Paniere Corretto Domande Aperte e A Risposta Multipla

August 6, 2022 | Author: Anonymous | Category: N/A

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Xbt Do`kldb

BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64)

Dohbltb9 Algkltb Nbllkro

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Aldahb Aldahb Cbzaola .. ......................... ........................................... ............................................. ............................................... ........................................... .............................. .........

p. :

Cbzaolb 66; ................... .......................................... ............................................. ............................................... .............................................. .................................... ...............

p. 4

Cbzaolb 66: ................... .......................................... ............................................. ............................................... .............................................. .................................... ...............

p. >

Cbzaolb 668 ................... .......................................... ............................................. ............................................... .............................................. .................................... ...............

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Cbzaolb 664 ....... ............................. ............................................... ............................................. ........................................... ............................................. ............................ ...... p. ;6 Cbzaolb 662 ....... ............................. ............................................... ............................................. ........................................... ............................................. ............................ ...... p. ;; Cbzaolb 667 ....... ............................. ............................................... ............................................. ........................................... ............................................. ............................ ...... p. ;2 Cbzaolb 66> ....... ............................. ............................................... ............................................. ........................................... ............................................. ............................ ...... p. ;7 Cbzaolb 66= ....... ............................. ............................................... ............................................. ........................................... ............................................. ............................ ...... p. ;> Cbzaolb 661 ....... ............................. ............................................... ............................................. ........................................... ............................................. ............................ ...... p. :6 Cbzaolb 6;6 ....... ............................. ............................................... ............................................. ........................................... ............................................. ............................ ...... p. :; Cbzaolb 6;; ....... ............................. ............................................... ............................................. ........................................... ............................................. ............................ ...... p. := Cbzaolb 6;: ....... ............................. ............................................... ............................................. ........................................... ............................................. ............................ ...... p. :1 Cbzaolb 6;8 ....... ............................. ............................................... ............................................. ........................................... ............................................. ............................ ...... p. 86 Cbzaolb 6;4 ....... ............................. ............................................... ............................................. ........................................... ............................................. ............................ ...... p. 8; Cbzaolb 6;2 ....... ............................. ............................................... ............................................. ........................................... ............................................. ............................ ...... p. 8: Cbzaolb 6;> ....... ............................. ............................................... ............................................. ........................................... ............................................. ............................ ...... p. 84 Cbzaolb 6;= ....... ............................. ............................................... ............................................. ........................................... ............................................. ............................ ...... p. 82 Cbzaolb 6;1 ....... ............................. ............................................... ............................................. ........................................... ............................................. ............................ ...... p. 87 Cbzaolb 6:6 ....... ............................. ............................................... ............................................. ........................................... .............................................. ............................ ..... p. 8> Cbzaolb 6:; ....... ............................. ............................................... ............................................. ........................................... .............................................. ............................ ..... p. 8= Cbzaolb 6:: ... ......................... ............................................. ............................................. ............................................... ............................................. .............................. .......... p. 81 Cbzaolb 6:8 ... ......................... ............................................. ............................................. ............................................... ............................................. .............................. .......... p. 4: Cbzaolb 6:2 ... ......................... ............................................. ............................................. ............................................... ............................................. .............................. .......... p. 48 Cbzaolb 6:7 ... ......................... ............................................. ............................................. ............................................... .............................................. .............................. ......... p. 47 Cbzaolb 6:> ... ......................... ............................................. ............................................. ............................................... .............................................. .............................. ......... p. 4> Cbzaolb 6:= ... ......................... ............................................. ............................................. ............................................... .............................................. .............................. ......... p. 4= Cbzaolb 6:1 ... ......................... ............................................. ............................................. ............................................... .............................................. .............................. ......... p. 41 Cbzaolb 686 ... ......................... ............................................. ............................................... ............................................... ............................................ .............................. ......... p. 26 Cbzaolb 68; ... ......................... ............................................. ............................................... ............................................... ............................................ .............................. ......... p. 2: Cbzaolb 68: ... ......................... ............................................. ............................................... ............................................... ............................................ .............................. ......... p. 28 Cbzaolb 688 ... ......................... ............................................. ................................................ ............................................... ........................................... .............................. ......... p. 24 Cbzaolb 684 ... ........................... ............................................. .............................................. ............................................... ........................................... .............................. ......... p. 27 Cbzaolb 682 ... ........................... ............................................. .............................................. ............................................... ........................................... .............................. ......... p. 2= Cbzaolb 687 ... ........................... ............................................. .............................................. ............................................... ........................................... .............................. ......... p. 21 Cbzaolb 68> ... ........................... ............................................. .............................................. ............................................... ........................................... .............................. ......... p. 76 Cbzaolb 68= ... ............................ ............................................. ............................................. ............................................... ........................................... .............................. ......... p. 78

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:7 - :/>8

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Cbzaolb 681 ... ......................... ............................................. ............................................. ............................................... .............................................. .............................. ......... p. 72 Cbzaolb 64; ... ......................... ............................................. ............................................. ............................................... .............................................. .............................. ......... p. 77 Cbzaolb 64: ... ......................... ............................................. ............................................. ............................................... .............................................. .............................. ......... p. 7> Cbzaolb 648 ... ......................... ............................................. ............................................. ............................................... .............................................. .............................. ......... p. 7= Cbzaolb 644 ... ......................... ............................................. ............................................... ............................................... ............................................ .............................. ......... p. 71 Cbzaolb 642 ... ......................... ............................................. ............................................... ............................................... ............................................ .............................. ......... p. >6 Cbzaolb 647 ... ......................... ............................................. ............................................... ............................................... ............................................ .............................. ......... p. >:

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:7 - 8/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 66; 6;. AC WKCOZB DBCCK ZBXAXTBLYK B‑ hostkltb b sa daggbrblzak soco pbr ck tapoconak da `ktbrakcb B‑ alvbrsk`bltb proporzaolkcb kcck sbzaolb dbc `ktbrakcb, kcck rbsastavatæ b darbttk`bltb proporzaolkcb kcck culnmbzzk B‑ darbttk`bltb proporzaolkcb kcck rbsastavatæ dbc `ktbrakcb, darbttk`bltb proporzaolkcb kcck culnmbzzk, b alvbrsk`bltb proporzao proporzaolkcb lkcb kcck sbzaolb B‑ vkrakjacb soco hol ck sbzaolb dbc `ktbrakcb hol hua í hostatuatk 6:. CK ZBXAXTBLYK XA @AXRZK AL OM@ ^KTT K@VBZB WOCT 68. CK DAGGBZBLYK DA VOTBLYAKCB TZK A VRLTA K B J LOL DAVBLDB DKC CKWOZO HO@VATRTO VBZ XVOXTKZB RLK HKZAHK DK K AL J DAVBLDB DKC VBZHOZXO XBNRATO DAVBLDB DKC CKWOZO HO@VARTO VBZ XVOXTKZB RLK HKZAHK DK K AL J XB K B J HOALHADOLO TKCB WKCOZB B' @KXXA@O 64. RL VOTBLYAO@BTZO B' RLK KVVKZBHHMAKTRZK AL NZKDO DA NBLBZKZB VOTBLYK BCBTTZAHK B' RL ZBXAXTOZB HOL ZBXAXTBLYK HOXTKLTB B' RL ZBXAXTOZB HOL ZBXAXTBLYK WKZAKJACB B' RL'KVVKZBHHMAKTRZK BCBTTZAHK AL NZKDO DA @KLTBLBZB HOXTKLTB CK ZBXAXTBLYK KC WKZAKZB DBCCK TB@VBZKTRZK 62. CK ZBXAXTAWATK' DA RL @KTBZAKCB B' DAZBTTK@BLTB VZOVOZYAOLKCB KCCK TB@VBZKTRZK WKZAK HOL CK TB@VBZKTRZK B' ALWBZXK@BLTB VZOVOZYAOLKCB KCCK TB@VBZKTRZK B' ALDAVBLDBLTB DKCCK TB@VBZKTRZK 67. CK HKZAHK BCBTTZAHK B' ALDAVBLDBLTB DKCCK HOZZBLTB B' ALWBZXK@BLTB VZOVOZYAOLKCB KCCK HOZZBLTB HMB KTTZKWBZXK CK XRVBZGAHAB X B' C'ALTBNZKCB DBCCK HOZZBLTB LBC TB@VO B' CK DBZAWKTK DBCCK HOZZBLTB LBC TB@VO 6>. ; WOCT 0 HOZZBLTB LBCCK XRVBZGAHAB RLATKZAK TBLXAOLB TZK DRB VRLTA VOXTA KD RL @BTZO DA DAXTKLYK ; HORCO@J/; IORCB ; IORCB/ ; HORCO@J

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:7 - 4/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

6=. CK DAGGBZBLYK DA VOTBLYAKCB TZK DRB VRLTA DAVBLDB DKC VBZHOZXO XBNRATO B' ALDAVBLDBLTB DKC VBZHOZXO XBNRATO AL KCHRLA HKXA DAVBLDB DKC VBZHOZXO XBNRATO WKCB XB@VZB YBZO 61. CK TBLXAOLB XA @AXRZK AL WOCT W*K K@VBZB OM@ ;6. CK HOZZBLTB BCBTTZAHK B' ALWBZXK@BLTB VZOVOZYAOLKCB KCCK HKZAHK HMB KTTZKWBZXK CK XRVBZGAHAB X B' CK DBZAWKTK DBCCK HKZAHK ZAXVBTTO KC TB@VO B' C'ALTBNZKCB DBCCK HKZAHK ZAXVBTTO KC TB@VO B' ALDAVBLDBLTB DKCCK HKZAHK

;;. RL KTO@O DA ZK@B HOLTABLB 4 BCBTTZOLA = BCBTTZOLA :1 BCBTTZOLA :7 BCBTTZOLA ;:. CK HOZZBLTB XA @AXRZK AL OM@ K@VBZB ^KTT WOCT ;8. CK GOZYK DA HORCO@J XA ZAGBZAXHB K9 CK GOZYK HOL HRA CB HKZAHMB BCBTTZAHMB ALTBZKNAXHOLO CK GOZYK HOL HRA HKZAHMB DA XBNLO OVVOXTO XA ZBXVALNOLO RL KTO@O BCBTTZAHK@BLTB LBRTZO CK GOZYK HOL HRA HKZAHMB DBCCO XTBXXO XBNLO XA KTTZKNNOLO ;4. AL RL KTO@O AC LR@BZO DBNCA BCBTTZOLA B' VKZA K [RKTTZO AC LR@BZO DBNCA BCBTTZOLA B' RNRKCB KC LR@BZO DA VZOTOLA XO@@KTO KC LR@BZO DBA LBRTZOLA AC LR@BZO DBNCA BCBTTZOLA B' RNRKCB KC LR@BZO DBA LBRTZOLA AC LR@BZO DBNCA BCBTTZOLA B' RNRKCB KC LR@BZO DBA VZOTOLA

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:7 - 2/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

;2. CK ZBXAXTAWATÆ DA RL @KTBZAKCB DAVBLDB Dkcck sbzaolb dbc `ktbrakcb Dkcck culnmbzzk dbc `ktbrakcb Dkcck tb`pbrkturk b dkcck ho`posazaolb hmaàhk. Dkcck tb`pbrkturk kc qukdrkto b dkcck ho`posazaolb hmaàhk dbc `ktbrakcb ;7. AC WKCOZB DBCCK ZBXAXTBLYK B' vkrakjacb soco hol ck sbzaolb dbc `ktbrakcb hol hua í hostatuatk. B' darbttk`bltb proporzaolkcb kcck rbsastavatæ dbc `ktbrakcb, darbttk`bltb darbttk`bltb proporzaolkcb kcck culnmbzzk, b alvbrsk`blt alvbrsk`bltbb proporzaolkcb kcck sbzaolb B' alvbrsk`bltb proporzaolkcb kcck sbzaolb dbc `ktbrakcb, kcck rbsastavatæ b darbttk`bltb proporzaolkcb kcck culnmbzzk culnmbzzk B' hostkltb b sa daggbrblzak soco pbr ck tapoconak da `ktbrakcb. `ktbrakcb. ;>. Tblsaolb bcbttrahk

Xb holsadbrakò ulk rbnaolb da spkzao al hua í prbsbltb ul hk`po bcbttraho B, b spostakò ulk hkrahk bcbttrahk q6 (posatavk) dkc pulto K kc pulto J, àsurkldo ac ckvoro ^KJ hmb jasonlk ho`pabrb holtro cb gorzb dbc hk`po possakò dbgalarb ck daggbrblzk da potblzakcb o tblsaolb trk a pulta K b J ho`b sbnub9 WK-WJ0^KJ/q66 ;voct 0 ; ioucb/; houco`j WK-WJ0^KJ/q Ac ckvoro ^KJ puú bssbrb posatavo, al tkc hkso ac potblzakcb dbc pulto J skræ `knnaorb da qubcco dbc pulto K5 lbnktavo al tkc hkso ac potblzakcb dbc pulto J skræ àlorb da qubcco dbc pulto K5 lucco al tkc hkso ac potblzakcb dbc pulto J skræ unukcb k qubcco dbc pulto K.

Xb a``knalakò da shbncabrb ac pulto K k dastklzk algalatk b nca kssbnlakò ul potblzakcb pkra k zbro possakò dbgalarb ac potblzakcb al ul pulto nblbraho ho`b W0^/q6 Al tkcb bsprbssaolb ^ í ac ckvoro hmb ul knbltb bstbrlo dbvb ho`pabrb succk hkrahk q6 pbr spostkrck dkcc‑algalato kc pulto al qubstaolb.

lba harhuata bcbttraha qukldo sa mk ul nblbrktorb da g.b.`. hoccbnkto kd ul harhuato sa hrbk ck horrbltb haoí ul òto da bcbttrola dovuto kcck daggbrblzk da potblzakcb bcbttraho trk a dub òrsbtta dbc nblbrktorb. Vossakò pbrtklto darb hmb ck tblsaolb í ck hkusk dbcck horrbltb. Dk ul pulto da vastk opbrktavo pbr hkchockrb ck daggbrblzk da potblzakcb bcbttraho WKJ trk ac pulto K bd ac pulto J jasonlk bsbnuarb ck sbnubltb daggbrblzk

;=. Horrbltb bcbttrahk

Xa mk ulk horrbltb bcbttrahk qukldo cb hkrahmb sa ùovolo al `klabrk ordalktk kcc‑altbrlo da ul holduttorb sotto c‑kzaolb da ul hk`po bcbttraho bstbrlo prodotto dk sornblta ho`b, kd bsb`pao, ulk pack. [ukldo h‑í ulk horrbltb bcbttrahk kc òto dasordalkto dbnca bcbttrola cajbra, (dovuto kcc‑knatkzaolb tbràhk, sa sovrkppolb ul òto da alsab`b kvbltb vbcohatæ `bdak davbrsk dk zbro al ulk dktk darbzaolb. Xb holsadbrakò ulk supbrgahab nblbrahk X, ul altbrvkcco da tb`po T (hmb alazak kcc‑astkltb t b tbràlk kcc‑astkltb t+∇T), dbgalakò ck hkrahk bcbttrahk lbttk hmb kttrkvbrsk ck supbrgahab X lbcc‑altbrvkcco (t, t +∇T) ho`b ck so``k, qX (t5t+∇T) 0 Ψ(»)qa Ac rkpporto AX(t5t+∇T)0qX(t5t+∇T)/ ∇T dbgalashb c‑altblsatæ `bdak dbcck horrbltb bcbttrahk hmb kttrkvbrsk ck supbrgahab X lbcc‑altbrvkcco (t,t+∇T). Xb altroduhakò qukltatæ [Xkvrbò (t) dbgalatk ho`b ck hkrahk bcbttrahk lbttk hmb kttrkvbrsk ck supbrgahab X lbcc‑altbrvkcco da ck tb`po (6, dt) aX (t) 0 d[X /dt. Vossakò kggbr`krb hmb c‑altblsatæ dbcck horrbltb bcbttrahk hmb kttrkvbrsk ck supbrgahab X kc nblbraho astkltb t í unukcb kcck dbravktk pra`k raspbtto kc tb`po dbcck hkrahk bcbttrahk lbttk hmb kttrkvbrsk ck supbrgahab X lbcc‑altbrvkcco (6,dt). C‑ulatæ da àsurk dbcck horrbltb A í c‑k`pbrb, UAP0 K, ;K0;H/;sbh5 © :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:7 - 7/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

;1. Zbsastblzk bcbttrahk

Ck rbsastblzk bcbttrahk í ul pkrk`btro hmb aldahk quklto ul dkto ho`polbltb harhuatkcb harhuatkcb sa oppolb kc pkssknnao dbcck horrbltb5 quklto `knnaorb í ac vkcorb dbcck rbsastblzk tklto pa ñ c‑bcb`blto sa oppolb kc pkssknnao dbcck horrbltb. Ck rbsastblzk dapbldb dkccb da`blsaola gasahmb dbc ho`polbltb (culnmbzzk b sbzaolb), dkcck strutturk ktoàhk dbc `ktbrakcb b dkcck tb`pbrkturk (rbsastavatæ). Ck rbckzaolb hmb holsbltb da hkchockrb ck rbsastblzk í ck sbnubltb9 . c / s (*)æ bcbttrahk U℧ x `P (í gulzaolb dbcck tb`pbrkturk) ϋZ0 0 ϋrbsastavat c 0 culnmbzzk holduttorb U`P s 0 sbzaolb holduttorb U`:P Lbc XA c‑ulatæ da àsurk dbcck rbsastblzk Z í c‑om` (℧), (UZP0 ℧). Rl‑kctrk hckssagahkzaolb utacb pbr cb rbsastblzb í qubcck hmb cb vuocb davasb al dub hckssa9 rbsastora k vkcorb gasso. Vbr rbsastora da pahhock potblzk ac vkcorb dbcck rbsastblzk (b dbcck toccbrklzk) solo aldavadukjaca trkàtb jkldb hocorktb ck hua horraspoldblzk h orraspoldblzk hol a vkcora í tkjbccktk. rbsastora b vkcorb vkrakjacb (al nbrno potblzao`btra). K coro voctk possolo bssbrb dastalta al rbsastora k holtktto rotkltb, rbsastora k holtktto strashakltb

© :6;7 :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus Dktk Xtk`pk 62/;6/:6;> ::9689:7 >/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 66: 6;. HMB HOXK XA ALTBLDB VBZ @KNCAK Rl pbrhorso hmauso hmb holtablb ul alsab`b da rbsastblzb hollbssb trk da coro Rl pbrhorso hmauso hol soca nblbrktora da tblsaolb b horrbltb Rl pbrhorso hmauso hol rbsastblzb hkpkhatæ b alduttklzb Rl pbrhorso hmauso hmb holtablb ul alsab`b da bcb`blta harhuatkca hollb hollbssa ssa trk da coro 6:. HMB HOXK XA ALTBLDB VBZ [RKDZAVOCO Dub japoca rbsastava hol ul bstrbò al hoùlb Rl ho`polbltb k qukttro òrsbtta da hua ul hoppak hostatuashb ck portk da alnrbsso b ulk hoppak hostatuashb ck portk da ushatk. Dub japoca hoccbnkta al òdo dk gor`krb ulk `kncak hmausk Dub japoca hkpkhatava hol lbssulo bstrbò al hoùlb. 68. Holvblzaolb dba nblbrktora

Al bcbttrotbhlahk ck holvblzaolb lor`kcb í ulk hoppak da hratbra uskta pbr gasskrb a ragbra`blta posatava da tblsaolb b horrbltb sua japoca. [ubsto dbtbràlk a sbnla dbccb vkrab nrkldbzzb hmb ca altbrbssklo. Gasskrb a ragbra`blta da tblsaolb b horrbltb í galkcazzkto kcck rbkcazzkzaolb da ul òdbcco dbc harhuato al hua tuttb cb nrkldbzzb saklo hobrblta raspbtto kc ragbra`blto kdottkto, í qualda a`portkltb rahordkrb hmb k prbshaldbrb dkc hratbrao utacazzkto a dub òdbcca skrbjjbro hoùlqub bquavkcblta lbc dbshravbrb co stbsso harhuato. holvbzaolb suadkc nblbrktora stkjacashb hmb CkCkhorrbltb bshb òrsbtto holtrkssbnlkto hol ac sbnlo + dbcck tblsaolb (òrsbtto K) bd bltrk lbc òrsbtto holtrkssbnlkto hoc sbnlo ‘ dbcck tblsaolb (òrsbtto J).

64. Holvblzaolb dbnca utacazzktora

Al bcbttrotbhlahk ck holvblzaolb lor`kcb í ulk hoppak da hratbra uskta pbr gasskrb a ragbra`blta posatava da tblsaolb b horrbltb sua japoca. [ubsto dbtbràlk a sbnla dbccb vkrab nrkldbzzb hmb ca altbrbssklo. Gasskrb a ragbra`blta da tblsaolb tblsa olb b horrbltb í galkcazzkto kcck rbkcazzkzaolb da ul òdbcco dbc harhuato al hua tuttb cb nrkldbzzb saklo hobrblta raspbtto kc ragbra`blto kdottkto, í qualda a`portkltb rahordkrb hmb k prbshaldbrb dkc hratbrao utacazzkto a dub òdbcca skrbjjbro hoùlqub bquavkcblta lbc dbshravbrb co stbsso harhuato.

Ck horrbltb bltrk dkc òrsbtto holtrkssbnlkto hol ac sbnlo dbcck tblsaolb + (òrsbtto K) b ckshak ac japoco dkc òrsbtto holtrkssbnlkto hoc sbnlo ‘ dbcck tblsaolb (òrsbtto J)

© :6;7 :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus Dktk Xtk`pk 62/;6/:6;> ::9689:7 =/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 668 6;. ZBXAXTOZA CALBKZA TB@VO WKZAKLTA CK XRK HKZKTTBZAXTAHK B' RLK [RKCXAKXA ZBTTK CK XRK HKZKTTBZAXTAHK B' RLK ZBTTK VKXXKLTB VBZ C'OZANALB HMB MK RLK VBLDBLYK HMB WKZAK LBC TB@VO CK XRK HKZKTTBZAXTAHK B' RLK ZBTTK VKXXKLTB VBZ C'OZANALB HMB MK RLK VBLDBLYK HMB WKZAK LBC TB@VO CK XRK HKZKTTBZAXTAHK B' RLK ZBTTK LOL VKXXKLTB VBZ C'OZANALB HMB LOL WKZAK LBC TB@VO 6:. DAODO ADBKCB CK XRK ZBXAXTBLYK B' XB@VZB @KNNAOZB DA YBZO B' RL HO@VOLBLTB LOL CALBKZB B' RL HO@VOLBLTB CALBKZB XA HO@VOZTK XB@VZB HO@B RL HOZTO HAZHRATO 68. DAODO ADBKCB XA HO@VOZTK XB@VZB HO@B RL HAZHRATO KVBZTO AC XRO HO@VOZTK@BLTO LOL DAVBLDB DK HO@B B' VOCKZAYYKTO XA HO@VOZTK XB@VZB HO@B RL HOZTO HAZHRATO AC XRO HO@VOZTK@BLTO DAVBLDB DK HO@B B' VOCKZAYYKTO 64. DAODO ZBKCB AC XRO HO@VOZTK@BLTO DAVBLDB DKCCK TB@VBZKTRZK AL HRA OVBZK AC XRO HO@VOZTK@BLTO LOL DAVBLDB DKCCK TB@VBZKTRZK AL HRA OVBZK XA HO@VOZTK XB@VZB HO@B RL HOZTO HAZHRATO XA HO@VOZTK XB@VZB HO@B RL HAZHRATO KVBZTO 62. NBLBZKTOZB DA TBLXAOLB ALDAVBLDBLTB CK XRK HKZKTTBZAXTAHK B' RLK ZBTTK CK XRK HKZKTTBZAXTAHK B' RLK XVBYYKTK VKXXKLTB VBZ C'OZANALB CK XRK HKZKTTBZAXTAHK LOL B' RLK ZBTTK LOL BXAXTOLO 67. JAVOCO HOZTO HAZHRATO LOL B' VOXXAJACB ZBKCAYYKZCO VZKTAHK@BLTB CK TBLXAOLB KA XROA @OZXBTTA VRO' KXXR@BZB [RKCXAKXA WKCOZB CK TBLXAOLB KA XROA @OZXBTTA WKCB ALGALATO CK TBLXAOLB KA XROA @OZXBTTA WKCB YBZO 6>. JAVOCO HOZTO HAZHRATO CK XRK ZBXAXTBLYK WKCB ALGALATO CK XRK ZBXAXTBLYK WKCB YBZO CK XRK ZBXAXTBLYK VRO' KXXR@BZB [RKCXAKXA WKCOZB CK XRK ZBXAXTBLYK KXXR@B WKCOZB HOXTKLTB B VOXAXTAWO

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:7 - 1/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

6=. ZBXAXTOZA CALBKZA TB@VO ALWKZAKL ALWKZAKLTA TA CK XRK HKZKTTBZAXTAHK B' RLK ZBTTK LOL VKXXKLTB VBZ C'OZANALB HMB LOL WKZAK LBC TB@VO CK XRK HKZKTTBZAXTAHK B' RLK [RKCXAKXA ZBTTK CK XRK HKZKTTBZAXTAHK B' RLK ZBTTK VKXXKLTB VBZ C'OZANALB HMB LOL WKZAK LBC TB@VO CK XRK HKZKTTBZAXTAHK B' RLK ZBTTK VKXXKLTB VBZ C'OZANALB HMB WKZAK LBC TB@VO 61. AC WKCOZB DBCCK HOLDRTTKLYK B' aldapbldbltb dkc vkcorb dbcck rbsastblzk. B' darbttk`bltb proporzaolkcb kc vkcorb dbcck rbsastblzk B' ac rbhaproho dbc vkcorb dbcck rbsastblzk B' c'opposto dbc vkcorb dbcck rbsastblzk ;6. ZBXAXTOZA CALBKZA TB@VO ALWKZAKLTA XOLO HO@VOLBLTA K DRB @OZXBTTA XOLO HO@VOLBLTA K [RKTTZO @OZXBTTA XOLO HO@VOLBLTA K TZB @OZXBTTA XOLO HO@VOLBLTA KD L @OZXBTTA

;;. HOXK XA ALTBLDB VBZ JAVOCO HAZHRATO KVBZTO Rl japoco hol rbsastblzk algalatk Rl japoco hol rbsastblzk galatk `k àlorb da ;666 om`. Rl japoco hol rbsastblzk lucck Rl japoco hol rbsastblzk galatk `k `knnaorb da ;666 om` ;:. HMB HOXK XA ALTBLDB VBZ JAVOCO LOL CALBKZB Rl japoco ck hua hkrkttbrastahk tblsaolb tblsaolb-horrbltb -horrbltb í bspraàjacb soco sotto gor`k da bspolblzakcb Rl japoco al hua ck hkrkttbrastahk tblsaolb-h tblsaolb-horrbltb orrbltb lol í ulk rbttk Rl japoco ck hua hkrkttbrastahk tblsaolb tblsaolb-horrbltb -horrbltb í ulk rbttk Rl japoco al hua ck hkrkttbrastahk tblsaolb-h tblsaolb-horrbltb orrbltb lol í bspraàjacb sotto gor`k da gulzaolb ;8. JAVOCO HAZHRATO KVBZTO CK XRK ZBXAXTBLYK VRO' KXXR@BZB [RKCXAKXA WKCOZB CK XRK ZBXAXTBLYK WKCB ALGALATO CK XRK ZBXAXTBLYK KXXR@B WKCOZB HOXTKLTB B VOXAXTAWO CK XRK ZBXAXTBLYK WKCB YBZO

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Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

;4. Japoco horto harhuato b japoco harhuato kpbrto

Japoco Horto harhuato, ck suk rbsastblzk vkcb Z06, ck tblsaolb ka suoa òrsbtta vkcb hostkltb`bltb zbro, ck horrbltb hmb co kttrkvbrsk puú kssu`brb tutta a vkcora possajaca al dapbldblzk dbc harhuato k hua bsso í hoccbnkto. Zaportakò da sbnuato ck suk hkrkttbrastahk horrbltb-tblsaolb.

Japoco Harhuato kpbrto, ck suk rbsastblzk vkcb Z0∜, ck tblsaolb ka suoa òrsbtta puú kssu`brb qukcsaksa vkcorb, ck horrbltb hmb co kttrkvbrsk vkcb A06. Zaportakò da sbnuato ck suk hkrkttbrastahk tblsaolb-horrbltb.

;2. Nblbrktorb da tblsaolb

Vbr ck trkttkzaolb dbcc‑krno`blto suppolbldo hmb ac nblbrktorb da tblsaolb sak adbkcb, b aldapbldbltb possakò kggbr`krb hmb bsso Í ul japoco hmb mk ck hkrkttbrastahk tblsaolb horrbltb rkpprbsbltkjacb trkàtb

ulk rbttk. Mk ck pbhucakratæ da `kltblbrb ka suoa òrsbtta ck tblsaolb v(t)0W*(t) hostkltb5 c‑altblsatæ da horrbltb a(t) puú kssu`brb tutta a vkcora possajaca. Bsso í tb`po-alvkrakltb sb ck v(t) í hostkltb, sb v(t) vkrak í tb`po-vkrakltb. Zaportakò ac sa`joco rkpprbsbltktavo b ck hkrkttbrastahk tblsaolb-horrbltb.

Ac japoco dbshratto lbcck rbkctæ lol bsastb, tuttkvak ha solo kchula dasposatava hmb kpprossa`klo ac suo ho`portk`blto5 qubsta dasposatava solo hmak`kta hoùlb`bltb jkttbrab. Lbc hkso al hua v*(t) í adbltahk`bltb lucck bsso sa ho`portk ho`b ul horto harhuato b ck suk hkrkttbrastahk hoalhadb hol c ‑kssb dbccb kshassb.

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:7 -

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro ;7. Daodo rbkcb

A daoda rbkca solo hostatuata dk ulk naulzaolb pl trk dub `ktbrakca sbàholduttora dronkta hol a`puratæ da davbrsk lkturk. Ac ho`portk`blto dbc daodo rbkcb, b qualda ck hkrkttbrastahk tblsaolb horrbltb da sbnuato raportktk, dapbldolo dkcck tb`pbrkturk kcck qukcb ac ho`polbltb opbrk. Xb a``knalakò da gkr ckvorkrb ul daodo al holdazaola da tb`pbrkturk vkrakjacb ottbrrbò ul ho`polbltb lol calbkrb b tb`po vkrakltb. .

;>. Daodo adbkcb

ac daodo adbkcb. B‑ ul japoco lol calbkrb al quklto ck suk hkrkttbrastahk tblsaolb-horrbltb lol í ulk rbttk `k ulk spbzzktk. Ac suo ho`portk`blto í ac sbnubltb9 qukldo ck tblsaolb ka suoa òrsbtta í lbnktavk (pockrazzkto alvbrsk`bltb) sa ho`portk ho`b ul harhuato kpbrto (OGG)5 qukldo ck tblsaolb ka suoa òrsbtta í posatavk (pockrazzkto darbttk`bltb) sa ho`portk ho`b ul horto harhuato (OL). Mk, al dapbldblzk dbc sbnlo dbcck tblsaolb kppcahktk ka suoa òrsbtta, ac ho`portk`blto dk altbrruttorb lbccb posazaola OL/OGG. Zaportakò da sbnuato ac sa`joco b ck suk hkrkttbrastahk tblsaolb-horrbltb. Ac tbràlkcb posatavo í dbtto klodo, ac tbràlkcb lbnktavo í dbtto hktodo

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:7 -

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 664 6;. CK HKVKHATK' XA @AXRZK AL OM@ XBHOLDA GKZKD MBLZQ 6:. RL NBLBZKTOZB B' HOLTZOCCKTO [RKLDO. Ac vkcorb dbc nblbrktorb dapbldb soco dkc vkcorb da ulk tblsaolb nblbrktk. Ac vkcorb dbc nblbrktorb hk`jak kc hk`jakrb da ulk tblsaolb nblbrktk dk ul kctro nblbrktorb. Ac vkcorb dbc nblbrktorb dapbldb dk ul'kctrk tblsaolb o horrbltb prbsbltb lbc harhuato b vkrak proporzaolkc`bltb kd bssk. Ac vkcorb dbc nblbrktorb dapbldb soco dkc vkcorb da ulk horrbltb nblbrktk 68. [RKC'B' CK ZBCKYAOLB TZK TBLXAOLB B HOZZBLTB KA HKVA DA RLK ALDRTTKLYK Al ulk alduttklzk, ck vkrakzaolb dbcck tblsaolb í alvbrsk`bltb proporzaolkcb proporzaolkcb kc vkcorb dbcck horrbltb b kcc'alduttklzk kcc'alduttklzk.. Al ulk alduttklzk ck vkrakzaolb dbcck horrbltb í darbttk`bltb proporzaolkcb proporzaolkcb kcck tblsaolb b alvbrsk`bltb proporzao proporzaolkcb lkcb kc vkcorb dbcc'alduttklzk stbssk. Al ulk alduttklzk ck vkrakzaolb dbcck horrbltb í darbttk`bltb proporzaolkcb proporzaolkcb kcck tblsaolb. Al ulk alduttklzk, ck vkrakzaolb dbcck tblsaolb í darbttk`bltb proporzaolkcb proporzaolkcb kc vkcorb dbcck horrbltb b kcc'alduttklz kcc'alduttklzk. k. 64. C'ALDRTTKLYK XA @AXRZK AL OM@ MBLZQ GKZKD XBHOLDA 62. HOXK XA ALTBLDB VBZ NBLBZKTOZB NBLBZKTOZB ALDAVBLDBLTB DA HOZZBLTB O DA TBLXAOLB Rl nblbrktorb ac hua vkcorb da horrbltb o da tblsaolb lol dapbldb dkcck tb`pbrktur tb`pbrkturkk Rl nblbrktorb ac hua vkcorb da horrbltb o da tblsaolb sol grk da coro aldapbldblta. aldapbldblta. Rl nblbrktorb ac hua vkcorb da horrbltb o da tblsaolb lol dapbldb dkc tb`po t. Rl nblbrktorb al hua ac vkcorb dbcck horrbltb o dbcck tblsaolb lol dapbldb dk lbssul'kctrk nrkldbzzk nrkldbzzk bcbttrahk dbc harhuato. 67. [RKC'B' CK ZBCKYAOLB TZK TBLXAOLB B HOZZBLTB KA HKVA DA RL HOLDBLXKTOZB Al ul holdblsktorb, ck vkrakzaolb dbcck tblsaolb ka hkpa dbccb dub kr`kturb, í darbttk`bltb proporzaolkcb kcck horrbltb. Al ul holdblsktorb holdblsktorb,, ck vkrakzaolb dbcck horrbltb í darbttk`bltb proporzaolkcb proporzaolkcb kcck tblsaolb Al ul holdblsktorb, ck vkrakzaolb dbcck tblsaolb ka hkpa dbccb dub kr`kturb, í darbttk`bltb proporzaolkcb kcck horrbltb b alvbrsk`bltb proporzaolkcb kc vkcorb dbcck hkpkhatæ stbssk. Al ul holdblsktorb holdblsktorb,, ck vkrakzaolb dbcck horrbltb b alvbrsk`bltb proporzao proporzaolkcb lkcb kcck tblsaolb.

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Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 664 6>. Nblbrktora holtrocckta

Dbgalazaolb9 ac nblbrktorb holtrocckto í ul nblbrktorb ck hua tblsaolb o horrbltb lol í dbtbràlktk dk ulk gulzaolb a`prbssk dkcc‑utbltb (ho`b lba nblbrktora aldapbldblta), `k dapbldb dk ulk nrkldbzzk (horrbltb o tblsaolb) prbsbltb al ulk pkrtb qukcsaksa dbc harhuato. Tapa k) Nblbrktorb da tblsaolb pacotkto al horrbltb Lo`b alncbsb9 HHWX - Hurrblt Holtroccbd Woctknb Xourhb Bqukzaolb9 W 0 r * a; W 0 tblsaolb prodottk dkc nblbrktorb r0 hobggahabltb da proporzaolkcatæ. Mk cb da`blsaola da ulk rbsastblzk, b í hmak`kto trkls-rbsastblzk a; 0 horrbltb pacotkltb j) Nblbrktorb da tblsaolb pacotkto al tblsaolb Lo`b alncbsb9 WHWX - Woctknb Holtroccbd Woctknb Xourhb Bqukzaolb9 W 0 λ* W; W 0 tblsaolb prodottk dkc nblbrktorb λ0 hobggahabltb da proporzaolkcatæ. Cbnk dub tblsaola, qualda í kda`blsaolkcb W; 0 tblsaolb pacotkltb h) Nblbrktorb da horrbltb pacotkto al horrbltb Lo`b alncbsb9 HHHX - Hurrblt Holtroccbd Hurrblt Xourhb Bqukzaolb9 A 0 κ * A; A 0 horrbltb prodottk dkc nblbrktorb κ 0 hobggahabltb da proporzaolkcatæ. Cbnk dub horrblta, qualda í kda`blsaolkcb A; 0 tblsaolb pacotkltb d) Nblbrktorb da horrbltb pacotkto al tblsaolb Lo`b alncbsb9 WHHX - Woctknb Holtroccbd Hurrblt Xourhb Bqukzaolb9 A 0 n * W; A 0 horrbltb prodottk dkc nblbrktorb n0 hobggahabltb da proporzaolkcatæ. Mk cb da`blsaola da ulk holduttklzk, b í hmak`kto trklsholduttklzk. W; 0 tblsaolb pacotkltb

6=. Alduttorb

Nca alduttora solo japoca al hua al onla astkltb da tb`po ac gcusso `knlbtaho holhktblkto Χ(t) b ck horrbltb a(t) hmb co kttrkvbrsk soddasgklo ulk rbckzaolb rkpprbsbltkjacb lbc paklo (Χ,a). Ac sa`joco dbcc‑alduttorb í raportkto al ganurk, ck nrkldbzzk hmb hkrkttbrazzk c‑alduttorb á c‑alduttklzk C ck hua ulatæ da àsurk í c‑Mblry (M), (UCP0M).

