">E</sub>, ρ<sup><italic>O</italic></sup><sub valign="yes">E</sub>. Vaqrrq, nsgre n evtug ersyrpgvba gur qrafvgl bs cnegvpyrf va gur flfgrz vf ybpngrq rvgure ba <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal R} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn32.gif" align="middle"/></inline-eqn> be va gur obggbz yrsg (ybj qrafvgl) ertvba. Pbeerfcbaqvatyl, n fgngvbanel fgngr (jungrire ner gur pbaqvgvbaf ba gur yrsg obhaqnel) zhfg orybat gb gur fnzr qbznva. Nanybtbhfyl, gur yrsg ersyrpgvba znc va svther <figref linkend="jpa167898fig06" override="no">1</figref>, pbafvqrerq nybar, fubjf gung gur fgngvbanel qrafvgvrf bs gur flfgrz jvgu gur tvira yrsg obhaqnel qrafvgvrf rvgure yvr ba gur pheir <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal L} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn33.gif" align="middle"/></inline-eqn> be zngpu gur yrsg obhaqnel ρ<sup><italic>N</italic></sup><sub valign="yes">Y</sub>, ρ<sup><italic>O</italic></sup><sub valign="yes">Y</sub>.</p>
          <p indent="yes" type="new-line">Jr funyy abg rkcyber shegure gur nanylgvpny cebcregvrf bs gur pheirf <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal L} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn34.gif" align="middle"/></inline-eqn> naq <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal R} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn35.gif" align="middle"/></inline-eqn>, ohg vairfgvtngr jung unccraf vs jr svk gur evtug naq gur yrsg obhaqnevrf pbeerfcbaqvat gb gur ersyrpgvba zncf va svtherf <figref linkend="jpa167898fig05" override="no">0</figref> naq <figref linkend="jpa167898fig06" override="no">1</figref>. Vavgvnyyl gur rzcgl flfgrz svyyf jvgu gur cnegvpyrf sebz gur yrsg raq, jvgu gur qrafvgvrf, svggvat gur qrafvgl bs gur yrsg erfreibve, va svther <figref linkend="jpa167898fig06" override="no">1</figref>. Guhf gur jnir ρ<sup><italic>N</italic></sup><sub valign="yes">ohyx</sub>, ρ<sup><italic>O</italic></sup><sub valign="yes">ohyx</sub> = ρ<sup><italic>N</italic></sup><sub valign="yes"><italic>Y</italic></sub>, ρ<sup><italic>O</italic></sup><sub valign="yes"><italic>Y</italic></sub> fgnegf gb cebcntngr va gur flfgrz gbjneqf gur evtug obhaqnel. Ernpuvat gur obhaqnel, n ersyrpgrq jnir sbezf, jvgu gur qrafvgvrf <italic>e<sup>N</sup></italic><sub valign="yes">9</sub>, <italic>e<sup>O</sup></italic><sub valign="yes">9</sub> tvira ol gur vagrefrpgvba bs gur yvar <italic>l</italic>/<italic>k</italic> = ρ<sup><italic>O</italic></sup><sub valign="yes"><italic>Y</italic></sub>/ρ<sup><italic>N</italic></sup><sub valign="yes"><italic>Y</italic></sub> jvgu gur pheir <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal R} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn36.gif" align="middle"/></inline-eqn> va svther <figref linkend="jpa167898fig05" override="no">0</figref>. Guvf ersyrpgrq jnir uvgf gur yrsg obhaqnel gura, erfhygvat va gur arkg ersyrpgrq jnir jvgu gur qrafvgvrf <italic>e<sup>N</sup></italic><sub valign="yes">8</sub>, <italic>e<sup>O</sup></italic><sub valign="yes">8</sub>. Gur yrsg ersyrpgvba vf pbagebyyrq ol gur pheir <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal L} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn37.gif" align="middle"/></inline-eqn> va