Que debemos saber de los decibeles?

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¼Suk

¼Suk `kfkdls `kfkdls scfkr scfkr `k `k gls gls `kaifkgks< `kaifkgks< Qcgvc`lr Qcgvc`lr Hcraäc Hcraäc Acstkggñj, Acstkggñj, YQ3HAYQ3HA

¼Sué `kfkdls scfkr `k gls `kaifkgks< ¼Sué `kfkdls scfkr `k gls `kaifkgks<

Vkgcailjks, kokdpgls, kjnlquks, auc`rls aldpcrctivls y auc`rls `k Vkgcailjks, kokdpgls, kjnlquks, auc`rls aldpcrctivls y auc`rls `k rksÿdkjks

rksÿdkjks

Qcgvc`lr Hcraäc Acstkggñj Qcgvc`lr Hcraäc Acstkggñj

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¼Suk

IJPVL@[AAIÑJ IJPVL@[AAIÑJ

Prcfcol `ks`k mcak yc tikdpl kj

Prcfcol `ks`k mcak yc tikdpl kj kg ãrkc `k kquipls `k rc`ilaldujiacaiñj y kquiplskg ãrkc `k kquipls `k rc`ilaldujiacaiñj y kquipls `k VN, aldkjaé aldl duamls kj kg acdpl, `k dl`l prãatial, alj gc ksaukgc `k gc `k VN, aldkjaé aldl duamls kj kg acdpl, `k dl`l prãatial, alj gc ksaukgc `k gc kxpkrikjaic `k gc vi`c (ñskc qukdcj`l kquipls, cghujcs vkaks), alj gl quk cghujls kxpkrikjaic `k gc vi`c (ñskc qukdcj`l kquipls, cghujcs vkaks), alj gl quk cghujls ncdigicrks y cdihls gk kxpgiacj c

ncdigicrks y cdihls gk kxpgiacj c ujl….ujl…. Rkrl kggls cg ihucg quk yl tkjäcj gcRkrl kggls cg ihucg quk yl tkjäcj gc

kxpkrikjaic `k gc vi`c. kxpkrikjaic `k gc vi`c.

Rlr pridkrc vkz vi gls @kaifkgks kj uj trcjsakptlr `k Fcj`c aiu`c`cjc, slgäc vkr gc Rlr pridkrc vkz vi gls @kaifkgks kj uj trcjsakptlr `k Fcj`c aiu`c`cjc, slgäc vkr gc chuoc ij`iaãj`ldk kg jivkg `k rkakpaiñj `k ltrls kquipls kj di aui`c`, Qcj chuoc ij`iaãj`ldk kg jivkg `k rkakpaiñj `k ltrls kquipls kj di aui`c`, Qcj Qcgvc`lr, aldprkj`äc quk kjtrk dcs jivkg

Qcgvc`lr, aldprkj`äc quk kjtrk dcs jivkg krc dcylr, pkrl jl scfic quk krc dcylr, pkrl jl scfic quk dk ijìacfcdk ijìacfc kxcatcdkjtk kstc dkì`c.

kxcatcdkjtk kstc dk`i`c.

Aljnlrdk dk dktäc dcs kj kg tkdc supk quk gls `kaifkgks jl slgl sk laupcfcj Aljnlrdk dk dktäc dcs kj kg tkdc supk quk gls `kaifkgks jl slgl sk laupcfcj pcrc rkaifir gc ijtkjsi`c`, si jl pcrc ujc skrik `k dk`i`cs `k? kgkatrñjiac, pcrc rkaifir gc ijtkjsi`c`, si jl pcrc ujc skrik `k dk`i`cs `k? kgkatrñjiac, kgkatriai`c`, pltkjaic, kta. Y ac`c vkz dk skjtäc dcs

kgkatriai`c`, pltkjaic, kta. Y ac`c vkz dk skjtäc dcs cgkoc`l `k ujc kxpgiacaiñj rkcg.cgkoc`l `k ujc kxpgiacaiñj rkcg. Aldl duamls kstu`ik `kspués kj gc [jivkrsi`c`, y ksauamk ujcs pcgcfrcs quk dk Aldl duamls kstu`ik `kspués kj gc [jivkrsi`c`, y ksauamk ujcs pcgcfrcs quk dk

sljcrlj `inäaigks pkrl rkcgks ‗Kg Ijhkjikrl `k Kgkatriai`c`, Pkgkaldujiacailjks y sljcrlj `inäaigks pkrl rkcgks ‗Kg Ijhkjikrl `k Kgkatriai`c`, Pkgkaldujiacailjks y

rcdcs cnijks, `kfk `k pkjscr kj uj duj`l kj @kaifkgks5 aldprkj`kr y kjtkj`kr rcdcs cnijks, `kfk `k pkjscr kj uj duj`l kj @kaifkgks5 aldprkj`kr y kjtkj`kr pkrnkatcdkjtk,

pkrnkatcdkjtk, kstk tkdc. Yc qukstk tkdc. Yc quk su duj`k su duj`l hirc cgrk`l hirc cgrk`k`lr `k kstcs k`lr `k kstcs uji`c`ks `kuji`c`ks `k

rknkrkjaic—

rknkrkjaic— tkjhl quk chrc`kakrgk Ijh. Ouãrkz, quk sus pcgcfrcs mly kj `äc cujtkjhl quk chrc`kakrgk Ijh. Ouãrkz, quk sus pcgcfrcs mly kj `äc cuj

sihukj prkskjtks kj di acfkzc, y mcstc cmlrc sihl utigizcj`l gls @kaifkgks sihukj prkskjtks kj di acfkzc, y mcstc cmlrc sihl utigizcj`l gls @kaifkgks aljstcjtkdkjtk kj di prlnksiñj.

aljstcjtkdkjtk kj di prlnksiñj.

Rlstkrilrdkjtk dk kjaljtré c uj aldpcókrl `k acrrkrc, y dk mizl ujc prkhujtc Rlstkrilrdkjtk dk kjaljtré c uj aldpcókrl `k acrrkrc, y dk mizl ujc prkhujtc sijhugcr

sijhugcr ‗‗¼Amcdfc, [`. kjtikj`k plr quk kxistkj gls `kaifkgks jkhctivls y aldl¼Amcdfc, [`. kjtikj`k plr quk kxistkj gls `kaifkgks jkhctivls y aldl

nujailjc kstc dkì`c kj gls kquipls<, yc quk yl mk prkhujtc`l kj gc kdprksc y nujailjc kstc dkì`c kj gls kquipls<, yc quk yl mk prkhujtc`l kj gc kdprksc y jcìk dk scfk rksplj`kr

jcìk dk scfk rksplj`kr —.—. Gk kxpgiquk slfrk gls `F, pkrl surhiñ di ù`c5 Gk kxpgiquk slfrk gls `F, pkrl surhiñ di ù`c5 ‗‗GcGc

disdc prkhujtc quk dk miak mcak duaml tikdpl, kstc ks ujc prkhujtc aldÿj disdc prkhujtc quk dk miak mcak duaml tikdpl, kstc ks ujc prkhujtc aldÿj `kjtrl `kg acdpl alj dis algkhcs

`kjtrl `kg acdpl alj dis algkhcs——. Ks plr ksl quk a. Ks plr ksl quk aldkjaé c rkalpigcr ijnlrdcaiñjldkjaé c rkalpigcr ijnlrdcaiñj

`k `inkrkjtks nukjtks, pcrc trctcr `k mcakr uj `laudkjtl skjaiggl, alrtl y sidpgk `k `k `inkrkjtks nukjtks, pcrc trctcr `k mcakr uj `laudkjtl skjaiggl, alrtl y sidpgk `k gls @kaifgks.

gls @kaifgks.

Kspkrl kstk dctkricg skc `k cyu`c, pcrc ustk`ks y sirvc pcrc `kscrrlggcr dkolr Kspkrl kstk dctkricg skc `k cyu`c, pcrc ustk`ks y sirvc pcrc `kscrrlggcr dkolr jukstrl skrviail prlnksiljcg, y quk cyu`kdls c duamls kxpkridkjtc`lrks, jukstrl skrviail prlnksiljcg, y quk cyu`kdls c duamls kxpkridkjtc`lrks, rc`ilcniailjc`ls, téajials y prlnksiljcgks slfrk gls `F°s.

rc`ilcniailjc`ls, téajials y prlnksiljcgks slfrk gls `F°s. Qcgvc`lr, YQ3HA

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¼Suk

@kaifkg @kaifkg

Kg `kaifkg nuk jldfrc`l plr Cgkxcj`kr Hrcmcd Fkgg5 sk utigizc pcrc dk`ir Jivkgks, Kg `kaifkg nuk jldfrc`l plr Cgkxcj`kr Hrcmcd Fkgg5 sk utigizc pcrc dk`ir Jivkgks, ijtkjsi`c`ks, pltkjaics, pkrl tcdfiéj sk ijtkjsi`c`ks, pltkjaics, pkrl tcdfiéj sk utigizc kj skócgks, kgkatrñjiac y utigizc kj skócgks, kgkatrñjiac y aldujiacaiñj. aldujiacaiñj. %, `F, `Fd y `F(»^) slj aljakptls %, `F, `Fd y `F(»^) slj aljakptls idplrtcjtks quk tl`l téajial `k acdpl l idplrtcjtks quk tl`l téajial `k acdpl l

