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Pdpck [lqulhkls & [lrcls Kgckj
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Mrctfnltck Qrderlsscdh (MQ) Mh mrctfnltck prderlsscdh cs m slqulhkl ch wfckf tlrns chkrlmsl dr `lkrlmsl by m kdh kdhstmh stmhtt hunb hunbl lr kmg kmggl` gl` tfl tfl kdnn kdnnd dh `ci `ciilr ilrlhkl lhkl.. (c) Pfl slqulhkl 2, 9, =1, =0, =6, 22… cs mh mrctfnltck prderlsscdh wfdsl icrst tlrn cs 2 mh` kdnndh `ciilrlhkl 0. (cc) Pfl slqulhkl 2, icrst tlrn ` > kdnndh `ciilrlhkl h > hunblr di tlrns ch tfl t fl prderlsscdh
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Pfl elhlrmg tlrn di mh mrctfnltck prderlsscdh cs ecvlh by P h > m + (h - =) `.
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Pfl sun di h tlrns di mh mrctfnltck prderlsscdh cs ecvlh by [, > h /2 /2 Z2m + (h ‛ (h ‛ =) `^ dr [h > 2 Z m + g ^ wflrl g cs tfl gmst tlrn di mrctfnltck prderlsscdh.
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Ci tfrll hunblrs mrl ch mrctfnltck prderlsscdh, tfl nc``gl hunblr cs kmggl` tfl mrctfnltck nlmh di tfl tfl dtflr twd tlrns.
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Ci m, b, k mrl ch mrctfnltck prderlsscdh, tflh b > m+k /2 wflrl b cs tfl tfl mrctfn tfnltck tck nlmh.
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[cncgm [cncgmrgy rgy,, ci ‖h– ci ‖h– tlr tlrns mg, m2, m;… mh mrl ch MQ, tflh tfl mrctfnltck nlmh di tflsl ‖h– tlrns cs ecvlh by MN >
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Ci tfl smnl qumhtcty cs m``l` dr nugtcpgcl` td lmkf tlrn di mh MQ, tflh tfl rlsugtch tche slr slrcls cs mgsd mh MQ.
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Ci tfrll tlrns mrl ch MQ, MQ, tflh tfly kmh bl tmjlh ms (m ‛ (m ‛ `), m, (m + `).
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Ci idur tlrns mrl ch MQ, tflh tfly kmh bl tmjlh ms (m ‛ ;`), (m ‛ `), (m + `), (m + ;`).
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Ci icvl tlrns mrl ch MQ, tflh tfly kmh bl tmjlh ms (m ‛ 2`), (m ‛ `), m, (m + `), (m + 2`).
Eldnltrck Qrderlsscdh (EQ)
M eldnltrck prderlsscdh cs m slqulhkl ch wfckf tlrns chkrlmsl dr `lkrlmsl by m kdhs kdhstm tmh ht rmtcd mtcd kmg kmggl` gl` tfl tfl kdnn kdnnd dh rmtcd mtcd.. ( c)
Pfl slqulhkl =, ;, 3, 25, 6=…cs m eldnltrck prderlsscdh wfdsl icrst tlrn cs = mh` kdnndh rmtcd ;.
(cc) Pfl sl slqulhkl tlrn cs = mh` kdnndh rmtcd =/;.
cs m eldnltrck pr p rderlsscdh wf wfdsl icrst
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‛=. M eldnltrck prderlsscdh cs rlprlslhtl` rlprlslhtl` by m, mr, mr 2…mr h ‛= Flrl, m > icrst tlrn r > kdnndh rmtcd h > hunblr di tlrns ch tfl prderlsscdh.
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‛= Pfl elhlrmg tlrn di m eldnltrck prderlsscdh cs ecvlh by P h > mh ‛=
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Pfl sun td h tlrns di m eldnltrck prderlsscdh cs ecvlh by wflh r 7 =
wflh r 8 =
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Ci tfrll hunblrs mrl ch eldnltrck prderlsscdh, tfl nc``gl hunblr cs kmggl` tfl eldnltrck nlmh di tfl dtflr twd tlrns.
• Ci m, b, k mrl ch eldnltrck prderlsscdh, tflh eldnltrck nlmh.
wflrl b cs tfl
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[cncgmrgy, ci h tlrns m=, m2, m;, m0,…mh mrl mrl ch eldn eldnlt ltrc rck k prde prderl rlss sscd cdh, h, tfl tflh • tfl eldnltrck nlmh di = tflsl h tlrns cs ecvlh by EN > •
Idr m `lkrlmsche eldnltrck prderlsscdh tfl sun td chichctl hunblr di tlrn tlrns s cs wflrl m > icrst tlrn mh` | r | 7 =.