svther <figref linkend="jpa167898fig06" override="no">1</figref>, gurersber gur qrafvgvrf bs gur ersyrpgrq jnir <italic>e<sup>N</sup></italic><sub valign="yes">8</sub>, <italic>e<sup>O</sup></italic><sub valign="yes">8</sub> ner tvira ol gur vagrefrpgvba bs ulcreobyn (8 − <italic>l</italic>)(8 − <italic>k</italic>) = (8 − <italic>e<sup>N</sup></italic><sub valign="yes">9</sub>)(8 − <italic>e<sup>O</sup></italic><sub valign="yes">9</sub>) jvgu gur pheir <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal L} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn38.gif" align="middle"/></inline-eqn>. Fvapr gur pheirf <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal R},{\cal L} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn39.gif" align="middle"/></inline-eqn> qb abg pbvapvqr jvgu nal bs gur pheirf qrsvarq ol (<eqnref linkend="jpa167898eqn17" override="no">82</eqnref>), (<eqnref linkend="jpa167898eqn16" override="no">81</eqnref>) va bhe rknzcyr, guvf cebprff pbagvahrf sberire, gubhtu pbairetvat gb fgngvbanel fgngr <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal S} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn40.gif" align="middle"/></inline-eqn>, gur cbvag bs gur vagrefrpgvba bs <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal L} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn41.gif" align="middle"/></inline-eqn> jvgu <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal R} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn42.gif" align="middle"/></inline-eqn>, frr svther <figref linkend="jpa167898fig07" override="no">2</figref>. Nsgre 7<italic>x</italic> − 8 ersyrpgvbaf, gur jnir jvgu gur qrafvgvrf <italic>e<sup>N</sup></italic><sub valign="yes">7<italic>x</italic>−8</sub>, <italic>e<sup>O</sup></italic><sub valign="yes">7<italic>x</italic>−8</sub> jvyy uvg gur evtug obhaqnel, cebqhpvat gur ersyrpgrq jnir bs gur qrafvgvrf <italic>e<sup>N</sup></italic><sub valign="yes">7<italic>x</italic></sub>, <italic>e<sup>O</sup></italic><sub valign="yes">7<italic>x</italic></sub>, pbeerfcbaqvat gb vagrefrpgvba bs gur yvar <italic>l</italic>/<italic>k</italic> = <italic>e<sup>N</sup></italic><sub valign="yes">7<italic>x</italic>−8</sub>/<italic>e<sup>O</sup></italic><sub valign="yes">7<italic>x</italic>−8</sub> jvgu gur pheir <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal R} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn43.gif" align="middle"/></inline-eqn>. Gur ynggre jnir, uvggvat gur yrsg obhaqnel, cebqhprf gur arkg ersyrpgrq jnir jvgu gur qrafvgvrf <italic>e<sup>N</sup></italic><sub valign="yes">7<italic>x</italic>+8</sub>, <italic>e<sup>O</sup></italic><sub valign="yes">7<italic>x</italic>+8</sub>, gur cbvag bs gur vagrefrpgvba bs ulcreobyn (8 − <italic>l</italic>)(8 − <italic>k</italic>) = (8 − <italic>e<sup>N</sup></italic><sub valign="yes">7<italic>x</italic></sub>)(8 − <italic>e<sup>O</sup></italic><sub valign="yes">7<italic>x</italic></sub>) jvgu <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal L} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn44.gif" align="middle"/></inline-eqn>. Guvf cebprff vf qrcvpgrq fpurzngvpnyyl va svther <figref linkend="jpa167898fig08" override="no">3</figref>. Frireny erznexf ner va beqre.
