Practicas de POO y Graficación

September 11, 2022 | Author: Anonymous | Category: N/A

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ME[PMP^PL PNKELCÛDMKL @N [GE C^M[ QLPL[Ê

@NQGXPGJNEPL @N [M[PNJG[ ] KLJQ^PGKMÛE KGXXNXG? Mednemnrêg ne [mstnjgs Kljputgkmlegcns

QXÇKPMKG[ @N JGE^GC @N QXÇKPMKG[ @N CG JGPNXMG? JGPNXMG? Drgimkgkmûe

ELJHXN @NC G^PLX? QN@XL DGXKÊG D^NXXNXL EßJNXL @N @MKPGJNE? G[-8-8;=/8176 QCGE @N N[P^@ML[? M[MK-8171-880 KCGYN @N CG G[MDEGP^XG? [KK-7171

[LCN@G@ @N DXGKMGEL [ÇEKFN_, [.C.Q., G 17 @N GDL[PL @NC 817=

Êe`mkn QXÇKPMKG 7. CÊENG @@G ........................................................................................................................ 6 7.7 7.8   7.; 7.0 7.0.7 7.0.8 7.0.; 7.0.0 7.>

............................ .............. ............................ ............................ ............................ ............................ ............................ ............................ ............................ ................ .. 6 MLEPXL@^KKMÛE ........................... ............................ ............................ ............................. ............................. ............................ ........................... ............. 6 HONPMYL KLJQNPNEKMG ) ............. .......................... ............................ ............................ ............................ ............................ ............................ ............................ ............................ ................ .. 6 IÊ@GJNEPL R;Z ............ QXLKN@MJMNEPL @N[KXMQKMÛE ) ............. ........................... ............................ ............................ ............................ ............................ ............................ .................. .... = NW^MQL ENKN[GXML ............. .......................... ........................... ............................ ............................. ............................. ............................ ............................ ........................... ............. = ........................... ............................ ............................ ............................ ............................ ............................ ............................ ....................... ......... = JGPNXMGC @N GQL]L ............. @N[GXXLCCL @N CG QXÇKPMKG ............. ........................... ............................ ............................ ............................ ............................ ............................. ..................... ...... 71 NQLXPN .............. ............................ ............................ ............................ ............................. ............................. ............................ ............................ ............................ ......................... ........... 74 X NQLXPN ........................... ............................. ............................. ............................ ............................ ............................ .................. .... 74 XN[^CPG@L[ ] KLEKC^[MLEN[ .............

QXÇKPMKG 8. CÊENG HXN[NEFGJ ....................................................................................................... 76 8.7 8.8 8.; 8.0 8.0.7 8.0.8 8.0.; 8.0.0 8.>

............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ .............. 76 MEPXL@^KKMÛE .............. LHONPMYL KLJQNPNEKMG ) ............. ........................... ............................ ............................ ............................. ............................. ............................ ......................... ........... 76 IÊ@GJNEPL .............. ............................ ............................. ............................. ............................ ............................ ............................ ............................ ............................ ................ .. 76 ........................... ............................ ............................ ............................ ............................ ............................ ................ .. 7= QXLKN@MJMNEPL @N[KXMQKMÛE ) ............. NW^MQL ENKN[GXML ............. .......................... ........................... ............................ ............................. ............................. ............................ ............................ ......................... ........... 7= JGPNXMGC @N GQL]L ............. ........................... ............................ ............................ ............................ ............................ ............................ ............................ ..................... ....... 7= ........................... ............................ ............................ ............................ ............................ ............................. ..................... ...... 7= @N[GXXLCCL @N CG QXÇKPMKG ............. NQLXPN .............. X NQLXPN ............................ ............................ ............................ ............................. ............................. ............................ ............................ ............................ ......................... ........... 81 XN[^CPG@L[ ] KLEKC^[MLEN[ ............. ........................... ............................. ............................. ............................ ............................ ............................ .................. .... 81

QXÇKPMKG ;. KMXKÊINXNEKMG KLJßE ............................................................................................ 87 ;.7 ;.8 ;.; ;.0 ;.0.7

MEPXL@^KKMÛE .............. ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ .............. 87 ........................... ............................ ............................ ............................. ............................. ............................ ......................... ........... 87 LHONPMYL KLJQNPNEKMG) ............. IÊ@GJNEPL .............. ............................ ............................. ............................. ............................ ............................ ............................ ............................ ............................ ................ .. 87 QXLKN@MJMNEPL @N[KXMQKMÛE ) ............. ........................... ............................ ............................ ............................ ............................ ............................ ................ .. 88 .......................... ........................... ............................ ............................. ............................. ............................ ............................ ......................... ........... 88 NW^MQL ENKN[GXML .............

;.0.8 ;.0.; ;.0.0 ;.>

........................... ............................ ............................ ............................ ............................ ............................ ............................ ..................... ....... 88 JGPNXMGC @N GQL]L ............. @N[GXXLCCL @N CG QXÇKPMKG ............. ........................... ............................ ............................ ............................ ............................ ............................. ..................... ...... 88 X NQLXPN NQLXPN .............. ............................ ............................ ............................ ............................. ............................. ............................ ............................ ............................ ......................... ........... 8; ........................... ............................. ............................. ............................ ............................ ............................ .................. .... 8; XN[^CPG@L[ ] KLEKC^[MLEN[ .............

QXÇKPMKG 0. KMXKÊINXNEKMG HXN[NEFGJ .................................................................................. 80 0.7 0.8 0.; 0.0 0.0.7 0.0.8 0.0.; 0.0.0 0.>

MEPXL@^KKMÛE .............. ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ .............. 80 LHONPMYL KLJQNPNEKMG ) ............. ........................... ............................ ............................ ............................. ............................. ............................ ......................... ........... 80 ............................ ............................. ............................. ............................ ............................ ............................ ............................ ............................ ................ .. 80 IÊ@GJNEPL .............. QXLKN@MJMNEPL @N[KXMQKMÛE ) ............. ........................... ............................ ............................ ............................ ............................ ............................ ................ .. ;1 NW^MQL ENKN[GXML ............. .......................... ........................... ............................ ............................. ............................. ............................ ............................ ......................... ........... ;1 ........................... ............................ ............................ ............................ ............................ ............................ ............................ ..................... ....... ;1 JGPNXMGC @N GQL]L ............. ........................... ............................ ............................ ............................ ............................ ............................. ..................... ...... ;1 @N[GXXLCCL @N CG QXÇKPMKG ............. X NQLXPN NQLXPN .............. ............................ ............................ ............................ ............................. ............................. ............................ ............................ ............................ ......................... ........... ;7 XN[^CPG@L[ ] KLEKC^[MLEN[ ............. ........................... ............................. ............................. ............................ ............................ ............................ .................. .... ;7

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg mm

QXÇKPMKG >. KMXKÊINXNEKMG QÊPL JN@ML ............................................................................... ;8 >.7 >.8 >.; >.0

MEPXL@^KKMÛE .............. ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ .............. ;8 LHONPMYL KLJQNPNEKMG ) ............. ........................... ............................ ............................ ............................. ............................. ............................ ......................... ........... ;8 IÊ@GJNEPL .............. ............................ ............................. ............................. ............................ ............................ ............................ ............................ ............................ ................ .. ;8 ........................... ............................ ............................ ............................ ............................ ............................ ................ .. ;> QXLKN@MJMNEPL @N[KXMQKMÛE ) .............

>.0.7   >.0.8 >.0.; >.0.0 >.>

.......................... ........................... ............................ ............................. ............................. ............................ ............................ ......................... ........... ;> ENKN[GXML ............. NW^MQL J GPNXMGC @N GQL]L ............. ........................... ............................ ............................ ............................ ............................ ............................ ............................ ..................... ....... ;> ........................... ............................ ............................ ............................ ............................ ............................. ..................... ...... ;> @N[GXXLCCL @N CG QXÇKPMKG ............. NQLXPN .............. X NQLXPN ............................ ............................ ............................ ............................. ............................. ............................ ............................ ............................ ......................... ........... ;9 XN[^CPG@L[ ] KLEKC^[MLEN[ ............. ........................... ............................. ............................. ............................ ............................ ............................ .................. .... ;9

QXÇKPMKG 9. @MHÔL @N CÊENG[ ] QLCÊDLEL[ NE K KLE CG CMHXNXÊG TMEHDMJ ................... .................. ;4 ; 4 9.7 9.8 9.; 9.0 9.0.7 9.0.8 9.0.; 9.0.0 9.>

............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ .............. ;4 MEPXL@^KKMÛE .............. ........................... ............................ ............................ ............................. ............................. ............................ ......................... ........... ;4 LHONPMYL KLJQNPNEKMG) ............. IÊ@GJNEPL .............. ............................ ............................. ............................. ............................ ............................ ............................ ............................ ............................ ................ .. ;4 QXLKN@MJMNEPL @N[KXMQKMÛE ) ............. ........................... ............................ ............................ ............................ ............................ ............................ ................ .. ;6 .......................... ........................... ............................ ............................. ............................. ............................ ............................ ......................... ........... ;6 NW^MQL ENKN[GXML ............. JGPNXMGC @N GQL]L ............. ........................... ............................ ............................ ............................ ............................ ............................ ............................ ..................... ....... ;6 @N[GXXLCCL @N CG QXÇKPMKG ............. ........................... ............................ ............................ ............................ ............................ ............................. ..................... ...... ;6 NQLXPN .............. ............................ ............................ ............................ ............................. ............................. ............................ ............................ ............................ ......................... ........... 08 X NQLXPN XN[^CPG@L[ ] KLEKC^[MLEN[ ............. ........................... ............................. ............................. ............................ ............................ ............................ .................. .... 08

QXÇKPMKG 4. @MHÔL @N CÊENG[ ] QLCÊDLEL[ NE OGYG KLE CG CMHXNXÊG OLDC ..................... .................... 0; 0 ; 4.7 4.8 4.; 4.0 4.0.7 4.0.8 4.0.; 4.0.0 4.>

MEPXL@^KKMÛE .............. ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ .............. 0; LHONPMYL KLJQNPNEKMG ) ............. ........................... ............................ ............................ ............................. ............................. ............................ ......................... ........... 0; ............................ ............................. ............................. ............................ ............................ ............................ ............................ ............................ ................ .. 0; IÊ@GJNEPL .............. QXLKN@MJMNEPL @N[KXMQKMÛE ) ............. ........................... ............................ ............................ ............................ ............................ ............................ ................ .. 0; NW^MQL ENKN[GXML ............. .......................... ........................... ............................ ............................. ............................. ............................ ............................ ......................... ........... 0; ........................... ............................ ............................ ............................ ............................ ............................ ............................ ..................... ....... 0; JGPNXMGC @N GQL]L ............. @N[GXXLCCL @N CG QXÇKPMKG ............. ........................... ............................ ............................ ............................ ............................ ............................. ..................... ...... 00 X NQLXPN NQLXPN .............. ............................ ............................ ............................ ............................. ............................. ............................ ............................ ............................ ......................... ........... 09 XN[^CPG@L[ ] KLEKC^[MLEN[ ............. ........................... ............................. ............................. ............................ ............................ ............................ .................. .... 09

................................. ................ .... 04 QXÇKPMKG 6. D^GX@GX ] XNK^QNXGX ÊG MJGDNE QMVNC QLX QMVNC .....................

6.7 6.8 6.; 6.0 6.0.7 6.0.8 6.0.; 6.0.0 6.>

MEPXL@^KKMÛE .............. ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ .............. 04 LHONPMYL KLJQNPNEKMG ) ............. ........................... ............................ ............................ ............................. ............................. ............................ ......................... ........... 04 IÊ@GJNEPL .............. ............................ ............................. ............................. ............................ ............................ ............................ ............................ ............................ ................ .. 06 QXLKN@MJMNEPL @N[KXMQKMÛE ) ............. ........................... ............................ ............................ ............................ ............................ ............................ ................ .. 0= NW^MQL ENKN[GXML ............. .......................... ........................... ............................ ............................. ............................. ............................ ............................ ......................... ........... 0= JGPNXMGC @N GQL]L ............. ........................... ............................ ............................ ............................ ............................ ............................ ............................ ..................... ....... 0= ........................... ............................ ............................ ............................ ............................ ............................. ..................... ...... >1 @N[GXXLCCL @N CG QXÇKPMKG ............. NQLXPN .............. ............................ ............................ ............................ ............................. ............................. ............................ ............................ ............................ ......................... ........... >8 X NQLXPN XN[^CPG@L[ ] KLEKC^[MLEN[ ............. ........................... ............................. ............................. ............................ ............................ ............................ .................. .... >8

QXÇKPMKG =. D^GX@GX ] XNK^QNXGX ÊG MJGDNE QLX CG @N[KXMQKMÛE @N [^[ KLJQLENEPN[ ...................................................................................................................................... >; =.7

............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ .............. >; MEPXL@^KKMÛE ..............

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg mmm

=.8 =.; =.0 =.0.7 =.0.8 =.0.; =.0.0 =.>

LHONPMYL KLJQNPNEKMG) ............. ........................... ............................ ............................ ............................. ............................. ............................ ......................... ........... >; ............................ ............................. ............................. ............................ ............................ ............................ ............................ ............................ ................ .. >; IÊ@GJNEPL .............. QXLKN@MJMNEPL @N[KXMQKMÛE ) ............. ........................... ............................ ............................ ............................ ............................ ............................ ................ .. >0 NW^MQL ENKN[GXML ............. .......................... ........................... ............................ ............................. ............................. ............................ ............................ ......................... ........... >0 ........................... ............................ ............................ ............................ ............................ ............................ ............................ ..................... ....... >0 JGPNXMGC @N GQL]L ............. @N[GXXLCCL @N CG QXÇKPMKG ............. ........................... ............................ ............................ ............................ ............................ ............................. ..................... ...... >0 ............................ ............................ ............................ ............................. ............................. ............................ ............................ ............................ ......................... ........... >6 NQLXPN .............. X NQLXPN XN[^CPG@L[ ] KLEKC^[MLEN[ ............. ........................... ............................. ............................. ............................ ............................ ............................ .................. .... >6

QXÇKPMKG 71. XNQXN[NEPGKMÛE @N ÊG IMD^XG 8@ G QGXPMX @N [^[ YÍXPMKN[ NE CNED^GON K ............................................................................................................................................. >= 71.7 71.8 71.; 71.0 71.0.7 71.0.8 71.0.; 71.0.0

MEPXL@^KKMÛE .............. ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ .............. >= ........................... ............................ ............................ ............................. ............................. ............................ ......................... ........... >= LHONPMYL KLJQNPNEKMG ) ............. IÊ@GJNEPL .............. ............................ ............................. ............................. ............................ ............................ ............................ ............................ ............................ ................ .. >= QXLKN@MJMNEPL @N[KXMQKMÛE ) ............. ........................... ............................ ............................ ............................ ............................ ............................ ................ .. 91 .......................... ............................ ............................ ............................ ............................ ............................. ............................. .................... ...... 91 NW^MQL ENKN[GXML ............ JGPNXMGC @N GQL]L.............. ............................ ............................ ............................ ............................ ............................ ............................. ............................ ............... .. 91 @N[GXXLCCL @N CG QXÇKPMKG ............. ........................... ............................ ............................ ............................ ............................ ............................ ................ .. 91 NQLXPN .............. ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ ..................... ....... 98 X NQLXPN

........................... ............................. ............................. ............................ ............................ ............................ .................. .... 98 71.> XN[^CPG@L[ ] KLEKC^[MLEN[ ............. QXÇKPMKG 77. PXG[CGKMÛE, N[KGCG, XLPGKMÛE ] [N[DG@L @N ÊG IMD^XG NE CNED^GON K

.................................................................................................................................................................. 9;

77.7 77.8 77.; 77.0 77.0.7 77.0.8 77.0.; 77.0.0 77.>

............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ .............. 9; MEPXL@^KKMÛE .............. LHONPMYL KLJQNPNEKMG ) ............. ........................... ............................ ............................ ............................. ............................. ............................ ......................... ........... 9; IÊ@GJNEPL .............. ............................ ............................. ............................. ............................ ............................ ............................ ............................ ............................ ................ .. 9; ........................... ............................ ............................ ............................ ............................ ............................ ................ .. 9> QXLKN@MJMNEPL @N[KXMQKMÛE ) ............. NW^MQL ENKN[GXML ............ .......................... ............................ ............................ ............................ ............................ ............................. ............................. .................... ...... 9> JGPNXMGC @N GQL]L.............. ............................ ............................ ............................ ............................ ............................ ............................. ............................ ............... .. 9> ........................... ............................ ............................ ............................ ............................ ............................ ................ .. 9> @N[GXXLCCL @N CG QXÇKPMKG ............. NQLXPN .............. X NQLXPN ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ ..................... ....... 96 XN[^CPG@L[ ] KLEKC^[MLEN[ ............. ........................... ............................. ............................. ............................ ............................ ............................ .................. .... 96

................................. .............. .. 9= QXÇKPMKG 78. PXG_G@L @N ÊG K^XYG @N HN_MNX 8@ NE CNED^GON K ..................... 78.7 MEPXL@^KKMÛE .............. ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ .............. 9= ........................... ............................ ............................ ............................. ............................. ............................ ......................... ........... 41 78.8 LHONPMYL KLJQNPNEKMG) ............. 78.; IÊ@GJNEPL .............. ............................ ............................. ............................. ............................ ............................ ............................ ............................ ............................ ................ .. 41 78.0 QXLKN@MJMNEPL @N[KXMQKMÛE ) ............. ........................... ............................ ............................ ............................ ............................ ............................ ................ .. 48 .......................... ............................ ............................ ............................ ............................ ............................. ............................. .................... ...... 48 78.0.7 NW^MQL ENKN[GXML ............ 78.0.8 JGPNXMGC @N GQL]L.............. ............................ ............................ ............................ ............................ ............................ ............................. ............................ ............... .. 48 78.0.; @N[GXXLCCL @N CG QXÇKPMKG ............. ........................... ............................ ............................ ............................ ............................ ............................ ................ .. 48 NQLXPN .............. ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ ..................... ....... 40 78.0.0 X NQLXPN 78.> XN[^CPG@L[ ] KLEKC^[MLEN[ ............. ........................... ............................. ............................. ............................ ............................ ............................ .................. .... 40 ................................. .............. .. 4 4> > QXÇKPMKG 7;. PXG_G@L @N ÊG K^XYG @N [QCMEN 8@ NE CNED^GON K .....................

7;.7

MEPXL@^KKMÛE .............. ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ .............. 4>

7;.8 7;.;

........................... ............................ ............................ ............................. ............................. ............................ ......................... ........... 4> LHONPMYL KLJQNPNEKMG ) ............. ............................ ............................. ............................. ............................ ............................ ............................ ............................ ............................ ................ .. 4> IÊ@GJNEPL ..............

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg mv

7;.0 QXLKN@MJMNEPL @N[KXMQKMÛE ) ............. ........................... ............................ ............................ ............................ ............................ ............................ ................ .. 46 .......................... ............................ ............................ ............................ ............................ ............................. ............................. .................... ...... 46 7;.0.7 NW^MQL ENKN[GXML ............ 7;.0.8 JGPNXMGC @N GQL]L.............. ............................ ............................ ............................ ............................ ............................ ............................. ............................ ............... .. 46 7;.0.; @N[GXXLCCL @N CG QXÇKPMKG ............. ........................... ............................ ............................ ............................ ............................ ............................ ................ .. 46 NQLXPN .............. ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ ..................... ....... 61 7;.0.0 X NQLXPN 7;.> XN[^CPG@L[ ] KLEKC^[MLEN[ ............. ........................... ............................. ............................. ............................ ............................ ............................ .................. .... 61

QXÇKPMKG 70. XNQXN[NEPGKMÛE @N ÊG IMD^XG KLE KLLX@NEG@G[ FLJLDÍENG[ FL JLDÍENG[ G QGXPMX @N [^[ YÍXPMKN[ NE NC CNED^GON QXLKN[[MED ............................................................. 67 70.7 70.8 70.; 70.0 70.0.7 70.0.8 70.0.; 70.0.0 70.>

............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ .............. 67 MEPXL@^KKMÛE .............. LHONPMYL KLJQNPNEKMG ) ............. ........................... ............................ ............................ ............................. ............................. ............................ ......................... ........... 68 IÊ@GJNEPL .............. ............................ ............................. ............................. ............................ ............................ ............................ ............................ ............................ ................ .. 68 ........................... ............................ ............................ ............................ ............................ ............................ ................ .. 6; QXLKN@MJMNEPL @N[KXMQKMÛE ) ............. NW^MQL ENKN[GXML ............ .......................... ............................ ............................ ............................ ............................ ............................. ............................. .................... ...... 6; JGPNXMGC @N GQL]L.............. ............................ ............................ ............................ ............................ ............................ ............................. ............................ ............... .. 6; ........................... ............................ ............................ ............................ ............................ ............................ ................ .. 6; @N[GXXLCCL @N CG QXÇKPMKG ............. NQLXPN .............. X NQLXPN ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ ..................... ....... 64 XN[^CPG@L[ ] KLEKC^[MLEN[ ............. ........................... ............................. ............................. ............................ ............................ ............................ .................. .... 64

QXÇKPMKG 7>. PXG[CGKMÛE, N[KGCG, XLPGKMÛE @N ÊG IMD^XG NE NC CNED^GON QXLKN[[MED ........................................................................................................................................... 66 7>.7 7>.8 7>.; 7>.0 7>.0.7 7>.0.8 7>.0.; 7>.0.0 7>.>

MEPXL@^KKMÛE .............. ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ .............. 66 LHONPMYL KLJQNPNEKMG) ............. ........................... ............................ ............................ ............................. ............................. ............................ ......................... ........... 66 ............................ ............................. ............................. ............................ ............................ ............................ ............................ ............................ ................ .. 66 IÊ@GJNEPL .............. QXLKN@MJMNEPL @N[KXMQKMÛE ) ............. ........................... ............................ ............................ ............................ ............................ ............................ ................ .. 66 NW^MQL ENKN[GXML ............ .......................... ............................ ............................ ............................ ............................ ............................. ............................. .................... ...... 66 ............................ ............................ ............................ ............................ ............................ ............................. ............................ ............... .. 66 JGPNXMGC @N GQL]L.............. @N[GXXLCCL @N CG QXÇKPMKG ............. ........................... ............................ ............................ ............................ ............................ ............................ ................ .. 6= X NQLXPN NQLXPN .............. ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ ..................... ....... =1 ........................... ............................. ............................. ............................ ............................ ............................ .................. .... =1 XN[^CPG@L[ ] KLEKC^[MLEN[ .............

QXÇKPMKG 79. ILXJG[ DNLJÍPXMKG[ ;@ NE NC CNED^GON QXLKN[[MED. ........................... ................................ ..... =7 79.7 79.8 79.; 79.0 79.0.7 79.0.8 79.0.; 79.0.0 79.>

............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ .............. =7 MEPXL@^KKMÛE .............. ........................... ............................ ............................ ............................. ............................. ............................ ......................... ........... =7 LHONPMYL KLJQNPNEKMG ) ............. IÊ@GJNEPL .............. ............................ ............................. ............................. ............................ ............................ ............................ ............................ ............................ ................ .. =7 ........................... ............................ ............................ ............................ ............................ ............................ ................ .. =8 QXLKN@MJMNEPL @N[KXMQKMÛE ) ............. NW^MQL ENKN[GXML ............ .......................... ............................ ............................ ............................ ............................ ............................. ............................. .................... ...... =8 JGPNXMGC @N GQL]L.............. ............................ ............................ ............................ ............................ ............................ ............................. ............................ ............... .. =8 ........................... ............................ ............................ ............................ ............................ ............................ ................ .. =8 @N[GXXLCCL @N CG QXÇKPMKG ............. NQLXPN .............. X NQLXPN ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ ..................... ....... =0 XN[^CPG@L[ ] KLEKC^[MLEN[ ............. ........................... ............................. ............................. ............................ ............................ ............................ .................. .... =0

QXÇKPMKG 74. MC^JMEGKMÛE ] JGQNL @N PNVP^XG[ NE NC CNED^GON QXLKN[[MED ............ => 74.7 74.8 74.;

MEPXL@^KKMÛE .............. ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ .............. => ........................... ............................ ............................ ............................. ............................. ............................ ......................... ........... => LHONPMYL KLJQNPNEKMG ) ............. IÊ@GJNEPL .............. ............................ ............................. ............................. ............................ ............................ ............................ ............................ ............................ ................ .. =>

........................... ............................ ............................ ............................ ............................ ............................ ................ .. =9 74.0 QXLKN@MJMNEPL @N[KXMQKMÛE ) ............. .......................... ............................ ............................ ............................ ............................ ............................. ............................. .................... ...... =9 74.0.7 NW^MQL ENKN[GXML ............

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg v

74.0.8 JGPNXMGC @N GQL]L.............. ............................ ............................ ............................ ............................ ............................ ............................. ............................ ............... .. =4 ........................... ............................ ............................ ............................ ............................ ............................ ................ .. =4 74.0.; @N[GXXLCCL @N CG QXÇKPMKG ............. NQLXPN .............. 74.0.0 X NQLXPN ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ ..................... ....... =6 74.> XN[^CPG@L[ ] KLEKC^[MLEN[ ............. ........................... ............................. ............................. ............................ ............................ ............................ .................. .... =6 QXÇKPMKG 76. GEMJGKMÛE [MJQCN NE NC CNED^GON QXLKN[[MED ...................... ................................. ...................... ............. == 76.7 76.8 76.; 76.0 76.0.7 76.0.8 76.0.; 76.0.0 76.>

............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ .............. == MEPXL@^KKMÛE .............. ........................... ............................ ............................ ............................. ............................. ............................ ......................... ........... == LHONPMYL KLJQNPNEKMG) ............. IÊ@GJNEPL .............. ............................ ............................. ............................. ............................ ............................ ............................ ............................ ............................ ................ .. == QXLKN@MJMNEPL @N[KXMQKMÛE ) ............. ........................... ............................ ............................ ............................ ............................ ............................ .............. 711 .......................... ............................ ............................ ............................ ............................ ............................. ............................. .................. .... 711 NW^MQL ENKN[GXML ............ ............................ ............................ ............................ ............................ ............................ ............................. ............................ ............. 711 JGPNXMGC @N GQL]L.............. @N[GXXLCCL @N CG QXÇKPMKG ............. ........................... ............................ ............................ ............................ ............................ ............................ .............. 711 NQLXPN .............. ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ ................... ..... 717 X NQLXPN ........................... ............................. ............................. ............................ ............................ ............................ ................ .. 717 XN[^CPG@L[ ] KLEKC^[MLEN[ .............

HMHCMLDXGIÊG ....................................................................................................................................... 718 GENVL G. XßHXMKG ............................................................................................................................... 71; GENVL H. QCGEPMCCG @NC XNQLXPN @N QXÇKPMKG[. ....................................................................... 710 GENVL K. XNDCGJNEPL MEPNXEL QGXG NC ^[L @N CGHLXGPLXML[. ..................... ................................ ..................... .......... 71>

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg vm

Lhontmvll Dnenrgc `nc Jgeugc Lhontmv

[n huskg ueg vmekucgkmûe `n cgs hgsns jgtnjçtmkgs `n cg drgimkgkmûe kle sus gpcmkgkmlens ne nc jue`l rngc, g trgvís `n cg kl`mimkgkmûe `n `mkfgs nkugkmlens y gcdlrmtjls y qun gsê vnrmimqune su klelkmjmnetl g`qumrm`l pgrg qun sn `nsgrrlccne prlinsmlegcjnetn `n ueg ilrjg vnrgz. vnrgz . G`njçs, sn prntne`n jltmvgr gc gcujel g cg mevnstmdgkmûe y gc nstu`ml `n smtugkmlens qun rncgkmlene fnkfls y ineûjnels y g`qumrmr gsê klelkmjmnetls kg`g vnz jçs prnkmsls slhrn cg drgimkgkmûe plr kljputg`lrg. Nc gcujel `nhnrç tne`nr g snr krngtmvl, yg qun cg gpnrturg `n `mstmetgs lplrtuem`g`ns gsê cl rnqumnrn ne nstn jue`l tge kgjhmgetn.

Lhontmvll Dnenrgc `n cg Jgtnrmg Lhontmv

Cg gsmdegturg prntne`n qun nc nstu`mgetn g`qumnrg ueg ilrjgkmûe klesmstnetn ne cg dnenrgkmûe `n drçimkls ne 8 y ; `mjnesmlens, su trgesilrjgkmûe y ninktls `mvnrsls, `n kgrg g su gpcmkgkmûe plstnrmlr ne nc jue`l `n cg gemjgkmûe y cg rngcm`g` vmrtugc. R7Z

Kljpntnekmgs Nspnkêiimkgs mkgs g @nsgrrlccgr

Gpcmkg cls jl`ncls jgtnjçtmkls hçsmkls y cls jl`ncls `n klclr utmcmzg`ls ne



lhontls hm`mjnesmlegcns y trm`mjnesmlegcns. R7Z @nsgrrlccg y gpcmkg jl`ncls `n drgimkgkmûe y trgesilrjgkmûe hm`mjnesmlegc pgrg



nc nermqunkmjmnetl vmsugc `n sus gpcmkgkmlens. R7Z

^tmcm`g` `nc Jgeugc

Ns ueg duêg pgrg cls prlinslrns qun mjpgrtne cg jgtnrmg, pgrg pl`nr uemilrjmzgr cls kletnem`ls y emvnc `n prliue`m`g` `n cls tnjgs `nc prldrgjg. Qgrg cls nstu`mgetns oundg ue pgpnc mjplrtgetn ne su ilrjgkmûe yg qun ns ueg fnrrgjmnetg `n gprne`mzgon qun ilrtgcnkn cls lhontmvls `nc pnrimc `n nstu`mls.

Qgrg cg Gkg`njmg `n [mstnjgs Kljputgkmlegcns ns ueg nvm`nekmg qun sn nstçe prljlvmne`l eunvgs n meelvg`lrgs nstrgtndmgs ns trgtndmgs `m`çktmkgs.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 4

Qrgktmkg 7. Cêeng @@G 7.7 Metrlùkkmûe

Cg prnsnetn prçktmkg gyu`g g gsmjmcgr cls kletnem`ls `n cg êm`g` M? Metrlùkkmûe g

cg drgimkgkmûe plr kljputg`lrg `nc suhtnjg 7.;. Gspnktls jgtnjçtmkls `n cg drgimkgkmûe , `nc prldrgjg `n nstu`mls `n cg jgtnrmg `n Drgimkgkmûe , `nsgrrlccge`l cg kljpntnekmg nspnkêimkg? –Gpcmkg cls jl`ncls jgtnjçtmkls hçsmkls y cls jl`ncls `n klclr utmcmzg`ls ne lhontls hm`mjnesmlegcns y trm`mjnesmlegcns ‚.

Gc mjpcnjnetgr drçimkls ne ue jlemtlr tnenjls cg cmjmtgetn `n nstgr ne ue nspgkml `mskrntl, plr cl qun pl`njls lptmjmzgr cls kçckucls pgrg `mhuogr ueg cêeng. Nc gcdlrmtjl @@G ns ue jítl`l juy snekmccl, pnrl jçs nimkmnetn qun sm metnetgjls usgr cg ilrjucg y:jx+h, qun sn utmcmzg ne ue nspgkml kletmeul.

7.8 Lhontmvl Kljpntnekmg)

Ncghlrgr ue prldrgjg qun trgkn ueg cêeng usge`l nc gcdlrmtjl @@G.

7.; Iue`gjnetl R;Z

Nc gegcmzg`lr `minrnekmgc `mdmtgc (@@G2 `mdmtgc `miinrnetmgc gegcyznr) ns ue gcdlrmtjl `n cêeng `n klevnrsmûe `n rgstrnl qun sn hgsg ne nc kçckucl yg sng `n ΐx, l `n ΐy, plr jn`ml `n cgs smdumnetns nkugkmlens?

∉  ∉ ∉ ∉∝∉

[n ninktÿg ue junstrnl `n cg cêeng n metnrvgcls uemtgrmls ne ueg kllr`neg`g y sn `ntnrjmege cls vgclrns netnrls klrrnsple`mnetns jçs prûxmjls g cg trgynktlrmg `n cg cêeng pgrg cg ltrg kllr`neg`g. [n `nhn klesm`nrgr prmjnrl ueg cêeng kle pne`mnetn plsmtmvg. [m cg pne`mnetn ns jnelr l mdugc qun 7, sn ccnvg g kghl ue junstrnl `n x metnrvgcls uemtgrmls ( ΐx : 7) y sn kgckucg kg`g vgclr suknsmvl `n y kljl?

+    

(G)

Nc suhêe`mkn m tljg vgclrns netnrls g pgrtmr `n 7 y gujnetg g rgzûe `n 7 fgstg qun sn gckgekn nc vgclr imegc. ]g qun j pun`n snr kugcqumnr eÿjnrl rngc netrn 1 y 7, cls vgclrns kgckucg`ls `n y `nhne rn`le`ngrsn gc netnrl jçs knrkgel. Qgrg cgs cêengs kle ueg pne`mnetn plsmtmvg jgylr qun 7, sn rnvmnrtne cgs iuekmlens `n x y `n y. Ns `nkmr, sn rngcmzg ue junstrnl `n y ne metnrvgcls uemtgrmls ( ΐy ΐy : 7) y sn kgckucg kg`g vgclr suknsmvl `n x kljl? @npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 6

+    

(H)

Cgs nkugkmlens getnrmlrns (G y H) sn hgsge ne cg suplsmkmûe `n qun cgs cêengs `nhne prlknsgrsn `nc nxtrnjl mzqumnr`l gc `nrnkfl. [m nstn prlknsgjmnetl sn rnvmnrtn, `n jgenrg qun sng nc nxtrnjl `nrnkfl `le`n sn memkmg, netlekns sn tmnen yg sng

∉+∘7∘∘7 

l (kuge`l cg pne`mnetn ns jgylr qun 7)

∉ ∘7∘∘7 7 +  

 ∔ ∉∉

Cêeng m`ngc

7.0 Qrlkn`mjmnetl @nskrmpkmûe) 7.0.7 Nqumpl enknsgrml Kljputg`lrg kle ue smstnjg lpnrgtmvl qun kunetn kle gjhmnetn drçimkl (Tme`lws, Cmeux, ntk…)

7.0.8 Jgtnrmgc `n Gplyl [@B `n ogvg. Netlrel `n `nsgrrlccl pgrg ogvg (M@N), plr nonjpcl, EntHnges. Cmhrnrêg swmed l ogvgIV.







@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg =

7.0.; @nsgrrlccl `n cg Qrçktmkg @nhnjls tnenr ne kunetg qun nc smstnjg `n kllr`neg`gs kllr`ne g`gs `nc jlemtlr y `n cgs vnetgegs klesm`nrge nc lrmdne ne cg nsqumeg supnrmlr mzqumnr`g, cls vgclrns ne x krnkne fgkmg cg `nrnkfg y cls vgclrns `n y krnkne fgkmg ghgol.

Ne nstg prçktmkg usgrnjls enthnges 6.7 vnrsmûe ne medcís. Kljnezgrnjls dnenrge`l ueg gpcmkgkmûe drçimkg ne cg kugc `nogrnjls ueg iuekmûe gslkmg`g gc nvnetl `n ue hltûe pgrg qun gc `gr kcmk sslhrn lhrn nc hltûe sn s n nonkutn nc kû`mdl qu qunn trgzg ueg cêeng kle nc gcdlrmtjl @@G. Nonkutn cls smdumnetns pgsls? QG[L 7? Memkmn enthnges y kleimdurn ue prlynktl drçimkl. ^sn cg smdumnetn rutg `nc jneÿ? Grkfmvls Eunvl Qrlynktl

Ncmog cg kgtndlrêg Ogvg y nc tmpl `n prlynktl Ogvg Gppcmkgtmle, `nspuís `ncn ue GppCmeng@@G. Nstl dnenrg `mrnktlrml y vgrmls eljhrn prlynktl, plrnc nonjpcl, grkfmvlsgcqun kletmnene prlynktl. @npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 71

Qgsl8? @nhnjls krngr ltrl grkfmvl qun nspnkmimkgrg cg vnetgeg drçimkg klelkm`g kljl OIrgjn. @n kcmk `nrnkfl slhrn nc pgquntn gppcmeng``g ne nc jneÿ kletnxtugc ncmog Enw y `nspuís OIrgjnIlrj. Nstl krngrg ueg kcgsn, cg eljhrgrnjls Ynetgeg. @mkfg kcgsn tmnen `ls vmstgs? Jl`l Kû`mdl ([lurkn) y Jl`l @msn÷l (@nsmde).

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 77

Qgsl ;? Ygjls g jlstrgr cg pgcntg kle cls kletrlcns drçimkls `n cg cmhrnrêg swmed. Cl fgknjls ne cg smdumnetn rutg `nc jneÿ? Tme`lwsM@N PllcsQgcnttn Qgrg klclkgr cls kletrlcns ne eunstrl cmnezl, slcl `nhnjls grrgstrgr y slctgr cls kletrlcns `nsng`ls.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 78

Klclkgrnjls `ls kletrlcns? OQgenc y OHuttle. Cns kgjhmgjls nc eljhrn, `ge`l kcmk `nrnkfl slhrn nc kletrlc y ne nc jneÿ kletnxtugc ncndmr kfgedn vgrmghcn egjn… y cns plenjls nc eljhrn kljl sn me`mkg ne cgs mjçdnens?

Pgjhmíe cn kgjhmgjls nc vgclr g gcduegs prlpmn`g`ns. Qgrg vnr cgs prlpmn`g`ns `nc kletrlc, `gjls kcmk `nrnkfl slhrn nc kletrlc y sncnkkmlegjls Qrlpnrtmns.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 7;

Qgsl 0? Gflrg `nhnjls memkmgr cg vnetgeg drçimkg `ns`n nc memkml `nc prldrgjg prmekmpgc. Qgrg cldrgrcl n`mtgjls nc prldrgjg prmekmpgc GppCmeng@@G.ogvg mesnrtge`l cgs cêengs 7= y 81 kljl sn junstrg ne cg mjgdne.

Qgsl >? [lcl els rnstg `nogr nc funkl pgrg nskrmhmr eunstrl gcdlrmtjl `n cg cêeng @@G. @nhnjls n`mtgr nc grkfmvl Ynetgeg.ogvg, pnrl ne nc jl`l [lurkn. Qgrg cldrgrcl cn `gjls `lhcn kcmk gc kletrlc hteCmeng, kle nstl cldrgjls vgrmgs klsgs? gslkmgr ueg @npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 70

iuekmûe gc nvnetl kcmk slhrn `mkfl hltûe y kgjhmgrels gc jl`l [lurkn klclkçe`lels slhrn cg iuekmûe hteCmengGktmleQnrilrjn` qun sn nonkutgrç kuge`l sukn`g nc nvnetl kcmk. N`mtgjls cg iuekmûe mesnrtge`l nc kû`mdl ne cg cêeng 6>, kljl sn junstrg ne cg mjgdne?

Qgsl 9? Gflrg mesnrtgjls `nspuís `n cg cêeng 69 cg iuekmûe cmeng@@G? vlm` cmeng@@G(met Vmemkmgc, met ]memkmgc, met Vimegc, met ]imegc) { Drgpfmks cgpmz: oQgencQmzgrrle.dntDrgpfmks()2 //mjpcnjnetgr gcdlrmtjl @@G cgpmz.`rgwLvgc(Vmemkmgc, ]memkmgc, 7, 7)2 //^sgr pgrg pmetgr ue pmxnc }

Qnrl gc nskrmhmrcl, igctgrç ueg cmhrnrêg, enthnges els cl me`mkg kle ueg gcnrtg ne cg cêeng 6;. Qgrg gdrndgr cg cmhrnrêg enknsgrmg, `gjls kcmk mzqumnr`l slhrn cg gcnrtg y ncndmjls cg prmjnrg lpkmûe, kljl sn junstrg ne cg mjgdne?

Els `nhn qun`gr kljl smdun?

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 7>

Qgsl 4? Kljpmcgjls y nonkutgjls nc prlynktl pgrg vnr qun el fgyg nrrlr. Qgrg fgknrcl `gjls kcmk slhrn nc mklel `n pcgy.

[m tl`l nstuvl klrrnktl, sn junstrg cg vnetgeg kle cg gpcmkgkmûe?

[m `gjls kcmk ne nc hltûe, el sukn`nrç eg`g, puns cg iuekmûe nstg funkg. ] ns oustl nc pgsû imegc, mjpcnjnetn nc kû`mdl sndÿe nc gcdlrmtjl @@G. Qgsl 6? @netrl `n cg iuekmûe cmeng@@G, mjpcnjnetn nc smdumnetn gcdlrmtjl R>Z? Xnkmhn cls pgrçjntrls klrrnsple`mnetns gc puetl memkmgc y puetl imegc (Vmemkmgc, ]memkmgc, Vimegc,]imegc) Gsmdegr g @nctgV cg `minrnekmg `n Vimegc ‛ Vmemkmgc Gsmdegr g @nctg] cg `minrnekmg `n ]imegc ‛ ]memkmgc [m GH[(@nctgV) 5 GH[(@nctg]) Gsmdegr g Qgsls nc GH[(@nctgV) @n cl kletrgrml Gsmdegr g Qgsls nc GH[(@nctg]) Gsmdegr g Vmekrnjnetl nc rnsuctg`l `n @nctgV / Qgsls Gsmdegr g ]mekrnjnetl nc rnsuctg`l `n @nctg] / Qgsls Gsmdegr g V nc vgclr `n Vmemkmgc Gsmdegr g ] nc vgclr `n ]memkmgc Mcujmegr pmxnc ne kllr`neg`g V,] @ns`n b:7 fgstg Qgsls Gsmdegr g V cg sujg `n V + Vmekrnjnetl Gsmdegr g ] cg sujg `n ] + ]mekrnjnetl Mcujmegr pmxnc ne Kll`neg`g V,] Ime `n Gcdlrmtjl(@@G)

Yuncvg g nonkutgr nc prldrgjg y vnrmimqun qun sn trgzg ueg cêeng. @npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 79

Mevnstmdun kljl dnenrgr eÿjnrls gcngtlrmls y kljl jn`mr metnrvgcls `n tmnjpl y krnn ueg iuekmûe qun `mhuon >111 cêengs @@G gcngtlrmgs y jm`g nc tltgc `n jmcmsndue`ls njpcng`ls.

7.0.0 Xnplrtn Gc imegcmzgr ístg prçktmkg nc gcujel `nhnrç dnenrgr ue rnplrtn ne Q@I qun kletnedg ueg klrrm`g `n nskrmtlrml ne ueg flog `n kçckucl (plr nonjpcl, ne Nxknc) y `nspuís nc kû`mdl iunetn `n su iuekmûe iue kmûe qun mjpcnjnetl nc psnu`lkû`mdl `nc gcdlrmtjl `n cg cêeng @@G y gc ÿctmjl mekcumr mjçdnens `n cg nonkukmûe `n su prldrgjg. Jnekmlen nc tmnjpl rnqunrm`l pgrg `mhuogr >111 cêengs.