Ijhkjikrl `kfkräc kjtkj`kr

pkrnkatcdkjtk y skr acpcz `k trcfcocr pkrnkatcdkjtk y skr acpcz `k trcfcocr alj kggls jlrdcgdkjtk. @k jl skr csä, sk alj kggls jlrdcgdkjtk. @k jl skr csä, sk kjaljtrcrã kj ujc agcrc `ksvkjtcoc kjaljtrcrã kj ujc agcrc `ksvkjtcoc ùrcjtk kg `kscrrlggl `k su trcfcol. ùrcjtk kg `kscrrlggl `k su trcfcol. Aucj`l kstls térdijls cpcrkakj kj ìsausiljks alj agikjtks l alj ltrls aldpcókrls, Aucj`l kstls térdijls cpcrkakj kj ìsausiljks alj agikjtks l alj ltrls aldpcókrls, tkj`rã skrils prlfgkdcs pcrc akjtrcrsk kj kg prlfgkdc si kstã laupc`l prkhujtãj`lsk tkj`rã skrils prlfgkdcs pcrc akjtrcrsk kj kg prlfgkdc si kstã laupc`l prkhujtãj`lsk si 1 `F sihjiniac uj ncatlr `k 6 l `k 0 (u ltrc alsc) l si gls `kaifkgks slj `k vcglr si 1 `F sihjiniac uj ncatlr `k 6 l `k 0 (u ltrc alsc) l si gls `kaifkgks slj `k vcglr jkhctivl -1`F, c quk alrrksplj`krã kstc dchjitu`. Dkrkak gc pkjc kg ksnukrzl `k jkhctivl -1`F, c quk alrrksplj`krã kstc dchjitu`. Dkrkak gc pkjc kg ksnukrzl `k rkviscr kstls aljakptls `k vkz kj aucj`l y ncdigicrizcrsk alj kggls.

rkviscr kstls aljakptls `k vkz kj aucj`l y ncdigicrizcrsk alj kggls.

Aucj`l sk utigizcj nñrdugcs y uji`c`ks, sk mcj skhui`l gls kstãj`crks ijtkrjcailjcgks Aucj`l sk utigizcj nñrdugcs y uji`c`ks, sk mcj skhui`l gls kstãj`crks ijtkrjcailjcgks nioc`ls kj gc IQL 13 y kj gc IKA 68

nioc`ls kj gc IQL 13 y kj gc IKA 6833 (tcdfiéj sk ij`iacj gls acsls kj gls quk ks ujc (tcdfiéj sk ij`iacj gls acsls kj gls quk ks ujc prãatiac aldÿj kg `ksvicrsk `k kstls kstãj`crks).

prãatiac aldÿj kg `ksvicrsk `k kstls kstãj`crks). ¼Rcrc quk utigizcdls gls `kaifkgils<

¼Rcrc quk utigizcdls gls `kaifkgils<

Gls @kaifkgil, puk`kj kdpgkcrsk pcrc `ksarifir kg rkjìdikjtl ij`kpkjìkjtkdkjtk `kg Gls @kaifkgil, puk`kj kdpgkcrsk pcrc `ksarifir kg rkjìdikjtl ij`kpkjìkjtkdkjtk `kg ^lgtcok l Rltkjaic `k lpkrcaiñj `k ujc cpgiacaiñj, plr tcjtl, ks ujc kspkainiacaiñj `k ^lgtcok l Rltkjaic `k lpkrcaiñj `k ujc cpgiacaiñj, plr tcjtl, ks ujc kspkainiacaiñj `k uj rkjìdikjtl hkjérial, si kj uj sistkdc prkskjtc uj cplrtk c gc skócg l jivkg `k uj rkjìdikjtl hkjérial, si kj uj sistkdc prkskjtc uj cplrtk c gc skócg l jivkg `k kjtrc`c (Hcjcjaic), kstc ks kxprksc`c aldl uj vcglr plsitivl y tl`l gl aljtrcril pcscräc kjtrc`c (Hcjcjaic), kstc ks kxprksc`c aldl uj vcglr plsitivl y tl`l gl aljtrcril pcscräc alj uj vcglr jkhctivl kj `kaifkgks, yc quk skrã ujc ctkjucaiñj kj gc scgi`c `kg sistkdc, alj uj vcglr jkhctivl kj `kaifkgks, yc quk skrã ujc ctkjucaiñj kj gc scgi`c `kg sistkdc, aucj`l sk tkjhc uj vcglr kj `kaifkgks `k 2, rkprkskjtc quk kg sistkdc jl cplrtc ji aucj`l sk tkjhc uj vcglr kj `kaifkgks `k 2, rkprkskjtc quk kg sistkdc jl cplrtc ji ctkjÿc, c gcs skócgks, tcjtl `k kjtrc`c aldl `k scgi`c

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¼Suk

¼Rlr qué utigizcdls gls `kaifkgils kj jukstrls aãgaugls< ¼Rlr qué utigizcdls gls `kaifkgils kj jukstrls aãgaugls<

Gls ijhkjikrls tkjkdls quk trcfcocr alj jÿdkrls tl`ls gls `äcs, y kstls jÿdkrls Gls ijhkjikrls tkjkdls quk trcfcocr alj jÿdkrls tl`ls gls `äcs, y kstls jÿdkrls puk`kj skr duy hrcj`ks l duy pkqukóls. Kj gc dcylräc `k gls acsls, gl quk ks dãs puk`kj skr duy hrcj`ks l duy pkqukóls. Kj gc dcylräc `k gls acsls, gl quk ks dãs idplrtcjtk ks gc rkgcaiñj kjtrk `ls dchjitu`ks quk alrrksplj`krãj c gc disdc uji`c` idplrtcjtk ks gc rkgcaiñj kjtrk `ls dchjitu`ks quk alrrksplj`krãj c gc disdc uji`c` `k dk`i`c.

`k dk`i`c.

Rlr kokdpgl, ujc kstcaiñj fcsk `k tkgknljäc dñvig puk`k trcjsditir ujc pltkjaic `k =2X Rlr kokdpgl, ujc kstcaiñj fcsk `k tkgknljäc dñvig puk`k trcjsditir ujc pltkjaic `k =2X cprlxidc`cdkjtk (hcjcjaic `k gc cjtkjc ijagui`c). Gls tkgénljls dñvigks sñgl rkaifkj cprlxidc`cdkjtk (hcjcjaic `k gc cjtkjc ijagui`c). Gls tkgénljls dñvigks sñgl rkaifkj ujls 2.222222226 X, gl quk supljk uj 2.222222226;% `k gc pltkjaic trcjsditi`c.

ujls 2.222222226 X, gl quk supljk uj 2.222222226;% `k gc pltkjaic trcjsditi`c. Qikdprk quk mcyc quk trcfcocr alj rcjhls judérials hrcj`ks, ks aljvkjikjtk utigizcr kg Qikdprk quk mcyc quk trcfcocr alj rcjhls judérials hrcj`ks, ks aljvkjikjtk utigizcr kg glhcritdl `k ksls jÿdkrls. Rlr kokdpgl, gc kstcaiñj fcsk `k jukstrl kokdpgl trcjsditk glhcritdl `k ksls jÿdkrls. Rlr kokdpgl, gc kstcaiñj fcsk `k jukstrl kokdpgl trcjsditk ujc pltkjaic `k +09 `Fd dikjtrcs quk kg tkgénljl dñvig rkaifk

ujc pltkjaic `k +09 `Fd dikjtrcs quk kg tkgénljl dñvig rkaifk ‑ ‑;8 `Fd, prl`uaikj`l;8 `Fd, prl`uaikj`l

ujc `inkrkjaic kj pltkjaic `k +09 `Fd

ujc `inkrkjaic kj pltkjaic `k +09 `Fd ‑ ‑ (-;8 `Fd) 4 32> `F. (-;8 `Fd) 4 32> `F.

Ltrl kokdpgl? si aljkatcdls `ls cdpginiac`lrks kj acsac`c alj hcjcjaics `k 36 y 3> Ltrl kokdpgl? si aljkatcdls `ls cdpginiac`lrks kj acsac`c alj hcjcjaics `k 36 y 3> rkspkativcdkjtk, lftkjkdls ujc hcjcjaic tltcg `k 36 x 3> 4 396. Kj térdijls rkspkativcdkjtk, lftkjkdls ujc hcjcjaic tltcg `k 36 x 3> 4 396. Kj térdijls glhcrätdials, gls `ls cdpginiac`lrks tikjkj ujc hcjcjaic `k 32.= `F y 36 `F, glhcrätdials, gls `ls cdpginiac`lrks tikjkj ujc hcjcjaic `k 32.= `F y 36 `F, rkspkativcdkjtk, prl`uaikj`l ujc hcjcjaic tltcg `k 32.= `F + 36 `F 4 66.= `F, quk ks rkspkativcdkjtk, prl`uaikj`l ujc hcjcjaic tltcg `k 32.= `F + 36 `F 4 66.= `F, quk ks duaml dãs nãaig `k acgaugcr.

duaml dãs nãaig `k acgaugcr.

Aucj`l trcfcocdls alj `kaifkgils, gls vcglrks slj duaml dãs nãaigks `k dcjipugcr. Ks Aucj`l trcfcocdls alj `kaifkgils, gls vcglrks slj duaml dãs nãaigks `k dcjipugcr. Ks duaml dãs skjaiggl sudcr y rkstcr `kaifkgils `k acfkzc quk dugtipgiacr y ìviìr vcglrks duaml dãs skjaiggl sudcr y rkstcr `kaifkgils `k acfkzc quk dugtipgiacr y ìviìr vcglrks gijkcgks. Kstc ks gc prijaipcg rczñj plr gc quk prknkridls utigizcr `kaifkgils kj jukstrls gijkcgks. Kstc ks gc prijaipcg rczñj plr gc quk prknkridls utigizcr `kaifkgils kj jukstrls aãgaugls.

aãgaugls.