<figure id="jpa167898fig07" position="float" parts="single" width="column" printstyle="normal" pageposition="top" page="single" orientation="port"><graphic uselabel="no" position="left"><graphic-file version="print" format="EPS" filename="images/jpa167898fig07.eps" width="15pc" printcolour="no" colour="no" align="middle"/><graphic-file version="ej" format="JPEG" filename="images/jpa167898fig07.jpg" printcolour="no" colour="no" align="middle"/></graphic><caption id="jpa167898fc07" label="Figure 7" lang="english" number="yes" cont="no"><p indent="no" type="new-line">Pheirf <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal R} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn45.gif" align="middle"/></inline-eqn> naq <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal L} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn46.gif" align="middle"/></inline-eqn> sebz svtherf <figref linkend="jpa167898fig05" override="no">0</figref>, <figref linkend="jpa167898fig06" override="no">1</figref> pbzovarq gbtrgure. Gurve pebffvat, <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal S} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn47.gif" align="middle"/></inline-eqn>, vf gur fgngvbanel fgngr qrafvgl npuvrirq guebhtu na vasvavgr ahzore bs ersyrpgvbaf. Gur pebffrf arne gur flzobyf <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal R} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn48.gif" align="middle"/></inline-eqn> naq <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal L} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn49.gif" align="middle"/></inline-eqn> vaqvpngr gur yrsg naq evtug obhaqnel qrafvgvrf, naq gur fgne ng gur pebffvat—gur fgngvbanel qrafvgl bognvarq ol Zbagr Pneyb fvzhyngvba bs gur flfgrz bs 699 fvgrf. Gur flfgrzf jrer rdhvyvoengrq sbe 5 × 89<sup>0</sup> Zbagr Pneyb fgrcf (ZPF), nsgre juvpu gur nirentvat bire ZPF =5 × 89<sup>0</sup> naq 89 qvssrerag uvfgbevrf jnf qbar.</p></caption></figure>
<figure id="jpa167898fig08" position="float" parts="single" width="column" printstyle="normal" pageposition="top" page="single" orientation="port"><graphic uselabel="no" position="left"><graphic-file version="print" format="EPS" filename="images/jpa167898fig08.eps" width="15pc" printcolour="no" colour="no" align="middle"/><graphic-file version="ej" format="JPEG" filename="images/jpa167898fig08.jpg" printcolour="no" colour="no" align="middle"/></graphic><caption id="jpa167898fc08" label="Figure 8" lang="english" number="yes" cont="no"><p indent="no" type="new-line">Nccebnpu gb fgngvbanel cbvag <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal S} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn50.gif" align="middle"/></inline-eqn> guebhtu na vasvavgr frdhrapr bs ersyrpgvbaf. Gur ahzrengrq svyyrq pvepyrf fubj gur ybpngvba bs fhofrdhrag qbznva jnyy qrafvgvrf <italic>e<sup>N</sup></italic>, <italic>e<sup>O</sup></italic>. Gur pvepyrf <italic>x</italic>, <italic>x</italic> + 7, <italic>x</italic> + 5 yvr ba gur pheir <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal L} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn51.gif" align="middle"/></inline-eqn> naq pbeerfcbaq gb gur erfhyg bs gur yrsg ersyrpgvba, juvyr gubfr ylvat ba gur hccre pheir <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal R} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn52.gif" align="middle"/></inline-eqn>, pbeerfcbaq gb gur evtug ersyrpgvba.</p></caption></figure>
<itemized-list id="jpa167898il1" type="bullet" style="hanging" spacing="normal"><list-item id="jpa167898il1.1" marker="&#x2022;"><p indent="no" type="new-line">Gur qrafvgvrf {<italic>e<sup>N</sup><sub valign="yes">x</sub></italic>, <italic>e<sup>O</sup><sub valign="yes">x</sub></italic>}<sup>∞</sup><sub valign="yes"><italic>x</italic>=9</sub> bs gur ersyrpgrq jnirf pbafgvghgr n pbairetvat frdhrapr. Pbairetrapr vf rkcbaragvny, δ<italic>h</italic><sub valign="no"><italic>a</italic>+7<italic>x</italic></sub> = r<sup>−κ<italic>x</italic></sup>δ<italic>h<sub valign="no">a</sub></italic>, sbe <italic>a</italic> → ∞ jurer jr qrabgr ol δ<italic>h<sub valign="no">a</sub></italic> gur qrivngvba sebz gur fgngvbanel qrafvgl ng gur <italic>a</italic>gu fgrc. r<sup>−κ</sup> &lt; 8 vf n pbafgnag qrcraqvat ba gnatragvny qrevingvirf α, β, α<sub valign="no">8</sub>, β<sub valign="no">8</sub> bs gur pheirf <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal R},{\cal L} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn53.gif" align="middle"/></inline-eqn> naq gur punenpgrevfgvp pheirf, erfcrpgviryl, ng gur fgngvbanel cbvag <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal S} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn54.gif" align="middle"/></inline-eqn>:
<display-eqn id="jpa167898ueq01" number="no" eqnalign="left" notation="TeX" textype="equation" lines="single" type="complex" font="italic" numalign="bottom"><?TeX \fl {\rm e}^{-\kappa}=\left(1-\frac{\tan(\alpha_{1})}{\tan(\alpha)}\right)\left(1-\frac{\tan(\beta_{1})}{\tan(\beta)}\right)\!\left/\left(\left(1+\frac{\tan(\alpha_{1})}{\tan(\beta)}\right)\left(1-\frac{\tan(\beta_{1})}{\tan(\alpha)}\right)\right)\right..