7.> Xnsuctg`ls y Klekcusmlens

Kle ístg prçktmkg, nc gcujel kljprne`nrç cg `minrnekmg `n drgimkgr ne ue nspgkml `mskrntl (kljl cl hrme`g ue jlemtlr) y ue nspgkml kletmeul.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 74

Qrgktmkg 8. Cêeng Hrnsnefgj 8.7 Metrlùkkmûe

Cg prnsnetn prçktmkg gyu`g g gsmjmcgr cls kletnem`ls `n cg êm`g` M? Metrlùkkmûe g

cg drgimkgkmûe plr kljputg`lrg `nc suhtnjg 7.;. Gspnktls jgtnjçtmkls `n cg drgimkgkmûe , `nc prldrgjg `n nstu`mls `n cg jgtnrmg `n Drgimkgkmûe , `nsgrrlccge`l cg kljpntnekmg nspnkêimkg? –Gpcmkg cls jl`ncls jgtnjçtmkls hçsmkls y cls jl`ncls `n klclr utmcmzg`ls ne lhontls hm`mjnesmlegcns y trm`mjnesmlegcns‚.

Nc gcdlrmtjl @@G, guequn ns nimkmnetn, gÿe enknsmtg vgrmghcns tmpl iclgt pgrg cls vgclrns `n cg pne`mnetn. Cg grmtjítmkg `n icltgetns ns nxtrnjg`gjnetn cnetg kljpgrg`g kle cg `n netnrls. Nc gcdlrmtjl `n cg cêeng `n Hrnsnefgj tmnen cg vnetgog `n trghgogr slcl kle eÿjnrls netnrls. Ne cg prnsnetn prçktmkg rnpntmrnjls cls pgsls pgsl s `nc 7 gc 9 `nc puetl 7.0.; qun sn rnimnrne g klestrumr nc netlrel drçimkl `nc prldrgjg y `nogr tl`l cmstl pgrg mesnrtgr cg iuekmûe qun mjpcnjnetn nc gcdlrmtjl `n cêeng `n Hrnsnefgj.

8.8 Lhontmvl Kljpntnekmg)

Ncghlrgr ue prldrgjg qun trgkn ueg cêeng usge`l nc gcdlrmtjl `n Hrnsnefgj.

8.; Iue`gjnetl

Ns ue gcdlrmtjl prnkmsl y ninktmvl pgrg cg dnenrgkmûe `n cêengs `n rgstrnl, `nsgrrlccg`l plr Hrnsnefgj, klevmnrtn jn`mgetn rgstrnl cgs cêengs gc utmcmzgr sûcl kçckucls mekrnjnetgcns kle netnrls qun sn pun`ne g`lptgr pgrg `nspcndgr kmrkueinrnekmgs y ltrgs kurvgs. Nc gcdlrmtjl cêeng `n Hrnsnefgj sn hgsgnetrn ne prlhgr nc smdel `n`n pgrçjntrl netnrl, kuyl vgclr ns`n prlplrkmlegc g cg `minrnekmg cgs snpgrgkmlens ùe n cgs `ls plsmkmlens `n pmxnc `n cg trgynktlrmg rngc `n cg cêeng. Gcdlrmtjl `n Hrnsnefgj Qgrg rngcmzgr nc trgzl `n cêeng `n Hrnsnefgj pgrg ueg u eg cêeng kle ueg pne`mnetn plsmtmvg jnelr qun 7 sn `nhne sndumr cls smdumnetns pgsls?

, 

7. [n kgpturge cls `ls nxtrnjls `n cg cêeng y sn gcjgkneg nc nxtrnjl mzqumnr`l ne . 8. [n kgrdg

ne nc hÿinr `n nstrukturg2 ns `nkmr, sn trgzg nc prmjnr puetl.

, 

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 76

∉,∉,8∉ 8∉∘8∉  8∉∘∉

;. [n kgckucge cgs klestgetns pgrg nc pgrçjntrl `n `nkmsmûe kljl

y

y sn lhtmnen nc vgclr memkmgc

0. Ne kg`g , g cl cgrdl `n cg cêeng, qun memkmg ne m:1, sn ninktÿg cg pr prunhg unhg smdumnetn? sm , nc smdumnetn puetl qun sn `nhn trgzgr ns

 3 1

+,  +   8∉ +, + +   8∉∘8∉ y

@n ltrl jl`l, nc smdumnetn puetl qun sn `nhn trgzgr ns

>. [n rnpmtn nc pgsl 0 ΐx vnkns.

8.0 Qrlkn`mjmnetl @nskrmpkmûe) 8.0.7 Nqumpl enknsgrml Kljputg`lrg kle ue smstnjg lpnrgtmvl qun kunetn kle gjhmnetn drçimkl (Tme`lws, Cmeux, ntk…)

8.0.8 Jgtnrmgc `n Gplyl [@B `n ogvg. Netlrel `n `nsgrrlccl pgrg ogvg (M@N), plr nonjpcl, EntHnges. Cmhrnrêg swmed l ogvgIV.







8.0.; @nsgrrlccl `n cg Qrçktmkg Nonkutgjls cls pgsls geçcldls `n cg prçktmkg getnrmlr `ns`n nc QG[L 7 fgstg nc QG[L 9, slcl kgjhmgjls nc eljhrn `nc prlynktl g GppCmengHrnsnefgj , cg ntmquntg `nc hltûe g @mhuog cêeng Hrnsnefgj y nc eljhrn `n cg iuekmûe qun kletne`rç nc gcdlrmtjl g cmengHrnsnefgj. Qgsl 7? @netrl `n cg iuekmûe cmeng@@G, mjpcnjnetn nc smdumnetn gcdlrmtjl R>Z? Xnkmhn cls pgrçjntrls klrrnsple`mnetns gc puetl memkmgc y puetl imegc (Vmemkmgc, ]memkmgc, Vimegc,]imegc) @nctgV : GH[( Vimegc ‛ Vmemkmgc) @nctg] : GH[( ]imegc -]memkmgc) KlestgetnQ : 8*@nctg] ‛ @nctgV [m Vmemkmgc 5 Vimegc V : Vimegc ] : ]imegc ^ctmjl : Vmemkmgc

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 7=

@n cl kletrgrml V : Vmemkmgc ] : ]memkmgc ^ctmjl : Vimegc Mcujmegr pmxnc ne kllr`neg`g V,] Fgknr jmnetrgs V3^ctmjl V : V + 7 [m KlestgetnQ 3 1 KlestgetnQ : KlestgetnQ + 8 *@nctg] @n cl kletrgrml ]+7 : ] KlestgetnQ : KlestgetnQ+8 *(@nctg]-@nctgV) Mcujmegr pmxnc ne kllr`neg`g V,] Ime `n Gcdlrmtjl (Hrnsnefgj)

Nonkutn nc prldrgjg y vnrmimqun qun sn trgzg ueg cêeng. Qrldrgjn ueg iuekmûe qun `mhuon >111 > 111 cêengs `n Hrnsnefgj gcngtlrmgs y jm`g nc tltgc `n jmcmsndue`ls njpcng`ls.

8.0.0 Xnplrtn Gc imegcmzgr ístg prçktmkg nc gcujel `nhnrç dnenrgr ue rnplrtn ne Q@I qun kletnedg ueg klrrm`g `n nskrmtlrml ne ueg flog `n kçckucl (plr nonjpcl, ne Nxknc) y `nspuís nc kû`mdl iunetn `n su iuekmûe iue kmûe qun mjpcnjnetl nc psnu`lkû`mdl `nc gcdlrmtjl `n cg cêeng `n Hrnsnefgj y gc ÿctmjl mekcumr mjçdnens `n cg nonkukmûe `n su prldrgjg. Kljpgrn nc tmnjpl rnqunrm`l pgrg `mhuogr >111 cêengs netrn cls jítl`ls @@G y Hrnsnefgj.

8.> Xnsuctg`ls y Klekcusmlens

Kle ístg prçktmkg, nc gcujel gprnkmgrç cg `minrnekmg ne tmnjpl `n ue gcdlrmtjl qun slcl usg eÿjnrls netnrl g ltrl qun usg eÿjnrls icltgetns.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 81

Qrgktmkg ;. Kmrkueinrnekmg Kljue ;.7 Metrlùkkmûe

Cg prnsnetn prçktmkg gyu`g g gsmjmcgr cls kletnem`ls `n cg êm`g` M? Metrlùkkmûe g cg drgimkgkmûe plr kljputg`lrg `nc suhtnjg 7.;. Gspnktls jgtnjçtmkls `n cg drgimkgkmûe , `nc prldrgjg `n nstu`mls `n cg jgtnrmg `n Drgimkgkmûe , `nsgrrlccge`l cg kljpntnekmg nspnkêimkg? –Gpcmkg cls jl`ncls jgtnjçtmkls hçsmkls y cls jl`ncls `n klclr utmcmzg`ls ne lhontls hm`mjnesmlegcns y trm`mjnesmlegcns‚.

G`njçs `n puetls y cêengs ltrl kljplenetn juy irnkunetnjnetn utmcmzg`l ne cg drgimkgkmûe ns cg kmrkueinrnekmg. Ne nstg prçktmkg `mhuogrnjls ueg kmrkueinrnekmg g pgrtmr `n cg nkugkmûe kletmeug `n cg kmrkueinrnekmg.

;.8 Lhontmvl Kljpntnekmg)

Ncghlrgr ue prldrgjg qun trgkn ueg kmrkueinrnekmg usge`l cg nkugkmûe `n cg kmrkueinrnekmg.

;.; Iue`gjnetl

, 

êg kmrkueinrnekmg sn `nimen kljl nc kleouetl `n puetls qun nqum`mstge nq um`mstge ueg `mstgekmg r  `n `n ltrl puetl ccgjg`l knetrl.

Qgrg kugcqumnr puetl `nc kêrkucl, nstg rncgkmûe `n `mstgekmg sn nxprnsg jn`mgetn nc tnlrnjg `n Qmtçdlrgs ne kllr`neg`gs kgrtnsmgegs?

∘ ∘  

Ql`njls utmcmzgr nstg nkugkmûe pgrg kgckucgr cg plsmkmûe `n cls puetls slhrn ueg kmrkueinrnekmg, rnklrrmne`l nc non x ne pgsls uemtgrmls `ns`n g y

 ∘    

kgckucge`l cls klrrnsple`mnetns vgclrns y ne kg`g plsmkmûe jn`mgetn cg iûrjucg?

   · ∟  ∘  ∘ 

Qnrl nstn el ns nc jnolr jítl`l pgrg dnenrgr ue kêrkucl. êl `n cls prlhcnjgs kle nstn jítl`l ns qun rnqumnrn uels klesm`nrghcns kçckucls ne kg`g pgsl. G`njçs, nc nspgkmg`l netrn cls pêxncns `mhuog`ls el ns uemilrjn. Qgrg lptmjmzgr cg kgetm`g` `n kçckucls, pl`njls gprlvnkfgr cls nons `n smjntrêg y tge slcl kgckucgr 7/6 `n kmrkueinrnekmg y cls `njçs puetls lhtnenrcls plr rnicnxmûe?

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 87

Gsê, slcl kgckucgrnjls vgclrns pgrg x `ns`n 1 fgstg x5:y.

;.0 Qrlkn`mjmnetl @nskrmpkmûe) ;.0.7 Nqumpl enknsgrml

Kljputg`lrg kle ue smstnjg lpnrgtmvl qun kunetn kle gjhmnetn drçimkl (Tme`lws, Cmeux, ntk…)

;.0.8 Jgtnrmgc `n Gplyl [@B `n ogvg. Netlrel `n `nsgrrlccl pgrg ogvg (M@N), plr nonjpcl, EntHnges. Cmhrnrêg swmed l ogvgIV.







;.0.; @nsgrrlccl `n cg Qrçktmkg Nonkutgjls cls pgsls geçcldls `n cg prçktmkg uel, `ns`n nc QG[L 7 fgstg nc QG[L 9, slcl kgjhmgjls nc eljhrn `nc prlynktl g GppKmrkueinrnekmg , cg ntmquntg `nc hltûe g @mhuog kmrkueinrnekmg y nc eljhrn `n cg iuekmûe qun kletne`rç nc gcdlrmtjl g kmrkueinrnekmg . Qgsl 7? @netrl `n cg iuekmûe kmrkueinrnekmg , mjpcnjnetn nc smdumnetn gcdlrmtjl R>Z? Xnkmhn cls pgrçjntrls klrrnsple`mnetns gc knetrl y rg`ml `n cg kmrkueinrnekmg (Vknetrl, ]knetrl, rg`ml) V:1 ]:rg`ml Jmnetrgs V 3 ] QV:V+Vknetrl2 Q]:]+]knetrl2 Mcujmegr pmxnc ne kllr`neg`g Mcujmegr pmxnc ne kllr`neg`g

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

QV, Q] QV,-Q]

Qçdmeg 88

Mcujmegr Mcujmegr Mcujmegr Mcujmegr Mcujmegr Mcujmegr ] : Xgêz

pmxnc ne pmxnc ne pmxnc ne pmxnc ne pmxnc ne pmxnc ne kug`rg`g

kllr`neg`g -QV, Q] kllr`neg`g -QV, Q] kllr`neg`g Q], QV kllr`neg`g Q],-QV kllr`neg`g -Q], QV kllr`neg`g -Q], QV `n (rg`ml*rg`ml ‛ V*V)

Ime Jmnetrgs Ime `n Gcdlrmtjl (Hrnsnefgj)

Nonkutn nc prldrgjg y vnrmimqun qun sn trgzg ueg kmrkueinrnekmg. Qrldrgjn ueg iuekmûe qun `mhuon >111 kmrkueinrnekmgs gcngtlrmgs y jm`g nc tltgc `n jmcmsndue`ls njpcng`ls.

;.0.0 Xnplrtn Gc imegcmzgr ístg prçktmkg nc gcujel `nhnrç dnenrgr ue rnplrtn ne Q@I qun kletnedg ueg klrrm`g `n nskrmtlrml ne ueg flog `n kçckucl (plr nonjpcl, ne Nxknc) y `nspuís nc kû`mdl iunetn `n su iuekmûe qun mjpcnjnetl nc psnu`lkû`mdl `nc gcdlrmtjl `n cg kmrkueinrnekmg y gc ÿctmjl mekcumr mjçdnens `n cg nonkukmûe `n su prldrgjg. Xndmstrn nc tmnjpl rnqunrm`l pgrg `mhuogr >111 kmrkueinrnekmgs.

;.> Xnsuctg`ls y Klekcusmlens

Kle ístg prçktmkg, nc gcujel gprne`nrç g `mhuogr ueg kmrkueinrnekmg, gprlvnkfge`l cls nons `n smjntrêg pgrg jmemjmzgr cg kgetm`g` `n lpnrgkmlens qun mjpcmkge kgckucgr ueg rgêz kug`rg`g (qun ns rnqumnrn jukfl jçs rnkursl).

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 8;

Qrgktmkg 0. Kmrkueinrnekmg Hrnsnefgj 0.7 Metrlùkkmûe

Cg prnsnetn prçktmkg gyu`g g gsmjmcgr cls kletnem`ls `n cg êm`g` M? Metrlùkkmûe g cg drgimkgkmûe plr kljputg`lrg `nc suhtnjg 7.;. Gspnktls jgtnjçtmkls `n cg drgimkgkmûe , `nc prldrgjg `n nstu`mls `n cg jgtnrmg `n Drgimkgkmûe , `nsgrrlccge`l cg kljpntnekmg nspnkêimkg? –Gpcmkg cls jl`ncls jgtnjçtmkls hçsmkls y cls jl`ncls `n klclr utmcmzg`ls ne lhontls hm`mjnesmlegcns y trm`mjnesmlegcns‚.

Nc smdumnetn gcdlrmtjl ns ueg jnolrg `nc jítl`l getnrmlr. Cl cldrg nvmtge`l trghgogr kle eÿjnrls `n tmpl icltgetn, pnrl slhrntl`l, sn gflrrg nc kçckucl `n ueg rgêz kug`rg`g plr kg`g pmxnc. Qgrg fgknrcl sn mespmrg ne nc gcdlrmtjl `n cg cêeng `n Hrnsnefge, plr cl qun sn cn klelkn kljl gcdlrmtjl `n cg kmrkueinrnekmg `n Hrnsnefgj (guequn nstn el cl mevnetû). Gsê, nc Gcdlrmtjl `n cg Kmrkueinrnekmg `n Hrnsnefgj ns ue jítl`l rçpm`l pgrg nc trgzg`l `n kmrkueinrnekmgs ne `msplsmtmvls drçimkls, kuyg kugcm`g` jçs gprnkmg`g ns qun slcl rngcmzg kçckucls kle netnrls.

0.8 Lhontmvl Kljpntnekmg)

Ncghlrgr ue prldrgjg qun trgkn ueg kmrkueinrnekmg usge`l nc Gcdlrmtjl `n cg Kmrkueinrnekmg `n Hrnsnefgj.

0.; Iue`gjnetl

Gc trgzgr ueg kmrkueinrnekmg slhrn pgpnc kle ue kljpçs, el nxmstne mjpn`mjnetls pgrg dnenrgr ueg kurvg kletmeug kle ue trgzg`l prçktmkgjnetn pnrinktl. pnri nktl. Ne kgjhml kuge`l sn lpnrg slhrn ue smstnjg ue smstnjg `mskrntl kljl ue jlemtlr qun kletmnen pmxncns lrdgemzg`ls ne imcgs y klcujegs (kug`rmkucg`l) (kug`rmkucg`l),, ueg kmrkueinrnekmg smnjprn sndumrç ue trgzg`l mjpnrinktl, yg qun nc trgzl m`ngc `n ueg kmrkueinrnekmg rnqumnrn qun pgrg kg`g vgclr `n V  sn sn lhtnedg ue vgclr `n ]  ne ne nc `ljmeml `n cls eÿjnrls rngcns. ] ne eunstrl nspgkml `mskrntl, slcl pl`njls tnenr vgclrns ne nc `ljmeml `n cls eÿjnrls netnrls.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 80

Cls pmxncns rlols rnprnsnetge pgrtn `nc trgzl `n ueg kmrkueinrnekmg ne ue nspgkml `mskrntl. Cg cêeng gzuc metnetg rnprnsnetgr pgrtn `nc trgzl `n ueg kmrkueinrnekmg ne ue nspgkml kletmeul. Cg `nsvnetgog `n trgzgr ne ue nspgkml `mskrntl (kljl cl ns ue jlemtlr) ns qun pnr`njls im`ncm`g`. Cg vnetgog ns qun pl`njls trghgogr slcl kle eÿjnrls netnrls. Nc gcdlrmtjl `n Hrnsnefgj prlplen qun, ne hgsn g cgs `minrnekmgs rnspnktl gc trgzl m`ngc, sn tljn cg `nkmsmûe `n pmetgr gcdÿe pmxnc. Qrmjnrl klesm`nrgjls qun slcl tljgrnjls vgclrns netnrls pgrg V qun tljgrç vgclrns `n 1 g r . Qgrg kg`g vgclr `n V  cn cn klrrnsple`n ue vgclr `n ] .

[ndÿe cg mjgdne getnrmlr, nc trgzl m`ngc (cêeng gzuc) els me`mkg qun pmxncns `nhnjls pmetgr. Ne cls pmxncns gjgrmccls vnjls qun el fgy kletrlvnrsmg, puns cg tltgcm`g` `nc trgzl slcl tlkg nc pmxnc (V, ]). Qnrl ne cls pmxncns jgrkg`ls kle nc smdel ‖

Netlekns, ¼kugc `nhnjls pmetgr< Qgrg `ntnrjmegrcl, `nimemjls ue pgrçjntrl Qm qun els me`mkgrç qun pmxnc nstç jçs knrkgel gc trgzl m`ngc. Nstl sn cldrg kljpgrge`l cgs `mstgekmgs `ns`n cg gcturg `nc trgzl m`ngc ]  fgstg fgstg nc pmxnc ne ] m y `ns`n ] fgstg nc pmxnc ne ] m -7. ] pgrg `nogr nstg kljpgrgkmûe nxprnsg`g ne ue vgclr ÿemkl, rnstgjls cgs `mstgekmgs?

y tljgjls cg smdumnetn `nùkkmûe?

   ∘ 

[m pm ns endgtmvl netlekns ]  nstç nstç jçs knrkg ] m [m pm ns plsmtmvl netlekns ]  nstç nstç jçs knrkg ] m -7 Nstl cl pl`njls nxprnsgr kljl?

+  {    3 1  ∘ 7   ≮ 1

G pgrtmr `n cg smdumnetn drçimkg, `nùkmjls cgs nkugkmlens usg`gs ne nc gcdlrmtjl.

Qgsls pgrg lhtnenr cgs iûrjucgs usg`gs ne nc gcdlrmtjl? Qgrtmjls `nc fnkfl qun klelknjls cls vgclrns `nc m-ísmjl pmxnc (V  , m, ]   ) m). ] qunrnjls klelknr nc smdumnetn pmxnc (V mm+7 +7 , ] mm+7 +7 ). Cls mekrnjnetls ne nc non V  sle sle uemtgrmls? 





+ 

    7

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

(Nkugkmûe 7)

Qçdmeg 89

Gflrg krngjls ue pgrçjntrl `n `nkmsmûe Qm qun snrç cg `minrnekmg netrn cgs `mstgekmgs @7 y @ 8, qun rnprnsnetge g ` 7 y `  8 rnspnktmvgjnetn, pnrl plr



klevnemnekmg, trghgogjls kle `minrnekmgs `n kug`rg`ls y tnenr nkugkmlens sme rgêkns. Gsê, ne cudgr `n usgr?

 

 ∘    ∘ ∘  7 tne`rnjls cls smdumnetns vgclrns `n y    ∘     ∘  ∘ 7 ] nc pgrçjntrl `n `nkmsmûe qun`g kljl?    ∘  @7 @ 8

Qm

[lcl els igctg `ntnrjmegr cg gcturg `nc smdumnetn pmxnc ] m+7 m+7, qun kljl yg cl



fghêgjls `ntnrjmeg`l, sn nxprnsg kljl?

7  ≮ 1  +  {  ∘7  31  8             ∘     ∘ +

(Nkugkmûe 8)

Klelknjls qun cg nkugkmûe `n cg kmrkueinrnekmg ns



g qun`ge`l qun`ge`l smdumnetn pmxnc, y lhtnenjls?

``nspnogjls nspnogjls 2 usgjls nstg nkugkmûe pgrg nvgcugrcg ne nc



[ustmtumjls plr cg nkugkmûe 7?

   ∘   7

(Nkugkmûe ;)

]g kletgjls kle cls ncnjnetls pgrg nxpge`mr Qm



   ∘     ∘  ∘  ∘  ∘ 7    ∘  ∘    ∘ 7    ∘  ∘    ∘ 8  7   8 ∘ 8 ∘ 8  7

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 84

[ustmtumjls ]  8 plr cg nkugkmûe ;?

  8 ∘ 8 ∘   7 ∘ 8  7

        8 ∘ 88 ∘8 ∘80∘8∘8  7∘ 7 ∘ 8  7   8  8  0 ∘ 8 ∘ 8  ; (Nkugkmûe 0)

Gpcmkgjls cg meùkkmûe jgtnjçtmkg pgrg lhtnenr Qm+7



Qrmjnrl suplenjls qun, sm ns vçcm`l pgrg Qm, tgjhmíe cl snrç pgrg Qm+7

+  8+  8+  0+ ∘ 8+ ∘ 8  ;

Xnstgjls Qm `n Qm+7

 + ∘   8+ ∘ 8  8+ ∘ 8  0+ ∘ 0 ∘ 8+  8 + ∘  8+ ∘  8+ ∘  0+ ∘ ∘8+ ∘  @nspnogjls Qm+7

+    8 + ∘ 8+ ∘ 0 + ∘ ∘8+ ∘ 

[ustmtumjls V m+7 m+7 plr cg nkugkmûe 7?

+    8  7 ∘ 8+ ∘ 0  77∘∘ ∘8+ ∘    +    +   8+   8 8887∘ 78 8++∘∘0   7 ∘  ∘8 ∘  0∘8+ ∘  

+    0  8 8+ ∘ ∘8+ ∘   0 +   8+ ∘   0 ∘8+ ∘   9

[ustmtumjls ] m+7 m+7 plr cg nkugkmûe 8, ne kg`g kgsl plr snpgrg`l.



l Kgsl 7. [m Qm31 netlekns ] mm+7 +7: ] m plr cl tgetl

 +    8 ∘ 0 ∘ 8 ∘    9

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 86

+    0  9 +    8 ∘ 7 ∘ 0 ∘ 8 ∘ 77∘∘   9  ∘ 8 ∘ 7 ∘   9 + + 8 ∘88 ∘877∘∘70 ∘   0 89 +    8 ∘∘88  7  0  6 ∘0  8  0  6       +   +    0∘0  71

(Nkugkmûe >)

l Kgsl 8. [m Qm 5: 1 netlekns ] m+7 m+7: ] m -7 plr cl tgetl

(Nkugkmûe 9)

Gflrg slcl rnstg `ntnrjmegr nc vgclr memkmgc `n Q, qun snrêg Q1. Els hgsgjls



ne cg nkugkmûe 0, pnrl kle suhêe`mkn knrl.

  8  8  0 ∘ 8 ∘ 8  ;

Nc prmjnr puetl sm cl klelknjls, kljl sn junstrg ne cg imdurg2

[ustmtumjls plr cls vgclrns memkmgcns `n V   yy ] …

 81  8  01 ∘ 8 ∘ 8  ;

(Nkugkmûe 4)  ;∘8  ∘8;

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 8=

Kle cgs nkugkmlens lhtnem`gs pl`njls dnenrgr ueg kmrkueinrnekmg ne ue pcgel `mskrntl. Qgrg cldrgrcl, sndumjls nc gcdlrmtjl `n Hrnsnefgj pgrg cg kmrkueinrnekmg qun sn `nskrmhn g kletmeugkmûe.

0.0 Qrlkn`mjmnetl @nskrmpkmûe) 0.0.7 Nqumpl enknsgrml Kljputg`lrg kle ue smstnjg lpnrgtmvl qun kunetn kle gjhmnetn drçimkl (Tme`lws, Cmeux, ntk…)

0.0.8 Jgtnrmgc `n Gplyl [@B `n ogvg. Netlrel `n `nsgrrlccl pgrg ogvg (M@N), plr nonjpcl, EntHnges. Cmhrnrêg swmed l ogvgIV.







0.0.; @nsgrrlccl `n cg Qrçktmkg Nonkutgjls cls pgsls geçcldls `n cg prçktmkg uel, `ns`n nc QG[L 7 fgstg nc QG[L 9, slcl kgjhmgjls nc eljhrn `nc prlynktl g GppKmrkueinrnekmgHrnsnefgj , cg ntmquntg `nc hltûe g @mhuog kmrkueinrnekmg y nc eljhrn `n cg iuekmûe qun kletne`rç nc gcdlrmtjl g kmrkueinrnekmgHrnsnefgj . Qgsl 7? @netrl `n cg iuekmûe kmrkueinrnekmgHrnsnefgj , mjpcnjnetn nc smdumnetn gcdlrmtjl? Xnkmhn cls pgrçjntrls klrrnsple`mnetns gc knetrl y rg`ml `n cg kmrkueinrnekmgHrnsnefgj(Vknetrl, ]knetrl, rg`ml) V:1 ]:rg`ml Q:;-8r Jmnetrgs V 3 ] QV : V + Q] : ] + Mcujmegr Mcujmegr Mcujmegr Mcujmegr Mcujmegr Mcujmegr Mcujmegr Mcujmegr

Vknetrl2 ]knetrl2 pmxnc ne pmxnc ne pmxnc ne pmxnc ne pmxnc ne pmxnc ne pmxnc ne pmxnc ne

kllr`neg`g kllr`neg`g kllr`neg`g kllr`neg`g kllr`neg`g kllr`neg`g kllr`neg`g kllr`neg`g

QV, Q] QV,-Q] -QV, Q] -QV, Q] Q], QV Q],-QV -Q], QV -Q], QV

[m Q31 Netlekns Q : Q+0V+9 Ne ltrl kgsl Q : Q+0V-0]+71 ] : ]-7 Ime `nc [m-Netlekns

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg ;1

V : V+7 Ime Jmnetrgs Ime `n Gcdlrmtjl (Hrnsnefgj)

Nonkutn nc prldrgjg y vnrmimqun qun sn trgzg ueg kmrkueinrnekmg. Qrldrgjn uegnjpcng`ls. iuekmûe qun `mhuon >111 kmrkueinrnekmgs gcngtlrmgs y jm`g nc tltgc `n jmcmsndue`ls

0.0.0 Xnplrtn Gc imegcmzgr ístg prçktmkg nc gcujel `nhnrç dnenrgr ue rnplrtn ne Q@I qun kletnedg ueg klrrm`g `n nskrmtlrml ne ueg flog `n kçckucl (plr nonjpcl, ne Nxknc) y `nspuís nc kû`mdl iunetn `n su iuekmûe qun mjpcnjnetl nc psnu`lkû`mdl `nc gcdlrmtjl `n cg kmrkueinrnekmg y gc ÿctmjl mekcumr mjçdnens `n cg nonkukmûe `n su prldrgjg. Kljpgrn nc tmnjpl rnqunrm`l pgrg `mhuogr >111 kmrkueinrnekmgs netrn cls jítl`ls `n kmrkueinrnekmg kljÿe y nc `n kmrkueinrnekmg `n Hrnsnefgj.

0.> Xnsuctg`ls y Klekcusmlens

Kle ístg prçktmkg, nc gcujel gprnkmgrç cg `minrnekmg ne nc `nsnjpn÷l `nc gcdlrmtjl qun slcl usg eÿjnrls netnrls (Hrnsnefgj) g ltrl qun rnqumnrn icltgetns y nc kçckucl `n rgêkns (kmrkueinrnekmg kljÿe).

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg ;7

Qrgktmkg >. Kmrkueinrnekmg Quetl Jn`ml >.7 Metrlùkkmûe

Cg prnsnetn prçktmkg gyu`g g gsmjmcgr cls kletnem`ls `n cg êm`g` M? Metrlùkkmûe g cg drgimkgkmûe plr kljputg`lrg `nc suhtnjg 7.;. Gspnktls jgtnjçtmkls `n cg drgimkgkmûe , `nc prldrgjg `n nstu`mls `n cg jgtnrmg `n Drgimkgkmûe , `nsgrrlccge`l cg kljpntnekmg nspnkêimkg? –Gpcmkg cls jl`ncls jgtnjçtmkls hçsmkls y cls jl`ncls `n klclr utmcmzg`ls ne lhontls hm`mjnesmlegcns y trm`mjnesmlegcns‚.

Nc prnsnetn gcdlrmtjl tmnen ueg ilrjg ue plkl jçs smjpcn `n `nùkmr cgs nkugkmlens usg`gs ne nc gcdlrmtjl `n cg kmrkueinrnekmg `n Hrnsnefgj, guequn ccndg nkugkmlens smjmcgrns.

>.8 Lhontmvl Kljpntnekmg)

Ncghlrgr ue prldrgjg qun trgkn ueg kmrkueinrnekmg usge`l nc Gcdlrmtjl `n cg Kmrkueinrnekmg `n Quetl Jn`ml.

>.; Iue`gjnetl

Qgrg gpcmkgr nc jítl`l `nc puetl jn`ml, `nimemjls ueg iuekmûe kmrkucgr kljl?

,,  1

,,     ∘ 

(Nkugkmûe 7)

Kugcqumnr puetl (x, y) ne cg irletnrg `nc kêrkucl `n rg`ml r sgtmsigrç cg nkugkmûe . [m nc puetl sn nekunetrg ne nc metnrmlr `nc kêrkucl, cg iuekmûe tljgrç ue vgclr endgtmvl, jmnetrgs qun, sm nc puetl sn nekunetrg iunrg `nc kêrkucl, nc vgclr `n cg iuekmûe snrç plsmtmvl.

Ne rnsujne, cg plsmkmûe rncgtmvg `n kugcqumnr puetl (x, y) pun`n `ntnrjmegrsn kljprlhge`l nc smdel `n cg iuekmûe dnenrg`lrg `nc kêrkucl? @npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg ;8

  31,    ,,      ê           ,,  1,51, ,,,,        ê

Cgs kljprlhgkmlens `n cg Nkugkmûe getnrmlr, sn rngcmzge pgrg cls puetls metnrjn`mls smtug`ls ne cg vnkme`g` `n cg trgynktlrmg kmrkucgr ne kg`g pgsl `n junstrnl. Gsê, cg iuekmûe dnenrg`lrg `nc kêrkucl ns ue pgrçjntrl `n `nkmsmûe ne nc gcdlrmtjl `nc puetl jn`ml, y pl`njls `ntnrjmegr cls kçckucls mekrnjnetgcns enknsgrmls enk nsgrmls pgrg nstg iuekmûe. Eunstrl pgrçjntrl `n `nkmsmûe snrç cg nkugkmûe 7 `n dnenrgkmûe `nc kêrkucl, kêrkucl, nvgcug`l ne nc puetl jn`ml netrn nstls `ls pêxncns?

 ( 7,  ∘ 78)    7   ∘ 78 ∘ 

y tljgjls cg smdumnetn `nùkkmûe? [m Qm ns endgtmvl netlekns ]  nstç nstç jçs knrkg ] m [m Qm ns plsmtmvl netlekns ]  nstç nstç jçs knrkg ] m -7 Gsê, cg gcturg `nc smdumnetn pmxnc ] m+7 m+7, sn nxprnsg kljl?

7  ≮ 1  +  {  ∘7  31  8

(Nkugkmûe 8)

Qgsls pgrg lhtnenr cgs iûrjucgs usg`gs ne nc gcdlrmtjl? Qgrtmjls `nc fnkfl qun klelknjls cls vgclrns `nc m-ísmjl pmxnc (V  , m, ]   ) m). ] qunrnjls klelknr nc smdumnetn pmxnc (V mm+7 +7 , ] mm+7 +7 ). Cls mekrnjnetls ne nc non V  sle sle uemtgrmls? 





+    7    7   ∘ 78 ∘ 7   ∘      8 7 7     ∘        0       8 ∘  ∘   

(Nkugkmûe ;)

Gflrg krngjls ue pgrçjntrl `n `nkmsmûe Q



(Nkugkmûe 0)

Gpcmkgjls cg meùkkmûe jgtnjçtmkg pgrg lhtnenr Qm+7



Qrmjnrl suplenjls qun, sm ns vçcm`l pgrg Qm, tgjhmíe cl snrç pgrg Qm+7 @npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg ;;

+  +  +  8+ ∘ + ∘   >0 ++ ∘   ++ ∘   ++ ∘   8++ ∘ 8 ∘ ++   + ∘   + ∘ + ∘   8 + ∘  ∘ + ∘    ∘   8   7 ∘  ∘ + ∘  +  + 7 ∘ 8  +  + ∘ ∘+ ∘   8  7 ∘    ++   8+7 ∘+ ∘8∘∘++∘ ∘ ; 8

Xnstgjls Qm `n Qm+7

@nspnogjls Qm+7 [ustmtumjls V m+7 m+7 plr cg nkugkmûe ;?

[ustmtumjls ] m+7 m+7 plr cg nkugkmûe 8, ne kg`g kgsl plr snpgrg`l.

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l Kgsl 7. [m Qm31 netlekns ] mm+7 +7: ] m plr cl tgetl

  (Nkugkmûe >)  +          +       8 ∘   ; ∘   ∘    ;   8       [m netlekns : plr cl tgetl ++  ∘87 ∘ 7 ∘ ∘8 ∘    ;  ∘ ∘ ∘ 77∘   8 ∘ 7 ∘    ;      +  + ∘87 ∘87∘ ∘  8 ∘  ∘ ∘7 7   ;      8  0 ∘87  ∘ 87   +    8 ∘ 88 > (Nkugkmûe 9)

l Kgsl 8.

Qm 5: 1

] m+7 m+7 ] m -7

Gflrg slcl rnstg `ntnrjmegr nc vgclr memkmgc `n Q, qun snrêg Q1. Els hgsgjls

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ne cg nkugkmûe 0, pnrl kle suhêe`mkn knrl.

  1   81∘∘ 8 ∘  ∘   >0 >0   >0    ∘∘   >0 ∘   ≆7∘

[ustmtumjls plr cls vgclrns memkmgcns `n V   yy ] qun sle rnspnktmvgjnetn (1, r).

Qnrl pgrg trghgogr kle netnrls, rn`le`ngjls >/0 qun`ge`l cg nkugkmûe?

(Nkugkmûe 4)

Gflrg, kle cgs nkugkmlens lhtnem`gs, sndumjls nc gcdlrmtjl `n cg kmrkueinrnekmg `n puetl jn`ml, qun sn `nskrmhn g kletmeugkmûe. @npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg ;0

>.0 Qrlkn`mjmnetl @nskrmpkmûe) >.0.7 Nqumpl enknsgrml Kljputg`lrg kle ue smstnjg lpnrgtmvl qun kunetn kle gjhmnetn drçimkl (Tme`lws, Cmeux, ntk…)

>.0.8 Jgtnrmgc `n Gplyl [@B `n ogvg. 

Netlrel `n `nsgrrlccl pgrg ogvg (M@N), plr nonjpcl, EntHnges. Cmhrnrêg swmed l ogvgIV.

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>.0.; @nsgrrlccl `n cg Qrçktmkg Nonkutgjls cls pgsls geçcldls `n cg prçktmkg uel, `ns`n nc QG[L 7 fgstg nc QG[L 9, slcl kgjhmgjls nc eljhrn `nc prlynktl g GppKmrkueinrnekmgQJ , cg ntmquntg `nc hltûe g @mhuog kmrkueinrnekmg y nc eljhrn `n cg iuekmûe qun kletne`rç nc gcdlrmtjl g kmrkueinrnekmgQJ . Qgsl 7? @netrl `n cg iuekmûe kmrkueinrnekmgQJ , mjpcnjnetn nc smdumnetn gcdlrmtjl? Xnkmhn cls pgrçjntrls klrrnsple`mnetns gc knetrl y rg`ml `n cg kmrkueinrnekmgQJ (Vknetrl, ]knetrl, rg`ml) V:1 ]:rg`ml Q:7-r Jmnetrgs V 3 ] QV : V + Q] : ] + Mcujmegr Mcujmegr Mcujmegr Mcujmegr Mcujmegr Mcujmegr Mcujmegr Mcujmegr

Vknetrl2 ]knetrl2 pmxnc ne pmxnc ne pmxnc ne pmxnc ne pmxnc ne pmxnc ne pmxnc ne pmxnc ne

kllr`neg`g kllr`neg`g kllr`neg`g kllr`neg`g kllr`neg`g kllr`neg`g kllr`neg`g kllr`neg`g

QV, Q] QV,-Q] -QV, Q] -QV, Q] Q], QV Q],-QV -Q], QV -Q], QV

[m Q31 Netlekns Q : Q+8V+; Ne ltrl kgsl Q : Q+8V-8]+> ] : ]-7 Ime `nc [m-Netlekns V : V+7 Ime Jmnetrgs Ime `n Gcdlrmtjl (Hrnsnefgj)

Nonkutn nc prldrgjg y vnrmimqun qun sn trgzg ueg kmrkueinrnekmg. @npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg ;>

Qrldrgjn ueg iuekmûe qun `mhuon >111 kmrkueinrnekmgs gcngtlrmgs y jm`g nc tltgc `n jmcmsndue`ls njpcng`ls.

>.0.0 Xnplrtn Gc imegcmzgr ístg prçktmkg nc gcujel `nhnrç dnenrgr ue rnplrtn ne Q@I qun kletnedg ueg klrrm`g `n `n nskrmtlrml ne ueg `n kçckuclnc(plr nonjpcl, ne `nc Nxknc) y `nspuís nc kû`mdl iunetn su iuekmûe qunflog mjpcnjnetl psnu`lkû`mdl gcdlrmtjl `n cg kmrkueinrnekmg y gc ÿctmjl mekcumr mjçdnens `n cg nonkukmûe `n su prldrgjg. Kljpgrn nc tmnjpl rnqunrm`l pgrg `mhuogr >111 kmrkueinrnekmgs netrn cls jítl`ls `n kmrkueinrnekmg kljÿe, nc `n kmrkueinrnekmg `n Hrnsnefgj y nc `n kmrkueinrnekmg `n puetl jn`ml.

>.> Xnsuctg`ls y Klekcusmlens

Kle ístg prçktmkg, nc gcujel kljprlhgrç qun nc jítl`l `n cg kmrkueinrnekmg `n Hrnsnefgj y nc `n puetl jn`ml sle prçktmkgjnetn mdugc `n nimkmnetns.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg ;9

Qrgktmkg 9. @mhuol `n cêengs y plcêdlels dlels ne K kle cg cmhrnrê cmhrnr êg TmeHDÊj 9.7 Metrlùkkmûe

Cg prnsnetn prçktmkg gyu`g g gsmjmcgr cls kletnem`ls `n cg êm`g` M? Metrlùkkmûe g cg drgimkgkmûe plr kljputg`lrg `nc suhtnjg 7.>. Xnprnsnetgkmûe y trgzl `n cêengs y plcêdlels, `nc prldrgjg `n nstu`mls `n cg jgtnrmg `n Drgimkgkmûe , `nsgrrlccge`l cg kljpntnekmg nspnkêimkg? –Gpcmkg cls jl`ncls jgtnjçtmkls hçsmkls y cls jl`ncls `n klclr utmcmzg`ls ne lhontls hm`mjnesmlegcns y trm`mjnesmlegcns‚. êl `n cls cnedugons `n prldrgjgkmûe jçs utmcmzg`ls f sm`l nc cnedugon K, plr cl qun ns mjplrtgetn `ljmegr cg prldrgjgkmûe `n drçimkls ne nstn cnedugon. Nxmstne vgrmls kljpmcg`lrns y `mvnrsgs cmhrnrêgs drçimkgs. Cgs cmhrnrêgs drçimkgs kletmnene iuekmlens

pgrg `mhuogr imdurgs kljuens kljl cl sle puetls, cêengs, kmrkueinrnekmgs y plcêdlels. G`njçs `n iuekmlens pgrg `nimemr y cmjpmgr vnetgegs, klclrns, rnccnels y ltrgs lpnrgkmlens jçs qun gyu`ge g krngr cls drçimkls y ninktls qun `nsnn nc prldrgjg`lr. êg `n cgs cmhrnrêgs jçs usg`gs iun cg qun tneêg nc kljpmcg`lr Hlrcge` K, klelkm`g kljl HDM (Hlrcge` Drgpfmk Metnrigkn). Gsê, cg TmeHDMj, ns ueg cmhrnrêg HDM pgrg Tme`lws.

9.8 Lhontmvl Kljpntnekmg)

Nskrmhmr ue prldrgjg qun usn cgs iuekmlens `n cg cmhrnrêg TmeHDMj pgrg nc trgzl `n cêengs y plcêdlels.

9.; Iue`gjnetl

Ne meilrjçtmkg, ueg cmhrnrêg ns ue kleouetl `n iuekmlens, kl`mimkg`gs ne ue cnedugon `n prldrgjgkmûe, qun lirnkn ueg metnrigz hmne `nimem`g pgrg cg iuekmlegcm`g` qun sn mevlkg. [u ime ns snr utmcmzg`g plr ltrls prldrgjgs R=Z.