¼Suk vkjtcoc tikjk utigizcr kg @kaifkg< ¼Suk vkjtcoc tikjk utigizcr kg @kaifkg<

Kg @kaifkg sk acgaugc kj ujc ksacgc glhcrätdiac `kniji`c, quk Kg @kaifkg sk acgaugc kj ujc ksacgc glhcrätdiac `kniji`c, quk pkrditk gcs kspkainiacailjks `kg rkj`idikjtl c trcvés `k uj pkrditk gcs kspkainiacailjks `kg rkj`idikjtl c trcvés `k uj cdpgil rcjhl `k gc skócg `k rknkrkjaic, skc ^lgtcok l pltkjaic, cdpgil rcjhl `k gc skócg `k rknkrkjaic, skc ^lgtcok l pltkjaic, plr kokdpgl

plr kokdpgl

Gls @kaifkgks puk`kj sudcrsk l rkstcrsk (dugtipgiacj`l y ìviìkj`l kj sus Gls @kaifkgks puk`kj sudcrsk l rkstcrsk (dugtipgiacj`l y ìviìkj`l kj sus alrrkspljìkjtks rkgcailjks), ncaigitcj`l `k ksk dl`l gls aãgaugls l slguailjks hrcniacs. alrrkspljìkjtks rkgcailjks), ncaigitcj`l `k ksk dl`l gls aãgaugls l slguailjks hrcniacs. Kg Fkg nuk lrihijcgdkjtk `kniji`l plr Cgkxcj`kr Hrcmcd Fkgg, pcrc dkìr rkgcailjks `k Kg Fkg nuk lrihijcgdkjtk `kniji`l plr Cgkxcj`kr Hrcmcd Fkgg, pcrc dkìr rkgcailjks `k slji`l, kj gcs gäjkcs tkgkhrãniacs, gcs aucgks aljtcfcj alj ujc idpk`cjaic `k >22 lmds. slji`l, kj gcs gäjkcs tkgkhrãniacs, gcs aucgks aljtcfcj alj ujc idpk`cjaic `k >22 lmds. @knijiaiñj `k `F

@knijiaiñj `k `F C

C pkscr pkscr `k `k quk quk kg kg glhcritdl glhcritdl kj kj fcsk fcsk 32 32 `k `k gc gc rkgcaiñj rkgcaiñj `k `k `ls `ls jivkgks jivkgks `k `k pltkjaic pltkjaic ksks cìdkjsiljcg, tikjk uji`c`ks `k fkgils kj mljlr `kg ijvkjtlr `kg tkgénljl (Cgkxcj`kr cìdkjsiljcg, tikjk uji`c`ks `k fkgils kj mljlr `kg ijvkjtlr `kg tkgénljl (Cgkxcj`kr Hrcmcd Fkgg). Rcrc lftkjkr acjti`c`ks dãs dcjkocfgks, utigizcdls kg `F (`kaifkgil) kj Hrcmcd Fkgg). Rcrc lftkjkr acjti`c`ks dãs dcjkocfgks, utigizcdls kg `F (`kaifkgil) kj guhcr `kg fkgil. Rcrc kggl mcy quk dugtipgiacr plr 32 gls vcglrks kxprksc`ls kj fkgils (cg guhcr `kg fkgil. Rcrc kggl mcy quk dugtipgiacr plr 32 gls vcglrks kxprksc`ls kj fkgils (cg ihucg quk dugtipgiacdls plr dig ujc ìstcjaic si qukrkdls trcfcocr alj digädktrls kj ihucg quk dugtipgiacdls plr dig ujc ìstcjaic si qukrkdls trcfcocr alj digädktrls kj guhcr `k alj dktrls).

guhcr `k alj dktrls).

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¼Suk

Kokdpgl? R3 ks ihucg c 622 X y R6 ks ihucg c 322 dX. ¼Auãg ks su rkgcaiñj kj `F< Kokdpgl? R3 ks ihucg c 622 X y R6 ks ihucg c 322 dX. ¼Auãg ks su rkgcaiñj kj `F<

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Rlr supukstl, cjtks `k ìviìr kstls jivkgks `k pltkjaic, mcy quk aljvkrtirgls c gc disdc Rlr supukstl, cjtks `k ìviìr kstls jivkgks `k pltkjaic, mcy quk aljvkrtirgls c gc disdc uji`c`, X l dX. Qi ìviìdls ìrkatcdkjtk 622 kjtrk 322, kg rksugtc`l lftkji`l skrã uji`c`, X l dX. Qi ìviìdls ìrkatcdkjtk 622 kjtrk 322, kg rksugtc`l lftkji`l skrã ijalrrkatl.

ijalrrkatl.

Mly kj `äc, sk utigizc kg glhcritdl kj fcsk 32 acsi `k nlrdc kxagusivc. Gc cfrkvicturc Mly kj `äc, sk utigizc kg glhcritdl kj fcsk 32 acsi `k nlrdc kxagusivc. Gc cfrkvicturc pcrc kstk glhcritdl ks

pcrc kstk glhcritdl ks ghgh. Kg cghujls gifrls `k tkxtl cjtihuls, sk puk`k kjaljtrcr gc. Kg cghujls gifrls `k tkxtl cjtihuls, sk puk`k kjaljtrcr gc utigizcaiñj `kg glhcritdl jcturcg, quk ks kg glhcritdl kj fcsk k (k 4 6.83= utigizcaiñj `kg glhcritdl jcturcg, quk ks kg glhcritdl kj fcsk k (k 4 6.83= cprlxidc`cdkjtk). Kj kstc jltc `k cpgiacaiñj sñgl sk utigizcrã kg glhcritdl kj fcsk 32, cprlxidc`cdkjtk). Kj kstc jltc `k cpgiacaiñj sñgl sk utigizcrã kg glhcritdl kj fcsk 32, quk cfrkvicrkdls aldl gh `k cquä kj c`kgcjtk.

quk cfrkvicrkdls aldl gh `k cquä kj c`kgcjtk.

Pcdfiéj ks plsifgk aljvkrtir `kaifkgils c uji`c`ks gijkcgks. Rridkrl mcy quk aljvkrtir Pcdfiéj ks plsifgk aljvkrtir `kaifkgils c uji`c`ks gijkcgks. Rridkrl mcy quk aljvkrtir gls `F c fkgils ìviìkj`l kg vcglr plr 32. Rlstkrilrdkjtk, mcy quk kgkvcr 32 (`c`l quk gls `F c fkgils ìviìkj`l kg vcglr plr 32. Rlstkrilrdkjtk, mcy quk kgkvcr 32 (`c`l quk kstcdls utigizcj`l kg glhcritdl kj fcsk 32) c ksc pltkjaic?

kstcdls utigizcj`l kg glhcritdl kj fcsk 32) c ksc pltkjaic?



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

 

 



Kokdpgl? c4 61`F, ¼aucjtl ks R

Kokdpgl? c4 61`F, ¼aucjtl ks R33 / R / R66<<

@kspuks `k acgaugcr pridkrl 61/3246.1, plstkrilrdkjtk sustituidls gls `ctls y @kspuks `k acgaugcr pridkrl 61/3246.1, plstkrilrdkjtk sustituidls gls `ctls y lftkjkdls? lftkjkdls?



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

 





           Mldlhkjki`c` `k ainrcs Mldlhkjki`c` `k ainrcs

Qi tldcdls glhcritdls c judkrls duy hrcj`ks y/l duy pkqukóls, sk vkrc quk kg Qi tldcdls glhcritdls c judkrls duy hrcj`ks y/l duy pkqukóls, sk vkrc quk kg

rksugtc`l `k ksc lpkrcaiñj dctkdctiac frij`c acjti`c`ks auyls judkrls `k ainrcs slj rksugtc`l `k ksc lpkrcaiñj dctkdctiac frij`c acjti`c`ks auyls judkrls `k ainrcs slj sidigcrks. C gl sudl mcfrc `inkrkjaic kj gls sihjls, gl quk ij`iacrc gl sihuikjtk?

sidigcrks. C gl sudl mcfrc `inkrkjaic kj gls sihjls, gl quk ij`iacrc gl sihuikjtk? Qihjl plsitivl? judkrl aljsi`krc`l :3

Qihjl plsitivl? judkrl aljsi`krc`l :3 Qihjl jkhctivl? judkrl aljsi`krc`l 73 Qihjl jkhctivl? judkrl aljsi`krc`l 73 Kokdpgls? Kokdpgls? Glh 3,222,222,222 4 +9 Glh 3,222,222,222 4 +9 Glh 2.222223 4 -> Glh 2.222223 4 ->

@k dcjkrc quk alj gc utigizcaiñj `kg `kaifkg ks plsifgk lpkrcr dctkdãtiacdkjtk uj @k dcjkrc quk alj gc utigizcaiñj `kg `kaifkg ks plsifgk lpkrcr dctkdãtiacdkjtk uj vcglr duy hrcj`k l duy pkqukól l cdfls sidugtcjkcdkjtk, sij tkjkr gc jkaksi`c` `k vcglr duy hrcj`k l duy pkqukól l cdfls sidugtcjkcdkjtk, sij tkjkr gc jkaksi`c` `k rkaurrir c judkrls quk plr su acjti`c` `k ainrcs mcricj plal prcatial su dcjkol.

rkaurrir c judkrls quk plr su acjti`c` `k ainrcs mcricj plal prcatial su dcjkol. ¼Sué sihjiniac `Fd<

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Qlfrk ;2 lmds. Kstc acjti`c` `k rknkrkjaic sk `ksihjc cóc`ikj`l ujc d (`k dX) c `F Qlfrk ;2 lmds. Kstc acjti`c` `k rknkrkjaic sk `ksihjc cóc`ikj`l ujc d (`k dX) c `F lftkjiéj`lsk `Fd.

lftkjiéj`lsk `Fd.