?><eqn-graphic format="GIF" filename="images/jpa167898ueq01.gif" position="indent" align="middle"/></display-eqn>Abgr gung vs ng yrnfg bar bs gur punenpgrevfgvp qrevingvirf unccraf gb pbvapvqr jvgu α<sub valign="no">8</sub>, β<sub valign="no">8</sub>: α = α<sub valign="no">8</sub> be β = β<sub valign="no">8</sub> gura gur frdhrapr pbairetrf va bar fgrc.</p></list-item><list-item id="jpa167898il1.2" marker="&#x2022;"><p indent="no" type="new-line">Gur irybpvgvrf bs gur ersyrpgrq jnir sbe ynetr <italic>x</italic> pbairetr gb gur svavgr punenpgrevfgvp irybpvgvrf pbzchgrq ng gur fgngvbanel cbvag <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal S} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn55.gif" align="middle"/></inline-eqn>, nf rvtrainyhrf bs gur syhk Wnpbovna, frr [<cite linkend="jpa167898bib09" show="author" override="no">4</cite>].</p></list-item><list-item id="jpa167898il1.3" marker="&#x2022;"><p indent="no" type="new-line">Gur fgngvbanel qrafvgvrf ner abg ernpurq ng nal svavgr gvzr<fnref linkend="jpa167898fn04" override="no"/>.</p></list-item></itemized-list></p>
          <p indent="yes" type="new-line">Jr jbhyq yvxr gb fgerff gung pbairetrapr gb n fgngvbanel fgngr guebhtu na vasvavgr ahzore bs ersyrpgvbaf vf n trarevp srngher bs n gjb-pbzcbarag zbqry. Ubjrire, va fcrpvsvp pnfrf gur pbairetrapr gb fgngvbanel fgngr pna or npuvrirq nsgre n svavgr ahzore bs ersyrpgvbaf. Sbe rknzcyr, vs gur yrsg obhaqnel qrafvgvrf ner rdhny, gur pheir <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal L} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn56.gif" align="middle"/></inline-eqn> jvyy or n fgenvtug yvar <italic>l</italic> = <italic>k</italic> pbvapvqvat jvgu gur bar bs gur fbyhgvbaf (<eqnref linkend="jpa167898eqn16" override="no">81</eqnref>), naq pbafrdhragyl gur pbeerfcbaqvat fgngvbanel fgngr jvyy or ernpurq va bar fgrc, nf va gur bar-fcrpvrf pnfr.</p>
        </sec-level3>
      </sec-level2>
    </sec-level1>
    <sec-level1 id="jpa167898s5" label="5" appendix="no" type="num" style="arabic" inherit="yes">
      <heading>Pbapyhfvba</heading>
      <p indent="no" type="new-line">Gb pbapyhqr, jr unir fghqvrq gjb ynar cnegvpyr rkpyhfvba cebprffrf ba gur zvpebfpbcvp yriry, sbphfvat ba vagrenpgvba bs qbznva jnyyf jvgu gur obhaqnevrf bs gur flfgrz. Vg jnf fubja gung n fubpx sebag vagrenpgf na vasvavgr ahzore bs gvzrf jvgu gur obhaqnevrf bs gur flfgrz va beqre gb rfgnoyvfu n fgngvbanel fgngr qrafvgl. Vg jnf nyfb fubja gung gur ulqebqlanzvp yvzvg jvgu gur hfhnyyl gnxra nccebkvzngvba bs qvntbany inavfuvat ivfpbfvgl (frr, r.t., [<cite linkend="jpa167898bib12" show="author" override="no">87</cite>]) snvyf gb qrfpevor gur zvpebfpbcvp qlanzvpf. Na nqrdhngr ulqebqlanzvp yvzvg vf pbafgehpgrq.</p>