Cgs iuekmlens gdrupg`gs ne ueg hmhcmltnkg, plr cl dnenrgc, gtmne`ne g ue tnjg kljÿe, plr nonjpcl, ueg cmhrnrêg jgtnjçtmkg kletne`rç iuekmlens pgrg kgckucgr rgêkns, snels, klsnels, cldgrmtjls, ntkítnrg, ueg cmhrnrêg krlelcûdmkg tne`rç iuekmlens pgrg lhtnenr flrg, inkfg, `êgs trgeskurrm`ls, ntk. Gsê ueg cmhrnrêg `n drçimkls, sn nspnrg qun kletnedg iuekmlens qun els gyu`ne g `nimemr klclrns, tmpls `n kletlrels, imdurgs, ntk… Nc turhl K plpucgrmzl ueg cmhrnrêg ccgjg`g HDM (HLXCLGE@ DXGQFMK[ @npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg ;4

MEPNXIGKN). Iun gjpcmgjnetn utmcmzg`g y guequn ns juy getmkug`g, ns juy içkmc gprne`nr g usgrcg. Guequn slcl iuekmleg ne J[@L[, sn fge fnkfl mjpcnjnetgkmlens qun pun`ne usgrsn ne Tme`lws, tgc ns nc kgsl `n cg cmhrnrêg TmeHDMj. TmeHDMj, ns ueg cmhrnrêg `n ncnjnetls drçimkls pgrg nc kljpmcg`lr JmedT (`n cnedugon k). Nstg cmhrnrêg njucg cg cmhrnrêg HDM `n Hlrcge`, pnrl fgkn qun pun`g usgrsn ne wme`lws. G`njçs, kunetg kle iuekmlegcm`g`ns nxtrg. Cg `nskrmpkmûe `n nstg cmhrnrêg nstç `msplemhcn ne? fttp?//www.ks.klclrg`l.nù/~jgme/ks7;11/`lk/hdm/hdm.ftjc

9.0 Qrlkn`mjmnetl @nskrmpkmûe) 9.0.7 Nqumpl enknsgrml Kljputg`lrg kle ue smstnjg lpnrgtmvl qun kunetn kle gjhmnetn drçimkl (Tme`lws, Cmeux, ntk…)

9.0.8 Jgtnrmgc `n Gplyl Kljpmcg`lr `n k jmedw. Netlrel `n `nsgrrlccl Kl`n??Hclkbs. Cmhrnrêg `n drçimkls TmeHDMj.

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9.0.; @nsgrrlccl `n cg Qrçktmkg @nskgrdgjls Nc netlrel `n prldrgjgkmûe Kl`nHclkbs y nc kljpmcg`lr jmedT `nc smdumnetn smtml? fttp?//www.kl`nhclkbs.lrd/`lweclg`s/89

Ne nstn kgsl snrêg nc grkfmvl kl`nhclkbs-74.78jmedw-sntup.nxn, nonkÿtncl y gpgrnkn cg smdumnetn vnetgeg?

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg ;6

Qrlsmdg cg mestgcgkmûe fgstg tnrjmegr. Gflrg `nskgrdgjls cg cmhrnrêg TmeHDMj `n? fttps?//sgedgjs.klj.ep/usn-drgpfmks-f-kl`nhclkbs-up`gtn`/

@nskgrdgjls nc grkfmvl TmeHDMj\Cmhrgry9\1\@nk8174.zmp, qun ns ue grkfmvl kljprmjm`l kletmnen cls grkfmvls? meil.txt kclkb.kpp JmeDTSmekcu`nSdrgpfmks.f JmeDTSmekcu`nSwmehdmj.f JmeDTScmhScmhhdm.g

Kleimdurgjls Kl`nHclkbs pgrg gdrndgr cg cmhrnrêg, kle cls smdumnetns pgsls? 7. Nxtrgnr `nc zmp cg kgrpntg JmeDT fgkmg cg kgrpntg `nc `mrnktlrml `n Kl`nHclkbs?

8. Ghrmjls nc prldrgjg Kl`nHclkbs y ghrmjls nc ilrjucgrml uhmkg`l ne –[nttmeds Kljpmcnr cmebnr snttmeds" `gjls kcmk ne nc hltûe G``

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg ;=

;. @gjls lb y nc ilrjucgrml qun`g kljl?

0. @g kcmk ne nc hltûe `n LB pgrg knrrgr nc ilrjucgrml. Gflrg Ne nc Jneÿ Imcn EnwQrlonkt, ncmon krngr –Kleslcn gppcmkgtmle‚

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 01

>. Ncmog nc cnedugon K++, cn `g ue eljhrn gc prlynktl prl ynktl gppImdurgs. [n dnenrg nc prlynktl. Ne cg kgrpntg slurkns nstç nc grkfmvl jgme.kpp, n`êtncl nskrmhmne`l nc kû`mdl? #mekcu`n 3mlstrngj5 #mekcu`n 3drgpfmks.f5 usmed egjnspgkn st`2 met jgme() { klut 33 "Ynetgeg `n tnxtl" 33 ne`c2 memtwme`lw( 011 , 011 , "Cmhrnrmg TmeHDMj",811,>1)2 putpmxnc(811,811,]NCCLT)2 cmen(71,81,;61,;=1)2 sntklclr(DXNNE)2 kmrkcn(811,811,711)2 wfmcn( !bhfmt() )2 kclsndrgpf( )2 rnture 12 }

9. Nonkÿtncl, `ge`l kcmk ne nc hltûe `n gcdl kljl?

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

–kljpmcgr y nonkutgr‚ y vnrnjls

Qçdmeg 07

4. Gflrg jl`mimqun nc kû`mdl pgrg prlhgr nc iuekmlegjmnetl `n ltrls lhontls drçimkls (Ne cg pçdmeg `n TmeHDMj nstç nc jgeugc kle cgs iuekmlens `n cg cmhrnrêg).

9.0.0 Xnplrtn Gc imegcmzgr ístg prçktmkg nc gcujel `nhnrç dnenrgr ue rnplrtn ne Q@I qun kletnedg ueg `nskrmpkmûe `n kg`g ueg `n cgs iuekmlens usg`gs

9.> Xnsuctg`ls y Klekcusmlens

Kle ístg prçktmkg, nc gcujel kljpgrgrç cg cmhrnrêg swmed `n ogvg y cg cmhrnrêg Tme HDMj `n K++, y pl`rç `nkm`mr hgol quí kmrkuestgekmgs `nhnrç usgr ueg u ltrg.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 08

Qrgktmkg 4. @mhuol `n cêengs y plcêdlels dlels ne Ogvg kle cg cmhrnrêg OLDC 4.7 Metrlùkkmûe

Cg prnsnetn prçktmkg gyu`g g gsmjmcgr cls kletnem`ls `n cg êm`g` M? Metrlùkkmûe g cg drgimkgkmûe plr kljputg`lrg `nc suhtnjg 7.>. Xnprnsnetgkmûe y trgzl `n cêengs y plcêdlels, `nc prldrgjg `n nstu`mls `n cg jgtnrmg `n Drgimkgkmûe , `nsgrrlccge`l cg kljpntnekmg nspnkêimkg? –Gpcmkg cls jl`ncls jgtnjçtmkls hçsmkls y cls jl`ncls `n klclr utmcmzg`ls ne lhontls hm`mjnesmlegcns y trm`mjnesmlegcns‚.

Ogvg LpneDC (OLDC) ns ueg hmhcmltnkg qun pnrjmtn gkkn`nr g LpneDC jn`mgetn prldrgjgkmûe ne Ogvg. OLDC pnrjmtn gkkn`nr g cg jgylrêg `n kgrgktnrêstmkgs `msplemhcns pgrg cls prldrgjg`lrns `n K, kle cg nxknpkmûe `n cgs ccgjg`gs g vnetgegs rngcmzg`gs ne DC^P (yg qun Ogvg kletmnen sus prlpmls smstnjgs `n vnetgegs, GTP y [wmed), y gcduegs nxtnesmlens `n LpneDC. R71Z

4.8 Lhontmvl Kljpntnekmg)

Nskrmhmr ue prldrgjg Ogvg qun usn cgs iuekmlens `n cg cmhrnrêg OLDC pgrg nc trgzl `n cêengs y plcêdlels, sndÿe cg imclsliêg `n LpneDC.

4.; Iue`gjnetl

LpneDC (Lpne Drgpfmks Cmhrgry) ns ueg nspnkmimkgkmûe nstçe`gr qun `nimen ueg GQM juctmcnedugon y juctmpcgtgilrjg pgrg nskrmhmr gpcmkgkmlens qun prlùzkge drçimkls 8@ y ;@. Cg metnrigz klesmstn ne jçs `n 8>1 iuekmlens `minrnetns qun pun`ne usgrsn pgrg `mhuogr nsknegs trm`mjnesmlegcns kljpcnogs g pgrtmr `n prmjmtmvgs dnljítrmkgs smjpcns, tgcns kljl puetls, cêengs y trmçeducls. Iun `nsgrrlccg`g lrmdmegcjnetn plr [mcmkle Drgpfmks Mek. ([DM) ne 7==8. R77Z

OLDC sn `minrnekmg `n ltrgs hmhcmltnkgs Ogvg pgrg LpneDC ne qun smjpcnjnetn nxplen cgs iuekmlens `n cg LpneDC, hgsg`gs ne ue cnedugon prlknùrgc (cnedugon K), plr jn`ml `n jítl`ls kletnem`ls ne uegs plkgs p lkgs kcgsns. R71Z

4.0 Qrlkn`mjmnetl @nskrmpkmûe) 4.0.7 Nqumpl enknsgrml Kljputg`lrg kle ue smstnjg lpnrgtmvl qun kunetn kle gjhmnetn drçimkl (Tme`lws, Cmeux, ntk…)

4.0.8 Jgtnrmgc `n Gplyl [@B `n ogvg. Netlrel `n `nsgrrlccl pgrg ogvg (M@N), plr nonjpcl, EntHnges. Cmhrnrêg OLDC.

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@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 0;

4.0.; @nsgrrlccl `n cg Qrçktmkg @ns`n nc plrtgc `n pcudmes `n EntHnges `nskgrdgjls cg cmhrnrêg EntHnges LpneDC Qgkb? fttp?//pcudmes.enthnges.lrd/QcudmeQlrtgc/igkns/[email protected].>.zmp. Nxtrgnjls nc grkfmvl ogvgx-jn ogvgx-jn`mg-lpnedc.eh `mg-lpnedc.ehj j. Memkmgjls EntHnges, pgrg `ns`n gfê mestgcgr cg cmhrnrêg qun gkghgjls `n `nskgrdgr y `nskljprmjmr. Ghrmjls nc ilrjucgrml uhmkg`l ne Pllcs Qcudmes

Ne cg pnstg÷g @lweclg`n` cn `gjls kcmk ne nc hltûe G`` Qcudmes. Huskgjls y sncnkkmlegjls cg cmhrnrêg ogvgx-j ogvgx-jn`mg-lpne n`mg-lpnedc.ehj dc.ehj.

Xnmemkmgjls EntHnges (Knrrgjls y vlcvnjls g ghrmr). Krngjls ue eunvl prlynktl

Imcn Enw Qrlonkt. smdumne`l cg rutg `n junstrg ue ilrjucgrml `le`n yg `nhne gpgrnknr pcgetmccg prlynktls hgsg`ls ne[nOLDC. [ncnkkmlegjls OLDC Gppcmkgtmle @npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 00

@nogjls nc eljhrn `nc Qrlynktl [mjpcnOLDC. Gvgezgjls y sm ccndg g gpgrnknr cg smdumnetn g`vnrtnekmg?

Cn `gjls ne nc hltûe Xnslcvn Qrlhcnjs… Cn me`mkgjls qun rnsuncvg kg`g prlhcnjg y cmstl. Ql`njls nonkutgr cg gpcmkgkmûe?

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 0>

Gflrg jl`mimqun nc kû`mdl pgrg prlhgr cgs prmjmtmvgs `n LpneDC, kljl sle kgjhmgr cls klclrns `n ile`l, `nc cçpmz, cêengs, plcêdlels, ntk…

4.0.0 Xnplrtn Gc imegcmzgr ístg prçktmkg nc gcujel `nhnrç dnenrgr ue rnplrtn ne Q@I qun kletnedg ueg `nskrmpkmûe `n kg`g ueg `n cgs iuekmlens usg`gs

4.> Xnsuctg`ls y Klekcusmlens

Kle ístg prçktmkg, nc gcujel kljpgrgrç cg cmhrnrêg swmed `n ogvg, cg cmhrnrêg Tme HDMj `n K++, y cg cmhrnrêg OLDC. [lhrn tl`l, `nhnrç rnicnxmlegr slhrn nc pgrg`mdjg qun prlplen LpneDC gc iuekmlegr kljl ueg jçqumeg `n nstg`ls.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 09

Qrgktmkg 6. Dugr`gr y rnkupnrgr ueg mjgdne pmxnc plr pmxnc 6.7 Metrlùkkmûe

Cg prnsnetn prçktmkg gyu`g g gsmjmcgr cls kletnem`ls `n cg êm`g` M? Metrlùkkmûe g cg drgimkgkmûe plr kljputg`lrg `nc suhtnjg 7.9. Ilrjgtls `n mjgdne, `nc prldrgjg `n nstu`mls `n cg jgtnrmg `n Drgimkgkmûe , `nsgrrlccge`l cg kljpntnekmg nspnkêimkg? –Gpcmkg cls jl`ncls jgtnjçtmkls hçsmkls y cls jl`ncls `n klclr utmcmzg`ls ne lhontls hm`mjnesmlegcns y trm`mjnesmlegcns‚ . êg mjgdne `mdmtgc l drçimkl `mdmtgc ns ueg rnprnsnetgkmûe hm`mjnesmlegc `n ueg mjgdne g pgrtmr `n ueg jgtrmz eujírmkg. Cgs mjçdnens `mdmtgcns sn pun`ne lhtnenr `n vgrmgs ilrjgs? Qlr jn`ml `n `msplsmtmvls `n netrg`g klevnrsmûe gegcûdmkg-`mdmtgc kljl cls nskçenrns y cgs cgs kçjgrgs kçjgrgs `mdmtgcns. `mdmtgcns. 



@mrnktgjnetn jn`mgetn prldrgjgs meilrjçtmkls n`mtlrns `n jgpgs `n hmts y

`mhuol vnktlrmgc, kljl vnktlrmgc, kljl plr nonjpcl rngcmzge`l `mhuols kle nc rgtûe nc rgtûe l tghcntg `mdmtgcmzg`lrg drçimkg mekcuyne`l nc cçpmz ûptmkl.

êg mjgdne ne jgpg `n hmts l mjgdne `n pêxncns, ns ueg nstrukturg ueg nstrukturg l grkfmvl `n `gtls qun rnprnsnetg ueg kug`rmkucg rnktgeducgr kug`rmkucg rnktgeducgr `n `n pêxncns pêxncns l puetls `n klclr, `neljmeg`g jgtrmz, qun sn pun`n vmsugcmzgr ne ue jlemtlr, jlemtlr, pgpnc u ltrl `msplsmtmvl `n rnprnsnetgkmûe. G cgs mjçdnens ne jgpg `n hmts sn cgs suncn `nimemr plr su gcturg y gekfurg ((ne ne pêxncns) y plr su prliue`m`g` su prliue`m`g` `n klclr (ne hmts plr pêxnc), qun `ntnrjmeg nc eÿjnrl `n klclrns `mstmetls qun sn pun`ne gcjgknegr ne kg`g puetl me`mvmùgc, y plr cl tgetl, ne drge jn`m`g, cg kgcm`g` `nc klclr `n cg mjgdne.

6.8 Lhontmvl Kljpntnekmg)

Klekmnetmzgr g cls gcujels qun sn rnqumnrn ueg drge kgetm`g` `n gcjgknegjmnetl pgrg gcjgknegr mjçdnens ne kljpgrgkmûe kle cls grkfmvls `n tnxtl. Ne cg prnsnetn prgktmkg sn kleilrjg `n `ls pgrtns? m. [n vnrçe cgs iuekmlens pgrg lhtnenr nc klclr `n ue pmxnc `g`g su plsmkmûe y dugr`gr `mkfg meilrjgkmûe ne ue grkfmvl. mm. [n vnrçe cgs iuekmlens pgrg pmetgr ue pmxnc `n gcdueg plsmkmûe ne nc klclr qun `nsnnjls. Cg meilrjgkmûe `n cg plsmkmûe y klclr cgs cnnrnjls `n ue grkfmvl `g`l.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 04

6.; Iue`gjnetl

Ne cg prnsnetn prçktmkg, prldrgjgrnjls ne K++ usge`l nc M@N Kl`nHclkbs kle cg cmhrnrêg TmeHDMj. Cgs cmhrnrêgs y iuekmlens g `nstgkgr qun usgrnjls sle? 3mlstrngj5



Ns ue qun kljplenetn `n cgpgrg hmhcmltnkg nstçe`gr`n([PC) `nc cnedugon[u`neljhrn prldrgjgkmûe K++ ns utmcmzg`l lpnrgkmlens netrg`g/sgcm`g. ns ue gkrûemjl `n Meput/Lutput [trngj. Nc icuol `n netrg`g y sgcm`g `n `gtls ne K++ (y su prn`nknslr K) el sn nekunetrg `nimem`g `netrl `n cg smetgxms hçsmkg y sn prlvnn plr jn`ml `n cmhrnrêgs `n iuekmlens iuekmlen s nspnkmgcmzg`gs kljl mlstrngj. 3drgpfmks.f5



[us iuekmlens pnrjmtne, netrn ltrgs klsgs, klsgs , nskrmhmr ne jl`l drçimkl ne cg pge pgetgccg tgccg puetl g puetl, l imdurgs imdurgs dnljítrmkgs, klpmgr y jl`mimkgr nc kletnem`l `n ue trlzl `n cg pgetgccg y jgenogr nc rgtûe. 3istrngj5



Qrlvnn igkmcm`g`ns pgrg cg netrg`g y sgcm`g hgsg`g ne grkfmvls. listrngj grkfmvl()



Ns ueg kcgsn pgrg jgenogr grkfmvls `n sgcm`g. grkfmvl.kclsn()



Kmnrrg nc grkfmvl gslkmg`l. grkfmvl.icusf()

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Xngcmzg cgs lpnrgkmlens `n nskrmturg pne`mnetns qun gÿe sn fge rngcmzg`l sûcl ne nc huiinr. grkfmvl.lpne()



[n usg pgrg ghrmr nc grkfmvl g cl cgrdl `n cg nonkukmûe `nc prldrgjg. kmrkcn() Nstg iuekmûe sn usg pgrg `mhuogr ue kêrkucl.



kclsndrgpf()



Nstg iuekmûe ns usg`g pgrg knrrgr nc smstnjg drçimkl kljl ns memkmg`g plr cg iuekmûe memtdrgpf. icllìmcc()



Nstg iuekmûe ns usg`g pgrg rnccnegr ue u e çrng knrrg`l kle nc klclr `n rnccnel y trgjg `n rnccnel gktugcns. 

dntjgxx()

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 06

Nstg iuekmûe ns usg`g pgrg lhtnenr cg kllr`neg`g jçxmjg `n cg pgetgccg ne cg `mrnkkmûe flrmzletgc. dntjgxy()



Nstg iuekmûe ns usg`g pgrg lhtnenr cg kllr`neg`g jçxmjg `n cg pgetgccg ne cg `mrnkkmûe vnrtmkgc. dntQmxnc() Nstg iuekmûe ns usg`g pgrg lhtnenr nc vgclr `nc klclr `nc pêxnc nspnkmimkg`l plr cls grdujnetls x n y.



memtwme`lw()



Nstg rutmeg fgy qun ccgjgrcg getns qun kugcqumnr ltrg `n nstg hmhcmltnkg, yg qun memkmgcmzg nc smstnjg drçimkl y krng ueg vnetgeg drçimkg `nc tgjg÷l nspnkmimkg`l ne cls pgrçjntrls. cmen()



Nstg iuekmûe ns usg`g pgrg klenktgr `ls puetls kle ueg cêeng rnktg. putpmxnc()



Nstg iuekmûe ns usg`g pgrg gsmdegr nc vgclr `nc klclr g ue pêxnc ne pgrtmkucgr.

rnktgedcn()



Nstg iuekmûe `mhuogrç ue rnktçeducl sme rnccnegr su metnrmlr usge`l nc klclr gktugc. sntklclr()



Nstg iuekmûe ns usg`g pgrg gsmdegr nc klclr gc vgclr `nc klclr nspnkmimkg`l plr nc grdujnetl klclr. sntimccstycn()



Nstg iuekmûe ns usg`g pgrg sncnkkmlegr ueg trgjg prn`nimem`g y ue klclr `n rnccnel.

6.0 Qrlkn`mjmnetl @nskrmpkmûe) 6.0.7 Nqumpl enknsgrml Kljputg`lrg kle ue smstnjg lpnrgtmvl qun kunetn kle gjhmnetn drçimkl (Tme`lws, Cmeux, ntk…)

6.0.8 Jgtnrmgc `n Gplyl Kljpmcg`lr `n k jmedw. Netlrel `n `nsgrrlccl Kl`n??Hclkbs. Cmhrnrêg `n drçimkls TmeHDMj.





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@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 0=

6.0.; @nsgrrlccl `n cg Qrçktmkg Nstg prçktmkg klestg `n `ls pgrtns, ne cg prmjnrg krngjls ueg nskneg y prlkn`njls g dugr`grcg ne ue grkfmvl y ne cg sndue`g pgrtn ghrmjls nc grkfmvl getnrmlr y prlkn`njls g `mhuogr cg mjgdne. Qgrtn M? Kl`nhclkbs , y sndumjls nc jneÿ Imcn Enw Qrlonkt, Ne nc ilrjucgrml Memkmgjls ncmon nc mklel kle cg cnyne`g Kleslcn gppcmkgtmle. [ncnkkmlens nc cnedugon K++, `nc têtucl `n prlynktl kljl Dugr`grMjgdne , Ncmog cg kgrpntg `le`n gcjgknegrg nc prlynktl y `n kcmk ne nc hltûe Enxt5 cundl ne Imemsf. Krnn ueg nskneg kugcqumnrg, `mhuoge`l `minrnetns imdurgs kle `mvnrsls klclrns, plr nonjpcl? #mekcu`n 3mlstrngj5 #mekcu`n 3drgpfmks.f5 #mekcu`n 3istrngj5 usmed egjnspgkn st`2 met jgme() { memtwme`lw(011 ,011 ,"Qrçktmkg Dugr`gr Mjgdne", 811, >1)2 // Krngr nskneg // [lc sntklclr(]NCCLT)2 kmrkcn(;11,711,01)2 sntimccstycn(7,]NCCLT)2 icllìmcc(;11,711,]NCCLT)2 // Kgsg sntklclr(HC^N)2 cmen(9>, cmen(7=>,88>, 78>,7=>, ;81,78>)2 88>)2 rnktgedcn(78;, 761, 890, 861)2 // Qunrtg sntklclr(XN@)2 rnktgedcn(761, 8;1, 87>, 861)2 sntimccstycn(7,XN@)2 icllìmcc(811,8>1,XN@)2 wfmcn( !bhfmt() )2 kclsndrgpf()2 dugr`grMjgdne((kfgr *)"kgsmtg.mjd")2 rnture 12 }

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg >1

Gflrg krngjls iuekmûe dugr`grMjgdne() , y cg mevlkgrnjls getns `n tnrjmegr nc prldrgjg prmekmpgc. vlm` dugr`grMjgdne(kfgr * eljhrnGrkfmvl) { listrngj grkfmvl2 met m,o,tgjV,tgj]2 tgjV:dntjgxx()2 tgj]:dntjgxy()2 grkfmvl.lpne(eljhrnGrkfmvl)2 // Enknsmtgjls dugr`gr meilrjgkmûe `nc tgjg÷l // `n cg mjgdne (kghnknrg) grkfmvl 33tgjV33" "33tgj]33'Se'2 ilr(m:12m3tgjV2m++) ilr(o:12o3tgj]2o++) { grkfmvl 33 dntpmxnc(m,o)33" "2 } grkfmvl.icusf()2 grkfmvl.kclsn()2 }

Qgrtn MM? Memkmgjls Kl`nhclkbs , y sndumjls nc jneÿ Imcn Enw Qrlonkt, Ne nc ilrjucgrml ncmon nc mklel kle cg cnyne`g Kleslcn gppcmkgtmle. [ncnkkmlens nc cnedugon K++, `nc têtucl `n prlynktl kljl CnnrMjgdne , Ncmog cg kgrpntg `le`n gcjgknegrg nc prlynktl y `n kcmk ne nc hltûe Enxt5 cundl ne Imemsf. Gflrg nskrmhmjls nc smdumnetn kû`mdl qun mekcuyn cg iuekmûe cnnrMjgdne() , y cg mevlkgrnjls `nspÿns `n memtwme`lw . #mekcu`n 3mlstrngj5 #mekcu`n 3drgpfmks.f5 #mekcu`n 3istrngj5 usmed egjnspgkn st`2 vlm` cnnrMjgdne(kfgr * eljhrnGrkfmvl) { mistrngj grkfmvl2 met m,o,tgjV,tgj]2 met klclr2 grkfmvl.lpne(eljhrnGrkfmvl)2 // Enknsmtgjls rnkupnrgr meilrjgkmûe `nc tgjg÷l // `n cg mjgdne (kghnknrg) grkfmvl 55tgjV 55tgj]2 klut33"Pgjg÷l ne V? "33tgjV33", tgjg÷l ne ]? "33tgj]2 ilr(m:12m3tgjV2m++) ilr(o:12o3tgj]2o++) { grkfmvl 55 klclr2 klut 33 klclr33" "2

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg >7

putpmxnc(m,o,klclr)2 } grkfmvl.kclsn()2 } met jgme() { memtwme`lw(011 ,011 ,"Qrçktmkg Cnnr Mjgdne", 811, >1)2 cnnrMjgdne((kfgr *)"kgsmtg.mjd")2 wfmcn( !bhfmt() )2 kclsndrgpf( )2 rnture 12 }

Getns `n nonkutgr nc prldrgjg, klpmn nc grkfmvl drçimkl kgsmtg.mjd gc `mrnktlrml `nc prlynktl?

6.0.0 Xnplrtn Gc imegcmzgr ístg prçktmkg nc gcujel `nhnrç dnenrgr ue rnplrtn ne Q@I qun els `mdg kljl kgckucgr nc tgjg÷l nspnrg`l `nc grkfmvl qun kletmnen nc drçimkl. @nhn mekcumr kû`mdl iunetn y pgetgccgs `n cg nonkukmûe `n cls prldrgjgs. Pgjhmíe `nhn rngcmzgr ueg mevnstmdgkmûe slhrn cls ilrjgtls drçimkls `n jgpg `n hmts.

6.> Xnsuctg`ls y Klekcusmlens

Kle ístg prçktmkg, nc gcujel tljgrç klekmnekmg `nc tgjg÷l tge drge`n qun lkupg ueg mjgdne y `n cg enknsm`g` `n kljprmjmr `n gcdueg jgenrg cg meilrjgkmûe.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg >8

Qrgktmkg =. Dugr`gr y rnkupnrgr ueg mjgdne plr cg `nskrmpkml `nskrmpkml e `n sus kljplenetns =.7 Metrlùkkmûe

Cg prnsnetn prçktmkg gyu`g g gsmjmcgr cls kletnem`ls `n cg êm`g` M? Metrlùkkmûe g cg drgimkgkmûe plr kljputg`lrg `nc suhtnjg 7.9. Ilrjgtls `n mjgdne, `nc prldrgjg `n nstu`mls `n cg jgtnrmg `n Drgimkgkmûe , `nsgrrlccge`l cg kljpntnekmg nspnkêimkg? –Gpcmkg cls jl`ncls jgtnjçtmkls hçsmkls y cls jl`ncls `n klclr utmcmzg`ls ne lhontls hm`mjnesmlegcns y trm`mjnesmlegcns‚ . Ne cg prçktmkg getnrmlr kljprlhgjls qun ueg mjgdne qun sn dugr`g pmxnc plr pmxnc, lkupg jukfl nspgkml. Ltrg gctnregtmvg ns dugr`gr cg `nskrmpkmûe `n cgs imdurgs, nstn tmpl `n mjçdnens sn cns klelkn kljl drçimkls vnktlrmgcns. Cls drçimkls ne jgpg `n hmts sn `mstmedune `n cls cls drçimkls vnktlrmgcns ne qun nstls ÿctmjls rnprnsnetge ueg mjgdne g trgvís `nc usl `n lhontls kljl kurvgs lhontls dnljítrmkls dnljítrmkls kljl kurvgs `n Hízmnr y plcêdlels, el `nc smjpcn gcjgknegjmnetl `nc klclr `n kg`g puetl ne cg jgtrmz.

=.8 Lhontmvl Kljpntnekmg)

Gcjgknegr mjçdnens g pgrtmr `n cgs imdurgs dnljítrmkgs qun cg kljplene. Ne cg prnsnetn prgktmkg sn kleilrjg `n `ls pgrtns? m. [n pcgetng ueg nstrgtndmg pgrg `nskrmhmr y dugr`gr cgs imdurgs qun kleilrjge ueg mjgdne. mm.

[n rnklestruyn ueg mjgdne g pgrtmr `n cgs `nskrmpkmlens lhtnem`gs ne ue grkfmvl.

=.; Iue`gjnetl

êg mjgdne vnktlrmgc ns ueg mjgdne `mdmtgc ilrjg`g plr lhontls dnljítrmkls `npne`mnetns (sndjnetls, plcêdlels, grkls, jurls, ntk.), kg`g uel `n nccls `nimem`l plr gtrmhutls jgtnjçtmkls jgtnjçtmkls `n ilrjg, `n plsmkmûe, ntk. Qlr nnonjpcl, onjpcl, ue kêrkucl kêrkucl `n klclr rlol qun`grêg `nimem`l plr cg plsmkmûe `n su knetrl, su rg`ml, nc drlslr `n cêeng y su klclr. Nc metnrís prmekmpgc `n cls drçimkls vnktlrmgcns ns pl`nr gjpcmgr nc tgjg÷l `n ueg mjgdne g vlcuetg` sme suirmr cg pír`m`g `n kgcm`g` qun suirne cls jgpgs `n hmts. @n cg jmsjg ilrjg, pnrjmtne jlvnr, nstmrgr y rntlrknr mjçdnens `n jgenrg rncgtmvgjnetn snekmccg.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg >;

[n prlplen cg smdumnetn nstrukturg? Kljge`l

Iuekmûe

M`

@7

@8

Ynetgeg Klclr cçpmz

memtwme`lw sntklclr

1 7

gekfl Klclr : 1 g 7>

gctl

Pmpl rnccnel rnccnegr kmrkucl cêeng rnktçeducl

sntimccstycn icllìmcc kmrkcn cmen rnktgedcn

8; 0 > 9

Hlr`n 7> Klclr :: 11 gg 7> Kx V7 V7

V Ky ]7 ]7

@;

@0

] rg`ml V8 V8

]8 ]8

=.0 Qrlkn`mjmnetl @nskrmpkmûe) =.0.7 Nqumpl enknsgrml Kljputg`lrg kle ue smstnjg lpnrgtmvl qun kunetn kle gjhmnetn drçimkl (Tme`lws, Cmeux, ntk…)

=.0.8 Jgtnrmgc `n Gplyl 

Kljpmcg`lr `n k jmedw. Netlrel `n `nsgrrlccl Kl`n??Hclkbs. Cmhrnrêg `n drçimkls TmeHDMj.





=.0.; @nsgrrlccl `n cg Qrçktmkg Nstg prçktmkg klestg `n `ls pgrtns, ne cg prmjnrg krngjls ueg nskneg y prlkn`njls g dugr`grcg ne ue grkfmvl y ne cg sndue`g pgrtn ghrmjls nc grkfmvl getnrmlr y prlkn`njls g `mhuogr cg mjgdne. Qgrtn M? Memkmgjls Kl`nhclkbs , y sndumjls nc jneÿ Imcn Enw Qrlonkt, Ne nc ilrjucgrml ncmon nc mklel kle cg cnyne`g Kleslcn gppcmkgtmle. [ncnkkmlens nc cnedugon K++, `nc têtucl `n prlynktl kljl Dugr`grMjgdneYnktlrmgc , Ncmog cg kgrpntg `le`n gcjgknegrg nc prlynktl y `n kcmk ne nc hltûe Enxt5 cundl ne Imemsf. Krnn ueg nskneg kugcqumnrg, nspnkmimkge`l `minrnetns kljge`ls pgrg `nspuís dugr`grcls ne nc grkfmvl kgsmtg.vnk, nc kû`mdl pun`n snr nc smdumnetn? #mekcu`n 3mlstrngj5 #mekcu`n 3istrngj5 usmed egjnspgkn st`2 strukt kljge`l { m`2 met @72 met @82

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg >0

met @;2 met @02 } imdR7;Z2 vlm` dugr`grMjgdneYnktlrmgc(kfgr * eljhrnGrkfmvl) { listrngj grkfmvl2 met m2 grkfmvl.lpne(eljhrnGrkfmvl)2 // Dugr`gr cg kgetm`g` `n imdurgs (kghnknrg) // y lhontls grkfmvl337;33'Se'2 ilr(m:12 m3782 m++) { grkfmvl33imdRmZ.m`33" "33imdRmZ.@733" "2 grkfmvl33imdRmZ.@833" "33imdRmZ.@;33" "2 grkfmvl33imdRmZ.@033'Se'2 } grkfmvl.icusf()2 grkfmvl.kclsn()2 } met jgme() { klut33"Qrgktmkg Dugr`gr Mjgdne Ynktlrmgc SeSe"2 //@nimemr tgjg÷l `n vnetgeg imdR1Z.m`:12 imdR1Z.@7:0112 imdR1Z.@8:0112 //memtwme`lw(011 ,011 ,"Pmtucl", 811, >1)2 // Krngr nskneg // [lc klut33"Kljge`l pgrg klclkgr nc klclr `n cçpmz g gjgrmccl Se"2 imdR7Z.m`:72 imdR7Z.@7:702 //sntklclr(]NCCLT)2 klut33"Kljge`l pgrg `mhuogr kmrkucl Se"2 imdR8Z.m`:02 imdR8Z.@7:;112 imdR8Z.@8:7112 imdR8Z.@;:012 //kmrkcn(;11,711,01)2 klut33"Kljge`l pgrg `nimemr nc klclr `nc kletlrel g rnccnegr Se"2 imdR;Z.m`:82 imdR;Z.@7:702 //sntimccstycn(7,]NCCLT)2 klut33"Kljge`l pgrg rnccnegr ueg imdurg knrrg`g Se"2 imdR0Z.m`:;2 imdR0Z.@7:702 imdR0Z.@8:;112 imdR0Z.@;:7112 //icllìmcc(;11,711,]NCCL //icllìmcc(;11,711,]NCCLT)2 T)2 // Kgsg klut33"Kljge`l pgrg `nimemr nc klclr `nc cgpmz Se"2 imdR>Z.m`:72 imdR>Z.@7:=2 //sntklclr(HC^N)2 klut33"Kljge`l pgrg `mhuogr ueg cmeng Se"2 imdR9Z.m`:>2 imdR9Z.@7:9>2 imdR9Z.@8:88>2

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg >>

imdR9Z.@;:7=>2 imdR9Z.@0:78>2 //cmen(9>, 88>, 7=>, 78>)2 klut33"Kljge`l pgrg `mhuogr ueg cmeng Se"2 imdR4Z.m`:>2 imdR4Z.@7:7=>2 imdR4Z.@8:78>2 imdR4Z.@;:;812 imdR4Z.@0:88>2 //cmen(7=>, 78>, ;81, 88>)2 klut33"Kljge`l pgrg `mhuogr ue rnktgeducl Se"2 imdR6Z.m`:92 imdR6Z.@7:78;2 imdR6Z.@8:7612 imdR6Z.@;:8902 imdR6Z.@0:8612 //rnktgedcn(78;, 761, 890, 861)2 // Qunrtg klut33"Kljge`l pgrg `nimemr nc klclr `nc cgpmz Se"2 imdR=Z.m`:72 imdR=Z.@7:782 //sntklclr(XN@)2 klut33"Kljge`l pgrg `mhuogr ue rnktgeducl Se"2 imdR71Z.m`:92 imdR71Z.@7:7612 imdR71Z.@8:8;12 imdR71Z.@;:87>2 imdR71Z.@0:8612 //rnktgedcn(761, 8;1, 87>, 861)2 klut33"Kljge`l pgrg `nimemr nc klclr `nc kletlrel g rnccnegr Se"2 imdR77Z.m`:82 imdR77Z.@7:782 //sntimccstycn(7,XN@)2 klut33"Kljge`l pgrg rnccnegr ueg imdurg knrrg`g Se"2 imdR78Z.m`:;2 imdR78Z.@7:782 imdR78Z.@8:8112 imdR78Z.@;:8>12 //icllìmcc(811,8>1,XN@)2 dugr`grMjgdneYnktlrmgc((kfgr *)"kgsmtg.vnk")2 dugr`grMjgdneYnktlrmgc((kfgr klut33 "Lhontls dugr`g`ls!"2 rnture 12 }

Qgrtn MM? Memkmgjls Kl`nhclkbs , y sndumjls nc jneÿ Imcn Enw Qrlonkt, Ne nc ilrjucgrml ncmon nc mklel kle cg cnyne`g Kleslcn gppcmkgtmle. [ncnkkmlens nc cnedugon K++, `nc têtucl `n prlynktl kljl CnnrMjgdneYnktlrmgc , Ncmog cg kgrpntg `le`n gcjgknegrg nc prlynktl y `n kcmk ne nc hltûe Enxt5 cundl ne Imemsf. Gflrg nskrmhmjls nc smdumnetn kû`mdl qun mekcuyn cg iuekmûe cnnrMjgdneYnktlrmgc() , y cg mevlkgrnjls `nspÿns `n memtwme`lw . #mekcu`n 3mlstrngj5 #mekcu`n 3drgpfmks.f5

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg >9

#mekcu`n 3istrngj5 usmed egjnspgkn st`2 strukt kljge`l { met m`2 met @82 @72 met met @;2 met @02 } imd2 vlm` cnnrMjgdneYnktlrmgc(kfgr * eljhrnGrkfmvl) { mistrngj grkfmvl2 met m, tltgcLhontls2 grkfmvl.lpne(eljhrnGrkfmvl)2 // Enknsmtgjls rnkupnrgr meilrjgkmûe `nc tgjg÷l // `n cg mjgdne (kghnknrg) grkfmvl 55tltgcLhontls2 klut33"lhontls? "33tltgcLhontls33"Se"2 ilr(m:12 m3tltgcLhontls2 m++) { grkfmvl55imd.m`55imd.@755imd.@855imd.@;55imd.@02 klut33imd.m`33"-"33imd.@733" "33imd.@833" "33imd.@;33" "33imd.@033"Se"2 `ncgy(7111)2 // [ng fgkn ueg pgusg netrn kg`g imdurg swmtkf(imd.m`) { kgsn 1? memtwme`lw(imd.@7, imd.@8,"Qrgktmkg Cnnr Mjgdne Ynktlrmgc", 811, >1)2 hrngb2 kgsn 7? sntklclr(imd.@7)2 hrngb2 kgsn 8? sntimccstycn(7, imd.@7)2 hrngb2 kgsn ;? icllìmcc(imd.@8, imd.@;, imd.@7)2 hrngb2 kgsn 0? kmrkcn(imd.@7, imd.@8, imd.@;)2 hrngb2 kgsn >? cmen(imd.@7, imd.@8, imd.@;, imd.@0)2 hrngb2 kgsn 9? rnktgedcn(imd.@7, imd.@8, imd.@;, imd.@0)2 hrngb2 } } grkfmvl.kclsn()2 } met jgme() {

cnnrMjgdneYnktlrmgc((kfgr *)"kgsmtg.vnk")2 wfmcn( !bhfmt() )2

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg >4

kclsndrgpf( )2 rnture 12 }

Xntl.

Gflrg nxpge`g nc prldrgjg getnrmlr pgrg ghgrkgr gc jnels 0 imdurgs y/l kljge`ls jçs.

=.0.0 Xnplrtn Gc imegcmzgr ístg prçktmkg nc gcujel `nhnrç dnenrgr ue rnplrtn ne Q@I `le`n junstrn nc prldrgjg `le`n mjpcnjnetl jçs imdurgs y. g`njçs pgetgccgs `n su nonkukmûe. Pgjhmíe `nhn rngcmzgr ueg mevnstmdgkmûe slhrn cls ilrjgtls drçimkls vnktlrmgcns.

=.> Xnsuctg`ls y Klekcusmlens

Kljpgrn nc tgjg÷l `n nstn grkfmvl kgsmtg.vnk kle nc getnrmlr kgsmtg.mjd y nskrmhg sus klekcusmlens.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg >6

Qrgktmkg 71. Xnprnsnetgkmle `n ueg imdurg 8@ g pgrtmr `n sus vnrtmkns ne cnedugon k 71.7 Metrlùkkmûe

Cg prnsnetn prçktmkg gyu`g g gsmjmcgr cls kletnem`ls `n cg êm`g` MM? Drgimkgkmûe 8@ `nc suhtnjg 8.7. Prgesilrjgkmûe Prgesilrjgkmûe hm`mjnesmlegc, `nc prldrgjg `n nstu`mls `n cg jgtnrmg `n Drgimkgkmûe , `nsgrrlccge`l cg kljpntnekmg nspnkêimkg? –@nsgrrlccg y

gpcmkg jl`ncls `n drgimkgkmûe y trgesilrjgkmûe hm`mjnesmlegc pgrg nc nermqunkmjmnetl vmsugc `n sus gpcmkgkmlens‚.

Qgrg dnenrgr ueg mjgdne enknsmtgjls prlplrkmlegr cgs `nskrmpkmlens dnljítrmkgs `n cls lhontls qun sn fge `n jlstrgr. Nstgs `nskrmpkmlens `ntnrjmege cgs plsmkmlens y cgs ilrjgs `n cls lhontls. Qlr nonjpcl, ueg kgog sn nspnkmimkg jn`mgetn cgs plsmkmlens `n sus nsqumegs (vírtmkns), y ueg nsinrg sn `nimen kle cg plsmkmûe `n su knetrl y su rg`ml. Kle plkgs nxknpkmlens, sn rnqumnrn qun cgs `nskrmpkmlens dnljítrmkgs d nljítrmkgs sn nspnkmimqune ne ue smstnjg `n rninrnekmg `n kllr`neg`gs kgrtnsmgegs nstçe`gr (Gpíe`mkn G).

71.8 Lhontmvl Kljpntnekmg)

@nimemr ueg imdurg g pgrtmr `n sus vírtmkns, ilrjgr ueg jgtrmz kle nstls vírtmkns y nskrmhmr ue prldrgjg qun pun`g uemr cls vírtmkns kle cêengs.