Gc rkgcaiñj `k pltkjaics kjtrk R3 y R6 sk aljvikrtk kj ujc rkgcaiñj kjtrk R3 y 3 dX, Gc rkgcaiñj `k pltkjaics kjtrk R3 y R6 sk aljvikrtk kj ujc rkgcaiñj kjtrk R3 y 3 dX, ij`iaãj`lsk kj `Fd. ij`iaãj`lsk kj `Fd.

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)

Qkhÿj kg kstãj`cr IKA 68, kxistk ltrc nlrdc `k ksarifir kstc nñrdugc. Gls jivkgks sk Qkhÿj kg kstãj`cr IKA 68, kxistk ltrc nlrdc `k ksarifir kstc nñrdugc. Gls jivkgks sk rkprkskjtcj alj gc gktrc G y kg vcglr `k rknkrkjaic sk `kfk ij`iacr `k nlrdc kxpgäaitc. Gc rkprkskjtcj alj gc gktrc G y kg vcglr `k rknkrkjaic sk `kfk ij`iacr `k nlrdc kxpgäaitc. Gc nñrdugc quk`c `k gc sihuikjtk nlrdc?

nñrdugc quk`c `k gc sihuikjtk nlrdc?





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( 

_

_{))}



Qk ksarifiräc GR/3dX 4 8 `F, plr kokdpgl. Qkhÿj gc IKA 68 jl kstã pkrditi`l utigizcr gc Qk ksarifiräc GR/3dX 4 8 `F, plr kokdpgl. Qkhÿj gc IKA 68 jl kstã pkrditi`l utigizcr gc kxprksiñj 8 `Fd. Aldl ks duaml dãs aldÿj ksarifir `Fd, skrã éstc gc kxprksiñj quk kxprksiñj 8 `Fd. Aldl ks duaml dãs aldÿj ksarifir `Fd, skrã éstc gc kxprksiñj quk sk utigizcrã kj kstc jltc `k cpgiacaiñj.

sk utigizcrã kj kstc jltc `k cpgiacaiñj.

Rcrc tkjkr ujc i`kc `k gls ñr`kjks `k dchjitu` quk sk dcjkocj, cquä mcy cghujls Rcrc tkjkr ujc i`kc `k gls ñr`kjks `k dchjitu` quk sk dcjkocj, cquä mcy cghujls kokdpgls? kg rcjhl `k gc pltkjaic `k scgi`c `k uj hkjkrc`lr `k skócg vc `ks`k gls

kokdpgls? kg rcjhl `k gc pltkjaic `k scgi`c `k uj hkjkrc`lr `k skócg vc `ks`k gls ‑ ‑302302

`Fd c +62 `Fd l `ks`k 2.23 pX c 2.3 X. Gcs kstcailjks fcsk `k tkgknljäc dñvig `Fd c +62 `Fd l `ks`k 2.23 pX c 2.3 X. Gcs kstcailjks fcsk `k tkgknljäc dñvig trcjsditkj c +01 `Fd l 62 X. Gls tkgénljls dñvigks trcjsditkj `k +32 `Fd c +11 `Fd trcjsditkj c +01 `Fd l 62 X. Gls tkgénljls dñvigks trcjsditkj `k +32 `Fd c +11 `Fd l `ks`k 32 dX c 6 X. Gls trcjsdislrks `k ìnusiñj `k rcìl y tkgkvisiñj lpkrcj alj l `ks`k 32 dX c 6 X. Gls trcjsdislrks `k ìnusiñj `k rcìl y tkgkvisiñj lpkrcj alj jivkgks `k scgi`c `k +82 `Fd c +92 `Fd l `ks`k 32 eX c 3 DX.

jivkgks `k scgi`c `k +82 `Fd c +92 `Fd l `ks`k 32 eX c 3 DX. ¼Sué ks uj jivkg<

¼Sué ks uj jivkg<

Aldl vidls cjtkrilrdkjtk, kg tkrdijl `Fd aljggkvc gc rknkrkjaic c uj jivkg `k pltkjaic Aldl vidls cjtkrilrdkjtk, kg tkrdijl `Fd aljggkvc gc rknkrkjaic c uj jivkg `k pltkjaic `k 3 dX. Ltrcs acjti`c`ks `k rknkrkjaic utigizc`cs jlrdcgdkjtk slj 3 X, 3 ^, 3 »^ y `k 3 dX. Ltrcs acjti`c`ks `k rknkrkjaic utigizc`cs jlrdcgdkjtk slj 3 X, 3 ^, 3 »^ y tcdfiéj 3 C l 3 »C. Qk `ksihjcj aldl `F (X), `F (^), `F (»^), `F (C) y `F (»C), tcdfiéj 3 C l 3 »C. Qk `ksihjcj aldl `F (X), `F (^), `F (»^), `F (C) y `F (»C), rkspkativcdkjtk, l kj dk`i`cs `k ijtkjsi`c` `k acdpl, `F (X/d

rkspkativcdkjtk, l kj dk`i`cs `k ijtkjsi`c` `k acdpl, `F (X/d66), `F (^/d), `F), `F (^/d), `F (»^/d), `F (C/d) y `F (»C/d). Aldl kj kg acsl `k gls `Fd, gc nlrdc aljvkjailjcg `k (»^/d), `F (C/d) y `F (»C/d). Aldl kj kg acsl `k gls `Fd, gc nlrdc aljvkjailjcg `k ksarifir kstcs uji`c`ks `FX, `F^, `F»^, `FC, `F»C, `FX/d

ksarifir kstcs uji`c`ks `FX, `F^, `F»^, `FC, `F»C, `FX/d66, `F^/d, `F »^/d, `FC/d, `F^/d, `F »^/d, `FC/d y `F »C/d sk `ksväcj `kg kstãj`cr, pkrl skrãj gcs utigizc`cs kj kstc jltc `k cpgiacaiñj. y `F »C/d sk `ksväcj `kg kstãj`cr, pkrl skrãj gcs utigizc`cs kj kstc jltc `k cpgiacaiñj. C pcrtir

C pcrtir `k gls vcglrk`k gls vcglrks rkgctivls `k s rkgctivls `k gc pltkjaic R3 gc pltkjaic R3 (tkjsiñj (tkjsiñj [3) rknkri`ls [3) rknkri`ls c gc plc gc pltkjaic R6tkjaic R6 (tkjsiñj [6), sk lftikjkj gls vcglrks cfslgutls utigizcj`l gls vcglrks `k rknkrkjaic (tkjsiñj [6), sk lftikjkj gls vcglrks cfslgutls utigizcj`l gls vcglrks `k rknkrkjaic

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¼Auãg ks gc `inkrkjaic kjtrk gls `kaifkgils `k tkjsiñj y gls `kaifkgils `k pltkjaic< ¼Auãg ks gc `inkrkjaic kjtrk gls `kaifkgils `k tkjsiñj y gls `kaifkgils `k pltkjaic< Rcrc kdpkzcr, ks jkakscril lgvi`crsk `k tl`l gl quk sk mcyc lä`l cakrac `k gls Rcrc kdpkzcr, ks jkakscril lgvi`crsk `k tl`l gl quk sk mcyc lä`l cakrac `k gls `kaifkgils `k tkjsiñj y `k pltkjaic. Qñgl kxistk uj tipl `k `kaifkgil, y rkprkskjtc gc `kaifkgils `k tkjsiñj y `k pltkjaic. Qñgl kxistk uj tipl `k `kaifkgil, y rkprkskjtc gc rkgcaiñj kjtrk `ls jivkgks `k pltkjaic R3 y R6. Rlr supukstl, sk puk`k kxprkscr rkgcaiñj kjtrk `ls jivkgks `k pltkjaic R3 y R6. Rlr supukstl, sk puk`k kxprkscr aucgquikr jivkg `k pltkjaic aldl ujc tkjsiñj si sk aljlak gc rksistkjaic.

aucgquikr jivkg `k pltkjaic aldl ujc tkjsiñj si sk aljlak gc rksistkjaic.

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_

Qk puk`k kxprkscr gc rkgcaiñj glhcrätdiac aldl sihuk? Qk puk`k kxprkscr gc rkgcaiñj glhcrätdiac aldl sihuk?

(

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) 

) 

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

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

[tigizcj`l gcs sihuikjtks rkhgcs, [tigizcj`l gcs sihuikjtks rkhgcs,

(

()

)







 

_{}



 





Lftkjkdls (utigizcj`l glh pcrc rknkrirjls cg glhcritdl kj fcsk 32)? Lftkjkdls (utigizcj`l glh pcrc rknkrirjls cg glhcritdl kj fcsk 32)?

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))    

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Lfsérvksk kg sihjl dkjls cjtks `kg térdijl `k gc rksistkjaic. Lfsérvksk kg sihjl dkjls cjtks `kg térdijl `k gc rksistkjaic.

Kj gc dcylräc `k gls acsls, gc rksistkjaic `k rknkrkjaic ks gc disdc pcrc cdfls jivkgks Kj gc dcylräc `k gls acsls, gc rksistkjaic `k rknkrkjaic ks gc disdc pcrc cdfls jivkgks `k pltkjaic, V3 4 V6. Rlr gl tcjtl? `k pltkjaic, V3 4 V6. Rlr gl tcjtl?



  

Qk puk`k sidpginiacr kj? Qk puk`k sidpginiacr kj?











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

_{Aljsi`krcj`l V}_Aljsi`krcj`l_V33_{4 V}_{4 V66}

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Dchjitu` `k rkgcaiñj Dchjitu` `k rkgcaiñj `F

`F

Kg `kaifkg kj su nlrdc fãsiac, ks gc kxprksiñj dãs hkjkrcg `k kstu`il aldl dchjitu` `k Kg `kaifkg kj su nlrdc fãsiac, ks gc kxprksiñj dãs hkjkrcg `k kstu`il aldl dchjitu` `k rkgcaiñj.

rkgcaiñj.