Xb ck hkrkttbrastahk lbc paklo (Χ,a) í ulk rbttk pksskltb pbr c‑oranalb bsso í calbkrb, kctra`blta í lol calbkrb5 sb ck hkrkttbrastahk lol hk`jak lbc tb`po í tb`po-alvkrakltb kctra`blta í tb`po vkrakltb. ALDRTTOZB CALBKZB TB@VO ALWKZAKLTB C‑alduttklzk C lol dapbldb dk t b dk a

Xb altbnrakò su ul altbrvkcco da tb`po (6-t) ottblakò

Al onla astkltb da tb`po ck horrbltb hmb kttrkvbrsk c‑alduttorb í dktk dkcck so``k da dub tbràla, ck horrbltb kcc‑astkltb alazakcb b ck horrbltb kcc‑astkltb t da ul alduttorb kvbltb alduttklzk C hmb k t06 mk ulk horrbltb lucck. ALDRTTOZB CALBKZB TB@VO-WKZAKLTB C‑alduttklzk C dapbldb dkc tb`po, ck hkrkttbrastahk í ulk rbttk hmb pkssk pbr c‑oranalb dbc paklo (Χ,a) `k mk ulk pbldblzk hmb vkrak lbc tb`po. ALDRTTOZB LOL CALBKZB C‑alduttorb lol calbkrb í ul alduttorb hmb mk lbc paklo ( Χ,a) mk ulk hkrkttbrastahk lol calbkrb (o hmb lol pkssk pbr c‑oranalb).

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:> - ;;/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 664

61. Holdblsktorb

A holdblsktora solo ho`polblta al nrkdo da a``knkzzalkrb hkrahk bcbttrahk succb kr`kturb. Rl holdblsktorb òcto dagguso hmb puú rkpprbsbltkrb ul holdblsktorb calbkrb tb`po alvkrakltb potrbjjb bssbrb qubcco kd kr`kturb paklb b pkrkccbcb. Vossakò holsadbrkrco hostatuato dk dub supbrgaha holduttraha dbttb kr`kturb, grk cb qukca í altbrposto ul `bzzo asockltb, dbtto dabcbttraho. Ck hkpkhatæ dapbldb al `klabrk darbttk`bltb proporzaolkcb dkcck hkrahk [, b al `klabrk alvbrsk`bltb proporzaolkcb dkcck tblsaolb kppcahktk kccb kr`kturb. Vossakò darb hmb ck hkpkhatæ í ck hkrkttbrastahk hmb mk ac holdblsktorb kd khhuùckrb ulk hbrtk hkrahk bcbttrahk. Lbc hkso da kr`kturb paklb b pkrkccbcb lbc vuoto sa mk9 H 0 [/W   Ossak, ck hkpkhatæ í unukcb kc prodotto trk ck hostkltb dabcbttrahk da haú hmb va í trk cb dub kr`kturb, pbr c‑krbk dbcck supbrgahab kggkhhaktk, haoí dbcck supbrgahab kttavk da bssb, davaso ck dastklzk trk cb stbssb kr`kturb. Wk aloctrb rahordkto hmb ck hostkltb dabcbttrahk kssocutk í dktk dkc prodotto dbcck hostkltb dabcbttrahk dbc vuoto pbr ck hostkltb dabcbttrahk proprak dbc `ktbrakcb. Vbr ul holdblsktorb kd kr`kturb paklb kvbltb ulk nbo`btrak ho`b qubcck raportktk al ganurk pbr ac hkchoco dbcck hkpkhatæ possakò shravbrb ck sbnubltb bqukzaolb H 0βk *X/d

Al tkcb bsprbssaolb X í ck supbrgahab s upbrgahab da ulk kr`kturk, d í ck c k dastklzk trk cb kr`kturb b βk í ck ck hostkltb dabcbttrahk dbc `bzzo hmb sa trovk altbrposto trk cb dub kr`kturb. Ck hostkltb dabcbttrahk kssocutk βk í dktk dkc prodotto trk ck hostkltb dabcbttrahk dbc vuoto βo b ck hostkltb dabcbttrahk rbcktavk dbc `ktbrakcb βr

A holdblsktora solo japoca al hua al onla astkltb da tb`po ck hkrahk q(t) a``knkzzalktk succb kr`kturb b ck tblsaolb v(t) prbsbltb trk cb kr`kturb stbssb soddasgklo ulk dktk rbckzaolb rkpprbsbltkjacb lbc paklo (v,q). ck nrkldbzzk hmb hkrkttbrazzk ac holdblsktorb á

ck hkpkhatæ H ck hua ulatæ da àsurk í ac Gkrkd (G) (UHP0G). Xb ck hkrkttbrastahk lbc paklo (v,q) í ulk rbttk pksskltb pbr c‑oranalb bsso í calbkrb, kctra`blta í lol calbkrb. Xb ck hkrkttbrastahk lol hk`jak lbc tb`po í tb`po-alvkrakltb kctra`blta í tb`po-vkrakltb. HOLDBLXKTOZA CALBKZA TB@VO-ALWKZAKLTA Ck hkpkhatæ H lol dapbldb dk t b dk v

Altbnrkldo su ul altbrvkcco da tb`po (6-t) ottblakò

Al onla astkltb da tb`po ck tblsaolb ka hkpa dbc holdblsktorb í dktk dkcck so``k da dub tbràla, ck tblsaolb kcc‑astkltb alazakcb v(6) b ck tblsaolb kcc‑astkltb t ddaa ul holdblsktorb H hmb k t06 í shkraho HOLDBLXKTOZB CALBKZB TB@VO-WKZAKLTB Ck hkpkhatæhmb H dapbldb tb`po, ck hkrkttbrastahk í ulk hmb pkssk pbr c‑oranalb kd dbckr`kturk paklo (v,q) `kbmkpkrkccbcb ulk dovb pbldblzk vkrak lbcdkc tb`po. Vossakò a``knalkrb da rbttk rbkcazzkrb ul holdblsktorb paklb ul‑kr`kturk í gassk b c‑kctrk sa ùovb lbc tb`po , vkrakldo X b/o d sa mk ho`b holsbnublzk ulk vkrakzaolb dbcck hkpkhatæ H. q(t ) 0 H (t )v(t )

HOLDBLXKTOZB LOL CALBKZB B‑ ul holdblsktorb hmb mk lbc paklo (v,q) mk ulk hkrkttbrastahk lol calbkrb (o hmb lol pkssk pbr c‑oranalb)

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Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 664 ;6. Nblbrktorb da horrbltb

Ac nblbrktorb da horrbltb í ul japoco hmb mk ck hkrkttbrastahk tblsaolb horrbltb rkpprbsbltkjacb trkàtb ulk rbttk5 qubsto mk, aloctrb, ck pbhucakratæ da `kltblbrb ck horrbltb pkra k a*(t) lbc ckto dbc harhuato al hua í alsbrato5 ck tblsaolb ka suoa òrsbtta puú kssu`brb qukcsaksa vkcorb. Bsso í tb`po-alvkrakltb sb ck a*(t) í hostkltb, sb a*(t) vkrak í tb`po-vkrakltb . K daggbrblzk dba nblbrktora da tblsaolb, tblsaolb, a nblbrktora da horrbltb solo pbr co pañ dasposatava adbkca, utacazzkta pbr shmb`ktazzkrb ac ho`portk`blto da ho`polblta bcbttrolaha (a trklsastor trklsastor,, kd bsb`pao). Ck `knnaor pkrtb dba nblbrktora da blbrnak bcbttrahk solo `bncao shmb`ktazzkta dk nblbrktora da tblsaolb, k `blo hmb lol kjjaklo ulk bcbvktassa`k rbsastblzk altbrlk. Lba harhuata bcbttraha, bcbttraha, hoùlqub, sa altroduholo nblbrktora rbkca ho`b ul nblbrktorb adbkcb al adbkcb al pkrkccbco hol rbsastblzk (rbsastblzk (rbsastblzk altbrlk). Nrkzab kc tborb`k da Lortol sa Lortol sa puú sostatuarb ul nblbrktorb rbkcb da tblsaolb hol ul ulk rbsastblzk nblbrktorb rbkcb da horrbltb (b vahbvbrsk, pbr ac tborb`k da Tmávblal). Tmávblal).

Zaportakò da sbnuato ac sa`joco rkpprbsbltktavo b ck hkrkttbrastahk tblsaolb-horrbltb

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:> - ;8/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 662 6;. CK CBNNB DA EAZHMMOOGG DBCCB HOZZBLTA DAHB HMB AL ONLA @KNCAK CK XO@@K DBCCB HOZZBLTA B' LRCCK BXVZA@B CK CBNNB DBCCK HOLXBZWKYAOLB DBCCK HKZAHK LOL XA KVVCAHK KA HAZHRATA LOL CALBKZA DAHB HMB AL ONLA LODO CK XO@@K DBCCB TBLXAOLA B' LRCCK 6:. KVVCAHKLDO CK CBNNB DA EAZHMMOO EAZHMMOOGG GG DBCCB HOZZBLT HOZZBLTAA TRTTA A TBZ@ALA DBCC'B[RKYAOLB OTTBLRTK VOXXOLO BXXBZB TBLXAOLA TRTTA A TBZ@ALA DBCC'B[RKYAOLB OTTBLRTK DBWOLO BXXBZB TBLXAOLA TRTTA A TBZ@ALA DBCC'B[RKYAOLB OTTBLRTK VOXXOLO BXXBZB HOZZBLTA TRTTA A TBZ@ALA DBCC'B[RKYAOLB OTTBLRTK DBWOLO BXXBZB HOZZBLTA 68. HOCCBNK@BLTO AL XBZAB DA NBLBZKTOZA DA TBLXAOLB VBZ ZBKCAYYKZCO B' LBHBXXKZAO HMB A NBLBZKTOZA KJJAKLO TRTTA CK XTBXXK TBLXAOLB CK VOTBLYK DBCCK XBZAB B' VKZA KCCK @KXXA@K VOTBLYK CK HOZZBLTB DBCCK XBZAB B' VKZA KCCK XO@@K KCNBJZAHK DBCCB HOZZBLTA DBA XALNOCA NBLBZKTOZA CK TBLXAOLB DBCCK XBZAB B' VKZA KCCK XO@@K KCNBJZAHK DBCCB TBLXAOLA DBA XALNOCA NBLBZKTOZA 64. VKZTATOZB ZBXAXTAWO DA HOZZBLTB CK TBLXAOLB WKCB XB@VZB YBZO KA HKVA DBC VKZKCCBCO CK TBLXAOLB XA XRDDAWADB B[RK@BLTB TZK CB ZBXAXTBLYB CK TBLXAOLB XA XRDDAWADB TZK CB ZBXAXTBLYB AL @KLABZK VZOVOZYAOLKCB KC COZO WKCOZB CK HOZZBLTB XA XRDDAWADB TZK CB ZBXAXTBLYB AL @KLABZK ALWBZXK@BLTB VZOVOZYAOLKCB KC COZO WKCOZB 62. HOCCBNK@BLTO AL VKZKCCBCO DA JAVOCA XOLO XOTTOVOXTA K DAWBZXK TBLXAOLB CK HOZZBLTB HMB CA KTTZKWBZXK B' DAWBZXK CK HOZZBLTB HMB CA KTTZKWBZXK B' CK XTBXXK XOLO XOTTOVOXTA KCCK XTBXXK TBLXAOLB 67. HOCCBNK@BLTO AL XBZAB DA JAVOCA CK HOZZBLTB HMB CA KTTZKWBZXK B' DAWBZXK CK TBLXAOLB HMB CA KTTZKWBZXK B' DAWBZXK CK TBLXAOLB HMB CA KTTZKWBZXK B' CK XTBXXK CK HOZZBLTB HMB CA KTTZKWBZXK B' CK XTBXXK 6>. KVVCAHKLDO CK CBNNB DA EAZHMMOOGG DBCCB TBLXAOLA TRTTA A TBZ@ALA DBCC'B[RKYAOLB OTTBLRTK DBWOLO BXXBZB TBLXAOLA TRTTA A TBZ@ALA DBCC'B[RKYAOLB OTTBLRTK DBWOLO BXXBZB HOZZBLTA TRTTA A TBZ@ALA DBCC'B[RKYAOLB OTTBLRTK VOXXOLO BXXBZB TBLXAOLA TRTTA A TBZ@ALA DBCC'B[RKYAOLB OTTBLRTK VOXXOLO BXXBZB HOZZBLTA

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:> - ;4/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

6=. CK CBNNB DA EAZHMMOO EAZHMMOOGG GG DBCCB TBLXAOLA CK XO@@K KCNBJZAHK DBCCB TBLXAOLA DBA CKTA DA RLK @KNCAK B' LRCCK DAHB HMB AL ONLA @KNCAK CK XO@@K DBCCB HOZZBLTA B' LRCCK LOL XA KVVCAHK KA HAZHRATA LOL CALBKZA DAHB HMB AL ONLA LODO CK XO@@K DBCCB TBLXAOLA B' LRCCK 61. VKZTATOZB ZBXAXTAWO DA TBLXAOLB CK TBLXAOLB XA XRDDAWADB TZK CB ZBXAXTBLYB AL @KLABZK VZOVOZYAOLKCB KC COZO WKCOZB CK TBLXAOLB WKCB XB@VZB YBZO KA HKVA DBCCK XBZAB CK TBLXAOLB XA XRDDAWADB B[RK@BLTB TZK CB ZBXAXTBLYB CK TBLXAOLB XA XRDDAWADB TZK CB ZBXAXTBLYB AL @KLABZK ALWBZXK@BLTB VZOVOZYAOLKCB KC COZO WKCOZB ;6. HOCCBNK@BLTO AL VKZKCCBCO DA NBLBZKTOZA DA HOZZBLTB CK VOTBLYK DBC VKZKCCBCO B' VKZA KCCK @KXXA@K VOTBLYK CK HOZZBLTB DBC VKZKCCBCO B' XB@VZB @KXXA@K VBZ ZBKCAYYKZCO B' LBHBXXKZAO HMB A NBLBZKTOZA KJJAKLO TRTTA CK XTBXXK HOZZBLTB CK HOZZBLTB DBC VKZKCCBCO B' VKZA KCCK XO@@K KCNBJZAHK DBCCB HOZZBLTA DBA XALNOCA NBLBZKTOZA ;;. LBCCB ZBXAXTBLYB AL XBZAB Ck horrbltb totkcb vablb suddavask trk cb rbsastblzb, tuttb cb rbsastblzb solo sonnbttb kcck stbssk tblsaolb Rlk sbrab da rbsastblzb sa mk soco qukldo dub rbsastblzk mkllo co stbsso vk vkcorb corb Ck tblsaolb totkcb vablb suddavask trk cb rbsastblzb, tuttb cb rbsastblzb solo kttrkvbrsktb dkcck stbssk horrbltb Rlk sbrab da rbsastblzb a`pcahk ulk pkrtazaolb dbcck horrbltb su onla rbsastblzk ;:. LBCCB ZBXAXTBLYB AL VKZKCCBCO V KZKCCBCO Vossolo bssbrb hoccbnktb al pkrkccbco soco rbsastblzb kvblta co stbsso vkcorb Rl pkrkccbco da rbsastblzb puú bssbrb sostatuato dk ulk rbsastblzk ac hua vkcorb í dkto dkcck so``k dbccb rbsastblzb hoalvoctb lbc pkrkccbco pkrkccbco Ck horrbltb totkcb vablb suddavask trk cb rbsastblzb, tuttb cb rbsastblzb solo sonnbttb kcck stbssk tblsaolb Ck tblsaolb totkcb vablb suddavask trk cb rbsastblzb, tuttb cb rbsastblzb solo kttrkvbrsktb dkcck stbssk horrbltb ;8. Cbnnb da Earhmmogg dbccb horrblta

Ck cbnnb da Earhmmogg bspra`b ck holsbrvkzaolb dbcck hkrahk bcbttrahk ka loda ,haoí ac gktto hmb al onla lodo tuttk ck hkrahk bcbttrahk al alnrbsso dbvb usharb5 ka loda lol sa vbragahklo lb khhuùca lb kk``klhma ``klhma da hkrahk. Ck CEH pu ú bssbrb blulhaktk hos ã9 pbr onla lodo, al onla astkltb da d a tb`po, ck so``k dbccb horrblta al alnrbsso í unukcb kcck so``k dbccb horrblta al ushatk. Dk ul pulto da vastk opbrktavo, lbcck rasocuzaolb dba harhuata, ho`b pra`k hosk jasonlk kssbnlkrb cb darbzaola da ragbra`blto k tuttb cb horrblta lba ckta b, suhhbssavk`bltb, holsadbrkrb lbccb so``b kcnb kcnbjrahmb jrahmb hoc sbnlo posatavo ,cb horrblta ushblta dkc lodo b hoc sbnlo lbnktavo cb horrblta bltrklta lbc lodo (o vahbvbrsk). Vossakò gkrb kchulb holsadbrkzaola9 dkcc‑kppcahkzaolb dbcck CEH ka vkra loda da ul harhuato shkturasholo bqukzaola kcnbjrahmb calbkra k hobggahablta hostklta 6,;,-; ck CEH mk vkcadatæ nblbrkcb, lbc sblso hmb bssk í aldapbldbltb dkcck lkturk dba ho`polblta pbr quklto kttablb k calbkratæ b tb`po alvkraklzk

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:> - ;2/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

;4.

Vbr ac harhuato al ganurk, al hua B0;: W,Z;0; ℧, Z:02 ℧, hkchockrb A. Kppcahkldo ck cbnnb da Earhmogg kcck `kncab

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:> - ;7/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

;2.

Vbr ac harhuato al ganurk, al hua B;0;: W, B:07 W, Z;0;6 ℧, Z:0:6 ℧. Hkchockrb ac vkcorb da I tkcb hmb ck horrbltb A sak pkra k zbro.

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:> - ;>/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

;7.

Vbr al harhuato al ganurk, al hua B0;:W, Z ;0; om`, Z:08 om`, Z08 om`, hkchockrb A.

XBNRB

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:> - ;=/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:> - ;1/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

;>.

Vbr ac harhuato al ganurk, al hua W;0;: W, Za0a om`, hkchockrb ck tblsaolb W.

XWOCNA@BLTO9

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:> - :6/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

;=.

Vbr ac harhuato al ganurk, al hua Za0a om`, Z08 om`, hkchockrb Zbq K-K'

;1. Hoccbnk`blto al pkrkccbco da japoca

dub japoca hoccbnkta trk bssa lbnca stbssa pulta hostatuasholo ul hoccbnk`blto al pkrkccbco da dub japoca. Al qubsto hoccbnk`blto ck CEH a`polb hmb a0a;+a:, ossak ck horrbltb totkcb kssorjatk dkc pkrkccbco í dktk dkcck so``k dbccb horrblta dba salnoca japoca, aloctrb rasuctk hmb v0v;0v:. Al nblbrkcb,alsbhoccbnk`blto a japoca mkllo onlulo ck proprak hkrkttbrastahk (W-A), va skræ ulk hkrkttbrastahk (W-A) dbc japoco bquavkcbltb pkrkccbco. Dk ul pulto da vastk nrkgaho ck hkrkttbrastahk dbc japoco pkrkccbco (Zp) í ottblajacb so``kldo pbr onla vkcorb da tblsaolb cb horrblta hmb kttrkvbrsklo a japoca, a; b da:, ho`b accustrkto al ganurk

HOCCBNK@BLTO AL VKZKCCBCO DA ZBXAXTBLYB Lbc hkso al hua nca l japoca solo rbsastora calbkra tb`po-alvkraklta sa mk ae0Ne*v pbr E0;..l, ck holduttklzk bquavkcbltb í pkrak

HOCCBNK@BLTO AL VKZKCCBCO DA NBLBZKTOZA DA HOZZBLTB HOZZ BLTB Rl hkso pkrtahockrb da hoccbnk`blto al pkrkccbco í qubcco al hua ha solo l nblbrktora da horrbltb kvblta onlulo horrbltb ae hol e0;..l, ac coro pkrkccbco í ul nblbrktorb bquavkcbltb hol horrbltb dktk dk

HOCCBNK@BLTO AL VKZKCCBCO DA NBLBZKTOZA DA TBLXAOLB Ac hoccbnk`blto al pkrkccbco hol ck tblsaolb dbc pkrkccbco.trk dub o pañ da dub nblbrktora da tblsaolb í possajacb soco sb mkllo tutta ck stbssk tblsaolb v hmb hoalhadb

HOCCBNK@BLTO AL VKZKCCBCO DA HOLDBLXKTOZA Holsadbrakò l holdblsktora kvblta hakshulo hkpkhatæ He hol e0;..l calbkra b tb`po alvkraklta. Xb suppolakò hmb tutta a holdblsktora saklo alazakc`bltb kcck stbssk tblsaolb va(6)0We(6) hol a0;..l, kvrbò

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:> - :;/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

HOCCBNK@BLTO AL VKZKCCBCO DA ALDRTTOZA Holsadbrakò l alduttora kvblta hakshulo alduttklzk Ce hol e0;..l calbkra b tb`po alvkraklta. Xb suppolakò hmb tutta nca alduttora saklo alazakc`bltb kttrkvbrskta dk ulk horrbltb a(6) kvrbò

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:> - ::/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro :6. Hoccbnk`blto al sbrab da japoca

Lba harhuata bcbttraha dub o pañ japoca possolo bssbrb hoccbnkta trk da coro al davbrsa òda. Lba hksa al hua a dub (o pañ) japoca solo hoccbnkta al òdo dk kvbrb bltrk`ja ul òrsbtto al hoùlb ac hoccbnk`blto dbc japoco skræ da tapo sbrab. Al qubsto hoccbnk`blto ck CET a`polb hmb W0WZ;+WZ: haoí ck tblsaolb totkcb ka hkpa dbcck sbrab í dktk dkcck so``k dbccb tblsaola ka hkpa dba salnoca japoca, aloctrb rasuctk hmb a0a;0a:. Al nblbrkcb, sb a japoca mkllo onlulo ck proprak hkrkttbrastahk (A-W), va skræ ulk hkrkttbrastahk (W-A) dbc japoco bquavkcbltb al hoccbnk`blto sbrab. Dk ul pulto da vastk nrkgaho, ck hkrkttbrastahk dbc japoco sbrab (Zs) í ottblajacb so``kldo pbr onla vkcorb dbcck horrbltb A cb tblsaola horraspoldblta sua dub japoca(Z; bd Z:), ho`b accustrkto al ganurk

HOCCBNK@BLTO AL XBZAB DA ZBXAXTBLYB Lbc hkso al hua nca l japoca solo rbsastora calbkra tb`po-alvkraklta sa mk hmb We0Ze*a pbr E0;..l í ck tblsaolb ka hkpa dbcck rbsastblzk e.Ck rbsastblzk bquavkcbltb vastk dka òrsbtta dbcck sbrab í pkra k

HOCCBNK@BLTO AL XBZAB DA NBLBZKTOZA DA TBLXAOLB Rl hkso pkrtahockrb da hoccbnk`blto sbrab í qubcco al hua a japoca solo l nblbrktora da tblsaolb kvblta onlulo tblsaolb ve hol e0;..l. Ck coro sbrab í ul nblbrktorb bquavkcbltb hol tblsaolb dktk dkcck so``k kcnbjrahk dbccb salnocb tblsaola

HOCCBNK@BLTO AL XBZAB DA HOLDBLXKTOZA Holsadbrakò l holdblsktora kvblta hakshulo hkpkhatæ He hol e0;..l, calbkra b tb`po alvkraklta. Kjjakò vasto hmb pbr onlulo da bssa sa mk sb a holdblsktora solo alazakc`bltb shkrahma kvrbò va(6)06 pbr a0;…l pbr ck CET kvrbò

HOCCBNK@BLTOALXBZABDAALDRTTOZA Holsadbrakò l alduttora calbkra b tb`po alvkraklta ,kvblta hakshulo alduttklzk Ce hol e0;..l., kjjakò vasto hmb pbr onlulo da bssa sa mk

Xb suppolakò hmb tuttb cb horrblta alazakca saklo luccb, kvrbò k vrbò ae(6)06 hol e0;..l, pbr ck CET kvrbò

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:> - :8/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro :;. Cbnnb da Earhmmogg dbccb tblsaola

Al nblbrkcb ck cbnnb da Earhmmogg dbccb tblsaola (CET o CEW o EWC) kggbr`k hmb ck so``k kcnbjrahk dbccb tblsaola knblta trk cb hoppab da pulta lbcco spkzao hmb gor`klo ulk qukcsaksa sbqublzk hmausk (orabltktk) í unukcb k zbro. Lbcck gorùckzaolb pañ sb`pcahb ck cbnnb dahb hmb ck so``k kcnbjrahk dbccb tblsaola culno ulk calbk hmausk (hol ac sbnlo kpproprakto al gulzaolb dbc vbrso da pbrhorrblzk dbcck `kncak stbssk) í pkra k zbro. Xb cb nrkldbzzb bcbttrahmb dbc harhuato solo rkpprbsbltktb lbc doàlao dbc tb`po (pbr bsb`pao sb í al horrbltb holtaluk) ck so``k vk altbsk ho`b so``k kcnbjrahk. Xb ac harhuato í al horrbltb kctbrlktk b cb nrkldbzzb bcbttrahmb solo rkpprbsbltktb dk gksora ck so``k puú bssbrb gkttk klhmb sua gksora horraspoldblta kccb tblsaola (qualda ho`b so``k vbttorakcb). Aldahkldo hol Wa cb tblsaola, al gorùck sa puú shravbrb9 ΨWa06 Rlk `kncak (vbda ganurk) í ul pbrhorso hmauso da ulk rbtb bcbttrahk hmb pkrtbldo dk ul lodo torlk kcco stbsso sblzk kttrkvbrskrb ulo stbsso rkò dub voctb, lol í lbhbsskrao hmb trk dub loda suhhbssava da ulk `kncak ha sak ul ho`polbltb "bggbttavo" (klhmb pbrhmá sa puú sb`prb a``knalkrb ck prbsblzk da ul ho`polbltb horto harhuato o harhuato kpbrto). Kd bsb`pao, kppcahmakò ck cbnnb kcck `kncak `kncak k,j,h,d, k dbc harhuato al ganurk. Vkrtakò dkc lodo k pbrhorrbldo ck `kncak al sblso orkrao b apotazzakò apotazzakò hmb a potblzakca bcbttraha dba loda dk k k d saklo vak vak dbhrbshblta. Xa mk9 W;+W:+W8-W406 dbcc'blbrnak pbr ul hk`po holsbrvktavo, holsbrvktavo, al quklto kggbr`k [ubstk cbnnb horraspoldb kcck cbnnb da holsbrvkzaolb dbcc'blbrnak pbr hmb ac ckvoro ckvoroho`pauto ho`pauto pbr gkr ho`pabrb kd ulk hkrahk ul pbrhorso hmauso dbvb bssbrb unukcb k zbro.

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:> - :4/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 667

6;.

Vbr ac harhuato al ganurk solo lota B0;: W, Za0a ℧, A80 2 K hkchockrb WKJ

XBNRB

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:> - :2/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:> - :7/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

6:.

Vbr ac harhuato al ganurk solo lota B0;: W, Za0a ℧ , A80 2 K, hkchockrb A.

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:> - :>/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

68. Xovrkpposazaolb dbnca bggbtta

[ubsto pralhapao rkpprbsbltk ulo stru`blto goldk`bltkcb pbr ck socuzaolb da harhuata calbkra. Xak dktk ulk rbtb calbkrb, holtblbltb l nblbrktora da tblsaolb bd ` nblbrktora da horrbltb sb aldahmakò hol â ulk nblbrahk tblsaolb-horrbltb dbc harhuato sa mk hmb

Ossak, qukcsaksa tblsaolb-horrbltb í ottblajacb ho`b so``k da ulk ho`jalkzaolb calbkrb dba nblbrktora da tblsaolb B b ulk ho`jalkzaolb calbkrb dba nblbrktora da horrbltb A.

Xolo hobggahablta hostklta hmb dapbldolo dka pkrk`btra hostatublta ac harhuato (bs. dkc vkcorb dbccb rbsastblzb) b dkc hoccbnk`blto trk a ho`polblta5 dbtta pkrk`btra lol dapbldolo dka nblbrktora da horrbltb b da tblsaolb. Gkhhakò kchulb holsadbrkzaola succ‑kppcahkjacatæ dbc pralhapao da sovrkpposazaolb dbnca bggbtta9 • ck rbtb dbvb bssbrb calbkrb, haoí dbvb bssbrb hostatuatk dk nblbrktora da tblsaolb b/o da horrbltb b dk bcb`blta calbkra qukca rbsastora calbkra, alduttora calbkra, holdblsktora calbkra bth.5 • ac pralhapao vkcb klhmb sb ck rbtb holtablb ho`polblta tb`po-vkraklta5 • ck gor`k d‑oldk dba nblbrktora puú bssbrb qukcsaksa. Dkc pulto da vastk dbcck rasocuzaolb dbccb rbta, ac holtrajuto da ul nblbraho nblbrktorb puú bssbrb vkcutkto holsadbrkldo ul harhuato holtblbltb sock`bltb ac nblbrktorb al qubstaolb al hua tutta a nblbrktora da tblsaolb solo sostatuata dk ul horto harhuato b tutta a nblbrktora da horrbltb solo sostatuata dk ul harhuato kpbrto.

64.

Vbr ac harhuato al ganurk solo lota W07 W, I02 K, Za0a ℧, hkchockrb ck tblsaolb WKJ.

XBNRB

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Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

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Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 66> 6;. [RKLDO B' VOXXAJACB HKCHOCK HKCHOCKZB ZB AC HAZHRATO B[RAWK B[RAWKCBLTB CBLTB KCCK TMBWBLAL Lol ha solo caàtkzaola, ohhorrb sb`pcahb`bltb potbr hkchockrb ck rbsastblzk bquavkcbltb vastk ka hkpa dba òrsbtta raspbtto ka qukca hkchockrb ac harhuato bquavkcbltb, ulk voctk rbso pkssavo ac harhuato su hua sa ckvork, b poa dbtbràlkrb ck horrbltb àsurktk àsurktk al horto harhuato ka hkpa dbnca stbssa òrsbtta, ulk voctk hmb sa í rbso kttavo ac harhuato stbsso. Lol ha solo caàtkzaola, ohhorrb sb`pcahb`bltb potbr hkchockrb ck rbsastblzk bquavkcbltb vastk ka hkpa dba òrsbtta raspbtto ka qukca hkchockrb ac harhuato bquavkcbltb, ulk voctk rbso kttavo ac harhuato su hua sa ckvork, b poa dbtbràlkrb ck tblsaolb àsurktk àsurktk k vuoto ka hkpa dbnca stbssa òrsbtta, ulk voctk hmb sa í rbso pkssavo ac harhuato stbsso. Dapbldb dkc harhuato hmb sa vuocb sostatuarb9 dbvb kvbrb soco nblbrktora da ulo stbsso tapo [ukldo ck rbsastblzk bquavkcbltb ka òrsbtta ka qukca sa vuocb hkchockrb ac harhuato bquavkcbltb í galatk.

6:.

Vbr ac harhuato al ganurk solo lota B0;: W, Za0a ℧, I0: K, hkchockrb ac harhuato bquavkcbltb da Tmbvblal ka òrsbtta KJ.

XBNRB

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Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro 68. Tmbvblal

Ac tborb`k da Tmbvblal puú bssbrb blulhakto ho`b sbnub9 dktk ulk rbtb calbkrb Z (tb`po-alvkrakltb o tb`po-vkrakltb) b dkta dub suoa òrsbtta K b J k hua í hollbssk ulk rbtb nblbrahk ZKJ da qukcsaksa lkturk (raspbtto k calbkratæ b tb`po alvkraklzk), suppolbldo hmb trk ck rbtb Z b ck rbtb ZKJ lol ha sak kchul hoccbnk`blto sb lol qubcco trk a òrsbtta KJ (bsb`pao khhoppak`blto da tapo `knlbtaho o hol nblbrktora holtrocckta), ck rbtb calbkrb Z í bquavkcbltb kd ul harhuato hostatuato dk ulk rbsastblzk ZTm al sbrab kd ul nblbrktorb da tblsaolb WTm.

Hol ac tbràlb bquavkcbltb sa altbldb hmb a dub harhuata (rbtb calbkrb Z b harhuato bquavkcbltb da Tmbvblal) ka òrsbtta KJ mkllo co stbsso ho`portk`blto bcbttraho. Dakò da sbnuato a hratbra pbr hkchockrb a ho`polblta dbc harhuato bquavkcbltb da Tmbvblal. ZTm í ck rbsastblzk bquavkcbltb hkchocktk ka òrsbtta K b J dopo kvbr rbso pkssavk ck rbtb Z (sa hortoharhuatklo a nblbrktora da tblsaolb b sa kprolo a nblbrktora da horrbltb). Xb ck rbtb calbkrb Z mk ulk rbsastblzk bquavkcbltb algalatk (harhuato kpbrto) lol sa puú kppcahkrb ac tborb`k da Tmbvblal. WTm í ck tblsaolb hmb sa àsurk trk a òrsbtta K b J qukldo qubsta solo shoccbnkta dkcck rbtb ZKJ (aldahkzaolb opbrktavk9 kttblzaolb kc vbrso da WTm, W Tm, dbvb bssbrb hol ac + al a l K b hol ac ‘ al J) J).. Dopo kvbr dbtbràlkto a pkrk`btra dbc harhuato bquavkcbltb da Tmbvblal, skræ possajacb dbtbràlkrb ac pulto da ckvoro da ulk qukcsaksa rbtb ZKJ hollbssk trk a òrsbtta KJ, bsso potræ bssbrb ottbluto ho`b altbrsbzaolb trk ck hkrkttbrastahk dbc nblbrktorb bquavkcbltb WKJ0WTm-ZTmA b ck hkrkttbrastahk (W,A) ka òrsbtta KJ dbcck rbtb ZKJ.