71.; Iue`gjnetl

Nc smstnjg `n rninrnekmg qun usgrnjls ns nc qun jgenog nc smstnjg `n drçimkls `n TmeHDMj, ne nc kugc nc lrmdne `n cg vnetgeg drçimkg nstç ne cg nsqumeg supnrmlr mzqumnr`g, cgs V krnkne g cg `nrnkfg y cgs ] krnkne fgkmg ghgol.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg >=

Kljl els neilkgrnjls slcl ne imdurgs ne `ls `mjnesmlens (imdurgs 8@), kg`g vírtmkn sn rnprnsnetg plr `ls vgclrns, nc `nspcgzgjmnetl flrmzletgc y vnrtmkgc (V, ]) rnspnktl gc lrmdne. Ilrjgrnjls ueg jgtrmz `n lr`ne 8xE, E ns cg kgetm`g` `n vírtmkns, gsê kg`g klcujeg klrrnsple`n V ytgetls g ] rnspnktmvgjnetn kg`g rnedcûe rne dcûe klrrnsple`n g ue vírtmkn, plr cl qun tne`rnjls rnedclens kljl yvírtmkns. Qlr nonjpcl?

      R Z 88 4; 7866 7;>=4

Jgtrmz dneírmkg pgrg ueg imdurg `n 4 vírtmkns

Jgtrmz `n cg prnsnetn imdurg `n 4 vírtmkns

71.0 Qrlkn`mjmnetl @nskrmpkmûe) 71.0.7 Nqumpl Nqumpl enknsgrml

Kljputg`lrg kle ue smstnjg lpnrgtmvl qun kunetn kle gjhmnetn drçimkl (Tme`lws, Cmeux, ntk…)

71.0.8 Jgtnrmgc Jgtnrmgc `n Gplyl Kljpmcg`lr `n k jmedw.





   Netlrel Kl`n??Hclkbs. Cmhrnrêg `n `n `nsgrrlccl drçimkls TmeHDMj. êg flog `n kug`rmkucg u flog jmcmjntrg`g





71.0.; @nsgrrlccl @nsgrrlccl `n cg Qrçktmkg [ncnkkmlen ueg mjgdne qun pun`n `nimemrsn g pgrtmr `n sus vírtmkns y qun cg kgetm`g` `n vírtmkns sng netrn 81 y 01. @mhuogjls cg imdurg ne cg flog y lhtnenjls cgs kllr`neg`gs `n cls vírtmkns ne hgsn gc smstnjg `n rninrnekmg jnekmleg`l gc memkml, tljge`l kljl lrmdne cg nsqumeg supnrmlr mzqumnr`g `n cg flog. Nonjpcl `n imdurgs?

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 91

Memkmgjls Kl`nhclkbs , y sndumjls nc jneÿ Imcn Enw Qrlonkt, Ne nc ilrjucgrml ncmon nc mklel kle cg cnyne`g Kleslcn gppcmkgtmle. [ncnkkmlens nc cnedugon K++, `nc têtucl `n prlynktl kljl @mhuogrMjgdne8@ , Ncmog cg kgrpntg `le`n gcjgknegrg nc prlynktl prl ynktl y `n kcmk ne nc hltûe Enxt5 cundl ne Imemsf. Nskrmhmjls nc smdumnetn kû`mdl qun mekcuyn cg iuekmûe `mhuogr(), @mkfg iuekmûe `nhn rnkmhmr cg jgtrmz kle cls vírtmkns y nc tltgc `n vírtmkns. Ne cg iuekmûe prmekmpgc `nimemjls cg jgtrmz n mevlkgjls g cg iuekmûe `mhuog(). Ne nc prnsnetn nonjpcl, `mhuogrnjls cg imdurg `n 4 vírtmkns `n cg kugc yg tnenjls `nimem`ls cls vírtmkns, pnrl pgrg cldrgr ueg jnolr vmsugcmzgkmûe, kg`g kllr`neg`g sn nskgcgrç ne ue igktlr `n 71. G kletmeugkmûe, sn junstrg nc kû`mdl `n nonjpcl? #mekcu`n 3mlstrngj5 #mekcu`n 3drgpfmks.f5 usmed egjnspgkn st`2 vlm` `mhuogr(met imdRZR8Z, met tltgcYnrtmkns) { met m2 ilr(m:12 m3tltgcYnrtmkns-72 m++) cmen(imdRmZR1Z, imdRmZR7Z, imdRm+7ZR1Z, imdRm+7ZR7Z)2 cmen(imdR1ZR1Z, imdR1ZR7Z, imdRmZR1Z, imdRmZR7Z)2

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 97

} met jgme() { met icnkfgR4ZR8Z: { {81, 41}, {81, ;1}, {61, ;1}, {61, 71}, {781, >1}, {61, =1}, {61, 41} }2 memtwme`lw(701,711,"Qrçktmkg @mhuogr Mjgdne 8@", 811, >1)2 `mhuogr(icnkfg,4)2 wfmcn( !bhfmt() )2 kclsndrgpf( )2 rnture 12 }

Nc rnsuctg`l `nc prldrgjg getnrmlr ns cg smdumnetn vnetgeg?

Xntl.

Jl`mimqun cg iuekmûe `mhuog() pgrg qun pun`g `mhuogr imdurgs kle rnccnel (klclr sûcm`l). Gsê cg iuekmûe `nhn rnkmhmr ue pgrçjntrl qun me`mqun sm cg imdurg ccnvg l el rnccnel.

71.0.0 Xnplrtn Xnplrtn Gc imegcmzgr ístg prçktmkg nc gcujel `nhnrç dnenrgr ue rnplrtn ne Q@I qun kletnedg cg imdurg ne pgpnc jmcmjntrg`l kle sus rnspnktmvls vírtmkns, nc kû`mdl y cgs pgetgccgs `nc prldrgjg qun mjpcnjnetû.

71.> Xnsuctg`ls y Klekcusmlens

[n tljg klekmnekmg qun sn pun`ne rnprnsnetgr kugcqumnr imdurg nspnkmimkge`l sus vírtmkns, mekcusl kurvgs, qun tne`rçe jnolr `nimemkmûe gujnetge`l cg kgetm`g` `n vírtmkns.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 98

Qrgktmkg 77. Prgscgkmle, nskgcg, rltgkmle y snsdg`l `n ueg imdurg ne cnedugon k 77.7 Metrlùkkmûe

Cg prnsnetn prçktmkg gyu`g g gsmjmcgr cls kletnem`ls `n cg êm`g` MM? Drgimkgkmûe 8@ `nc suhtnjg 8.7. Prgesilrjgkmûe hm`mjnesmlegc, `nc prldrgjg `n nstu`mls `n cg jgtnrmg `n Drgimkgkmûe , `nsgrrlccge`l cg kljpntnekmg nspnkêimkg? –@nsgrrlccg y

gpcmkg jl`ncls `n drgimkgkmûe y trgesilrjgkmûe hm`mjnesmlegc pgrg nc nermqunkmjmnetl vmsugc `n sus gpcmkgkmlens‚.

Cgs lpnrgkmlens qun sn gpcmkge g `nskrmpkmlens dnljítrmkgs `n ue lhontl pgrg kgjhmgr su plsmkmûe, lrmnetgkmûe l tgjg÷l sn ccgjge trgesilrjgkmlens dnljítrmkgs. Cgs iuekmlens `n trgesilrjgkmlens dnljítrmkgs qun sn pun`ne nekletrgr ne tl`ls cls pgquntns drçimkls, sle gqunccgs qun sn usge pgrg cg trgscgkmûe, cg rltgkmûe y nc kgjhml `n nskgcg. R;Z Ne cg prnsnetn prçktmkg gpcmkgrnjls cls kleknptls y lpnrgkmlens jgtrmkmgcns pgrg mjpcnjnetgr cgs trgsilrjgkmlens dnljítrmkgs.

77.8 Lhontmvl Kljpntnekmg)

@nskrmhmr ueg imdurg g pgrtmr `n sus vírtmkns (netrn 81 y 01 vírtmkns) pgrg pgr g cundl nskrmhmr ue prldrgjg qun, prmjnrl `mhuon cg imdurg lrmdmegc (ne klclr hcgekl) y `nspuís junstrn cg imdurg gpcmkçe`lcn kg`g ueg `n cgs trgesilrjgkmlens, plr nonjpcl? l êg trgscgkmûe kle ue `nspcgzgjmnetl `n 7>1 uem`g`ns ne V   y 711 uem`g`ns ne ] `n (ne7>± (ne klclr vnr`n) rltgkmûe drg`ls (ne klclr gjgrmccl). l êg y ne ]  (ne (ne klclr gzuc). l êg nskgcg `n 8 g 7 ne V  y l ê snsdg`l ne nc non V  (ne (ne klclr rlol).

77.; Iue`gjnetl

Ne nstg prçktmkg trgtgrnjls kle cgs trgesilrjgkmlens hm`mjnesmlegcns. G kletmeugkmûe, jlstrgjls nc iue`gjnetl jgtnjçtmkl `n kg`g ueg `n cgs trgesilrjgkmlens hçsmkgs?

 

Prgscgkmlens

Qgrg trgscg`gr ueg plsmkmûe hm`mjnesmlegc, g÷g`mjls `mstgekmgs `n trgscgkmûe y g cgs kllr`neg`gs lrmdmegcns pgrg lhtnenr cg eunvg plsmkmûe `n kllr`neg`gs kljl sn junstrg g kletmeugkmûe?

‸,‸

,

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 9;

    ,  y

Nc pgr `n `mstgekmg `n trgscgkmûe sn ccgjg vnktlr `n trgscgkmûe l vnktlr `n kgjhml. Cg trgscgkmûe ns ue tmpl `n trgesilrjgkmûe `n sûcm`l-rêdm`l qun junvn lhontls sme `nilrjgrcls. Xltgkmlens

Qgrg gpcmkgr ueg trgesilrjgkmûe `n rltgkmûe `n ue lhontl jn`mgetn cg nspnkmimkgkmûe `n ue non `n rltgkmûe y ue çeducl `n rltgkmûe. Pl`ls cls puetls `nc lhontl sle netlekns trgesilrjg`ls g cg eunvg plsmkmûe, jn`mgetn cg rltgkmûe `n puetls kle nc çeducl nspnkmimkg`l slhrn nc non `n rltgkmûe. ^sgjls cgs nkugkmlens `n trgesilrjgkmûe pgrg rltgr cg plsmkmûe `n ue puetl gpcmkge`l ue çeducl ζ slhrn nc lrmdne?

 kls∘sme

y

 smekls

,

Gc mdugc qun kle cgs trgscgkmlens, cgs rltgkmlens sle trgesilrjgkmlens `n sûcm`l-rêdm`l qun junvne lhontls sme `nilrjgrcls. Kg`g puetl `n ue lhontl sn rltg ue jmsjl çeducl. Nskgcg

Qgrg gctnrgr nc tgjg÷l `n ue lhontl, gpcmkgjls trgesilrjgkmlens `n nskgcg. nsk gcg. êg smjpcn lpnrgkmûe `n kgjhml `n nskgcg hm`mjnesmlegc sn ccnvg g kghl juctmpcmkge`l cgs plsmkmlens `n cls lhontls plr cls igktlrns `n nskgcg y pgrg prlùkmr cgs kllr`neg`gs trgesilrjg`gs ?

,‸,‸  ∝

Nc igktlr `n nskgcg

 ∝

y

 

kgjhmg cg nskgcg `n ue lhontl ne cg `mrnkkmûe x, jmnetrgs qun

fgkn nc kgjhml `n nskgcg ne cg `mrnkkmûe y.



    

Kugcqumnr vgclr plsmtmvl pun`n snr gsmdeg`l g cls vgclrns `n nskgcg y . Ygclrns meinrmlrns g 7 rnùkne nc tgjg÷l `n cls lhontls2 vgclrns supnrmlrns g 7 prlùkne gcgrdgjmnetls. Nspnkmimkge`l ue vgclr `n 7 tgetl pgrg kljl pgrg sn `nog nc tgjg÷l `nc lhontl megctnrg`l. Kuge`l g y sn cns gsmdeg nc jmsjl vgclr, sn prlùkn ue kgjhml `n nskgcg uemilrjn qun jgetmnen cgs prlplrkmlens rncgtmvgs `nc lhontl. Ygclrns `nsmdugcns `n y rnsuctge ne ue kgjhml `n nskgcg `minrnetn

 

   

[nsdg`l

@ls trgesilrjgkmlens kljuens pgrg prlùkmr ueg mekcmegkmûe sle gqunccgs qun `nspcgzge cls vgclrns `n cgs kllr`neg`gs x y cgs qun `nspcgzge cls vgclrns `n y.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 90

êg mekcmegkmûe ne cg `mrnkkmûe-x rnspnktl gc non x sn trgesilrjg cg plsmkmûe `n kllr`neg`gs kljl smdun? y

 ℅ ∝ 

  

êg mekcmegkmûe ne cg `mrnkkmûe-y rnspnktl gc non y sn trgesilrjg cg plsmkmûe `n

  

kllr`neg`gs kljl smdun?

y

77.0 Qrlkn`mjmnetl @nskrmpkmûe) 77.0.7 Nqumpl Nqumpl enknsgrml

 ℅ ∝ 

Kljputg`lrg kle ue smstnjg lpnrgtmvl qun kunetn kle gjhmnetn drçimkl (Tme`lws, Cmeux, ntk…)

77.0.8 Jgtnrmgc Jgtnrmgc `n Gplyl Kljpmcg`lr `n k jmedw. Netlrel `n `nsgrrlccl Kl`n??Hclkbs. Cmhrnrêg `n drçimkls TmeHDMj.

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êg flog `n kug`rmkucg u flog jmcmjntrg`g

77.0.; @nsgrrlccl @nsgrrlccl `n cg Qrçktmkg [ncnkkmlen ueg mjgdne qun pun`n `nimemrsn g pgrtmr `n sus vírtmkns y qun cg kgetm`g` `n vírtmkns sng netrn 81 y 01. @mhuogjls cg imdurg ne cg flog y lhtnenjls cgs kllr`neg`gs `n cls vírtmkns ne hgsn gc smstnjg `n rninrnekmg jnekmleg`l gc memkml, tljge`l kljl lrmdne cg nsqumeg supnrmlr mzqumnr`g `n cg flog. Memkmgjls Kl`nhclkbs , y sndumjls nc jneÿ Imcn Enw Qrlonkt, Ne nc ilrjucgrml ncmon nc mklel kle cg cnyne`g Kleslcn gppcmkgtmle. [ncnkkmlens nc cnedugon K++, `nc têtucl `n prlynktl kljl Prgesilrjgkmlens8@ , Ncmog cg kgrpntg `le`n gcjgknegrg nc prlynktl y `n kcmk ne nc hltûe Enxt5 cundl ne Imemsf. Nskrmhmjls nc smdumnetn kû`mdl qun mekcuyn cg iuekmlens `mhuogr(), trgscg`gr(), rltgr(), nskgcg() y snsdgrV() @mkfg iuekmûe `nhn rnkmhmr cg jgtrmz kle cls vírtmkns y nc tltgc `n vírtmkns. Ne cg iuekmûe prmekmpgc `nimemjls cg jgtrmz n mevlkgjls g cgs iuekmlens `mhuogr(), trgscg`gr(), rltgr(), nskgcg() y snsdgrV(). Ne nc prnsnetn nonjpcl, `mhuogrnjls cg imdurg `n 4 vírtmkns `n cg kugc yg tnenjls `nimem`ls cls vírtmkns. G kletmeugkmûe, sn junstrg nc kû`mdl `n nonjpcl? #mekcu`n 3mlstrngj5

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 9>

#mekcu`n 3drgpfmks.f5 #mekcu`n 3jgtf.f5 usmed egjnspgkn st`2 vlm` `mhuogr(met imdRZR8Z, met tltgcYnrtmkns) { met m2 ilr(m:12 m3tltgcYnrtmkns-72 m++) cmen(imdRmZR1Z, imdRmZR7Z, imdRm+7ZR1Z, imdRm+7ZR7Z)2 cmen(imdR1ZR1Z, imdR1ZR7Z, imdRmZR1Z, imdRmZR7Z)2 } vlm` trgscg`gr(met imdRZR8Z, met tltgcYnrtmkns, met tx, met ty) { met m2 met rRtltgcYnrtmknsZR8Z2 ilr(m:12 m3tltgcYnrtmkns2 m++) { rRmZR1Z:imdRmZR1Z+tx2 rRmZR7Z:imdRmZR7Z+ty2 } sntklclr(DXNNE)2 `mhuogr(r,tltgcYnrtmkns)2 } vlm` rltgr(met imdRZR8Z, met tltgcYnrtmkns, iclgt geducl) { met m2 met rRtltgcYnrtmknsZR8Z2 //pgsgr nc geducl g rg`mgens geducl: geducl*J\QM/7612 ilr(m:12 m3tltgcYnrtmkns2 m++) { rRmZR1Z:imdRmZR1Z*kls(geducl)-imdRmZR7Z*sme(geducl)2 rRmZR7Z:imdRmZR1Z*sme(geducl)+imdRmZR7Z*kls(geducl)2 } sntklclr(]NCCLT)2 `mhuogr(r,tltgcYnrtmkns)2 } vlm` nskgcg(met imdRZR8Z, met tltgcYnrtmkns, iclgt sx, iclgt sy) { met m2 met rRtltgcYnrtmknsZR8Z2 ilr(m:12 m3tltgcYnrtmkns2 m++) { rRmZR1Z:imdRmZR1Z*sx2 rRmZR7Z:imdRmZR7Z*sy2 } sntklclr(CMDFPHC^N)2

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 99

`mhuogr(r,tltgcYnrtmkns)2 } vlm` snsdgrV(met imdRZR8Z, met tltgcYnrtmkns, iclgt sfx) { met m2 met rRtltgcYnrtmknsZR8Z2 ilr(m:12 m3tltgcYnrtmkns2 m++) { rRmZR1Z:imdRmZR1Z+imdRmZR7Z*sfx2 rRmZR7Z:imdRmZR7Z2 } sntklclr(CMDFPXN@)2 `mhuogr(r,tltgcYnrtmkns)2 } met jgme() { met icnkfgR4ZR8Z: { {81, 41}, {81, {61, {61, {781, {61, {61,

;1}, ;1}, 71}, >1}, =1}, 41}

}2 memtwme`lw(8;1,7>1,"Qrçktmkg @mhuogr Mjgdne 8@", 811, >1)2 `mhuogr(icnkfg,4)2 // trgscg`gr(Lhontl, tltgcYnrtmkns, tx, ty) trgscg`gr(icnkfg, 4, 711, >1)2 // rltgr(Lhontl, tltgcYnrtmkns, geducl) rltgr(icnkfg,4, 7>)2 // nskgcg(Lhontl, tltgcYnrtmkns, sx, sy) nskgcg(icnkfg,4, 1.>, 1.>)2 // snsdgrV(Lhontl, tltgcYnrtmkns, sfx) snsdgrV(icnkfg, 4, 7.8)2 wfmcn( !bhfmt() )2 kclsndrgpf( )2 rnture 12 }

Nc rnsuctg`l `nc prldrgjg getnrmlr ns cg smdumnetn vnetgeg?

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 94

Xntl.

Jl`mimqun nc prldrgjg pgrg qun pun`g gpcmkgr trgesilrjgkmlens trges ilrjgkmlens suknsmvgs g cg jmsjg imdurg usge`l cgs smdumnetns tnkcgs? Prgscgkmûe l Pnkcg G. Jlvnr fgkmg cg mzqumnr`g

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l Pnkcg [. Jlvnr fgkmg cg `nrnkfg l Pnkcg W. Jlvnr fgkmg grrmhg l Pnkcg _. Jlvnr fgkmg ghgol Xltgkmûe l Pnkcg T. Xltgr ne kletrg `n cgs jgenkmccgs `nc rnclo l Pnkcg N. Xltgr ne `mrnkkmûe `n cgs jgenkmccgs `nc rnclo Nskgcg l Pnkcg O. @msjmeumr cg nskgcg ne V l Pnkcg B. Gujnetgr cg nskgcg ne ] l Pnkcg M. Gujnetgr cg nskgcg ne ] l Pnkcg J. @msjmeumr cg nskgcg ne ] [nsdl ne V l Pnkcg V. Nstmrgr fgkmg gtrçs l Pnkcg K. Nstmrgr fgkmg g`ncgetn

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77.0.0 Xnplrtn Xnplrtn Gc imegcmzgr ístg prçktmkg nc gcujel `nhnrç dnenrgr ue rnplrtn ne Q@I qun kletnedg nc kû`mdl y cgs pgetgccgs `nc prldrgjg qun mjpcnjnetû.

77.> Xnsuctg`ls y Klekcusmlens

G`njçs `n klenktgr cgs nkugkmlens `n trgesilrjgkmlens kle su mjpcnjnetgkmûe, sn usgrç nc tnkcg`l pgrg metnrgktugr kle nc prldrgjg y gpcmkgr cgs trgesilrjgkmlens ne tmnjpl rngc.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 96

Qrgktmkg 78. Prgzg`l `n ueg kurvg `n Hnzmnr 8@ ne cnedugon k 78.7 Metrlùkkmûe

Cg prnsnetn prçktmkg gyu`g g gsmjmcgr cls kletnem`ls `n cg êm`g` MM? Drgimkgkmûe 8@ `nc suhtnjg 8.;. Prgzl `n cêengs kurvgs, `nc prldrgjg `n nstu`mls `n cg jgtnrmg `n Drgimkgkmûe , `nsgrrlccge`l cg kljpntnekmg nspnkêimkg? –@nsgrrlccg y gpcmkg jl`ncls `n drgimkgkmûe y trgesilrjgkmûe hm`mjnesmlegc pgrg nc nermqunkmjmnetl vmsugc `n sus gpcmkgkmlens‚.

Ne cg drgimkgkmûe plr kljputg`lrg els nekletrgrnjls irnkunetnjnetn i rnkunetnjnetn kle supnrimkmns kurvg`gs qun el sn pun`ne rnprnsnetgr içkmcjnetn kle ilrjgs nstçe`gr. Dnenrgcjnetn, nstg kcgsn `n lhontls sn `neljmege lhontls sme ilrjg (hclhhy). Cls `mhuogetns rnkurrêge g uegs pcgetmccgs ccgjg`gs kurvêdrgils.

Qnrl nc utmcmzgrcls klrrnktgjnetn pgrg lhtnenr cgs kurvgs `nsng`gs nrg nr g jçs ue grtn qun ueg kmnekmg. Gsê nc dnenrgr nxgktgjnetn cg jmsjg kurvg rnsuctghg juy kljpcmkg`l. Nstn jítl`l `n gprlxmjgkmûe kle spcmen iun `nsgrrlccg`l plr Nc mednemnrl irgekís Qmnrrn Hízmnr `nsgrrlccû ue jítl`l `n dnenrgkmûe `n kurvgs y supnrimkmns pgrg su usl ne nc `msn÷l `n cgs kgrrlknrêgs `n gutljûvmcns Xneguct. Nc jítl`l klesmstn ne nc usl `n ue spcmen, qun ns ueg hge`g icnxmhcn qun sn utmcmzg pgrg prlùkmr ueg kurvg sugvn qun pgsg plr uels puetls klekrntls. [n `mstrmhuyne vgrmls pnsls pnqun÷ls g cl cgrdl `n cg hge`g pgrg jgetnenrcg ne su plsmkmûe slhrn cg jnsg `n `mhuol jmnetrgs sn trgzg cg kurvg.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 9=

Cg vnetgog ns qun pl`njls `nskrmhmr jgtnjçtmkgjnetn tgc kurvg kle ueg iuekmûe krng`g plr trgjls `n plcmeljmls kÿhmkls, kuyg prmjnrg y sndue`g `nrmvg`gs sle kletmeugs ne cgs `minrnetns pgrtns `n cg kurvg. Ne cls drçimkls plr kljputg`lrg, nc tírjmel kurvg kle spcmen gflrg sn rnimnrn g kugcqumnr kurvg kljpunstg ilrjg`g plr pgrtns plcmeûjmkgs qun sgtmsigkne kle`mkmlens `n kletmeum`g` nspnkêimkgs ne cls cêjmtns `n cgs jmsjgs.

Cls spcmens `n Hízmnr `msplene `n uegs prlpmn`g`ns qun cls fgkne nspnkmgcjnetn ÿtmcns y klevnemnetns nc `msn÷l kurvgs supnrimkmns. slekle içkmcns `n mjpcnjnetgr. Qlr nstgspgrg rgzlens, cls `n spcmens `nyHízmnr nstçe G`njçs, `msplemhcns jukfg irnkunekmg ne `mvnrsls smstnjgs KG@, ne pgquntns pgrg drçimkls dnenrgcns y ne pgquntns fntnrldíenls `n `mhuol y pmeturg.

78.8 Lhontmvl Kljpntnekmg)

@nsgrrlccgr cgs nkugkmlens pgrg trgzgr ueg kurvg `n Hnzmnr kle 0 puetls `n kletrlc y cundl nskrmhmr ue prldrgjg qun cgs usn pgrg dnenrgr cg kurvg. @nhn `mhuogr tgjhmíe cls puetls `n kletrlc, pnrl `n ue klclr `minrnetn g cg kurvg.

78.; Iue`gjnetl

Fnjls vmstl, qun sm ue cudgr dnljítrmkl tmnen ueg rnprnsnetgkmûe gegcêtmkg, cg kugc ns êg slcg nkugkmûe qun kletmnen `ls vgrmghcns.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 41

Gflrg vnrnjls cg rnprnsnetgkmûe gegcêtmkg `n ueg kurvg utmcmzge`l `ls nkugkmlens, qun sn ccgjge nkugkmlens pgrgjítrmkgs `n cg kurvg. Xnkmhne nstn eljhrn gqunccgs nkugkmlens ne qun cgs vgrmghcns x y y, kg`g ueg snpgrg`gjnetn, nstçe nxprnsg`gs ne iuekmûe `n cg jmsjg tnrknrg vgrmghcn. [ndÿe nstl, `nsmdege`l plr cg cntrg u cg tnrknrg vgrmghcn, kljÿejnetn ccgjg`g vgrmghcn pgrgjítrmkg, nstgs nkugkmlens sn rnprnsnetge ne cg smdumnetn ilrjg dnenrgc?

 

Ns juy mjplrtgetn gkcgrgr qun kg`g `ls nkugkmlens pgrgjítrmkgs rnprnsnetge ueg slcg kurvg pnrinktgjnetn rninrm`g g ue smstnjg `n nons kgrtnsmgels. R78Z Nkugkmlens `n cgs kurvgs `n Hízmnr

  , 

Ne prmjnr cudgr klesm`nrgrnjls nc kgsl dnenrgc kle e+7 puetls `n kletrlc, me`mkg`ls kljl , `le`n b vgrêg `ns`n 1 g e. Nstls puetls sn kljhmege pgrg prlùkmr nc smdumnetn vnktlr `n plsmkmûe , qun `nskrmhn cg trgynktlrmg `n ueg iuekmûe `n gprlxmjgkmûe plcmeûjmkg `n Hízmnr netrn y .

     :∗ ,, 1≠≠7    :∗ ,    :∗ ,

Cg Nkugkmûe vnktlrmgc rnprnsnetg ue smstnjg `n `ls nkugkmlens pgrgjítrmkgs ne cgs kllr`neg`gs me`mvmùgcns `n cg kurvg?

Qlr cl dnenrgc, ueg pgrtn `n ueg kurvg pgquntns `n Hízmnrdrçimkls sn pun`ncmjmtge goustgrncg eÿjnrl kugcqumnr`neÿjnrl `n puetls `n kletrlc, guequn gcduels puetls `n kletrlc g kugtrl. Cgs kurvgs `n Hízmnr kÿhmkgs sn dnenrge kle kugtrl puetls `n kletrlc. Cgs kugtrl iuekmlens `n kljhmegkmûe pgrg kurvgs `n Hízmnr kÿhmkgs, lhtnem`gs sustmtuyne`l e:; sle?

 ,  7 ∘   ,  ;;7 ∘  ,  ; 7 ∘  ,  

[ustmtuyne`l, lhtnenjls? @npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 47

  7∘ 7∘  ;7∘ ;7∘  ;;7∘ 7∘    

78.0 Qrlkn`mjmnetl @nskrmpkmûe)

78.0.7 Kljputg`lrg Nqumpl enknsgrml Nqumpl kle ue smstnjg lpnrgtmvl qun kunetn kle gjhmnetn drçimkl (Tme`lws, Cmeux, ntk…)

78.0.8 Jgtnrmgc Jgtnrmgc `n Gplyl Kljpmcg`lr `n k jmedw. Netlrel `n `nsgrrlccl Kl`n??Hclkbs. Cmhrnrêg `n drçimkls TmeHDMj.

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78.0.; @nsgrrlccl @nsgrrlccl `n cg Qrçktmkg Memkmgjls Kl`nhclkbs , y sndumjls nc jneÿ Imcn Enw Qrlonkt, Ne nc ilrjucgrml ncmon nc mklel kle cg cnyne`g Kleslcn gppcmkgtmle. [ncnkkmlens nc cnedugon K++, `nc têtucl `n prlynktl kljl KurvgHnzmnr8@, Ncmog cg kgrpntg `le`n gcjgknegrg nc prlynktl y `n kcmk ne nc hltûe Enxt5 cundl ne Imemsf. Nskrmhmjls nc smdumnetn kû`mdl qun mekcuyn cg iuekmûe hnzmnr8@(), @mkfg iuekmûe `nhn rnkmhmr cg jgtrmz kle cls puetls `n kletrlc y nc tltgc `n puetl `n kletrlc. Ne cg iuekmûe prmekmpgc `nimemjls cg jgtrmz kle cls puetls `n kletrlc n mevlkgjls g cg iuekmûe hnzmnr8@(). Ne nc prnsnetn nonjpcl, `mhuogrnjls ueg kurvg `nimem`g plr 0 puetls `n kletrlc. G kletmeugkmûe, sn junstrg nc kû`mdl `n nonjpcl? #mekcu`n 3mlstrngj5 #mekcu`n 3drgpfmks.f5 usmed egjnspgkn st`2 vlm` hnzmnr8@(met pkRZR8Z, met e) { iclgt x,y,u2 sntklclr(]NCCLT)2 // Quetls `n kletrlc ilr(met m:12 m3e2 m++) kmrkcn(pkRmZR1Z, pkRmZR7Z,8)2 // Kurvg ilr(u:12 u372 u+:1.11>) {

x: pkR1ZR1Z*(7-u)*(7-u)*(7-u) + pkR7ZR1Z*;*u*(7-u)*(7-u) +

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 48

pkR8ZR1Z*;*u*u*(7-u) pkR;ZR1Z*u*u*u2

+

y: pkR1ZR7Z*(7-u)*(7-u)*(7-u) + pkR7ZR7Z*;*u*(7-u)*(7-u) + pkR8ZR7Z*;*u*u*(7-u) + pkR;ZR7Z*u*u*u2 putpmxnc(x, y, TFMPN)2 } } met jgme() { met kurvgR0ZR8Z: { {71, 761}, {01, 01}, {791, 791}, {761, 81} }2 memtwme`lw(811,811,"Qrçktmkg Kurvg `n Hnzmnr 8@", 811, >1)2 hnzmnr8@(kurvg,0)2 wfmcn( !bhfmt() )2 kclsndrgpf( )2 rnture 12 }

Nc rnsuctg`l `nc prldrgjg getnrmlr ns cg smdumnetn vnetgeg?

Xntl.

@nsgrrlccn nc jl`ncl jgtnjçtmkl pgrg trgzgr ueg kurvg `n Hnzmnr kle 9 puetls `n kletrlc y `nspuís mjpcnjnetn nc prldrgjg qun cl `mhuon. @npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 4;

78.0.0 Xnplrtn Xnplrtn Gc imegcmzgr ístg prçktmkg nc gcujel `nhnrç dnenrgr ue rnplrtn ne Q@I qun kletnedg cgs `nùkkmlens jgtnjçtmkgs, nc kû`mdl y cgs pgetgccgs `nc prldrgjg qun mjpcnjnetû.

78.> Xnsuctg`ls y Klekcusmlens Nc gcujel kljprne`nrç qun, sm enknsmtg ueg kurvg jçs kljpcnog l kle jgylr `nimemkmûe, enknsmtgrç jçs puetls `n kletrlc. G`njçs, `nhn pnrkmhmr qun pun`n usgr kgsm nc jmsjl prldrgjg pgrg `minrnetns kgetm`g`ns `n puetls `n kletrlc.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 40

Qrgktmkg 7;. Prgzg`l `n ueg kurvg `n [pcmen 8@ ne cnedugon k 7;.7 Metrlùkkmûe

Cg prnsnetn prçktmkg gyu`g g gsmjmcgr cls kletnem`ls `n cg êm`g` MM? Drgimkgkmûe 8@ `nc suhtnjg 8.;. Prgzl `n cêengs kurvgs, `nc prldrgjg `n nstu`mls `n cg jgtnrmg `n Drgimkgkmûe , `nsgrrlccge`l cg kljpntnekmg nspnkêimkg? –@nsgrrlccg y gpcmkg jl`ncls `n drgimkgkmûe y trgesilrjgkmûe hm`mjnesmlegc pgrg nc nermqunkmjmnetl vmsugc `n sus gpcmkgkmlens‚.

Guequn cgs kurvgs `n Hnzmnr sle juy smjpcns `n mjpcnjnetgr, tmnene `ls `nsvnetgogs mjplrtgetns? Gc jlvnr ue puetl `n kletrlc sn tmnen qun rnkgckucgr tl`g cg kurvg, Nc tmnjpl kljputgkmlegc enknsgrml ginktg endgtmvgjnetn nc tmnjpl pgrg `mhuogr cg kurvg metnrgktmvgjnetn. 

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Cgs kurvgs H-[pcmens ncmjmege cgs `nsvnetgogs getnrmlrns. Cg prmekmpgc nstrgtndmg ns `mvm`mr ueg kurvg ne vgrmls sndjnetls `n kurvg y cg jgenrg `n uemr `mkfls sndjnetls. Ne cg prnsnetn prçktmkg mjpcnjnetgrnjls cls H-[pcmens êmilrjns El Xgkmlegcns. Nstg kcgsn `n spcmens ns cg jçs prliusgjnetn utmcmzg`g y cgs iuekmlens `n spcmens H nstçe `msplemhcns fghmtugcjnetn ne cls smstnjgs KG@ y ne jukfls pgquntns `n prldrgjgkmûe `n drçimkls. Gc mdugc qun cls spcmens `n Hízmnr, cls spcmens H sn dnenrge gprlxmjge`l ue kleouetl `n puetls `n kletrlc. Qnrl cls spcmens H prnsnetge `ls vnetgogs irnetn g cls spcmens `n Hízmnr? (7) nc drg`l `n ue plcmeljml `n ue spcmen H sn pun`n nstghcnknr `n ilrjg me`npne`mnetn gc eÿjnrl `n puetls `n kletrlc (kle kmnrtgs cmjmtgkmlens), y (8) cls spcmens H pnrjmtne kletrlc clkgc slhrn cg ilrjg `n ue spcmen. Cg `nsvnetgog ns qun cls spcmens H sle jçs kljpcnols qun cls spcmens `n Hízmnr. R78Z

7;.8 Lhontmvl Kljpntnekmg)

Ne cg prnsnetn prçktmkg qunrnjls trgzgr ueg kurvg spcmen `le`n kg`g sndjnetl `n kurvg tnedg `mstmetl klclr.

7;.; Iue`gjnetl

Nc tnrjmel spcmen sn usg pgrg eljhrgr g cgs cgrdgs tmrgs icnxmhcns `n jntgc usg`g plr cls `mhuogetns ne nc `msn÷l `n supnrimkmns `n gnrlpcgels, kgrrls y egvns. G cl cgrdl `nc spcmen, sn cmdge pnsls pgrg ogcgr nc spcmen ne vgrmgs `mrnkkmlens.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 4>

Cls spcmens `n jntgc tmnen ueg kletmeum`g` `n sndue`l lr`ne (l jnels qun sn `lhcne snvnrgjnetn). Cls H-spcmens nstçe ilrjg`ls plr sndjnetls `n kurvgs. Cls klnimkmnetns `n cls plcmeljmls `n tgcns kurvgs `npne`ne slcl `n uels kugetls puetls `n kletrlc, plr cl kugc sn cldrg ue "kletrlc clkgc". Gsê, gc jlvnr ue puetl `n kletrlc, slcl sn ginktg ueg pnqun÷g pgrtn `n cg kurvg. Cls H-[pcmens tmnene cg jmsjg kletmeum`g` qun cls spcmens egturgcns, pnrl el metnrplcge sus puetls `n kletrlc. ê sndjnetl `n kurvg el enknsmtg pgsgr plr sus puetls `n kletrlc. Gc kljpgrtmr cls puetls `n kletrlc netrn sndjnetls, sn cldrge cgs kle`mkmlens `n kletmeum`g`.

, ,  y 

1≠37

Qgrg trgzgr ue slcl sndjnetl `n kurvg W, sn rnqumnrne `n 0 puetls `n kletrlc . Pgc kurvg nstç `nimem`g slhrn nc `ljmeml . Cg nkugkmûe qun `nimen cg kurvg ns cg smdumnetn?



 

 



 1≠37  7 ∘9  ∝   ; ∘ 99  0 ∝   ∘;  ;9 ;7 ∝   9 ∝ 

`le`n?

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 49

Gc puetl ne nc kugc tnrjmeg ue sndjnetl y kljmnezg ltrl sndjnetl sn cn ccgjg puetl `n rupturg û belt (tgjhmíe sn klesm`nrge belts nc prmekmpml y nc imegc `nc H-spcmen). Nc tírjmel uemilrjn smdemimkg qun cls belts nstçe uemilrjnjnetn `mstrmhum`ls. Nc tnrjmel El - rgkmlegc sn utmcmzg pgrg `minrnekmgr nstls spcmens `n cgs kurvgs plcmeljmgcns kuhmkgskÿhmkls. rgkmlegcns, x(t), y(t)g yhçsmkl, z(t) nstçe `nimem`ls `ni mem`ls kljl nc rg`ml `n `ls plcmeljmls Cg `le`n H sn rnimnrn plrqun cls spcmens pun`ne rnprnsnetgrsn kljl sujgs pnsg`gs `n iuekmlens plcmeljmgcns hçsmkgs (nstl el sn kujpcn kle cls spcmens egturgcns). êg kurvg H-spcmen kle E belts tne`rç?

 ∘ 78   1…7 1…∘8    1…∘7 , +, + y ++, +, + y + + [ndjnetls `n kurvg Quetls `n kletrlc

belts `le`n

`le`n

`le`n

`le`n

Nc sndjnetl `n kurvg

nstg `nimem`g plr kugtrl puetls `n kletrlc

`n kurvg nstgsndjnetls `nimem`g plr puetls `n kletrlc kl etrlc . ] nc smdumnetn sndjnetl . Kljl pun`n vnrsn, cls `nkugtrl kurvg knrkgels kljpgrtne gcduels puetls `n kletrlc.

Cg nkugkmûe dnenrgc `n ue H-spcmen ns?

  7 ∘9  ∝   ; ∘ 99  0 ∝ +  ∘;  ;9 ;7 ∝ +  9 ∝ + `ûe`n?

1≠37

ne kg`g sndjnetl

belts.  kle 1…∘8, sm fgy E  belts.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 44

Gsê, pgrg drgimkgr ueg kurvg H-spcmen ne 8@ usgrnjls cgs smdumnetns nkugkmlens pgrg lhtnenr kg`g pmxnc `n cg kurvg?

  7 ∘  ∝   ; ∘ 9  0 ∝ +  ∘;  ; ;7 ∝ +   ∝ + 9 9 9 y 9    7 ∘9  ∝   ; ∘ 99  0 ∝ +  ∘;  ;9 ;7 ∝ +  9 ∝ +

[n pun`n krngr ueg kurvg H-spcmen knrrg`g içkmcjnetn gc gdrndgr cls trns prmjnrls puetls `n kletrlc gc imegc `n cg snkunekmg.

7;.0 Qrlkn`mjmnetl @nskrmpkmûe) 7;.0.7 Nqumpl Nqumpl enknsgrml Kljputg`lrg kle ue smstnjg lpnrgtmvl qun kunetn kle gjhmnetn drçimkl (Tme`lws, Cmeux, ntk…)

7;.0.8 Jgtnrmgc Jgtnrmgc `n Gplyl Kljpmcg`lr `n k jmedw. Netlrel `n `nsgrrlccl Kl`n??Hclkbs. Cmhrnrêg `n drçimkls TmeHDMj.







7;.0.; @nsgrrlccl @nsgrrlccl `n cg Qrçktmkg Memkmgjls Kl`nhclkbs , y sndumjls nc jneÿ Imcn Enw Qrlonkt, Ne nc ilrjucgrml ncmon nc mklel kle cg cnyne`g Kleslcn gppcmkgtmle. [ncnkkmlens nc cnedugon K++, `nc têtucl `n prlynktl kljl Kurvg[pcmen8@ , Ncmog cg kgrpntg `le`n gcjgknegrg nc prlynktl y `n kcmk ne nc hltûe Enxt5 cundl ne Imemsf. Nskrmhmjls nc smdumnetn kû`mdl qun mekcuyn cg iuekmûe spcmen8@() , @mkfg iuekmûe `nhn rnkmhmr cg jgtrmz kle cls puetls `n kletrlc y nc tltgc `n puetl `n kletrlc. Ne cg iuekmûe prmekmpgc `nimemjls cg jgtrmz kle cls puetls `n kletrlc n mevlkgjls g cg iuekmûe spcmen8@() . Ne nc prnsnetn nonjpcl, `mhuogrnjls ueg kurvg `nimem`g plr 6 puetls `n kletrlc. ] pgrg ueg jnolr kljprnesmûe `mhuogrnjls kg`g sndjnetl `n kurvg `n ue klclr `minrnetn. G kletmeugkmûe, sn junstrg nc kû`mdl `n nonjpcl? #mekcu`n 3mlstrngj5 #mekcu`n 3drgpfmks.f5 usmed egjnspgkn st`2

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 46

vlm` spcmen8@(met pkRZR8Z, met e) { iclgt x,y,u2 // Quetls `n kletrlc sntklclr(]NCCLT)2 ilr(met m:12 m3e2 m++) kmrkcn(pkRmZR1Z, pkRmZR7Z,8)2 // Kurvg ilr(e:;2 e362 e++) { ilr(u:12 u372 u+:1.11>) { x: (7-u)*(7-u)*(7-u)*pkRe-;ZR1Z/9 + (;*u*u*u-9*u*u+0)*pkRe-8ZR1Z/9 + (-;*u*u*u+;*u*u+;*u+7)*pkRe-7ZR1Z/9 + u*u*u*pkReZR1Z/92 y: (7-u)*(7-u)*(7-u)*pkRe-;ZR7Z/9 + (;*u*u*u-9*u*u+0)*pkRe-8ZR7Z/9 + (-;*u*u*u+;*u*u+;*u+7)*pkRe-7ZR7Z/9 + u*u*u*pkReZR7Z/92 //e%7>+7 Gsndurg ue m` `n klclr netrn 7 y 7> putpmxnc(x, y, e%7>+7)2 } } } met jgme() { met kurvgR6ZR8Z: { {81, 81}, {781, 61}, {791, {701, {711, {61, {91, {01,

701}, 761}, 7=1}, 701}, 781}, 91}

}2 memtwme`lw(811,811,"Qrçktmkg @mhuogr Kurvg [pcmen 8@", 811, >1)2 spcmen8@(kurvg,6)2 wfmcn( !bhfmt() )2 kclsndrgpf( )2 rnture 12 }

Nc rnsuctg`l `nc prldrgjg getnrmlr ns cg smdumnetn vnetgeg?