Gcs kaucailjks dãs kdpgkc`cs pcrc gls pcrãdktrls kgéatrials? pltkjaic, tkjsiñj y Gcs kaucailjks dãs kdpgkc`cs pcrc gls pcrãdktrls kgéatrials? pltkjaic, tkjsiñj y alrrikjtk, alrrksplj`kj c gcs kaucailjks fãsiacs, `k gc gky `k lmds.

alrrikjtk, alrrksplj`kj c gcs kaucailjks fãsiacs, `k gc gky `k lmds. `Fr

`Fr

K   dfé u d  ñ      ufä ‗—  K   dfé u d  ñ      ufä ‗— 

quk ks uj vcglr `k pltkjaic `k rknkrkjaic l rkgctivl cg lrihkj `kg sistkdc l airauitl quk ks uj vcglr `k pltkjaic `k rknkrkjaic l rkgctivl cg lrihkj `kg sistkdc l airauitl cjcgizc`l (c gc kjtrc`c `kg disdl).

cjcgizc`l (c gc kjtrc`c `kg disdl).



 

_

_{}



R ks gc pltkjaic dk`i`c kj uj pujtl aucgquikrc `k uj sistkdc l airauitl aucj`l sk kjväc R ks gc pltkjaic dk`i`c kj uj pujtl aucgquikrc `k uj sistkdc l airauitl aucj`l sk kjväc ujc skócg kj kg lrihkj `kg disdl R

ujc skócg kj kg lrihkj `kg disdl Rlrihkjlrihkj ks g pltkjaic `k skócg kj kg lrihkj `kg airauitl l ks g pltkjaic `k skócg kj kg lrihkj `kg airauitl l sistkdc, dk`i`l kj gc disdc uji`c` quk R.

sistkdc, dk`i`l kj gc disdc uji`c` quk R.

Qi sk vcräc gc pltkjaic ijykatc`c kj kg lrihkj `kg airauitl, gls `Fr pkrdcjkakrãj Qi sk vcräc gc pltkjaic ijykatc`c kj kg lrihkj `kg airauitl, gls `Fr pkrdcjkakrãj aljstcjtks k ij`kpkj`ikjtks `kg jivkg `k gc skócg ijykatc`c. Ks `kair quk gls `Fr slj aljstcjtks k ij`kpkj`ikjtks `kg jivkg `k gc skócg ijykatc`c. Ks `kair quk gls `Fr slj ujc acrcatkrästiac prlpic `kg airauitl l sistkdc y jl vcräcj dikjtrcs jl vcrié gc Hcjcjaic ujc acrcatkrästiac prlpic `kg airauitl l sistkdc y jl vcräcj dikjtrcs jl vcrié gc Hcjcjaic l ctkjucaiñj `k ac`c kgkdkjtl `kg disdl.

l ctkjucaiñj `k ac`c kgkdkjtl `kg disdl. `Fw

`Fw

Ks ltrl tipl `k `kaifkg `lj`k gc pltkjaic `k rknkrkjaic 3Xctt Ks ltrl tipl `k `kaifkg `lj`k gc pltkjaic `k rknkrkjaic 3Xctt







_{ }

_

Qu kquivcgkjaic alj gls `Fd ks? Qu kquivcgkjaic alj gls `Fd ks? 3`FX 4 12 `Fd 3`FX 4 12 `Fd `Fe `Fe

Qk utigizc dcylrdkjtk `lj`k gls jivkgks gls jivkgks `k pltkjaic kj oukhl slj kgkvc`ls, Qk utigizc dcylrdkjtk `lj`k gls jivkgks gls jivkgks `k pltkjaic kj oukhl slj kgkvc`ls, tcgks aldl gcs rk`ks `k `istrifuaiñj kgéatriac.

tcgks aldl gcs rk`ks `k `istrifuaiñj kgéatriac. Kg vcglr

Kg vcglr `k rknkrkjaic `k rknkrkjaic ks 3 ks 3 Eiglwctt.Eiglwctt.



(18)

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(19)

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¼Suk

Ks `kair kg `Fdl ks uj jivkg `k pltkjaic `k ujc skócg rknkri`l kj ac`c pujtl cg vcglr Ks `kair kg `Fdl ks uj jivkg `k pltkjaic `k ujc skócg rknkri`l kj ac`c pujtl cg vcglr jldijcg `k gc skócg `k kjtrc`c. Rlr kokdpgl -62 `F plr `kfcol `kg vcglr kxistkjtk kj kg jldijcg `k gc skócg `k kjtrc`c. Rlr kokdpgl -62 `F plr `kfcol `kg vcglr kxistkjtk kj kg lrihkj `kg airauitl l sistkdc.

lrihkj `kg airauitl l sistkdc. `Fdlp

`Fdlp

Ks kg vcglr `kg rui`l dk`il kj gc nlrdc pslnldétriac (c trcvés `k uj nigtrl alj Ks kg vcglr `kg rui`l dk`il kj gc nlrdc pslnldétriac (c trcvés `k uj nigtrl alj

ä  uñ m ≍ u)

ä  uñ m ≍ u) y rknkri`l cg jivkg `k gc skócg `k prukfcy rknkri`l cg jivkg `k gc skócg `k prukfc

kj `iaml pujtl. kj `iaml pujtl. `F»

`F» (Qistkdcs `k Aldujiacailjks) (Qistkdcs `k Aldujiacailjks)

Ks ujc uji`c` `k cdpgic cpgiacaiñj kj kg ãrkc `k gcs aldujiacailjks, pcrtiaugcrdkjtk Ks ujc uji`c` `k cdpgic cpgiacaiñj kj kg ãrkc `k gcs aldujiacailjks, pcrtiaugcrdkjtk kj kg cjãgisis `k prlpchcaiñj `k skócgks kgkatrldchjétiacs kj kg kspcail gifrk.

kj kg cjãgisis `k prlpchcaiñj `k skócgks kgkatrldchjétiacs kj kg kspcail gifrk.

Kg vcglr `k gc skócg `k rknkrkjaic ks kg `k ujc ijtkjsi`c` `k acdpl kgéatrial `k 3 diarl Kg vcglr `k gc skócg `k rknkrkjaic ks kg `k ujc ijtkjsi`c` `k acdpl kgéatrial `k 3 diarl ^/d (3»^/d).Kj cghujls crtäaugls y/l pufgiacailjks sukgk aljnuj`ir kg `Fu (quk ^/d (3»^/d).Kj cghujls crtäaugls y/l pufgiacailjks sukgk aljnuj`ir kg `Fu (quk alrrksplj`k c Pkgknljäc) alj `F» (Qistkdc `k Aldujiacailjks) plr gc ijagusiñj `k gc alrrksplj`k c Pkgknljäc) alj `F» (Qistkdc `k Aldujiacailjks) plr gc ijagusiñj `k gc

 ‗u— y    hh ‗du— (»). Q f  ñ  x    ‗u— y    hh ‗du— (»). Q f  ñ  x  

kxprksiñj cjcgizc`c pcrc ìnkrkjaicr alrrkatcdkjtk gc uji`c` `k dkì`c dkjailjc`c. kxprksiñj cjcgizc`c pcrc ìnkrkjaicr alrrkatcdkjtk gc uji`c` `k dkì`c dkjailjc`c. Qk utigizc kg `F» pcrc niocr gls gäditks `k gcs ãrkcs `k alfkrturc `k gls acjcgks `k Qk utigizc kg `F» pcrc niocr gls gäditks `k gcs ãrkcs `k alfkrturc `k gls acjcgks `k tkgkvisiñj l `k gcs kdislrcs `k rcìlìnusiñj pÿfgiac `k CD y ND, `ktkrdijcj`l kg jivkg tkgkvisiñj l `k gcs kdislrcs `k rcìlìnusiñj pÿfgiac `k CD y ND, `ktkrdijcj`l kg jivkg `kg acdpl kgéatrial dkì`l kj »^/d kj ìaml pujtl.

`kg acdpl kgéatrial dk`i`l kj »^/d kj `iaml pujtl.

Ãrkc `k alfkrturc `k gls acjcgks > cg 31? 88 `F» 4 82=2 »^/d Ãrkc `k alfkrturc `k gls acjcgks > cg 31? 88 `F» 4 82=2 »^/d

`F^ `F^

Kxprksc gc rkspukstc kj `kaifkgks `k uj diarñnljl c ujc nrkaukjaic `ktkrdijc`c. Kxprksc gc rkspukstc kj `kaifkgks `k uj diarñnljl c ujc nrkaukjaic `ktkrdijc`c.

Kg Jivkg `k rknkrkjaic `k 2 `F ks ihucg c 3^ (2 `F^) aucj`l sk slfrk uj diarñnljl ujc Kg Jivkg `k rknkrkjaic `k 2 `F ks ihucg c 3^ (2 `F^) aucj`l sk slfrk uj diarñnljl ujc prksiñj caÿstiac `k 3 `ijc/ad

prksiñj caÿstiac `k 3 `ijc/ad66







_{ }



`Fd^

Ks ujc uji`c` `k dk`i`c, surhi`c pcrc kstcfgkakr ujc uji`c` `k rknkrkjaic pcrc AAP^ Ks ujc uji`c` `k dk`i`c, surhi`c pcrc kstcfgkakr ujc uji`c` `k rknkrkjaic pcrc AAP^ l Pkgkvisiñj plr acfgk.

l Pkgkvisiñj plr acfgk.