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Ci lvlry tlrn di m EQ cs nugtcpgcl` by m icxl` rlmg hunblr, tflh tfl rlsug sugtche slrcls cs mgsd m EQ.
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Ci lvlry tlrn di m EQ cs rmcsl` td tfl smnl pdwlr, tflh tfl rlsugtche slrcls cs mgsd m EQ.
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Pfl rlkcprdkmgs di tfl tlrns di m EQ cs mgsd m EQ. EQ.
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Ci tfrll hunblrs mrl ch EQ, tflh tfly kmh bl tmjlh ms m/r , m, mr.
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Ci idur hunblrs mrl ch EQ, tflh tfly kmh bl tmjlh ms
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Ci icvl hunblrs mrl ch EQ, tflh tfly kmh bl tmjlh ms
Fmrndhck Qrderlsscdh (FQ) Ci tfl rlkcprdkmgs di tfl tlrns di m slrcls idrn mh mrctfnltck prderlsscdh, tflh tfl slrc slrcls ls cs kmgg kmggl` l` m fmrn fmrndh dhck ck prde prderl rlss sscd cdh. h.
( c)
Pfl slqulhkl 0/;, ;/2, =2/5, …. cs m fmrndhck prderlsscdh ms ;/0, 2/;, 5/=2 /=2 cs ch mrct mrctfn fnl ltck tck prde prderl rlss sscd cdh h.
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Ci m, b, k mrl ch fmrndhck prderlsscdh, tflh b > 2mk / m+k wflrl b cs tfl fmrnd fmrndhck hck nlmh. nlmh.
[un di Hmturmg [lrcls •
Pfl sun di tfl icrst h hmturmg hunblrs > h (h+=) / 2 .
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Pfl sun di tfl squmrl di tfl icrst i crst h hmturmg hunblrs > h (h+=) (2h+=) / 9
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Pfl sun di tfl kubls di tfl icrst h hmturmg hunblrs >
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Pfl sun di icrst h lvlh hunblrs > h(h + =)
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Pfl sun di icrst h d`` hunblrs > h2
Lxmn Lx mnpg pgl l =? Ich` tfl htf tlrn mh` tfl icitllhtf tlrn di tfl mrctfn ctfnl ltck prder erl lsscdh ;, 3, =<, 2=… [dgutcdh. [dgutcdh. Ch tfl ecvlh MQ wl fmvl m > ;, ` > (3 ‛ ;) > 9 Ph > m + (h ‛ (h ‛ =)` > ; + (h ‛ (h ‛ =)9 > 9h ‛ 9h ‛ ; P=< > (9 (9 Õ =< ‛ ;) > 65 Lxmnpgl 2? Ich` tfl =1tf tlrn di tfl MQ =;, 6, ;, ‛2,… [dgutcdh. Ch tfl ecvlh MQ, wl fmvl m > =;, ` > (6 ‛ (6 ‛=;) =;) > ‛ > ‛< < Ph > m + (h ‛ (h ‛ =)` > =; + (h ‛ (h ‛ =)( ‛<) ‛<) > =6 ‛ =6 ‛ =6 ‛ =6 ‛ < (=1) > ‛ > ‛;2 ;2
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Lxmn Lx mnpg pgl l ;? Pfl icrst tlrn di mh MQ cs -= mh` tfl kdnndh `ciilrlhkl cs -;, tfl =2tf tlrn cs [dgutcdh. P= > m > ‛ > ‛=, =, ` > ‛ > ‛; ; Ph > m + (h ‛ (h ‛ =)` > ‛ > ‛= = + (h ‛ (h ‛ =)( ‛;) ‛;) > 2 ‛ 2 ‛ ;h P=2 > 2 ‛ 2 ‛ ; Õ =2 > ‛ > ‛;0 ;0 Lxmnpgl 0? Ufckf tlrn di tfl MQ =1, 6, 9, 0… cs ‛ 264 [dgutcdh. Ul fmvl, m > =1,` > (6 ‛ (6 ‛ =1) > ‛ > ‛2, 2, Ph > ‛26 ‛26 ‛2) > h > 21 Ph > m + (h ‛ =)` ‛ 26 > =1 + (h ‛ =)( ‛ Lxmnpgl m + 5` >=5 ...(c) P=3 > m + =6` > ;3 ... (cc) Dh subtrmktche Lq. (c) irdn Lq. (cc), wl elt ==` ==` > 22 >`>2
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Quttche ` > 2 ch Lq. (c), wl elt m + 5(2) > =5 m > (=5 ‛ (=5 ‛ =0) > ; . . . Icrst tlrn > ;, Kdnndh `ciilrlhkl > 2 P21> m + =3` > ; + =3(2) > 0=
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