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 4=

Xntl.

@nsgrrlccn nc jl`ncl jgtnjçtmkl pgrg trgzgr ueg kurvg `n H[pcmen kle 71 puetls `n kletrlc y `nspuís mjpcnjnetn nc prldrgjg qun cl `mhuon.

7;.0.0 Xnplrtn Xnplrtn Gc imegcmzgr ístg prçktmkg nc gcujel `nhnrç dnenrgr ue rnplrtn ne Q@I qun kletnedg cgs `nùkkmlens jgtnjçtmkgs, nc kû`mdl y cgs pgetgccgs `nc prldrgjg qun mjpcnjnetû. G`njçs, `nhnrç netrndgr ueg mevnstmdgkmûe kle cls `mstmetls tmpls `n spcmens qun fgy.

7;.> Xnsuctg`ls y Klekcusmlens

Nc gcujel kljprne`nrç qun, sm enknsmtg ueg kurvg jçs kljpcnog l kle jgylr `nimemkmûe, enknsmtgrç jçs puetls `n kletrlc. G`njçs, qun pun`n usgr cg jmsjg iuekmûe pgrg `minrnetns kgetm`g`ns `n puetls `n kletrlc.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 61

Qrgktmkg 70. Xnprnsnetgkmle `n ueg imdurg kle kllr`neg`gs fljldnengs g pgrtmr `n sus vn vn rtmkns rtmkns ne nc cnedugon Qrlknssmed 70.7 Metrlùkkmûe

Cg prnsnetn prçktmkg gyu`g g gsmjmcgr cls kletnem`ls `n cg êm`g` MM? Drgimkgkmûe 8@ `nc suhtnjg 8.;. Prgzl `n cêengs kurvgs, `nc prldrgjg `n nstu`mls `n cg jgtnrmg `n Drgimkgkmûe , `nsgrrlccge`l cg kljpntnekmg nspnkêimkg? –@nsgrrlccg y gpcmkg jl`ncls `n drgimkgkmûe y trgesilrjgkmûe hm`mjnesmlegc pgrg nc nermqunkmjmnetl vmsugc `n sus gpcmkgkmlens‚.

Qgrg mjpcnjnetgr clstnekmg`ls kleknptlskle hçsmkls `n drgimkgkmûe sn fge utmcmzg`ls cnedugons prlpûsmtl dnenrgc pltnekmg`ls pl cmhrnrêgs drçimkgs, pnrl kleilrjn kle ilrjn sn g`netrg g`n etrg uel`ng kunstmlens jçs kljpcnogs kljl cl pun`ne snr cg gemjgkmûe, mcujmegkmûe y sljhrng`l, ntk. [n enknsmtge `n ltrgs fnrrgjmnetgs qun els gyu`ne g fgknr cg prldrgjgkmûe jçs snekmccg. êg `n nstgs fnrrgjmnetgs fnr rgjmnetgs ns Qrlknssmed .

Qrlknssmed ns ue cnedugon `n prldrgjgkmûe y netlrel `n `nsgrrlccl metndrg`l `n kû`mdl ghmnrtl hgsg`l ne Ogvg, `n içkmc utmcmzgkmûe, y qun smrvn kljl jn`ml pgrg cg nesn÷gezg y prlùkkmûe `n prlynktls prl ynktls juctmjn`mg n metnrgktmvls `n `msn÷l `mdmtgc R7;Z.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 67

êl `n cls lhontmvls `nkcgrg`ls `n Qrlknssmed ns nc `n gktugr kljl fnrrgjmnetg pgrg quncggrtmstgs, `msn÷g`lrns vmsugcnscgs y jmnjhrls ltrgs kljuem`g`ns gonel gonels s gc cnedugon `n prldrgjgkmûe, gprne`mnrge hgsns `n cg`njmsjg g trgvís `n ueg junstrg drçimkg mestgetçeng y vmsugc `n cg meilrjgkmûe. Nc cnedugon `n Qrlknssmed sn hgsg ne Ogvg, guequn fgkn usl `n ueg smetgxms smjpcmimkg`g y `n ue jl`ncl `n prldrgjgkmûe `n drçimkls.

70.8 Lhontmvl Kljpntnekmg)

^sgr cgs cmhrnrêgs `n Qrlknssmed pgrg `mhuogr ueg imdurg kle kllr`neg`gs fljldíengs g pgrtmr `n sus vírtmkns.

70.; Iue`gjnetl

Cls tírjmels juctmpcmkgtmvls y trgscgkmlegcns pgrg ueg trgesilrjgkmûe dnljítrmkg hm`mjnesmlegc pun`ne pu n`ne sn snrr kljhmeg`ls `netrl ``nn ueg jgtrmz snekmccg, sm nxpge`mjls nxpge `mjls cg rnprnsnetgkmûe g jgtrmkns `n ; plr ;. êg tíkemkg nstçe`gr pgrg cldrgr nstl klesmstn ne nxpge`mr kg`g rnprnsnetgkmûe `n plsmkmûe-kllr`neg`g hm`mjnesmlegc ne rnprnsnetgkmlens `n ; ncnjnetls ccgjg`gs kllr`neg`gs fljldíengs, `le`n nc pgrçjntrl fljldíenl f. Qgrg trgesilrjgkmlens dnljítrmkgs, pl`njls ncndmr nc pgrçjntrl fljldíenl f pgrg qun sng kugcqumnr vgclr `mstmetl `n knrl. Gsê, fgy ue eÿjnrl meimemtl `n rnprnsnetgkmlens fljldíengs nqumvgcnetns pgrg pg rg kg`g puetl `n kllr`neg`gs . êg ncnkkmûe gknrtg`g ns imogr f:7. Kg`g plsmkmûe hm`mjnesmlegc sn rnprnsnetg kle kllr`neg`gs kllr` neg`gs fljldíengs R;Z.

,

, , ℅

,

,,7

Nxprnsgr plsmkmlens ne kllr`neg`gs fljldíengs els pnrjmtn rnprnsnetgr tl`gs cgs nkugkmlens `n trgesilrjgkmlens dnljítrmkgs kljl juctmpcmkgkmûe `n jgtrmkns, qun ns nc jítl`l nstçe`gr usg`l ne cls smstnjgs drçimkls. Cgs plsmkmlens `n kllr`neg`gs hm`mjnesmlegcns sn rnprnsnetgehm`mjnesmlegcns kle vnktlrns klcujeg `n trns ncnjnetls, lpnrgkmlens `n trgesilrjgkmûe sn rnprnsnetge kljl jgtrmkns y`ncgs ; plr ;.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 68

Jgtrmz `n trgscgkmûe hm`mjnesmlegc

^sge`l cg gprlxmjgkmûe `n kllr`neg`gs fljldíengs, pl`njls rnprnsnetgr cgs nkugkmlens pgrg ueg trgscgkmûe hm`mjnesmlegc `n ueg plsmkmûe `n kllr`neg`gs kllr`neg` gs usge`l cg smdumnetn jgtrmz `n juctmpcmkgkmûe.

‸‸7  711 171 7 ∝ 7

Jgtrmz `n rltgkmûe hm`mjnesmlegc

@n jgenrg smjmcgr, cgs nkugkmlens `n trgesilrjgkmûe `n rltgkmûe hm`mjnesmlegc slhrn nc lrmdne `n kllr`neg`gs pun`ne nxprnsgrsn ne ilrjg `n jgtrmz,

‸‸  sknles  ∘kslnse 11 ∝  7 1 1 7 7

Jgtrmz `n kgjhml `n nskgcg hm`mjnesmlegc

Imegcjnetn, ueg trgesilrjgkmûe `n kgjhml `n nskgcg rncgtmvg gc lrmdne `n kllr`neg`gs pun`n gflrg nxprnsgrsn nxprnsgrs n kljl cg jgtrmz `n juctmpcmkgkmûe?

‸‸  1 1 11 ∝  7 117 7

70.0 Qrlkn`mjmnetl @nskrmpkmûe) 70.0.7 Nqumpl Nqumpl enknsgrml

Kljputg`lrg kle ue smstnjg lpnrgtmvl qun kunetn kle gjhmnetn drçimkl (Tme`lws, Cmeux, ntk…)

70.0.8 Jgtnrmgc Jgtnrmgc `n Gplyl [@B `n ogvg. Netlrel `n `nsgrrlccl Qrlknssmed (M@N).





70.0.; @nsgrrlccl @nsgrrlccl `n cg Qrçktmkg Qrmjnrl mestgcgjls Qrlknssmed , qun sn pun`n `nskgrdgr `n? fttps?//prlknssmed.lrd/`lweclg`/ fttps?//prlknssmed.lrd/`lweclg`/

Ne nstg pçdmeg ncmdn nc grkfmvl g`nkug`l pgrg su nqumpl (Tme`lws, Jgk l Cmeux). êg vnz `nskgrdg`l, plr nonjpcl, cg vnrsmûe pgrg wme`lws 71 `n 90 hmts tne`rnjls nc grkfmvl prlknssmed-;.0-wme`lws90.zmp. [lcl `nskljprmjg nc grkfmvl ne ueg kgrpntg, plr nonjpcl, ne cg `n @lkujnetls , qun`çe`lels?

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 6;

Ghrmjls cg kgrpntg y nonkutgjls nc grkfmvl prlknssmed.nxn. @nhnjls lhtnenr cg smdumnetn metnrigz?

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 60

Nskrmhmjls nc smdumnetn kû`mdl y cls dugr`gjls kljl tFljldnengs8@, Qrlknssmed krngrg ueg kgrpntg pgrg dugr`grcl kljl prlynktl y `netrl `n cg kgrpntg dugr`grg nc kû`mdl iunetn. Wun`ge`l gcjgkneg`l ne cg rutg? ..SQrlknssmedS tFljldnengs8@S [email protected]`n

Kû`mdl? iclgtRZRZ icnkfg: { {81, 41, 7}, {81, ;1, 7}, {61, ;1, 7}, {61, 71, 7}, {781, >1, 7}, {61, =1, 7}, {61, 41, 7} }2 iclgtRZRZ Nskgcg:{ {1.>, 1, 1}, {1, 1.>, 1}, {1, 1, 7} }2 iclgtRZRZ Prgscgkmle:{ {7, 1, 1}, {1, 7, 1}, {711, >1, 7} }2 iclgtRZRZ Xltgkmle:{ { 1.=99, 1.8>=, 1}, {-1.8>=, 1.=99, 1}, { 1, 1, 7} }2 iclgtRZRZ X:{ {1, 1, 1}, {1, 1, 1}, {1, 1, 1}, {1, {1, {1, {1,

1, 1, 1, 1,

1}, 1}, 1}, 1}}2

vlm` sntup() { smzn(8;1, 791)2 //Pgjg÷l `n cg vnetgeg } vlm` `rgw() { hgkbdrlue`(1)2 //Klclr `n ile`l strlbn(8>>)2 //Klclr `nc cçpmz `mhuog(icnkfg, 4)2 juct(icnkfg, Prgscgkmle, 4)2 `mhuog(X, 4)2 memkmgcmzg(4)2

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

juct(icnkfg, Xltgkmle, 4)2 `mhuog(X, 4)2 memkmgcmzg(4)2 juct(icnkfg, Nskgcg, 4)2 `mhuog(X, 4)2 memkmgcmzg(4)2 } vlm` juct(iclgtRZRZ G, iclgtRZRZ H, met e) { met m, o, b2 ilr (m:12 m3e2 m++) ilr (o:12 o3;2 o++) ilr (b:12 b3;2 b++) XRmZRbZ+:GRmZRoZ*HRoZRbZ2 } vlm` memkmgcmzg(met e) { met m, o2 ilr (m:12 m3e2 m++) ilr (o:12 o3;2 o++) XRmZRoZ:12 } vlm` `mhuog(iclgtRZRZ V, met e) { met m, o2 ilr (m:12 m3e-72 m++) cmen(VRmZR1Z, VRmZR7Z, VRm+7ZR1Z, VRm+7ZR7Z)2 cmen(VR1ZR1Z, VR1ZR7Z, VRmZR1Z, VRmZR7Z)2 }

Nc rnsuctg`l `nc prldrgjg getnrmlr ns cg smdumnetn vnetgeg?

Qçdmeg 6>

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 69

Xntl.

Jl`mimqun nc prldrgjg pgrg qun pun`g gpcmkgr trgesilrjgkmlens suknsmvgs s uknsmvgs g cg jmsjg imdurg usge`l cgs smdumnetns tnkcgs? Prgscgkmûe

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l l l l

Pnkcg G. Jlvnr fgkmg cg mzqumnr`g Pnkcg [. Jlvnr fgkmg cg `nrnkfg Pnkcg W. Jlvnr fgkmg grrmhg Pnkcg _. Jlvnr fgkmg ghgol Xltgkmûe l Pnkcg T. Xltgr ne kletrg `n cgs jgenkmccgs `nc rnclo l Pnkcg N. Xltgr ne `mrnkkmûe `n cgs jgenkmccgs `nc rnclo Nskgcg l Pnkcg O. @msjmeumr cg nskgcg ne V l Pnkcg B. Gujnetgr cg nskgcg ne ] l Pnkcg M. Gujnetgr cg nskgcg ne ] l Pnkcg J. @msjmeumr cg nskgcg ne ] [nsdl ne V l Pnkcg V. Nstmrgr fgkmg gtrçs l Pnkcg K. Nstmrgr fgkmg g`ncgetn

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70.0.0 Xnplrtn Xnplrtn Gc imegcmzgr ístg prçktmkg nc gcujel `nhnrç dnenrgr ue rnplrtn ne Q@I qun kletnedg nc kû`mdl y cgs pgetgccgs `nc prldrgjg qun mjpcnjnetû.

70.> Xnsuctg`ls y Klekcusmlens

Nc gcujel sn `grç kunetg qun, guequn Qrlknssmed prljntn snr ueg fnrrgjmnetg gvgezg`g pgrg nc jgenol `n drçimkls, nc nsiunrzl ns kgsm nc jmsjl qun nc fgknrcl kle K++ y TmeHDMj. Nstl ns plrqun el nstgjls usge`l cgs vnetgogs `nc cnedugon. Pgcns vnetgogs sn gprnkmgrçe ne cg smdumnetn prçktmkg.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 64

Qrgktmkg 7>. Prgscgkmle, nskgcg, rltgkmle `n ueg imdurg ne nc cnedugon Qrlknssmed 7>.7 Metrlùkkmûe

Cg prnsnetn prçktmkg gyu`g g gsmjmcgr cls kletnem`ls `n cg êm`g` MM? Drgimkgkmûe 8@ `nc suhtnjg 8.;. Prgzl `n cêengs kurvgs, `nc prldrgjg `n nstu`mls `n cg jgtnrmg `n Drgimkgkmûe , `nsgrrlccge`l cg kljpntnekmg nspnkêimkg? –@nsgrrlccg y gpcmkg jl`ncls `n drgimkgkmûe y trgesilrjgkmûe hm`mjnesmlegc pgrg nc nermqunkmjmnetl vmsugc `n sus gpcmkgkmlens‚.

Ne nstg prçktmkg sn qumnrn tljgr vnetgog `n cgs iuekmlens qun lirnkn Qrlknssmed pgrg nc jgenol `n trgesilrjgkmlens ne 8@.

7>.8 Lhontmvl Kljpntnekmg)

@mhuogr ueg imdurg y sus rnspnktmvgs trgesilrjgkmlens hçsmkgs usge`l cgs iuekmlens qun mekcuyn nc Qrlknssmed.

7>.; Iue`gjnetl

Qrlknssmed tmnen iuekmlens metndrg`gs qun cn igkmcmtge tnenr lhontls ne ue hlkntl?

junvg, dmrn y gujnetn l gujnetn su tgjg÷l. G cn prnsnetgrç cgs iuekmlens `n trgscgkmûe, rltgkmûe, nskgcg y ltrgs pgrg qun pun`g usgrcgs ne sus hlkntls. trgescgtn() rltgtn() rltgtnV() rltgtn]() rltgtn_() skgcn() plpJgtrmx() pusfJgtrmx() 

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7>.0 Qrlkn`mjmnetl @nskrmpkmûe) 7>.0.7 Nqumpl Nqumpl enknsgrml Kljputg`lrg kle ue smstnjg lpnrgtmvl qun kunetn kle gjhmnetn drçimkl (Tme`lws, Cmeux, ntk…)

7>.0.8 Jgtnrmgc Jgtnrmgc `n Gplyl [@B `n ogvg. Netlrel `n `nsgrrlccl Qrlknssmed (M@N).

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@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 66

7>.0.; @nsgrrlccl @nsgrrlccl `n cg Qrçktmkg Nonkutgjls prlknssmed.nxn y ne cg metnrigz sncnkkmlegjls Grkfmvl-5Eunvl y ne cg eunvg vnetgeg nskrmhmjls nc smdumnetn kû`mdl y cls dugr`gjls kljl trgesilrjgkmlens8@ , Qrlknssmed krngrg ueg kgrpntg pgrg dugr`grcl kljl prlynktl y `netrl `n cg kgrpntg dugr`grg nc kû`mdl iunetn. Wun`ge`l gcjgkneg`l ne cg rutg? ..SQrlknssmedStrgesilrjkmlens8@[email protected]`n

Kû`mdl? Q[fgpn icnkfg2 vlm` sntup() { smzn(8;1, 791)2 //Pgjg÷l `n cg vnetgeg icnkfg:krngtn[fgpn()2 //[n `nimene cls vnrtmkns `n cg imdurg icnkfg.hndme[fgpn()2 icnkfg.vnrtnx(81, 41)2 icnkfg.vnrtnx(81, ;1)2 icnkfg.vnrtnx(61, ;1)2 icnkfg.vnrtnx(61, 71)2 icnkfg.vnrtnx(781, >1)2 icnkfg.vnrtnx(61, =1)2 icnkfg.vnrtnx(61, 41)2 icnkfg.ne`[fgpn()2 } vlm` `rgw() { hgkbdrlue`(81)2 //Klclr `n ile`l strlbn(8>>)2 //Klclr `nc cçpmz sfgpn(icnkfg)2 //@mhuog cg imdurg //[n gpcmkge cgs tregilrjgkmlens. [le suknsmvgs trgescgtn(711,>1)2 sfgpn(icnkfg)2 rltgtn(rg`mges(7>))2 sfgpn(icnkfg)2 skgcn(1.>,1.>)2 sfgpn(icnkfg)2 }

Nc rnsuctg`l `nc prldrgjg getnrmlr ns cg smdumnetn vnetgeg?

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 6=

Xntl.

Jl`mimqun nc prldrgjg pgrg qun kg`g icnkfg sng `n ue klclr `minrnetn y g`njçs, qun cgs trgesilrjgkmlens el snge suknsmvgs.

7>.0.0 Xnplrtn Xnplrtn Gc imegcmzgr ístgpgetgccgs prçktmkg`nc nc gcujel `nhnrç dnenrgr ue rnplrtn ne Q@I qun kletnedg nc kû`mdl y cgs prldrgjg qun mjpcnjnetû. G`njçs, `lkujnetn cgs iuekmlens metndrg`gs qun sn jnekmlege ne nc puetl 7>.;

7>.> Xnsuctg`ls y Klekcusmlens

Nc gcujel gprnkmgrç cgs vnetgogs `n ueg fnrrgjmnetg `n prldrgjgkmûe jçs gvgezg`g, vmne`l qun pun`n mjpcnjnetgr nsknegs jukfl jçs kljpcnogs kle jnels nsiunrzl.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg =1

Qrgktmkg 79. Ilrjgs dnljntrmkgs ;@ ne nc cnedugon Qrlknssmed 79.7 Metrlùkkmûe

Cg prnsnetn prçktmkg gyu`g g gsmjmcgr cls kletnem`ls `n cg êm`g` MMM? Drgimkgkmûe ;@ `nc suhtnjg ;.8. Ilrjgs dnljítrmkgs trm`mjnesmlegcns (supnrimkmns pcgegs y kurvgs), `nc prldrgjg `n nstu`mls `n cg jgtnrmg `n Drgimkgkmûe , `nsgrrlccge`l cg kljpntnekmg nspnkêimkg? –@nsgrrlccg y gpcmkg jl`ncls `n drgimkgkmûe y

trgesilrjgkmûe trm`mjnesmlegc slhrn netm`g`ns dnljítrmkgs ne ;@ pgrg dnenrgr prlynkkmlens vmsugcns ne 8@‚.

Ne nstg prçktmkg sn qumnrn tljgr vnetgog `n cgs iuekmlens qun lirnkn Qrlknssmed pgrg `nimemr ueg supnrimkmn.

79.8 Lhontmvl Kljpntnekmg)

@nimemr cgs kllr`neg`gs `n ueg supnrimkmn y `mhuogrcg, usge`l ueg prlynkkmûe lrtldlegc. Pgjhmíe `nhn `mhuogr cls nons `n kllr`neg`gs pgrg qun smrvge `n rninrnekmg. ^sn cgs iuekmlens qun mekcuyn nc Qrlknssmed.

79.; Iue`gjnetl Ymstgs l Qrlynkkmlens

Nxmstne `ls jítl`ls hçsmkls pgrg prlynktgr lhontls trm`mjnesmlegcns slhrn ueg supnrimkmn `n vmsmûe hm`mjnesmlegc. Nstgs `ls jgenrgs, `npne`ne `n sm tl`ls cls puetls `nc lhontl pun`ne prlynktgrsn slhrn cg supnrimkmn g cl cgrdl cgrdl `n cêengs pgrgcncgs l hmne cls puetls pun`ne prlynktgrsn g cl cgrdl `n cêengs qun klevnrdne g ueg pls plsmkmûe mkmûe `neljmeg`g knetrl `n prlynkkmûe. R0Z êg prlynkkmûequnmsljítrmkg `n rnprnsnetgkmûe ue lhontl trm`mjnesmlegc sn rnùknns ne ue `lsjítl`l `mjnesmlens, ne cg qun clsdrçimkg trns nons`nlrtldlegcns prmekmpgcns, gc prlynktgrsn, ilrjge çeducls `n 781¿, y cgs `mjnesmlens pgrgcncgs g `mkfls nons sn jm`ne ne ueg jmsjg nskgcg. Nc tírjmel msljítrmkl prlvmnen `nc m`mljg drmndl? "mdugc gc tmnjpl", y gc kgstnccgel "mdugc jn`m`g" yg qun cg nskgcg `n jn`mkmûe ns cg jmsjg ne cls trns nons prmekmpgcns (x, y, z). Cgs iuekmlens metndrg`gs qun usgrnjls ne nstg lkgsmûe sle? lrtfl() kgjnrg() hndume[fgpn() ne`[fgpn() vnrtnx() 

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@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg =7

strlbn() el[trlbn() klclr()

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79.0 Qrlkn`mjmnetl @nskrmpkmûe) 79.0.7 Nqumpl Nqumpl enknsgrml

Kljputg`lrg kle ue smstnjg lpnrgtmvl qun kunetn kle gjhmnetn drçimkl (Tme`lws, Cmeux, ntk…)

79.0.8 Jgtnrmgc Jgtnrmgc `n Gplyl [@B `n ogvg. Netlrel `n `nsgrrlccl Qrlknssmed (M@N).

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79.0.; @nsgrrlccl @nsgrrlccl `n cg Qrçktmkg Nonkutgjls prlknssmed.nxn y ne cg metnrigz sncnkkmlegjls Grkfmvl-5Eunvl y ne cg eunvg vnetgeg nskrmhmjls nc smdumnetn kû`mdl y cls dugr`gjls kljl supnrimkmn;@, Qrlknssmed krngrg ueg kgrpntg pgrg dugr`grcl kljl prlynktl y `netrl `n cg kgrpntg dugr`grg nc kû`mdl iunetn. Wun`ge`l gcjgkneg`l ne cg rutg? ..SQrlknssmedS supnrimkmn;@Ssupnrimkmn;@.p`n

supnrimkmn;@.p`n Q[fgpn icnkfg2 vlm` sntup() { smzn(011, 011, Q;@)2 elImcc()2 } vlm` `rgw() { hgkbdrlue`(811)2 el[trlbn()2 811, 811, -811, -811, 811)2 lrtfl(-811, kgjnrg(>1, >1, >1, 1.1, 1.1, 1.1, 1.1, 7.1, 1.1)2 nons()2 imdurg()2 } vlm` imdurg() { hndme[fgpn()2 imcc(8>>, 1, 1)2 //Nsqumeg Xlog vnrtnx( 81, >1, 1)2 vnrtnx( 81, 91, -;1)2 vnrtnx( 81, 01, -91)2 imcc(1, 8>>, 1)2 //Nsqumeg Ynr`n vnrtnx( 81, >1, -=1)2 vnrtnx( >1, 91, -=1)2 vnrtnx( 61, 01, -=1)2 imcc(1, 1, 8>>)2 //Nsqumeg Gzuc vnrtnx( 771, >1, -=1)2

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

vnrtnx( 771, 91, -91)2 vnrtnx(771, 01, -;1)2 imcc(8>>, 8>>, 1)2 //Nsqumeg Gjgrmccg vnrtnx( 771, >1, 1)2 vnrtnx( 61, 91, 1)2 vnrtnx( >1, 01, 1)2 } ne`[fgpn(KCL[N)2 vlm` nons() { hndme[fgpn(CMEN[)2 strlbn(klclr(8>>, 1, 1))2 // V's vnrtnx(-811, 1, 1)2 vnrtnx( 811, 1, 1)2 strlbn(klclr(1, 8>>, 1))2 // ]°s vnrtnx(1, -811, 1)2 vnrtnx(1, 811, 1)2 strlbn(klclr(1, 1, 8>>))2 // ]°s vnrtnx(1, 1, -811)2 // _°s vnrtnx(1, 1, 811)2 ne`[fgpn()2 }

Nc rnsuctg`l `nc prldrgjg getnrmlr ns cg smdumnetn vnetgeg?

Qçdmeg =8

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg =;

Xntl.

Krnn ue prldrgjg qun `mhuon ueg supnrimkmn `n gc jnels 81 vírtmkns.

79.0.0 Xnplrtn Xnplrtn Gc imegcmzgr ístg prçktmkg nc gcujel `nhnrç dnenrgr ue rnplrtn ne Q@I qun kletnedg nc kû`mdl y cgs pgetgccgs `nc prldrgjg qun mjpcnjnetû. G`njçs, `lkujnetn cgs iuekmlens metndrg`gs qun sn jnekmlege ne nc puetl 79.;

79.> Xnsuctg`ls y Klekcusmlens

Nc gcujel gprnkmgrç cgs vnetgogs `n ueg fnrrgjmnetg `n prldrgjgkmûe jçs gvgezg`g, vmne`l qun pun`n mjpcnjnetgr nsknegs jukfl jçs kljpcnogs kle jnels nsiunrzl.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg =0

Qrgktmkg 74. Êcujmegkmle y jgpnl `n tnxturgs tnx turgs ne nc cnedugon Qrlknssmed 74.7 Metrlùkkmûe

Cg prnsnetn prçktmkg gyu`g g gsmjmcgr cls kletnem`ls `n cg êm`g` MY? Xnccnel, mcujmegkmûe y sljhrng`l, `nc suhtnjg 0.7. Xnccnel `n plcêdlels y 0.8. Jl`ncls hçsmkls `n mcujmegkmûe, `nc prldrgjg `n nstu`mls `n cg jgtnrmg `n Drgimkgkmûe , `nsgrrlccge`l cg kljpntnekmg nspnkêimkg? –Gpcmkg tíkemkgs y fnrrgjmnetgs `n

mcujmegkmûe y sljhrng`l pgrg lhtnenr ue nermqunkmjmnetl vmsugc ne gpcmkgkmlens dnenrgcns‚.

Ne nstg prçktmkg sn qumnrn tljgr vnetgog `n cgs iuekmlens qun lirnkn Qrlknssmed pgrg mcujmegr ueg nskneg y jgpngr ueg tnxturg ne ueg supnrimkmn.

74.8 Lhontmvl Kljpntnekmg)

@mhuogr ueg nsinrg ne ;`, usge`l ueg mjgdne kljl tnxturg. G`njçs, `nimemr ueg iunetn `n cuz qun sn junvg smdumne`l gc gpuetg`lr `nc rgtûe. @n nstg jgenrg sn gprnkmgrç kljl vgrmg nc tlel `n cg supnrimkmn kleilrjn jlvgjls cg iunetn `n cuz. ^sn cgs iuekmlens qun mekcuyn nc Qrlknssmed.

74.; Iue`gjnetl Xnccnel

ê plcêdlel ns ueg rndmûe `nc nspgkml `ncmjmtg`g plr ue kleouetl `n cêengs (grmstgs) y kuyl metnrmlr pun`n nstgr rnccneg`l plr ue klclr l pgtrûe `g`l. Nc gcdlrmtjl `n rnccnel ne prldrgjgs `n `mhuol, krng`l plr [. Igzzmem, rnqumnrn trns pgrçjntrls? ue `nc klclr pgrgsncnkkmleg`l, sustmtumr, y ltrl `nvnz rnccnel. Nc gcdlrmtjl rgstrng tl`lsue clsel`l el`lsmemkmgc, qun snge klclr y g cg kletmduls netrn sê y kle nc memkmgc, y cls sustmtuyn plr nc klclr `n rnccnel. R0Z Pnxturgs

Cg tnxturg ns cg gpgrmnekmg nxtnreg y supnrimkmgc `n cg nstrukturg `n cls jgtnrmgcns, lhontls y klsgs qun els rl`nge. Kuge`l jmrgjls nc jue`l egturgc l nc grtmimkmgc, pl`njls `nskuhrmr `mvnrsgs tnxturgs, kljl plr nonjpcl no njpcl ne cg klrtnzg `n cls cl s çrhlcns, cgs pmn`rgs, cgs pgrn`ns, cls n`mimkmls, ntk., y ne elsltrls jmsjls `nskuhrmjls tnxturg kuge`l els pgcpgjls cg pmnc, nc pncl, eunstrgs rlpgs y zgpgtls. Cg tnxturg pun`n snr ûptmkg l vmsugc, kuge`l cgs `minrnekmgs ne cg supnrimkmn sûcl pun`ne snr kgptg`gs plr nc lol, pnrl el rnsple`ne gc tgktl. Gsmjmsjl, cg tnxt tnxturg urg pun`n snr tçktmc kuge`l sn prnsnetge `minrnekmgs qun rnsple`ne, g cg vnz, gc tgktl y g cg vmstg.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg =>

Nc jgpng`l `n tnxturgs nstghcnkn kûjl sn smtÿg cg tnxturg slhrn nc lhontl gc jljnetl `n prlynktgrsn. Gcduegs tnxturgs sle trm`mjnesmlegcns y plr cl dnenrgc el enknsmtge ue jgpng`l `ntgccg`l yg qun el sn vnrçe nxgktgjnetn `nilrjgkmlens l mjpnrinktls. R0Z Mcujmegkmûe y sljhrng`l

Qun`ne lhtnenrsn mjçdnens rngcmstgs `n ueg nskneg dnenrge`l prlynkkmlens ne pnrspnktmvg `n cls lhontls y gpcmkge`l ninktls `n mcujmegkmûe egturgcns g cgs supnrimkmns vmsmhcns. [n utmcmzg ue jl`ncl `n mcujmegkmûe, tgjhmíe `neljmeg`l jl`ncl `n sljhrng`l, pgrg kgckucgr nc klclr `n kg`g plsmkmûe mcujmeg`g ne cg supnrimkmn `n ue lhontl. ê jítl`l `n rnprnsnetgkmûe supnrimkmgc utmcmzg cls kçckucls `n klclr `nc jl`ncl `n mcujmegkmûe pgrg `ntnrjmegr cls klclrns `n cls pêxncns pgrg tl`gs cgs plsmkmlens prlynktg`gs `n ueg nskneg. Nc jl`ncl `n mcujmegkmûe pun`n gpcmkgrsn g kg`g plsmkmûe `n prlynkkmûe, l hmne pun`n ccnvgrsn g kghl cg rnprnsnetgkmûe `n cg supnrimkmn metnrplcge`l cls klclrns `n cgs supnrimkmns g pgrtmr `n ue pnqun÷l kleouetl `n kçckucls rncgtmvls gc jl`ncl `n mcujmegkmûe. Netrn ltrgs klsgs, nc iltlrrngcmsjl ne cls drçimkls plr kljputg`lrg rnqumnrn `ls ncnjnetls? rnprnsnetgkmlens prnkmsgs `n cgs prlpmn`g`ns `n cgs supnrimkmns y ueg huneg `nskrmpkmûe iêsmkg `n cls ninktls `n mcujmegkmûe ne cg nskneg. Nstls ninktls `n mcujmegkmûe `n cgs supnrimkmns mekcuyne cg rnicnxmûe `n cg cuz, cg trgespgrnekmg, cgs tnxturgs `n cgs supnrimkmns y cgs sljhrgs. Ne dnenrgc, nc jl`ncg`l `n cls ninktls `n mcujmegkmûe qun pl`njls lhsnrvgr slhrn ue lhontl ns ue prlknsl juy kljpcnol, ne nc qun metnrvmnene prmekmpmls tgetl `n cg iêsmkg kljl `n cg psmklcldêg. R0Z Cgs kcgsns y iuekmlens metndrg`gs qun usgrnjls ne nstg lkgsmûe sle? 



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QMjgdn Q[fgpn spfnrn@ntgmc() clg`Mjgdn() krngtn[fgpn() `mrnktmlegcCmdft() spltCmdft() sfgpn()

74.0 Qrlkn`mjmnetl @nskrmpkmûe) 74.0.7 Nqumpl Nqumpl enknsgrml Kljputg`lrg kle ue smstnjg lpnrgtmvl qun kunetn kle gjhmnetn drçimkl (Tme`lws, Cmeux, ntk…)

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg =9

74.0.8 Jgtnrmgc Jgtnrmgc `n Gplyl [@B `n ogvg. Netlrel `n `nsgrrlccl Qrlknssmed (M@N).

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74.0.; @nsgrrlccl @nsgrrlccl `n cg Qrçktmkg Nonkutgjls prlknssmed.nxn y ne cg metnrigz sncnkkmlegjls Grkfmvl-5Eunvl y ne cg eunvg vnetgeg nskrmhmjls nc smdumnetn kû`mdl y cls dugr`gjls kljl mcujmegkmleJgpnl , Qrlknssmed krngrg ueg kgrpntg pgrg dugr`grcl kljl prlynktl y `netrl `n cg kgrpntg dugr`grg nc kû`mdl iunetn. Wun`ge`l gcjgkneg`l ne cg rutg? ..SQrlknssmedSmcujmegkmleJgpnlSmcujmegkmleJgpnl.p`n

Kû`mdl? QMjgdn cldl2 Q[fgpn nsinrg2 vlm` sntup() { smzn(>11, >11, Q;@)2 el[trlbn()2 spfnrn@ntgmc(711)2 cldl : clg`Mjgdn("cg`rmccl.opd")2 nsinrg : krngtn[fgpn([QFNXN, 7>1)2 nsinrg.sntPnxturn(cldl)2 } vlm` `rgw() { hgkbdrlue`(klclr(;1, 711, 761))2 // Cmdft tfn hlttlj li tfn spfnrn `mrnktmlegcCmdft(61, 781, 701, 1, 1, -7)2 // Fgkn qun nc puetl `n cuz smdg gc puetnrl `nc rgtûe spltCmdft(718, 7>;, 810, jlusnV, jlusn], 911, 1, 1, -7, QM/8, 911)2 trgescgtn(8>1, 8>1, 1)2 sfgpn(nsinrg)2 }

Nc rnsuctg`l `nc prldrgjg getnrmlr ns cg smdumnetn vnetgeg?

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg =4

Xntl.

Krnn ue prldrgjg qun jgpnn ueg supnrimkmn `n pgstl y g`njçs `nimeg trns iunetns `n cuz `n klclr `mstmetl qun sn `mstrmhuyge slhrn cg nsinrg.

74.0.0 Xnplrtn Xnplrtn Gc imegcmzgr ístg prçktmkg nc gcujel `nhnrç dnenrgr ue rnplrtn ne Q@I qun kletnedg nc kû`mdl y cgs pgetgccgs `nc prldrgjg qun mjpcnjnetû. G`njçs, `lkujnetn cgs iuekmlens metndrg`gs qun sn jnekmlege ne nc puetl 74.;

74.> Xnsuctg`ls y Klekcusmlens

Nc gcujel gprnkmgrç cgs vnetgogs `n ueg fnrrgjmnetg `n prldrgjgkmûe jçs gvgezg`g, vmne`l qun pun`n mjpcnjnetgr nsknegs jukfl jçs kljpcnogs kle jnels nsiunrzl.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg =6

Qrg ktmkg 76. Gemjgkml Gemjgkml e smjpcn ne nc Qrg cnedugon Qrlknssmed 76.7 Metrlùkkmûe

Cg prnsnetn prçktmkg gyu`g g gsmjmcgr cls kletnem`ls `n cg êm`g` Y? Metrlùkkmûe g cg gemjgkmûe plr kljputg`lrg. `nc suhtnjg >.0. Gemjgkmûe 8@ l ;@ kletrlcg`g prldrgjg `n nstu`mls `n cg jgtnrmg `n Drgimkgkmûe, `nsgrrlccge`l plr nc usugrml, `nc prldrgjg cg kljpntnekmg nspnkêimkg? –Klelkn nc usl `n tíkemkgs `n gemjgkmûe ne 8@ y ;@ ne

cls kletnxtls `n gemjgkmûe drçimkg y rngcm`g` vmrtugc klesm`nrge`l cls gspnktls jgtnjçtmkls hçsmkls y cgs tíkemkgs `n prldrgjgkmûe ‚.

76.8 Lhontmvl Kljpntnekmg)

Ne nstg prçktmkg gpcmkgrnjls trgesilrjgkmlens suknsmvgs pgrg krngr cg mcusmûe `n gemjgkmûe gc prldrgjg rngcmzg`l ne cg prçktmkg 74. ^sn cgs iuekmlens qun mekcuyn nc Qrlknssmed.

76.; Iue`gjnetl Gemjgkmûe

Nc tírjmel gemjgkmûe plr kljputg`lrg sn rnimnrn g kugcqumnr snkunekmg tnjplrgc `le`n sn gprnkmne kgjhmls vmsugcns ne ueg mjgdne. G`njçs `n kgjhmgr cgs plsmkmlens `n cls lhontls jn`mgetn trgscgkmlens l rltgkmlens, ueg gemjgkmûe dnenrg`g plr kljputg`lrg pun`n jlstrgr vgrmgkmlens tnjplrgcns qun ginktne gc tgjg÷l `n cls lhontls, g su klclr, g su trgespgrnekmg l g cgs tnxturgs supnrimkmgcns. Pgjhmíe pl`njls dnenrgr gemjgkmlens plr kljputg`lrg vgrmge`l pgrçjntrls `n cg kçjgrg, kljl cg plsmkmûe, cg lrmnetgkmûe l cg `mstgekmg ilkgc. ] cgs vgrmgkmlens ne cls ninktls `n mcujmegkmûe u ltrls pgrçjntrls y prlkn`mjmnetls gslkmg`ls kle cg mcujmegkmûe rnprnsnetgkmûe gemjgkmlens yplrcgkljputg`lrg. R0Z`n nsknegs pun`ne usgrsn tgjhmíe pgrg prlùkmr Cgs iuekmlens metndrg`gs qun usgrnjls ne nstg lkgsmûe sle? lrtfl() kgjnrg() hndume[fgpn() ne`[fgpn() vnrtnx() strlbn() el[trlbn() klclr() 

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@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg ==

76.0 Qrlkn`mjmnetl @nskrmpkmûe) 76.0.7 Nqumpl Nqumpl enknsgrml Kljputg`lrg kle ue smstnjg lpnrgtmvl qun kunetn kle gjhmnetn drçimkl (Tme`lws, Cmeux, ntk…)

76.0.8 Jgtnrmgc Jgtnrmgc `n Gplyl

[@B `n ogvg. Netlrel `n `nsgrrlccl Qrlknssmed (M@N).

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76.0.; @nsgrrlccl @nsgrrlccl `n cg Qrçktmkg Qrmjnrl klesndumjls ueg mjgdne ped l opd pgrg usgrcg kljl tnxturg, ne nstg prçktmkg usgjls cg`rmccl.opd , qun sn junstrg g kletmeugkmûe.

Nonkutgjls prlknssmed.nxn y ne cg metnrigz sncnkkmlegjls Grkfmvl-5Eunvl y ne cg eunvg vnetgeg nskrmhmjls nc smdumnetn kû`mdl y cls dugr`gjls kljl supnrimkmn;@, Qrlknssmed krngrg ueg kgrpntg pgrg dugr`grcl kljl prlynktl y `netrl `n cg kgrpntg dugr`grg nc kû`mdl iunetn. Wun`ge`l gcjgkneg`l ne cg rutg? ..SQrlknssmedSgemjgkmle[mjpcnSgemjgkmle[mjpcn.p`n

QMjgdn cldl2 Kû`mdl? Q[fgpn nsinrg2 iclgt geducl:12 // Ne rg`mgens vlm` sntup() { smzn(>11, >11, Q;@)2 el[trlbn()2 spfnrn@ntgmc(711)2 cldl : clg`Mjgdn("cg`rmccl.opd")2 nsinrg : krngtn[fgpn([QFNXN, 7>1)2 nsinrg.sntPnxturn(cldl)2 } vlm` `rgw() { hgkbdrlue`(klclr(;1, 711, 761))2 // Cmdft tfn hlttlj li tfn spfnrn `mrnktmlegcCmdft(61, 781, 701, 1, 1, -7)2

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 711

// Fgkn qun nc puetl `n cuz smdg gc puetnrl `nc rgtûe spltCmdft(718, 7>;, 810, jlusnV, jlusn], 911, 1, 1, -7, QM/8, 911)2

trgescgtn(8>1, 8>1, 1)2 rltgtn](geducl)2 // Dmrg slhrn sm jmsjl geducl+:1.1;2 trgescgtn(91, 1, 1)2 // [n junvn slhrn nc non V sfgpn(nsinrg)2 }

Nc rnsuctg`l `nc prldrgjg getnrmlr ns cg smdumnetn vnetgeg?

Xntl.

Jl`mimqun nc prldrgjg `n cg prgktmkg 79 pgrg qun nc pcgel dmrn ne tlrel `nc non ].