K ^  ñ    3 d^ f u d  8; ℮ K ^  ñ    3 d^ f u d  8; ℮

(20)

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(21)

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¼Suk

`F` `F`

Aldl rc`ic`lr Isltrñpial ks ujc cfstrcaaiñj dctkdãtiac `kniji`c pcrc plsifigitcr gls Aldl rc`ic`lr Isltrñpial ks ujc cfstrcaaiñj dctkdãtiac `kniji`c pcrc plsifigitcr gls aãgaugls rkspkativls, ks usucg rknkrir gc hucjcaic `k ujc cjtkjc aucgquikrc, rkspkatl `kg aãgaugls rkspkativls, ks usucg rknkrir gc hucjcaic `k ujc cjtkjc aucgquikrc, rkspkatl `kg cgujc ltrc `k ncatifgk rkcgizcaiñj prcatiac.

cgujc ltrc `k ncatifgk rkcgizcaiñj prcatiac.

Rcrc kggl sk kdpgkc uj ìplgl `k dkìc lj`c aldl rknkrkjaic. Rcrc kggl sk kdpgkc uj ìplgl `k dkìc lj`c aldl rknkrkjaic.



 







@ñj`k? R

@ñj`k? RrCrC ? Rltkjaic rc`ic`c plr ujc cjtkjc ? Rltkjaic rc`ic`c plr ujc cjtkjc R

Rr@C/6?r@C/6?Rltkjaic rcìc`c plr uj rcìc`lr isltrñpialRltkjaic rcìc`c plr uj rcìc`lr isltrñpial

Rcrc aljvkrtir `Fi c `F` y Rcrc aljvkrtir `Fi c `F` y viakvkrsc, sk kdpgkc gc viakvkrsc, sk kdpgkc gc sihuikjtk nlrdugc? sihuikjtk nlrdugc? `F` 4 `Fi + 6.3; `F` 4 `Fi + 6.3;  



 



__



  _{}_{}



   

 

    



_{}_{ }_{ }_{}  

  







UU



TT

 



 



__



  _{}_{}



  



 





 

 





UU



TT

   

 



∖∖



 

  

  



++





__



__

UU

__

TT

Lftkjkr `kaifkgks `k ujc pltkjaic `k rknkrkjaic Lftkjkr `kaifkgks `k ujc pltkjaic `k rknkrkjaic

Aljvkrtir `F c Rltkjaic kj Xctts Aljvkrtir `F c Rltkjaic kj Xctts

^lgtcok c pcrtir `k rksistkjaic `k Vknkrkjaic (Vksistkjaic skhÿj kg airauitl `k idpk`cjaic) ^lgtcok c pcrtir `k rksistkjaic `k Vknkrkjaic (Vksistkjaic skhÿj kg airauitl `k idpk`cjaic)

@kaifkgks c pcrtir ^lgtcok `k rknkrkjaic @kaifkgks c pcrtir ^lgtcok `k rknkrkjaic

Aljvkrtir Xctts c `Fη^ Aljvkrtir Xctts c `Fη^

Aljvkrtir `Fd

Aljvkrtir `Fd c η^c η^lgtilslgtils

Auc`rl rksudkj `k aljvkrsiñj

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(23)

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¼Suk

Gc nujaiñj `k trcjsnkrkjaic jlrdcgdkjtk sk kspkainiac kj `F? Gc nujaiñj `k trcjsnkrkjaic jlrdcgdkjtk sk kspkainiac kj `F?

 

  

  

     







UUTT    





Qi gc pltkjaic `k scgi`c R6 `k uj airauitl `k `ls pukrtls ks dcylr quk gc pltkjaic `k Qi gc pltkjaic `k scgi`c R6 `k uj airauitl `k `ls pukrtls ks dcylr quk gc pltkjaic `k kjtrc`c R3, kjtljaks gc rkgcaiñj glhcrätdiac kjtrk R6 y R3 ks plsitivc. Kstl sk aljlak kjtrc`c R3, kjtljaks gc rkgcaiñj glhcrätdiac kjtrk R6 y R3 ks plsitivc. Kstl sk aljlak aldl cdpginiacaiñj l hcjcjaic.

aldl cdpginiacaiñj l hcjcjaic.

Qi gc pltkjaic `k scgi`c R6 `k uj airauitl `k `ls pukrtls ks dkjlr quk gc pltkjaic `k Qi gc pltkjaic `k scgi`c R6 `k uj airauitl `k `ls pukrtls ks dkjlr quk gc pltkjaic `k kjtrc`c R3, kjtljaks gc rkgcaiñj glhcrätdiac kjtrk R6 y R3 ks jkhctivc. Kstl sk aljlak kjtrc`c R3, kjtljaks gc rkgcaiñj glhcrätdiac kjtrk R6 y R3 ks jkhctivc. Kstl sk aljlak aldl ctkjucaiñj l pér`i`c (sk lditk kg sihjl dkjls).

aldl ctkjucaiñj l pér`i`c (sk lditk kg sihjl dkjls).

   

   

_



_

UUTT      

_{  }

 

_{}

Rcrc gc kvcgucaiñj `k gc rkgcaiñj `k pltkjaics l `k gc rkgcaiñj `k tkjsiljks c pcrtir `k Rcrc gc kvcgucaiñj `k gc rkgcaiñj `k pltkjaics l `k gc rkgcaiñj `k tkjsiljks c pcrtir `k gls vcglrks kj `kaifkgils sk utigizcj gcs sihuikjtks nñrdugcs?

gls vcglrks kj `kaifkgils sk utigizcj gcs sihuikjtks nñrdugcs?









 

 

⁀⁀





LL









 

 

⁀⁀





Rcrc Rcrc VVlutlut 4 V 4 Vijij

Gls cdpginiac`lrks aljvkjailjcgks aljsihukj hcjcjaics `k mcstc 02 `F kj ujc slgc Gls cdpginiac`lrks aljvkjailjcgks aljsihukj hcjcjaics `k mcstc 02 `F kj ujc slgc ktcpc, gl quk sk alrrksplj`k alj rkgcailjks `k tkjsiñj `k mcstc 322 vkaks y rkgcailjks ktcpc, gl quk sk alrrksplj`k alj rkgcailjks `k tkjsiñj `k mcstc 322 vkaks y rkgcailjks `k pltkjaic `k mcstc 32222 vkaks. Rcrc vcglrks dcylrks kxistk kg rikshl `k quk kg `k pltkjaic `k mcstc 32222 vkaks. Rcrc vcglrks dcylrks kxistk kg rikshl `k quk kg cdpginiac`lr lsaigk. Qk puk`kj lftkjkr hcjcjaics dãs kgkvc`cs aljkatcj`l vcrics cdpginiac`lr lsaigk. Qk puk`kj lftkjkr hcjcjaics dãs kgkvc`cs aljkatcj`l vcrics

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Kokdpgl? Nih. 6 dukstrc gcs ktcpcs `k kjtrc`c `k uj rkakptlr. Gc hcjcjaic tltcg sk Kokdpgl? Nih. 6 dukstrc gcs ktcpcs `k kjtrc`c `k uj rkakptlr. Gc hcjcjaic tltcg sk acgaugc `k gc sihuikjtk dcjkrc?

acgaugc `k gc sihuikjtk dcjkrc?

c

c 4 -2.8 `F + 36 `F - 8 `F + 61 `F 4 68.1 `F.4 -2.8 `F + 36 `F - 8 `F + 61 `F 4 68.1 `F.

Aljvkrsiñj `k `kaifkgils c plrakjtcok y viakvkrsc Aljvkrsiñj `k `kaifkgils c plrakjtcok y viakvkrsc

K éd ‗ — h ‗ —.  3% h  éd   u K éd ‗ — h ‗ —.  3% h  éd   u vcglr. vcglr. 3 % `k x 4 2,23 3 % `k x 4 2,23

⋋⋋

x x

Cg utigizcr plrakjtcoks, ks jkakscril nlrdugcrsk gl sihuikjtk? Cg utigizcr plrakjtcoks, ks jkakscril nlrdugcrsk gl sihuikjtk?

• ¼Kd u v  ñ   < • ¼Kd u v  ñ   < • ¼Kd   u 

• ¼Kd   u  %x `k ujc acjti`c` l uj %x dãs l dkjls `k ujc%x `k ujc acjti`c` l uj %x dãs l dkjls `k ujc

acjti`c`< acjti`c`<

Pcg y aldl sk mc dkjailjc`l cjtkrilrdkjtk, gcs dchjitu`ks `k tkjsiñj slj? tkjsiñj, Pcg y aldl sk mc dkjailjc`l cjtkrilrdkjtk, gcs dchjitu`ks `k tkjsiñj slj? tkjsiñj, alrrikjtk, ijtkjsi`c` `k acdpl y alkniaikjtk `k rkngkxiñj, plr kokdpgl.

alrrikjtk, ijtkjsi`c` `k acdpl y alkniaikjtk `k rkngkxiñj, plr kokdpgl.

Gcs dchjitu`ks `k pltkjaic ijaguykj gc pltkjaic, rksistkjaic, nihurc `k rui`l y `kjsi`c` Gcs dchjitu`ks `k pltkjaic ijaguykj gc pltkjaic, rksistkjaic, nihurc `k rui`l y `kjsi`c` `k pltkjaic.

`k pltkjaic.

Aljvkrsiñj `k % `k tkjsiñj c `kaifkgils y viakvkrsc Aljvkrsiñj `k % `k tkjsiñj c `kaifkgils y viakvkrsc

Kg tcjtl plr aikjtl x% `k ujc dchjitu` `k tkjsiñj sk aljvikrtk c `kaifkgils `k gc Kg tcjtl plr aikjtl x% `k ujc dchjitu` `k tkjsiñj sk aljvikrtk c `kaifkgils `k gc sihuikjtk nlrdc?

sihuikjtk nlrdc?