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Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 66= 6;. HOXK XANLAGAHK HOLXADBZKZB AC HAZHRATO B[RAWKCBLTB KCCK TMBWBLAL B KCCK LOZTOL HOXK XANLAGAHK HKCHOCKZB AC HAZHRATO B[RAWKCBLTB KCCK TMBWBLAL B KCCK LOZTOL Xanlagahk sostatuarb ac harhuato hol ulo bskttk`bltb bquavkcbltb bquavkcbltb hostatuato sb`prb dk ul nblbrktorb da tblsaolb b ulk rbsastblzk al pkrkccbco Xanlagahk sostatuarb ac harhuato hol ulo bskttk`bltb bquavkcbltb hostatuato sb`prb dk ul nblbrktorb da horrbltb b ulk rbsastblzk al sbrab sostatuarb harhuato holdaulo bquavkcbltb da vastk bcbttraho hostatuato dk ulk sock rbsastblzk b dk ul soco nblbrktorb da horrbltb (o da tblsaolb) k sbholdk hmb Xanlagahk sa trktta dbc harhuatoacbquavkcbltb Lortol o qubccodkc da pulto Tmbvblal Xanlagahk sostatuarb ac harhuato hol ulo bskttk`bl bskttk`bltb tb bquavkcbltb hostatuato sb`prb dk ul nblbrktorb da tblsaolb al pkrkccbco kd ulk rbsastblzk 6:. VBZ RLK ZBTB CALBKZB HO@VZBXK TZK A @OZXBTTA KJ XB HKCHOCAK@O AC HAZHRATO B[RAWKCBLTB DA TMBWBLAL LOL VOXXAK@O HKCHOCKZB AC HAZHRATO B[RAWKCBLTB DA LOZTOL AL NBLBZKCB, O BXAXTB AC HAZHRATO B[RAWKCBLTB DA TMBWBLAL OVVRZB BXAXTB AL HAZHRATO B[RAWKCBLTB DA LOZTOL A HAZHRATA B[RAWKCBLTA DA TMBWBLAL B DA LOZTOL BXAXTOLO XB@VZB AL NBLBZKCB, B' VOXXAJACB HKCHOCKZB XAK AC HAZHRATO B[RAWKCBLTB DA TMBWBLAL, XAK [RBCCO DA LOZTOL 68. CK HOZZBLTB DBC NBLBZKTOZB DA HOZZBLTB B[RAWKCBLTB DA LOZTOL TZK A @OZXBTTA KJ HOALHADB HOL CK HOZZBLTB K WROTO TZK A @OZXBTTA KJ HOALHADB HOL CK TBLXAOLB AL HOZTO HAZHRATO TZK A @OZXBTTA KJ HOALHADB HOL CK HOZZBLTB AL HOZTOHAZHRATO TZK A @OZXBTTA KJ HOALHADB HOL CK TBLXAOLB AL HOZTO HAZHRATO TZK A @OZXBTTA KJ KVBZTA 64. CK TBLXAOLB DBC NBLBZKTOZB DA TBLXAOLB B[RAWKCBLTB DA TMBWBLAL TZK A @OZXBTTA KJ HOALHADB HOL CK TBLXAOLB K WROTO TZK A @OZXBTTA KJ HOALHADB HOL CK HOZZBLTB K WROTO TZK A @OZXBTTA KJ HOALHADB HOL CK TBLXAOLB AL HOZTO HAZHRATO TZK A @OZXBTTA KJ HOALHADB HOL CK TBLXAOLB AL HOZTO HAZHRATO TZK A @OZXBTTA KJ KVBZTA 62. VBZ HAZHRATO ] B[RAWKCBLTB KC HAZHRATO Q ALTBLDAK@O AC GKTTO HMB ] BD Q MKLLO CO XTBXXO LR@BZO DA JAVOCA DRB HAZHRATA ADBLTAHA AC GKTTO HMB ] BD Q MKLLO CO XTBXXO HO@VOZTK@BLTO BCBTTZAHO HOLTBLNOLO O XOCO NBLBZKTOZA DA HOZZBLTB O XOCO NBLBZKTOZA DA TBLXAOLA 67. KGGALHMB', KA @OZXBTTA KJ, BXAXTKLO BLTZK@JA A HAZHRATA B[RAWKCBLTA B[RAWKCBLTA DA TMBWBLAL B DA LOZTOL CK ZBXAXTBLYK B[RAWKCBLTB KA @OZXBTTA KJ VRO' KXXR@BZB [RKCXAKXA WKCOZB CK ZBXAXTBLYK B[RAWKCBLTB KA @OZXBTTA KJ VRO' WKCBZB ALGALATO CK ZBXAXTBLYK B[RAWKCBLTB KA @OZXBTTA KJ VRO' WKCBZB YBZO CK ZBXAXTBLYK B[RAWKCBLTB B[RAWKCBLTB KA @OZXBTTA KJ DBWB BXXBZB @KNNAOZB DA YBZO B @ALOZB DA ALGALATO 6>. VBZ ZBLDBZB RLK ZBTB VKXXAWK XA HOZTOHAZHRATKLO A NBLBZKTOZA DA TBLXAOLB B XA HOZTOHAZHRATKLO A NBLBZKTOZA DA HOZZBLTB XA HOZTOHAZHRATKLO A NBLBZKTOZA DA HOZZBLTB B XA KVZOLO A NBLBZKTOZA DA HOZZBLTB XA KVZOLOLO A NBLBZKTOZA DA TBLXAOLB B XA KVZOLO A NBLBZKTOZA DA HOZZBLTB XA HOZTOHAZHRATKLO A NBLBZKTOZA DA TBLXAOLB B B XA KVZOLO A NBLBZKTOZA DA HOZZBLTB

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Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

6=. CB ZBXAXTBLYB B[RAWKCBLTA DA TMBWBLAL B DA LOZTOL MKLLO WKCOZA DAVBLDBLTA DKA HAZHRATA B ,AL NBLBZKCB, DAWBZXA TZK DA COZO XA HKCHOCKLO KCCO XTBXXO @ODO VOXXOLO BXXBZB WKCRTKTB XOCO XB AC HAZHRATO LOL B' CALBKZB DAVBLDOLO XOCO DKA WKCOZA DBCCB ZBXAXTBLYB VZBXBLTA LBC HAZHRATO 61. HOXK XANLAGAHK HOLXADBZKZB AC HAZHRATO B[RAWKCBLTB KCCK TMBWBLAL B KCCK LOZTOL XANLAGAHK XOXTATRAZB AC HAZHRATO HOL RLO BXKTTK@BLTB B[RAWKCBLTB HOXTATRATO XB@VZB DK RL NBLBZKTOZB DA HOZZBLTB B RLK A@VBDBLYK AL XBZAB XANLAGAHK XOXTATRAZB AC HAZHRATO HOL RLO BXKTTK@BLTB B[RAWKCBLTB HOXTATRATO XB@VZB DK RL NBLBZKTOZB DA TBLXAOLB AL VKZKCCBCO KD RLK A@VBDBLYK XANLAGAHK XOXTATRAZB AC HAZHRATO HOL RLO B[RAWKCBLTB DKC VRLTO DA WAXTK BCBTTZAHO HOXTATRATO DK RLK XOCK A@VBDBLYK B DK RL XOCO NBLBZKTOZB DA HOZZBLTB (O DA TBLXAOLB) K XBHOLDK HMB XA TZKTTA DBC HAZHRATO B[RAWKCBLTB DA LOZTOL O [RBCCO DA TMBWBLAL XANLAGAHK XOXTATRAZB AC HAZHRATO HOL RLO BXKTTK@BLTB B[RAWKCBLTB HOXTATRATO XB@VZB DK RL NBLBZKTOZB DA TBLXAOLB B RLK A@VBDBLYK AL VKZKCCBCO ;6. AC HAZHRATO B[RAWKCBLTB DA TMBWBLAL VRO' BXXBZB WKCRTKTO XOCO VBZ KCHRLA TATVA DA HAZHRATA CALBKZA VRO' BXXBZB WKCRTKTO XB@VZB TZK A @OZXBTTA KJ DA RLK ZBTB LOL CALBKZB VRO' BXXBZB WKCRTKTO KLHMB VBZ ZBTA LOL CALBKZA VRO' BXXBZB WKCRTKTO XOCO VBZ ZBTA CALBKZA ;;. AC HAZHRATO B[RAWKCBLTB DA LOZTOL VRO' BXXBZB WKCRTKTO XOCO VBZ ZBTA CALBKZA VRO' BXXBZB WKCRTKTO XOCO VBZ KCHRLA TATVA DA HAZHRATA CALBKZA VRO' BXXBZB WKCRTKTO XB@VZB TZK A @OZXBTTA KJ DA RLK ZBTB LOL CALBKZB VRO' BXXBZB WKCRTKTO KLHMB VBZ ZBTA LOL CALBKZA ;:. AC TBOZB@K DA TMBWBLAL DAHB HMB [RKCXAKXA ZBTB CALBKZB HO@VZBXK TZK A @OZXBTTA K B J B' B[RAWKCBLTB KD RL HAZHRATO HOXTATRATO DK RLK ZBXAXTBLYK HOCCBNKTK KD RL NBLBZKTOZB DA TBLXAOLB [RKCXAKXA ZBTB CALBKZB HO@VZBXK TZK A @OZXBTTA K B J B' B[RAWKCBLTB KD RL HAZHRATO HOXTATRATO DK RLK ZBXAXTBLYK AL XBZAB KD RL NBLBZKTOZB DA TBLXAOLB [RKCXAKXA ZBTB CALBKZB HO@VZBXK TZK A @OZXBTTA K B J B' B[RAWKCBLTB KD RL HAZHRATO HOXTATRATO DK RLK ZBXAXTBLYK AL XBZAB KD RL NBLBZKTOZB DA HOZZBLTB [RKCXAKXA ZBTB CALBKZB HO@VZBXK TZK A @OZXBTTA K B J B' B[RAWKCBLTB KD RL HAZHRATO HOXTATRATO DK RLK ZBXAXTBLYK AL VKZKCCBCO KD RL NBLBZKTOZB DA TBLXAOLB ;8. AC TBOZB@K DA LOZTOL DAHB HMB [RKCXAKXA ZBTB CALBKZB HO@VZBXK TZK A @OZXBTTA K B J B' B[RAWKCBLTB KD RL HAZHRATO HOXTATRATO DK RLK ZBXAXTBLYK HOCCBNKTK KD RL NBLBZKTOZB DA TBLXAOLB [RKCXAKXA ZBTB CALBKZB HO@VZBXK TZK A @OZXBTTA K B J B' B[RAWKCBLTB KD RL HAZHRATO HOXTATRATO DK RLK ZBXAXTBLYK AL VKZKCCBCO KD RL NBLBZKTOZB DA HOZZBLTB [RKCXAKXA ZBTB CALBKZB HO@VZBXK TZK A @OZXBTTA K B J B' B[RAWKCBLTB KD RL HAZHRATO HOXTATRATO DK RLK ZBXAXTBLYK AL XBZAB KD RL NBLBZKTOZB DA HOZZBLTB [RKCXAKXA ZBTB CALBKZB HO@VZBXK TZK A @OZXBTTA K B J B' B[RAWKCBLTB KD RL HAZHRATO HOXTATRATO DK RLK ZBXAXTBLYK AL VKZKCCBCO KD RL NBLBZKTOZB DA TBLXAOLB

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Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

;4.

Vbr ac harhuato al ganurk solo lota W0;: W, Z a0a ℧, dbtbràlkrb ac harhuato bquavkcbltb da Lortol ka òrsbtta KJ.

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;2. Lortol

Ac tborb`k da Lortol puú bssbrb blulhakto ho`b sbnub9 dktk ulk rbtb calbkrb Z (tb`poalvkrakltb o tb`po-vkrakltb) b dkta dub suoa òrsbtta K b J k hua í hollbssk ulk rbtb nblbrahk ZKJ da qukcsaksa lkturk (raspbtto k calbkratæ b tb`po alvkraklzk), suppolbldo hmb trk ck rbtb Z b ck rbtb ZKJ lol ha sak kchul hoccbnk`blto sb lol qubcco trk a òrsbtta òr sbtta KJ (bsb`pao khhoppak`blto da tapo `knlbtaho o hol nblbrktora holtrocckta), ck rbtb calbkrb Z í bquavkcbltb kd ul harhuato hostatuato dk ulk rbsastblzk ZL al pkrkccbco kd ul nblbrktorb da horrbltb AL.

Hol ac tbràlb bquavkcbltb sa altbldb hmb a dub harhuata (rbtb calbkrb Z b harhuato bquavkcbltb da Lortol) ka òrsbtta KJ mkllo co stbsso ho`portk`blto bcbttraho. a ho`polblta dbc harhuato bquavkcbltb da Lortol solo a sbnublta9 ZL í ck rbsastblzk bquavkcbltb hkchocktk ka òrsbtta K b J dopo kvbr rbso pkssavk ck c k rbtb calbkrb Z (sa hortoharhuatklo a nblbrktora da tblsaolb b sa kprolo a nblbrktora da horrbltb), bssk hoalhadb hol ZTm. Xb ck rbtb calbkrb Z mk ulk rbsastblzk bquavkcbltb lucck (horto harhuato), lol sa puú kppcahkrb ac tborb`k da Lortol. AL í ck horrbltb hmb sa àsurk trk a òrsbtta K b J qukldo qubsta solo hortoharhuatkta (aldahkzaolb opbrktavk9 kttblzaolb kc vbrso dbcck AL dbvb bssbrb qubcco dk K vbrso J). Dopo kvbr dbtbràlkto a pkrk`btra dbc harhuato bquavkcbltb da Lortol, skræ possajacb dbtbràlkrb ac pulto da ckvoro da ulk qukcsaksa rbtb ZKJ hollbssk trk a òrsbtta K b J. (Lbc hkso al hua 63Zbq0ZTm0ZL3∜ bsastolo bltrk`ja a harhuata da Tmbvblal b Lortol. Xb Zbq0∜ bsastb soco c‑bquavkcbltb da Lortol, sb Zbq06 bsastb soco c‑bquavkcbltb da Tmbvblal).

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Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 661 6;. AC TBOZB@K DA @ACC@KL B' kppcahkjacb qukldo ac lu`bro da loda dbc harhuato í pkra k dub B‑kppcahkjacb qukldo ac lu`bro da `kncab í pkra B' kppcahkjacb soco qukldo lbc harhuato ha solo dub loda b soco nblbrktora da tblsaola B' kppcahkjacb qukldo ac lu`bro da loda dbc harhuato í pkra k trb bd ulo sa prbldb ho`b ragbra`blto 6:. @acc`kll

ck hkdutk da tblsaolb ka hkpa da ulk rbtb hostatuatk dk dub soca loda (jalodkcb) í dktk dkc rkpporto trk ck so``k kcnbjrahk dbccb horrblta da hortoharhuato (hmb sa hkchocklo a`polbldo WKJ06) b ck so``k dbccb holduttklzb da onla rkò.

Kppcahkldo ac tborb`k da @acc`kl kc harhuato su dasbnlkto sa ottbrræ hmb

Ac hkchoco dbccb horrblta al onla rkò sa bggbttuk kppcahkldo ck cbnnb da Om` nblbrkcazzktk, pbr hua9

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ; ;;/;:/:6;7 ;/;:/:6;7 ;>9;>9;7 - ;>/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

68.

Vbr ac harhuato al ganurk, al hua solo s olo lota B01 W, Za0a ℧, dbtbràlkrb cb trb horrblta lba ckta. ckta.

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ; ;;/;:/:6;7 ;/;:/:6;7 ;>9;>9;7 - ;=/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 6;6 6;. C'BLBZNAK BCBTTZAHK B' C'ALTBNZKCB DBCCK VOTBLYK LBC TB@VO B' XB@VZB VKZA KCCK VOTBLYK AXTKLTB VBZ AXTKLTB B' CK DBZAWKTK DBCCK VOTBLYK LBC TB@VO B' XB@VZB YBZO LBCCB ZBXAXTBLYB 6:. AC TBOZB@K DA TBCCBNBL DAHB HMB CK XO@@K BXTBXK K TRTTA A CKTA DA RL HAZHRATO DBA VZODOTTA TZK TBLXAOLB B HOZZBLTB B' XB@VZB LBNKTAWK CK XO@@K BXTBXK K TRTTA A CKTA DA RL HAZHRATO DBA VZODOTTA TZK TBLXAOLB B HOZZBLTB B' LRCCK CK XO@@K BXTBXK K TRTTA A CKTA DA RL HAZHRATO DBA VZODOTTA TZK TBLXAOLB B HOZZBLTB LOL B' [RKLTAGAHKJACB K VZAOZA CK XO@@K BXTBXK K TRTTA A CKTA DA RL HAZHRATO DBA VZODOTTA TZK TBLXAOLB B HOZZBLTB B' XB@VZB VOXATAWK 68. AC DAKNZK@@K DA HKZAHO ZKVVZBXBLTK C'BLBZNAK KXXOZJATK DK RL HAZHRATO AL :4 OZB C'KLDK@BLTO DBCCK VOTBLYK AL GRLYAOLB DBCCK HOZZBLTB C'KLDK@BLTO DBCCK VOTBLYK AL GRLYAOLB DBCCK TBLXAOLB C'KLDK@BLTO DBCCK VOTBLYK AL GRLYAOLB DBC TB@VO 64. RL JAVOCO B' DBTTO VKXXAWO [RKLDO CK VOTBLYK KXXOZJATK B' HOXTKLTB VRO' GOZLAZB VOTBLYK KCC'BXTBZLO VBZ ONLA t CK HKZKTTBZAXTAHK B' O LBC A O LBC AAA [RKDZKLTB GOZLAXHB XB@VZB VOTBLYK KCC'BXTBZLO 62. RL JAVOCO B' DBTTO KTTAWO [RKLDO GOZLAXHB XB@VZB VOTBLYK KCC'BXTBZLO CK VOTBLYK KXXOZJATK B' HOXTKLTB VBZ ONLA t CK HKZKTTBZAXTAHK LOL B' TRTTK O LBC A O LBC AAA [RKDZKLTB LOL VRO' GOZLAZB VOTBLYK KCC'BXTBZLO 67. CK VOTBLYK BCBTTZAHK VBZ RL DKTO JAVOCO XOCO VOXATAWK XOCO LBNKTAWK VRO' BXXBZB VOXATAWK-LBNKTAWK-LRCCK XB@VZB LRCCK 6>. RL NBLBZKTOZB VRO' KXXOZJAZB VOTBLYK XB@VZB XOCO XB HOCCBNKTO KD RL ZBXAXTOZB @KA AL KCHRLA HKXA VKZTAHOCKZA

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ; ;;/;:/:6;7 ;/;:/:6;7 ;>9;>9;7 - ;1/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

6=. VOTBLYB BCBTTZAHK p(t)0v(t)a(t) í sb`prb lbnkt lbnktavk avk p(t)0Zv(t)a(t) p(t)0v(t)a(t) p(t)0v(t)a(t) í sb`prb posatavk 61. CK VOTBLYK KTTAWK XA @AXRZK @A XRZK AL ^KTT IORCB WKZ WK ;6. VBZ RL NBLBZKTOZB ZBKCB AC ZBLDA@BLTO B' VKZA K ZKVVOZTO TZK VOTBLYK BZONKTK KCC'BXTBZLO B VOTBLYK NBLBZKTK YBZO RLO ZKVVOZTO TZK VOTBLYK BZONKTK KCC'BXTBZLO B VOTBLYK DAXXAVKTK KC XRO ALTBZLO ;;. AC CBNK@B BXAXTBLTB TZK VOTBLYK BD BLBZNAK B' AC XBNRBLTB C'blbrnak í ck dbravktk dbcck potblzk lbc tb`po C'blbrnak í c'altbnrkcb dbcck potblzk lbc tb`po C'blbrnak í ac prodotto potblzk pbr rbsastblz rbsastblzkk Ck potblzk í c'altbnrkcb dbcc'blbrnak a``knkz a``knkzzalktk zalktk lbc tb`po ;:. CK VOTBLYK DAXXAVKTK DK RLK ZBXAXTBLYK XA HKCHOCK BXBNRBLDO Ac prodotto dbcck tblsaolb kc qukdrkto pbr ck rbsastblzk stbssk Ac prodotto dbcck horrbltb kc qukdrkto pbr ck tblsaolb Ac prodotto dbcck rbsastblzk kc qukdrkto pbr ck horrbltb Ac prodotto dbcck horrbltb kc qukdrkto pbr ck rbsastblzk stbssk

;8. BLRLHAKTO DBC TBOZB@K DA TBCCBNBL Ck so``k dba prodotta dbccb tblsaola pbr cb horrblta kc qukdrkto da onla ckto, dbvb bssbrb lucck Ck so``k kcnbjrahk dba prodotta dbccb tblsaola pbr cb horrblta da onla ckto dbvb bssbrb lucck Ck so``k dbccb potblzb kc qukdrkto da onla ckto dbvb bssbrb lucck Ck so``k dba prodotta dbccb tblsaola kc qukdrkto succb horrblta da onla ckto dbvb bssbrb lucck ;4. CK VOTBLYK DAXXAVKTK VBZ BGGBTTO IORCB DAVBLDB XOCO DKC WKCOZB DBCCK HOZZBLTB HMB KTTZKWBZXK AC HOLDRTTOZB XA MK ONLA WOCTK HMB RLK HOZZBLTB KTTZKWBZXK RL HOLDRTTOZB B' ALDAVBLDBLTB DKCCK HOZZBLTB B' ALDAVBLDBLTB DKCCK ZBXAXTBLYK

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ; ;;/;:/:6;7 ;/;:/:6;7 ;>9;>9;7 - :6/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

;2.

Vbr ac harhuato al ganurk solo lota W0;: W, I0: K, Za0a ℧ dbtbràlkrb ck potblzk V dbc nblbrktorb da tblsaolb.

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ; ;;/;:/:6;7 ;/;:/:6;7 ;>9;>9;7 - :;/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

;7. Votblzk al horrbltb holtaluk

Holsadbrkldo ac japoco sbnubltb5

Ck potblzk p(t) bsprbssk al ^ktt (^) bltrkltb lbc japoco í pkra kc prodotto trk ck tblsaolb v(t) b ck horrbltb a(t), sa utacazzk pbr ac japoco ck holvblzaolb dbnca utacazzktora. Klkcazzakò ac sbnlo dbcck potblzk al ul japoco5 onla japoco í hkrkttbrazzkto dk ulk hurvk lbc paklo W-A (o A-W), ulk voctk stkjacato ac pulto da ckvoro (haoí ck hoppak tblsaolb v(t) b horrbltb a(t)) ck potblzk p(t)0v(t)a(t) í ulavohk`bltb dbtbràlktk bd í pkra kcc‑krbk gor`kto trkckac potblzk pulto daíckvoro b ncahaoí kssaacW-A. Xb rahbvb ac pultopotblzk da ckvoro sa trovk lbc A o dbc lbc rbttklnoco AAA qukdrkltb (v*a9;>9;7 - ::/7:

Xb holsadbrakò ac nblbrktorb ho`b ul sastb`k al hua aldavaduakò c‑alnrbsso b c‑ushatk,

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

possakò dbgalarb ac rblda`blto dbc sastb`k nblbrktorb ho`b rkpporto trk t rk ck potblzk bronktk kcc‑bstbrlo b ck potblzk nblbrktk

;>.

Vbr ac harhuato al ganurk al hua solo lota B0;6 W, B20;6 W, A02 K, Z;0:6  , Z:02  , Z802  , Z40;6 , hkchockrb ck potblzk V dbc nblbrktorb da tblsaolb B2 B2

XBNRB © :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ; ;;/;:/:6;7 ;/;:/:6;7 ;>9;>9;7 - :8/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ; ;;/;:/:6;7 ;/;:/:6;7 ;>9;>9;7 - :4/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

;=.

Vbr ac harhuato al ganurk, al hua solo s olo lota B;0;: W, I:0: K, Za0a ℧, hkchockrb cb potblzb b vbragahkrl vbragahkrlbb ac jacklhao blbrnbtaho.

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ; ;;/;:/:6;7 ;/;:/:6;7 ;>9;>9;7 - :2/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

;1.

Vbr ac harhuato raportkto al ganurk , solo lota Wa0;6¾a W , Z0Za0; ℧, dbtbràlkrb ac vkcorb da I tkcb hmb ck potblzk dassapktk lbcck rbsastblzk Z sak lucck.

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ; ;;/;:/:6;7 ;/;:/:6;7 ;>9;>9;7 - :7/7:

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus Dktk X Xtk`pk tk`pk ; ;;/;:/:6;7 ;/;:/:6;7 ;>9;>9;7 :7/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

:6.

Vbr ac harhuato al ganurk, al hua solo s olo lota W;0;: W, W:07 W, A80; K, A40: K, Za0a ℧, hkchockrb ck potblzk VZ; dassapktk lbcck rbsastblzk Z;. Z;.

XBNRB

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus Dktk X Xtk`pk tk`pk ; ;;/;:/:6;7 ;/;:/:6;7 ;>9;>9;7 :>/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus Dktk X Xtk`pk tk`pk ; ;;/;:/:6;7 ;/;:/:6;7 ;>9;>9;7 :=/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

:;.

Vbr ac harhuato al ganurk, al hua solo lota BK0>2 W, I;07 K, Z;0;: ℧, Z:0:6 ℧, Z8086 ℧, Z4016 ℧, Z2076 ℧ , ZK0;6,2 ℧

dbtbràlkrb ck potblzk dassapktk lbcck rbsastblzk ZK.

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ; ;;/;:/:6;7 ;/;:/:6;7 ;>9;>9;7 - :1/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ; ;;/;:/:6;7 ;/;:/:6;7 ;>9;>9;7 - 86/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

::.

Vbr ac harhuato raportkto al ganurk, g anurk, solo lota B;0B0;: W, Z;0; ℧, Z08 ℧, dbtbràlkrb ck potblzk bronktk dkc nblbrktorb B.

XBNRB

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ; ;;/;:/:6;7 ;/;:/:6;7 ;>9;>9;7 - 8;/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ; ;;/;:/:6;7 ;/;:/:6;7 ;>9;>9;7 - 8:/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

:8.

Vbr ac harhuato al ganurk , al hua solo lota Za0a ℧ , I0: K Dbtbràlkrbb ac vkcorb da W; tkcb hmb ck potblzk dassapktk lbcck rbsastblzk Z8 sak Dbtbràlkr s ak lucck.

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ; ;;/;:/:6;7 ;/;:/:6;7 ;>9;>9;7 - 88/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

:4.

Vbr ac harhuato al ganurk, al hua solo s olo lota W;0;: W, W807 W, I;0: K, I804 K, Z:07 ℧, hkchockrb cb potblzb b vbragahkrl vbragahkrlbb ac jacklhao blbrnbtaho.

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ; ;;/;:/:6;7 ;/;:/:6;7 ;>9;>9;7 - 84/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

:2.

Vbr ac harhuato al ganurk solo lota W ;0;: W, Ia0a K, Za0a ℧, hkchockrb ck potblzk kssorjatk dkcck rbsastblzk Z;.

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ; ;;/;:/:6;7 ;/;:/:6;7 ;>9;>9;7 - 82/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

:7.

Vbr ac harhuato al ganurk solo lota W0;: W, I ;07 K, I 808 K, Za0a ℧, Z08 ℧, hkchockrb ck potblzk VI8 dbc nblbrktorb da horrbltb I 8.

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ; ;;/;:/:6;7 ;/;:/:6;7 ;>9;>9;7 - 87/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

:>.

Vbr ac harhuato al ganurk solo lota W0;: W, Z a0a ℧, hkchockrb cb potblzb b vbragahkrl vbragahkrlbb ac jacklhao.

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ; ;;/;:/:6;7 ;/;:/:6;7 ;>9;>9;7 - 8>/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

:=.

Vbr ac harhuato al ganurk solo lota A0= K, Z0: ℧, Z;0;6 ℧, Z:07 ℧, Z807 ℧, ZR08 ℧, hkchockrb ck potblzk dassapktk al ZR.

XBNRB

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ; ;;/;:/:6;7 ;/;:/:6;7 ;>9;>9;7 - 8=/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 6;; 6;. Blbrnak al horrbltb holtaluk

Loto hmb c‑blbrnak lol sa hrbk b lol sa dastrunnb, `k puú bssbrb soco trksgor`ktk al ul kctro tapo da blbrnak b pbr tkcb trksgor`kzaolb sa a`pabnmbræ ul hbrto altbrvkcco da tb`po, possakò possakò dbgalarb ac holhbtto da blbrnak ^(t6,t) , c‑altbnrkcb dbcck potblzk lbc tb`po, tb `po, possakò Xhravbrb qualda

C‑ulatæ da àsurk dbcc‑blbrnak í ac ioucb,;I0;^*;sbh, spbsso lbcck prktahk tbhlahk utacazzakò a suoa ùctapca ho`b kd bsb`pao ac e^*m

Cbzaolb 6;: 6;. @btodo dbccb horrblta hahcahmb da `kncak

holsbltb da radurrb ac lu`bro da bqukzaola. Vbr ul dkto harhuato holsadbrakò tuttb (b soco) cb ` `kncab aldapbldblta b altroduhakò ulk horrbltb gattazak harhockltb al onlulk da bssb. Xhravbldo ck CET k tkca `kncab sa ottablb ul sastb`k da `0c-(l-;) bqukzaola hmb rasocto rbstatuashb cb horrblta gattazab da `kncak. Xb so`àkò kcnbjrahk`bltb cb horrblta gattazab hmb altbrbssklo a vkra ckta (holsadbrkldocb hoc sbnlo posatavo sb solo holhorda kcck horrbltb harhockltb lbc ckto), kvrbò ul cbnk`b trk cb horrblta gattazab b cb horrblta sua ckta, skræ hosã possajacb vkcutkrb qubstb ucta`b. Ck prohbdurk dk sbnuarb pbr kppcahkrb ac `btodo í ck sbnubltb9 - shbncabrb ulk horrbltb gattazak pbr onla `kncak aldapbldbltb aldahkldolb ac vbrso5 - orabltkrb tuttb cb horrblta gattazab lbcco stbsso vbrso (kd bsb`pao ac vbrso orkrao)5 - rkpprbsbltkrb tutta a ckta lol purk`bltb rbsastava trkàtb ac harhuato bquavkcbltb da Tmbvblal (pbr nca la ckta holtblblta soco ul nblbrktorb da horrbltb sa altroduhklo la bqukzaola)5 -tblsaola shravbrbsuaac sastb`k da `+la bqukzaola hmb rasocto gorlashb cb horrblta gattazab kccb `kncab pañ cb nblbrktora da horrbltb. Vossakò nblbrkcazzkrb ac `btodo ho`b sbnub9 ulk voctk rahkvktk ck `ktrahb dbccb rbsastblzb, sa a`polb ac sbnubltb cbnk`b trk qubst‑ucta`k ac vbttorb dbccb horrblta gattazab bd ac vbttorb dbccb tblsaola (dopo kvbrb sostatuato bvbltukca ckta holtblblta nblbrktora da horrbltb b rbsastblzb hoc

harhuato bquavkcbltb da Tmbvblal)9

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ;;/;:/:6;7 ;;/;:/:6;7 ;>9;>9;7 - 81/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Zaa 9 kuto-rbsastblzk dbcck `kncak a, sa hkchock ho`b so``k da tuttb cb rbsastblzb hmb sa alholtrklo culno ck `kncak a (prbsb hoc sbnlo posatavo). Zai 9 ùtuk rbsastblzk trk ck `kncak a-bsa`k b ck `kncak i-bsa`k, í ck rbsastblzk prbsk hoc sbnlo lbnktavo dbc ckto hoùlb trk cb `kncab a b i. Xb cb `kncab a b i lol mkllo ckta al hoùlb sa holsadbrk Zai06. Ia horrbltb gattazak dbcck `kncak a. Ba nblbrktorb da tblsaolb dbcck `kncak (sb solo pañ da ulo sa so``klo holsadbrkldo posatavb cb tblsaola hoc vbrso holhordb kcck horrbltb gattazak dbcck `kncak).

6:.

Vbr ac harhuato al ganurk ;, al hua solo lota W;0;: W , W:07 W , I0: I 0: K, Za0a ℧ Dbtbràlkrbb ck potblzk dassapktk lbcck rbsastblzk Z:. Dbtbràlkr

XBNRB

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ;;/;:/:6;7 ;;/;:/:6;7 ;>9;>9;7 - 46/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ; ;;/;:/:6;7 ;/;:/:6;7 ;>9;>9;7 - 4;/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 6;8

6;.

Vbr ac harhuato al ganurk, al hua solo s olo lota W;026 W, I076 K, Z;02 ℧, Z:046 ℧, Z80=6 ℧, Z40;:6 ℧, dbtbràlkrb ck tblsaolb WJH.

XBNRB

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ; ;;/;:/:6;7 ;/;:/:6;7 ;>9;>9;7 - 4:/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

6:. @btodo dbc potblzakcb ka loda

Ac `btodo dbc potblzakcb ka loda holsbltb da rasocvbrb ulk rbtb kvbltb c ckta rasocvbldo ul sastb`k da da`blsaola àlora da c. Holsadbrakò ul harhuato kvbltb l loda b shbncakòlb ulo da ragbra`blto5 c‑ojabttavo í qubcco da hkchockrb cb tblsaola trk nca l-; loda bd ac a c lodo da ragbra`blto, gktto qubsto possakò dbtbràlkrb qukcsaksa tblsaolb d‑altbrbssb. Cb l-; tblsaola sa possolo hkchockrb rasocvbldo ul sastb`k da l-; bqukzaola ottblutb kppcahkldo ck CEH knca l-; loda. A pkssa dk sbnuarb pbr kppcahkrb horrbttk`bltb ac `btodo al bsk`b solo a sbnublta9 - shbncabrb ul lodo ho`b ragbra`blto bd aldahkrb hol W;,W:, … Wl-; cb tblsaola bsastblta trk nca l-; loda bd ac lodo da ragbra`blto5 - rkpprbsbltkrb tutta a japoca dbcck rbtb hmb lol solo purk`bltb rbsastava trkàtb ac harhuato bquavkcbltb da Lortol. Xb ha solo lb ckta al hua í prbsbltb sock`bltb ul nblbrktorb da tblsaolb knnaulnbrb lb bqukzaola kc sastb`k5 -loda shravbrb sastb`kulk da pbr l-;+lb ho`bprbsbltb sbnub9 l-; kppcahkldo bd lbul adbltatæ, onlabqukzaola nblbrktorbottblutb da tblsaolb dk soco suc ckto.ck CEH knca l-; Xhravbldo cb bqukzaola gor`k `ktrahakcb nblbrahk`bltb sa mk

dovb Naa í dbttk kuto-holduttklzk dbc lodo a b sa hkchock ho`b so``k (hoc sbnlo posatavo) da tuttb cb holduttklzb hmb gkllo hkpo kc lodo a. Nai í dbttk ùtuk holduttklzk trk a loda a b i b sa hkchock holsadbrkldo hoc sbnlo lbnktavo cb holduttklzb prbsblta trk a loda a b i. Xb trk a loda a b i lol ha solo rbsastblzb Nai06. Ck `ktrahb dbccb holduttklzb í sa``btrahk. tblsaolb alhonlatk ac lodo a bd aca`prbssb lodo prbso k ragbra`blto. iaWaííckckso``k kcnbjrahk da trk tuttb cb horrblta kc lodo a (posatavb sb bltrklta kc lodo)

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ;;/;:/:6;7 ;;/;:/:6;7 ;>9;>9;7 - 48/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 6;4 6;. HMB HOXK XA ALTBLDB VBZ ?VOZTK? Rlk hoppak da òrsbtta al hua ck so``k dbccb horrblta (qubcck bltrkltb al ul òrsbtto b qubcck ushbltb lbcc'kctro òrsbtto) í lucck. Rlk hoppak da òrsbtta al hua ck horrbltb hmb bltrk al ul òrsbtto í ck `btæ da qubcck hmb bshb dkcc'kctro. Rlk hoppak da òrsbtta al hua ck horrbltb hmb bltrk al ul òrsbtto í ac doppao d oppao da qubcck hmb bshb dkcc'kctro. Rlk hoppak da òrsbtta al hua ck so``k dbccb horrblta (qubcck bltrkltb al ul òrsbtto b qubcck ushbltb lbcc'kctro òrsbtto) í hostkltb.

6:.

Vbr ac harhuato al ganurk, al hua í loto Z0; ℧ dbtbràlkrb ck `ktrahb dbccb rbsastblzb dbc doppao japoco ho`prbso trk cb portb ;-;‑ b :-:‑.

XBNRB

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ; ;;/;:/:6;7 ;/;:/:6;7 ;>9;>9;7 - 44/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

68.

Vbr ac harhuato al ganurk, al hua solo s olo lota Z0; ℧ , A;0; K, A:0: K, dbtbràlkrb ck potblzk kssorjatk dkc doppao japoco ho`prbso trk cb portb ;-;‑ b :-:‑.

XBNRB

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ; ;;/;:/:6;7 ;/;:/:6;7 ;>9;>9;7 - 42/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

64. Doppa japoca

Rl qukdra-poco vablb dbtto doppao-japoco sb dub dbccb horrblta da dub tbràlkca dapbldolo dkccb kctrb dub. Al pkrtahockrb sb rasuctk soddasgkttk ck holdazaolb

Al Gan.8 kjjakò nblbraho doppao-japoco. Ck holdazaolb (4) puú bssbrb vbragahktk dkcck lkturk [ubst‑uctaò altralsbhk dbc hkso ho`polbltb, ho`brkpprbsbltkto kvvablb pbr acultrksgor`ktorb, oppurb dk ho`b ac ho`polbltb í alsbrato lbc rbsto dbc harhuato. ranukrdk a doppa-japoca rbsastava b pañ al nblbrkcb a doppa-japoca hostatuata dk rbsastora, holdblsktora b alduttora. Al qubstk cbzaolb bskàlbrbò pra`k a doppa-japoca rbsastava, al pkrtahockrb altrodurrbò ck coro hkrkttbrazzkzaolb b cb proprabtæ rbcktavb b poa a doppa japoca da a`pbdblzb

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ; ;;/;:/:6;7 ;/;:/:6;7 ;>9;>9;7 - 47/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Al ul doppao-japoco a qukttro tbràlkca dbcc‑L-poco sa khhoppaklo k dub k dub. A tbràlkca hmb gor`klo ulk hoppak sa hmak`klo portk b sa prbgbrashb aldahkrca hol ;-;‑, :-:‑ ho`b gktto al Gan.8.

al ul doppao japoco cb dub portb ;-;‑ b :-:‑ solo hkrkttbrazzktb dkccb coro tblsaola, v; b v: b dkccb coro horrblta, a; b a: Woncakò ork hkrkttbrazzkrb ac doppao-japoco. Woncakò, haoí, dbtbràlkrb ck rbckzaolb gulzaolkcb hmb cbnk cb qukttro nrkldbzzb ka tbràlkca. Woncakò hbrhkrb, haoí, ul sastb`k da : bqukzaola al hua bspraàkò ul cbnk`b trk dub dbccb qukttro nrkldbzzb al gulzaolb dbccb kctrb dub. Bsastolo vkra òda da rkpprbsbltkrb tkcb cbnk`b k sbholdk sb holsadbro vkrakjaca dapbldblta tkculb nrkldbzzb klzahmá kctrb. Lbc sbnuato bcblhmakò a vkra hksa9 ;. a; b a: al gulzaolb da v; b v:. Al qubsto hkso pkrcbrbò da hkrkttbrazzkzaolb al tblsaolb. :. v; b v: al gulzaolb da a; b a:. Al qubsto hkso pkrcbrbò da hkrkttbrazzkzaolb al horrbltb. 8. v; b a: (o a; b v:) al gulzaolb da a; b v: (o v; b a:). Al qubsto hkso kjjakò ulk hkrkttbrazzkzaolb ajradk. 4. W; b ck horrbltb A; solo cb vkrakjaca aldapbldblta, ck tblsaolb W: b ck horrbltb A: solo cb vkrakjaca dapbldblta (o ac dukcb).Hkrkttbrazzkzaolb da trksàssaolb Wocbldo bskàlkrb a japoca rbsastora k tb`po alvkraklta Lbcck rkpprbsbltkzaolb su jksb horrbltb cb tblsaola W; b W: vblnolo bsprbssb al gulzaolb dbccb horrblta A; b A: kttrkvbrso cb sbnublta bqukzaola9

A pkrk`btra Z;;, Z;:, Z:; b Z:: dbc doppao japoco possolo bssbrb dbtbràlkta ho`b sbnub. Z;; í ck rbsastblzk vastk dkcck portk ; qukldo ck portk : í kpbrtk (harhuato kpbrto), í ck rbsastblzk bquavkcbltb vastk dka òrsbtta dbcck portk ; qukldo ck portk : í kpbrtk

Z:: í ck rbsastblzk vastk dkcck portk : qukldo ck portk ; í kpbrtk (harhuato kpbrto), í ck rbsastblzk bquavkcbltb vastk dka òrsbtta dbcck portk : qukldo ck portk ; í kpbrtk

Z;: bd Z:; solo hmak`ktb rbsastblzb ùtub dbc doppao japoco9 Z;: í ac rkpporto trk ck tblsaolb W; dbcck portk ; qukldo bssk í kpbrtk b c‑altblsatæ dbcck horrbltb A: . Vbr ac suo hkchoco jasonlk bspcahatkrb W; al gulzaolb da A:.

XBNRB

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ;;/;:/:6;7 ;;/;:/:6;7 ;>9;>9;7 - 4>/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Z:; í ac rkpporto trk ck tblsaolb W: dbcck portk : qukldo bssk í kpbrtk b c‑altblsatæ dbcck horrbltb A; . Vbr ac suo hkchoco jasonlk bspcahatkrb W: al gulzaolb da A;.