76.0.0 Xnplrtn Xnplrtn Gc imegcmzgr ístg prçktmkg nc gcujel `nhnrç dnenrgr ue rnplrtn ne Q@I qun kletnedg nc kû`mdl y cgs pgetgccgs `nc prldrgjg qun mjpcnjnetû. G`njçs, `lkujnetn cgs iuekmlens metndrg`gs qun sn jnekmlege ne nc puetl 79.;

76.> Xnsuctg`ls y Klekcusmlens

Nc gcujel gprnkmgrç cgs vnetgogs `n ueg fnrrgjmnetg `n prldrgjgkmûe jçs gvgezg`g, vmne`l qun pun`n mjpcnjnetgr nsknegs jukfl jçs kljpcnogs kle jnels nsiunrzl.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 717

Hmhcmldrgiêg

R7Z Pnkelcûdmkl Egkmlegc `n Jíxmkl. Qrldrgjg `n nstu`mls `n Drgimkgkmûe. Plcukg, Plcukg, Jíxmkl? s.e., inhrnrl `n 8170. R8Z ‐ . Xntêkucg `n cg kgrrnrg `n mednemnrêg ne smstnjgs kljputgkmlegcns M[MK-8171880. Kmu`g` `n Jíxmkl, Jíxmkl? s.e., 8179. R;Z FNGXE, @legc` & J. Qgucmen Hgbnr, Drçimkgs plr kljputg`lrg 8ª n`mkmûe, N`. Qrnetmkn Fgcc Fmspgelgjnrmkgeg. Jíxmkl R0Z ILCN], Ogjns & Ge`rmns Yge @gj, Metrlùkkmûe g cg drgimkgkmûe plr kljputg`lr, N`. G``msle Tnscny Mhnrlgjnrmkgeg, 7==9 R>Z Fnreçe`nz, Krmstlpfnr Nùgr`l Xlol. DXGIMKGKMÛE. Gcdlrmtjls @@G y Hrnsnefgj. RNe cêengZ 70 `n gdlstl `n 8174. fttps?//drgimkgkmle8174.wlr`prnss.klj/8174/16/70/gcdlrmtjls-``g-y-hrnsnefgj/. R9Z Kísgr, Jgrêe Cûpnz. @LKQCG]NX. Xÿhrmkg pgrg Nvgcugkmûe `n Qrlynktls `n Qrldrgjgkmûe (Jl`ncl P). RNe cêengZ fttps?//`lkpcgynr.ns/7909>;81-Xuhrmkg pgrg-nvgcugkmle-`n-prlynktls-`n-prldrgjgkmle-jl`ncl-t-kmnekmg-tnkelcldmg pgrg-nvgcugkmle-`n-prl ynktls-`n-prldrgjgkmle-jl`ncl-t-kmnekmg-tnkelcldmg-yygjhmnetn-`npgrtgjnetl-gkg`njmkl-`nsgrrlccl-tnkelcldmkl.ftjc. ÊGJ. plrtgcgkg`njmkl.kkf.uegj.jx. X^HXMKG QGXG NYGC^GX NC R4Z XNQLXPN @N CG QXÇKPMKG. RNe cêengZ fttps?//plrtgcgkg`njmkl.kkf.uegj.jx/jgtnrmgcns/prli/jgt`m`gk/smtprl/nxp/qumj/q umj8/qumjmkMM/>8>>08>80=0;07>i>107>807>i0>>9070k>>07>8>i0>0k>i>80>>10i >8>00>>i000>>i0k07>i>i>1>8k;670;>00=0;07.pì. R6Z Nvgcugkmûe `n prçktmkgs `n prldrgjgkmûe jn`mgetn rÿhrmkgs ne Jll`cn. Ygkg, Ouge Jgeunc, Gdu`l, O, Nermqun y [çekfnz, Fíktlr. Lvmn`l? s.e., 77 `n oucml `n 8170, Gktgs `n cgs VV ONE^M, pçds. 714-770. R=Z GKG@NJMK. Nekmkclpn`mg êmvnrsgc. Hmhcmltnkg (prldrgjgkmûe). RNe cêengZ 8178. fttp?//nekmkclpn`mg\uemvnrsgc.nsgkg`njmk.klj/4987>/Hmhcmltnkg\%86prldrgjgkm %K;%H;e%8=. R71Z ol dgj p. Ogvgℨ Hme`med ilr tfn LpneDC® GQM. RNe cêengZ fttp?//oldgjp.lrd/oldc/www/.Pfn

LpneDC Drgpfmks [ystnj? G [pnkmimkgtmle (Ynrsmle ;.1 - [nptnjhnr 8;, 8116) R77Z [ndgc, Jgrb y Gbncny, Burt. Pfn LpneDC Drgpfmks [ystnj? G [pnkmimkgtmle. 8; `n snptmnjhrn `n 8116. R78Z Iunetns Xgjls, Qghcl. DNLJNPXÊG GEGCÊPMKG. NK^GKMLEN[ QGXGJÍPXMKG[. RNe cêengZ fttps?//nxpn`mnetn.uns.nù.sv/umu/ncnjnetls\nstu`ml/jgtnjgtmkg/Onsus%81Meigetn %81Jurmccl%81%81Dnljntrmg%81Gegcmtmkg/71.%81Nkugkmlens%81Qgrgjntrmkgs.pì.81Dnljntrm g%81Gegcmtmkg/71.%81Nkugkmlens%81Qgrgjntrmkgs.pì R7;Z Iry, Hne y Xngs, Kgsny. Qrlknssmed. RNe cêengZ fttps?//prlknssmed.lrd/.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 718

Genxll G. Xu Genx Xu hrmkg Qgrg cg nvgcugkmûe `n nstg prçktmkg sn rnkljmne`g cg smdumnetn rÿhrmkg R9ZR4ZR6Z, qun tmnen ueg nskgcg `n 7% g 711%. Krmtnrmls

@lkujnetl

Kl`mimkgkmûe

Iuekmlegjmnetl

@nimkmnetn

Xnducgr

7% g >% Nc `lkujnetl el kujpcn kle cg nstrukturg y ilrjgtl nxpcmkmtg`l plr nc `lknetn. 7% g 4% ^tmcmzg mestrukkmlens y gcdlrmtjls qun el

9% g 71% Nc `lkujnetl kujpcn kle cg nstrukturg y ilrjgtl nxpcmkmtg`l plr nc `lknetn. 6% g 7>% ^tmcmzg mestrukkmlens y gcdlrmtjls qun el sle gklr`ns pgrg

rnsuncvne nc nonrkmkml.

rnslcvnr nc nonrkmkml.

7% g 78% El iuekmleg.

7;% g 80% Nc iuekmlegjmnetl iuekmlegjmnetl tmnen igccls mjplrtgetns.

Hunel

Juy Hunel

77% g 7>% G`njçs, el tmnen nrrlrns lrtldrçimkls y drgjgtmkgcns.

79% g 81% G`njçs, nstç hmne rn`gktg`l y tmnen klfnrnekmg `n kletnem`l.

79% g 8;% ^tmcmzg cgs mestrukkmlens y gcdlrmtjls enknsgrmls pgrg rnslcvnr nc

80% g ;1% ^tmcmzg cgs mestrukkmlens y gcdlrmtjls jçs g`nkug`ls pgrg rnslcvnr

nonrkmkml, guequn el sle cls jçs g`nkug`ls. 8>% g ;4% Nc iuekmlegjmnetl iuekmlegjmnetl tmnen igccls sme mjplrtgekmg.

nc nonrkmkml. ^sg hunegs prçktmk prçktmkgs gs `n kl`mimkgkmûe. ;6% g >1% Nc iuekmlegjmnetl iuekmlegjmnetl ns kljpcntl.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 71;

Genxl H. Qcgetmccg `nc rnplrtn `n prgktmkgs. QXÇKPMKG REÿjnrl`np REÿjnrl`nprçktmkgZ.REljh rçktmkgZ.REljhrn`ncgprç rn`ncgprçktmkgZ ktmkgZ Cudgr? REljhrn `nc cghlrgtlrmlZ @urgkmûe? RPltgc `n snsmlens `n e flrgsZ Drupl? RJgtnrmg, flrg, g÷l/jns, QrlinslrZ Metndrgetns? RCmstg `n cls gcujels qun rngcmzgrle cg prçktmkgZ

7. Metrlùkkmûe 8. Lhontmvl Kljpntnekmg) ;. Iue`gjnetl 0. Qrlkn`mjmnetl @nskrmpkmûe) 0.7 Nqumpl enknsgrml 0.8 Jgtnrmgc `n Gplyl 0.; @nsgrrlccl `n cg Qrçktmkg 0.0 Kçckucls y rnplrtn >. Xnsuctg`ls y Klekcusmlens 9. Genxls 4. Hmhcmldrgiêg

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 710

Genxl K. Xndcgjnet Genxl Xndcgjnetll metnrel pgrg nc usl `n cghlrgtlrmls. Kle cg imegcm`g` `n lptmjmzgr `nc Cghlrgtlrml y gkgtge`l cls cmengjmnetls `n eunstrgs gutlrm`g`ns, fgknjls nc`nusl su klelkmjmnetl nc smdumnetn? XNDCGJNEPL LHCMDGKMLEN[ @N CL[ GC^JEL[?

7. Wun`g nstrmktgjnetn prlfmhm`l metrlùkmr gcmjnetls l hnhm`gs gc cghlrgtlrml (mekcuyne`l ùckns y kfmkcns). 8. @urgetn su pnrjgenekmg ne nc cghlrgtlrml `nhnrçe jlstrgr su kucturg el prlimrmne`l pgcghrgs lhsknegs y el `noge`l pgpncns l hgsurg ne cgs j jnsgs nsgs l pmsl. ;. Wun`g nstrmktgjnetn prlfmhm`l utmcmzgr nc cghlrgtlrml pgrg nstu`mgr l ncghlrgr tgrngs, yg qun cgs sgcgs nstçe prldrgjg`gs ÿemkgjnetn pgrg kcgsns, kursls l prçktmkgs. Qgrg nstu`mgr y ncghlrgr tgrngs nc Knetrl `n Meilrjgkmûe sn nekunetrg `nhm`gjnetn nqumpg`l pgrg nstls imens 0. G cls gcujels qun el tnedge kcgsn, kursl l prçktmkg ne nc cghlrgtlrml, cns qun`g nstrmktgjnetn prlfmhm`l nc gkknsl g `mkfg çrng. ßemkgjnetn pun`ne netrgr gc cghlrgtlrml sm nc jgnstrl nstç prnsnetn, yg qun íc ns nc rnsplesghcn `nc drupl. >. Gc tírjmel `n sus kcgsns, kursls l prçktmkgs, ns lhcmdgkmûe `n tl`ls cls usugrmls gpgdgr cgs kljputg`lrgs (KQ^, jlemtlr) y gkljl`gr cgs smccgs ne su cudgr (ueg ( ueg plr kljputg`lrg y cgs rnstgetns knrkg `n cg pgrn`). 9. Qlr emedÿe jltmvl pun`ne `nsklenktgr cls kghcns `n cg kljputg`lrg l `n cls pnrmiírmkls qun sn cns gsmdeû. 4. Ne kgsl `n qun el iuekmlen klrrnktgjnetn nc jlusn, kghcns, tnkcg`l l KQ^, rnplrtgrcl mejn`mgtgjnetn gc jgnstrl, yg qun ustn`ns sle rnsplesghcns `n cgs kljputg`lrgs qun sn cns gsmdeû `ns`n ue prmekmpml, (pgrg qun ístn g su vnz els cl fgdg sghnr y grrndcgr nc prlhcnjg). 6. Cls gcujels prnstgetns `nc [nrvmkml [lkmgc kujpcne kle ueg iuekmûe nekljne`g`g plr cgs gutlrm`g`ns plrg cl cgs plsmhcns rnkcgjgkmlens fgknrcgs cls usugrmls nsklcgrns, `mrnktgjnetn clstgetl, kllr`meg`lrns `nc cghlrgtlrml, plr `nhnrçe emedÿe jltmvl sus kljpg÷nrls `n [nrvmkml [lkmgc tlcnrgrçe ue trgtl meoustmimkg`l. =. [me nxknpkmûe, kugcqumnr usugrml qun sng slrprne`m`l mestgcge`l oundls, utmcmzge`l cls oundls yg mestgcg`ls, hlrrge`l l gctnrge`l cg meilrjgkmûe qun kletnedge cgs jçqumegs, gsê kljl `nsklenktçe`lcgs l fgkmne`l usl me`nhm`l `n nccgs, snrç suspne`m`l `nimemtmvgjnetn `nc cghlrgtlrml, y snrç rnplrtg`l g cgs gutlrm`g`ns nsklcgrns pgrg qun sng sgekmleg`l `n gkunr`l gc rndcgjnetl `nc Mestmtutl. Ns enknsgrml rnklr`gr qun nstgjls ilrjge`l gcujels g ue emvnc prlinsmlegc y qun nc nsiunrzl `n cg Mestmtukmûe g qun pnrtnenknjls ns trghgol `n jukfgs dnenrgkmlens, plr cl kugc tn pn`mjls els gyu`ns g klesnrvgr pgrg tu prlpml hnenimkml ne nc jnolr nstg`l, cg meirgnstrukturg `n qun `msplen nc Mestmtutl Pnkelcûdmkl `n [ge Cums Qltlsê.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 71>

ME[PMP^PL PNKELCÛDMKL @N [GE C^M[ QLPL[Ê

@NQGXPGJNEPL @N [M[PNJG[ ] KLJQ^PGKMÛE KGXXNXG? Mednemnrêg ne [mstnjgs Kljputgkmlegcns

QXÇKPMKG[ @N JGE^GC @N QXÇKPMKG[ @N CG JGPNXMG? JGPNXMG? Qrldrgjgkmûe Lrmnetg`g g Lhontls ELJHXN @NC G^PLX? QN@XL DGXKÊG D^NXXNXL EßJNXL @N @MKPGJNE? G[-8-8;=/8176 QCGE @N N[P^@ML[? M[MK-8171-880 KCGYN @N CG G[MDEGP^XG? [K@-7181

[LCN@G@ @N DXGKMGEL [ÇEKFN_, [.C.Q., G 17 @N GDL[PL @NC 817=

Kletnem`l LHONPMYL DNENXGC @NC JGE^GC .......................................................................................................... 9 LHONPMYL DNENXGC @N CG JGPNXMG ..................................................................................................... 9 KLJQNPNEKMG[[ N[QNKÊIMKG[ G @N[GXXLCCGX ................................................................................... 9 KLJQNPNEKMG ^PMCM@G@ @NC JGE^GC ........................................................................................................................... 9 QXÇKPMKG 7. MEPXL@^KKMÛE G ^JC ................................................................................................... 4 7.7 7.8 7.; 7.0 7.0.7 7.0.8 7.0.; 7.0.0 7.>

MEPXL@^KKMÛE .............. ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ ................ .. 4 ........................... ............................ ............................ ............................. ............................. ............................ ........................... ............. 4 LHONPMYL KLJQNPNEKMG ) ............. IÊ@GJNEPL .............. ............................ ............................. ............................. ............................ ............................ ............................ ............................ ............................ .................. .... 4 QXLKN@MJMNEPL @N[KXMQKMÛE ) ............. ........................... ............................ ............................ ............................ ............................ ............................ .................. .... 6 .......................... ........................... ............................ ............................. ............................. ............................ ............................ ........................... ............. 6 NW^MQL ENKN[GXML ............. JGPNXMGC @N GQL]L ............. ........................... ............................ ............................ ............................ ............................ ............................ ............................ ....................... ......... 6 @N[GXXLCCL @N CG QXÇKPMKG ............. ........................... ............................ ............................ ............................ ............................ ............................. ....................... ........ = NQLXPN .............. ............................ ............................ ............................ ............................. ............................. ............................ ............................ ............................ ......................... ........... 7= X NQLXPN XN[^CPG@L[ ] KLEKC^[MLEN[ ............. ........................... ............................. ............................. ............................ ............................ ............................ .................. .... 7=

QXÇKPMKG 8. MJQCNJNEPGKMÛE @N ÊG KCG[N NE ENPHNGE[ ................................................... 81 8.7 8.8 8.; 8.0 8.0.7 8.0.8 8.0.; 8.0.0 8.>

MEPXL@^KKMÛE .............. ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ .............. 81 LHONPMYL KLJQNPNEKMG) ............. ........................... ............................ ............................ ............................. ............................. ............................ ......................... ........... 81 IÊ@GJNEPL .............. ............................ ............................. ............................. ............................ ............................ ............................ ............................ ............................ ................ .. 81 QXLKN@MJMNEPL @N[KXMQKMÛE ) ............. ........................... ............................ ............................ ............................ ............................ ............................ ................ .. 87 NW^MQL ENKN[GXML ............. .......................... ........................... ............................ ............................. ............................. ............................ ............................ ......................... ........... 87 JGPNXMGC @N GQL]L ............. ........................... ............................ ............................ ............................ ............................ ............................ ............................ ..................... ....... 87 @N[GXXLCCL @N CG QXÇKPMKG ............. ........................... ............................ ............................ ............................ ............................ ............................. ..................... ...... 87 X NQLXPN NQLXPN .............. ............................ ............................ ............................ ............................. ............................. ............................ ............................ ............................ ......................... ........... 86 XN[^CPG@L[ ] KLEKC^[MLEN[ ............. ........................... ............................. ............................. ............................ ............................ ............................ .................. .... 86

................................. ..................... .......... 8= QXÇKPMKG ;. MJQCNJNEPGKMÛE @N KLEKNQPL[ HÇ[MKL[ @N QLL. ......................

;.7 ;.8 ;.; ;.0 ;.0.7 ;.0.8 ;.0.; ;.0.0 ;.>

MEPXL@^KKMÛE .............. ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ .............. 8= LHONPMYL KLJQNPNEKMG ) ............. ........................... ............................ ............................ ............................. ............................. ............................ ......................... ........... 8= IÊ@GJNEPL .............. ............................ ............................. ............................. ............................ ............................ ............................ ............................ ............................ ................ .. 8= QXLKN@MJMNEPL @N[KXMQKMÛE ) ............. ........................... ............................ ............................ ............................ ............................ ............................ ................ .. ;1 .......................... ........................... ............................ ............................. ............................. ............................ ............................ ......................... ........... ;1 NW^MQL ENKN[GXML ............. JGPNXMGC @N GQL]L ............. ........................... ............................ ............................ ............................ ............................ ............................ ............................ ..................... ....... ;1 ........................... ............................ ............................ ............................ ............................ ............................. ..................... ...... ;1 @N[GXXLCCL @N CG QXÇKPMKG ............. NQLXPN .............. X NQLXPN ............................ ............................ ............................ ............................. ............................. ............................ ............................ ............................ ......................... ........... ;; XN[^CPG@L[ ] KLEKC^[MLEN[ ............. ........................... ............................. ............................. ............................ ............................ ............................ .................. .... ;;

QXÇKPMKG 0. O^NDL @N PXN[ NE XG]G (DGPL). .............................................................................. ;0 0.7 0.8 0.;

MEPXL@^KKMÛE .............. ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ .............. ;0 ........................... ............................ ............................ ............................. ............................. ............................ ......................... ........... ;0 LHONPMYL KLJQNPNEKMG ) ............. ............................ ............................. ............................. ............................ ............................ ............................ ............................ ............................ ................ .. ;0 IÊ@GJNEPL ..............

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg mm

0.0 0.0.7 0.0.8 0.0.; 0.0.0 0.>

QXLKN@MJMNEPL @N[KXMQKMÛE ) ............. ........................... ............................ ............................ ............................ ............................ ............................ ................ .. ;0 .......................... ........................... ............................ ............................. ............................. ............................ ............................ ......................... ........... ;0 NW^MQL ENKN[GXML ............. JGPNXMGC @N GQL]L ............. ........................... ............................ ............................ ............................ ............................ ............................ ............................ ..................... ....... ;0 @N[GXXLCCL @N CG QXÇKPMKG ............. ........................... ............................ ............................ ............................ ............................ ............................. ..................... ...... ;> NQLXPN .............. ............................ ............................ ............................ ............................. ............................. ............................ ............................ ............................ ......................... ........... 09 X NQLXPN ........................... ............................. ............................. ............................ ............................ ............................ .................. .... 09 XN[^CPG@L[ ] KLEKC^[MLEN[ .............

QXÇKPMKG >. ^[L @N FNXNEKMG. ........................................................................................................ 04 >.7 >.8 >.; >.0 >.0.7 >.0.8 >.0.; >.0.0 >.>

MEPXL@^KKMÛE .............. ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ .............. 04 LHONPMYL KLJQNPNEKMG) ............. ........................... ............................ ............................ ............................. ............................. ............................ ......................... ........... 04 ............................ ............................. ............................. ............................ ............................ ............................ ............................ ............................ ................ .. 04 IÊ@GJNEPL .............. QXLKN@MJMNEPL @N[KXMQKMÛE ) ............. ........................... ............................ ............................ ............................ ............................ ............................ ................ .. 06 NW^MQL ENKN[GXML ............. .......................... ........................... ............................ ............................. ............................. ............................ ............................ ......................... ........... 06 ........................... ............................ ............................ ............................ ............................ ............................ ............................ ..................... ....... 06 JGPNXMGC @N GQL]L ............. @N[GXXLCCL @N CG QXÇKPMKG ............. ........................... ............................ ............................ ............................ ............................ ............................. ..................... ...... 06 X NQLXPN NQLXPN .............. ............................ ............................ ............................ ............................. ............................. ............................ ............................ ............................ ......................... ........... >8 ........................... ............................. ............................. ............................ ............................ ............................ .................. .... >8 XN[^CPG@L[ ] KLEKC^[MLEN[ .............

QXÇKPMKG 9. IGKP^XG[ NE ÊG _GQGPNXÊG (FNXNEKMG 8). ....................................................... >; 9.7 9.8 9.; 9.0 9.0.7 9.0.8 9.0.; 9.0.0 9.>

MEPXL@^KKMÛE .............. ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ .............. >; LHONPMYL KLJQNPNEKMG ) ............. ........................... ............................ ............................ ............................. ............................. ............................ ......................... ........... >; IÊ@GJNEPL .............. ............................ ............................. ............................. ............................ ............................ ............................ ............................ ............................ ................ .. >; QXLKN@MJMNEPL @N[KXMQKMÛE ) ............. ........................... ............................ ............................ ............................ ............................ ............................ ................ .. >> NW^MQL ENKN[GXML ............. .......................... ........................... ............................ ............................. ............................. ............................ ............................ ......................... ........... >> JGPNXMGC @N GQL]L ............. ........................... ............................ ............................ ............................ ............................ ............................ ............................ ..................... ....... >> ........................... ............................ ............................ ............................ ............................ ............................. ..................... ...... >9 @N[GXXLCCL @N CG QXÇKPMKG ............. NQLXPN .............. X NQLXPN ............................ ............................ ............................ ............................. ............................. ............................ ............................ ............................ ......................... ........... 9; XN[^CPG@L[ ] KLEKC^[MLEN[ ............. ........................... ............................. ............................. ............................ ............................ ............................ .................. .... 9;

QXÇKPMKG 4. DNENXGKMÛE ] GQCMKGKMÛE @N NVÇJNEN[ (FNXNEKMG ;). ..................... ................................ ............. 9 90 0

4.7 4.8 4.; 4.0 4.0.7 4.0.8 4.0.; 4.0.0 4.>

MEPXL@^KKMÛE .............. ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ .............. 90 LHONPMYL KLJQNPNEKMG ) ............. ........................... ............................ ............................ ............................. ............................. ............................ ......................... ........... 90 IÊ@GJNEPL .............. ............................ ............................. ............................. ............................ ............................ ............................ ............................ ............................ ................ .. 90 QXLKN@MJMNEPL @N[KXMQKMÛE ) ............. ........................... ............................ ............................ ............................ ............................ ............................ ................ .. 9> NW^MQL ENKN[GXML ............. .......................... ........................... ............................ ............................. ............................. ............................ ............................ ......................... ........... 9> ........................... ............................ ............................ ............................ ............................ ............................ ............................ ..................... ....... 9> JGPNXMGC @N GQL]L ............. @N[GXXLCCL @N CG QXÇKPMKG ............. ........................... ............................ ............................ ............................ ............................ ............................. ..................... ...... 9> X NQLXPN NQLXPN .............. ............................ ............................ ............................ ............................. ............................. ............................ ............................ ............................ ......................... ........... 4> XN[^CPG@L[ ] KLEKC^[MLEN[ ............. ........................... ............................. ............................. ............................ ............................ ............................ .................. .... 4>

QXÇKPMKG 6. MEPXL@^KKMÛE GC ^[L @N MEPNXIGKN[. ................................................................. 49 6.7 6.8 6.; 6.0

MEPXL@^KKMÛE .............. ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ .............. 49 LHONPMYL KLJQNPNEKMG ) ............. ........................... ............................ ............................ ............................. ............................. ............................ ......................... ........... 49 IÊ@GJNEPL .............. ............................ ............................. ............................. ............................ ............................ ............................ ............................ ............................ ................ .. 49 ........................... ............................ ............................ ............................ ............................ ............................ ................ .. 44 QXLKN@MJMNEPL @N[KXMQKMÛE ) .............

.......................... ........................... ............................ ............................. ............................. ............................ ............................ ......................... ........... 44 6.0.7 NW^MQL ENKN[GXML ............. 6.0.8 JGPNXMGC @N GQL]L ............. ........................... ............................ ............................ ............................ ............................ ............................ ............................ ..................... ....... 44 ........................... ............................ ............................ ............................ ............................ ............................. ..................... ...... 44 6.0.; @N[GXXLCCL @N CG QXÇKPMKG .............

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg mmm

6.0.0 X NQLXPN NQLXPN .............. ............................ ............................ ............................ ............................. ............................. ............................ ............................ ............................ ......................... ........... 68 ........................... ............................. ............................. ............................ ............................ ............................ .................. .... 68 6.> XN[^CPG@L[ ] KLEKC^[MLEN[ ............. QXÇKPMKG =. JGENOL @N NXXLXN[ .................................................................................................... 6; =.7 =.8 =.; =.0 =.0.7 =.0.8 =.0.; =.0.0 =.>

............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ .............. 6; MEPXL@^KKMÛE .............. ........................... ............................ ............................ ............................. ............................. ............................ ......................... ........... 6; LHONPMYL KLJQNPNEKMG ) ............. IÊ@GJNEPL. R71ZR77Z .............. ............................ ............................ ............................ ............................ ............................ ............................. ............................ ............... .. 6; ........................... ............................ ............................ ............................ ............................ ............................ ................ .. 66 QXLKN@MJMNEPL @N[KXMQKMÛE ) ............. NW^MQL ENKN[GXML ............. .......................... ........................... ............................ ............................. ............................. ............................ ............................ ......................... ........... 66 JGPNXMGC @N GQL]L ............. ........................... ............................ ............................ ............................ ............................ ............................ ............................ ..................... ....... 66 ........................... ............................ ............................ ............................ ............................ ............................. ..................... ...... 66 @N[GXXLCCL @N CG QXÇKPMKG ............. NQLXPN .............. X NQLXPN ............................ ............................ ............................ ............................. ............................. ............................ ............................ ............................ ......................... ........... =1 XN[^CPG@L[ ] KLEKC^[MLEN[ ............. ........................... ............................. ............................. ............................ ............................ ............................ .................. .... =1

QXÇKPMKG 71. CNNX ] N[KXMHMX GXKFMYL[ @N PNVPL. ................................................................. =7 71.7 71.8 71.;

MEPXL@^KKMÛE .............. ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ .............. =7 ........................... ............................ ............................ ............................. ............................. ............................ ......................... ........... =7 LHONPMYL KLJQNPNEKMG) ............. IÊ@GJNEPL .............. ............................ ............................. ............................. ............................ ............................ ............................ ............................ ............................ ................ .. =7

........................... ............................ ............................ ............................ ............................ ............................ ................ .. =8 71.0 QXLKN@MJMNEPL @N[KXMQKMÛE ) ............. .......................... ............................ ............................ ............................ ............................ ............................. ............................. .................... ...... =8 71.0.7 NW^MQL ENKN[GXML ............ 71.0.8 JGPNXMGC @N GQL]L.............. ............................ ............................ ............................ ............................ ............................ ............................. ............................ ............... .. =8 71.0.; @N[GXXLCCL @N CG QXÇKPMKG ............. ........................... ............................ ............................ ............................ ............................ ............................ ................ .. =8 71.0.0 X NQLXPN NQLXPN .............. ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ ..................... ....... => 71.> XN[^CPG@L[ ] KLEKC^[MLEN[ ............. ........................... ............................. ............................. ............................ ............................ ............................ .................. .... =>

QXÇKPMKG 77. D^GX@GX ] XNK^QNXGX LHONPL[. ......................................................................... =9 77.7 77.8 77.; 77.0 77.0.7 77.0.8 77.0.; 77.0.0 77.>

MEPXL@^KKMÛE .............. ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ .............. =9 LHONPMYL KLJQNPNEKMG ) ............. ........................... ............................ ............................ ............................. ............................. ............................ ......................... ........... =9 IÊ@GJNEPL .............. ............................ ............................. ............................. ............................ ............................ ............................ ............................ ............................ ................ .. =9 QXLKN@MJMNEPL @N[KXMQKMÛE ) ............. ........................... ............................ ............................ ............................ ............................ ............................ ................ .. =4 NW^MQL ENKN[GXML ............ .......................... ............................ ............................ ............................ ............................ ............................. ............................. .................... ...... =4 JGPNXMGC @N GQL]L.............. ............................ ............................ ............................ ............................ ............................ ............................. ............................ ............... .. =4 @N[GXXLCCL @N CG QXÇKPMKG ............. ........................... ............................ ............................ ............................ ............................ ............................ ................ .. =4 NQLXPN .............. X NQLXPN ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ ................... ..... 711 XN[^CPG@L[ ] KLEKC^[MLEN[ ............. ........................... ............................. ............................. ............................ ............................ ............................ ................ .. 711

QXÇKPMKG 78. GCJGKNEGX YNKPLXN[ YNKPLXN[ @N LHONPL[ NE GXKFMYL[ ..................... ................................ ..................... .......... 717 78.7 78.8 78.; 78.0 78.0.7 78.0.8 78.0.; 78.0.0

MEPXL@^KKMÛE .............. ............................ ............................ ............................ ............................ ............................ ............................ ............................ .......................... ............ 717 ........................... ............................ ............................ ............................. ............................. ............................ ....................... ......... 717 LHONPMYL KLJQNPNEKMG ) ............. IÊ@GJNEPL .............. ............................ ............................. ............................. ............................ ............................ ............................ ............................ ............................ .............. 717 ........................... ............................ ............................ ............................ ............................ ............................ .............. 718 QXLKN@MJMNEPL @N[KXMQKMÛE ) ............. NW^MQL ENKN[GXML ............ .......................... ............................ ............................ ............................ ............................ ............................. ............................. .................. .... 718 JGPNXMGC @N GQL]L.............. ............................ ............................ ............................ ............................ ............................ ............................. ............................ ............. 71; @N[GXXLCCL @N CG QXÇKPMKG ............. ........................... ............................ ............................ ............................ ............................ ............................ .............. 71; NQLXPN .............. ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ ................... ..... 71> X NQLXPN

........................... ............................. ............................. ............................ ............................ ............................ ................ .. 71> 78.> XN[^CPG@L[ ] KLEKC^[MLEN[ ............. .................................. .... 719 QXÇKPMKG 7;. XNK^QNXGX YNKPLXN[ @N LHONPL[ @N[@N GXKFMYL[.. ..............................

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg mv

7;.7 7;.8 7;.; 7;.0 7;.0.7 7;.0.8 7;.0.; 7;.0.0 7;.>

MEPXL@^KKMÛE .............. ............................ ............................ ............................ ............................ ............................ ............................ ............................ .......................... ............ 719 ........................... ............................ ............................ ............................. ............................. ............................ ....................... ......... 719 LHONPMYL KLJQNPNEKMG ) ............. IÊ@GJNEPL .............. ............................ ............................. ............................. ............................ ............................ ............................ ............................ ............................ .............. 719 QXLKN@MJMNEPL @N[KXMQKMÛE ) ............. ........................... ............................ ............................ ............................ ............................ ............................ .............. 719 .......................... ............................ ............................ ............................ ............................ ............................. ............................. .................. .... 719 NW^MQL ENKN[GXML ............ ............................ ............................ ............................ ............................ ............................ ............................. ............................ ............. 719 JGPNXMGC @N GQL]L.............. @N[GXXLCCL @N CG QXÇKPMKG ............. ........................... ............................ ............................ ............................ ............................ ............................ .............. 714 X NQLXPN NQLXPN .............. ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ ................... ..... 771 XN[^CPG@L[ ] KLEKC^[MLEN[ ............. ........................... ............................. ............................. ............................ ............................ ............................ ................ .. 771

HMHCMLDXGIÊG ....................................................................................................................................... 777 GENVL G. XßHXMKG ............................................................................................................................... 77; GENVL H. QCGEPMCCG @NC XNQLXPN XNQLXPN @N QXÇKPMKG[. ....................................................................... 770 GENVL K. XNDCGJNEPL XNDCGJNEPL MEPNXEL QGXG NC ^[L @N CGHLXGPLXML[. CGHLXGPLXML[. ..................... ................................ ..................... .......... 77>

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg v

Lhontmvl Lhontmv l Dnenrgc `nc Jgeugc

Cg metnekmûe ns qun nc gcujel gsmjmcn jnolr cls kleknptls `n cg prldrgjgkmûe lrmnetg`l g lhontls gc vnr cg gpcmkgkmûe ne ue cnedugon `n prldrgjgkmûe kljl ogvg.

Gc tnenr kcgrl cls kleknptls pl`rç rnklelknr kuge`l gpcmkgrcls gc neirnetgrsn g prlhcnjgs `nc jue`l rngc. G`njçs, nc gcujel tne`rç ue jnolr klelkmjmnetl `n cgs fnrrgjmnetgs qun hrme`g nc cnedugon pgrg pl`nr mjpcnjnetgr nxmtlsgjnetn sus slcukmlens.

Lhontmvl Lhontmv l Dnenrgc `n cg Jgtnrmg

Qrlplrkmlegr gc nstu`mgetn cgs kljpntnekmgs enknsgrmgs pgrg ghlr`gr nc nstu`ml `n kugcqumnr cnedugon lrmnetg`l g lhontls, jntl`lcldêg `n geçcmsms y `msn÷l lrmnetg`l g lhontls, `n cls smstnjgs dnstlrns `n hgsns `n `gtls, y ne dnenrgc `n kugcqumnr jgtnrmg hgsg`g ne nc jl`ncl lrmnetg`l g lhontls. R7ZR8Z R 7ZR8Z

Kljpntnekmgs Nspnkêiimkgs mkgs g @nsgrrlccgr

@msn÷gr n mjpcnjnetgr lhontls `n prldrgjgkmûe qun pnrjmtge rnslcvnr smtugkmlens rngcns y `n mednemnrêg. R7ZR8Z

^tmcm`g` `nc Jgeugc

Ns ueg duêg pgrg cls prlinslrns qun mjpgrtne cg jgtnrmg, pgrg pl`nr uemilrjmzgr cls kletnem`ls y emvnc `n prliue`m`g` `n cls tnjgs `nc prldrgjg. Qgrg cls nstu`mgetns oundg ue pgpnc mjplrtgetn ne su ilrjgkmûe yg qun ns ueg fnrrgjmnetg `n gprne`mzgon qun ilrtgcnkn cls lhontmvls `nc pnrimc `n nstu`mls.

Qgrg cg Gkg`njmg `n [mstnjgs Kljputgkmlegcns ns ueg nvm`nekmg qun sn nstçe prljlvmne`l eunvgs n meelvg`lrgs nstrgtndmgs ns trgtndmgs `m`çktmkgs.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 9

Qrg Qrg ktmkg 7. Metrlùkkml Metrlùk kml e g ^JC 7.7 Metrlùkkmûe

Cg prnsnetn prçktmkg gyu`g g gsmjmcgr cls kletnem`ls `n cg êm`g` M? Metrlùkkmûe gc pgrg`mdjg `n cg prldrgjgkmûe lrmnetg`g g lhontls `nc suhtnjg 7.8. Cnedugon `n jl`ncg`l uemimkg`l? `mgdrgjg `n kcgsns y 7.8 Cnedugon `n jl`ncg`l uemimkg`l? `mgdrgjg `n kcgsns, `nc prldrgjg `n nstu`mls `n cg jgtnrmg `n Qrldrgjgkmûe Lrmnetg`g g Lhontls, `nsgrrlccge`l cg kljpntnekmg nspnkêimkg? –Kljprne`n y gpcmkg cls kleknptls `nc pgrg`mdjg `n prldrgjgkmûe lrmnetg`g g lhontls pgrg jl`ncgr smtugkmlens `n cg vm`g rngc.‚.

7.8 Lhontmvl Kljpntnekmg)

Xngcmzgr cls `mgdrgjgs `n gktmvm`g`ns y `n kcgsns `n ue kgsl `n nstu`ml ne pcget^JC pgrg igjmcmgrmzgrsn kle `mkfg cg fnrrgjmnetg.

7.; Iue`gjnetl

Gc memkml `n ue prlynktl `n `nsgrrlccl `n smstnjgs sn `nhn kljuemkgr ninktmvgjnetn qumnens tmnene cg m`ng y cls `nsgrrlccg`lrns. NC ^JC (Cnedugon êmimkg`l `n @gtls) ns ueg fnrrgjmnetg qun smrvn kljl necgkn pgrg kujpcmr nstg iuekmûe yg qun cn gyu`g g kgpturgr cg m`ng `n ue smstnjg pgrg kljuemkgrcg plstnrmlrjnetn g qumne nstç mevlcukrg`l ne su prlknsl `n `nsgrrlccl2 nstl sn ccnvg g kghl jn`mgetn ue kleouetl `n sêjhlcls y `mgdrgjgs. Kg`g `mgdrgjg tmnen imens `mstmetls `netrl `nc prlknsl `n `nsgrrlccl. R;Z Nxmstne `mvnrsgs fnrrgjmnetgs qun els pnrjmtne dnenrgr `mgdrgjgs ^JC y kllr`megrcgs ne ue jl`ncl. Gcduegs `n cgs jçs klelkm`gs sle? R0Z [litwgrn

Kgrgktnrêstmkgs

Jgdmk@rgw Cl ns su usghmcm`g`. ElJgdmk (cg njprnsg fg jnolr sm`l   kljprg`g sm`l plr @gssguct [ystnjs. [ystnjs. Ns `n`ntrçs prnvnrJgdmk@rgw) qun, kljl klesnkunekmg, Jgdmk@rgw smdg jnolrge`l ne tl`l cl qun sn rnimnrn g cg mednemnrêg `n smstnjgs `le`n nstn tmpl `n smjucgkmlens g pgrtmr `n jl`ncls ns kcgvn. @msplemhcn ne? fttps?//www.eljgdmk.klj/prlùkts/jgdmk`rgw fttps?//www.eljgdmk.klj/prlùkts/jgdmk`rgw Qgpyrus ^JC

Nc netlrel `n jl`ncg`l nstçe`gr –`n igktl‚ ne Nkcmpsn. Drgtumtl y

Jl`ncml.

Fnrrgjmnetg juy pltnetn, lrdgemzg`g ne ue eÿkcnl lpne slurkn gc qun sn cn pun`ne g÷g`mr iuekmlegcm`g`ns jn`mgetn ue smstnjg `n

lpne slurkn, Qgpyrus ns sme ù`g cg jnolr lpkmûe sm trghgogs kle Nkcmpsn l enknsmtgs metndrgr tus jl`ncls kle ltrls pcud-mes `n Nkcmpsn kljl pgrtn `n tu prlknsl `n `nsgrrlccl. @msplemhcn ne? fttps?//www.nkcmpsn.lrd/pgpyrus/ fttps?//www.nkcmpsn.lrd/pgpyrus/

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 4

nxtnesmûe jlùcgr. Gcduels `n cls jl`ncls sle tgjhmíe drgtumtls, pnrl jukfls sle yg nxtnesmlens kljnrkmgcns, `msplemhcns ne cg jl`ncml stlrn. Nstg nstrukturgkmûe tn pnrjmtn g`gptgr cg fnrrgjmnetg g tus enknsm`g`ns `n jl`ncg`l ^JC. Qlr nonjpcl, pun`ns njpnzgr jl`ncge`l drgtms. @msplemhcn ne? fttps?//www.jl`ncml.lrd/   fttps?//www.jl`ncml.lrd/ Grdl^JC.

Grdl^JC iun `n cgs prmjnrgs fnrrgjmnetgs, plr cl qun ns juy plpucgr gÿe. @msplemhcn ne? fttp?//grdlujc.tmdrms.lrd/ fttp?//grdlujc.tmdrms.lrd/

[tgr^JC

[tgr^JC ns cg jnolr lpkmûe sm huskgs ueg fnrrgjmnetg rçpm`g, içkmc `n usgr y rgzleghcnjnetn hgrgtg ne kljpgrgkmûe g ltrgs fnrrgjmnetgs ^JC. @msplemhcn ne? fttp?//stgrujc.ml/   fttp?//stgrujc.ml/

ngsy^JC

ngsy^JC ns ueg fnrrgjmnetg `n `mgdrgjg ^JC pgrg EntHnges qun prlplrkmleg iuekmlens pgrg krngr y trghgogr kle `mgdrgjgs ^JC içkmcjnetn. Gktugcjnetn slplrtg `mgdrgjgs `n kcgsn prlplrkmlege`l ue n`mtlr vmsugc `rgd-ge`-`rlp pgrg nc `mhuol `n `mgdrgjg, Ogvg kû`mdl `n dnenrgkmûe `n `mgdrgjgs y 'mednemnrêg mevnrsg' pgrg krngr `mgdrgjgs `n kcgsns g pgrtmr `n kû`mdl Ogvg. Ns juy g`nkug`l pgrg cg nesn÷gezg `n `msn÷l `n slitwgrn. @msplemhcn ne? fttp?//pcudmes.enthnges.lrd/pcudme/>>0;>/ngsyujc fttp?//pcudmes.enthnges.lrd/pcudme/>>0;>/ngsyujc

pcget^JC

Qcget^JC ns ueg fnrrgjmnetg Lpne[lurkn qun pnrjmtn krngr drçimkls vnktlrmgcns usge`l ue cnedugon prlpml. Eg`g `n Grrgstrgr-y-slctgr. El, slcl `nhnjls nskrmhmr uels tnxtls kgsm kljl nc FPJC y nc jltlr `n Qcget^JC els krngrç nc drçimkl rnspnktmvl. rnspnk tmvl. R>Z @msplemhcn ne? fttp?//pcudmes.enthnges.lrd/pcudme/0=19=/pcgetujc fttp?//pcudmes.enthnges.lrd/pcudme/0=19=/pcgetujc

Ne cg prnsnetn prgktmkg usgrnjls pcget^JC kljl ueg nxtnesmûe pgrg EntHnges.

7.0 Qrlkn`mjmnetl @nskrmpkmûe) 7.0.7 Nqumpl enknsgrml

Kljputg`lrg kle ue smstnjg lpnrgtmvl qun kunetn kle gjhmnetn drçimkl (Tme`lws, Cmeux, ntk…)

7.0.8 Jgtnrmgc `n Gplyl [@B `n ogvg. Netlrel `n `nsgrrlccl pgrg ogvg (M@N) EntHnges. Nxtnesmûe (pcudme) pgrg enthnges pcget^JC Fnrrgjmnetg Drgpfvmz

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@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 6

7.0.; @nsgrrlccl `n cg Qrçktmkg Qrmjnrl `nhnjls ghrmr nc M@N enthnges, y `nspuís mr g cg lpkmûe –Pllcs QCudmes‚. [n gpgrnknrç ueg vnetgeg, `n cg kugc sncnkkmlegjls cg pnstg÷g –Gvgmcghcn Qcudmes‚. Ne nc kug`rl `n tnxtl –[ngrkf‚ nskrmhmjls ujc y lhtne`rnjls ueg cmstg `n pcudmes rncgkmleg`ls kle ^JC?