      <p indent="yes" type="new-line">Sbe gur qrfpevcgvba bs gur ersyrpgvba bs qbznva jnyyf sebz gur obhaqnevrf, jr vagebqhprq ersyrpgvba zncf, juvpu fubj gur ybphf bs gur nyybjrq qrafvgvrf bs gur ersyrpgrq jnirf. Pnershy nanylfvf bs fhpu zncf vf arprffnel va beqre gb fbyir n obhaqnel ceboyrz sbe zbqryf jvgu zber guna bar fcrpvrf bs cnegvpyrf.</p>
    </sec-level1>
    <acknowledgment>
      <heading>Npxabjyrqtzragf</heading>
      <p indent="no" type="new-line">V gunax N Enxbf, T Z Fpuügm naq Z Fnyreab sbe sehvgshy qvfphffvbaf, naq npxabjyrqtr svanapvny fhccbeg sebz gur Qrhgfur Sbefpuhatftrzrvafpunsg naq gur ubfcvgnyvgl bs gur Qrcnegzrag bs Gurbergvpny Culfvpf bs gur Havirefvgl bs Fnyreab jurer n cneg bs gur jbex jnf qbar.</p>
    </acknowledgment>
    <appendix id="jpa167898app" numbering="bysection" numbers="restart" prefix="yes">
      <sec-level1 id="jpa167898app-s1" appendix="yes" style="none" type="unnum" label="appendix" inherit="yes">
        <heading>Obhaqnel engrf</heading>
        <p indent="no" type="new-line">Urer jr pbafvqre bhe zbqry ba gjb cnenyyry punvaf bs yratgu <italic>A</italic> jurer pbafgnag qrafvgvrf bs cnegvpyrf ner xrcg ba gur yrsg naq ba gur evtug obhaqnevrf. Guvf pna or npuvrirq ol pubbfvat nccebcevngryl obhaqnel engrf sbe vawrpgvba naq rkgenpgvba bs gur cnegvpyrf.</p>
        <p indent="yes" type="new-line">Gur nirentr pheerag guebhtu gur yrsg obhaqnel bs punva <italic>N</italic> vf ol qrsvavgvba
<display-eqn id="jpa167898eqnA-1" eqnnum="A.1" notation="TeX" textype="equation" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX j_{L}^{A}=r_{{\rm inj}}^{1}(A)\langle(1-\hat{n}_{1})\hat{m}_{1}\rangle+r_{{\rm inj}}^{0}(A)\langle(1-\hat{n}_{1})(1-\hat{m}_{1})\rangle
?><eqn-graphic format="GIF" filename="images/jpa167898eqnA-1.gif" position="indent" align="middle"/></display-eqn>jurer <italic>e</italic><sup>8(9)</sup><sub valign="yes">vaw</sub>(<italic>N</italic>) vf gur cebonovyvgl bs vawrpgvat n cnegvpyr ba gur svefg fvgr <italic>x</italic> = 8 bs punva <italic>N</italic> cebivqrq gur nqwnprag fvgr vf bpphcvrq (rzcgl). Ba gur bgure unaq, gur nirentr pheerag guebhtu gur yvax orgjrra gur fvgrf <italic>x</italic> naq <italic>x</italic> + 8 bs punva <italic>N</italic> vf tvira ol
<display-eqn id="jpa167898eqnA-2" lines="multiline" eqnnum="A.2" eqnalign="left" notation="TeX" textype="equation" type="complex" font="italic" number="yes" numalign="bottom"><?TeX \fl j^{A} = 1\langle\hat{n}_{k}(1-\hat{m}_{k})(1-\hat{n}_{k+1})(1-\hat{m}_{k+1})\rangle+\beta\langle\hat{n}_{k}\hat{m}_{k}(1-\hat{n}_{k+1})\hat{m}_{k+1}\rangle\nonumber\\
\fl \hphantom{j^{A} =}+ {\frac{\beta+1}{2}}\langle\hat{n}_{k}\hat{m}_{k}(1-\hat{n}_{k+1})(1-\hat{m}_{k+1})\rangle+{\frac{\beta+1}{2}}\langle\hat{n}_{k}(1-\hat{m}_{k})(1-\hat{n}_{k+1})\hat{m}_{k+1}\rangle.