Xb pbr ac doppao japoco, sa rkpprbsbltklo cb tblsaola al gulzaolb dbccb horrblta ottblakò ck @ktrahb dbccb holduttklzb

Xb voncakò dbtbràlkrb ac cbnk`b bsastbltb trk ck horrbltb al ushatk A: b ck tblsaolb al alnrbsso W;, hol ck horrbltb da alnrbsso A; b dbcck tblsaolb da ushatk W:, dojjakò vkcutkrb ck @ktrahb ajradk M

Xb sa holsadbrklo ck tblsaolb b ck horrbltb da alnrbsso al gulzaolb dbcck horrbltb b dbcck tblsaolb da ushatk, sa ottablb ck @ktrahb da trksàssaolb T dbc doppao japoco

62. Doppa japoca k T

Ac doppao japoco k T í rkpprbsbltkto dkcck sbnubltb holganurkzaolb bcbttrahk

B‑ possajacb rkpprbsbltkrb ul doppao japoco da hua í lotk ck `ktrahb dbccb rbsastblzb trkàtb ck holganurkzaolb k T

Xb solo lota a vkcora dbcck `ktrahb dbccb rbsastblzb (Z;;, Z;:, Z::, Z:;) sa possolo rahkvkrb cb rbsastblzb dbcck holganurkzaolb k T (Zk, Zj bd Zh) b vahbvbrsk. Xa utacazzklo cb sbnublta bsprbssaola9

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ;;/;:/:6;7 ;;/;:/:6;7 ;>9;>9;7 - 4=/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

B‑ possajacb pksskrb dkcck rkpprbsbltkzaolb k T k qubcck k Φ b vahbvbrsk trkàtb cb sbnublta bsprbssaola

67. Doppa japoca k pa-nrbhk

Ac doppao japoco k Φ í rkpprbsbltkto dkcck sbnubltb holganurkzaolb bcbttrahk

B‑ possajacb rkpprbsbltkrb ul doppao japoco pbr ac qukcb í lotk ck `ktrahb dbccb holduttklzb trkàtb ck holganurkzaolb k Φ. Xb solo lota a vkcora dbcck `ktrahb dbccb holduttklzb (N;;, N;:, N::, N:;) sa possolo rahkvkrb cb holduttklzb dbcck holganurkzaolb k Φ (Nx, Ny b Nz) b vahbvbrsk. Xa utacazzklo cb sbnublta bsprbssaola9

B‑ possajacb pksskrb dkcck rkpprbsbltkzaolb k T k qubcck k Φ b vahbvbrsk trkàtb cb sbnublta bsprbssaola XBNRB

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ;;/;:/:6;7 ;;/;:/:6;7 ;>9;>9;7 - 41/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ;;/;:/:6;7 ;;/;:/:6;7 ;>9;>9;7 - 26/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 6;2 6;. Harhuata lol calbkra

A harhuata lol calbkra solo harhuata al hua kc`blo ul ho`polbltb lol í calbkrb. Vbr studakrb tkca harhuata í possajacb prohbdbrb pbr vak klkcatahk `k ac òdo pañ sb`pcahb í prohbdbrb pbr vak nrkgahk. Ac sa`joco nrkgaho utacazzkto pbr aldahkrb ul japoco lol calbkrb í ac sbnubltb

A japoca lol calbkra solo hkrkttbrazzkta dk ulk hkrkttbrastahk lbc paklo W-A (o A-W) hmb lol í ulk rbttk oppurb í ulk rbttk hmb lol pkssk pbr c‑oranalb. Ho`b khhbllkto í a`portkltb dbtbràlkrb pbr vak nrkgahk ac pulto da ckvoro dbc japoco lol calbkrb hmb hoalhadb hol c‑altbrsbzaolb trk dub hurvb9 ck hkrkttbrastahk W-A dbc japoco lol calbkrb b ck hkrkttbrastahk W-A bquavkcbltb dbcck rbtb k hua ac ho`polbltb lol calbkrb í hollbsso. Al dapbldblzk dk ho`b í gkttk ck hkrkttbrastahk dbc japoco lol calbkrb potrbjjbro bssbrha pañ da ul pulto da altbrsbzaolb. Wocbldo gkrb ul bsb`pao holsadbrkldo ul daodo b ul rbsastorb al sbrab

Zaportkldo cb hkrkttbrastahb W-A pbr a dub japoca

Vbr ottblbrb ck hkrkttbrastahk dbc hoccbnk`blto sbrab jasonlk so``krb cb tblsaola sua japoca k pkratæ da horrbltb hmb ca kttrkvbrsk, sa ottablb ck hkrkttbrastahk W-A trkttbnnaktk.

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ;;/;:/:6;7 ;;/;:/:6;7 ;>9;>9;7 - 2;/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

6:.

Vbr ac harhuato al ganurk, al hua solo s olo lota W0;: W, Z0: ℧, Z;0; ℧, dbtbràlkrb ck potblzk VZ; kssorjatk dkcck rbsastblzk Z; b ck tblsaolb WKJ hol ac tksto T kpbrto. kpbrto.

XWOCNA@BLTO

XBNRB

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ; ;;/;:/:6;7 ;/;:/:6;7 ;>9;>9;7 - 2:/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

68.

Vbr ac harhuato al ganurk, al hua solo s olo lota W0;: W, Za0a ℧, dbtbràlkrb c‑blbrnak c‑blbrnak ^ trksgbratk dkc sastb`k kcc‑utacazzktorb R al :4 orb.

XBNRB

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ; ;;/;:/:6;7 ;/;:/:6;7 ;>9;>9;7 - 28/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

64.

Vbr ac harhuato al ganurk, al hua solo s olo lota W0;: W , Za0a ℧ , Dbtbràlkrbb c‑blbrnak ^ trksgbratk dkc ssastb`k Dbtbràlkr astb`k kcc‑utacazzktorb R al :4 orb.

XBNRB

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ; ;;/;:/:6;7 ;/;:/:6;7 ;>9;>9;7 - 24/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ; ;;/;:/:6;7 ;/;:/:6;7 ;>9;>9;7 - 22/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

62.

Vbr ac harhuato raportkto al ganurk, al hua solo lota W0;: W , Za0a ℧, dbtbràlkrb ac vkcorb dbcck rbsastblzk Z tkcb hmb ac trksgbra`blto da potblzk ka òrsbtta KJ sak `kssaò.

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ; ;;/;:/:6;7 ;/;:/:6;7 ;>9;>9;7 - 27/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

67.

Dkto ac harhuato lol calbkrb al ganurk, al hua solo lotb B0;: W, Z;0; ℧, Z:0; ℧, Z80: ℧, ck hkrkttbrastahk (W-A) dbc japoco lol calbkrb, dbtbràlkrb ck potblzk kssorjatk (o nblbrktk) dkc japoco lol calbkrb.

XBNRB

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ; ;;/;:/:6;7 ;/;:/:6;7 ;>9;>9;7 - 2>/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ; ;;/;:/:6;7 ;/;:/:6;7 ;>9;>9;7 - 2=/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 6;> 6;. DKTK CK NZKLDBYYK XALRXOADKCB x(t)0]@sbl(o`bnkt+ga) x(t)0]@sbl(o`bnkt+ga) ac suo gksorb í9 ]0v:]bi(o`bnkt) ]0v:]bi(ga) ]0v:]bi(o`bnkt+ga) ]0]bi(ga) 6:. CK GZB[RBLYK XA @AXRZK AL MY HAHCA/@AL XBHOLDA ZKD/XBH 68. g026 Mz XANLAGAHK pucskzaolb08;44 rkd/sbh pucskzaolb08; ck pucskzaolb lol í dbgalajacb pucskzaolb0algalato pucskzaolb0algal ato rkd/sbh pucskzaolb06 rkd/sbh 64. Nrkldbzzb salusoadkca

Ck nrkldbzzk salusoadkcb í ulk nrkldbzzb kctbrlktk, . A òtava dbcc‑a`portklzk da tkca nrkldbzzb solo òctbpcaha9 al Atkcak cb tblsaola b cb horrblta pbr usa a`pakltastaha solo da tapo salusoadkcb hol grbqublzk pkra k 26 Mz5 aloctrb, sb holoshakò ac ho`portk`blto da ul harhuato calbkrb b tb`po-alvkrakltb lba holgrolta da qukculqub salusoadb holoshakò ac ho`portk`blto dbc harhuato lba holgrolta da qukcsaksa sbnlkcb. Dbgalakò nrkldbzzk salusoadkcb ulk nrkldbzzk ck hua bsprbssaolb klkcatahk í ck sbnubltb9 v(t ) 0W@ ⋂ sbl(ρt +λ ) (gor`k tranolo`btrahk)

Ck rkpprbsbltkzaolb nrkgahk í raportktk lbcck ganurk sbnubltb. A pkrk`btra hmb hkrkttbrazzklo cb nrkldbzzb salusoadkca solo9 - ac pbraodo T, hmb í ac tb`po a`pabnkto dkcck nrkldbzzk pbr kssu`brb tutta a possajaca vkcora. Ho`b darbttk holsbnublzk sa mk ck grbqublzk g0;/T hmb í ac lu`bro da hahca kc sbholdo ho`pauta dkcck `kssaò nrkldbzzk5 - ac vkcorb W@ haoí ac vkcorb `kssaò kssulto dkcck nrkldbzzk5 - ac vkcorb bggahkhb Wbgg 0W@/∙: (lbc hkso da horrblta bcbttrahmb ac vkcorb bggahkhb í qubc vkcorb hmb dovrbjjb kvbrb ulk horrbltb holtaluk pbr kvbrb nca stbssa bggbtta tbràha)5 - ck pucskzaolb ρ o grbqublzk klnockrb ρ0:φg sa àsurk al rkd/sbh.5 - λ klnoco da gksb dbcck nrkldbzzk kcc‑astkltb kcc‑astklt b t06 bsprbsso al rkdaklta o al nrkda

Xaklo dktb dub nrkldbzzb salusoadkca bsprbssb al gor`k tranolo`btrahk v;(t) b v:(t) (kd bsb`pao dub tblsaola),

XBNRB © :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ;;/;:/:6;7 ;;/;:/:6;7 ;>9;>9;7 - 21/7:

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 6;>

62. Nrkldbzzb pbraodahmb

Cb nrkldbzzb pbraodahmb solo rkpprbsbltkjaca trkàtb gulzaola dbc tb`po hmb kssuòlo tutta a vkcora possajaca al ul dbtbràlkto altbrvkcco da tb`po T. Tutta a vkcora sa rapbtolo ordalktk`bltb lbnca altbrvkcca da tb`po suhhbssava b da k`pabzzk T. Ac pkrk`btro T hkrkttbrazzk ck gulzaolb, í hmak`kto pbraodo b ck suk ulatæ da àsurk í ac sbholdo. Xb ck nrkldbzzk pbraodahk mk ac vkcorb `bdao lbc pbraodo pkra k zbro darbò hmb bssk í ulk nrkldbzzk kctbrlktk. Ck qukltatæ hmb sa ottablb dkcc‑bsprbssaolb g0;/T í dbttk grbqublzk b rkpprbsbltk ac lu`bro da pbraoda kc sbholdo, bssk sa àsurk al mbrtz (Mz). Octrb kc pbraodo, ul kctro pkrk`btro lbhbsskrao k dbgalarb cb nrkldbzzb kctbrlktb í ck gor`k d‑oldk, haoíbsprbssaolb ck cbnnb holklkcatahk hua vkrakoppurb ck nrkldbzzk ul pbraodo. Tkcb cbnnb puú bssbrb dbgalatk trkàtb ul‑ al gor`kalnrkgahk. Lbcck ganurk hmb sbnuolo raportakò ul bsb`pao da nrkldbzzk pbraodahk

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ;;/;:/:6;7 ;;/;:/:6;7 ;>9;>9;7 - 76/7:

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Cbzaolb 6;>

67. Lu`bra ho`pcbssa al gor`k bspolblzakcb

Rskldo ck gorùck da Bucbro

o bquavkcbltb`bltb ck dbgalazaolb da bspolblzakcb ho`pcbsso, í possajacb rkpprbsbltkrb ul lu`bro ho`pcbsso al gor`k bspolblzakcb

Xak dkto ul lu`bro ho`pcbsso W al gor`k hkrtbsaklk, qualda saklo lotb ck suk pkrtb rbkcb Wx b ck suk pkrtb a``knalkrak Wy, possakò hkchockrb ac suo òduco b ck suk gksb, qubsta dub vkcora holsbltolo da rkpprbsbltkrb ac lu`bro ho`pcbsso al gor`k bspolblzakcb

[ubstk í ck lotkzaolb hmb vablb pañ grbqubltb`bltb utacazzktk lbccb kppcahkzaola al hua òduco b gksb kjjaklo ul sanlagahkto prbàlbltb raspbtto k pkrtb rbkcb bd a``knalkrak (kd bsb`pao pbr ck dbshrazaolb dba gksora), b prbgbratk kcck rkpprbsbltkzaolb pockrb pbr ck `knnaor ho`pkttbzzk b pbr ck `knnaor prktahatæ lbcco svocna`blto da opbrkzaola da òctapcahkzaolb (b holsbnubltb`bltb da bcbvk`blto k potblzk).

6>. Lu`bra ho`pcbssa al gor`k hkrtbsaklk

Rl blu`bro ho`pcbsso –W‐ í alWy. gor`k hkrtbsaklk, sb bsso í rkpprbsbltkto lbc paklo ho`pcbsso trkàtb ck suk pkrtb rbkcb Wx ck suk pkrtb a``knalkrak

Wkcnolo cb sbnublta rbckzaola

Kppcahkldo c‑opbrktorb i kd ul lu`bro ho`pcbsso –W‐ , sa ottablb ul lu`bro ho`pcbsso hmb mk co stbsso òduco,

`k rasuctk sgkskto da φ /: lbc sblso kltaorkrao (darbò φ /: o 16¶ al kltahapo). © :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ;;/;:/:6;7 ;;/;:/:6;7 ;>9;>9;7 - 7;/7:

XBNRB

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Cbzaolb 6;>

6=. Lu`bra ho`pcbssa al gor`k pockrb

Vossakò rkpprbsbltkrb ul lu`bro ho`pcbsso W al gor`k pockrb holsadbrkldo ac òduco W b ck gksb λ. Xak dkto ul lu`bro ho`pcbsso W al gor`k hkrtbsaklk, qualda saklo lotb ck suk pkrtb rbkcb Wx b ck suk pkrtb a``knalkrak Wy, possakò hkchockrb ac suo òduco b ck suk gksb (o krno`blto), qubsta dub vkcora holsbltolo da rkpprbsbltkrb ac lu`bro ho`pcbsso al gor`k pockrb

XBNRB

© :6;7 Rlavbrsatæ Rlavbrsatæ Tbcb`ktahk Tbcb`ktahk bHk`pus bHk`pus - Dktk X Xtk`pk tk`pk ;;/;:/:6;7 ;;/;:/:6;7 ;>9;>9;7 - 7:/7:

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Cbzaolb 6;>

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Cbzaolb 6;= 6;. ]0]bi(ga) B' AC GKXOZB DBCCK NZKLDBYYK XALRXOADKCB XALRXOADKCB x(t)0v:]sbl(ga) x(t)0v:]sbl(o`bnkt+ga)

x(t)0]sbl(o`bnkt+ga) x(t)0]sbl(o`bnkt)

6:.

Vbr ac harhuato raportkto al ganurk, g anurk, gulzaolkltb al rbna`b salusoadkcb, suppolbldo lotb tuttb cb nrkldbzzb. dasbnlkrb ac daknrk``k vbttorakcb qukcatktavo dbccb stbssb (prbldbrb AZ k gksb zbro).

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Cbzaolb 6;=

68. Zkpprbsbltkz Zkpprbsbltkzaolb aolb da salusoada hol gksora

Rlk nrkldbzzk salusoadkcb , dovb W@, ρ b λ solo raspbttavk`bltb ac vkcorb `kssaò, ck pucskzaolb b ck gksb, í possajacb rkpprbsbltkrck kttrkvbrso ck proabzaolb su ul kssb (holsadbrakò qu qubcco bcco a``knalkrao) , da ul vbttorb rotkltb hol vbcohatæ klnockrb

ac vbttorb rotkltb mk òduco pkra k W@ hmb ruotk al sblso kltaorkrao lbc paklo ho`pcbsso ho`pabldo ul naro ho`pcbto pbr onla pbraodo T dbcck salusoadb5 sb holsadbrakò ck proabzaolb da tkcb vbttorb rotkltb succ‑kssb a``knalkrao ottblakò pbr onla t ac vkcorb dbcck v(t).

Dbgalakò gksorb da ulk nrkldbzzk salusoadkcb v(t) ck qukltatæ

64.

Vbr ac harhuato raportkto al ganurk, al hua solo lota Ya0a+i4 ℧, Y08+i: ℧, dbtbràlkrb c‑a`pbdblzk c‑a`pbdblzk bquavkcbltb ka òrsbtta K-K‑.

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Cbzaolb 6;=

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Cbzaolb 6;1 6;. AL RLK ZBXAXTBLYK HOZZBLTB B TBLXAOLB XOLO AL GKXB CK HOZZBLTB B' AL ZATKZDO DA 16¶ XRCCK TBLXAOL TBLXAOLB B HOZZBLTB B TBLXAOLB XOLO AL OVVOXAYAOLB DA GKXB CK HOZZBLTB B' AL KLTAHAVO DA 16¶ XRCCK TBLXAOLB 6:. VBZ RL ALDRTTOZB CALBKZB B TB@VO ALWKZAKLT ALWKZAKLTB B Ck tblsaolb í al kltahapo da 16¶ succk horrbltb Ck horrbltb í al kltahapo da 16¶ succk tblsaolb Horrbltb b tblsaolb solo al gksb W0CA 68. C'A@VBDBLYK XA @AXRZK AL ^KTT K@VBZB OM@ WOCT 64. DKTK C'A@VBDBLYK Y0Z+i]C 9 Z0Ytnga Z0W/A Z0Ysblga Z0Yhosga 62. Harhuato purk`bltb hkpkhatavo

Rl harhuato purk`bltb hkpkhatavo í hostatuato dk ul nblbrktorb da tblsaolb hoccbnkto kd ulk holdblsktorb, sb apotazzakò hmb ac nblbrktorb da tblsaolb sak salusoadkcb hmb cb ac holdblsktorb sak Calbkrb k tb`po alvkrakltb ck horrbltb harhockltb suc harhuato a(t) skræ cbnktk kcck tblsaolb ka hkpa dbc holdblsktorb Wh(t) dkcck sbnubltb rbckzaolb , kldkldo kd bsbnuarb a hkchoca ottblakò 9

Dkccb bqukzaola prbhbdblta sa bvalhb hmb9 • ac òduco W@ dbc gksorb rbcktavo kcck vH(t) í pkra kc òduco A@ dbc gksorb dbcck a(t) òctapcahkto ;/ρH, dovb ]h0;/ρH vablb dbgalatk ho`b rbkttklzk hkpkhatavk U℧P5 • a dub gksora solo sgkskta trk da coro da φ /: (16¶) hol ck tblsaolb al ratkrdo. Wocbldo saltbtazzkrb ac ho`portk`blto dbc harhuato apotazzkldo ]h0:om`5

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Cbzaolb 6;1 67. Harhuato purk`bltb omàho

Rl harhuato purk`bltb omàho í hostatuato dk ul nblbrktorb da tblsaolb hoccbnkto kd ulk rbsastblzk, sb apotazzakò hmb ac nnblbrktorb blbrktorb da tblsaolb sak salusoadkcb hmb ck rbsastblzk sak Calbkrb k tb`po alvkrakltb ck horrbltb harhockltb suc harhuato a(t)

ck tblsaolb ka hkpa dbcck rbsastblzk skræ salusoadkcb b pbr ck cbnnb da Om` vkrræ vZ(t)0Z*a(t)

Dkccb bqukzaola sa bvalhb hmb9 • ac òduco W@ dbc gksorb dbcck vZ(t) í pkra kc òduco A@ dbc gksorb dbcck a(t) òctapcahkto Z5 • a dub gksora mkllo ck stbssk gksb (darbò hmb tblsaolb b horrbltb solo al gksb).

Wocbldo saltbtazzkrb ac ho`portk`blto dbc harhuato purk`bltb omàho apotazzkldo Z0: ℧.

6>. Harhuato purk`bltb alduttavo

Rl harhuato purk`bltb alduttavo í hostatuato dk ul nblbrktorb da tblsaolb hoccbnkto kd ul alduttorb, alduttorb, sb apotazzakò hmb ac nblbrktorb da tblsaolb sak salusoadkcb hmb c‑alduttorb sak Calbkrb k tb`po alvkrakltb, ck horrbltb harhockltb suc harhuato a(t)

ck tblsaolb ka hkpa dbcc‑alduttorb skræ salusoadkcb b vkrræ vC(t)0C*da(t)/dt

Dkccb bqukzaola sa bvalhb hmb9 • ac òduco W@ dbc gksorb rbcktavo kcck tblsaolb vC(t) í pkra kc òduco A @ dbc gksorb dbcck horrbltb a(t) òctapcahkto ρC, dbgalakò ]C0ρC ho`b rbkttklzk alduttavk U℧P5 • a dub gksora solo sgkskta trk da coro da φ /: (16¶) hol ck tblsaolb al kltahapo.

Wocbldo saltbtazzkrb ac ho`portk`blto dbc harhuato purk`bltb alduttavo apotazzkldo apota zzkldo ]C0: Om`

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:= - 81/>8

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Cbzaolb 6;1

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Cbzaolb 6:6 6;. A TZB VKZK@BTZA DA RL'A@VBDBLYK (Z,],Y) VOXXOLO BXXBZB ZKVVZBXBLTKTA TZK@ATB RL TZAKLNOCO XA DBWOLO ZKVVZBXBLTKZB TZK@ATB RL TZAKLNOCO ZBTTKLNOCO LOL VOXXOLO BXXBZB ZKVVZBXBLTKTA TZK@ATB RL TZAKLNOCO ZBTTKLNOCO VOXXOLO BXXBZB ZKVVZBXBLTKTA XR RLK ZBTTK 6:. Harhuato ZC pkrkccbco

Rl harhuato ZC pkrkccbco í hostatuato dk ul nblbrktorb da tblsaolb hoccbnkto kd ul alduttorb al pkrkccbco kd ulk rbsastblzk (vbda ganurk), sb apotazzakò hmb ac nblbrktorb da tblsaolb sak salusoadkcb hmb c‑alduttorb b ck rbsastblzk sak Calbkrb k tb`po alvkrakltb, ck horrbltb harhockltb suc harhuato a(t) kppcahkldo ck CEH kc lodo skræ dktk dk 9

Q í c‑k``bttblzk, N0;/Z í ck holduttklzk, JC0;/]C í ck sushbttklzk alduttavk. Q, N b JC sa àsurklo al Xab`bls UXP.

Wkcnolo cb sbnublta rbckzaola

Q í ac òduco dbcc‑k``bttblzk, θ í c‑klnoco hkrkttbrastaho dbcc‑k``bttblzk ovvbro c‑klnoco trk ck horrbltb b ck tblsaolb ovvbro klhork c‑klnoco ho`prbso trk a gksora dbcck horrbltb b dbcck tblsaolb. Ck horrbltb A í al ratkrdo succk tblsaolb B dbcc‑klnoco hkrkttbrastaho θ. A vbttora tblsaolb b horrbltb stkllo trk coro ho`b raportkto lbc sbnubltb daknrk``k vbttorakcb.

Vbr ottblbrb ac traklnoco dbcc‑k``bttblzk jkstk davadbrb ac daknrk``k vbttorak pbr B

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Cbzaolb 6:6 68. Harhuato ZH pkrkccbco

Rl harhuato ZH pkrkccbco í hostatuato dk ul nblbrktorb da tblsaolb hoccbnkto kd ul holdblsktorb al pkrkccbco kd ulk rbsastblzk (vbda ganurk), sb apotazzakò hmb ac nblbrktorb da tblsaolb sak salusoadkcb hmb ac holdblsktorb b ck rbsastblzk saklo Calbkra k tb`po alvkrakltb, ck horrbltb harhockltb suc harhuato a(t) kppcahkldo ck CEH kc lodo skræ dktk dk 9

í c‑k``bttblzk, N0;/Z í ck holduttklzk, JH0;/]H í ck sushbttklzk hkpkhatavk. Q, N b JH sa àsurklo al Xab`bls UXP. Wkcnolo cb sbnublta rbckzaola Q

í ac òduco dbcc‑k``bttblzk, θ í c‑klnoco hkrkttbrastaho dbcc‑k``bttblzk ovvbro c‑klnoco trk ck horrbltb b ck tblsaolb ovvbro klhork c‑klnoco ho`prbso trk a gksora dbcck horrbltb b dbcck tblsaolb . Ck horrbltb í al kltahapo succk tblsaolb dbcc‑klnoco hkrkttbrastaho θ. Xb raportakò su ul daknrk``k cb horrblta b cb tblsaola ottbrrbò ac sbnubltb daknrk``k vbttorakcb.

Vbr ottblbrb ac traklnoco dbcc‑k``bttblzk jkstk davadbrb ac daknrk``k vbttorakcb pbr B

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Cbzaolb 6:6

64.

Vbr ac harhuato raportkto al ganurk, g anurk, suppolbldo lotb cb nrkldbzzb W0:86 W, Z;0:6 ℧, Z:0;6 ℧, Z808 ℧, ]C;08>,> ℧, ]H:028,; ℧, ]C804 ℧ Dbtbràlkrbb ck horrbltb A , ck tblsaolb WKJ, cb horrblta AZ bd AC Dbtbràlkr AC

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Cbzaolb 6:6 62. Harhuato ZC sbrab

Rl harhuato Zc pkrkccbco í hostatuato dk ul nblbrktorb da tblsaolb hoccbnkto kd ul alduttorb al sbrab kd ulk rbsastblzk (vbda ganurk), sb apotazzakò hmb ac nblbrktorb da tblsaolb sak salusoadkcb hmb c‑alduttorb b ck rbsastblzk saklo Calbkra k tb`po alvkrakltb, kppcahkldo

ck CEH CEH kcck `kncak ck tblsaolb tblsaolb skræ dktk dk

Wkcnolo cb sbnublta rbckzaola9

Y í ac òduco dbcc‑a`pbdblzk, θ í c‑klnoco hkrkttbrastaho dbcc‑a`pbdblzk, ovvbro c‑klnoco trk cb dub salusoada horrbltb a(t) b tblsaolb b(t) ovvbro klhork c‑klnoco ho`prbso trk a rbcktava gksora. Ck horrbltb í al ratkrdo succk tblsaolb dbcc‑klnoco hkrkttbrastaho θ. A vbttora stkllo trk da coro ho`b raportkto lbc sbnubltb daknrk``k vbttorakcb.

Vbr ottblbrb ac traklnoco dbccb a`pbdblzb davadakò ac daknrk``k vbttorakcb pbr A

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Cbzaolb 6:6 67. Harhuato ZH sbrab

Rl harhuato ZH sbrab í hostatuato dk ul nblbrktorb da tblsaolb hoccbnkto kd ul holdblsktorb al sbrab kd ulk rbsastblzk (vbda ganurk), sb apotazzakò hmb ac nblbrktorb da tblsaolb sak salusoadkcb hmb ac holdblsktorb b ck rbsastblzk saklo Calbkra k tb`po alvkrakltb, kppcahkldo ck CEH kcck `kncak ck tblsaolb skræ dktk dk

Wkcnolo cb sbnublta rbckzaola9

Y í ac òduco dbcc‑a`pbdblzk, θ í c‑klnoco hkrkttbrastaho dbcc‑a`pbdblzk, ovvbro c‑klnoco trk cb dub salusoada horrbltb a(t) b tblsaolb b(t) ovvbro klhork c‑klnoco ho`prbso trk a raspbttava gksora. Ck horrbltb í al kltahapo succk tblsaolb dbcc‑klnoco hkrkttbrastaho θ. A vbttora stkllo trk da coro ho`b raportkto lbc sbnubltb daknrk``k vbttorakcb

Vbr ottblbrb ac traklnoco dbccb a`pbdblzb davadakò ac daknrk``k vbttorakcb pbr A

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Cbzaolb 6:; 6;. LBCCB A@VBDBLYB AL VKZKCCBCO V KZKCCBCO VOXXOLO BXXBZB HOCCBNKTB AL VKZKCCBCO XOCO A@VBDBLYB KWBLTA CO XTBXXO WKCOZB CK TBLXAOLB TOTKCB WABLB XRDDAWAXK TZK CB A@VBDBLYB, TRTTB CB A@VBDBLYB XOLO KTTZKWBZXKTB DKCCK XTBXXK HOZZBLTB CK HOZZBLTB TOTKCB WABLB XRDDAWAXK TZK CB A@VBDBLYB, TRTTB CB A@VBDBLYB XOLO XONNBTTB KCCK XTBXXK TBLXAOLB RL VKZKCCBCO DA A@VBDBLYB VRÚ BXXBZB XOXTATRATO DK RLK A@VBDBLYB AC HRA WKCOZB Í DKTO DKCCK XO@@K DBCCB A@VBDBLYB HOALWOCTB LBC VKZKCCBCO

6:. LBCCB A@VBDBLYB AL XBZAB CK TBLXAOLB TOTKCB WABLB XRDDAWAXK TZK CB A@VBDBLYB, TRTTB CB A@VBDBLYB XOLO KTTZKWBZXKTB DKCCK XTBXXK HOZZBLTB RLK XBZAB DA A@VBDBLYB A@VCAHK RLK VKZTAYAOLB DBCCK HOZZBLTB XR ONLA A@VBDBLYB CK HOZZBLTB TOTKCB WABLB XRDDAWAXK TZK CB A@VBDBLYB, TRTTB CB A@VBDBLYB XOLO XONNBTTB KCCK XTBXXK TBLXAOLB RLK XBZAB DA A@VBDBLYB XA MK XOCO [RKLDO DRB A@VBDBLYB MKLLO CO XTBXXO WKCOZB

68. Harhuato ZCH pkrkccbco

Rl harhuato ZCH pkrkccbco í hostatuato dk ul nblbrktorb da tblsaolb hoccbnkto kd ul holdblsktorb, ul alduttorb b ulk rbsastblzk al pkrkccbco(vbda ganurk), sb apotazzakò hmb ac nblbrktorb da tblsaolb sak salusoadkcb hmb ac holdblsktorb ck rbsastblzk b c‑alduttorb saklo Calbkra k tb`po alvkrakltb, kppcahkldo ck CEH kc lodo, ck horrbltb skræ dktk dk

Q

í c‑k``bttblzk, N0;/Z í ck holduttklzk, JC0;/]C í ck sushbttklzk alduttavk, JH0;/]H í ck sushbttklzk hkpkhatavk.

θ í

c‑klnoco hkrkttbrastaho dbcc‑k``bttblzk ovvbro c‑klnoco trk ck horrbltb b ck tblsaolb ovvbro klhork c‑klnoco ho`prbso trk a gksora dbcck horrbltb b dbcck tblsaolb. Ck horrbltb í al ratkrdo/kltahapo succk tblsaolb dbcc‑klnoco hkrkttbrastaho θ. Ac daknrk``k vbttorakcb hmb sbnub accustrk cb posazaola rbhaprohmb trk a vbttora.

Davadbldo ac daknrk``k pbr B ottblakò ac traklnoco dbcc‑k``bttblzk

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:= - 47/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 6:; 64. Harhuato ZCH sbrab

Rl harhuato ZCH sbrab í hostatuato dk ul nblbrktorb da tblsaolb hoccbnkto kd ul holdblsktorb, ul alduttorb b ulk rbsastblzk al sbrab (vbda ganurk), sb apotazzakò hmb ac nblbrktorb da tblsaolb sak salusoadkcb hmb ac holdblsktorb ck rbsastblzk b c‑alduttorb saklo Calbkra k tb`po alvkrakltb, kppcahkldo ck CEH kcck `kncak , ck tblsaolb skræ dktk dk

θ í c‑klnoco hkrkttbrastaho dbcc‑a`pbdblzk ovvbro c‑klnoco trk ck horrbltb b ck tblsaolb ovvbro klhork c‑klnoco ho`prbso trk a raspbttava gksora. Ck horrbltb í al ratkrdo/kltahapo succk tblsaolb dbcc‑klnoco hkrkttbrastaho θ. Ac daknrk``k vbttorakcb

hmb sbnub accustrk cb posazaola rbhaprohmb trk a vbttora.

Davadbldo ac daknrk``k pbr A ottblakò ac traklnoco dbcc‑a`pbdblzk

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Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 6:: 6;. AL RL HAZHRATO9 Ck potblzk kttavk nblbrktk í lucck Ck so``k dbccb potblzb kttavb kssorjatb í pkra k zbro Ck so``k dbccb potblzb kttavb kssorjatb í unukcb kcck so``k dbccb potblzb kttavb nblbrktb Ck so``k dbccb potblzb rbkttavb nblbrktb í pkra k zbro 6:. C'BLBZNAK KTTAWK XA @AXRZK AL OM@ WKZ ^m WK 68. VBZ RL HAZHRATO CK VOTBLYK KVVKZBLTB HO@VCBXXK TOTKCB K VRO' BXXBZB OTTBLRTK9 Xo``kldo vbttorakc`bltb vbttorakc`bltb cb Ka da tutta a japoca Xo``kldo krat`btahk`bltb cb Ka da tutta a japoca Ho`b K0WA Xo``kldo kcnbjrahk`bltb kcnbjrahk`bltb cb Ka da tutta a japoca 64. VBZ RLK HKVKHATK' XA MK9 V 06, [ davbrsk dk 6, K0[ V davbrsk dk 6, [ 0 6, K0V V davbrsk dk 6, [ davbrsk dk 6, K0[ V 06, [ davbrsk dk 6, K0V 62. CB VOTBLYB KTTAWK-ZBKTTAWK-KVVK KTTAWK-ZBKTTAWK-KVVKZBLTB ZBLTB HO@VCBXXK VOXXOLO BXXBZB ZKVVZBXBLTKTB TZK@ATB RL TZAKLNOCO VOXXOLO BXXBZB ZKVVZBXBLTKTB XR RLK ZBTTK VOXXOLO BXXBZB ZKVVZBXBLTKTB TZK@ATB RL TZAKLNOCO ZBTTKLNOCO LOL VOXXOLO BXXBZB ZKVVZBXBLTKTB TZK@ATB RL TZAKLNOCO ZBTTKLNOCO 67. VBZ RLK ALDRTTKLYK XA MK9 V 06, [ davbrsk dk 6, K0[ V davbrsk dk 6, [ 0 6, K0V V davbrsk dk 6, [ davbrsk dk 6, K0[ V 06, [ davbrsk dk 6, K0V 6>. VBZ RLK ZBXAXTBLYK XA MK9 V davbrsk dk 6, [ davbrsk dk 6, K0[ V 06, [ davbrsk dk 6, K0V V 06, [ davbrsk dk 6, K0[ V davbrsk dk 6, [ 0 6, K0V

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6=. CK VOTBLYK ZBKTTAWK XA @AXRZK AL IORCB WK ^KTT WKZ 61. CK VOTBLYK KVVKZBLTB HO@VCBXXK K0V+i[ VRO' BXXBZB HKCHOCKTK HO@B9 K0v(V:+[:) K0WA* K0W*A K0WA

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;6. Votblzb al horrbltb salusoadkcb

p(t) 0 0 v(t)¾a(t) Vossakò dbgalarb ck potblzk astkltklbk ho`b prodotto9 p(t) hmb, í rkpprbsbltktk dk ulk salusoadb, pbrú hol grbqublzk doppak raspbtto k qubcck da tblsaolb b horrbltb. Al rbckzaolb kc tapo da hkraho (omàho, alduttavo, hkpkhatavo, bhh), tblsaolb b horrbltb prbsbltbrkllo horrbltb prbsbltbrkllo rkpporta da gksb davbrsa, gktto hmb kvræ a`portklta rapbrhussaola succk potblzk. Vbr ul hkraho purk`bltb omàho (soco omàho (soco rbsastblzk) ossbrvakò hmb cb hurvb da tblsaolb b horrbltb solo al gksb9 zbra, `kssaà b àlaà sa horraspoldolo. Al qubsto hkso ck potblzk astkltklbk astkltklbk í ulk salusoadb da grbqublzk doppak b tuttk posatavk. Xb ac hkraho í purk`bltb alduttavo alduttavo (soco (soco alduttorb) ck horrbltb í al qukdrkturk al ratkrdo raspbtto kcck tblsaolb. Ck potblzk astkltklbk í astkltklbk í sb`prb ulk salusoadb da grbqublzk doppak, `k kctbrlktavk`bltb posatavk b lbnktavk. hkpkhatavo (soco (soco holdblsktorb), ck horrbltb í al qukdrkturk al kltahapo succk tblsaolb, b ck potblzk Hol hkraho purk`bltb hkpkhatavo astkltklbk mk astkltklbk mk ul kldk`blto saàcb k qubcco dbc hkso prbhbdbltb, `k opposto. Dub salusoada solo al qukdrkturk qukldo solo spostktb da φ /: (16¶) c'ulk raspbtto kcc'kctrk. Haú gk sã hmb knca zbra dbcc'ulk horraspoldklo a `kssaà (àlaà) dbcc'kctrk. Lbc hkso nblbraho japoco v(t)0W@hos(ρt+ΧW) b hmb a(t)0A@hos(ρt+Χa), ck potblzk astkltklbk p(t) vkcb

kjjakò posto W0W@/∙:, A0A@/∙: b Χ0ΧW-ΧA , tkca nrkldbzzb rkpprbsbltklo raspbttavk`bltb a vkcora bggahkha dbcck tblsaolb b dbcck horrbltb b c‑klnoco da gksb trk tblsaolb b horrbltb. Darbò hmb V í ck potblzk kttavk b hmb hosΧ í ac gkttorb da potblzk. Klkcazzakò `bncao ck potblzk astkltklbk

Dkcc‑ucta`k bsprbssaolb possakò darb hmb ck potblzk astkltklbk í dktk dkcck so``k da dub ho`polblta, ulo hostkltb pkra kcck potblzk kttavk o `bdak, c‑kctro salusoadkcb k pucskzaolb doppak (:ρ) raspbtto kcck pucskzaolb da v(t) bd a(t), (ρ). @bdakltb kchula krtagaha `ktb`ktaha í possajacb pbrvblarb kcck sbnubltb bsprbssaolb pbr ck potblzk astkltklbk

Al qubst‑ucta`k bsprbssaolb [0W*A*sblΧ í dbttk potblzk rbkttavk , sa àsurk al Woct K`pbrb Zbkttava UWKZP, hoalhadb hol ck potblzk `bssk al naoho dknca alduttora b dka holdblsktora (lol í dassapktk `k íb shk`jaktk). Holsadbrakò ac prodotto trk ac gksorb dbcck tblsaolb W bd ac ho`pcbsso holaunkto dbc gksorb dbcck horrbltb A*, k tkcb prodotto dakò ac lo`b da potblzk kppkrbltb ho`pcbssk K.