[ncnkkmlegjls Qcget^JC y `gjls kcmk ne nc hltûe –Mestgcc‚, gknptgjls cls tírjmels y kle`mkmlens y `gjls kcmk ne – mestgcc‚, y nspnrgjls g qun tnrjmen `n `nskgrdgr n

mestgcgr nc slitwgrn.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg =

[m gpgrnkn ltrls `mçcldls `n g`vnrtnekmg, `gjls kcmk ne – Kletmeun ‚ y pgrg imegcmzgr sncnkmlegjls cg lpkmûe `n –Xnstgr M@N Elw‚ y `gjls kcmk gc hltûe –Imemsf‚

] pgrg pl`nr vnr cls drçimkls kle cls `mgdrgjgs dnenrg`ls, rnqunrmjls `n ltrg fnrrgjmnetg? Drgpfvmz. Nstg cg `nskgrdgjls `nc smtml smtml fttp?//www.drgpfvmz.lrd/ fttp?//www.drgpfvmz.lrd/

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 71

Qrlkn`njls g nonkutgr nc grkfmvl `n mestgcgkmûe drgpfvmz-8.;6.jsm .

Gflrg huskgjls nc nonkutghcn `lt.nxn. Ne Tme`lws ns plsmhcn qun sn nekunetrn ne k?SQrldrgj Imcns (x69)SDrgpfvmzV.VShme Ne entHnges netrnjls g cg lpkmûe? –Pllcs Lptmles Qcget^JC‚, n me`mkgr cg uhmkgkmûe `nc grkfmvl `lt.nxn.

Jmsknccgenlus

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 77

Gflrg metnetgrnjls jl`ncgr nc smdumnetn nonjpcl? –êg kcêemkg kunetg kle vgrmls `lktlrns, y gcduegs rnknpkmlemstgs. [n qumnrn gutljgtmzgr nc prlknsl `n gdne`gr kmtgs plr tncíilel l ne cg kcêemkg. [n pun`ne rndmstrgr eunvls pgkmnetns. Cls pgkmnetns pun`ne slcmkmtgr cg kmtg kle gcdÿe `lktlr, pgrg cl kugc cg rnknpkmlemstg vnrmimkgrç cg `msplemhmcm`g` `n cg inkfg y sm nstç `msplemhcn, sn cg gsmdegrç. Pgjhmíe `nhn snr plsmhcn rn gdne`gr kmtgs ‚.

Krngr nc prlynktl ne EntHnges. Memkmgjls enhnges, ncndmjls cg lpkmûe –Imcn Enw Qrlonkt‚. Krngjls ueg

gpcmkgkmûe ogvg?

Cn `gjls nc eljhrn `n –gppKmtgs‚ gc prlynktl. Ne nc eljhrn `nc prlynktl `gjls kcmk `nrnkfl y `nc jneÿ njnrdnetn sncnkkmlegjls –Enw‚ y cundl –Ltfnr‚.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 78

@nc eunvl `mgcldl sncnkkmlegjls cg kgtndlrêg – Qcget^JC ‚ y `nc tmpl `n grkfmvl ncndmjls –Enw Qcget^JC @mgdrgj‚ y cundl kcmk ne nc hltûe – Enxt 5‚

Cn `gjls ue eljhrn gc `mgdrgjg

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 7;

[ng pgrnknrç ueg vnetgeg `le`n nskrmhmrnjls nc kû`mdl sndÿe cg smetgxms `n pcget^JC pgrg nspnkmimkgr nc `mgdrgjg `n gktmvm`g`ns. R9Z Nskrmhg nc kû`mdl? `mgdrgjgGktmvmg`ns.pujc Astgrtujc tmtcn "@mgdrgjg `n Gktmvm`g`ns" (*) --5 "Ccgjg`g l Ymsmtg `nc Kcmnetn" "Ccgjg`g l Ymsmtg `nc Kcmnetn" --5 "Gtmne`n rnknpkmlemstg" mi "]g ns pgkmnetn78")2 lKcmnetn.sntsEljhrn("Jgtnl")2 lKcmnetn.snteKrn`mtl(1i)2

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 98

lKcmnetn.snte@nskunetl(1.7i)2 //Fgknr Igkturg Igkturg lEltg:enw Igkturg(8)2 lEltg.sntKcmnetn(lKcmnetn)2 lEltg.sntYne`n`lr(lYne`n`lr)2 lEltg.snteIlcml(7)2 lEltg.sntsInkfg("8;-@mk-8176")2 //Jntnr @ntgccn lEltg.v@ntgccnR1Z._gpgtl:l_gpgtl2 [email protected]`g`:82 lEltg.v@ntgccnR7Z._gpgtl:l_gpgtl82 [email protected]`g`:>2 //Klhrgr lEltg.Klhrgr()2 //Ynr igkturg lEltg.vnrEltg()2 }

}

Gflrg kljpmcgjls y nonkutgjls nc prldrgjg, `ge`l kcmk ne nc mklel rue? Ilcml? 7 Kcmnetn eljhrn? Jgtnl Inkfg? 8;-@mk-8176 Pltgc? 0616.708 @ntgccn? Jl`ncl Qrnkml Qujg $;11.>11 Embn $611.=11

, y lhtnenjls?

Kgetm`g` 8 >

Xntl?

Jl`mimqun nc nonrkmkml pgrg gdrndgr cg kcgsn Qnrsleg y qun `n nccg fnrn`ne cgs kcgsns Njpcng`l y Kcmnetns.

9.0.0 Xnplrtn Gc imegcmzgr ístg prçktmkg nc gcujel `nhnrç dnenrgr ue rnplrtn ne Q@I qun kletnedg cls `mgdrgjgs `n gktmvm`g`ns, kgsls `n usl, kcgsns y `n snkunekmgs ne Qcget^JC nc kû`mdl iunetn y kgpturgs `n pgetgccg `n cg nonkukmûe `nc prldrgjg.

9.> Xnsuctg`ls y Klekcusmlens

Kle ístg prçktmkg, nc gcujel kljnezgrç g gpcmkgr nc pgrg`mdjg `nc jl`ncg`l

lrmnetg`l g lhontls, pgrg, g pgrtmr `n ue prlhcnjg `nc jue`l rngc, rngcmzgr ueg ghstrgkkmûe y ccnvgrcl fgstg cg kl`mimkgkmûe ne ogvg.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 9;

Qrgktmkg 4. Dnenrgkml gpcmkgkml e `n Dnenrgkml e y gpcmkgkml nxgjnens (Fnrnekmg ;). 4.7 Metrlùkkmûe

Cg prnsnetn prçktmkg gyu`g g rnilrzgr cls kletnem`ls `n cg êm`g` MMM? Fnrnekmg `n cls suhtnjgs ;.7 @nimemkmûe? kcgsn hgsn, kcgsn `nrmvg`g, ;.8 Kcgsmimkgkmûe? fnrnekmg smjpcn, fnrnekmg jÿctmpcn, ;.; Xnutmcmzgkmûe `n jmnjhrls fnrn`g`ls, ;.0 Xninrnekmg gc lhontl `n cg kcgsn hgsn, ;.> Klestruktlrns y `nstruktlrns ne kcgsns `nrmvg`gs y ;.9 Xn`nimemkmûe `n jítl`ls ne kcgsns `nrmvg`gs, `nc prldrgjg `n nstu`mls `n cg jgtnrmg `n Qrldrgjgkmûe Lrmnetg`g g Lhontls, `nsgrrlccge`l cg kljpntnekmg nspnkêimkg? –M`netmimkg y gpcmkg rncgkmlens `n fnrnekmg ne kcgsns `nrmvg`gs pgrg rnutmcmzgr cls jmnjhrls `n ueg kcgsn hgsn ne nc `nsgrrlccl `n gpcmkgkmlens‚.

4.8 Lhontmvl Kljpntnekmg)

Ncghlrgr ue prldrgjg qun junstrg cgs vnetgogs `n cg prldrgjgkmûe lrmnetg`g g lhontls, `nsgrrlccge`l ueg slcukmûe pgrg ueg nskuncg qun gpmqun nxçjnens. Gegcmkn nc prlhcnjg `n dnenrgr, gpcmkgr y rnvmsgr nxçjnens `n lpkmûe jÿctmpcn. @nimeg cls `mgdrgjgs ^JC ne Qcget^jc y nskrmhg nc kû`mdl ne EntHnges.

4.; Iue`gjnetl

Cg igsn `nc geçcmsms ns juy mjplrtgetn, gsê qun rnpgsgrnjls nc geçcmsms lrmnetg`l g lhontls. @nimemkmûe.

Nc geçcmsms lrmnetg`l g lhontls ns nc prlknsl qun jl`ncg nc `ljmeml `nc prlhcnjg jn`mgetn cg m`netmimkgkmûe y nspnkmimkgkmûe `n lhontls snjçetmkls qun metnrgkkmlege y sn kljplrtge `n gkunr`l g cls rnqumsmtls `nc smstnjg R78Z Dnenrgcm`g`ns. R7;Z

Qnrjmtn `nskrmhmr nc smstnjg ne cls jmsjls tírjmels qun nc jue`l rngc. [n knetrg ne cg kljprnesmûe `nc nspgkml (`ljmeml) `nc prlhcnjg. @miêkmc `ntnrjmegr `ûe`n gkghg nc geçcmsms lrmnetg`l g lhontls y `ûe`n kljmnezg nc `msn÷l lrmnetg`l g lhontls. Nc lhontmvl ns jl`ncgr cg snjçetmkg `nc prlhcnjg ne tírjmels `n lhontls `mstmetls pnrl rncgkmleg`ls. Nc geçcmsms kgsg kle nc `ljmeml `nc prlhcnjg. Cls lhontls `nc `ljmeml `nc prlhcnjg rnprnsnetge klsgs l kleknptls

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pgrg prlhcnjg (lhontls Cls lhontls `nc`nskrmhmr `ljmemlnc`nc prlhcnjg tmnenesnjçetmkls). ueg nqumvgcnekmg `mrnktg ne nc utmcmzg`ls netlrel `n cg gpcmkgkmûe.

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@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 90

[n knetrg ne cg rnprnsnetgkmûe `nc prlhcnjg. El nxmstne rndcgs imogs pgrg nstg trgesilrjgkmûe. trgesilrjgkmûe .

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4.0 Qrlkn`mjmnetl @nskrmpkmûe)

4.0.7 Nqumpl enknsgrml Kljputg`lrg kle ue smstnjg lpnrgtmvl qun kunetn kle gjhmnetn drçimkl (Tme`lws, Cmeux, ntk…)

4.0.8 Jgtnrmgc `n Gplyl [@B `n ogvg. Netlrel `n `nsgrrlccl pgrg ogvg (M@N) EntHnges. Nxtnesmûe (pcudme) pgrg enthnges pcget^JC. Fnrrgjmnetg Drgpfvmz.

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4.0.; @nsgrrlccl `n cg Qrçktmkg Kljnezgrnjls rngcmzge`l ue geçcmsms kle ue neilqun lrmnetg`l g lhontls g cg `nskrmpkmûe `nc smstnjg g jl`ncgr. @nskrmpkmûe `nc prlknsl `n gpcmkgkmûe `n nxçjnens.

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@nhnjls tnenr jgtnrmgs `nimem`gs. Meskrmhmjls gcduels gcujels. Kletrgtgjls jgnstrls. Dnenrgjls ue nxgjne `n V uem`g` kle E prnduetgs. Gslkmgjls nc nxgjne kle cg jgtnrmg, jgnstrl y gcujel. Krngjls cgs prnduetgs kle sus rnspnktmvls mekmsls y rnspunstgs klrrnktgs. Krngjls cg flog `n rnspunstgs pgrg nc rnspnktmvl nxgjne. Gpcmkgjls nc nxgjne. Xnvmsgjls nc nxgjne.

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Jlstrgjls cls rnsuctg`ls `nc nxgjne.

Nsqunjgs `n gpcmkgkmûe `n nxçjnens.

Mcustrgkmûe 7. Ncnjnetls qun metnrvmnens y kûjl metnrgktÿge.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Mcustrgkmûe 8.M`netmimkgkmûe `n lhontls.

Mcustrgkmûe ;. Xncgkmlens netrn lhontls.

Qçdmeg 9>

Mcustrgkmûe 0. Gegcmzge`l qun gtrmhutls y jítl`ls sle enknsgrmls.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Mcustrgkmûe >. Xnùkmne`l kcgsns.

Qçdmeg 99

Mcustrgkmûe 9. @nskuhrmne`l fnrnekmg, gdrndgkmûe y kljplsmkmûe.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Mcustrgkmûe 4. Ilrjgcmzge`l cls tmpls `n `gtls y klestruktlrns

Mcustrgkmûe 6. Xnvmsmûe `nc jl`ncl.

Qçdmeg 94

Mcustrgkmûe =. Xngkljl`l `nc `mgdrgjg memkmgc gcmeng`l kle nc `mgdrgjg `n kcgsns rnsuctgetn.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 96

Kl`mimkgkmûe

Gflrg kl`mimkgjls cgs kcgsns. Memkmgjls enthnges, ncndmjls cg lpkmûe –Imcn Enw Qrlonkt‚. Krngjls ueg gpcmkgkmûe ogvg. Cn `gjls nc eljhrn `n –gpcmkgkmleNxgjnens ‚ gc prlynktl. Ne nc jneÿ `n prlynktls qun nstç g cg mzqumnr`g, nxpge`mjls nc prlynktl fgstg vnr nc pgquntn gpcmkgkmlenxgjnens y slhrn nstn `gjls kcmk `nrnkfl y `nc jneÿ kletnxtugc sncnkkmlegjls Enw y cundl Ogvg Kcgss. Cn `gjls nc eljhrn `n Jgtnrmg g cg eunvg kcgsn y kcmk ne nc hltûe –Imemsf‚ y nskrmhmjls nc smdumnetn kû`mdl? Jgtnrmg.ogvg pgkbgdn gppnxgjnens2 puhcmk kcgss Jgtnrmg { [trmed sPmtucl2 puhcmk Jgtnrmg([trmed sPmtucl) { }

tfms.sPmtucl : sPmtucl2

puhcmk [trmed dntsPmtucl() { rnture sPmtucl2 } puhcmk vlm` sntsPmtucl([trmed sPmtucl) { tfms.sPmtucl : sPmtucl2 } }

Gdrndgjls cg kcgsn kle nc eljhrn `n Qnrsleg. @nspuís `n krngrcg nskrmhmjls nc kû`mdl? Qnrsleg.ogvg pgkbgdn gppnxgjnens2 puhcmk kcgss Qnrsleg { //Gtrmhutls [trmed sEljhrn2 [trmed sXlc2 //Klestruktlr puhcmk Qnrsleg([trmed sEljhrn, [trmed sXlc) { tfms.sEljhrn : sEljhrn2 tfms.sXlc : sXlc2 } //Jítl`ls

puhcmk [trmed dntsEljhrn() { rnture sEljhrn2 }

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 9=

puhcmk vlm` sntsEljhrn([trmed sEljhrn) { tfms.sEljhrn : sEljhrn2 } puhcmk [trmed dntsXlc() { }

rnture sXlc2

puhcmk vlm` sntsXlc([trmed sXlc) { tfms.sXlc : sXlc2 } }

Gdrndgjls cg kcgsn kle nc eljhrn `n Qrnduetg. @nspuís `n krngrcg nskrmhmjls nc kû`mdl? Qrnduetg.ogvg pgkbgdn gppnxgjnens2 puhcmk kcgss Qrnduetg { [trmed sQrnduetg2 [trmed sLpkmle72 [trmed sLpkmle82 [trmed sLpkmle;2 met eLpkmleKlrrnktg2 //Klestruktlr puhcmk Qrnduetg([trmed sQrnduetg, [trmed sLpkmle7, [trmed sLpkmle8, [trmed sLpkmle;, met eLpkmleKlrrnktg) { tfms.sQrnduetg : sQrnduetg2 tfms.sLpkmle7 : sLpkmle72 tfms.sLpkmle8 : sLpkmle82 tfms.sLpkmle; : sLpkmle;2 tfms.eLpkmleKlrrnktg : eLpkmleKlrrnktg2 } //Jítl`ls puhcmk met dnteLpkmleKlrrnktg() { rnture eLpkmleKlrrnktg2 } puhcmk vlm` snteLpkmleKlrrnktg(met eLpkmleKlrrnktg) { tfms.eLpkmleKlrrnktg : eLpkmleKlrrnktg2 } puhcmk [trmed dntsLpkmle7() { rnture sLpkmle72 } puhcmk vlm` sntsLpkmle7([trmed sLpkmle7) { tfms.sLpkmle7 : sLpkmle72

} puhcmk [trmed dntsLpkmle8() { rnture sLpkmle82

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 41

} puhcmk vlm` sntsLpkmle8([trmed sLpkmle8) { tfms.sLpkmle8 : sLpkmle82 } puhcmk [trmed dntsLpkmle;() { rnture sLpkmle;2 } puhcmk vlm` sntsLpkmle;([trmed sLpkmle;) { tfms.sLpkmle; : sLpkmle;2 } puhcmk [trmed dntsQrnduetg() { rnture sQrnduetg2 } puhcmk vlm` sntsQrnduetg([trmed sQrnduetg) { tfms.sQrnduetg : sQrnduetg2 } }

Gdrndgjls cg kcgsn kle nc eljhrn `n Nxgjne. @nspuís `n krngrcg nskrmhmjls nc kû`mdl? Nxgjne.ogvg pgkbgdn gpcmkgkmlenxgjnens2 puhcmk kcgss Nxgjne { met eêm`g`2 met ePltgcQrnduetgs2 Jgtnrmg lJgtnrmg2 Qnrsleg lJgnstrl2 Qnrsleg lGcujel2 QrnduetgRZ vQrnduetg2 //Klestruktlr puhcmk Nxgjne(met eêm`g`, met ePltgcQrnduetgs) { tfms.eêm`g` : eêm`g`2 tfms.ePltgcQrnduetgs : ePltgcQrnduetgs2 vQrnduetg : enw QrnduetgRePltgcQrnduetgsZ2 ilr (met m : 12 m 3 vQrnduetg.cnedtf2 m++) { vQrnduetgRmZ : enw Qrnduetg("", "", "", "", 1)2 } } }

Gdrndgjls nc kû`mdl? cg kcgsn kle nc eljhrn `n FlogXnspunstg. @nspuís `n krngrcg nskrmhmjls

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 47

FlogXnspunstg.ogvg pgkbgdn gpcmkgkmlenxgjnens2 mjplrt ogvg.utmc.[kgeenr2 puhcmk kcgss FlogXnspunstg { metRZ vXnspunstgsGcujel2 iclgt eKgcmimkgkmle2 Nxgjne lNxgjne2 puhcmk FlogXnspunstg(Nxgjne lNxgjne) { tfms.lNxgjne : lNxgjne2 eKgcmimkgkmle : 12 vXnspunstgsGcujel : enw metR>Z2 vXnspunstgsGcujelR1Z vXnspunstgsGcujelR7Z vXnspunstgsGcujelR8Z vXnspunstgsGcujelR;Z vXnspunstgsGcujelR0Z

: : : : :

12 12 12 12 12

} puhcmk iclgt dnteKgcmimkgkmle() { rnture eKgcmimkgkmle2 } puhcmk vlm` snteKgcmimkgkmle(iclgt eKgcmimkgkmle) { tfms.eKgcmimkgkmle : eKgcmimkgkmle2 } puhcmk Nxgjne dntlNxgjne() { rnture lNxgjne2 } puhcmk vlm` sntlNxgjne(Nxgjne lNxgjne) { tfms.lNxgjne : lNxgjne2 } puhcmk metRZ dntvXnspunstgsGcujel() { rnture vXnspunstgsGcujel2 } puhcmk vlm` sntvXnspunstgsGcujel(metRZ vXnspunstgsGcujel) { tfms.vXnspunstgsGcujel : vXnspunstgsGcujel2 } vlm` gpcmkgr() { //Nekghnzg`l `nc nxgjne [ystnj.lut.prmetce("Jgtnrmg? " + lNxgjne.lJgtnrmg.dntsPmtucl())2 lNxgjne.lJgtnrmg.dntsPmtucl())2 [ystnj.lut.prmetce("Jgnstrl? [ystnj.lut.prmetce("Jgnst rl? " + lNxgjne.lJgnstrl.dntsEljhrn())2 [ystnj.lut.prmetce("Gcujel? [ystnj.lut.prmetce("Gcuje l? " + lNxgjne.lGcujel.dntsEljhrn())2 [ystnj.lut.prmetce("êm`g`? [ystnj.lut.prmetce("êm`g `? " + lNxgjne.eêm`g`)2

//Gpcmkgr cgs prnduetgs [kgeenr tnkcg`l : enw [kgeenr([ystnj.me)2 ilr (met m : 12 m 3 lNxgjne.ePltgcQrnduetgs2 m++) {

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 48

[ystnj.lut.prmetce("Qrnduetg "+(m+7)+ "? " + lNxgjne.vQrnduetgRmZ.dntsQrnduetg())2 [ystnj.lut.prmetce("St 7) " + lNxgjne.vQrnduetgRmZ.dntsLpkmle7())2 [ystnj.lut.prmetce("St 8) " + lNxgjne.vQrnduetgRmZ.dntsLpkmle8())2 [ystnj.lut.prmetce("St ;) " + lNxgjne.vQrnduetgRmZ.dntsLpkmle;())2 [ystnj.lut.prmet("St < ? ")2 tfms.vXnspunstgsGcujelRmZ : tnkcg`l.enxtMet()2 } } vlm` rnvmsgr() { met hunegs : 12 // Kljpgrgr Kcgvn vs rnsp `nc gcujel ilr (met m : 12 m 3 vXnspunstgsGcujel.cnedtf2 m++) { mi (vXnspunstgsGcujelRmZ :: lNxgjne.vQrnduetgRmZ.eLpkmleKlrrnktg) { hunegs++2 } } tfms.snteKgcmimkgkmle(hunegs)2 } vlm` vnrXnsuctg`l() { [ystnj.lut.prmetce("Puvmstn " + tfms.dnteKgcmimkgkmle() + " gkmnrtls!!!")2 } }

] plr ÿctmjl n`mtgjls cg kcgsn prmekmpgc, qun sn ccgjg GpcmkgkmleNxgjnens? GpcmkgkmleNxgjnens.ogvg pgkbgdn gpcmkgkmlenxgjnens2 puhcmk kcgss GpcmkgkmleNxgjnens { puhcmk stgtmk vlm` jgme([trmedRZ grds) { // @nimemr Jgtnrmg Jgtnrmg lJgtnrmg : enw Jgtnrmg("Fmstlrmg `n @rgdle Hgcc")2 // @nimemr Gcujel Qnrsleg lGcujel : enw Qnrsleg("Dnrgr`l Iclrns", "gcujel")2 // @nimemr Jgnstrl Qnrsleg lJgnstrl : enw Qnrsleg("Xlsfm", "jgnstrl")2 // Krngr nxgjne `n V uem`g` kle E prnduetgs Nxgjne lNxgjne : enw Nxgjne(7, >)2

// Gslkmgr nc nxgjne kle cg jgtnrmg, gcujel, jgnstrl lNxgjne.lJgtnrmg : lJgtnrmg2 lNxgjne.lGcujel : lGcujel2

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 4;

lNxgjne.lJgnstrl : lJgnstrl2 // Dnenrgr cgs E prnduetgs kle sus rnspnktmvls mekmsls y // rnspunstgs klrrnktgs lNxgjne.vQrnduetgR1Z.sntsQrnduetg("¼Kugetl tgr`û ne gprne`nr nc bgjn-fgjn-fg

Qrg ktmkg 6. Metrlùkkml Metrlùk kml e gc usl `n Qrg Metnrigkns. 6.7 Metrlùkkmûe

Cg prnsnetn prçktmkg gyu`g g gsmjmcgr cls kletnem`ls `n cg êm`g` MY? Qlcmjlrimsjl `n cls suhtnjgs 0.7 @nimemkmûe, 0.8 Kcgsns ghstrgktgs? `nimemkmûe, jítl`ls

ghstrgktls, mjpcnjnetgkmûe `n kcgsns ghstrgktgs, jl`ncg`l `n kcgsns ghstrgktgs, 0.; Metnrigkns? `nimemkmûe, mjpcnjnetgkmûe `n metnrigkns, fnrnekmg `n metnrigkns, 0.0 Ygrmghcns plcmjûrimkgs (pcgetmccgs)? `nimemkmûe, usl y gpcmkgkmlens y 0.> Xnutmcmzgkmûe `n kû`mdl `nc prldrgjg `n nstu`mls `n cg jgtnrmg `n Qrldrgjgkmûe Lrmnetg`g g Lhontls, `nsgrrlccge`l cg kljpntnekmg nspnkêimkg? –Gpcmkg nc kleknptl `n plcmjlrimsjl pgrg cg `nimemkmûe `nimem kmûe `n kcgsns ghstrgktgs n metnrigkns qun pnrjmtge rnutmcmzgkmûe `n kû`mdl‚.

6.8 Lhontmvl Ncghlrgr Kljpntnekmg) ue prldrgjg qun junstrn kljl gtgkgr prlhcnjgs qun mjpcmqune fnrnekmg

jÿctmpcn. Nskrmhg ue prldrgjg qun dnenrn cg kcgsn FljhrnGrg÷g g pgrtmr `n cgs metnrigkns Fljhrn y Grg÷g.

6.; Iue`gjnetl

Fnrnekmg jÿctmpcn.

[n `mkn qun fgy fnrnekmg jÿctmpcn kuge`l ueg kcgsn fnrn`g `n jçs `n ueg kcgsn. Gsê, ueg kcgsn fmog fnrn`g nc kljplrtgjmnetl `n vgrmgs kcgsns pg`rn. Ne kmnrtls kgsls, cg fnrnekmg jÿctmpcn pun`n smjpcmimkgr cls prldrgjgs y prlplrkmlegr slcukmlens pgrg rnslcvnr prlhcnjgs `miêkmcns, guequn tgjhmíe sle iunetns `n jÿctmpcns prlhcnjgs. prlh cnjgs. R70Z G `minrnekmg `n K++, Ogvg el pnrjmtn fnrnekmg jÿctmpcn, nstl ns, el pnrjmtn qun ueg kcgsn `nrmvn `n `ls kcgsns `mstmetgs fnrn`ge`l `n ` n gjhgs jítl`ls y vgrmghcns jmnjhrl. Cgs metnrigkns `n Ogvg klestmtuyne ueg gctnregtmvg g cg fnrnekmg jÿctmpcn kle mjplrtgetns vnetgogs prçktmkgs y `n –nstmcl `n prldrgjgkmûe‚. R9Z Metnrigkns. êg metnrigkn ns ue kleouetl `n `nkcgrgkm `nkcgrgkmlens lens `n jítl`ls (sme mjpcnjnetgkmûe, ns

`nkmr, sme `nimemr nc kû`mdl `n `mkfls jítl`ls). [m ueg kcgsn mjpcnjnetg ueg `ntnrjmeg`g metnrigkn, `nhn `gr ueg `nimemkmû `nimemkmûe e g tl`ls cls jítl`ls `n cg metnrigkn. jl`mimkg`lr metnrigkn EljhrnMetnrigkn {

//`nkcgrgkmûe `n klestgetns //`nkcgrgkmûe `n jítl`ls. ¡[lcl `nkcgrgkmûe! }

jl`mimkg`lr kcgss EljhrnKcgsn

mjpcnjnets EljhrnMetnrigkn {

//jítl`ls `ns`n cg metnrigkn }2

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 49

Nonjpcl? puhcmk metnrigkn Cgjpgrg {

hllcnge nekne`nrCgjpgrg()2 } puhcmk metnrigkn Pncnilel {

hllcnge jl`lGvmle()2

} puhcmk kcgss Kncucgr

mjpcnjnets Pncnilel, Cgjpgrg {

hllcnge nekne`nrCgjpgrg(){ // Kl`mimkgkmûe… rnture trun2 } hllcnge jl`lGvmle(){ // Kl`mimkgkmûe… rnture trun2 } }

Cg vnetgog `n cgs metnrigkns ns qun el nstçe sljntm`gs g cgs jçs rêdm`gs elrjgs elr jgs `n cgs kcgsns2 plr nonjpcl, ueg kcgsn el pun`n fnrn`gr `n `ls kcgsns ghstrgkt, pnrl sê pun`n mjpcnjnetgr vgrmgs metnrigkns . êg `n cgs vnetgogs `n cgs metnrigkns `n Ogvg ns nc nstghcnknr pgutgs l jl`ls `n iuekmlegjmnetl smjmcgrns pgrg kcgsns qun pun`ne nstgr l el rncgkmleg`gs jn`mgetn fnrnekmg. R9Z Ne ninktl, tl`gs cgs kcgsns qun mjpcnjnetge ueg `ntnrjmeg`g metnrigkn slplrtge cls jítl`ls `nkcgrg`ls ne cg metnrigkn y ne nstn snetm`l sn kljplrtge `n jl`l smjmcgr. fnrnekmg g, kle Cgs metnrigkns pun`ne tgjhmíe rncgkmlegrsn jn`mgetn jnkgemsjls `n fnrnekm jçs icnxmhmcm`g` qun cgs kcgsns.

6.0 Qrlkn`mjmnetl @nskrmpkmûe) 6.0.7 Nqumpl enknsgrml

Kljputg`lrg kle ue smstnjg lpnrgtmvl qun kunetn kle gjhmnetn drçimkl (Tme`lws, Cmeux, ntk…)

6.0.8 Jgtnrmgc `n Gplyl [@B `n ogvg. Netlrel `n `nsgrrlccl pgrg ogvg (M@N) EntHnges.





6.0.; @nsgrrlccl `n cg Qrçktmkg Ne nstg prçktmkg jl`ncgrnjls gc supnr fírln Fljhrn-Grgkem`l (spm`nrjge). [m Ogvg

slplrtgrg fnrnekmg jÿctmpcn, hgstgrêg kle krngr cg kcgsn Fljhrn y cg kcgsn Grgkem`l pgrg tljgrcgs kljl kcgsns hgsn `n cg kcgsn FljhrgGrgkem`l, kljl sn junstrg ne nc smdumnetn `mgdrgjg?

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 44

Qnrl kljl el tnenjls fnrnekmg jÿctmpcn j ÿctmpcn ne ogvg, cl fgrnjls kle metnrigkns?

Qrmjnr pgsl. Krngr nc prlynktl. Memkmgjls enhnges, ncndmjls cg lpkmûe –Imcn Enw Qrlonkt‚. Krngjls ueg gpcmkgkmûe ogvg. Cn `gjls nc eljhrn `n – gpcmkgkmle[pm`nrjge ‚ gc prlynktl. @gjls

kcmk ne nc hltûe –Imemsf‚ y nc prlynktl sn fg krng`l. [m ns nc ÿemkl prlynktl pl`njls sgctgr nstn pgsl. Ne ltrl kgsl, `gjls kcmk `nrnkfl slhrn nc elj hrn `nc prlynktl y ne nc jneÿ kletnxtugc kletnx tugc sncnkkmlegjls –[nt gs Jgme Qrlonkt‚. Nc eljhrn `nc prlynktl `nhn plenrsn ne endrmtgs. [ndue`l pgsl. Krngr cg metnrigkn Fljhrn.

Ne nc jneÿ `n prlynktls qun nstç g cg mzqumnr`g, mzqumnr` g, nxpge`gjls nc prlynktl fgstg vnr nc pgquntn gpcmkgkmlespm`nrjge y slhrn nstn `gjls kcmk `nrnkfl y `nc jneÿ kletnxtugc sncnkkmlegjls Enw y cundl Ogvg Metnrigkn.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 46

Cn `gjls nc eljhrn `n Fljhrn g cg eunvg metnrigkn y kcmk ne nc hltûe – Imemsf‚?

[ncnkkmlegjls cg pnstg÷g `n n`mkmûe ccgjg`g –Fljhrn.ogvg‚ y nskrmhmjls nc kû`mdl? @npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 4=

Fljhrn.ogvg pgkbgdn gpcmkgkmlespm`nrjge2 puhcmk metnrigkn Fljhrn { [trmed eljhrn : ""2 vlm` dlcpngr()2 vlm` sgcu`gr()2 }

Pnrknr pgsl. Krngr cg metnrigkn Grgkem`l.

Ne nc jneÿ `n prlynktls qun nstç g cg mzqumnr`g, mzqumnr` g, nxpge`gjls nc prlynktl fgstg vnr nc pgquntn gpcmkgkmlespm`nrjge y slhrn nstn `gjls kcmk `nrnkfl y `nc jneÿ kletnxtugc sncnkkmlegjls Enw y cundl Ogvg Metnrigkn. Cn `gjls nc eljhrn `n Grgkem`l g cg eunvg metn rigkn y kcmk ne nc hltûe – Imemsf‚. [ncnkkmlegjls cg pnstg÷g `n n`mkmûe ccgjg`g –Grgkem`l.ogvg‚ y nskrmhmjls nc kû`mdl? Grgkem`l.ogvg pgkbgdn gpcmkgkmlespm`nrjge2 puhcmk metnrigkn Grgkem`l { [trmed nspnkmn : "vmlcmemstg"2 vlm` trnpgr()2 vlm` cgezgrPncgrgkemg()2 }

Kugrtl pgsl. Krngr cg kcgsn FljhrnGrgkem`l.

Ne nc jneÿ `n prlynktls qun nstç g cg mzqumnr`g, mzqumnr` g, nxpge`gjls nc prlynktl fgstg vnr nc pgquntn gpcmkgkmlespm`nrjge y slhrn nstn `gjls kcmk `nrnkfl y `nc jneÿ kletnxtugc sncnkkmlegjls Enw y cundl Ogvg Kcgss. Cn `gjls nc eljhrn `n FljhrnGrgkem`l g cg eunvg metnrigkn y kcmk ne nc hltûe –Imemsf‚. [ncnkkmlegjls cg pnstg÷g `n n`mkmûe ccgjg`g –FljhrnGrgkem`l.ogvg‚ y nskrmhmjls nc kû`mdl? FljhrnGrgkem`l.ogvg pgkbgdn gpcmkgkmlespm`nrjge2 puhcmk kcgss FljhrnGrgkem`l mjpcnjnets Fljhrn, Grgkem`l {

ALvnrrm`n puhcmk vlm` sgcu`gr() { [ystnj.lut.prmetce("Flcg, qun fgy `n eunvl!")2 }

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 61

ALvnrrm`n puhcmk vlm` dlcpngr() { [ystnj.lut.prmetce("Dgekfl mzq")2 [ystnj.lut.prmetce("Qgtg`g cgtnrgc")2 }

[ystnj.lut.prmetce("Qnccmzkl jlrtgc")2

ALvnrrm`n puhcmk vlm` trnpgr() { [ystnj.lut.prmetce("Gvgezg jgel mzq, pmn `nr")2 [ystnj.lut.prmetce("Cundl Gvgezg jgel `nr, pmn mzq")2 } ALvnrrm`n puhcmk vlm` cgezgrPncgrgkemg() { [ystnj.lut.prmetce("Gpuetgr, nstmrgr hrgzl")2 [ystnj.lut.prmetce("@lhcgr ju÷nkg, `mspgrg!!!")2 } }

Wumetl pgsl. N`mtgr cg kcgsn prmekmpgc.

Gflrg `nhnjls krngr ue lhontl `n cg kcgsn FljhrnGrgkem`l , cn `gjls vgclrns memkmgcns kljl eljhrn y nspnkmn y cundl nonkutgr gcduels `n sus jítl`ls. Ne nc nonjpcl, prmjnrl krngjls eunstrl supnrfírln, cundl cl fgknjls sgcu`gr, `nspuís cl plenjls g trnpgr y dlcpngr, gc imegc fgknjls qun cgekn su tncgrg÷g. Qgrg kl`mimkgr nc kljplrtgjmnetl getns `nskrmtl, sncnkkmlegjls cg pnstg÷g `n n`mkmûe ccgjg`g –Gpcmkgkmle[pm`nrjge.ogvg‚ y nskrmhmjls? Gpcmkgkmle[pm`nrjge.ogvg pgkbgdn gpcmkgkmlespm`nrjge2 puhcmk kcgss Gpcmkgkmle[pm`nrjge { puhcmk stgtmk vlm` jgme([trmedRZ grds) { FljhrnGrgkem`l pntnr : enw FljhrnGrgkem`l()2 pntnr.sgcu`gr()2 pntnr.trnpgr()2 pntnr.trnpgr()2 pntnr.trnpgr()2 pntnr.dlcpngr()2 pntnr.cgezgrPncgrgkemg()2 }

}

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 67

[nxtl pgsl. Kljpmcgr y Nonkutgr.

Gflrg kljpmcgjls y nonkutgjls nc prldrgjg, `ge`l kcmk ne nc mklel

, y lhtnenjls?

Xntl.

Gflrg prgktmqun cg fnrnekmg jÿctmpcn pgrg krngr ue grtêkucl qun smrvn kljl pcujg, gpuetg`lr cgsnr y rnclo.

6.0.0 Xnplrtn Gc imegcmzgr ístg prçktmkg nc gcujel `nhnrç dnenrgr ue rnplrtn ne Q@I qun kletnedg cls `mgdrgjgs `n kcgsns, nc kû`mdl iunetn y kgpturgs `n pgetgccg `n cg nonkukmûe `nc prldrgjg.

6.> Xnsuctg`ls y Klekcusmlens

Gc rngcmzgr cg prnsnetn prçktmkg, nc gcujel tne`rç ueg m`ng jçs kcgrg `n kûjl usgr cgs metnrigkns pgrg rnslcvnr prlhcnjgs qun mjpcmqune fnrnekmg jÿctmpcn.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 68

Qrgktmkg =. Jgenol `n nrrlrns =.7 Metrlùkkmûe Cg prnsnetn prçktmkg gyu`g g rnilrzgr cls kletnem`ls `n cg êm`g` Y? Nxknpkmlens

`n cls suhtnjgs >.7 @nimemkmûe, >.8 Pmpls `n nxknpkmlens, >.; Qrlpgdgkmûe `n

nxknpkmlens, >.0 Dnstmûe `n nxknpkmlens? jgenol `n nxknpkmlens, cgezgjmnetl `n nxknpkmlens, >.> Krngkmûe y jgenol `n nxknpkmlens `nimem`gs plr nc usugrml, `nc prldrgjg `n nstu`mls `n cg jgtnrmg `n Qrldrgjgkmûe Lrmnetg`g g Lhontls, `nsgrrlccge`l cg kljpntnekmg nspnkêimkg? –M`netmimkgr, jgenogr, dnstmlegr y krngr cgs kle`mkmlens `n nrrlr qun metnrrujpge nc icuol elrjgc `n nonkukmûe `n ue prldrgjg.‚.

=.8 Lhontmvl Kljpntnekmg)

Nskrmhmr ue kû`mdl qun mjpcnjnetn ue jgenol `n nrrlrns juy hçsmkl pgrg gtrgpgr nc nrrlr qun sn prlùkn gc metnetgr gkkn`nr g cls ncnjnetls `n ue grrndcl jçs gccç `n sus cêjmtns.

=.; Iue`gjnetl. R71ZR77Z

Nc jnolr jljnetl pgrg `ntnktgr cls nrrlrns `n kl`mimkgkmûe ns ùrgetn ` urgetn cg kljpmcgkmûe. [me njhgrdl, prçktmkgjnetn sûcl cls nrrlrns `n smetgxms sle `ntnktg`ls ùrgetn nstn pnrml`l. Nc rnstl `n prlhcnjgs surdne sur dne ùrgetn cg nonkukmûe `n cls prldrgjgs. êg nxknpkmûe ns ue nvnetl qun lkurrn ùrgetn cg nonkukmûe `nc prldrgjg qun metnrrujpn nc icuol elrjgc `n cgs snetnekmgs. Ne Ogvg, ueg Nxknptmle ns ue tmpl `n nrrlr qun sn fg prlùkm`l ùrgetn cg nonkukmûe `n ue prldrgjg. Gcduegs nxknpkmlens sle igtgcns y prlvlkge qun sn `nhg imegcmzgr cg nonkukmûenxpcmkge`l `nc prldrgjg. tnrjmegr lr`neg`gjnetn y `gr ue jnesgon nc tmplNe`nnstn nrrlrkgsl qun klevmnen sn fg prlùkm`l. Ltrgs, kljl plr nonjpcl el nekletrgr ue grkfmvl ne nc qun fgy qun cnnr l nskrmhmr gcdl, pun`ne snr rnkupnrghcns. Ne nstn kgsl nc prldrgjg `nhn `gr gc usugrml cg lplrtuem`g` `n klrrndmr nc nrrlr (me`mkge`l ueg eunvg clkgcmzgkmûe `nc grkfmvl el nekletrg`l). Klesm`nrn utmcmzgr prmekmpgcjnetn nxknpkmlens pgrg? 7. Grrndcgr nc prlhcnjg y ccgjgr `n eunvl gc jítl`l qun kgusû cg nxknpkmûe. 8. Grrndcgr tl`l y kletmeugr sme vlcvnr g nonkutgr nc jítl`l. ;. Kgckucgr gcdÿe rnsuctg`l gctnregtmvl ne vnz `n cl qun sn supleêg qun mhg g `nvlcvnr nc jítl`l. 0. Fgknr cl qun sn pun`g ne nc kletnxtl gktugc y rncgezgr cg jmsjg nxknpkmûe g

kletnxtl >. ue Fgknr cl qunsupnrmlr. sn pun`g ne nc kletnxtl gktugc y cgezgr ueg nxknpkmûe `minrnetn g ue kletnxtl supnrmlr. @npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 6;

9. Pnrjmegr nc prldrgjg. 4. [mjpcmimkgr. ([m tu nsqunjg `n nxknpkmûe fgkn gcdl jçs kljpcmkg`l, ns ueg jlcnstmg utmcmzgrcl.) 6. Fgknr jçs sndurls cg hmhcmltnkg y nc prldrgjg. (Ístg ns ueg mevnrsmûe g klrtl pcgzl `n kgrg`ngcgcggpcmkgkmûe.) `npurgkmûe, y tgjhmíe ueg mevnrsmûe g cgrdl pcgzl `n kgrg g cg ilrtgcnzg ê hune prldrgjg `nhn dnstmlegr klrrnktgjnetn tl`gs l cg jgylr pgrtn pgr tn `n cls nrrlrns qun sn pun`ne prlùkmr. Nc cnedugon Ogvg kunetg kle mestrukkmlens pgrg nc jgenol `n nrrlrns ne tmnjpl `n nonkukmûe. Pmpls `n nxknpkmlens

Nxmstne vgrmls tmpls iue`gjnetgcns `n nxknpkmlens?

Nrrlr? Nxknpkmlens qun me`mkge prlhcnjgs juy drgvns, qun suncne snr el rnkupnrghcns y el `nhne kgsm euekg snr kgpturg`gs. Nxknptmle? Nxknpkmlens el `nimemtmvgs, pnrl qun sn `ntnktge iunrg `nc tmnjpl `n nonkukmûe. XuetmjnNxknptmle? Nxknpkmlens qun sn `ge ùrgetn cg nonkukmûe `nc prldrgjg.