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(

( 

))

Rcrc lftkjkr kg vcglr x% kj `kaifkgils, sk `kfk aljvkrtir pridkrl kg vcglr x `kg Rcrc lftkjkr kg vcglr x% kj `kaifkgils, sk `kfk aljvkrtir pridkrl kg vcglr x `kg plrakjtcok c uj jÿdkrl rcailjcg ìviìéj`lgl plr 322. Rcrc aljvkrtir c `kaifkgils, sk plrakjtcok c uj jÿdkrl rcailjcg ìviìéj`lgl plr 322. Rcrc aljvkrtir c `kaifkgils, sk dugtipgiac kg glhcritdl `kg jÿdkrl rcailjcg plr 32 (dchjitu` `k pltkjaic).

dugtipgiac kg glhcritdl `kg jÿdkrl rcailjcg plr 32 (dchjitu` `k pltkjaic).

Kokdpgl? Csudikj`l quk gc pltkjaic `k scgi`c `k uj airauitl `k `ls pukrtls ks ihucg cg Kokdpgl? Csudikj`l quk gc pltkjaic `k scgi`c `k uj airauitl `k `ls pukrtls ks ihucg cg 1% `k gc pltkjaic `k kjtrc`c, ¼auãg ks gc ctkjucaiñj kj `F<

1% `k gc pltkjaic `k kjtrc`c, ¼auãg ks gc ctkjucaiñj kj `F<

 

(

( 

)

)

Rcrc aljvkrtir kg vcglr kj `F c plrakjtcok? Rcrc aljvkrtir kg vcglr kj `F c plrakjtcok?

 

 

⁀⁀



Kokdpgl? Acgaugcr gc pltkjaic `k scgi`c `k uj ctkjuc`lr `k 1 `F aldl plrakjtcok `k gc Kokdpgl? Acgaugcr gc pltkjaic `k scgi`c `k uj ctkjuc`lr `k 1 `F aldl plrakjtcok `k gc tkjsiñj `k kjtrc`c.

tkjsiñj `k kjtrc`c.

 

∖

∖



Gc pltkjaic c gc scgi`c `k uj ctkjuc`lr `k 1 `F ks gc ditc` ;2% `k gc pltkjaic `k Gc pltkjaic c gc scgi`c `k uj ctkjuc`lr `k 1 `F ks gc ditc` ;2% `k gc pltkjaic `k kjtrc`c.

kjtrc`c.

Jltc? Aldl cjtkrilrdkjtk, ctkjucaiñj sihjiniac vcglrks kj `kaifkgils jkhctivls Jltc? Aldl cjtkrilrdkjtk, ctkjucaiñj sihjiniac vcglrks kj `kaifkgils jkhctivls

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



 







 



(( 

_))

Rcrc gc aljvkrsiñj c `kaifkgils sk utigizc gc sihuikjtk nñrdugc? Rcrc gc aljvkrsiñj c `kaifkgils sk utigizc gc sihuikjtk nñrdugc?

     (( 

))

Jltc? [tigizcr kg ncatlr `k 32 pcrc dchjitu`ks `k pltkjaic. Jltc? [tigizcr kg ncatlr `k 32 pcrc dchjitu`ks `k pltkjaic.

Kokdpgl? Gc pltkjaic `k scgi`c `k uj ctkjuc`lr ks 62% dkjlr quk gc pltkjaic `k Kokdpgl? Gc pltkjaic `k scgi`c `k uj ctkjuc`lr ks 62% dkjlr quk gc pltkjaic `k kjtrc`c. ¼Auãg ks gc ctkjucaiñj kj `kaifkgils<

kjtrc`c. ¼Auãg ks gc ctkjucaiñj kj `kaifkgils<

     ((



_

_{)}

)

Cg ihucg

Cg ihucg quk quk kj kg kj kg acsl `kg acsl `kg aãgaugl alj aãgaugl alj tkjsiljks, kg tkjsiljks, kg aãgaugl `kg aãgaugl `kg tcjtl plr tcjtl plr aikjtl dãs aikjtl dãs `k`k ujc acjti`c` `c aldl rksugtc`l uj vcglr kj `kaifkgils `inkrkjtk quk kg aãgaugl `kg tcjtl ujc acjti`c` `c aldl rksugtc`l uj vcglr kj `kaifkgils `inkrkjtk quk kg aãgaugl `kg tcjtl plr aikjtl dkjls.

plr aikjtl dkjls.

[tigizcaiñj `k vcglrks kj `F kj gls aãgaugls [tigizcaiñj `k vcglrks kj `F kj gls aãgaugls

Kj kstc skaaiñj sk `ksarifk añdl sudcr jivkgks `k pltkjaic y tkjsiñj kj `kaifkgils. Kj kstc skaaiñj sk `ksarifk añdl sudcr jivkgks `k pltkjaic y tkjsiñj kj `kaifkgils. Qudc `k jivkgks `k pltkjaic

Qudc `k jivkgks `k pltkjaic

¼12 `Fd + 12 `Fd 4 >2 `Fd< ¡Rlr supukstl quk jl! Qi aljvkrtidls kstls jivkgks c ¼12 `Fd + 12 `Fd 4 >2 `Fd< ¡Rlr supukstl quk jl! Qi aljvkrtidls kstls jivkgks c vcglrks gijkcgks, rksugtc lfvil quk 3 X + 3 X 4 6 X, quk slj 11 `Fd y jl >2 `Fd. Rkrl vcglrks gijkcgks, rksugtc lfvil quk 3 X + 3 X 4 6 X, quk slj 11 `Fd y jl >2 `Fd. Rkrl kstl ks vkr`c` sñgl si

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Ruk`k quk kj kstk dldkjtl surhk, gc sihuikjtk prkhujtc, ¼si gc uji`c` lrihijcgdkjtk Ruk`k quk kj kstk dldkjtl surhk, gc sihuikjtk prkhujtc, ¼si gc uji`c` lrihijcgdkjtk kstc kj `Fd, skric dãs nãaig, sudcrgc kj nlrdc ìrkatc<, si [`. rkcgizc gc lpkrcaiñj kstc kj `Fd, skric dãs nãaig, sudcrgc kj nlrdc ìrkatc<, si [`. rkcgizc gc lpkrcaiñj ìrkatc, 2 `Fd, +1 `Fd y -> `Fd, kg vcglr rksugtcjtk, sudc`l kj nlrdc gijkcg ks -1`Fd, ìrkatc, 2 `Fd, +1 `Fd y -> `Fd, kg vcglr rksugtcjtk, sudc`l kj nlrdc gijkcg ks -1`Fd, kstl ìnikrk kjlrdkdkjtk `k gc rkspukstc cjtkrilr, gl aucg ks ijalrrkatl, yc quk aldl kstl ìnikrk kjlrdkdkjtk `k gc rkspukstc cjtkrilr, gl aucg ks ijalrrkatl, yc quk aldl aldprkj`krã gcs skócgks `k pltkjaic aucj`l sk sudc su dchjitu` gijkcg, hkjkrc ujc aldprkj`krã gcs skócgks `k pltkjaic aucj`l sk sudc su dchjitu` gijkcg, hkjkrc ujc pltkjaic rksugtcjtk, kg aucg kstk rkprkskjtc ujc rknkrkjaic kj uji`c`ks `Fd, ks plr kstc pltkjaic rksugtcjtk, kg aucg kstk rkprkskjtc ujc rknkrkjaic kj uji`c`ks `Fd, ks plr kstc rczñj quk gc lpkrcaiñj sk rkcgizc pridkrl aljvirtiéj`lgcs, pcrc gukhl pcscrgcs c gc rczñj quk gc lpkrcaiñj sk rkcgizc pridkrl aljvirtiéj`lgcs, pcrc gukhl pcscrgcs c gc rknkrkjaic kj `Fd.

rknkrkjaic kj `Fd.

Rkrl aldl téajial l ijhkjikrl `kg ãrkc, aldprkj`k quk kstk ks uj acsl mipltétial. Rkrl aldl téajial l ijhkjikrl `kg ãrkc, aldprkj`k quk kstk ks uj acsl mipltétial. Dk`i`c `k skócgks akrac `kg jivkg `k rui`l

Dk`i`c `k skócgks akrac `kg jivkg `k rui`l

[jc `k gcs tcrkcs dãs aldujks ks gc `k dkìr skócgks `éfigks akracjcs cg jivkg `k [jc `k gcs tcrkcs dãs aldujks ks gc `k dkìr skócgks `éfigks akracjcs cg jivkg `k rui`l `k uj ijstrudkjtl `k dkì`c, aldl uj rkakptlr l uj cjcgizc`lr `k kspkatrl.

rui`l `k uj ijstrudkjtl `k dk`i`c, aldl uj rkakptlr l uj cjcgizc`lr `k kspkatrl.

Kg ijstrudkjtl `k dkì`c dukstrc gc sudc tltcg `kg rui`l ijmkrkjtk y gc pltkjaic `k gc Kg ijstrudkjtl `k dkì`c dukstrc gc sudc tltcg `kg rui`l ijmkrkjtk y gc pltkjaic `k gc skócg, cujquk i`kcgdkjtk sñgl `kfkräc dlstrcr gc pltkjaic VDQ `k gc skócg, quk ks gl skócg, cujquk i`kcgdkjtk sñgl `kfkräc dlstrcr gc pltkjaic VDQ `k gc skócg, quk ks gl quk jlrdcgdkjtk laurrk cg utigizcr uj dkì`lr `k pltkjaic. Kj kg acsl `k uj cjcgizc`lr quk jlrdcgdkjtk laurrk cg utigizcr uj dkì`lr `k pltkjaic. Kj kg acsl `k uj cjcgizc`lr `k kspkatrl ks jkakscril cativcr kg `ktkatlr VDQ.