Cb potblzb kttavk V, rbkttavk [ b kppkrbltb ho`pcbssk K, stkllo trk da coro ho`b a ckta da ul traklnoco dbtto traklnoco dbcck potblzk.

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;;. Tborb`k da Jouqubrot J ouqubrot

Xb holsadbrakò ul harhuato hoùlqub ho`pcbsso dovb solo prbsblta rbsastora, alduttora b holdblsktora ac hkchoco dbccb potblzb puú bssbrb gktto utacazzkldo ac tborb`k da Jouhmbrot. Ac tborb`k dahb hmb ck potblzk kttavk totkcb VT í dktk dkcck so``k krat`btahk dbccb potblzb dassapktb dk onla rbsastorb9 VT  0 V; + V: +...+ V L   Ck potblzk rbkttavk totkcb [T í dktk dkcck so``k kcnbjrahk dbccb salnocb potblzb rbkttavb. Cb potblzb alduttavk b hkpkhatavk mkllo sbnlo opposto, qualda lbc ò`blto al hua solo unukca al vkcorb kssocuto ck potblzk rbkttavk ho`pcbssavk í pkra k zbro. [T  0 [ C; +[ C: +...+[ CL  √ ([H ; +[H : +...+[HL  ) Ck potblzk kppkrbltb ho`pcbssk totkcb KT í dktk dkcck so``k vbttorakcb dbccb salnocb potblzb kppkrblta ho`pcbssb.

ck potblzk kppkrbltb totkcb puú bssbrb hkchocktk ho`b9

Xb holsadbrakò kd bsb`pao ul harhuato hostatuato dk trb ho`polblta (trb hkrahma), onlulo dba qukca mk cb sub Va, [a b Ka, dk ul pulto da vastk nrkgaho kvrbò hmb cb potblzb pkrzakca b cb potblzb totkca stkllo trk da coro ho`b raportkto al ganurk. Xa lota hmb nca klnoca θa rkpprbsbltklo co sgksk`blto trk ck tblsaolb b ck horrbltb dbc hkraho a.

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;:.

Vbr ac harhuato raportkto al ganurk, gulzaolkltb al rbna`b salusoadkcb, al hua solo lota Z;0;6 ℧, WZ:0::6 W, g026 Mz, Z :0:6 ℧, ]C;02 ℧, ]C:0;2 ℧, dbtbràlkrb ac vkcorb dbcck hkpkhatæ hkpkhatæ H, dk hoccbnkrb ka òrsbtta KJ, al òdo hmb c‑klnoco da gksb trk W bd A sak pkra k 6¶ (ragksk`blto totkcb).

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;8.

Vbr ac harhuato raportkto al ganurk, g anurk, gulzaolkltb al rbna`b salusoadkcb, al hua solo lota W0::6+i6 W (vkcorb bggahkhb) Yc0; ℧, YR0i: ℧ Wbragahkrb dbc jacklhao blbrnbtaho pbr cb potblzb kppkrblta ho`pcbssb.

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;4.

Vbr ac harhuato raportkto al ganurk, gulzaolkltb al rbna`b salusoadkcb, al hua solo lota Bk 0::6+i6 W (bggahkhb), Z0; ℧, ]0; ℧ R9 VR0: e^, hos χR06,12 (rat.) Dbtbràlkrb a trb hosta rbcktava kcc‑blbrnak kttavk pbr c‑utacazzktorb ^R, ck calbk ^c b dbc nblbrktorb ^p5 í loto hmb ; e^m hostk 6,;: ₣, ac harhuato gulzaolk pbr :4 orb kc naorlo pbr 76 naorla.

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Cbzaolb 6:8 6;. VBZ ZAGKXKZB K hos ga0; RL HKZAHO OM@AHO HKVKHATAWO HMB KXXOZJB [ B' LBHBXXKZAK RLK VOTBLYK ZBKTTAWK [C 9 [C0[ [C0V [C0WA [C0Z*A [RKDZO 6:. VBZ ZAGKXKZB K hos ga0; RL HKZAHO OM@AHO ALDRTTAWO HMB KXXOZJB [ B' LBHBXXKZAK RLK VOTBLYK ZBKTTAWK [H9 [H0ZA: [H0[ [H0WA [H0V 68. Zagksk`blto pkrzakcb

Vbr ragksk`blto sa altbldb qubcck prktahk hmb pbr`bttb da suppcarb kcco sgksk`blto altrodotto lbcck calbk dk ul hkraho rbkttavo. Ac pkrk`btro pañ sanlagahktavo í co sgksk`blto χ trk ck tblsaolb b ck horrbltb bcbttrahk da kca`bltkzaolb. Zagkskrb vuoc darb gorlarb al coho, tuttk (ragksk`blto totkcb) o pkrtb ho`b dbc tbsto dbcck do`kldk (ragksk`blto pkrzakcb) dbcck potblzk rbkttavk bcbttrahk lbhbsskrak kc hkraho .

ZAGKXK@BLTO VKZYAKCB Al qubsto hkso sa raduhb ck potblzk rbkttavk al òdo dk pksskrb dk qubcck `bssk al naoho lor`kc`bltb dkc hkraho [ (k hua horraspoldb c‑klnoco Χ) k qubcck `bssk al naoho dkcc‑alsab`b hkraho+holdblsktorb da ragksk`blto [‑ (k hua horraspoldb c‑klnoco Χ‑). Xb holsadbrkldo ac traklnoco dbccb potblzb ck [H dbc holdblsktorb í pkra k [0VtnΧ [0VtnΧ `blo ck [‑0V*tnΧ‑. Lotk ck potblzk rbkttavk b ck tblsaolb dbc holdblsktorb hkchocbrbò ck rbkttklzk hkpkhatavk b qualda ck hkpkhatæ dk utacazzkrb.

64. Zagksk`blto totkcb

Vbr ragksk`blto sa altbldb qubcck prktahk hmb pbr`bttb da suppcarb kcco sgksk`blto altrodotto lbcck calbk dk ul hkraho rbkttavo. Ac pkrk`btro pañ sanlagahktavo í co sgksk`blto χ trk ck tblsaolb b ck horrbltb bcbttrahk da kca`bltkzaolb. Zagkskrb vuoc darb gorlarb al coho, tuttk (ragksk`blto totkcb ) o pkrtb (ragksk`blto pkrzakcb) dbcck potblzk rbkttavk bcbttrahk lbhbsskrak kc hkraho.

ZAGKXK@BLTO TOTKCB Al qubsto hkso sa bcaàlk ho`pcbtk`bltb ck potblzk rbkttavk [. Dopo ac ragksk`blto sa mk K0V5Χ‑065 [‑06. Opbrktavk`bltb hkchocbrbò ac vkcorb dbcck potblzk rbkttavk dbc hkraho [u b co porrbò unukcb kcck potblzk rbkttavk dbc holdblsktorb [H dk uskrb pbr ragkskrb. Lotk ck potblzk pot blzk rbkttavk b ck tblsaolb hmb altbrbssklo ac holdblsktorb hkchocbrbò ck rbkttklzk hkpkhatavk b qualda ck hkpkhatæ dk utacazzkrb. XBNRB

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Cbzaolb 6:8

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Cbzaolb 6:2 6;. TBZLK DBCCB TBLXAOLA XTBCCKTB B;,B:, B8 VBZ RL XAXTB@K XA@@BTZAHO BD B[RACAJZKTO Ck coro so``k al onla astkltb da tb`po vkcb zbro Tuttb cb kctrb trb Cb trb tblsaola solo sgksktb trk da coro da ;:6 nrkda Cb trb tblsaola mkllo co stbsso òduco 6:. CK TZKXGOZ@KYAOLB TZAKLNOCO-XTBCCK DA A@VBDBLYB VRO' BXXBZB BXBNRATK XOCO XB CB A@VBDBLYB K TZAKLNOCO XOLO ADBLTAHMB VRO' BXXBZB BXBNRATK VBZ [RKCXAKXA WKCOZB DBCCB A@VBDBLYB K TZAKLNOCO LOL VRO' BXXBZB BXBNRATK VBZ [RKCXAKXA WKCOZB DBCCB A@VBDBLYB K TZAKLNOCO LOL VRO' BXXBZB @KA BXBNRATK 68. HOZZBLTB XRC LBRTZO VBZ RL XAXTB@K XA@@BTZAHO BD B[RACAJZKTO K XTBCCK HOL LBRTZO Hoalhadb hol ck so``k dbccb horrblta da calbk davaso pbr sqrt(8) Hoalhadb hol ck so``k dbccb horrblta da calbk òctapcahktk pbr sqrt(8) Wkcb zbro al onla astkltb ast kltb da tb`po Hoalhadb hol ulk dbccb horrblta da calbk 64. CK TZKXGOZ@KYAOLB XTBCCK-TZAKLNOCO DA A@VBDBLYB LOL VRO' BXXBZB @KA BXBNRATK VRO' BXXBZB BXBNRATK XOCO XB CB A@VBDBLYB K XTBCCK XOLO ADBLTAHMB VRO' BXXBZB BXBNRATK VBZ [RKCXAKXA WKCOZB DBCCB A@VBDBLYB K XTBCCK LOL VRO' BXXBZB BXBNRATK VBZ [RKCXAKXA WKCOZB DBCCB A@VBDBLYB K XTBCCK

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62.

Vbr ac harhuato tragksb raportkto al ganurk, al hua solo lota B; 06+i::6 W (tbrlk sa``btrahk kcck sbqublzk darbttk, vkcorb bggahkhb) YC0:+i4 ℧, YR 02+i2 ℧, dbtbràlkrb ck potblzk kttavk kssorjatk dkcc‑utacazzktorb dkcc‑utacazzktorb VR.

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67.

Vbr ac harhuato tragksb raportkto al ganurk, al hua solo lota B;0::6+i6 W (tbrlk sa``btrahk kcck sbqublzk darbttk, vkcorb bggahkhb) YQ0;6+i;6 ℧ Dbtbràlkrb cb trb horrblta da calbk, b vbragahkrb hmb ck coro so``k í pkra k zbro.

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6>. A`pbdblzb k stbcck b k traklnoco

Trb a`pbdblzb possolo bssbrb hoccbnktb trk da coro k stbcck o k traklnoco. [ubsta hoccbnk`blta solo daggusa lbccb `khhmalb b lbnca a`paklta, kd bsb`pao lba òtora bcbttraha tragksb A@VBDBLYB HOCCBNKTB K XTBCCK(Q) trb a`pbdblzb (hmb possolo bssbrb adbltahmb o davbrsb trk da coro), solo hoccbnktb k stbcck sb mkllo ul bstrbò hoccbnkto al hoùlb (pulto o) bnca kctra trb bstrbà hoccbnkta kd kctrbttklta pulta dbc harhuato(;-:-8).

A@VBDBLYB HOCCBNKTB K TZAKLNOCO (D) trb a`pbdblzb (hmb possolo bssbrb adbltahmb o davbrsb trk da coro), solo hoccbnktb k traklnoco sb ac òrsbtto galkcb dbcck pra`k í hoccbnkto kc òrsbtto alazakcb dbcck sbholdk, ac òrsbtto galkcb dbcck sbholdk í hoccbnkto kc òrsbtto alazakcb dbcck tbrzk b ac òrsbtto galkcb dbcck tbrzk í hoccbnkto kc òrsbtto alazakcb dbcck pra`k. Ac hoccbnk`blto hmb sa ottablb í raportkto al ganurk.

Ho`b lbc hkso dbccb rbsastblzb í possajacb bsbnuarb trksgor`kzaola Traklnoco-Xtbcck o stbcck ‘Tralknoco dbccb a`pbdblzb, utacazzkldo cb sbnublta rbckzaola9

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:= - 7;/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro 6=. Xastbà tragksb k stbcck s tbcck bquacajrktb

[ubsto tapo da hoccbnk`blto í hostatuato dk ul nblbrktorb tragksb hoccbnkto kd ul utacazzktorb hostatuato dk trb a`pbdblzb adbltahmb hollbssb trk da coro k stbcck. Ac pulto al hoùlb O í dbtto hbltro stbcck. Holsadbrbrbò a`pbdblzb omàho-alduttavb al quklto rkpprbsbltklo ck quksa totkcatæ dba hkrahma bcbttraha.

Kppcahkldo ck cbnnb da Om` Al onla gksb dbcck stbcck harhocbræ ulk horrbltb Dktk dkccb sbnublta rbckzaola

Al ul hoccbnk`blto tragksb k stbcck bquacajrktk

Ck horrbltb hmb kttrkvbrsk a holduttora da calbk hoalhadb hol ck horrbltb hmb kttrkvbrsk a holduttora da gksb5 pbr onla t ck so``k dbccb trb horrblta da calbk, hmb hoalhadb hol ck horrbltb hmb kttrkvbrsk ac holduttorb da lbutro, í pkra k zbro (pbrtklto ac holduttorb da lbutro í supbrgcuo) ac òduco dbcck tblsaolb holhktblktk W í pkra k ∙8 voctb ac òduco dbcck tblsaolb stbccktk B. Wocbldo rkpprbsbltkrb vbttorakc`bltb tblsaola b horrblta da ul sastb`k k stbcck bquacajrkto

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:= - 7:/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

61.

Vbr ac harhuato tragksb raportkto al ganurk, solo lota B;0::6+i6 W (tbrlk sa``btrahk kcck sbqublzk darbttk, vkcorb bggahkhb) Y;0;+i ℧, Y:0:+i: ℧, Y8 0;+i ℧, dbtbràlkrb ck horrbltb suc lbutro.

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:= - 78/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

;6.

Vbr ac harhuato tragksb raportkto al ganurk, al hua solo lota B;0::6+i6 W (tbrlk sa``btrahk kcck sbqublzk darbttk, vkcorb bggahkhb) YD0;6+i;6 ℧, dbtbràlkrb cb trb horrblta da calbk b vbragahkrb hmb ck coro so``k í pkra k zbro.

XBNRB © :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:= - 74/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:= - 72/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 6:7 6;. LBA XAXTB@A K XTBCCK X[RACAJZKTA XBLYK LBRTZO CK T TBLXAOLB BLXAOLB DBC HBLTZO XTBCCK ZBKCB VRO' BXXBZB WKCRTKTK KNBWOC@BLTB TZK@ATB XOWZKVVOXAYAOLB DBNCA BGGBTTA @ACC@KLL TMBWBLAL

LOZTOL 6:. TBZLK DBCCB HOZZBLTA DA GKXB VBZ V BZ RL XAXTB@K XA@@BTZAHO BD B[RACAJZKTO K XTBCCK Cb trb horrblta mkllo co stbsso òduco b ck stbssk gksb Hoalhadb hol ck tbrlk dbccb horrblta da calbk davask pbr sqrt(8) Hoalhadb hol ck tbrlk dbccb horrblta da calbk Hoalhadb hol ck tbrlk dbccb horrblta da calbk òctapcahk òctapcahktk tk pbr sqrt(8) 68. HOZZBLTB XRC LBRTZO VBZ RL XAXTB@K XA@@BTZAHO B X[RACAJZKTO K XTBCCK HOL LBRTZO Hoalhadb hol ck tbrlk dbccb tblsaola holhktblktb Hoalhadb hol ck so``k dbccb horrblta da gksb davaso pbr sqrt(8) Lbssulk dbccb kctrb trb Hoalhadb hol ck so``k dbccb horrblta da calbk davaso pbr sqrt(8) 64. VOTBLYAKCB DBC HBLTZO XTBCCK VBZ RL XAXTB@K XA@@BTZAHO B X[RACAJZKTO K XTBCCK XBLYK LBRTZO B' davbrso dk zbro Hoalhadb hol ck so``k dbccb tblsaola da calbk davaso c'a`pbdblzk da gksb Wkcb zbro al onla astkltb ast kltb da tb`po Hoalhadb hol ck so``k dbccb tblsaola da calbk

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:= - 77/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

62. Xastbà tragksb k stbcck s tbcck squacajrktk sblzk lbutro

[ubsto tapo da hoccbnk`blto í hostatuato dk ul nblbrktorb tragksb hoccbnkto kd ul utacazzktorb hostatuato dk trb a`pbdblzb davbrsb trk da coro hollbssb k stbcck. Ac pulto al hoùlb O‑ í dbtto hbltro stbcck. Lol bssbldo prbsbltb ac holduttorb da lbutro, cb horrblta dovrkllo kvbrb ulk rasuctkltb lucck b dovrkllo rahmaudbrsa sua holduttora dbccb trb gksa. [ubsto ho`portk hmb vkrabrkllo cb tblsaola stbccktb succb salnocb a`pbdblzb sa mk ac hosaddbtto spostk`blto dbc hbltro stbcck, holsastbltb lbc gktto hmb cb tblsaola stbccktb dbvolo nblbrkrb ulk tbrlk da horrblta kvbltb rasuctkltb lucck.

Zkpprbsbltkldo vbttorakc`bltb ac sastb`k kjjakò5

B;, B: bd B8 solo cb trb tblsaola da gksb lbc hkso da stbcck bquacajrktk (adbkcb), ( adbkcb), B‑;, B‑: bd B‑8 cb trb tblsaola da gksb lbc hkso da stbcck squacajrktk (rbkcb). Ac vbttorb Wo‑-o rkpprbsbltk ck tblsaolb bsastbltb trk ac hbltro stbcck rbkcb b ac hbltro stbcck adbkcb, Xolo vkcadb cb sbnublta rbckzaola

Dovbldo bssbrb vbragahktk ck holdazaolb hmb ck so``k dbccb trb horrblta í pkra k zbro, possakò shravbrb cb sbnublta bqukzaola b qualda dbtbràlkrb ck tblsaolb Wo‑-o

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:= - 7>/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

67. Xastbà tragksb k stbcck s tbcck squacajrktk hol lbutro

Al qubsto tapo da hoccbnk`blto, ac nblbrktorb tragksb í hoccbnkto k trb a`pbdblzb trk da coro davbrsb hollbssb k stbcck, ac pulto al hoùlb O í dbtto hbltro stbcck.

Kppcahkldo ck cbnnb da om` pbr dbtbràlkrb kjjakò5

Dkccb rbckzaola sa puú bvalhbrb hmb5 • cb horrblta hmb kttrkvbrsklo a trb holduttora da calbk hoalhadolo hol cb horrblta hmb kttrkvbrsklo a holduttora da gksb5 • ck so``k dbccb trb horrblta da calbk hoalhadb hol ck horrbltb hmb kttrkvbrsk ac holduttorb da lbutro. Al nblbrkcb lol í pkra k zbro, pbrtklto ac holduttorb da lbutro í lbhbsskrao Zkpprbsbltkldo ac sastb`k vbttorakc`bltb rasuctk5

Dovb cb tbrlb dbccb tblsaola stbccktb b dbccb horrblta da calbk (o da gksb) stkllo trk da coro ho`b raportkto lbc daknrk``k. Al onla gksb ck tblsaolb b ck horrbltb solo sgksktb da ul klnoco pkra kcc‑klnoco hkrkttbrastaho dbcc‑a`pbdblzk da gksb. Ck horrbltb hmb kttrkvbrsk ac lbutro í ottblajacb ho`b so``k vbttorakcb dbccb horrblta dbccb trb gksa (CEH kc lodo O).

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:= - 7=/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 6:> 6;. TBZLK DBCCB HOZZBLTA DA GKXB VBZ V BZ RL XAXTB@K XA@@BTZAHO BD B[RACAJZKTO K TZAKLNOCO Hoalhadb hol ck tbrlk dbccb horrblta da calbk davask pbr sqrt(8) Hoalhadb hol ck tbrlk dbccb horrblta da calbk òctapcahk òctapcahktk tk pbr sqrt(8) Hoalhadb hol ck tbrlk dbccb horrblta da calbk Cb trb horrblta mkllo co stbsso òduco b ck stbssk gksb 6:. TBZLK DBCCB HOZZBLTA DA CALBK VBZ RL XAXTB@K XA@@BTZAHO B X[RACAJZKTO K TZAKLNOCO Al onla astkltb da tb`po ck coro so``k vkcb zbro Al onla astkltb da tb`po ck coro so``k s o``k í davbrsk dk zbro Cb trb horrblta mkllo co stbsso òduco b ck stbssk gksb Hoalhadb hol ck tbrlk dbccb horrblta da gksb òctapcahktk pbr sqrt(8) 68. Xastbà tragksb k traklnoco bquacajrkto

Al qubsto tapo da hoccbnk`blto ac nblbrktorb tragksb í hoccbnkto k trb a`pbdblzb adbltahmb hollbssb trk da coro k traklnoco.

Rtacazzkldo ck cbnnb da Om` ottblakò b sbnublta rbckzaola 5

Dovb sa bvalhb hmb • c‑ a`pbdblzk da gksb í sonnbttk kcck tblsaolb holhktblktk5 • ck horrbltb hmb kttrkvbrsk a holduttora da calbk lol hoalhadb hol ck horrbltb hmb kttrkvbrsk a holduttora da gksb dbc traklnoco `k rasuctk ∙8 voctb `knnaorb (vbda daòstrkzaolb gkttk pbr cbtblsaola)5 • al onla astkltb da tb`po ck so``k dbccb horrblta da calbk í pkra k zbro.

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:= - 71/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 6:>

64. Xastbà tragksb k traklnoco squacajrkto

Al qubsto tapo da hoccbnk`blto, ac nblbrktorb tragksb í hoccbnkto k trb a`pbdblzb davbrsb hollbssb trk da coro k traklnoco.

Rtacazzkldo ck cbnnb da Om` ottblakò cb sbnublta rbckzaola5

Dovb sa bvalhb • onla a`pbdblzk da gksb í sonnbttk kcck tblsaolb holhktblktk5 • ck horrbltb hmb kttrkvbrsk a holduttora da gksb í ottblajacb ho`b rkpporto trk ck tblsaolb holhktblktk b c‑a`pbdblzk dbcck gksb5 • c‑klnoco da sgksk`blto trk ck tblsaolb holhktblktk b ck horrbltb da gksb í qubcco hkrkttbrastaho dbcc‑a`pbdblzk5 • cb horrblta da calbk possolo bssbrb hkchocktb kppcahkldo ck CEH ka loda5 • al onla astkltb da tb`po ck so``k dbccb horrblta da calbk í pkra k zbro

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:= - >6/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 6:= 6;. LBA XAXTB@A TZAGKXB AC TBOZB@K DA JOR[RBZOT MK WKCADATK' XOCO VBZ CB VOTBLYB KTTAWB AC TBOZB@K DA JOR[RBZOT MK WKCADATK' XOCO XB AC XATB@K B' XA@@BTZAHO BD B[RACAJZKTO AC TBOZB@K DA JOR[RBZOT MK XB@VZB WKCADATK' AC TBOZB@K DA JOR[RBZOT LOL MK @KA WKCADATK' 6:. VBZ RL XAXTB@K TZAGKXB XA@@BTZAHO BD B[RACAJZKTO V 0 sqrt(8)WAhosga V davbrsk dk 6, [ 0 6, K0[ V 0 sqrt(8)BAhosga V davbrsk dk 6, [ davbrsk dk 6, K0[ 68. VBZ RL XAXTB@K TZAGKXB XA@@BTZAHO BD B[RACAJZKTO V davbrsk dk 6, [ 0 6, K0[ V davbrsk dk 6, [ davbrsk dk 6, K0[ [0 sqrt(8)BAsblga [ 0 sqrt(8)WAsblga

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:= - >;/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 6:=

64. Votblzb lba sastbà tragksb sa``btraha bd bquacajrkta

Xkppakò hmb cb rbckzaola hmb cbnklo cb davbrsb nrkldbzzb al naoho al ul sastb`k tragksb sa``btraho bd bquacajrkto solo cb sbnublta9

Cb a`pbdblzb dbc sastb`k solo dbcck gor`k Dapbldbltb`bltb dkc hoccbnk`blto dbccb a`pbdblzb da hkraho ( Xtbcck o k traklnoco), cb potblzb possolo bssbrb hosã dbtbràlktb5 hkraho k stbcck

lba sastbà sa``btraha bd bquacajrkta hol hkraho k traklnoco cb potblzb solo dbtbràlkjaca dkccb sbnublta rbckzaola

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:= - >:/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 6:= 62. Votblzb lba sastbà tragksb

Aldahkldo hol b;(t), a vkcora astkltklba da gksb bbsprbssaolb9 hol a;(t), a:(t) bd a8(t) a vkcora astkltklba dbccb horrblta hmb kttrkvbrsklo cb trbb:(t) gksa.bdckb8(t) potblzk astkltklbk p(t)dbccb í dktktblsaola dkcck sbnubltb p(t)0p;(t)+p:(t)+p8(t)0b;(t)*a;(t)+b:(t)*a:(t)+b8(t)*a8(t). Bssbldo9 b;(t)0B@sbl(ρt) b:(t)0B@sbl(ρt-;:6¶) b8(t)0B@sbl(ρt-:46¶) (B@ í ac vkcorb `kssaò dbcck tblsaolb succb trb gksa, B0B@ / ∙: í ac vkcorb bggahkhb dbcck tblsaolb succb trb gksa) a;(t)0A@sbl(ρt+ϒ) a:(t)0A@sbl(ρt+ϒ-;:6¶) a8(t)0A@sbl(ρt+ϒ-:46¶) A@ í ac vkcorb `kssaò dbcck horrbltb lbccb trb gksa, A0A@/ ∙: í ac vkcorb bggahkhb dbcck horrbltb lbccb trb gksa,

ϒ í c‑klnoco hkrkttbrastaho dbcc‑a`pbdblzk da gksb Kldkldo k Xostatuarb ottblakò9 p(t)0p;(t)+p:(t)+p8(t)0b;(t)*a;(t)+b:(t)*a:(t)+b8(t)*a8(t)08/:(B@A@hos ϒ)08BAhosϒ Lotakò hmb ck potblzk astkltklbk p(t) í hostkltb lbc tb`po, bssk hoalhadb hol ck potblzk kttavk o `bdak V.

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:= - >8/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 6:1 6;. ALXBZYAOLB KZOL DA DRB ^KTT@BTZA HOLXBLTB DA @AXRZKZB CK VOTBLYK KTTAWK DA XAXTB@A TZAGKXB K TZB HOLDRTTOZA LOL HOLXBLTB DA @AXRZKZB CK VOTBLYK KTTAWK DA XAXTB@A TZAGKXB K TZB HOLDRTTOZA HOLXBLTB DA @AXRZKZB CK VOTBLYK KTTAWK DA XAXTB@A TZAGKXB K [RKTTZO HOLDRTTOZA HOLXBLTB DA @AXRZKZB CK VOTBLYK KVVKZBLTB DA XAXTB@A TZAGKXB K TZB HOLDRTTOZA 6:. @asurb bcbttrahmb b stru`blta da àsurk

@asurkrb nrkldbzzk bcbttrahk, sanlagahk dbtbràlkrlb ac vkcorb al rkpporto kd ul‑kctrk nrkldbzzk dbcco stbsso tapo kssultk ho`b ulatæ da àsurk. Trk ac vkcorb àsurkto K` bd ac vkcorb vbro dbcck nrkldbzzk KW h‑í sb`prb ulk daggbrblzk (al dagbtto o al bhhbsso) hmb hostatuashb c‑brrorb da àsurk. B‑ goldk`bltkcb stkjacarb ac nrkdo da prbhasaolb hmb sa vuocb rknnaulnbrb lbcck àsurk, sa dastalnuolo k tkc proposato dub davbrsb àsurb5 àsurb aldustrakca (qubccb al hua ac nrkdo da prbhasaolb lol mk a`portklzk) àsurb da ckjorktorao (qubccb al hua ac nrkdo da prbhasaolb mk a`portklzk) . Vbr potbr bggbttukrb cb àsurkzaola ha kvvkcakò dbnca stru`blta da àsurk cb pañ a`portklta hkrkttbrastahmb da qubsta stru`blta solo C‑BZZOZB KXXOCRTO B ck hckssb5 Dbgalakò brrorb kssocuto ∇K dbcck àsurk ck daggbrblzk trk ac vkcorb àsurkto K` bd ac vkcorb vbro Kv dbcck nrkldbzzk (k``bsso hmb sa possk holoshbrb). Dbgalakò hckssb dbcco stru`blto Hc c‑brrorb kssocuto `kssaò bsprbsso al % raspbtto kcck portktk V (`kssaò vkcorb àsurkjacb dkcco stru`blto), kvrbò Hc0(∇K/V)*;66. Xb kd bsb`pao ul voct`btro (stru`blto kdktto kcck àsurk dbcck tblsaolb ) mk ulk hckssb da 6,2 b portktk V0866 W sb àsurakò W`0::6 W al bggbtta WW0W`»∇ 0::6 » ;,2 W dovb ∇K0Hc*V/;66 0;,2 W í c‑brrorb `kssaò ho``bsso dkcco stru`blto. Al nblbrb cb hckssa dbnca stru`blta vkllo dk Hc06,62 dbnca stru`blta hk`paolb k Hc0; stru`blta portktaca pbr vbragahmb su a`paklta k Hc02 pbr stru`blta dk qukdro. Da sbnuato sa raportklo nca stru`blta da àsurk da utacazzo hoùlb5 Ac voct`btro í ulo stru`blto al nrkdo da àsurkrb ck tblsaolb sak al holtaluk (dh) hmb al kctbrlktk (kh). Dbvb bssbrb hoccbnkto trk a dub pulta trk hua sa vuocb àsurkrb ck tblsaolb. Bssbldo hollbsso al í kuspahkjacb hmb ck suk rbsastblzk altbrlk tbldk kd algalato, al òdo hmb lol vblnk kttrkvbrskto dk horrbltb b qualda lol pbrturja ac gulzaolk`blto dbc harhuato hol ck suk prbsblzk. C‑k`pbro`btro í ulo stru`blto da àsurk al nrkdo da àsurkrb ck horrbltb sak al holtaluk (dh) hmb al kctbrlktk (kh). Dbvb bssbrb hoccbnkto al sbrab kc ckto al hua sa vuocb àsurkrb ck horrbltb. Bssbldo hollbsso al sbrab í kuspahkjacb hmb ck suk rbsastblzk altbrlk tbldk k zbro al òdo hmb ck hkdutk da tblsaolb ka suoa òrsbtta rasucta lucck (hkso adbkcb) b qualda lol –pbrturja‐ hol ck suk prbsblzk gulzaolk`blto Ac wktt`btro í ulo acstru`blto al nrkdodbcdaharhuato àsurkrb ck potblzk sak al holtaluk (dh) hmb al kctbrlktk (kh). Vbr onla gksb sa mkllo dub harhuata ulo voct`btraho bd ulo k`pbro`btraho. Ac praò dbvb bssbrb hoccbnkto al dbravkzaolb kc hkraho, ac sbholdo al sbrab. Bssbldo hollbsso sak al pkrkccbco hmb al sbrab í a`portkltb hmb ck rbsastblzk altbrlk dbc harhuato k`pbro`btraho tbldk k zbro b hmb ck rbsastblzk dbc harhuato voct`btraho tbldk kd algalato al òdo hmb ck suk alsbrzaolb kcc‑altbrlo dbc harhuato da àsurk lol –pbrturja‐ ac gulzaolk`blto dbc harhuato (vkrakzaola da tblsaolb b horrbltb suc hkraho dovutb kcck prbsblzk dbcco stru`blto lbc harhuato). Ac ùcta`btro í ulo stru`blto al nrkdo da àsurkrb ck horrbltb b ck tblsaolb sak al holtaluk (dh) hmb al kctbrlktk (kh) b ck rbsastblzk. B‑ lbhbsskrao sbcbzaolkrb ac tapo da àsurk dk bggbttukrb (tblsaolb holtaluk/kctbrlktk, horrbltb holtaluk/kctbrlktk o rbsastblzk) b ck portktk dbcco stru`blto

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:= - >4/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 6:1 68. @asurb da potblzk lba sastbà tragksb

Vbr ck àsurkrb dbcck potblzk al ul sastb`k tragksb nblbraho possakò dastalnubrb davbrsb hksastahmb5 hkso da ul sastb`k holklhmb lbutroda(4ulholduttora) pbr potbr àsurkrbbcksquacajrkto. potblzk al ul sastb`k tragksb ha kvvkcakò da trb wktt`btra holsadbrkldo klhmbtragksb c‑apotbsa hkso da sastb`k dassa`btraho .Bssbldo ck potblzk dbgalatk dkcck sbnubltb rbckzaolb5 Xa mk V0V;+V:+V80B;A;hosϒ;+B:A:hosϒ:+B8A8hosϒ8 @bltrb ck rbkttavk skræ dktk utacazzkldo dba vkr`btra kc posto da wktto`btra dk [0[;+[:+[80B;A;sbl ϒ;+B:A:sblϒ:+B8A8sblϒ8 Vbr tkcb sastb`k ck horrbltb suc lbutro í pkra kcck so``k vbttorakcb dbccb horrblta succb gksa (hk`jaktk da sbnlo) AL0-(A;+A:+A8). Ck potblzk kttavk totkcb í dktk dkcck so``k dbccb potblzb àsurktb dka trb wktt`btra.

Lbc hkso da ul sastb`k k trb holduttora sblzk lbutro hmb potrbjjb kvbrb ul hkraho squacajrkto possakò àsurk ck potblzk ol c‑kusacao da trb wktto`btra

Al qubsto hkso ck so``k dbccb horrblta succb trb gksa í al onla astkltb da tb`po lucck, haoí A;+A:+A806 A trb wktto`btra hoccbnkta ho`b dk ganurk kldrkllo k hrbkrb krtagahakc`bltb ac hbltro stbcck O Ck potblzk kttavk V skræ dktk dk V0V;+V:+V80B;A;hosϒ;+B:A:hosϒ:+B8A8hosϒ8 Lbc hkso pkrtahockrb al hua ac sastb`k í sa``btraho bd bquacajrkto a trb wktt`btra dkllo ck stbssk aldahkzaolb, skræ possajacb àsurkrb ck potblzk kttavk utacazzkldo ul soco wktt`btro. Vbr lol squacajrkrb ac sastb`k skræ lbhbsskrao knnaulnbrb, al sbrab kcck rbsastblzk Z succb dub gksa al hua lol ha solo wktt`btra, ulk rbsastblzk pkra kcck rbsastblzk voct`btrahk dbc wktt`btro. Al tkc hkso sa kvræ V08V; bssbldo V; c‑aldahkzaolb dbcc‑ulaho wktt`btro. Vbr Rl sastb`k k trb holduttora í possajacb àsurkrb ck potblzk klhmb hol c‑kusacao da dub w wktto`btra ktto`btra (alsbrzaolb Krol) ac `btodo í kppcahkjacb klhmb k sastbà dassa``btraha b squacajrkta Al tkcb `btodo sa gk hoalhadbrb ac hbltro stbcck hol ulo dba holduttora da gksb (al qubsto hkso ac tbrzo). A dub wktt`btra sbnlklo raspbttavk`bltb9

V;80W;8*A;*hos(W;8-A;), b V:80W:8*A:*hos(W:8-A:) al hua (Wai-Aa) í c‑klnoco ho`prbso trk a dub vbttora Wai bd Aa. Klhmb al qubsto hkso al onla astkltb da tb`po ck so``k dbccb trb horrblta da calbk dbvb bssbrb lucck, haoí A;+A:+A806. XBNRB © :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:= - >2/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 6:1

Ck potblzk kttavk V í dktk dk V0V;8+V:8 bssbldo V;8 b V:8 cb aldahkzaola dba wktt`btra hol voct`btrahk sua holduttora da gksb ;-8 b :-8 raspbttavk`bltb. Vbr ck àsurk dbcck rbkttavk kldkldo k sostatuarb sostatuarb kc wktt`btro dba vkr`btra bssbldo [;80W;8*A;*hos(W;8-A;), [:80W:8*A:*hos(W:8-A:) Ck potblzk rbkttavk [ í dktk dk [0[;8+[:8

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:= - >7/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 686 6;. VBZ ZAGKXKZB K hos ga0; RL HKZAHO OM@AHO ALDRTTAWO TZAGKXB B' LBHBXXKZAK RLK VOTBLYK ZBKTTAWK [H [H0W*A [H0[ [H0Z+A [H0V 6:. VBZ ZAGKXKZB K hos ga0; RL HKZAHO OM@AHO-HKVKHATAWO TZAGKXB B' LBHBXXKZAK RLK VOTBLYK ZBKTTAWK [C [C0[ [C0Z+A [C0W*A [C0V

68.

Vbr ac harhuato tragksb raportkto al ganurk, al hua solo lota W08=6 W (tbrlk sa``btrahk kcck sbqublzk darbttk, vkcorb bggahkhb) VR02 e^ , hosga R06,7, g026 Mz, hosto ^k06,;2 ₣/e^¾m, hosto ^r06,:2 ₣/eWKZ¾m, hol ac tksto T hmauso provvbdbrb kc ragksk`blto totkcb dbtbràlkldo ac vkcorb da HQ.