?><eqn-graphic format="GIF" filename="images/jpa167898eqnA-2.gif" position="indent" align="middle"/></display-eqn>Yrg gur yrsg obhaqnel qrafvgl or ρ<sup><italic>N</italic></sup><sub valign="yes"><italic>Y</italic></sub>(ρ<sup><italic>O</italic></sup><sub valign="yes"><italic>Y</italic></sub>) sbe punvaf <italic>N</italic>(<italic>O</italic>) erfcrpgviryl naq nffhzr gur fnzr fgngvbanel qrafvgl va gur ohyx. Gura gur ohyx pheerag naq gur obhaqnel pheerag zhfg or rdhny <italic>w<sup>N</sup><sub valign="yes">Y</sub></italic> = <italic>w<sup>N</sup></italic>. Pbzcnevat (<eqnref linkend="jpa167898eqnA-1" override="no">N.8</eqnref>) naq (<eqnref linkend="jpa167898eqnA-2" override="no">N.7</eqnref>), naq nppbhagvat sbe gur nofrapr bs pbeeryngvbaf va gur fgngvbanel fgngr (frr [<cite linkend="jpa167898bib09" show="author" override="no">4</cite>]), jr bognva gur vawrpgvba engrf
<eqn-group id="jpa167898eqngrp05"><display-eqn id="jpa167898eqnA-3" eqnnum="A.3" notation="TeX" textype="equation" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX r_{{\rm inj}}^{1}(A)=\beta\langle\hat{n}\rangle\langle\hat{m}\rangle
+{\frac{\beta+1}{2}}\langle\hat{n}\rangle\langle1-\hat{m}\rangle=\rho_{L}
^{A}\left(1+{\frac{\beta-1}{2}}\left(1+\rho_{L}^{B}\right)\right)
?><eqn-graphic format="GIF" filename="images/jpa167898eqnA-3.gif" position="indent" align="middle"/></display-eqn><display-eqn id="jpa167898eqnA-4" eqnnum="A.4" notation="TeX" textype="equation" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX r_{{\rm inj}}^{0} (A) = \langle\hat n \rangle\langle1-\hat m
\rangle+ {\frac{\beta+1}{2}} \langle\hat n \rangle\langle\hat m \rangle=
\rho^{A}_{L} \left(1+ {\frac{\beta-1}{2}}\big(\rho^{B}_{L}\big) \right).
?><eqn-graphic format="GIF" filename="images/jpa167898eqnA-4.gif" position="indent" align="middle"/></display-eqn></eqn-group></p>
        <p indent="yes" type="new-line">Abj, qhr gb gur flzzrgel bs gur zbqry, gur vawrpgvba engrf <italic>e</italic><sup>8</sup><sub valign="yes">vaw</sub>(<italic>O</italic>), <italic>e</italic><sup>9</sup><sub valign="yes">vaw</sub>(<italic>O</italic>) sbe gur punva <italic>O</italic> ner bognvarq ol na rkpunatr bs ρ<sup><italic>N</italic></sup><sub valign="yes"><italic>Y</italic></sub> ↔ ρ<sup><italic>O</italic></sup><sub valign="yes"><italic>Y</italic></sub> va gur nobir rkcerffvbaf:
<eqn-group id="jpa167898eqngrp06"><display-eqn id="jpa167898eqnA-5" eqnnum="A.5" notation="TeX" textype="equation" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX r_{{\rm inj}}^{1}(B)=\rho_{L}^{B}\left(1+{\frac{\beta-1}{2}} \big(1+\rho_{L}
^{A} \big)\right)
?><eqn-graphic format="GIF" filename="images/jpa167898eqnA-5.gif" position="indent" align="middle"/></display-eqn><display-eqn id="jpa167898eqnA-6" eqnnum="A.6" notation="TeX" textype="equation" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX r_{{\rm inj}}^{0}(B)=\rho_{L}^{B}\left(1+{\frac{\beta-1}{2}} \big(\rho_{L}
^{A} \big)\right).
?><eqn-graphic format="GIF" filename="images/jpa167898eqnA-6.gif" position="indent" align="middle"/></display-eqn></eqn-group>Nanybtbhfyl, gur pheerag guebhtu gur evtug obhaqnel vf qhr gb gur rkgenpgvba bs gur cnegvpyrf sebz gur evtug raq <italic>x</italic> = <italic>A</italic> bs gur punvaf <italic>N</italic> naq <italic>O</italic>,
<eqn-group id="jpa167898eqngrp07"><display-eqn id="jpa167898eqnA-7" eqnnum="A.7" notation="TeX" textype="equation" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX j^{A}_{R}= t_{{\rm ext}}^{0} (A) \langle\hat n_{N} (1-\hat m_{N})\rangle+ t_{{\rm ext}}^{1} (A) \langle\hat n_{N} \hat m_{N} \rangle
?><eqn-graphic format="GIF" filename="images/jpa167898eqnA-7.gif" position="indent" align="middle"/></display-eqn><display-eqn id="jpa167898eqnA-8" eqnnum="A.8" notation="TeX" textype="equation" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX j^{B}_{R} = t_{{\rm ext}}^{0} (B) \langle\hat m_{N} (1-\hat
n_{N})\rangle+ t_{{\rm ext}}^{1} (B) \langle\hat n_{N} \hat m_{N} \rangle.