`k kspkatrl ks jkakscril cativcr kg `ktkatlr VDQ.

Rridkrl sk `ktkrdijc kg jivkg `k rui`l ijmkrkjtk Rr `kg ijstrudkjtl `k dk`i`c Rridkrl sk `ktkrdijc kg jivkg `k rui`l ijmkrkjtk Rr `kg ijstrudkjtl `k dk`i`c

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Qk puk`k lfskrvcr quk sij rkcgizcr jijhujc aldpkjscaiñj, kg rui`l `kg ijstrudkjtl `k Qk puk`k lfskrvcr quk sij rkcgizcr jijhujc aldpkjscaiñj, kg rui`l `kg ijstrudkjtl `k dkì`c prlvlacrã uj krrlr `k 3.> `F, quk ks uj vcglr rkgctivcdkjtk kgkvc`l pcrc uj dkì`c prlvlacrã uj krrlr `k 3.> `F, quk ks uj vcglr rkgctivcdkjtk kgkvc`l pcrc uj ijstrudkjtl `k dkì`c `k prkaisiñj.

ijstrudkjtl `k dk`i`c `k prkaisiñj. JLPCQ?

JLPCQ?

Dcjkocr vcglrks kj `kaifkgils ks duaml dãs skjaiggl si sk dkdlrizcj ujls Dcjkocr vcglrks kj `kaifkgils ks duaml dãs skjaiggl si sk dkdlrizcj ujls aucjtls vcglrks, c pcrtir `k gls aucgks sk puk`kj lftkjkr ltrls. Qk puk`k aucjtls vcglrks, c pcrtir `k gls aucgks sk puk`kj lftkjkr ltrls. Qk puk`k sidpginiacr kg prlfgkdc rk`lj`kcj`l mcaic crrifc l mcaic cfcol cghujls `k gls sidpginiacr kg prlfgkdc rk`lj`kcj`l mcaic crrifc l mcaic cfcol cghujls `k gls rksugtc`ls pcrc quk skc dãs nãaig rkalr`cr kstcs ainrcs.

rksugtc`ls pcrc quk skc dãs nãaig rkalr`cr kstcs ainrcs.

Pl`l gl quk mcy quk mcakr ks dkdlrizcr gls vcglrks cprlxidc`ls, plr kokdpgl, Pl`l gl quk mcy quk mcakr ks dkdlrizcr gls vcglrks cprlxidc`ls, plr kokdpgl, uj ncatlr `k 6 kj pltkjaic sk alrrksplj`k alj 1 `F (kj guhcr `kg vcglr kxcatl `k uj ncatlr `k 6 kj pltkjaic sk alrrksplj`k alj 1 `F (kj guhcr `kg vcglr kxcatl `k 1.26 `F).

1.26 `F).

1 `F jl sk alrrksplj`k kxcatcdkjtk alj ujc rkgcaiñj `k pltkjaic `k 6 y > `F jl 1 `F jl sk alrrksplj`k kxcatcdkjtk alj ujc rkgcaiñj `k pltkjaic `k 6 y > `F jl sk alrrksplj`k kxcatcdkjtk alj ujc rkgcaiñj `k pltkjaic `k 0. Qij kdfcrhl, sk alrrksplj`k kxcatcdkjtk alj ujc rkgcaiñj `k pltkjaic `k 0. Qij kdfcrhl,

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Cghujcs ainrcs ÿtigks Cghujcs ainrcs ÿtigks

Gcs sihuikjtks ainrcs tcdfiéj puk`kj skr ÿtigks c gc mlrc `k rkcgizcr gls aãgaugls? Gcs sihuikjtks ainrcs tcdfiéj puk`kj skr ÿtigks c gc mlrc `k rkcgizcr gls aãgaugls? 31 `Fd sk alrrksplj`k alj [VDQ 4 3 ^ slfrk ;2 31 `Fd sk alrrksplj`k alj [VDQ 4 3 ^ slfrk ;2 ℮℮ 2 `Fd sk alrrksplj`k alj [VDQ 4 2.660 ^ slfrk ;2 2 `Fd sk alrrksplj`k alj [VDQ 4 2.660 ^ slfrk ;2 ℮℮ 328 `F (»^) sk alrrksplj`k alj 2 `Fd slfrk ;2 328 `F (»^) sk alrrksplj`k alj 2 `Fd slfrk ;2 ℮℮ 362 `F (»^) sk alrrksplj`k alj 3 ^ 362 `F (»^) sk alrrksplj`k alj 3 ^ -380 `Fd ks gc pltkjaic `k r

-380 `Fd ks gc pltkjaic `k rui`l térdial alj uj cjaml `ui`l térdial alj uj cjaml `k fcj`c `k 3 Mz c ujck fcj`c `k 3 Mz c ujc tkdpkrcturc cprlxidc`c 62 ²A (>= ²N).

tkdpkrcturc cprlxidc`c 62 ²A (>= ²N). Ltrcs dchjitu`ks `k rknkrkjaic Ltrcs dchjitu`ks `k rknkrkjaic

Mcstc cmlrc, mkdls utigizc`l aldl dchjit

Mcstc cmlrc, mkdls utigizc`l aldl dchjitu   3 dX y ;2 Ω u   3 dX y ;2 Ω ijij

kdfcrhl, mcy sistkdcs quk utigizcj rknkrkjaics `istijtcs, aldl kj tkgkvisiñj quk sk uscj kdfcrhl, mcy sistkdcs quk utigizcj rknkrkjaics `istijtcs, aldl kj tkgkvisiñj quk sk uscj

8; Ω y  ÿ   d    >22 Ω. G d  VN  8; Ω y  ÿ   d    >22 Ω. G d  VN  >2 Ω d d     d  >22 Ω   K   >2 Ω d d     d  >22 Ω   K  

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Pcfgc `k % `k pér`i`cs kj `F

Rkr`i`c Rkr`i`c

`F

`F plrakjtucgplrakjtucgRkrì`cRkrì`c Rkrì`cRkrì`c`F`F plrakjtucgplrakjtucgRkrì`cRkrì`c Rkrì`cRkrì`c`F`F plrakjtucgplrakjtucgRkrì`cRkrì`c Rkrì`cRkrì`c`F`F plrakjtucgplrakjtucgRkrì`cRkrì`c 6.2 6.2 18 18 % % 0.2 0.2 >2 >2 % % >.2 >.2 8; 8; %% 2.6 2.6 0 % 0 % 6.6 6.6 19 19 % % 0.6 0.6 >6 >6 % % 8.2 8.2 =2 =2 %% 2.0 2.0 = % = % 6.0 6.0 06 06 % % 0.0 0.0 >1 >1 % % =.2 =.2 =0 =0 %% 2.> 2.> 31 31 % % 6.> 6.> 0; 0; % % 0.> 0.> >; >; % % 9.2 9.2 =8 %=8 % 2.= 2.= 38 38 % % 6.= 6.= 08 08 % % 0.= 0.= >8 >8 % % 32.2 32.2 92 92 %% 3.2 3.2 63 63 % % 1.2 1.2 ;2 ;2 % % ;.2 ;.2 >= >= % % 62.2 62.2 99 99 %% 3.6 3.6 60 60 % % 1.6 1.6 ;6 ;6 % % ;.6 ;.6 82 82 % % 12.2 12.2 322 322 %% 3.0 3.0 68 68 % % 1.0 1.0 ;0 ;0 % % ;.0 ;.0 83 83 % % 02.2 02.2 322 322 %% 3.> 3.> 12 12 % % 1.> 1.> ;> ;> % % ;.> ;.> 81 81 %% 3.= 3.= 11 11 % % 1.= 1.= ;= ;= % % ;.= ;.= 80 80 %%

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Qlfrk gls vcglrks kj `F

Qlfrk gls vcglrks kj `F kjtrk y gc rkgcaiñj `k kjtrk y gc rkgcaiñj `k pltkjaic / Pkjsiñjpltkjaic / Pkjsiñj

Aldl sk puk`k vkr ks duaml dãs nãaig sudcr gcs uji`c`ks kj `kaifkg quk ujc Aldl sk puk`k vkr ks duaml dãs nãaig sudcr gcs uji`c`ks kj `kaifkg quk ujc dugtipgiacaiñj aldpgkoc, kokdpgl alj `F kj pltkjaic?

dugtipgiacaiñj aldpgkoc, kokdpgl alj `F kj pltkjaic? 3222 3222 4 4 6 6 x x ; ; x x 322 322 4: 4: 1 `F 1 `F + + 8 8 `F `F + + 62 62 `F `F 4 4 12 12 `F`F 4 4 32 32 x x 32 32 x x 32 32 4: 4: 32 32 `F `F + + 32 32 `F `F + + 32 32 `F `F 4 4 12 12 `F`F 4 4 32 32 x x 322 322 4: 4: 32 32 `F `F + + 62 62 `F `F 4 4 12 12 `F`F 6222 6222 4 4 6 6 x x 3222 3222 4: 4: 1 `F 1 `F + + 12 12 `F `F 4 4 11 11 `F`F Ltrc nlrdc `k rkgcailjcr? Ltrc nlrdc `k rkgcailjcr? = = `F `F 4 4 1 1 `F `F + + ;`F ;`F 4: 4: 6 6 x x 1 1 4 4 >>

(Gc hcjcjaic rkgcailjc`c pcrc = `F ks dÿgtipgl `k > (Gc hcjcjaic rkgcailjc`c pcrc = `F ks dÿgtipgl `k > cprlxidc`cdkjtk)

cprlxidc`cdkjtk) Aucj`l gcs idpk`cjaics `