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:= - >>/>8

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64.

Vbr ac harhuato tragksb raportkto al ganurk, solo lota B;0::6+i6 W (tbrlk sa``btrahk kcck sbqublzk darbttk, vkcorb bggahkhb) YC06,;+i6,; ℧, Y;0;6+i;6 ℧, Y:0:6+i:6 ℧, dbtbràlkrb ac harhuato bquavkcbltb da Tmbvblal tragksb kcck sbzaolb X.

XBNRB

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:= - >=/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:= - >1/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

62. Zagksk`blto pkrzakcb da hkraho tragksb

Vbr ragksk`blto sa altbldb qubcck prktahk hmb pbr`bttb da suppcarb kcco sgksk`blto altrodotto lbcck calbk dk ul hkraho rbkttavo Lb hkso da sastb`k tragksb sa``btraho bd bquacajrkto, pbr ragkskrb pkrzakc`bltb ul hkraho, qualda radurrb ck potblzk rbkttavk sa puú utacazzkrb ulk tbrlk da holdblsktora hoccbnkta al pkrkccbco kc hkraho stbsso. A trb holdblsktora possolo bssbrb hoccbnkta trk da coro k stbcck o k traklnoco.

Aldahkldo hol [T ck potblzk rbkttavk dbc hkraho b hol [H ck potblzk rbkttavk dbcck jkttbrak da holdblsktora. ragksakò pkrzakc`bltb qukldo ck [H3[T. Xtakò suppolbldo hmb ac hkraho kssorjk ulk potblzk rbkttavk alduttavk b haoí hmb sak da tapo omàho-alduttavo. Xb hosã lol dovbssb bssbrb, haoí sb ac hkraho dovbssb bssbrb da tapo omàho-hkpkhatavo ac ragksk`blto dovræ bssbrb bsbnuato utacazzkldo ul tbrlk da alduttklzb

ragkskrb pkrzakc`bltb ac hkraho, qualda pksskrb dk ul klnoco da gksb ϒ kd ul klnoco da gksb ϒ‑, jasonlbræ holsadbrkrb lbccb bsprbssaola prbhbdblta [H0VT(tnϒ-tnϒ‑). Kchulb holsadbrkzaola9 • sa bvalhb hmb ck hkpkhatæ dba holdblsktora hoccbnkta k traklnoco H ∇ í ck tbrzk pkrtb dbcck hkpkhatæ dba holdblsktora hoccbnkta k stbcck HQ • a holdblsktora hoccbnkta k traklnoco solo sonnbtta kcck tblsaolb holhktblktk W, `bltrb a holdblsktora hoccbnkta k stbcck solo sonnbtta kcck tblsaolb stbccktk B, pbrtklto a holdblsktora hollbssa k traklnoco rahmabdolo khhorna`blta hostruttava `knnaora (hmb nblbrkc`bltb ho`portklo ul ku`blto da prbzzo) • al nblbrb ck potblzk rbkttavk totkcb [T kssorjatk dkc hkraho lol í hostkltb `k vkrak lbc tb`po sbholdo, kd bsb`pao, ck hurvk raportktk hol calbk holtaluk lbc daknrk``k da hkraho sbnubltb. Ck hurvk hol calbk trkttbnnaktk aldahk ck [H dba holdblsktora. Xa lotk hmb cb hurvb lol sa sovrkppolnolo pbrgbttk`bltb al quklto cb hbltrkcalb da ragksk`blto –alsbnuolo‐ ck potblzk rbkttavk dbc hkraho `k lol rabsholo kd kzzbrkrck ho`pcbtk`bltb (hos ϒ‑06,1111). Al prktahk a vkcora da [H lol solo holtalua `k, bssbldo ottbluta hoccbnkldo al sbrab b pkrkccbco ul hbrto lu`bra da holdblsktora, vkraklo sbholdo ul kldk`blto k nrkdala

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:= - =6/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

67. Zagksk`blto pkrzakcb da hkraho òlogksb

Vbr ragksk`blto sa altbldb qubcck prktahk hmb pbr`bttb da suppcarb kcco sgksk`blto altrodotto lbcck calbk dk ul hkraho rbkttavo. Ac pkrk`btro pañ sanlagahktavo í co sgksk`blto χ trk ck tblsaolb b ck horrbltb bcbttrahk da kca`bltkzaolb. Zagkskrb vuoc darb gorlarb al coho, tuttk (ragksk`blto totkcb) o pkrtb ho`b dbc tbsto dbcck do`kldk (ragksk`blto pkrzakcb) dbcck potblzk rbkttavk bcbttrahk lbhbsskrak kc hkraho .

ZAGKXK@BLTO VKZYAKCB Al qubsto hkso sa raduhb ck potblzk rbkttavk al òdo dk pksskrb dk qubcck `bssk al naoho lor`kc`bltb dkc hkraho [ (k hua horraspoldb c‑klnoco Χ) k qubcck `bssk al naoho dkcc‑alsab`b hkraho+holdblsktorb da ragksk`blto [‑ (k hua horraspoldb c‑klnoco Χ‑). Xb holsadbrkldo ac traklnoco dbccb potblzb ck [H dbc holdblsktorb í pkra k [0VtnΧ [0VtnΧ `blo ck [‑0V*tnΧ‑. Lotk ck potblzk rbkttavk b ck tblsaolb dbc holdblsktorb hkchocbrbò ck rbkttklzk hkpkhatavk b qualda ck hkpkhatæ dk utacazzkrb.

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:= - =;/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 68; 6;. CB TBZLB KCCK XB[RBLYK O@OVOCKZB MKLLO A TZB WBTTOZA ADBLTAHA MKLLO A TZB WBTTOZA HOL XTBXXO @ODRCO B DAWBZXK GKXB MKLLO A TZB WBTTOZA HOL XTBXXK GKXB B DAWBZXO @ODRCO LOL BXAXTOLO AL VZKTAHK 6:. LBA XAXTB@A XA@@BTZAHA HOL TBZLB KCCK XB[RBLYK DAZBTTK CK TBZLK DBCCB TBLXAOLA HOLHKTBLKTB B' AL KLTAHAVO DA RL KLNOCO DAVBLDBLTB DKC HKZAHO XRCCK TBZLK DBCCB TBLXAOLA XTBCCKTB CK TBZLK DBCCB TBLXAOLA HOLHKTBLKTB LOL B' AL KLTAHAVO DA 86¶ XRCCK TBZLK DBCCB TBLXAOLA XTBCCKTB CK TBZLK DBCCB TBLXAOLA HOLHKTBLKTB B' AL ZATKZDO DA 86¶ XRCCK TBZLK DBCCB TBLXAOLA XTBCCKTB CK TBZLK DBCCB TBLXAOLA HOLHKTBLKTB B' AL KLTAHAVO DA 86¶ XRCCK TBZLK DBCCB TBLXAOLA XTBCCKTB 68. DKTK RLK TBZLK NBLBZAHK DA WBTTOZA BXXK LOL VRO' BXXBZB XB@VZB OTTBLRTK XO@@KLDO TZB TBZLB KCCB XB[RBLYB DAZBTTK, ALWBZXK B O@OVOCKZB VRO' BXXBZB XB@VZB OTTBLRTK XO@@KLDO TZB TBZLB KCCB XB[RBLYB DAZBTTK, ALWBZXK B O@OVOCKZB VRO' BXXBZB XB@VZB OTTBLRTK XO@@KLDO DRB TBZLB KCCB XB[RBLYB DAZBTTK B ALWBZXK VRO' BXXBZB XB@VZB OTTBLRTK XO@@KLDO TZB TBZLB KCCB XB[RBLYB DAZBTTK

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:= - =:/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

64. Tbrlb kcck sbqublzk darbttk-alvbrsk-oòpoc darbttk-alvbrsk-oòpockrb krb

Vbr potbr accustrkrb cb tbrlb da vbttora kcck sbqublzk darbttk alvbrsk b oòpockrb í opportulo altrodurrb c‑opbrktorb `ktb`ktaho λ (λ0 ), hmb sb kppcahkto kd ul vbttorb nblbraho W ottbrrbò ul luovo vbttorb W”0λW hmb sa trovk k ;:6¶ al kltahapo raspbtto k W bd mk co stbsso òduco da W.

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:= - =8/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

62. Xho`posazaolb kccb sbqublzb da tbrlb

Rlk tbrlk dassa``btrahk (hol sgksk`blta b òduca rbhaproha davbrsa trk da coro )hostatuatk kd bsb`pao da trb vbttora hmak`kta kd bsb`pao K;, K: b K8 possakò ottblbrck dkcck so``k da trb tbrlb opportulk`bltb hkchocktb, ulk kcck sbqublzk darbttk, ulk kcck sbqublzk alvbrsk bd ulk kcck sbqublzk oòpockrb.

[ubsto rasuctkto í utacazzkjacb lbcck socuzaolb dba harhuata tragksb dassa``btraha b squacajrkta b/o al holdazaola da nuksto. C‑adbk opbrktavk holsastb lbcc‑opbrkrb su trb harhuata òlogksb ottbluta holsadbrkldo cb sbqublzb darbttk-alvbrsk oòpockrb, b poa –so``krb‐ a rasuctkta ottbluta.

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:= - =4/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 68: 6;. AC HAZHRATO B[RAWKCBLTB DA TMBWBLAL VBZ A XAXTB@A TZAGKXB VRÚ BXXBZB HKCHOCKTO XOCO VBZ HKZAHMA Z-H VRÚ BXXBZB HKCHOCKTO XOCO VBZ HKZAHMA Z-C VRÚ BXXBZB HKCHOCKTO RTACAYYKLDO CB ZBNOCB WAXTB VBZ CK HOLTALRK B CK @OLOGKXB LOL VRÚ BXXBZB @KA HKCHOCKTO

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:= - =2/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 688 6;. RL HAZHRATO ZCH VKZKCCBCO B' AL ZAXOLKLYK [RKLDO9 LBXXRLK DBCCB KCTZB AL LBXXRL HKXO CK VKZTB A@@KNALKZAK DBCC'K@@BTTBLYK B' LRCCK CK VKZTB A@@KNALKZAK DBCC'K@@BTTBLYK B' DAWBZXK DK YBZO 6:. AL RL HAZHRATO Z-C-H XBZAB VBZ WKCOZA DA VRCXKYAOLB O@BNK @KNNAOZA DBCCK VRCXKYAOLB DA ZAXOLKLYK AC HAZHRATO B' OM@AHO-HKVKHATAWO AC HAZHRATO B' OM@AHO-ALDRTTAWO AC HAZHRATO B' VRZK@BLTB OM@AHO LBXXRLK DBCCB KCTZB 68. CK ZAXOLKLYK DA RL HAZHRATO Z-C-H VKZKCCBCO XA VRO' OTTBLBZB LBXXRLK DBCCB KCTZB WKZAKLDO CK TBLXAOLB DA KCA@BLTKYAOLB AL LBXXRL HKXO WKZAKLDO CK GZB[RBLYK DA KCA@BLTKYAOLB 64. AL RL HAZHRATO Z-C-H VKZKCCBO AL HOLDAYAOLA DA ZAXOLKLYK, K VKZATK' DA HOZZBLTB LBXXRLK DBCCB KCTZB CK TBLXAOLB B' @KXXA@K CK HOZZBLTB B' @KXXA@K C'A@VBDBLYK B' @KXXA@K 62. AL RL HAZHRATO Z-C-H VKZKCCBCO KCC'KR@BLTKZB DBCCK GZB[RBLYK DA@ALRAXHB CK TBLXAOLB KCC'KR@BLTKZB DBCCK GZB[RBLYK CK TBLXAOLB ZA@KLB HOXTKLTB LBXXRLK DBCCB KCTZB KCC'KR@BLTKZB DBCCK GZB[RBLYK KR@BLTK CK TBLXAOLB 67. AL RL HAZHRATO Z-C-H XBZAB KCC'KR@BLTKZB DBCCK GZB[RBLYK CK HOZZBLTB ZA@KLB HOXTKLTB KCC'KR@BLTKZB DBCCK GZB[RBLYK KR@BLTK CK HOZZBLTB LBXXRLK DBCCB KCTZB KCC'KR@BLTKZB DBCCK GZB[RBLYK DA@ALRAXHB CK HOZZBLTB 6>. AL RL HAZHRATO Z-C-H XBZAB AL HOLDAYAOLA DA ZAXOLKLYK, K VKZATK' DA TBLXAOLB C'A@VBDBLYK B' @KXXA@K CK HOZZBLTB B' @KXXA@K CK TBLXAOLB B' @KXXA@K LBXXRLK DBCCB KCTZB

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:= - =7/>8

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6=. CK ZAXOLKLYK DA RL HAZHRATO Z-C-H XBZAB XA VRO' OTTBLBZB WKZAKLDO CK TBLXAOLB DA KCA@BLTKYAOLB LBXXRLK DBCCB KCTZB WKZAKLDO CK GZB[RBLYK DA KCA@BLTKYAOLB AL LBXXRL HKXO 61. AL RL HAZHRATO Z-C-H VKZKCCBCO VBZ WKCOZA DA VRCXKYAOLB O@BNK @KNNAOZA DBCCK VRCXKYAOLB DA ZAXOLKLYK AC HAZHRATO B' OM@AHO-ALDRTTAWO AC HAZHRATO B' VRZK@BLTB OM@AHO LBXXRLK DBCCB KCTZB AC HAZHRATO B' OM@AHO-HKVKHATAWO ;6. RL HAZHRATO ZCH XBZAB B' AL ZAXOLKLYK [RKLDO9 LBXXRLK DBCCB KCTZB AL LBXXRL HKXO CK VKZTB A@@KNALKZAK DBCC'A@VBDBLYK B' LRCCK CK VKZTB A@@KNALKZAK DBCC'A@VBDBLYK B' DAWBZXK DK YBZO ;;. Hobggahabltb da rasolklzk

Ac hobggahabltb da rasolklzk [r í dbgalato ho`b ac rkpporto trk ck potblzk rbkttavk b ck potblzk kttavk al holdazaola da rasolklzk. Vbr a harhuata rasolklta al sbrab ac hobggahabltb da rasolklzk í dkto dk9

Vbr a harhuata rasolklta al pkrkccbco ac hobggahabltb í dkto dk

Ck jkldk pksskltb í cbnktk kcck grbqublzk da tkncao dkcck rbckzaolb

Dk qubstk rbckzaolb sa dbduhb hmb quklto pañ í bcbvkto [r tklto pañ í strbttk ck jkldk b qualda pañ sbcbttavk ck raspostk al grbqublzk dbc harhuato rasolkltb. Xa ho`prbldb pbrhaú ac òtavo pbr hua a harhuata rasolklta vblnolo utacazzkta pbr sbcbzaolkrb altbrvkcca da grbqublzk, ho`b kd bsb`pao lbcck saltolak da kppkrkta rkdao rahbvblta

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:= - =>/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro ;:. Harhuata rasolklta pkrkccbco

Rl harhuato rasolkltb al pkrkccbco sa ottablb qukldo sa a`polb k zbro ck pkrtb a``knalkrak dbcc‑k``bttblzk ,ovvbro holsadbrkldo k tatoco da bsb`pao ac harhuato al ganurk qukldo

ὦr b g r solo dbttb pucskzaolb b grbqublzk da rasolklzk

C‑k``bttblzk totkcb dbc harhuato vasto dkc nblbrktorb í dktk dkcck sbnubltb rbckzaolb

Al holdazaola da rasolklzk ac òduco dbcc‑k``bttblzk í àlaò b hoalhadb hol ac vkcorb dbcck holduttklzk5 da holsbnublzk ck tblsaolb lbc harhuato, k pkratæ da òduco dbcck horrbltb, í `kssa`k. Xb ck pkrtb a``knalkrak dbcc‑k``bttblzk Q lol í lucck, ac harhuato lol í al rasolklzk bd ohhorrb spbhagahkrb dub hksa9

;8. Harhuata rasolklta sbrab

Rl harhuato rasolkltb al pkrkccbco sa ottablb qukldo ck pkrtb a``knalkrak dbcc‑a`pbdblzk í lucck ,ovvbro holsadbrkldo k tatoco da bsb`pao ac harhuato al ganurk qukldo

ὦr b g r solo dbttb pucskzaolb b grbqublzk da rasolklzk C‑a`pbdblzk totkcb dbc harhuato vastk ka hkpa dbc nblbrktorb í pkra k

Al holdazaola da rasolklzk ac òduco dbcc‑a`pbdblzk í àlaò b hoalhadb hol ac vkcorb dbcck rbsastblzk. Da holsbnublzk ck horrbltb lbc harhuato, k pkratæ da òduco dbcck tblsaolb, í `kssa`k, aloctrb tblsaolb b horrbltb solo al gksb. Xb ck pkrtb a``knalkrak dbcc‑a`pbdblzk Y lol í lucck, ac harhuato lol í al rasolklzk bd ohhorrb spbhagahkrb dub hksa9

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:= - ==/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 684 6;. CK HOXTKLTB DA TB@VO DA RL HAZHRATO ZH XA @AXRZK AL Z*H OM@ XBH W*K 6:. CK XOCRYAOLB DA RLK B[RKYAOLB DAGGBZBLYAKCB CALBKZB DBC VZA@O OZDALB K HOBGGAHABLTA HOXTKLTA B' sb`prb lucck Xa ottablb so``kldo kcck socuzaolb nblbrkcb ulk socuzaolb pkrtahockrb B' ulk socuzaolb ottblutk holsadbrkldo co stkto alazakcb dbc sastb`k Xa ottablb rasocvbldo c'bqukzaolb oònblbk kssohaktk 68. AC TZKLXATOZAO B' C'altbrvkcco da tb`po al hua ac a c harhuato pkssk dk ulk holdazaolb da gulzaolk`blto K kd ulk holdazaolb da gulzaolk`blto J Rlk pkrtahockrb holdazaolb da gulzaolk`blto k rbna`b dbc harhuato Halqub voctb Tku C'altbrvkcco da tb`po al hua ck tblsaolb ka òrsbtta dbc holdblsktorb pkssk dk 6 kd B 64. Ac GRLYAOLK@BLTO DBC TZKLXATOZAO ZH B' DBXHZAWAJACB TZK@ATB Rl'bqukzaolb Rl'bqukzao lb daggbrblzakcb dbc sbholdo ordalb Rl'bqukzaolb Rl'bqukzao lb kcnbjrahk da praò nrkdo Rl'bqukzaolb Rl'bqukzao lb daggbrblzakcb dbc praò ordalb oònblbk k hobggahablta hostklta Rl'bqukzaolb Rl'bqukzao lb daggbrblzakcb dbc praò ordalb lol oònblbk k hobggahablta hostklta 62. DRZKLTB AC TZKLXATOZAO Wkcnolo tuttb cb cbnna dbcc'bcbttrotbhlahk Wkcb soco ck cbnnb da Earhmmogg kccb `kncab Wkcb soco ck cbnnb da Om` ka òrsbtta dbc ho`polbltb Wkcb soco ck cbnnb da Earhmmogg ka loda 67. DRZKLTB CK GKXB DA HKZAHK DA RL HOLDBLXKTOZB Ck horrbltb lbc harhuato vkcb zbro Ck tblsaolb ka suoa òrsbtta hrbshb Ck tblsaolb ka suoa òrsbtta ra`klb hostkltb Ck tblsaolb ka suoa òrsbtta dbhrbshb 6>. CK HOXTKLTB DA TB@VO DBC HAZHRATO ZH XA @AXRZK AL Om` Gkrkd B' kda`blsaolkcb Xbholda

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Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

6=. DRZKLTB CK GKXB DA XHKZAHK DA RL HOLDBLXKTOZB Ck horrbltb lbc harhuato vkcb zbro Ck tblsaolb ka suoa òrsbtta dbhrbshb Ck tblsaolb ka suoa òrsbtta hrbshb Ck tblsaolb ka suoa òrsbtta ra`klb hostkltb 61. K TZKLXATOZAO BXKRZATO RL HOLDBLXKTOZB B' kttrkvbrskto dkcck horrbltb da horto harhu harhuato ato Mk sb`prb ulk tblsaolb lucck ka suoa òrsbtta Xa ho`portk ho`b ul horto harhuato Xa ho`portk ho`b ul harhuato kpbrto

;6.

Vbr ac harhuato al ganurk, al hua solo s olo lota Z0; ℧, Z;0: ℧, Z:04 ℧, W;0;: W, H0 ; G, dbtbràlkrb ck tblsaolb vH(t) pbr -∜3t3+∜ skpbldo hmb ac tksto T í kpbrto dk òctassaò tb`po b hmb kcc‑astkltb t06 vablb hmauso.

XBNRB © :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:1 - 2>/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:1 - 2=/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro ;;. Harhuato ZH al hkrahk

[ukldo ul harhuato bcbttraho, lbc qukcb solo prbsblta holdblsktora, pkssk dk ulk holdazaolb da rbna`b da gulzaolk`blto kd ul‑kctrk, ck luovk holdazaolb da gulzaolk`blto vablb rknnaultk al ul altbrvkcco da tb`po lol lucco , tutto haú hmb kvvablb al tkcb altbrvkcco da tb`po (durktk dbcc‑altbrvkcco, òdkcatæ da vkrakzaolb dbccb nrkldbzzb bcbttrahmb bhh.) vablb dbgalato hol ac tbràlb da trklsatorao. Holsadbrakò ac harhuato rkpprbsbltkto al ganurk, lbc qukcb ul nblbrktorb da gorzk bcbttroòtrahb holtaluk B í hoccbnkto, pbr `bzzo da ul tksto T, kcck sbrab da ul holdblsktorb H bd ul rbsastorb Z. Aldahmakò hol t0t606 c‑astkltb alazakcb dbc gblo`blo trklsatorao b hol t0t∜ c‑astkltb al hua tkcb gblo`blo puú holsadbrkrsa bskurato. Xuppolakò hmb ac holdblsktorb sak alazakc`bltb shkraho, qualda9 vH(t6) 06. Hol ac tksto T hmauso sa puú shravbrb ck CET kcck `kncak

Zashravbldo c‑bqukzaolb ottblutk lbcck sbnubltb gor`k5

dovb τ0ZH í ck hostkltb da tb`po dbc harhuato5 τ í ul pkrk`btro hmb aldahk ck rkpadatæ da bvocuzaolb dbc trklsatorao b sa àsurk al sbholda. Trkshorso ul tb`po t pkra k harhk 2τ ac gblo`blo trklsatorao puú holsadbrkrsa bskurato. Torlakò kcck socuzaolb dbcc‑bqukzaolb b rasocvakò c‑bqukzaolb oònblbk kssohaktk9

C‑altbnrkcb nblbrkcb skræ dkto dk C‑altbnrkcb pkrtahockrb í dkto dkc vkcorb k rbna`b dbcck vH(t), hmb vkcb9 vH(t∜ )0B, al quklto ac holdblsktorb sa ho`portk, al holtaluk, ho`b ul harhuato kpbrto.

Holoshbldo c‑kldk`blto dbcck Wh(t) í possajacb dbtbràlkrb ck horrbltb trkàtb ck rbckzaolb9

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:1 - 21/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro ;:. Harhuato ZH al shkrahk

Holsadbrkldo ac harhuato al ganurk, lbc qukcb sa suppolb hmb ac holdblsktorb sak alazakc`bltb hkraho9 vH(t6)0B. Xa vuocb dbtbràlkrb c‑kldk`blto dbcck vH(t) k pkrtarb dkcc‑astkltb t6 da hmausurk dbc tksto. Al qubsto hkso c‑bqukzaolb daggbrblzakcb, hmb sa shravb kppcahkldo ck CET kcck `kncak, hoalhadb hol c‑bqukzaolb oònblbk kssohaktk9

C‑kldk`blto dbcck Wh(t) í dktk dkc sbnubltb nrkgaho5

Holoshbldo c‑kldk`blto dbcck vh(t) í possajacb rahkvkrb ck horrbltb dktk dkcck sbnubltb rbckzaolb

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:1 - 76/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 682 6;. CK HOXTKLTB DA TB@VO DA RL HAZHRATO ZC ALDAHK Ac tb`po a`pabnkto dkcc'alduttorb pbr shkrahkrsa C'astkltb da tb`po alazakcb Ck rkpadatæ hol hua ac trklsatorao sa bskurashb Ac tb`po a`pabnkto dkcc'alduttorb pbr hkrahkrsa 6:. CK HOXTKLTB DA TB@VO DA RL HAZHRATO ZC XA @AXRZK AL XBH Z*H W*K OM@ 68. K TZKLXATOZAO BXKRZATO RL ALDRTTOZB Mk sb`prb ulk tblsaolb lucck ka suoa òrsbtta Xa ho`portk ho`b ul harhuato kpbrto Xa ho`portk ho`b ul horto harhuato B' kttrkvbrskto dkcck horrbltb da horto harhuato

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:1 - 7;/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro 64. Harhuato ZC al hkrahk

Vbr studakrb ac gblo`blo holsadbrakò ac harhuato raportkto al ganurk, lbc qukcb ul nblbrktorb da gorzk bcbttroòtrahb holtaluk B í hoccbnkto, pbr `bzzo da ul tksto T, kcck sbrab da ul alduttorb C bd ul rbsastorb Z. Aldahmbrbò hol t0t606 c‑astkltb alazakcb dbc trklsatorao b hol t0t∜ c‑astkltb al hua tkcb gblo`blo puú holsadbrkrsa bskurato. Xuppolakò hmb c‑alduttorb sak alazakc`bltb shkraho, qualda9 a (t6)06. Hol ac tksto T hmauso sa puú shravbrb ck CET kcck `kncak9

C‑bqukzaolb daggbrblzakcb puú bssbrb rashrattk9

Dovb sa polb C/Z0tku ovvbro ck hostkltb da tb`po dbc harhuato Vbr ck socuzaolb dbcc‑bqukzaolb sa rasocvb c‑bqukzaolb oònblbk kssohaktk

C‑altbnrkcb pkrtahockrb í dkto dkc vkcorb k rbna`b dbcck a(t), hmb vkcb9 a(t ∜) 0 B/Z, al quklto c‑alduttorb sa ho`portk, al holtaluk, ho`b ul hortoharhuato. Ck socuzaolb dbcc‑bqukzaolb daggbrblzakcb í, qualda9

pbrtklto c‑bsprbssaolb dbcck horrbltb lbc harhuato í dktk dk9 Kldk`blto dbcck horrbltb al gulzaolb dbc tb`po durkltb ck hkrahk dbcc‑alduttorb

Loto c‑kldk`blto dbcck a(t), c‑kldk`blto dbcck tblsaolb ka hkpa dbcc‑alduttorb sa dbtbràlk kppcahkldo ck CET kccb ` `kncab kncab ho`b

sbnub

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:1 - 7:/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

62. Harhuato ZC al shkrahk

Vbr studakrb ac gblo`blo holsadbrakò ac harhuato raportkto al ganurk, lbc qukcb sa suppolb hmb c‑alduttorb sak alazakc`bltb hkraho9 a(t6)0B/Z. Xa vuocb dbtbràlkrb c‑kldk`blto dbcck a(t) k pkrtarb dkcc‑astkltb t6 al hua vablb hortoharhuatkto ac nblbrktorb B hmb kca`bltkvk ac harhuato. Al qubsto hkso c‑bqukzaolb daggbrblzakcb hmb sa shravb hoalhadb hol c‑bqukzaolb oònblbk kssohaktk, ck hua socuzaolb í9

Loto c‑kldk`blto dbcck a(t), c‑kldk`blto dbcck tblsaolb ka hkpa dbcc‑alduttorb sa dbtbràlk kppcahkldo ck CET kccb ` `kncab kncab ho`b sbnub9

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:1 - 78/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

67.

Vbr ac harhuato al ganurk, al hua solo s olo lota W;0;6 W, C0;66 `M, Za0a e℧, dbtbràlkrb ck horrbltb aC(t) pbr -∜3t3+∜ skpbldo hmb ac tksto T í hmauso dk tb`po culnmassaò b hmb k t06 vablb kpbrto.

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:1 - 74/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 687 6;. Harhuato dbc sbholdo ordalb ZCH Vbr co studao da ul harhuato ZCH prbldakò al bsk`b ck ganurk sbnubltb9

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:1 - 72/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 68> 6;. VBZ RL HOLDRTTOZB ZBTTACALBO KTTZKWBZXKTO DK RLK HOZZBLTB A, AC WBZXO DBC HK@VO @KNLBTAHO Vuú bssbrb aldavadukto uskldo ck rbnock dbcck `klo dbstrk B' holhordb kc vbrso dbcck horrbltb Vuú bssbrb aldavadukto uskldo ck rbnock dbcck `klo salastrk Lol sa puú dbtbràlkrb k praora 6:. C'ALDRYAOLB @KNLBTAHK J XA @AXRZK AL TBXCK ^BJBZ ^KTT ^BJBZ*@

68. C'ALDRYAOLB @KNLBTAHK J B' Ck dblsatæ dbc gcusso `knlbtaho Ac gcusso `knlbtaho pbr ck sbzaolb Rlk nrkldbzzk kda`blsaolkcb Aldapbldbltbb dkcc'altblsatæ dbc hk`po `knlbtaho Aldapbldblt 64. VBZ RL HOLDRTTOZB ZBTTACALBO KTTZKWBZXKTO DK RLK HOZZBLTB A, C'ALTBLXATK' DBC HK@VO @KNLBTAHO Hrbshb `kl `klo hmb ha kccoltklakò dkc holduttorb Dbhrbshb `kl `klo hmb ha kccoltklakò dkc holduttorb Za`klb hostkltb bd aldapbldbltb dkcck dastklzk dkc holduttorb B' sb`prb lucck 62. GOZYK DA COZBLTY9 XR RL HOLDRTTOZB DA CRLNMBYYK C KTTZKWBZXKTO DK RLK HOZZBLTB A ,A@@BZXO AL RL HK@VO @KNLBTAHO DA ALDRYAOLB J (VBZVBLDAHOCKZB KCCK HOZZBLTB), KNAXHB RLK GOZYK Hmb í sb`prb lucck G0A*J/C G0J*C/A G0A*J*C 67. KCC'ALTBZLO DA RL XOCBLOADB HOXTATRATO DK L XVAZB KTTZKWBZXKTB DK RLK HOZZBLTB A , KWBLTB CRLNMBYYK C C'ALTBLXATK' DBC HK@VO @KNLBTAHO M WKCB9 M0L*A Lol sa puú dbtbràlkrb k praora M0L*C/A M0L*A/C 6>. LBA @KTBZAKCA GBZZO@KNLBTAHA HOLXADBZKLDO CK HRZWK DA @KNLBTAYYKYAOLB J0g(M) LOTAK@O HMB9 Vbr a `ktbrakca gbrro`knlbt gbrro`knlbtaha aha lol í possajacb dbtbràlkrb ck hurvk da `knlbtazzkzaolb Ck pbr`bkjacatæ `knlbtahk dba `ktbrakca lol í hostkltb Lol bsastb kchul cbnk`b trk J bd M Ck pbr`bkjacatæ `knlbtahk dba `ktbrakca í hostkltb

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:1 - 77/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

6=. AC GCRXXO @KNLBTAHO GA XA @AXRZK AL TBXCK ^BJBZ*@

^KTT ^BJBZ 61. CB VBZDATB VBZ HOZZBLTA VKZKX VKZKXXATB XATB AL RL @KTBZAKCB GBZZO@KNLBT GBZZO@KNLBTAHO AHO Xolo proporzaolkca kc qukdrkto dbcck grbqublzk Wkraklo calbkr`bltb hol ck grbqublzk Dapbldolo soco dkcco spbssorb Xolo aldapbldblta dkcck grbqublzk ;6. CK VBZ@BKJACATK' @KNLBTAHK KXXOCRTK XA @AXRZK AL MBLZQ*@BTZO MBLZQ/@BTZO KDA@BLXAOLKCB

^BJBZ ;;. CK VBZ@BKJACATK' @KNLBTAHK ZBCKTAWK XA @AXRZK AL ^BJBZ MBLZQ/@BTZO KDA@BLXAOLKCB

MBLZQ*@BTZO ;:. CB VBZDATB VBZ AXTBZBXA Xolo alvbrsk`bltb proporzaolkca kcc'krbk dbc hahco da astbrbsa Lol dapbldolo dkc `ktbrakcb Lol dapbldolo dkcck grbqublzk Xolo darbttk`bltb proporzaolkca kcc'krbk dbc hahco da astbrbsa ;8. CB VBZDATB VBZ AXTBZBXA Lol dapbldolo dkcck grbqublzk Xolo alvbrsk`bltb proporzaolkca kcc'krbk dbc hahco da astbrbsa Xolo darbttk`bltb proporzaolkca kcck grbqublzk Lol dapbldolo dkc `ktbrakcb ;4. A @KTBZAKCA GBZZO@KNL GBZZO@KNLBTAHA BTAHA MKLLO RLK VB VBZ@BKJACATK' Z@BKJACATK' @KNLBTAHK ZBCKTAWK @octo `knnaorb da ulo Rnukcb kd ulo @octo àlorb da ulo Xb`prb pkra k qubcck dbc vuoto

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:1 - 7>/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

;2. CK CBNNB DBCC'ALDRY DBCC'ALDRYAOLB AOLB BCBTTZO@KNLBTAHK DAHB HMB Ck gorzk bcbttroòtrahb aldottk í sb`prb salusoadkcb Ck gorzk bcbttroòtrahb aldottk lol dapbldb dkcck vkrakzaolb da gcusso lbc tb`po Ck gorzk bcbttroòtrahb aldottk dapbldb dkcck vkrakzaolb da gcusso lbc tb`po Ck gorzk bcbttroòtrahb aldottk lol sa oppolb kcck hkusk hmb c'mk nblbrktk ;7. CB VBZDATB VBZ HOZZBLTA VKZKX VKZKXXATB XATB AL RL @KTBZAKCB GBZZO@KNLBT GBZZO@KNLBTAHO AHO Wkraklo calbkr`bltb hol co spbssorb Dapbldolo soco dkcck grbqublzk Xolo aldapbldblta dkcco spbssorb Xolo proporzaolkca kc qukdrkto dbcco spbssorb ;>. Cbnnb da Gkrkdky-Cblz

Ck cbnnb da Gkrkdky-Lbu`kll kggbr`k hmb Xb al ul altbrvkcco da tb`po ∇t sa mk ulk vkrakzaolb ∇Χ(J) dbc gcusso da

hk`po `knlbtaho J holhktblkto hol ul harhuato, lbc harhuato í aldottk ulk gorzk bcbttroòtrahb –b‐ hmb nblbrk ulk

horrbltb A hmb sa oppolb kcck vkrakzaolb da gcusso hmb c‑mk nblbrktk‐.

lbc hkso sa kjjaklo L sparb altbrbssktb

kcck vkrakzaolb da gcusso c‑bsprbssaolb davbltk

;=. Vbrdatb pbr horrblta pkrksatb VHV

Xb holsadbrakò ul ckàbralo da `ktbrakcb gbrro`knlbtaho da spbssorb δ sonnbtto kd ul gcusso `knlbtaho vkrakjacb salusoadkc`bltb, pbr ck cbnnb dbcc‑alduzaolb bcbttro`knlbtahk lksholo dbccb gorzb bcbttroòtraha aldottb lba harhuata bcbttraha holhbltraha ortonolkca kccb calbb da gorzk. Tkca tblsaola provohklo ck harhockzaolb da horrblta dbttb da Gohkuct. Ck pbrdatk da potblzk pbr ulatæ da vocu`b puú bssbrb vkcutktk hol ck sbnubltb bsprbssaolb9 al hua Ehp í ul hobggahabltb hmb dapbldb dkc `ktbrakcb5 g í ck grbqublzk UMzP5 J@ í ac vkcorb `kssaò dbcc‑alduzaolb UTbsckP

δ í co spbssorb dbc ckàbralo U``P

Vbr radurrb cb pbrdatb pbr horrblta pkrkssatb a harhuata `knlbtaha dbccb `khhmalb bcbttrahmb vblnolo rbkcazzkta utacazzkldo ckàbrala hol spbssora δ ho`prbsa trk 6,8 - 6,2 ``. Tkca ckàbrala solo asockta trk da coro trkàtb hkrtb spbhakca, vbrlaha, gac`. ;1. Vbrdatb pbr astbrbsa

Lba `ktbrakca gbrro`knlbtaha sonnbtta k `knlbtazzkzaola kctbrlktavb sa mkllo dbccb pbrdatb da potblzk pbr astbrbsa `knlbtahk. Tkca pbrdatb solo proporzaolkca kcc‑krbk dbc hahco da astbrbsa dbc `ktbrakcb qukltagahkldocb pbr ulatæ da vocu`b5 @ U^/`8P al hua Ea í ul hobggahabltb hostkltb hmb dapbldb dkc `ktbrakcb, g í ck grbqublzk aall Mz, J@ í c‑alduzaolb `kssa`k al Tbsck. T bsck. Vbr daàluarb cb pbrdatb pbr astbrbsa b lbcco stbsso tb`po ckshakrb alvkraktb cb proprabtæ `knlbtahmb í socato pbr a hostrattora knnaulnbrb ac 8-4% da sacahao sua ckàbrala durkltb ac prohbs prohbsso so da gkjjrahkzaolb al òdo dk radurrb ck

holduhajacatæ. Ac pkrk`btro hmb saltbtazzk ck qukcatæ dbc `ktbrakcb lba holgrolta dbccb pbrdatb da potblzk í ck hagrk da pbrdatk, hmb rkpprbsbltk ck potblzk dassapktk pbr astbrbsa b horrblta pkrkssatb al ul En da `ktbrakcb hol J@0; T bd g026 g0 26 Mz. Wkcora tapaha solo dbcc‑ordalb da ; ^/En. © :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:1 - 7=/>8

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:6. Gorzb knblta su ulk spark

Holsadbrakò ulk spark9 ul harhuato hmauso al hua shorrb ulk horrbltb A. Vbr sb`pcahatfk kssuàkò ulk spark rbttklnockrb da ckta k b j. Al ul hk`po `knlbtaho J (vbttorb) hostkltb, ck gorzk totkcb knbltb succk spark fb lucck9 ckta opposta dkllo holtrajuta kcck gorzk totkcb da vbrso opposto. Xa pufo daòstrkrb hmb hao‑ fb vbro qukculqub sak ck gor`k dbcck spark.