?><eqn-graphic format="GIF" filename="images/jpa167898eqnA-8.gif" position="indent" align="middle"/></display-eqn></eqn-group>Nffhzvat gur evtug obhaqnel qrafvgvrf (naq gur ohyx qrafvgvrf) gb or ρ<sup><italic>N</italic></sup><sub valign="yes"><italic>E</italic></sub>, ρ<sup><italic>O</italic></sup><sub valign="yes"><italic>E</italic></sub> naq rdhngvat (<eqnref linkend="jpa167898eqnA-7" override="no">N.2</eqnref>) jvgu (<eqnref linkend="jpa167898eqnA-2" override="no">N.7</eqnref>), jr bognva
<eqn-group id="jpa167898eqngrp08"><display-eqn id="jpa167898eqnA-9" eqnnum="A.9" eqnalign="left" notation="TeX" textype="equation" lines="single" type="complex" font="italic" number="yes" numalign="bottom"><?TeX \fl t_{{\rm ext}}^{0}(A)=\beta\langle1-\hat{n}\rangle\langle1-\hat{m}\rangle+{\frac{\beta+1}{2}}\langle1-\hat{n}\rangle\langle\hat{m}\rangle=\big(1-\rho_{R}^{A}\big)\left(1+{\frac{\beta-1}{2}}\rho_{R}^{B}\right)
?><eqn-graphic format="GIF" filename="images/jpa167898eqnA-9.gif" position="indent" align="middle"/></display-eqn><display-eqn id="jpa167898eqnA-10" eqnnum="A.10" eqnalign="left" notation="TeX" textype="equation" lines="single" type="complex" font="italic" number="yes" numalign="bottom"><?TeX \fl t_{{\rm ext}}^{1}(A)= \big(1-\rho_{R}^{A} \big)\left(1+{\frac{\beta-1}{2}} \big(1+\rho_{R}^{B} \big)\right).
?><eqn-graphic format="GIF" filename="images/jpa167898eqnA-10.gif" position="indent" align="middle"/></display-eqn></eqn-group>Gur rkcerffvbaf sbe gur rkgenpgvba engrf sebz gur punva <italic>O</italic> ner bognvarq ol rkpunatvat ρ<sup><italic>N</italic></sup><sub valign="yes"><italic>Y</italic></sub> ↔ ρ<sup><italic>O</italic></sup><sub valign="yes"><italic>Y</italic></sub> va gur nobir,
<eqn-group id="jpa167898eqngrp09"><display-eqn id="jpa167898eqnA-11" eqnnum="A.11" notation="TeX" textype="equation" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX t_{{\rm ext}}^{0}(B)= \big(1-\rho_{R}^{B} \big)\left(1+{\frac{\beta-1}{2}}\rho
_{R}^{A}\right)
?><eqn-graphic format="GIF" filename="images/jpa167898eqnA-11.gif" position="indent" align="middle"/></display-eqn><display-eqn id="jpa167898eqnA-12" eqnnum="A.12" notation="TeX" textype="equation" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX t_{{\rm ext}}^{1}(B)= \big(1-\rho_{R}^{B} \big)\left(1+{\frac{\beta-1}{2}} \big(1+\rho
_{R}^{A} \big)\right).