H‑b‑ pbrfo ul ò`blto torhbltb hmb knashb succk spark. Lbcc‑bsb`pao qua sotto, al hua J (vbttorb) fb darbtto culno a ckta ; b 8, ac ò`blto fb τ 0kc :(j/:)(kAJ) (kjA)J, dovb j/:ulk 0 jrkhhao dbc al ò`blto, kAJ 0 òduco dbcck gorzk knbltb sua ckta : b 45 τ (vbttorb) b‑torhbltb ortonolkcb paklo dbcck 0pknalk b provohk rotkzaolb sblso orkrao.

Xb J (vbttorb) gor`k ul klnoco ν hol ck lor`kcb kc paklo dbcck spark, ac ò`blto torhbltb davbltk τ 0 (kjA)J sal ν. Altroduhakò ul vbttorb K (vbttorb) da òduco X 0 kj, supbrgahab dbcck spark, b darbzaolb ortonolkcb kc paklo dbcck spark. Ac vbrso da K(vbttorb) fb shbcto sbholdo ck rbnock dbcck `klo dbstrk

[ubsto nblbrk ac ò`blto da dapoco `knlbtaho9 ²(vbttorb) 0 AK(vbttorb). Hmb í ul vbttorb darbtto ho` ho`bb K (vbttorb) soprk dbgalato.

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Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro :;. Vbr`bkjacatæ `knlbtahk

ck pbr`bkjacatæ `knlbtahk da ul `ktbrakcb í ulk nrkldbzzk gasahk hmb bspra`b c'kttatudalb dbc `ktbrakcb k `knlbtazzkrsa al prbsblzk da ul hk`po `knlbtaho. Ck pbr`bkjacatæ `knlbtahk sa àsurk al mblry kc `btro (M/`), bquavkcbltb k lbwtol kcc'k`pbrb qukdrkto (L/K\:). [uksa tutta a `bzza oònblba mkllo ulk pbr`bkjacatæ `knlbtahk hmb puú bssbrb holsadbrktk hostkltb, tuttkvak pbr kchulb sostklzb (ho`b gbrro, hojkcto, lahmbc) bssk mk ul ho`portk`blto hmb `klagbstk ulk hbrtk astbrbsa, ovvbro ck pbr`bkjacatæ òstrk ulk dapbldblzk dkccb prbhbdblta `knlbtazzkzaola b s`knlbtazzkzaola sujatb dk tkca `ktbrakca. Cb sostklzb pbr cb qukca sa vbragahk tkcb ho`portk`blto solo dbttb gbrro`knlbtahmb. Lbccb sostklzb lol gbrro`knlbtahmb ac vkcorb dbcck pbr`bkjacatæ `knlbtahk daggbrashb da poho raspbtto k qubcck dbc vuoto, b sa davadolo al (--< lol sa "davadolo al" `k "dak`knlbtahmb b pkrk`knlbtahmb solo sostklzb daggbrblta dkccb gbrro`knlbtahmb) dak`knlbtahmb (al hua ck pbr`bkjacatæ rbcktavk í àlorb dbcc'ulatæ) b pkrk`knlbtahmb (al hua ck pbr`bkjacatæ rbcktavk í `knnaorb dbcc'ulatæ). Haú sa daggbrblzak raspbtto kcck pbràttavatæ bcbttrahk, hmb puú daggbrarb da òcto dkc vkcorb lbc vuoto b hk`jak sblsajaca`bltb k sbholdk dbcck sostklzk, kssu`bldo pbrú sb`prb vkcora `knnaora raspbtto k qubcco lbc vuoto. Ck pbr`bkjacatæ `knlbtahk dbc vuoto ²6 í ulk dbccb hostklta gasahmb goldk`bltkca. Ac suo vkcorb al ulatæ dbc XA í9

²604φ* ;6\->M/`. Xpbsso ck pbr`bkjacatæ sa bspra`b ho`b ac prodotto ²0²r*²6 dbcck pbr`bkjacatæ rbcktavk ²r b da qubcck dbc vuoto ²6 Ck pbr`bkjacatæ `knlbtahk í cbnktk kc hk`po `knlbtaho (M) b kcc‑alduzaolb `knlbtahk(J) dkcck rbckzaolb ²0J/M

::. Zbnock dbcck `klo salastrk

Ck rbnock dbcck `klo salastrk í ul `btodo pbr aldavadukrb ck darbzaolb dbcck gorzk. Opbrktavk`bltb holsastb lbc dasporrb cb pra`b trb datk dbcck `klo salastrk k 16¶ c‑ulk raspbtto kcc‑kctrk, polbldo • c‑aldahb lbcck darbzaolb dbc vbttorb alduzaolb , • ac `bdao lbcck darbzaolb dbcck horrbltb (hkrahmb da bcbttrola al òva`blto), • ck gorzk kvræ ck darbzaolb dbc poccahb

:8. Zbnock dbcck `klo dbstrk

B‑ loto hmb ul gaco pbrhorso dk horrbltb bcbttrahk nblbrk kttorlo k sb ul hk`po `knlbtaho.Xb ac holduttorb í rbttacalbo cb calbb dbc hk`po `knlbtaho solo harholgbrblzb holhbltrahmb kc gaco hmb nakhhaolo su pakla pbrpbldahockra kc gaco stbsso. Ck rbnock dbcck `klo dbstrk í ul prohbda`blto opbrktavb pbr dbtbràlkrb ac vbrso dbc hk`po `knlbtaho. Xb aldahmakò hol ac poccahb ck darbzaolb dbcck horrbltb , cb datk dbcck `klo dbstrk hmaudbldosa aldahmbrkllo ac vbrso dbc hk`po `knlbtaho. cb dub nrkldbzzb ovvbro ck horrbltb b ac hk`po `knlbtaho solo cbnktb trk da coro dkcck cbnnb dbcck harhuatkzaolb `knlbtahk

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:4. Gorzb knblta su holduttora pkrkccbca

Holsadbrakò dub holduttora rbttacalba kttrkvbrskta dk dub horrblta kvblta altblsatæ davbrsk A; bd A: posta al krak k dastklzk d trk coro. Ac holduttorb kttrkvbrskto dkcck horrbltb A; kcck dastklzk d hrbk ul hk`po `knlbtaho da alduzaolb J;,

Ac holduttorb kttrkvbrskto dkcck horrbltb A: skræ sonnbtto kd ulk gorzk kvbltb òduco G:;0A:*c*J; . Ck darbzaolb bd ac vbrso da G:; solo dbtbràlkjaca hol ck rbnock dbcck `klo salastrk. Klkconk`bltb, suc holduttorb kttrkvbrskto dkcck horrbltb A; sa mk ck gorzk G;:0A;*c*J:. [ubstb gorzb gkrkllo kttrkrrb a holduttora sb cb dub horrblta mkllo co stbsso vbrso , `bltrb gkrkllo rbspalnbrb a holduttora a vbrsa dbccb horrblta hmb pbrhorrolo a holduttora solo opposta.

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:2. Hahco da astbrbsa

Vbr accustrkrb tkcb gblo`blo sa suppolnk da `knlbtazzkrb ul luhcbo da `ktbrakcb altorlo kc qukcb solo kvvoctb L sparb pbrhorsb dk horrbltb b da raportkrb su ul nrkgaho hkrtbsaklo cb rbcktavb hoppab da vkcora J-M, apotazzkldo hmb ck horrbltb `knlbtazzkltb possk vkrakrb sak al altblsatæ (dk zbro k A@) hmb ho`b vbrso da pbrhorrblzk dbcc‑ kvvocna`blto, dbtbràlkldo, da holsbnublzk, ho`b loto dkccb sbnublta rbckzaola raportktb ulk hk`po `knlbtaho vkrakjacb trk nca bstrbà M@al b M@kx. Vrohbdbldo hol co studao dbc hahco gkhhakò vkrakrb ck horrbltb alazakc`bltb pkra k zbro galo kc vkcorb A@kx (k hua horraspoldb c‑altblsatæ da hk`po `knlbtaho M@kx), c‑alduzaolb `knlbtahk hrbshb sbholdo ulk hurvk dbttk da pra`k `knlbtazzkzaolb. [ukldo sa raportk ac hk`po dk M@kx k 6 c‑alduzaolb `knlbtahk kcc‑altbrlo dbc `ktbrakcb lol ratorlk k 6 al quklto ac `ktbrakcb ra`klb –`knlbtazzkto‐. Vbr raportkrb k zbro ac vkcorb dbcc‑alduzaolb dbcc‑alduzaolb jasonlk alvbrtarb ck horrbltb. Xb sa gk vkrakrb vkrakrb hahcahk`bltb ck horrbltb, b qualda c‑altblsatæ dbc hk`po M, trk Màl b M`kx c‑alduzaolb `knlbtahk pbrhorrbræ ck hurvk dbshrattk prbhbdbltb`bltb.

ac nblbrktorb dbvb gorlarb blbrnak kggalhmb ac `ktbrakcb `ktbrakcb sa possk `knlbtazzkrb kctbrlktavk`bltb .C‑blbrnak dassapktk í proporzaolkcb kcc‑krbk dbc hahco da astbrbsa. C‑blbrnak sa dassapk al hkcorb lba doàla `knlbtaha. Vossakò a``knalkrb hmb a doàla `knlbtaha pbr hk`jakrb ac coro orabltk`blto sujasholo urta b qualda produzaolb da hkcorb. Vbr tkcb òtavo lbcck rbkcazzkzaolb dba luhcba `knlbtaha dbccb `khhmalb bcbttrahmb í prbgbrajacb utacazzkrb `ktbrakca hmb mkllo ul hahco da astbrbsa hol c‑krbk –pahhock‐. Xb prbldakò al holsadbrkzaolb ck hurvk da `knlbtazzkzaolb sa bvalhb hmb9 ac cbnk`b bsastbltb trk M b J lol í calbkrb b qualda ck pbr`bkjacatæ ² lol í hostkltb.

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Cbzaolb 68= 6;. LBCCK DRKCATK' TZK HAZHRATA BCBTTZAHA B HAZHRATA @KNLBTAHA Ck horrbltb hoalhadb hol ck gorzk `knlbto-òtrahb Lol ha solo horraspoldblzb trk nrkldbzzb bcbttrahmb b nrkldbzzb `knlbtahmb Ck rbsastblzk hoalhadb hol ac gcusso `knlbtaho Ck horrbltb hoalhadb hol ac gcusso `knlbtaho 6:. LBCCK DRKCATK' TZK HAZHRATA BCBTTZAHA B HAZHRATA @KNLBTAHA Ck horrbltb hoalhadb hol ck gorzk `knlbto-òtrahb Ck rbsastblzk hoalhadb hol ac gcusso Ck tblsaolb hoalhadb hol L*A (gorzk `knlbto-òtrahb) Lol ha solo horraspoldblzb trk nrkldbzzb bcbttrahmb b nrkldbzzb `knlbtahmb 68. CK ZACRTTKLYK DA RL @KTBZAKCB @KNLBTAHO B' darbttk`bltb proporzaolkcb kcck culnmbzzk Hoalhadb hol qubcck dbc vuoto B' darbttk`bltb proporzaolkcb kcck sbzaolb B' aldapbldbltb dkcck culnmbzzk 64. AL ONLA LODO DA RL HAZHRATO @KNLBTAHO Ck so``k dba gcussa lol í qukltagahkjacb Ck so``k dba gcussa í lucck Ck so``k dba gcussa í sb`prb lbnktavk Ck so``k dba gcussa í sb`prb posatavk

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62. Dukcatæ harhuata bcbttraha-har bcbttraha-harhuata huata `knlbtaha

A harhuata `knlbtaha solo dbc tutto klkconma k qubcca bcbttraha , pbrtklto í possajacb opbrkrb b kppcahkrb ka praà cb cbnna hmb rbnocb`bltklo ac gulzaolk`blto qubst‑uctaà. Rl harhuato bcbttraho í ul alsab`b opportulk`bltb hoordalkto da `ktbrakca bcbttraha, kvbltb co shopo da stkjacarb ul dbtbràlkto kldk`blto (o pbrhorso) dbcck horrbltb bcbttrahk A, nblbrktk dk ulk kdbnuktk g.b.`. R ( gorzk bcbttro-òtrahb) klkconk`bltb ul harhuato `knlbtaho í ul alsab`b opportulk`bltb hoordalkto da `ktbrakca `knlbtaha, kvbltb co shopo da stkjacarb ul dbtbràlkto kldk`blto (o pbrhorso) dbc gcusso `knlbtaho aldotto Χ nblbrkto dk ulk kdbnuktk g.`.`. LA (gorzk `knlbto-òtrahb) Lba projcbà rbcktava ka harhuata bcbttraha sa rahmabdb da dbtbràlkrb ck daggbrblzk da potblzakcb b cb horrblta lba davbrsa rkà b bcb`blta dbcck rbtb bcbttrahk dovutb kcck prbsblzk da nblbrktora da tblsaolb b da horrbltb. Klkconk`bltb a projcbà rbcktava ka harhuata `knlbtaha ranukrdklo ck dbtbràlkzaolb dba gcussa `knlbtaha b altblsatæ da hk`pa `knlbtaha lbccb davbrsb pkrta dba harhuata hkusktb dkccb horrblta hmb harhocklo lbnca jojalb kvvoctb altorlo ka luhcba `knlbtaha (k`pbrsparb)

Al jksb kccb rbckzaola ottblutb, solo dbduhajaca a pralhapa goldk`bltkca pbr a harhuata `knlbtaha, klkconma ka pralhapa da Earhmmogg pbr cb rbta bcbttrahmb9

hmb kggbr`klo hmb 9 • ck so``k kcnbjrahk da tutta a gcussa `knlbtaha hmb kttrkvbrsk kttrkvbrsklo lo ul lodo al ul harhuato `knlbt `knlbtaho aho í lucck b hmb • culno ul pbrhorso hmauso al ul harhuato `knlbtaho ck so``k kcnbjrahk dbccb k`pbrsparb í unukcb kcck so``k kcnbjrahk dba prodotta dbccb racuttklzb pbr a rbcktava gcussa.

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67. Zacuttklzk `knlbtahk

Mopealsol kc

ck racuttklzk àsurk c'opposazaolb da ul `ktbrakcb kc trklsato da ul gcusso `knlbtaho. Bssk í cbnktk dkcck cbnnb da rkpporto trk ck gorzk `knlbtoòtrahb (g.`.`.) kppcahktk kd ul harhuato `knlbtaho b ac gcusso da alduzaolb dk bssk nblbrkto b holhktblkto hol ac harhuato. G`.`.

Ck racuttklzk `knlbtahk `knlbtahk í spbsso aldahktk hol ck cbttbrk dbcc'Mblry (M√;).

b sa àsurk lbc sastb`k XA al K`pbrb-sparb/^j, bquavkcblta kcc'alvbrso

Ck racuttklzk í darbttk`bltb proporzaolkcb kcck culnmbzzk dbc pbrhorso `knlbtaho dbc gcusso, `bltrb í alvbrsk`bltb proporzaolkcb proporzaolkcb kcck pbr`bkjacatæ dbc `ktbrakcb (gkhacatæ k ckshakrsa kttrkvbrskrb) b kcck sbzaolb (quklto pañ í kctk, tklto àlorb í c‑ostkhoco kc gcusso).

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6>.

Dbc harhuato `knlbtaho raportkto al ganurk solo lota L;0 266 sparb, A ;0 4 K X 0 6,2 `: (sbzaolb ortonolkcb kccb calbb da gcusso) L:0 466 sparb, A :0 = K, c0 ;,: `, ²r0 :.666. Tutta a trolhma mkllo unukcb sbzaolb X b unukcb culnmbzzk c ²60 ;,:2> ;6-7 M/` ¾

Dbtbràlkrb ac vkcorb dbcc‑alduzaolb `knlbtahk J lbc trolho KJ.

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6=.

Ck spark òstrktk al ganurk í a`òjacb b aldbgor`kjacb, kc suo altbrlo sa mk ul hk`po `knlbtaho da alduzaolb J(t) vkrakjacb lbc tb`po (ortonolkcb kc paklo dbc goncao, g oncao, bltrkltb lbc goncao), solo lota x 0 : `, y 0 6,2 `, J(t)0 J(t )0 :¾t T, Z0 ; ℧, hkchockrb ck horrbltb harhockltb lbcck spark b ac vbrso da harhockzaolb.

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61.

Ck spark òstrktk al ganurk mk trb ckta gassa bd ul ckto òjacb k vbcohatæ hostkltb v(t). Kc suo altbrlo sa mk ul hk`po `knlbtaho da alduzaolb J(t) hostkltb (ortonolkcb kc paklo dbc goncao, bltrkltb lbc goncao)5 solo lota v(t) 0 6,8 `/sbh, y 0 ; `, J(t)0 : T, Z0 ; ℧, dbtbràlkrb ck horrbltb harhockltb lbcck spark bd ac vbrso da harhockzaolb.

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Cbzaolb 681 6;. AC HOBGGAHABLTB DA @RTRK ALDRYAOLB @ XA @AXRZK AL MBLZQ OM@ GKZKD XBHOLDA 6:. AC HOBGGAHABLTB DA @RTRK ALDRYAOL A LDRYAOLB B B' aldapbldbltb dka vkcora dba hobggahabl hobggahabltata da kuto alduzaolb Wkcb zbro pbr harhuata pbrgbttk`bltb khhoppak khhoppaktata Wkcb zbro pbr harhuata `knlbtahk` `knlbtahk`bltb bltb daskhhoppakta B' sb`prb lucco 68. AC HOBGGAHABLTB DA KRTO ALDRYAOLB C Lol dapbldb dkccb hkrkttbrastahmb gasahmb dbc harhuato `knlbtaho Xa àsurk al Mblry/`b Mblry/`btro tro Dapbldb dkccb hkrkttbrastahmb gasahmb dbc harhuato `knlbtaho B' darbttk`bltb proporzaolkcb kcck racuttklzk dbc harhuato 64. AC HOBGGAHABLTB DA @RTRK ALDRYAOLB @ TZK DRB JOJALB ; B : Í sb`prb @0 @;:*@:; B' sb`prb @;:0@:; @;:0@:;0@ B' sb`prb lucco 62. Alduttklzk

C'alduttklzk í ck proprabtæ dba harhuata bcbttraha tkcb bcbttraha tkcb pbr hua ck horrbltb horrbltb (altbsk (altbsk vkrakjacb lbc tb`po) hmb ca kttrkvbrsk alduhb ulk gorzk bcbttroòtrahb hmb, bcbttroòtrahb hmb, pbr ck cbnnb da Cblz, Cblz, í proporzaolkcb kcck vkrakzaolb dbc gcusso `knlbtahoholhktblkto `knlbtaho holhktblkto dkc harhuato. Ac rkpporto trk gcusso `knlbtaho holhktblkto dkc harhuato b ck horrbltb hmb nblbrk tkcb gcusso í ul pkrk`btro gasso. Xb holsadbrakò ulk jojalk jojalk hol L sparb quklto bsposto puú bssbrb rakssulto rakssulto lbccb sbnublta rbckzaola

Dk hua possakò dbgalarb c‑alduttklzk5 c‑alduttklzk5

Xostatubldo

C‑alduttklzk dapbldbltb dkcck dkcck nbo`btrak b dasposazaolb dasposazaolb dba harhuata, dbtto hobggahabltb da kutoalduzaolb sb ragbrato k gcusso b horrbltb succo stbsso harhuato, hobggahabltb da ùtuk alduzaolb sb ragbrato kd ul gcusso g cusso su ul harhuato nblbrkto dk ulk horrbltb hmb harhock al ul kctro harhuato. Ck nrkldbzzk gasahk kssohaktk í aldahktk hol ac sa`joco C al olorb dbc gasaho Mbalrahm Cblz. Cblz. b sa àsurk al Mblry (M).

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Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

67. Hobggahabltb da khhoppak`b khhoppak`blto lto

ac hobggahabltb da khhoppak`blto khhoppak`blto í dkto dkcck rbckzaolb E0|@|/∙C;*C:. Dovb @ al vkcorb kssocuto í ac hobggahabltb da ùtuk alduzaolb b C; b C: solo a vkcora da alduttklzk dbc harhuato prbsuppolbldo pbr ck trkttkzaolb dbcc‑krno`blto ac sbnubltb harhuato9

E í sb`prb ho`prbso trk zbro b ulo. Ac hobggahabltb da ùtuk alduzaolb @ puú kvbrb sbnlo lbnktavo o posatavo, dapbldb dka gcussa ùtuk`bltb holhktblkta, lbcco spbhagaho sb bssa rasuctalo holhorda o dashorda hol a gcussa dovuta kccb kuto alduzaola. Holvbzaolkc`bltb sa aldahk hol ul pulto `krhkto a dub òrsbtta horraspoldblta kd ul hobggahabltb @ posatavo. Al prktahk ac sbnlo da @ dapbldb dkc vbrso hol hua solo kvvocta a dub kvvocna`blta. Al nblbrkcb ul kvvocna`blto skræ sonnbtto sak kc gcusso hmb mk prodotto sak kc gcusso prodotto dk kctra kvvocna`blta hol hua bsso í `knlbtahk`bltb khhoppakto. Lbc hkso da dub kvvocna`blta kvrbò9

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Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro 6>. Hobggahabltb da ùtuk alduzaolb

Ho`b loto ck sb`pcahb horrbltb bcbttrahk klhmb gcuashb al ul harhuato, sb í ulk horrbltb da vkrakjacb altblsatæ, nblbrk ul hk`po `knlbtaho vkrakjacb, hmb puú aldurrb horrbltb bcbttrahk al ul kctro. Rlk vkrakzaolb da horrbltb bcbttrahk nblbrk ulk vkrakzaolb dbc gcusso dbc hk`po `knlbtaho lbc sbholdo harhuato5 da holsbnublzk al bsso hoàlhak k shorrbrb horrbltb. Xa puú daòstrkrb hmb ac gcusso dbc hk`po `knlbtaho rbcktavo kd ulo dba dub harhuata í darbttk`bltb proporzaolkcb kcck horrbltb hmb co nblbrk, b hmb shorrb lbcc‑kctro harhuato5 ck rbckzaolb í dktk dkcck sbnubltb gorùck9 a:   Χ;↚:0@⋂a; , Χ:↚;0@⋂a: dovb @ rkpprbsbltk ulk hostkltb, dbttk hobggahabltb da ùtuk alduzaolb dba harhuata. Klhmb qubsto hobggahabltb, hosã ho`b ac hobggahabltb da kutoalduzaolb, vablb àsurkto al mblry (M). Klhmb al qubsto hkso, possakò rahkvkrb c‑bsprbssaolb dbcck gorzk bcbttroòtrahb aldottk al hakshulo dba dub harhuata, b dovutk kcck prbsblzk dbcck horrbltb hmb shorrb lbcc‑kctro9 g;↚:b`0 ‘@⋂∇a;/ ∇t

,

g:↚;b`0 ‘@⋂∇a:/ ∇t

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Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 64; 6;. CK HAGZK DA VBZDATK DBCCB CK@ABZB K HZAXTKCCA OZABLTKTA B' VZKTAHK@BLTB VKZA K YBZO ^KTT/EN WKCB ALTOZLO K ;66 ^KTT/EN WKCB ALTOZLO K 6,2 ^KTT/EN WKCB ALTOZLO K 26 ^KTT/EN 6:. LBC TZKXGOZ T ZKXGOZ@KTOZB @KTOZB ADBKCB e0B;/B: e0A;/A: E0B;/B:0A;/A: e0; 68. AL RL TZKXGOZ@KTOZB TZKXGOZ@KTOZB ADBKCB K;0K: K;2% DBC HKZAHO LO@ALKCB AC ZBLDA@BLTO B' @ALOZB DA RLO AC ZBLDA@BLTO LOL B' [RKLTAGAHKJACB

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Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 64; 6>. Trksgor`ktorb adbkcb k vuoto

Ac trksgor`ktorb í ulk `khhmalk bcbttrahk stktahk, hmb sbrvb pbr vkrakrb (trksgor`krb) a pkrk`btra al alnrbsso (tblsaolb b altblsatæ da horrbltb) raspbtto k qubcca al ushatk, `kltblbldo hostkltb ck potblzk bcbttrahk . Xb Kca`bltakò ac pra`krao hol ulk tblsaolb W; salusoadkcb ckshakldo a òrsbtta sbholdkra kpbrta sakò al prbsblzk dbc gulzaolk`blto k vuoto dbc trksgor`ktorb Bltrkldo lbc `brato dbcck trkttkzaolb dbcc‑krno`blto Kppcahkldo ck tblsaolb W; harhock lbcc‑kvvocna`blto pra`krao ulk horrbltb A² (`knlbtazzkltb) hmb nblbrk ul gcusso `knlbtaho lbc lbc luhcbo klhm‑bsso khhbttkjac`bltb kpprossa`kjacb k salusoadkcb. Kca`bltkldo ck `khhmalk ac ho`portk`blto í qubcco da ul harhuato purk`bltb alduttavo A²0 W; /(i]bccb). Ck vkrakzaolb dbc gcusso Χ(t) holhktblkto hol nca kvvocna`blta pra`krao (hostatuato dk L; sparb) b sbholdkrao (hostatuato dk L: sparb) nblbrk pbr ck cbnnb da Gkrkdky dub gb` salusoadkca B; bd B: Kldkldo k svocnbrb a hkchoca5

Holsadbrkldo ac harhuato bquavkcbltb

Daknrk``k vbttorakcb

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Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 64;

6=. Rso dbc trksgor`ktorb lbnca a`paklta bcbttraha

Ac trksgor`ktorb í ulk `khhmalk bcbttrahk stktahk, hmb sbrvb pbr vkrakrb (trksgor`krb) a pkrk`btra al alnrbsso (tblsaolb b altblsatæ da horrbltb) raspbtto k qubcca al ushatk, `kltblbldo hostkltb ck potblzk bcbttrahk . Xocatk`bltb ul trksgor`ktorb í utacazzkto pbr ottblbrb ul vkcorb da tblsaolb davbrso dk qubcco daspolajacb b pbr qubsto puú bssbrb holsadbrkto ulk spbhab da –kdkttktorb‐ hmb pbr`bttb da hoccbnkrb ulk sornbltb da blbrnak kd ul utacazzktorb hmb gulzaolk k tblsaolb davbrsk   davbrsk Lbcck produzaolb b dastrajuzaolb dbcc'blbrnak bcbttrahk a trksgor`ktora pbr`bttolo da a`pabnkrb a vkcora da tblsaolb b horrbltb pañ opportula. Algktta pbr ulk `knnaorb bggahablzk dbnca a`paklta í `bncao kvbrb kctb tblsaola b jkssb horrblta hosã dk9 radurrb cb sbzaola dba hkva (qualda `blo `ktbrakcb, `blo pbso, hk`pktb pañ culnmb trk a trkcahha) b kjjksskrb ac hosto dbcc'a`paklto radurrb cb pbrdatb radurrb cb hkdutb da tblsaolb Kccork dovb í lbhbsskrao trksportkrb nrklda qukltatktava da potblzk pbr culnmb dastklzb, sa utacazzbrkllo sastbà al kctk tblsaolb ( Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::9689:1 - =2/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 64; 61. Trksgor`ktorb adbkcb sotto hkraho

Ac trksgor`ktorb `khhmalk bcbttrahk stktahk, hostkltb hmb sbrvbckpbr vkrakrbbcbttrahk (trksgor`krb) a pkrk`btra al alnrbsso (tblsaolb b altblsatæ da horrbltb) raspbttoí kulk qubcca al ushatk, `kltblbldo potblzk . Holsadbrkldo c‑apotbsa da ul trksgor`ktorb adbkcb Xb Kca`bltakò ac pra`krao hol ulk tblsaolb W; salusoadkcb b Trk a òrsbtta dbc sbholdkrao í prbsbltb ul hkraho da a`pbdblzk Y nblbrkc`bltb Omàho alduttavk, sakò al prbsblzk dbc gulzaolk`blto sotto hkraho dbc trksgor`ktorb Bltrkldo lbc `brato dbcck trkttkzaolb dbcc‑krno`blto Kppcahkldo ulk tblsaolb salusoadkcb W; harhock lbcc‑kvvocna`blto pra`krao ulk horrbltb A ² dbttk horrbltb `knlbtazzkltb, hmb nblbrk ul gcusso kcc‑altbrlo dbc luhcbo klhm‑bsso khhbttkjac`bltb kpprossa`kjacb k salusoadkcb. Ck vkrakzaolb dbc gcusso holhktblkto hol nca kvvocna`blta pra`krao (hostatuato dk L; sparb) b sbholdkrao (hostatuato dk L: sparb) nblbrk pbr ck cbnnb da Gkrkdky dub gorzb bcbttroòtraha aldottb salusoadkca B; bd B:. Ka hkpa dba òrsbtta dbcc‑kvvocna`blto sbholdkrao hmb í hmauso su ul‑a`pbdblzk Y í prbsbltb ulk tblsaolb W: b da holsbnublzk ulk horrbltb A: sgksktk succk tblsaolb W: da ul klnoco pkra kcc‑klnoco hkrkttbrastaho dbcc‑a`pbdblzk Y. Ck horrbltb A: harhockldo lbccb L: sparb dbc sbholdkrao nblbrk ul gcusso `knlbtaho Χ: hmb sa sovrkppolb kc gcusso prbbsastbltb Χ. [ubstk sovrkpposazaolb tbldbrbjjb k gkr vkrakrb ac gcusso Χ, `k pbr ck cbnnb da CEG kcck `kncak W;0B; b kggalhmí ck holdazaolb B;0Eost04,44*g*L;*Χ@ sak soddasgkttk, ac hmb ho`portk hmb ac gcusso dbvb ra`klbrb hostkltb, ck `khhmalk rahmak`k dkcck rbtbCkdahorrbltb kca`bltkzaolb ulk horrbltb da rbkzaolb pra`krak A;‑ hmb so``ktk kd A² gor`k ck A;. da rbkzaolb pra`krakdbttk nblbrbræ ulk gorzk `knlbtoòtrahb L;*A;‑ unukcb bd oppostk kcck gorzk `knlbtoòtrahb nblbrktk dkcck horrbltb A: (haoí L:*A:). B‑ hmakro hmb lbc gulzaolk`blto sottto hkraho ck `khhmalk kssorjb ulk qukltatavo da horrbltb `knlbtazzkltb `knnaorb raspbtto kc gulzaolk`blto k vuoto. Zkppprbsbltkldo ac daknrk``k vbttorakcb dbc Trksgor`ktorb al gulzaolk`blto sotto hkraho kjjakò9

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Cbzaolb 64; ;6. Holdazaola da adbkcatæ pbr ul trksgor`ktorb trksgor`ktorb

Ck holdazaolb da trksgor`ktorb adbkcb holsastb lbcc‑apotazzkrb hmb succk `khhmalk va saklo cb sbnublta hkrkttbrastahmb 5 lucck suncadakvvocna`blta (al rk`b) pra`krao •.rbsastblzk lol ha solo pbrdatb potblzk pbr astbrbsa b pbr horrbltab sbholdkrao5 pkrkssatb Lbc luhcbo `knlbtaho5 • ac luhcbo `knlbtaho kjjak racuttklzk `knlbtahk lucck5 • Lol va saklo dspbrsaolb da gcussa, ovvbro hmb ac gcusso nblbrkto dkcck horrbltb A; (kvvocna`blto pra`krao) sa holhktbla tutto hol c‑kvvocna`blto sbholdkrao, b vahbrvbrsk ovvbro hmb ac gcusso nblbrkto dkcck horrbltb A: (kvvocna`blto sbholdkrao) sa holhktbla tutto hol c‑kvvocna`blto pra`krao) A dub harhuata saklo pbrgbttk`bltb khhoppakta `knlbtahk`bltb

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Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 64: 6;. AC JACKLHAO BLBZNBTAHO DBC TZKXGOZ@KTOZB ZBKCB XOTTO HKZAHO XA BXVZA@B HO@B9 V:0V;-VI+VHR V;06 VHR+VI0V:-V; V;0V:+VI+VGB 6:. AL RL TZKXGOZ@KTOZB ZBKCB XOTTO HKZAHO A;'0A6+A: (WBTTOZA) A;0e*A6 (WBTTOZA) A;0A6+A;' (WBTTOZA) A;'0A6+A: (@ODRCA)

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Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 64:

68. Trksgor`ktorb rbkcb sotto hkraho

Ac trksgor`ktorb í ulk `khhmalk bcbttrahk stktahk, hmb sbrvb pbr vkrakrb (trksgor`krb) a pkrk`btra al alnrbsso (tblsaolb b altblsatæ da horrbltb) raspbtto k qubcca al ushatk, `kltblbldo hostkltb ck potblzk bcbttrahk . Bltrkldo lbc `brato dbcck trkttkzaolb dbcc‑krno`blto Kppcahkldo ulk tblsaolb salusoadkcb W; harhock lbcc‑kvvocna`blto pra`krao ulk horrbltb dbttk horrbltb k vuoto A6 ck qukcb mk ck ho`polbltb `knlbtazzkltb A² hmb nblbrk ul gcusso `knlbtaho salusoadkcb Χ kcc‑altbrlo dbc luhcbo. Ck vkrakzaolb dbc gcusso holhktblkto hol nca kvvocna`blta pra`krao (L; sparb) b sbholdkrao (L:sparb) nblbrk pbr ck cbnnb d Gkrkdky dub gorzb bcbttroòtraha aldottb B; bd B:. Ka hkpa dba òrsbtta dbcc‑kvvocna`blto sbholdkrao hmb í hmauso su ul‑a`pbdblzk Y í prbsbltb ulk tblsaolb W: b da holsbnublzk ulk horrbltb A: sgksktk succk tblsaolb W: da ul klnoco pkra kcc‑klnoco hkrkttbrastaho dbcc‑a`pbdblzk Y. Ck horrbltb A: harhockldo lbccb L: sparb dbc sbholdkrao nblbrk ul gcusso `knlbtaho Χ: hmb sa sovrkppolb kc gcusso prbbsastbltb Χ. [ubstk sovrkpposazaolb tbldbrbjjb k gkr vkrakrb ac gcusso Χ, `k pbr ck cbnnb da CEG kcck `kncak W;0B; b kggalhmí ck holdazaolb B;0Eost04,44*g*L;*Χ@ sak soddasgkttk, ac hmb ho`portk hmb ac gcusso dbvb ra`klbrb hostkltb, ck `khhmalk rahmak`k dkcck rbtb da kca`bltkzaolb ulk horrbltb dbttk da rbkzaolb pra`krak A;‑ tkcb dk nblbrkrb ulk gorzk `knlbtoòtrahb L;A;‑ unukcb bd oppostk kcck gorzk `knlbtoòtrahb L:A: nblbrktk dkcck horrbltb A:. Durkltb ac gulzaolk`blto sotto hkraho ck `khhmalk kssorjb ulk horrbltb hmb vk dk A6 kd A;0A6+A;‑. Trkttkldosa da ul trksgor`ktorb rbkcb va skrkllo dba gcussa daspbrsa hmb vocbldoca qukltagahkrb solo pkra

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Cbzaolb 64: 64. Trksgor`ktorb rbkcb k vuoto

Ac trksgor`ktorb í ulk `khhmalk bcbttrahk stktahk, hmb sbrvb pbr vkrakrb (trksgor`krb) a pkrk`btra al alnrbsso (tblsaolb b altblsatæ da horrbltb) raspbtto k qubcca al ushatk, `kltblbldo hostkltb ck potblzk bcbttrahk . Xb Kca`bltakò ac pra`krao hol ulk tblsaolb W; salusoadkcb ckshakldo a òrsbtta sbholdkra kpbrta sakò al prbsblzk dbc gulzaolk`blto k vuoto dbc trksgor`ktorb Bltrkldo lbc `brato dbcck trkttkzaolb dbcc‑krno`blto Kppcahkldo ck tblsaolb W; , ck `khhmalk kssorjaræ dkcck rbtb ulk horrbltb hmak`ktk horrbltb k vuoto( A6), hostatuatk dkcck horrbltb `knlbtazzkltb A ² b dkcck horrbltb Ak cbnktk kccb pbrdatb da potblzk lbc gbrro . Ck vkrakzaolb dbc gcusso Χ(t) holhktblkto hol nca kvvocna`blta pra`krao (hostatuato dk L; sparb) b sbholdkrao (hostatuato dk L: sparb) nblbrk pbr ck cbnnb da Gkrkdky dub gb` aldottb B;6 bd B:6

Ac harhuato bquavkcbltb skræ dkto9

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Cbzaolb 64:

62. Jacklhao blbrnbtaho trksgor`ktorb rbkcb

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Cbzaolb 64:

67. Harhuato bquavkcbltb trksgor`ktorb rbkcb

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Cbzaolb 64:

6>. Daknrk``k vbttorakcb trksgor`ktorb rbkcb sotto hkraho Vkrtbldo dkc harhuato bquavkcbltb da ul trksgor`ktorb rbkcb sotto hkraho hmb puú bssbrb hosã shmb`ktazzkto

Kppcahkldo cb cbnna hmb novbrlklo ac harhuato albsk`b ottblakò cb sbnublta rbckzaola5

Ac daknrk``k vbttorakcb skræ hosã dbsanlkto5

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Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

Cbzaolb 648 6;. CK TBLXAOLB DA HOZTO HAZHRATO DA RL TZKXGOZ@KTOZB9 WKCB XB@VZB YBZO B' CK TBLXAOLB DK KVVCAHKZB KC VZA@KZAO AL HOZTO HAZHRATO AL @ODO DK GKZ HAZHOCKZB CB HOZZBLTA LO@ALKCA B' CK TBLXAOLB DK KVVCAHKZB KD RL KWWOCNA@BLTO, HOL C'KCTZO KWWOCNA@BLTO AL HOZTO HAZHRATO, AL NZKDO DA GKZ HAZHOCKZB CB HOZZBLTA LO@ALKCA B' CK TBLXAOLB LO@ALKCB DBCCK @KHHMALK HMB GK HAZHOCKZB CB HOZZBLTA LO@ALKCA 6:. A TZKXGOZ@K TZKXGOZ@KTOZA TOZA DA @AXRZK WOCT@BTZAHA NBLBZKC@BLTB XOLO BCBWKTOZA DA TBLXAOLB LBC LOZ@KCB GRLYAOLK@BLTO DBWOLO KWBZB HOZZBLTA TZKXHRZKJACA VBZ CA@ATKZB CB HKDRTB DA TBLXAOLB LBC LOZ@KCB GRLYAOLK@BLTO DBWOLO KWBZB HOZZBLTA BCBWKTB VBZ KWBZB BCBWKTB HKDRTB DA TBLXAOLB DBWOLO KWBZB ZKVVOZTO DA TZKXGOZ@KYAOLB VKZA KD RLO 68. DAZB@O HMB DRB TZKXGOZ@KTOZA GOZ@KLO RL VKZKCCBCO VBZGBTTO [RKLDO9 ONLRLO GOZLAXHB @BTK' DBCCK VOTBLYK KXXOZJATK DKC HKZAHO ONLRLO GOZLAXHB KC HKZAHO RLK TBLXAOLB VZOVOZYAOLKCB KCCK XRK A@VBDBLYK DA HOZTO HAZHRATO ONLRLO GOZLAXHB KC HKZAHO RLK VOTBLYK VZOVOZYAOLKCB KCCK XRK VOTBLYK LO@ALKCB LOL B' VOXXAJACB ZBKCAYYKZB RL VKZKCCBCO VBZGBTTO 64. CK TBLXAOLB DA HOZTO HAZHRATO DBC TZKXGOZ@KTOZB B' DBCC'OZDALB DBC 86% DBCCK TBLXAOLB LO@ALKCB B' DBCC'OZDALB DBC 4%->% DBCCK TBLXAOLB LO@ALKCB DAVBLDB DKCCK HOZZBLTB KXXOZJATK DKC HKZAHO LOL B' VOXXAJACB [RKLTAGAHKZCK 62. Vkrkccbco da trksgor`ktor trksgor`ktoraa òlogksb

Dub trksgor`ktora solo al pkrkccbco qukldo solo hoccbnkta kd ulk stbssk calbk b kcco stbsso hkraho. Bssa qualda prbcbvklo dk ul‑ulahk ul‑ulahk Calbk c‑blbrnak lbhbsskrak pbr kca`bltkrb co stbsso hkraho. Xa dbgalashb gulzaolk`blto al pkrkccbco í pbrgbtto qukldo onla `khhmalk gorlashb kcck calbk ulk potblzk kppkrbltb proporzaolkcb kcck suk potblzk loàlkcb. Lbc gulzaolk`blto k vuoto, sb a trksgor`ktora hoccbnkta kcck stbssk calbk pra`krak lol mkllo hkraho, grk cb hoppab da òrsbtta sbholdkra lol dbvb bssbrb prbsbltb kchulk daggbrblzk da potblzakcb al òdo hmb lol ha saklo horrblta da harhockzaolb sua dub sbholdkra. Kggalhmí qubsto sak possajacb pbr a trksgor`ktora òlogksa í lbhbsskrao hmb saklo hostruata pbr ck stbssk tblsaolb pra`krak b kjjaklo co stbsso rkpporto da trksgor`kzaolb. Lbc gulzaolk`blto sotto hkraho pbr a trksgor`ktora hmb dovrkllo bssbrb hoccbnkta al pkrkccbco b‑ lbhbsskrao hmb ck rapkrtazaolb dbc hkraho trk cb dub `khhmalb sak proporzaolkcb kcck potblzk Loàlkcb da onlulo da bssa. Holdazaolb hmb sa soddasgk qukldo a trksgor`ktora mkllo stbssk tblsaolb da horto harhuato Whh b co stbsso gkttorb da potblzk al horto harhuato hosϒhh. Lbc hkso da ul pkrkccbco lol pbrgbtto c‑opportulatæ da khhoppakrb dub trksgor`ktora í cbnktk kcck vkcutkzaolb dbcck horrbltb da harhockzaolb k vuoto hmb potræ bssbrb toccbrktk soco lbc hkso al hua rasucta dbcco stbsso ordalb da nrkldbzzk dbcck horrbltb k vuoto. b kc davbrso holtrajuto dkto dk onla `khhmalk hol ragbra`blto kccb potblzb loàlkca. B‑ hoùlqub lbhbsskrao hmb a dub rksgor`ktora kjjaklo ck stbssk tblsaolb loàlkcb pra`krak, b kppkrtblnklo kcco stbsso nruppo..