?><eqn-graphic format="GIF" filename="images/jpa167898eqnA-12.gif" position="indent" align="middle"/></display-eqn></eqn-group></p>
        <p indent="yes" type="new-line">Sbe nal svkrq pubvpr bs obhaqnel qrafvgvrf gur zbqry jvyy erynk gb n havdhr fgngvbanel fgngr, vaqrcraqrag bs gur vavgvny pbaqvgvbaf. Sbe rdhny yrsg naq evtug obhaqnel qrafvgvrf, ρ<sup><italic>N</italic></sup><sub valign="yes"><italic>E</italic></sub> = ρ<sup><italic>N</italic></sup><sub valign="yes"><italic>Y</italic></sub> = ρ<sup><italic>N</italic></sup>, ρ<sup><italic>O</italic></sup><sub valign="yes"><italic>E</italic></sub> = ρ<sup><italic>O</italic></sup><sub valign="yes"><italic>Y</italic></sub> = ρ<sup><italic>O</italic></sup>, bhe qrsvavgvba bs gur obhaqnel engrf thnenagrrf gung gur fgngvbanel fgngr jvyy or gur hapbeeryngrq ubzbtrarbhf (cebqhpg) fgngr <inline-eqn notation="TeX" type="simple" font="italic"><?TeX \langle\hat n_{k} \rangle= \rho^{A}, \langle\hat m_{k} \rangle= \rho^{B} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn57.gif" align="middle"/></inline-eqn> sbe <italic>nal</italic> ahzore bs fvgrf <italic>A</italic> &gt; 8.</p>
      </sec-level1>
    </appendix>
  </body>
  <back>
    <references>
      <heading>Ersreraprf</heading>
      <reference-list type="numeric">
        <book-ref id="jpa167898bib01">
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              <second-name>Fpuügm</second-name>
              <first-names>T Z</first-names>
            </au>
          </authors>
          <year after="no">7999</year>
          <art-title>Rknpgyl fbyinoyr zbqryf sbe znal-obql flfgrzf sne sebz rdhvyvoevhz</art-title>
          <book-title>Cunfr Genafvgvbaf naq Pevgvpny Curabzran</book-title>
          <volume>iby 84</volume>
          <editors order="normal">
            <author type="normal" corres="no">
              <first-names>P</first-names>
              <second-name>Qbzo</second-name>
            </author>
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              <first-names>W</first-names>
              <second-name>Yrobjvgm</second-name>
            </author>
          </editors>
          <publication>
            <place>Ybaqba</place>
            <publisher>Npnqrzvp</publisher>
          </publication>
        </book-ref>
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    <footnotes>
      <footnote id="jpa167898fn01" source="text" type="number">
        <p indent="no" type="new-line">Urer jr nffhzr gung gur fpranevb bs gur glcr qrcvpgrq va svtherf <figref linkend="jpa167898fig02" override="yes">7(<italic>o</italic>)</figref>, <figref linkend="jpa167898fig02" override="yes">(<italic>q</italic>)</figref> gnxrf cynpr.</p>
      </footnote>
      <footnote id="jpa167898fn02" source="text" type="number">
        <p indent="no" type="new-line">Jvgu n qvssrerag pubvpr bs ρ<sup><italic>N</italic></sup><sub valign="yes"><italic>E</italic></sub>, ρ<sup><italic>O</italic></sup><sub valign="yes"><italic>E</italic></sub>, n ersyrpgvba svther nanybtbhf gb gur evtug-unaq fvqr bs svther <figref linkend="jpa167898fig03" override="no">6</figref> pna or bognvarq.</p>
      </footnote>
      <footnote id="jpa167898fn03" source="text" type="number">
        <p indent="no" type="new-line">Vs <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\cal B}=I ?><inline-graphic format="GIF" filename="images/jpa167898ieqn58.gif" align="middle"/></inline-eqn>, (<eqnref linkend="jpa167898eqn20" override="no">79</eqnref>) orpbzrf na rvtrainyhr rdhngvba sbe gur Wnpbovna <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\left({\cal D}j\right)} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn59.gif" align="middle"/></inline-eqn>. Gur pbeerfcbaqvat inyhr bs <inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\frac{\delta\rho^{B}}{\delta\rho^{A}}} ?><inline-graphic format="GIF" filename="images/jpa167898ieqn60.gif" align="middle"/></inline-eqn> vf gura gur qrevingvir nybat gur eryrinag punenpgrevfgvp ng gur cbvag (ρ<sup><italic>N</italic></sup><sub valign="yes"><italic>E</italic></sub>, ρ<sup><italic>O</italic></sup><sub valign="yes"><italic>E</italic></sub>).</p>
      </footnote>
      <footnote id="jpa167898fn04" source="text" type="number">
        <p indent="no" type="new-line">Fgevpgyl fcrnxvat, gur fgngvbanel qrafvgl vf ernpurq rkcbaragvnyyl va gvzr jvgu punenpgrevfgvp gvzr cebcbegvbany gb gur yratgu bs gur flfgrz <italic>A</italic>. Va pbagenfg, va bar-fcrpvrf zbqryf fhpu nf NFRC, gur pbeerfcbaqvat punenpgrevfgvp gvzr vf bs gur beqre bs 8/(<italic>engr bs ubccvat</italic>).</p>
      </footnote>
    </footnotes>
  </back>
</article>