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Cbzaolb 648

67. Gulzaolk`blto al horto harhuato

Rl trksgor`ktorb gulzaolk al horto harhuato qukldo bsso í kca`bltkto dk ulk tblsaolb W; dka òrsbtta dbc pra`krao b a òrsbtta sbholdkra solo hmausa al hortoharhuato (Yu06). Bssbldo c‑a`pbdblzk da hkraho lucck, holsadbrkldo hmb ck `khhmalk sak kca`bltktk kc pra`krao dkcck tblsaolb loàlkcb cb horrbltb hmb harhock lba dub kvvocna`blta skræ da harhk :6 voctb `knnaorb raspbtto kcck loàlkcb, tkcb holdazaolb sb lol vablb tb`pbstavk`bltb altbrrottk kttrkvbrso c‑altbrruzaolb dbc harhuato da kca`bltkzaolb portbrbjjb kc dkllbnnak`blto dbcck `khhmalk Xb holsadbrakò ul trksgor`ktorb hmb mk ho`b harhuata bquavkcblta qubcca sbnublta.

Holsadbrkldo ac harhuato bquavkcbltb sbholdkrao b Apotazzakò da kppcahkrb kc pra`krao ulk tblsaolb Whh (da horto harhuato) dbcc‑ordalb dbc 4%->% dbcck tblsaolb loàlkcb

Ck tblsaolb B:hh prbsbltb succb sparb sbholdkrab skræ dktk dkcck sbnubltb rbckzaolb

Lol potbldo gorlarb potblzk kcc‑bstbrlo ck `khhmalk, tuttk ck potblzk kssorjatk(Whh*A;l*hosχhh) sa trksgor`k al pbrdatb kcc‑altbrlo dbcck `khhmalk cohkcazzktb lbc rk`b pra`krao b sbholdkrao.

[ualda al dbgalatavk kca`bltkldo ck `khhmalk k tblsaolb radottk í possajacb khquasarb algor`kzaola prbzaosb succb hkrkttbrastahmb dbcck `khhmalk

.

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Cbzaolb 648

6>. Trksgor`ktora da àsurk voct`btraha

A trksgor`ktora da àsurk pbr`bttolo da stkldkrdazzkrb a vkcora da tblsaolb kc sbholdkrao. Xolo a`pabnkta al harhuata lba qukca ck tblsaolb rknnaulnb vkcora lol ho`pktajaca hol qubcca dbnca stru`blta da uso stkldkrd, dba rbcí da holtrocco b dba sastbà da protbzaolb5 nkrkltasholo aloctrb ul àncaork`blto dbccb holdazaola da sahurbzzk pbr nca opbrktora A TW da àsurk al holdazaolb adbkca solo hkrkttbrazzkta dk ulk tblsaolb pra`krak W;b dk ulk tblsaolb sbholdkrak W: hol rkpporto da trksgor`kzaolb E dkto dkcck rbckzaolb W;/W: Al holdazaola rbkca sunca kvvocna`blta va solo hkdutb da tblsaolb b ac rkpporto da trksgor`kzaolb lol skræ dkto dk W;/v: `k jblsã dkc rkpporto da B;/B: (tblsaolb rbkcb ka hkpa dbnca kvvocna`blta ) qualda ac rkpporto Eskræ `knnaorb raspbtto kc hkso adbkcb bssbldo B;3W; b B:3W:, Tkcb satukzaolb nblbrbræ qualda ul brrorb lbc raskcarb kcck tblsaolb dk àsurkrb pkrtbldo dk qubcc àsurktk Vbr àlaàzzkrb kc `kssaò qubsta brrora a TW vblnolo hostruata utacazzkldo khhorna`blta ktta k radurrb cb hkdutb da tblsaolb sunca Kvvocna`blta, kd bsb`pao sa ku`bltk ac nrkdo da khhoppak`blto trk a harhuato pra`krao b sbholdkrao al òdo dk daàluarb a gcussa daspbrsa b da holsbnublzk radurrb cb alduttklzb da daspbrsaolb C; b C:. .

6=. Trksgor`ktora da àsurk k`pbro`btr k`pbro`btraha aha

A trksgor`ktora da àsurk pbr`bttolo da stkldkrdazzkrb a vkcora da horrbltb kc sbholdkrao. Xolo a`pabnkta al harhuata lba qukca ck horrbltb rknnaulnb vkcora lol ho`pktajaca hol qubcca dbnca stru`blta da uso stkldkrd, dba rbcí da holtrocco b dba sastbà da protbzaolb5 nkrkltasholo aloctrb ul àncaork`blto dbccb holdazaola da sahurbzzk pbr nca opbrktora Al holdazaola rbkca succ‑ kvvocna`blto pra`krao harhock ulk horrbltb A6, ck qukcb ho`polbltb `knlbtazzkltb b acA;‑í ck rkpporto da trksgor`kzaolb lol skræ dkto ho`b lbccb holdazaola adbkcak vuoto dkc rkpporto A:/A; mk `kulk jblsã dkc rkpporto da A:/A;‑, dovb horrbltb da rbkzaolb pra`krak dktk dk A;-A6 (A; í ck horrbltb kssorjatk dkcck rbtb) Tkcb satukzaolb nblbrbræ qualda ul brrorb lbc raskcarb kcck horrbltb dk àsurkrb pkrtbldo dk qubcck àsurktk Vbr àlaàzzkrb kc `kssaò qubsta brrora a TK vblnolo hostruata utacazzkldo khhorna`blta ktta k radurrb ck horrbltb k vuoto, ul tapaho bsb`pao b ck rbkcazzkzaolb da luhcba `knlbtaha toroadkca b lol k gor`k rbttklnockrb al òdo dk radurrb ck racuttklzk dbc luhcbo `knlbtaho b qualda dbcck horrbltb A6

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Cbzaolb 644 6;. C'KVVKZTBLBLYK KC NZRVVO DA RL TZKXGOZ@KTOZB ;: XA OTTABLB9 AC NZRVVO ;: LOL BXAXTB LBA HOCCBNK@BLTA XTBCCK-XTBCCK OVVRZB TZAKLNOCO-TZAKLNOCO HOL KWWOCNA@BLTA KWWOCTA LBCCO XTBXXO WBZXO LBA HOCCBNK@BLTA XTBCCK-XTBCCK OVVRZB TZAKLNOCO-TZAKLNOCO HOL KWWOCNA@BLTA KWWOCTA AL WBZXO OVVOXTO LBA HOCCBNK@BLTA XTBCCK-TZAKLNOCO OVVRZB TZAKLNOCO-XTBCCK HOL KWWOCNA@BLTA KWWOCTA AL WBZXO OVVOXTO 6:. C'KVVKZTBLBLYK DA RL TZKXGOZ@KTOZB KC NZRVVO YBZO XANLAGAHK9 CB TBZLB DBCCB TBLXAOLA VZA@KZAK B XBHOLDKZAK XOLO XGKXKTB DA 86' CB TBZLB DBCCB TBLXAOLA VZA@KZAK B XBHOLDKZAK XOLO AL OVVOXAYAOLB DA GKXB TBLXAOLB B HOZZBLTB XOLO K 16 NZKDA CB TBZLB DBCCB TBLXAOLA VZA@KZAK B XBHOLDKZAK XOLO AL GKXB 68. AL RL TZKXGOZ@KTOZB TZAGKXB TZAGKXB HOL CB GKXA V VZA@KZAB ZA@KZAB K XTBCCK B CB GKXA XBHOLDKZAB K XTBCCK LOL B' [RKLTAGAHKJACB K VZAOZA AC ZKVVOZTO DA TZKXGOZ@KYAOLB HOALHADB HOL AC ZKVVOZTO XVAZB DAWAXO ZKDAHB [RKDZKTK DA TZB AC ZKVVOZTO DA TZKXGOZ@KYAOLB HOALHADB HOL AC ZKVVOZTO XVAZB AC ZKVVOZTO DA TZKXGOZ@KYAOLB HOALHADB HOL AC ZKVVOZTO XVAZB @OCTAVCAHKTO ZKDAHB [RKDZKTK DA TZB 64. CK VZOWK K WROTO DA RL TZKXGOZ@KTOZB DBWB BXXBZB BXBNRATK KCA@BLTKLDO DK RL CKTO KCCK TBLXAOLB LO@ALKCB B @KLTBLBLDO KVBZTO C'KCTZO CKTO KCA@BLTKLDO DK RL CKTO KCCK TBLXAOLB DA HOZTO HAZHRATO B @KLTBLBLDO KVBZTO C'KCTZO CKTO KCA@BLTKLDO DK RL CKTO KCCK TBLXAOLB LO@ALKCB B @KLTBLBLDO AL HOZTO HAZHRATO C'KCTZO CKTO KCA@BLTKLDO DK BLTZK@JA A CKTA KCCK TBLXAOLB LO@ALKCB 62. Vrovk al horto harhuato da trksgor`ktorb tragksb

Ck provk al horto harhuato da ul trksgor`ktorb tragksb sa bsbnub kcck grbqublzk loàlkcb (g026 Mz) kca`bltkldo ac trksgor`ktorb dk ul ckto hol ulk Whh al nrkdo da gkr harhockrb lbnca kvvocna`blta pra`krao b sbholdkrao cb horrblta loàlkca, `bltrb suc sbholdkrao a òrsbtta vkllo hortoharhuatkta. Tkcb provk í a`portkltb pbr dbtbràlkrb a pkrk`btra dbc harhuato bquavkcbltb dbcck `khhmalk. Opbrktavk`bltb vablb àsurktk ck potblzk kssorjatk Vhh b kttrkvbrso cb rbckzaola hmb cbnklo a davbrsa pkrk`btra bcbttraha í possajacb dbtbràlkrb ac hosϒhh, a vkcora Zbq‑‑ bd ]bq‑‑. A hkchoca vkllo bsbnuata hol ragbra`blto kcck horrbltb A;L. Ck Vhh àsurktk, vasto ac vkcorb loàlkcb dbccb horrblta A; bd A: bd ac jksso vkcorb dbcck tblsaolb (b qualda dbccb pbrdatb lbc luhcbo), hoalhadb hol cb pbrdatb da potblzk lbc rk`b dbcck `khhmalk. Cb gorùcb hmb vblnolo utacazzktb pbr dbtbràlkrb a davbrsa pkrk`btra solo cb sbnublta

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Cbzaolb 644

67. Nruppa dba trksgor`ktora tragksb

Vra`k da dbgalarb ac holhbtto da –Nruppo da da kppkrtblblzk da ul trksgor`ktorb tragksb‐ í da gold goldk`bltkcb k`bltkcb a`portklzk pkrckrb dbcco spostk`blto klnockrb λ, ac qukcb í dbgalato ho`b co sgksk`blto trk tblsaola da pra`krao b sbholdkrao dbcck stbssk gksb bd íklnockrb gulzaolbpuú dbcvkcbrb tapo da6¶,;26¶,;=6¶886¶. hoccbnk`blto dbcc'kvvocna`blto KT b dbcc'kvvocna`blto jt dbcck `khhmalk. Co spostk`blto Dbgalakò ho`b nruppo ac lu`bro hmb sa ottablb davadbldo λ (Xpostk`blto klnockrb) pbr 86¶ , b kvrbò qukttro nruppa 6-2-7-;;. - NZRVVO –6‐9 hol hoccbnk`blto stbcck-stbcck b traklnoco-traklnoco b kvvocna`blta lbcco stbsso vbrso, spostk`blto klnockrb da 6¶5 - NZRVVO –2‐9 hol hoccbnk`blto stbcck-traklnoco b traklnoco-stbcck b kvvocna`blta al vbrso opposto, spostk`blto klnockrb da ;26¶5 - NZRVVO –7‐9 hol hoccbnk`blto stbcck-stbcck b traklnoco-traklnoco b kvvocna`blta al vbrso opposto, spostk`blto klnockrb da ;=6¶5 - NZRVVO –;;‐9 hol hoccbnk`blto stbcck-traklnoco b traklnoco-stbcck b kvvocna`blta lbcco stbsso vbrso, spostk`blto klnockrb da 886¶5 6>. Vrovk k vuoto da trksgor`ktorb tragksb

Ck provk al horto harhuato da ul trksgor`ktorb tragksb sa bsbnub kcck grbqublzk loàlkcb (g026 Mz) kca`bltkldo ac trksgor`ktorb dk ul kcck tblsaolb loàlkcb W;L b ckshakldo aa òrsbtta kpbrta dbcc‑kctro ckto. Tkcb provk í a`portkltb pbr dbtbràlkrb a pkrk`btra dbc ckto harhuato bquavkcbltb dbcck `khhmalk. Opbrktavk`bltb vablb àsurktk ck horrbltb k vuoto Ao ((A60A6;+A6:+A68)/8 al quklto ac luhcbo gbrro`knlbtaho lol í sa``btraho), ck potblzk kssorjatk k vuoto V6 b `bdakltb cb rbckzaola hmb cbnklo a davbrsa pkrk`btra bcbttraha í possajacb dbtbràlkrb ac hos ϒ6, bd a vkcora da Z6 b ]6 rbcktava kc hkppao pkrkccbco. Ck potblzk V6, vasto ac vkcorb lucco dbcck horrbltb A:, hoalhadb hol cb pbrdatb da potblzk lbc gbrro lbc luhcbo Cb gorùcb pbr dbtbràlkrb a davbrsa pkrk`btra solo cb sbnublta5

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Cbzaolb 644 6=. Trksgor`ktora tragksb b rkpporto da trksgor`kzaolb

Rl trksgor`ktorb tragksb puú bssbrb pblskto ho`b trb trksgor`ktora òlogksb onlulo dba qukca –trksgor`k‐ ulk gksb dbc sastb`k. Vbr bholoàhatæ b sb`pcahatæ da lor`k sa rbkcazzklo a trksgor`ktora tragksa hol dub naonma b trb hocollb, al qubst‑ucta`b sa kvvocnolo nca kvvocna`blta pra`kra b sbholdkra dbccb trb gksa) . Nca kvvocna`blta tragksb qubcco pra`krao b qubcco sbholdkrao, possolo bssbrb hollbssa k stbcck o k traklnoco. Bsastolo dub tbrlb da tblsaola qubcck pra`krak hoalhadbltb hol qubcck dbcck rbtb da kca`bltkzaolb dbcck `khhmalk, b qubcck sbholdkrak hoalhadbltb hol qubcck dbcck rbtb kca`bltktk dkc trksgor`ktorb Lbc suo lor`kcb gulzaolk`blto ac trksgor`ktorb produhb hkcorb hkuskto dkccb pbrdatb da potblzk lbc gbrro b lbc rk`b, tkcb dbvb bssbrb s`kctato qualda í a`portkltb hmb ck `khhmalk vblnk rkggrbddktk5 Ac rkggrbddk`blto dbcck `khhmalk kvvablb kttrkvbrso ck harhockzaolb da ocao (àlbrkcb (àlbrkcb o lkturkcb) hmb vbrræ rkggrbddkto trkàtb krak (lkturkcb o/b gorzktk).Lbnca uctaà klla stkllo prbldbldo pabdb a trksgor`ktora alncojkta al rbsalk. Rl trksgor`ktorb lkturkc`bltb í horrbdkto dka suoa dkta da tkrnk dovb solo raportkta a pkrk`btra hmb hkrkttbrazzklo ck `khhmalk, (Grbqublzk, Horrblta b tblsaola loàlkca, hoccbnk`blto dbnca kvvocna`blta pra`kra b sbholdkra, Votblzk, rkpporto da trksgor`kzaolb, bhh) Ac rkpporto da trksgor`kzaolb tragksb ET í dbgalato ho`b ac rkpporto trk cb tblsaola holhktblktb pra`krak b sbholdkrak, bsso dapbldb dkc hoccbnk`blto dbccb gksa. Ac ET í dapbldbltb dkc tapo da hoccbnk`blto dbccb gksa kc Vra`krao b kc sbholdkrao Hoccbnk`blto stbcck-stbcck Q/Q Ac rkpporto da trksgor`kzaolb tragksb hoalhadb hol ac rkpporto sparb, algktta9

Hoccbnk`blto stbcck-traklnoco Q/D Ac rkpporto da trksgor`kzaolb tragksb hoalhadb hol ac rkpporto sparb òctapcahkto pbr ∙8. [ubsto gktto puú bssbrb uskto lba hksa al hua k pkratæ da sparb pra`krab b sbholdkrab í lbhbsskrao kvbrb ul rkpporto da trksgor`kzaolb `knnaorb.

Hoccbnk`blto traklnoco-traklnoco D/D Ac rkpporto da trksgor`kzaolb tragksb hoalhadb hol ac rkpporto sparb.

Hoccbnk`blto traklnoco-stbcck D/Q Ac rkpporto da trksgor`kzaolb tragksb hoalhadb hol ac rkpporto sparb davaso pbr ∙8. [ubsto gktto puú bssbrb uskto lba hksa al hua k pkratæ da sparb pra`krab b sbholdkrab í lbhbsskrao kvbrb ul rkpporto da trksgor`kzaolb àlorb.

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Cbzaolb 642 6;. CO XHOZZA@BLTO s AL ATKCAK WKCB XB@VZB 8666 NAZA/@ALRTO B' CK GZKYAOLB DA NAZO VBZXK DKC ZOTOZB VBZ ONLA NAZO DBC HK@VO @KNLBTAHO ZOTKLTB B' CK GZKYAOLB DA NAZO VBZXK DKCCO XTKTOZB VBZ ONLA NAZO DBC ZOTOZB B' CK GZKYAOLB DA NAZO VBZXK DKCCO XTKTOZB VBZ ONLA NAZO DBC HK@VO @KNLBTAHO ZOTKLTB 6:. CO XHOZZA@BLTO s VRO' KXXR@BZB A XBNRBLTA WKCOZA -;30s30; @KA s3; XB@VZB s. DBGALAK@O YOLK DA GRLYAOLK@BLTO XTKJACB [RBCCK AL HRA KD RL KR@BLTO DBCCK HOVVAK ZBXAXTBLTB HOZZAXVOLDB RL KR@BLTO DBCCK HOVVAK @OTZAHB BD RLK DA@ALRYAOLB DBCCK WBCOHATK' VBZ A @OTOZA KXALHZOLA LOL B' DBGALAJACB AC @OTOZB GRLYAOLBZK' XB@VZB AL HOLDAYAOLA DA ZBNA@B

KD RL KR@BLTO DBCCK HOVVAK ZBXAXTBLTB HOZZAXVOLDB RL KR@BLTO DBCCK HOVVAK @OTZAHB BD RL KR@BLTO DBCCK WBCOHATK'

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Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

6=. AL HOLDAYAOLA LOZ@KCA KCCO XVRLTO CK HOVVAK @OTZAHB LOL B' @KXXA@K CK HOVVAK @OTZAHB B' @KXXA@K CK HOVVAK @OTZAHB B' LRCCK CK HOVVAK @OTZAHB LOL VRO' BXXBZB @ODAGAHKTK 61. JACKLHAO BLBZNBTAHO (VK0VOTBLYK KXXOZJATK, KXXOZJATK, VHR VBZDATB LBC ZK@B, VGB0VBZDATBZ LBC GBZZO, V@ VBZDATB @BHHKLAHMB,VZ @BHHKLAHMB, VZ VOTBLYK KCC'KXXB) VK+ VZ0VHR+VGB+V@ VZ0VHR+VGB+V@ VK0VHR+VGB+V@+VZ VK0VHR+VGB+V@ ;6. VOTBLYB AC @OTOZB KXALHZOLO ZAHBWB VOTBLYK V OTBLYK BCBTTZAHK B ZBXTATRAXHB VOTBLYK BCBTTZO@KNLBTAHK AC @OTOZB KXALHZOLO ZAHBWB VOTBLYK BCBTTZAHK B ZBXTATRAXHB VOTBLYK BCBTTZAHK AC @OTOZB KXALHZOLO ZAHBWB VOTBLYK @BHHKLAHK B ZBXTATRAXHB VOTBLYK @BHHKLAHK AC @OTOZB KXALHZOLO ZAHBWB VOTBLYK BCBTTZAHK B ZBXTATRAXHB VOTBLYK @BHHKLAHK ;;. XALHZOLAX@O B ZOTOZB JCOHHKTO (l;0WBCOHATÆ DA ZOTKYAOLB h.`.r., l:0WBCOHATÆ DA ZOTKYAOLB DBC ZOTOZB) XOLO HOLDAYAOLA DA GRLYAOLK@BLTO AZZBKCAYYKJACA l:0l; B l:06 l:06 B l:0 l; VRO' BXXBZB ZBKCAYYKTO XOCO AC XALHZOLAX@O ;:. CK ZBNOCKYAOLB DBCCK WBCOHATK' DA ZOTKYAOLB DBA @OTOZA KXALHZOL KXALHZOLAA TZAGKXB VRO' BXXBZB OTTBLRTK XOCK@BLTB WKZAKLDO CB HOVVAB VOCKZA LOL B' VOXXAJACB VRO' BXXBZB OTTBLRTK WKZAKLDO CK GZB[RBLYK DA KCA@BLTKYAOLB B CB HOVVAB VOCKZA VRO' BXXBZB OTTBLRTK XOCK@BLTB WKZAKLDO CK GZB[RBLYK DA KCA@BLTKYAOLB ;8. CK ZBNOCKYAOLB DBCCK WBCOHATK' DA ZOTKYAOLB DBA @OTOZA KXALHZOLA TZAGKXB OTTBLRTK WKZAKLDO AC LR@BZO DA HOVVAB VOCKZA LOL B' VOXXAJACB B' VOXXAJACB XOCO VBZ CB @KHHMALB HOL ZOTOZB K NKJJAK B' VOXXAJACB XOCO VBZ CB @KHHMALB HOL ZOTOZB KWWOCTO XA OTTABLB ALXBZBLDO RL ZBOXTKTO XRCCB GKXA ZOTOZAHMB

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Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

;4. Zbnockzaolb dbcck vbcohatæ dbcck `khhmalk ksalhrolk

Vbr vkrakrb ck vbcohatæ da rotkzaolb dbcck `khhmalk (l:) sa possolo kdottkrb davbrsb socuzaola. Zbostkto al sbrab kc rotorb [ubsto khhorna`blto holsastb lbc lbc hoccbnkrb al sbrab ulk ulk rbsastblzk succb gksa rotorahmb galkcazzktk kd ottblbrb ulo spostk`blto dbcck hkrkttbrastahk `bhhklahk b pbr ulk gassktk hoppak rbsastbltb ottblakò dbccb vbcohatæ vkrakjaca. Wkrakzaolb dbcck grbqublzk (l;076*g;/p) Wkrakldo ck grbqublzk da kca`bltkzaolb g; al dub òda9 kca`bltkldo ck `khhmalk hol ul proprao kctbrlktorb oppurb kca`bltkldo ck `khhmalk hol ul vkraktorb da grbqublzk (alvbrtbr). Wkrakzaolb dbc lu`bro da hoppab pockra Kjjakò vasto hmb l;076*g;/p, k pkratæ da grbqublzk kcc‑ku`bltkrb dbc lu`bro da hoppab pockra p daàluashb ck vbcohatæ dbc h.`.r. l; b da holsbnublzk ck vbcohatæ da rotkzaolb dbc rotorb. Lotakò hmb cb vkrakzaola da vbcohatæ possolo kvvblarb soco k shktta lbc sblso hmb pbr p0; sa mk l;08666 nara/àl, pbr p0: sa mk l;0;266 nara/àl, pbr p08 sa mk l;0>26 nara/àl (g;026 Mz).

hmb í possajacb pbr `khhmalb hol rotorb k nkjjak al quklto cb hoppab pockra rotorahmb solo kuto`ktahk`bltb unukca kccb hoppab pockra stktorahmb. Co stbsso lol sa puú darb lbc hkso da rotorb kvvocto. Al qubsto hkso kd onla vkrakzaolb dbc lu`bro da hoppab pockra stktorahmb dbvb bssbrb bsbnuatk ulk vkrakzaolb dbc lu`bro da hoppab pockra rotorahmb. ;2. Xastbà da kvvak`blto dbcck `khhmalk ksalhrolk

Kcc‑kvvak`blto kjjakò vasto hmb ac òtorb kssorjb ulk horrbltb bcbvktk b gorlashb kcc‑kssb ulk hoppak àlorb kcck hoppak `kssa`k. A sastbà da kvvak`blto pbr cb ` `khhmalb khhmalb ksalhrolb solo galkcazzkta k gkrb kssorjarb kcco spulto ulk àlorb horrbltb b gorlarb kcc‑kssb ulk hoppak `knnaorb raspbtto kcck hoppak kvbltb sblzk ul sastb`k da kvvak`blto Hostruttavk`bltb sa optk pbr c‑kvvak`blto rbostktaho hmb holsastb lbcc‑alsbrarb ul rbostkto al sbrab kccb gksa rotorahmb, al tkc òdo sa mk ul ku`blto dbcck rbsastblzk b da holsbnublzk ulk daàluzaolb dbccb horrblta, bd ul ku`blto dbcck hoppak kcco spulto. C‑kvvak`blto rbostktaho í aldaspblskjacb pbr `khhmalb hmb dbvolo pkrtarb hol bcbvkta hkrahma `bhhklaha. Opbrktavk`bltb sa dbvb knnaulnbrb kc rotorb ulk rbsastblzk tkcb hmb ck rbsastblzk ho`pcbssavk dbc harhuato rotoraho ( Z:+ZZbostkto) sak unukcb kcck rbkttklzk ]:(;). Rl kctro khhorna`blto í hostruarb ul òtorb hol rotorb k doppak nkjjak sa ottablb ulk hkrkttbrastahk `bhhklahk hmb prbsbltk ulk hoppak da kvvak`blto, pkra kcck hoppak `kssa`k b lbcco stbsso tb`po horrblta kcco spulto radottb. Rlk `khhmalk ksalhrolk puú bssbrb kvvakta al dub òda davbrsa 5 Kvvak`blto k tblsaolb radottk B‑ possajacb lba hksa al hua lol í lbhbsskrak ulk hoppak kcco spulto bcbvktk., kca`bltkldo k tblsaolb radottk Bssbldo ck hoppak proporzaolkcb kc qukdrkto dbcck tblsaolb kjjakò ulk caàtkzaolb dbcck horrbltb kcco spulto. Kvvak`blto stbcck/traklnoco Vbr radurrb ck horrbltb kcco spulto possakò kcc‑kvvak`blto sa gk pkrtarb ck `khhmalk hol cb gksa stktorahmb hoccbnktb k stbcck, dopo co spulto cb gksa stktorahmb vblnolo hoccbnktb k traklnoco. [ubsto ho`portk ulk raduzaolb dbcck tblsaolb dbcck gksb da ul gkttorb pkra k ∙8 . Ck horrbltb da calbk vablb radottk kd ;/8 dbc vkcorb.

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Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

;7. Jacklhao blbrnbtaho dbcck `khhmalk ksalhrolk

Xhmb`ktahk`bltb í possajacb rkpprbsbltkrb ac jacklhao blbrnbtaho dbcck `khhmalk ksalhrolk utacazzkldo ac sbnubltb daknrk``k

Dovb5 Vk0Votblzk kssorjatk dkcck rbtb Vr0Votblzk `bhhklahk rbsk kcc‑kssb Vhu0potblzk dassapktk dkc rk`b Vgb0Votblzk dassapktk dkc gbrro pbr astbrbsa b horrblta pkrkssatb V`0Votblzk `bhhklahk dassapktk pbr kttrato Vt0potblzk trks`bssk kc rotorb dkcco stktorb [ulktagahkldo cb vkrab nrkldbzzb kjjakò

Ac rblda`blto skræ dkto dk

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::968986 - =6/>8

Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro ;>. Gulzaolk`blto k vuoto dbcck `khhmalk ksalhrolk

[ukldo ul òtorb í kca`bltkto kcck tblsaolb W ; b lol mk kchul hkraho `bhhklaho kppcahkto kcc‑kssb sa mk ck holdazaolb da gulzaolk`blto k vuoto dbcck `khhmalk ksalhrolk. Xhmb`ktahk`bltb

Al qubstk holdazaolb co shorra`blto s06 b A:(s)06, ck horrbltb kssorjatk k vuoto pbr òtora da nrkldb potblzk vkcb 82-26%, pbr òtora da pahhock potblzk puú krravkrb kc 26%. Blbrnbtahk`bltb 9 ck `khhmalk lol hbdb potblzk kcc‑kssb5 tuttk ck potblzk kssorjatk sbrvb k jacklhakrb cb pbrdatb lbc rk`b stktorahmb, cb pbrdatb lbc gbrro 



stktorahmb, b cb pbrdatb pbr kttrato b vbltackzaolb.

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Xbt Do`kldb9 BCBTTZOTBHLAHK ALNBNLBZAK ALDRXTZAKCB (D.@. :>6/64) Dohbltb9 Algkltb Nbllkro

;=. Hkrkttbrastahk `bhhklahk dbcck `khhmalk ksalhrolk

Ck hkrkttbrastahk `bhhklahk rkpprbsbltk c‑kldk`blto dbcck dbcc k hoppak òtrahb rbsk H daspolajacb kcc‑kssb, kc vkrakrb dbcco shorra`blto pbrhbltukcb. Lbcco spbhagaho sb kcco spulto kppcahmakò kcc‑kssb ulk hoppak rbsastbltb Hr algbraorb kcck hoppak da kvvak`blto Hk ck `khhmalk sa kvvabræ ku`bltkldo ck suk vbcohatæ galo k qukldo sa kvræ unukncaklzk trk hoppak òtrahb b hoppak rbsastbltb H0Hr . Ck `khhmalk ckvork lbcck zolk da stkjacatæ lbc ò`blto al hua kd ul ku`blto dbcck hoppak rbsastbltb nca horraspoldb ul ku`blto dbcck hoppak òtrahb b ulk daàluzaolb dbcck vbcohatæ. Kc holtrkrao, lbcck zolk da alstkjacatæ kvvablb hmb kd onla rkccbltk`blto dbc òtorb horraspoldb ulk daàluzaolb dbcck hoppak òtrahb. c‑bsprbssaolb klkcatahk dbcck hoppak òtrahb al gulzaolb dba pkrk`btra dk hua bssk dapbldb skræ dkto dkccb sbnublta rbckzaola

Dkccb rbckzaola sa bvalhb hmb ck hoppak, pbr ul dkto vkcorb da shorra`blto, í proporzaolkcb kc qukdrkto dbcck tblsaolb da kca`bltkzaolb. Ac vkcorb da hoppak `kssa`k sa ottablb pbr qubc vkcorb da shorra`blto (s*) tkcb hmb ck rbsastblzk omàhk b ck rbkttklzk dba harhuata rotoraha sa unukncaklo Xb sostatuakò lbcc‑bsprbssaolb dbcck hoppak kd s ac vkcorb da s* ottblakò

Ac vkcorb dbcck hoppak `kssa`k í aldapbldbltb dkc vkcorb dbcck rbsastblzk rotorahk `k rasuctk alvbrsk`bltb proporzaolkcb kcc‑alduttklzk da daspbrsaolb rotorahk. Al bggbtta possakò holhcudbrb dahbldo hmb, vkrakldo ac vkcorb da Z: , raushakò k trksckrb succ‑kssb dbnca shorra`blta ck hkrkttbrastahk `bhhklahk dbcck `khhmalk. Xb dovbssb bssbrb utacb vkrakldo opportulk`bltb ac vkcorb dbcck rbsastblzk rotorahk sa potrbjjb kvbrb ac vkcorb da hoppak `kssa`k al horraspoldblzk dbcco spulto (s0;). [ubsto holsbltarbjjb c‑kvvak`blto al holdazaola da hkraho nrkvoso (bs. ul òtorb hmb dbvb soccbvkrb ul jcohho da `krò prbhbdbltb`bltb knnklhakto).

© :6;7 - :6;> Rlavbrsatæ Tbcb`ktahk bHk`pus - Dktk Xtk`pk 62/;6/:6;> ::968986 - =:/>8

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;1. Gulzaolk`blto k rotorb jcohhkto dbcck `khhmalk ksalhrolk

Ac gulzaolk`blto dbcck `khhmalk ksalhrolk k rotorb jcohhkto í ulk pkrtahockrb holdazaolb hmb sa mk [ukldo c‑kssb dbcck `khhmalk í jcohhkto, ac harhuato bquavkcbltb

Tuttk ck potblzk bcbttrahk kssorjatk dkcck rbtb da kca`bltkzaolb sa trksgor`k al pbrdatb da potblzk lbcck `khhmalk. Xa mk hmb Vt0Vhu‑ ‑ b V@065 tuttk ck potblzk trks`bssk dkc h.`.r. kc rotorb sa trksgor`k al pbrdatb lbc rk`b rotoraho. r otoraho. Ck horrbltb kssorjatk dkcck `khhmalk í da harhk =/;6 voctb ck horrbltb loàlkcb

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