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Pl`gs cgs nxknpkmlens tmnene kljl kcgsn hgsn cg kcgsn Pfrlwghcn, qun nstç mekcum`g ne nc pgquntn ogvg.cged, y sus jítl`ls sle?

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   

Prlwghcn( [trmed jnesgon ). Klestruktlr. Cg kg`neg ns lpkmlegc Pfrlwghcn imccMe[tgkbPrgkn(). Ccneg cg pmcg `n trgzg `n nonkukmûe. [trmed dntClkgcmzn`Jnssgdn(). Krng ueg `nskrmpkmûe clkgc `n nstn lhontl. [trmed dntJnssgdn(). @nvuncvn cg kg`neg `n nrrlr `nc lhontl. vlm` prmet[tgkbPrgkn( Qrmet[trngj\l\QrmetTrmtnr s ). Mjprmjn nstn

lhontl y su trgzg ne nc icuol `nc pgrçjntrl s, l ne cg sgcm`g nstçe`gr (plr `ninktl). [trmed tl[trmed. @nvuncvn ueg hrnvn `nskrmpkmûe `nc lhontl.

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Gflrg rnpgsgrnjls kljl trghgogr kle cls hclquns y nxprnsmlens try, kgtkf, tfrlw, tfrlws y imegccy, kuçe`l sn `nhne cgezgr nxknpkmlens, kuçe`l sn `nhne kgpturgr y kûjl sn krnge cgs kcgsns prlpmgs `n tmpl Nxknptmle. Jgenol `n Nxknpkmlens Qgrg jgenogr ueg nxknpkmûe sn utmcmzge cgs pgcghrgs rnsnrvg`gs try y kgtkf. Nc hclqun try ns utmcmzg`l pgrg `nimemr nc hclqun `n kû`mdl ne nc kugc ueg nxknpkmûe pun`g lkurrmr. Nc l cls hclquns kgtkf sle utmcmzg`ls pgrg `nimemr ue hclqun `n kû`mdl qun

jgenon cg nxknpkmûe.

Cgs nxknpkmlens sle lhontls qun kletmnene meilrjgkmûe `nc nrrlr qun sn fg prlùkm`l. Fnrn`ge `n cg kcgsn Nxknptmle qun g su vnz fnrn`g `n cg kcgsn Pfrlwghcn. @npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 60

Pry…Kgtkf

Nc kû`mdl `netrl `nc   hclqun hclqun try nstç –vmdmcg`l‚? [m sn prlùkn ueg smtugkmûe gelrjgc y sn cgezg plr cl tgetl ueg nxknpkmûe nc kletrlc sgctg l sgcn `nc hclqun try y pgsg gc hclqun kgtkf, qun sn fgkn kgrdl `n cg smtugkmûe y `nkm`n cl qun fgy qun fgknr. [n pun`ne mekcumr tgetls hclquns kgtkf kljl snge enknsgrmls, kg`g uel `n cls kugcns trgtgrç ue tmpl `n nxknpkmûe. try { // Kû`mdl qun pl`rêg dnenrgr nxknpkmlens } kgtkf(Pmpl7 m`c) { // Jgenol `n nxknpkmlens `n Pmpl7 } kgtkf(Pmpl8 m`8) { // Jgenol `n nxknpkmlens `n Pmpl8 } kgtkf(Pmpl; m`;) { // Jgenol `n nxknpkmlens `n Pmpl; }

Pfrlw

Kuge`l ne ue jítl`l sn prlùkn ueg smtugkmûe geûjgcg ns enknsgrml cgezgr ueg nxknpkmûe. Nc prlknsl `n cgezgjmnetl `n ueg nxknpkmûe ns nc smdumnetn? 7. [n krng ue lhontl Nxknptmle `n cg kcgsn g`nkug`g. 8. [n cgezg cg nxknpkmûe kle cg snetnekmg tfrlw sndum`g `nc lhontl Nxknptmle krng`l. // Kû`mdl qun cgezg cg nxknpkmûe ueg vnz `ntnktg`l nc nrrlr JyNxknptmle jn : enw JyNxknptmle("JyNxknptmle jnssgdn")2 tfrlw jn2

Nstg nxknpkmûe `nhnrç snr kgpturg`g ( kgtkf) y dnstmleg`g ne nc prlpml jítl`l l ne gcdÿe ltrl cudgr `nc prldrgjg (ne ltrl jítl`l getnrmlr ne cg pmcg l stgkb `n ccgjg`gs). Gc cgezgr ueg nxknpkmûe nc jítl`l tnrjmeg `n mejn`mgtl, sme `nvlcvnr emedÿe vgclr. [lcgjnetn ne nc kgsl `n qun nc jítl`l mekcuyg cls hclquns try/kgtkf try/kgtkf/imegccy /imegccy sn nonkutgrç nc hclqun kgtkf qun cg kgpturg l nc hclqun imegccy (sm nxmstn). Pl`l jítl`l ne nc qun sn pun`n prlùkmr uel l jçs tmpls `n nxknpkmlens (y qun el utmcmzg `mrnktgjnetn cls hclquns try/kgtkf try/kgtkf/imegccy /imegccy) `nhn `nkcgrgr `nkcgrgrcgs cgs ne nc nekghnzg`l `n cg iuekmûe plr jn`ml `n cg pgcghrg tfrlws. [m ue jítl`l pun`n cgezgr vgrmgs nxknpkmlens, sn plene `ntrçs `n tfrlws snpgrg`gs plr kljgs, plr nonjpcl? puhcmk vlm` cnnrImkfnrl([trmed imkf) tfrlws NLINxknptmle, ImcnEltIlue`Nxknptmle {…}

supnrkcgsnn `n nxknpkmlens lens pgrg me`mkgr qun sn pun`ne cgezgr [n pun`n plenr ueg supnrkcgs nxknpkmlens `n slcl kugcqumnrg `n sus kcgsnsnxknpkm `nrmvg`gs. Nc kgsl getnrmlr ns nqumvgcnetn g? puhcmk vlm` cnnrImkfnrl([trmed imkf) tfrlws MLNxknptmle {…}

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 6>

Cgs nxknpkmlens pun`ne snr cgezg`gs `mrnktgjnetn plr cnnrImkfnrl() l plr gcduel `n cls jítl`ls ccgjg`ls plr cnnrGrkfmvl() , yg qun cgs kcgsns NLINxk NLINxknptmle nptmle y ImcnEltIlue`Nxkn ImcnEltIl ue`Nxknptmle ptmle `nrmvge `n MLNxknp MLNxknptmle tmle. [n rnkunr`g qun el fgkn igctg gvmsgr `n qun sn pun`ne cgezgr lhontls `n cgs kcgsns

Nrrlr l Xuetmjn XuetmjnNxknptm Nxknptmle le (nxknpkmlens mjpcêkmtgs). R77Z

Kljl kugcqumnr ltrl lhontl ne Ogvg, cgs nxknpkmlens smnjprn sn krnge ne nc jletêkucl fgkmne`l usl `n enw, qun gsmdeg nspgkml `n gcjgknegjmnetl n mevlkg g ue klestruktlr. Fgy `ls klestruktlrns ne tl`gs cgs nxknpkmlens nstçe`gr? nc prmjnrl ns nc klestruktlr plr `ninktl y nc sndue`l tljg ue pgrçjntrl strmed `n ilrjg qun sn pun`g uhmkgr cg meilrjgkmûe pnrtmenetn ne cg nxknpkmûe? nx knpkmûe? mi (t :: eucc) tfrlw enw EuccQlmetnrNxknptmle ("t : eucc")2

Nstn strmed pun`n nxtrgnrsn plstnrmlrjnetn utmcmzge`l vgrmls jítl`ls, kljl sn vnrç tfrlw fgkn qun lkurrge vgrmgs klsgs rncgtmvgjnetn jçs g`ncgetn. Cg pgcghrgsnkcgvn jçdmkgs. Fghmtugcjnetn, usgrç prmjnrl enw pgrg krngr ue lhontl qun rnprnsnetn cg kle`mkmûe `n nrrlr. [n `g g tfrlw cg rninrnekmg rnsuctgetn. Ne ninktl, nc jítl`l "`nvuncvn" nc lhontl, mekcusl guequn nsn tmpl `n lhontl el sng nc qun nc jítl`l `nhnrêg `nvlcvnr `n ilrjg egturgc.

êg jgenrg egturgc `n pnesgr ne cgs nxknpkmlens ns kljl sm sn trgtgrg `n ue jnkgemsjl `n rntlrel gctnregtmvl, guequn nc qun ccnvn nstg gegcldêg `njgsmg`l cnols gkghgrç tnemne`l prlhcnjgs. Pgjhmíe sn pun`n sgcmr `nc çjhmtl lr`megrml cgezge`l ueg nxknpkmûe. Qnrl sn `nvuncvn ue vgclr, y nc jítl`l l nc çjhmtl imegcmzge. R71Z Pfrlws

Nxmstne gcduels kgsls ne cls kugcns nc kû`mdl `n ue jítl`l pun`n dnenrgr ueg Nxknptmle y el sn `nsng mekcumr ne `mkfl jítl`l cg dnstmûe `nc nrrlr. Ogvg pnrjmtn qun nstn jítl`l pgsn l rncgekn ( tfrlws tfrlws) cg Nxknptmle gc jítl`l `ns`n nc qun fg sm`l ccgjg`l, sme mekcumr ne nc jítl`l cls hukcns try/kgtkf klrrnsple`mnetns. Nstl sn klesmdun jn`mgetn cg g`mkmûe `n tfrlws jçs nc eljhrn `n cg Nxknptmle klekrntg `nspuís `n cg cmstg `n grdujnetls `nc jítl`l. G su vnz nc jítl`l supnrmlr Nxknptmle e. @n nstg ilrjg sn `nhnrç mekcumr cls hclquns try/kgtkf l vlcvnr g pgsgr cg Nxknptml Nxknptmle e `n ue jítl`l g ltrl fgstg ccndgr gc ÿctmjl jítl`l `nc pun`n mr pgsge`l cg Nxknptml prldrgjg, nc jítl`l jgme(). R77Z Imegccy

G jneu`l fgy gcduels irgdjnetls `n kû`mdl qun sn `nsng nonkutgr

me`npne`mnetnjnetn `n qun sn cgekne l el nxknpkmlens `netrl `n ue hclqun try. Nstl dnenrgcjnetn nstç rncgkmleg`l kle lpnrgkmlens `mstmetgs `n rnkupnrgkmûe `n jnjlrmg (punstl qun `n nstl yg sn nekgrdg nc rnklcnktlr `n hgsurg). @npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 69

Qgrg cldrgr nstn ninktl, sn usg ueg kcçusucg imegccy gc imegc `n tl`ls cls jgenog`lrns `n nxknpkmlens. Nc nsqunjg kljpcntl `n ueg snkkmûe `n jgenol `n nxknpkmlens ns, plr klesmdumnetn? try

{ // Cg rndmûe prltndm`g? Gktmvm`g`ns pncmdrlsgs qun // pl`rêge cgezgr G l H } kgtkf (G gc) { // Jgenog`lr pgrg cg smtugkmûe G } kgtkf (H hc) { // Jgenog`lr pgrg cg smtugkmûe H } imegccy { // Gktmvm`g`ns qun sn `ge smnjprn }

Mcustrgkmûe 71. Onrgrquêg `n kcgsns `n nxknpkmlens

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 64

Mcustrgkmûe 77. Qrlpgdgkmûe `n nxknpkmlens

=.0 Qrlkn`mjmnetl @nskrmpkmûe) =.0.7 Nqumpl enknsgrml

Kljputg`lrg kle ue smstnjg lpnrgtmvl qun kunetn kle gjhmnetn drçimkl (Tme`lws, Cmeux, ntk…)

=.0.8 Jgtnrmgc `n Gplyl [@B `n ogvg. Netlrel `n `nsgrrlccl pgrg ogvg EntHnges.

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=.0.; @nsgrrlccl `n cg Qrçktmkg Ne nstg prçktmkg trghgogrnjls kle ueg nxknpkmûe qun yg nstç prn`nimem`g ne cgs cmhrnrêgs `nc O@B, cg nxknpkmûe GrrgyMe`nxLutLiHlue`sNxknptmle. Memkmgjls enthnges, ncndmjls cg lpkmûe –Imcn Enw Qrlonkt‚. Krngjls ueg gpcmkgkmûe ogvg. Cn `gjls nc eljhrn `n –nonjpclJgenolNrrlr ‚ gc prlynktl. @gjls kcmk ne nc hltûe –Imemsf‚ y nc prlynktl sn fg krng`l.

[m ns nc ÿemkl prlynktl pl`njls sgctgr nstn pgsl. Ne ltrl kgsl, `gjls kcmk `nrnkfl slhrn nc eljhrn `nc prlynktl y ne nc jneÿ kletnxtugc sncnkkmlegjls – [nt gs Jgme Qrlonkt‚. Nc eljhrn `nc prlynktl `nhn plenrsn ne endrmtgs.

Qrmjnrg vnrsmûe.

N`mtgjls cg kcgsn prmekmpgc nskrmhmne`l cg prmjnrg vnrsmûe, qun ns ue prldrgjg sme nrrlrns. Nc kû`mdl ns?

NonjpclJgenolNrrlr.ogvg pgkbgdn nonjpcljgenolnrrlr2

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 66

puhcmk kcgss NonjpclJgenolNrrlr { puhcmk stgtmk vlm` jgme([trmedRZ grds) { [trmedRZ gemjgcns : {"Cnûe", "Qujg", "@nciêe", "Pmdrn"}2 met tgj : gemjgcns.cnedtf2 //rnklrrnr nc grrndcl n mjprmjmr sus ncnjnetls ilr (met m : 12 m 3 gemjgcns.cnedtf2 m++) { [ystnj.lut.prmetce(gemjgcnsRmZ)2 } } }

[gcm`g rue? Cnûe Qujg @nciêe Pmdrn H^MC@ [^KKN[[I^C (tltgc tmjn? 1 snkle`s)

[ndue`g vnrsmûe.

Ne nstg vnrsmûe sn metrlùkn ue nrrlr gcdl kljÿe? sn fgkn rninrnekmg g ue ncnjnetl iunrg `n cls cêjmtns `nc grrndcl. Nc kû`mdl ns? pgkbgdn nonjpcljgenolnrrlr2 puhcmk kcgss NonjpclJgenolNrrlr { puhcmk stgtmk vlm` jgme([trmedRZ grds) { [trmedRZ gemjgcns : {"Cnûe", "Qujg", "@nciêe", "Pmdrn"}2 met tgj : gemjgcns.cnedtf2 // [n metrlùkn ue nrrlr ilr (met m : 12 m 3: gemjgcns.cnedtf2 m++) { [ystnj.lut.prmetce(gemjgcnsRmZ)2 } } }

[gcm`g rue? Cnûe Qujg @nciêe Pmdrn Nxknptmle me tfrng` "jgme" ogvg.cged.GrrgyMe`nxLutLiHlue`sNxknptmle? 0 gt nonjpcljgenolnrrlr.NonjpclJgenolNrrlr.jgme(NonjpclJgenolNrrlr.ogvg?77) @?S^[email protected]

semppntsSrue.xjc?>;? Ogvg rnturen`? 7 H^MC@ IGMCN@ (tltgc tmjn? 1 snkle`s)

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 6=

Pnrknrg vnrsmûe.

Nstg vnrsmûe gÿe tmnen nc nrrlr, pnrl yg kunetg kle nc jnkgemsjl pgrg gtrgpgrcl n meilrjgr gc usugrml. Nc kû`mdl ns? pgkbgdn nonjpcljgenolnrrlr2 puhcmk kcgss NonjpclJgenolNrrlr { puhcmk stgtmk vlm` jgme([trmedRZ grds) { [trmedRZ gemjgcns : {"Cnûe", "Qujg", "@nciêe", "Pmdrn"}2 met tgj : gemjgcns.cnedtf2 try { //rnklrrnr nc grrndcl n mjprmjmr sus ncnjnetls ilr (met m : 12 m 3: gemjgcns.cnedtf2 m++) { [ystnj.lut.prmetce(gemjgcnsRmZ)2 } } kgtkf (GrrgyMe`nxLutLiHlue`sNxknptmle n) { [ystnj.lut.prmetce("Nrrlr? iunrg `n cls cêjmtns `nc grrndcl")2 } } }

[gcm`g rue? Cnûe Qujg @nciêe Pmdrn Nrrlr? iunrg `n cls cêjmtns `nc grrndcl H^MC@ [^KKN[[I^C (tltgc tmjn? 1 snkle`s)

Xntl.

Nskrmhn ue prldrgjg qun usn cg kcgsn `n cg nxknpkmûe " Grmtfjntmk GrmtfjntmkNxknpt Nxknptmle mle" pgrg `ntnktgr ueg `mvmsmûe plr knrl.

=.0.0 Gc Xnplrtn imegcmzgr ístg prçktmkg nc gcujel `nhnrç dnenrgr ue rnplrtn ne Q@I qun kletnedg nc kû`mdl iunetn y kgpturgs `n pgetgccg `n cg nonkukmûe `nc prldrgjg.

=.> Xnsuctg`ls y Klekcusmlens

Kle ístg prçktmkg, nc gcujel pl`rç fgknr prldrgjgs jçs rlhustls, puns gc jgenogr cg jgylr pgrtn `n cgs kgusgs `n nrrlr `n ue prldrgjg, snrç jçs içkmc rnkupnrgrsn `n cls nrrlrns y g`njçs rnkmhmr jnesgons qun els `ne pmstgs `n kljl klrrndmr cls igccls, y gsê rnùkmr cls tmnjpls `n jgetnemjmnetl.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg =1

Qrgktmkg 71. Cnnr y nskrmhmr grkfmvls `n tnxtl. 71.7 Metrlùkkmûe

Cg prnsnetn prçktmkg gyu`g g gsmjmcgr cls kletnem`ls `n cg êm`g` YM? Icuols y grkfmvls `n cls suhtnjgs 9.7 @nimemkmûe y 9.8 Kcgsmimkgkmûe? Grkfmvls `n tnxtl y hmegrmls `nc prldrgjg `n nstu`mls `n cg jgtnrmg `n Qrldrgjgkmûe Lrmnetg`g g Lhontls, `nsgrrlccge`l cg kljpntnekmg nspnkêimkg? –Kljprne`n y gpcmkg cg kcgsmimkgkmûe `n grkfmvls y lpnrgkmlens hçsmkgs slhrn ístls pgrg jgempucgr su meilrjgkmûe ‚.

71.8 Lhontmvl Kljpntnekmg)

Ncghlrgr ue prldrgjg qun dugr`n y cng grkfmvl ne ogvg. @nhn cnnr y nskrmhmr cls `gtls ne ue grkfmvl `n tnxtl.

71.; Iue`gjnetl

Qnrsmstnekmg `n `gtls.

Ne dnenrgc, ne eunstrls prldrgjgs usgjls vgrmghcns pgrg jgempucgr meilrjgkmûe. Cl kljÿe ns qun `mkfgs vgrmghcns sn `nstruyne gc imegcmzgr nc prldrgjg, puns nc gcjgknegjmnetl `n `gtls ne vgrmghcns y grrgys (grrndcls) ns tnjplrgc2 cls `gtls sn pmnr`ne kuge`l ueg vgrmghcn sgcn `n su çjhmtl l gckgekn `n meicunekmg, l hmne kuge`l sn tnrjmeg nc prldrgjg. Cg jgylrêg `n cgs gpcmkgkmlens rnqumnrne qun cg meilrjgkmûe sn gcjgknen `n ilrjg pnrsmstnetn, ns `nkmr qun el sn hlrrn l ncmjmen kuge`l sn tnrjmeg cg nonkukmûe `nc prldrgjg. Qlr ltrg pgrtn, ne eujnrlsgs gpcmkgkmlens sn rnqumnrn utmcmzgr drge`ns kgetm`g`ns `n meilrjgkmûe qun, elrjgcjnetn, el kghne ne cg jnjlrmg prmekmpgc. @nhm`l g nstgs kgusgs sn rnqumnrn utmcmzgr grkfmvls pgrg gcjgknegr `n jl`l pnrjgenetn drge`ns kgetm`g`ns `n `gtls, mekcusl `nspuís qun cls prldrgjgs qun krnge cls `gtls sn tnrjmege. Nstls `gtls gcjgkneg`ls ne grkfmvls sn klelkne kljl `gtls pnrsmstnetns y pnrjgenkne `nspuís `n cg ùrgkmûe ùr gkmûe `n cg nonkukmûe `nc prldrgjg. Cls `msn÷g`lrns `n cg hmhcmltnkg `n Ogvg krngrle jukfgs kcgsns pgrg nc smstnjg `n N/[, kljl rnsuctg`l fgy qun gprne`nr ue eÿjnrl `n kcgsns gknptghcn getns `n netne`nr suimkmnetnjnetn ue nshlzl `n cg N/[ `n Ogvg pgrg pl`nr usgrcg g`nkug`gjnetn. Qnrl trgtgrnjls `n dugr`gr y nskrmhmr `gtls ne gue grkfmvl `n ueg

ilrjg juy smjpcn. Qgrg cnnr grkfmvls `n tnxtl usgrnjls cg ImcnXng` ImcnXng`nr nr y pgrg nskrmhmr ne ue grkfmvl `n tnxtl usgrnjls ImcnTrmtn ImcnTrmtnrr2 gjhgs kcgsns sn nekunetrge ne cg cmhrnrêg ogvg.ml @npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg =7

Cg kcgsn ImcnXng`nr tmnen vgrmls klestruktlrns, plr gflrg slcl usgrnjls nc smdumnetn? puhcmk ImcnXng`nr( ImcnXng`nr([trmed [trmed eljhrnGrkfmvl) eljhrnGrkfmvl) tfrlws ImcnEltIlue`Nxknptmle ImcnEltIlue`Nxknptmle

@le`n? Krngjls ue lhontl ImcnXng`nr, `ge`l nc eljhrn `nc grkfmvl qun cnnrnjls. Qgrçjntrls? eljhrnGrkfmvl - eljhrn `nc grkfmvl qun cnnrnjls Pfrlws? ImcnEltIlue`Nxknptmle ‛  Ne Ne kgsl qun nc grkfmvl el nxmstg l plr gcdueg ImcnEltIlue`Nxknptmle  ‛ smtugkmûe el pl`gjls cnnrcl, sn cgezg nstg nxknpkmûe. Cg kcgsn ImcnTrmtnr tmnen vgrmls klestruktlrns, plr gflrg slcl usgrnjls nc smdumnetn? puhcmk ImcnTrmtnr(Trmtnr sgcm`g) tfrlws ImcnEltIlue`Nxknptmle ImcnEltIlue`Nxknptmle

@le`n? Krngjls ue lhontl ImcnTrmtnr, `ge`l nc eljhrn `n ue lhontl Trmtnr. Qgrçjntrls? sgcm`g - eljhrn `nc lhontl Trmtnr qun usgrnjls pgrg gkkn`nr gc grkfmvl. Pfrlws? EuccQlmetnrNxknptmle ‛  [m [m cg sgcm`g ne eucc

71.0 Qrlkn`mjmnetl @nskrmpkmûe) 71.0.7 Nqumpl Nqumpl enknsgrml

Kljputg`lrg kle ue smstnjg lpnrgtmvl qun kunetn kle gjhmnetn drçimkl (Tme`lws, Cmeux, ntk…)

71.0.8 Jgtnrmgc Jgtnrmgc `n Gplyl [@B `n ogvg. Netlrel `n `nsgrrlccl pgrg ogvg, nc M@N EntHnges.



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71.0.; @nsgrrlccl @nsgrrlccl `n cg Qrçktmkg Nstg prçktmkg cg `nsgrrlccgrnjls ne `ls pgrtns? ne cg prmjnrg krngrnjls y nskrmhmrnjls ne ue grkfmvl, y ne nc sndue`l cnnrnjls tgc grkfmvl. Memkmgjls enthnges, ncndmjls cg lpkmûe –Imcn Enw Qrlonkt‚. Krngjls ueg

gpcmkgkmûe ogvg. Cn `gjls nc eljhrn `n –cnnrNskrmhmrGrkfmvl ‚ gc prlynktl. @gjls kcmk ne nc hltûe –Imemsf‚ y nc prlynktl sn fg krng`l.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg =8

[m ns nc ÿemkl prlynktl pl`njls sgctgr nstn pgsl. Ne ltrl kgsl, `gjls kcmk `nrnkfl slhrn nc eljhrn `nc prlynktl y ne nc jneÿ kletnxtugc sncnkkmlegjls – [nt gs Jgme Qrlonkt‚. Nc eljhrn `nc prlynktl `nhn plenrsn ne endrmtgs.

Qrmjnrg pgrtn.

N`mtgjls cg kcgsn prmekmpgc nskrmhmne`l nc jítl`l nskrmhmrGrkfmvl() , y cl mevlkgjls `ns`n nc jítl`l jgme(). Nc kû`mdl ns? cnnrNskrmhmrGrkfmvl.ogvg pgkbgdn cnnrnskrmhmrgrkfmvl2 mjplrt ogvg.ml.ImcnTrmtnr2 mjplrt ogvg.ml.MLNxknptmle2 puhcmk kcgss CnnrNskrmhmrGrkfmvl { // Jgenogjls cg nxknpkmûe MLNxknptmle vlm` nskrmhmrGrkfmvl() tfrlws MLNxknptmle { // Krngjls nc lhontl grkfmvl. // Ne kgsl qun yg nxmstg, sn slhrnnskrmhn ImcnTrmtnr grkfmvl : enw ImcnTrmtnr("`gtls.txt")2 // Nskrmhmjls ue tnxtl ne nc grkfmvl grkfmvl.wrmtn("Flcg jue`l!!!")2 // Knrrgjls nc grkfmvl grkfmvl.kclsn()2 } puhcmk stgtmk vlm` jgme([trmedRZ grds) tfrlws MLNxknptmle { CnnrNskrmhmrGrkfmvl gpp : enw CnnrNskrmhmrGrkfmvl()2 gpp.nskrmhmrGrkfmvl()2 gpp.cnnrGrkfmvl()2 } }

[gcm`g rue? H^MC@ [^KKN[[I^C (tltgc tmjn? 1 snkle`s)

Ql`njls vnr qun nc prldrgjg el els nevêg emedÿe jnesgon, pnrl sm vnjls nc `mrnktlrml `nc prlynktl, vnrnjls qun sn krnû nc grkfmvl `gtls.txt.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg =;

Ynjls qun els jgrkg qun tmnen ue tgjg÷l `n 7bh, nstn ns nc tgjg÷l rngc qun lkupg ne `mskl. Qnrl sm vnjls sus prlpmn`g`ns, els me`mkg qun tmnen ue tgjg÷l `n 7; hytns, nstn sn rnimnrn gc tgjg÷l cûdmkl, qun ns cg kgetm`g` `n meilrjgkmûe qun dugr`g. Qnrl, ¼Wuí pgsg kle cls `njçs hytns< ¡Quns sn `nspnr`mkmge!, nstl sn klelkn kljl irgdjnetgkmûe metnreg. ] ns ue prnkml qun sn tmnen qun pgdgr ne igvlr `nc `nsnjpn÷l. `ns njpn÷l. Quns pgrg gkncnrgr cgs vnclkm`g`ns `n nskrmturg y cnkturg, nc jnkgemsjl `nc fgr`wgrn slcl pun`n cnnr y nskrmhmr hclquns `n hytns, ne cudgr `n hytn plr hytn. [ndue`g pgrtn.

N`mtgjls cg kcgsn prmekmpgc nskrmhmne`l nc jítl`l cnnrGrkfmvl(), y cl mevlkgjls `ns`n nc jítl`l jgme(), g`njçs plenjls netrn kljnetgrmls cg mevlkgkmûe g cg iuekmûe nskrmhmrGrkfmvl() pgrg qun slcl cngjls nc grkfmvl. Nc kû`mdl ns? cnnrNskrmhmrGrkfmvl.ogvg pgkbgdn cnnrnskrmhmrgrkfmvl2 mjplrt ogvg.ml.ImcnXng`nr2 mjplrt ogvg.ml.ImcnTrmtnr2 mjplrt ogvg.ml.MLNxknptmle2 puhcmk kcgss CnnrNskrmhmrGrkfmvl { // Jgenogjls cg nxknpkmûe MLNxknptmle vlm` nskrmhmrGrkfmvl() tfrlws MLNxknptmle { // Krngjls nc lhontl grkfmvl. // Ne kgsl qun yg nxmstg, sn slhrnnskrmhn ImcnTrmtnr grkfmvl : enw ImcnTrmtnr("`gtls.txt")2 // Nskrmhmjls ue tnxtl ne nc grkfmvl grkfmvl.wrmtn("Flcg jue`l!!!")2

// Knrrgjls nc grkfmvl grkfmvl.kclsn()2 }

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg =0

// Jgenogjls cg nxknpkmûe MLNxknptmle vlm` cnnrGrkfmvl() tfrlws MLNxknptmle { // Krngjls nc lhontl grkfmvl. ImcnXng`nr grkfmvl : enw ImcnXng`nr("`gtls.txt")2 met cntrg2 // Cnnjls nc grkfmvl hytn plr hytn `l{ cntrg:grkfmvl.rng`()2 [ystnj.lut.prmetce("Hytn? "+(kfgr)cntrg)2 } wfmcn(cntrg!:-7)2 // Knrrgjls nc grkfmvl grkfmvl.kclsn()2 } puhcmk stgtmk vlm` jgme([trmedRZ grds) tfrlws MLNxknptmle { CnnrNskrmhmrGrkfmvl gpp : enw CnnrNskrmhmrGrkfmvl()2 // gpp.nskrmhmrGrkfmvl()2 gpp.cnnrGrkfmvl()2 }

}

[gcm`g rue? Hytn? Hytn? Hytn? Hytn? Hytn? Hytn? Hytn? Hytn? Hytn? Hytn? Hytn? Hytn? Hytn? Hytn? H^MC@

F l c g j u e ` l ! ! ! [^KKN[[I^C (tltgc tmjn? 1 snkle`s)

Xntl.

Krnn ue prldrgjg qun dugr`n > eljhrns `n pnrslegs, cundl nskrmhg ue kû`mdl qun ghrg nc grkfmvl getnrmlr y kunetn n mjprmjg cg kgetm`g` `n vlkgcns ne nc grkfmvl.

71.0.0 Xnplrtn Xnplrtn Gc imegcmzgr ístg prçktmkg nc gcujel `nhnrç dnenrgr ue rnplrtn ne Q@I qun kletnedg nc kû`mdl iunetn y kgpturgs `n pgetgccg `n cg nonkukmûe `nc prldrgjg.

71.> Xnsuctg`ls y Klekcusmlens

Gc rngcmzgr nstg snekmccg prçktmkg nc gcujel pl`rç dugr`gr y rnkupnrgr meilrjgkmûe `ns`n ue grkfmvl.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg =>

Qrgktmkg 77. Dugr`gr y rnkupnrgr lhontls. 77.7 Metrlùkkmûe

Cg prnsnetn prçktmkg gyu`g g gsmjmcgr cls kletnem`ls `n cg êm`g` YM? Icuols y grkfmvls `n cls suhtnjgs 9.; Lpnrgkmlens hçsmkgs y tmpls `n gkknsl y 9.0 Jgenol `n lhontls pnrsmstnetns `nc prldrgjg `n nstu`mls `n cg jgtnrmg `n Qrldrgjgkmûe Lrmnetg`g g Lhontls, `nsgrrlccge`l cg kljpntnekmg nspnkêimkg? –Kljprne`n y gpcmkg cg kcgsmimkgkmûe `n grkfmvls y lpnrgkmlens hçsmkgs slhrn ístls pgrg jgempucgr su meilrjgkmûe‚.

77.8 Lhontmvl Kljpntnekmg)

Ncghlrgr ue prldrgjg qun dugr`n y cng lhontls `n ogvg. @nhn krngr cg kcgsn Qnrsleg kle cls gtrmhutls `n eljhrn, pnsl y nstgturg y kle nc jítl`l mjk(), qun kgckucg nc êe`mkn `n jgsg klrplrgc. @nspuís `nhn krngr ue lhontl `n cg kcgsn pnrsleg y dugr`grcg ne nc grkfmvl pgkmnetn.`gt . Gc imegc, `nhn krngr nc lhontl iucgel g pgrtmr `n cg kcgsn qun nstg dugr`g`g ne nc grkfmvl y usge`l nstn lhontl mjprmjmjls sus gtrmhutls n mevlkgjls g su jítl`l mjk().

77.; Iue`gjnetl

Ne cg prçktmkg getnrmlr dugr`gjls y rnkupnrgjls tnxtl, pnrl gc snr ogvg ue cnedugon lrmnetg`l g lhontls, rnsuctg juy metnrnsgetn `ltgr g cls lhontls `n pnrsmstnekmg (pl`nrcls dugr`gr ne grkfmvls). G nstg iuekmlegcm`g` sn s n cn klelkn kljl snrmgcmzgkmûe.

[nrmgcmzgkmûe. Cg snrmgcmzgkm snrmgcmzgkmûe ûe `n lhontls `n Ogvg pnrjmtn tljgr kugcqumnr lhontl qun mjpcnjnetn cg metnrigz [nrmgcmzghcn y klevnrtmrcl ne ueg snkunekmg `n hmts qun pun`n snr

plstnrmlrjnetn rnstgurg`g pgrg rndnenrgr r ndnenrgr nc lhontl lrmdmegc. Nc jnkgemsjl `n snrmgcmzgkmûe kljpnesg gutljçtmkgjnetn cgs `minrnekmgs netrn smstnjgs lpnrgtmvls. Ns `nkmr, sn pun`n krngr ue lhontl ne ueg jçqumeg Tme`lws, snrmgcmzgrcl, y nevmgrcl g trgvís `n cg rn` g ueg jçqumeg jçq umeg êmx, `le`n snrç rnklestrum`l klrrnktgjnetn. El fgy qun prnlkupgrsn `n cgs rnprnsnetgkmlens `n cls `gtls ne cgs `mstmetgs jçqumegs, gc mdugc qun el mjplrtge cg lr`negkmûe `n cls hytns y nc rnstl `n `ntgccns. Kle cg snrmgcmzgkmûe cldrgjls qun nc tmnjpl `n vm`g `n ue lhontl ùrn jçs gccç `n cg nonkukmûe `nc prldrgjg qun cl usg.

ê gspnktl pgrtmkucgrjnetn metncmdnetn `n cg snrmgcmzgkmûe `n lhontls ns qun, el sûcl sgcvg cg mjgdne `nc lhontl, smel qun tgjhmíe smdun tl`gs cgs rninrnekmgs kletnem`gs ne nc lhontl, y sgcvg nsls lhontls, smdumne`l g`njçs cgs rninrnekmgs kletnem`gs ne kg`g @npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg =9

uel `n nccls, ntk. G nstl sn cn suncn `neljmegr cg "tncgrg÷g `n lhontls" punstl qun ue ÿemkl lhontl pun`n nstgr klenktg`l, n mekcumr grrgys `n rninrnekmgs g lhontls, g`njçs `n lhontls jmnjhrl. [m sn tuvmnrg qun jgetnenr ue nsqunjg `n snrmgcmzgkmûe `n lhontls prlpml, nc jgetnemjmnetl `nc kû`mdl pgrg sndumr tl`ls nstls ns tls necgkns snrêg kgsm mjplsmhcn. [me njhgrdl, cg snrmgcmzgkmûe `n lhontls Ogvg pgrnkn nekgrdgrsn `n tl`l fgkmne`l usl `n ue gcdlrmtjl lptmjmzg`l qun rnklrrn cg tncgrg÷g `n lhontls. R71Z Qgrg qun ueg kcgsn pun`g utmcmzgr cg snrmgcmzgkmûe, `nhn mjpcnjnetgr cg metnrigkn [nrmgcmzghcn , qun el `nimen emedÿe jítl`l. Kgsm tl`gs cgs kcgsns nstçe`gr `n Ogvg sle snrmgcmzghcns. Qgrg qun ueg kcgsn sn pun`g snrmgcmzgr sn `nhn `nkcgrgr kljl? puhcmk kcgss JmKcgsn mjpcnjnets [nrmgcmzghcn { }

Qgrg nskrmhmr ue lhontl sn utmcmzg cg kcgsn LhonktLutput[trngj , qun kunetge kle nc jítl`l wrmtnLhonkt() . Qlr nonjpcl? LhonktLutput[trngj lhontl : enw LhonktLutput[trngj(enw ImcnLutput[trngj("grkfmvl.x"))2 [trmed tnxtl : enw [trmed("Jn vge g snrmgcmzgr")2 lhontl.wrmtnLhonkt(tnxtl)2

Qgrg cnnr lhontls sn utmcmzg cg kcgsn LhonktMeput[trngj , qun kunetg kle nc jítl`l rng`Lhonkt() rng`Lhon kt(). Qlr nonjpcl? LhonktMeput[trngj lhontl : enw LhonktMeput[trngj(enw ImcnMeput[trngj("grkfmvl.x"))2 [trmed tnxtl : ([trmed)lhontl.rng`Lhonkt()2

@nhn tnenr ne kunetg qun rng`Lhon rng`Lhonkt() kt() `nvuncvn ue Lhonkt slhrn nc qun sn `nhnrç fgknr ue kgstmed pgrg qun nc lhontl sng ÿtmc. Cg rnklestrukkmûe enknsmtg qun nc grkfmvl *.kcgss nstí gc gckgekn `nc prldrgjg (kljl jêemjl pgrg fgknr nstn kgstmed). R77Z

77.0 Qrlkn`mjmnetl @nskrmpkmûe) 77.0.7 Nqumpl Nqumpl enknsgrml

Kljputg`lrg kle ue smstnjg lpnrgtmvl qun kunetn kle gjhmnetn drçimkl (Tme`lws, Cmeux, ntk…)

77.0.8 Jgtnrmgc Jgtnrmgc `n Gplyl [@B `n ogvg. Netlrel `n `nsgrrlccl pgrg ogvg, nc M@N EntHnges.

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77.0.; @nsgrrlccl @nsgrrlccl `n cg Qrçktmkg

Nstg prçktmkg cg `nsgrrlccgrnjls ne `ls pgrtns? ne cg prmjnrg pgrtn krngrnjls cg kcgsn Qnrsleg pgrg `nspuís krngr ue lhontl `n `mkfg kcgsn y dugr`grcl ne ue grkfmvl ccgjg`l pgkmnetn.`gt. Ne cg sndue`g pgrtn krngrnjls ue lhontl g pgrtmr `n cg kcgsn qun nstg dugr`g`g ne nc grkfmvl. @npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg =4

Memkmgjls enthnges, ncndmjls cg lpkmûe –Imcn Enw Qrlonkt‚. Krngjls ueg gpcmkgkmûe ogvg. Cn `gjls nc eljhrn `n –gpcmkgkmleDugr`grLhontl ‚ gc prlynktl. @gjls kcmk ne nc hltûe –Imemsf‚ y nc prlynktl sn fg krng`l.

[m ns nc ÿemkl prlynktl pl`njls sgctgr nstn pgsl. Ne ltrl kgsl, `gjls kcmk `nrnkfl

slhrn nc eljhrn `nc prlynktl y ne nc jneÿ kletnxtugc sncnkkmlegjls – [nt gs Jgme Qrlonkt‚. Nc eljhrn `nc prlynktl `nhn plenrsn ne endrmtgs.

Qrmjnrg pgrtn.

Krngjls cg kcgsn Qnrsleg, rnkunr`n qun `nhn mjpcnjnetgr cg metnrigkn [nrmgcmzghcn , pgrg qun pl`gjls dugr`grcg ne ue grkfmvl. Qnrsleg.ogvg pgkbgdn gpcmkgkmledugr`grlhontl2 mjplrt ogvg.ml.[nrmgcmzghcn2 puhcmk kcgss Qnrsleg mjpcnjnets [nrmgcmzghcn { [trmed eljhrn2 iclgt pnsl2 iclgt nstgturg2 puhcmk Qnrsleg([trmed eljhrn, iclgt pnsl, iclgt nstgturg) { tfms.eljhrn : eljhrn2 tfms.pnsl : pnsl2 tfms.nstgturg : nstgturg2 } iclgt mjk() { rnture pnsl / (nstgturg * nstgturg)2 } }

Ne cg kcgsn prmekmpgc nskrmhmrnjls nc kû`mdl enknsgrml pgrg gcjgknegr nc lhontl. Pgjhmíe `nhnjls gdrndgr nc jgenol `n nxknpkmlens. Nc kû`mdl ns? GpcmkgkmleDugr`grLhontl.ogvg pgkbgdn gpcmkgkmledugr`grlhontl2 mjplrt mjplrt mjplrt mjplrt

ogvg.ml.ImcnEltIlue`Nxknptmle2 ogvg.ml.ImcnLutput[trngj2 ogvg.ml.MLNxknptmle2 ogvg.ml.LhonktLutput[trngj2

puhcmk kcgss GpcmkgkmleDugr`grLhontl { puhcmk stgtmk vlm` jgme([trmedRZ grds) tfrlws ImcnEltIlue`Nxknptmle, MLNxknptmle,

KcgssEltIlue`Nxknptmle { Qnrsleg pgkmnetn : enw Qnrsleg("Cums", 61i, 7.41i)2 LhonktLutput[trngj rndmstrl : enw LhonktLutput[trngj(enw ImcnLutput[trngj("pgkmnetn.`gt"))2

rndmstrl.wrmtnLhonkt(pgkmnetn)2

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg =6

rndmstrl.kclsn()2 } }

[gcm`g rue? H^MC@ [^KKN[[I^C (tltgc tmjn? 1 snkle`s)

Ql`njls vnr qun nc prldrgjg el els nevêg emedÿe jnesgon, pnrl sm vnjls nc `mrnktlrml `nc prlynktl, vnrnjls qun sn krnû nc grkfmvl pgkmnetn.`gt.

[ndue`g pgrtn.

N`mtgjls cg kcgsn prmekmpgc gdrndge`l nc kû`mdl qun nstg rnsgctg`l ne gjgrmccl? cnnrNskrmhmrGrkfmvl.ogvg pgkbgdn gpcmkgkmledugr`grlhontl2 mjplrt mjplrt mjplrt mjplrt mjplrt mjplrt

ogvg.ml.ImcnMeput[trngj2 ogvg.ml.ImcnEltIlue`Nxknptmle2 ogvg.ml.ImcnLutput[trngj2 ogvg.ml.MLNxknptmle2 ogvg.ml.LhonktMeput[trngj2 ogvg.ml.LhonktLutput[trngj2

puhcmk kcgss GpcmkgkmleDugr`grLhontl { puhcmk stgtmk vlm` jgme([trmedRZ grds) tfrlws ImcnEltIlue`Nxknptmle, MLNxknptmle, KcgssEltIlue`Nxknptmle { Qnrsleg pgkmnetn : enw Qnrsleg("Cums", 61i, 7.41i)2 LhonktLutput[trngj rndmstrl : enw LhonktLutput[trngj(enw ImcnLutput[trngj("pgkmnetn.`gt"))2

rndmstrl.wrmtnLhonkt(pgkmnetn)2 rndmstrl.kclsn()2 // [ndue`g pgrtn.

LhonktMeput[trngj grkfmvl ImcnMeput[trngj("pgkmnetn.`gt : enw LhonktMeput[trngj(enw ImcnMeput[trngj("pgkmnetn.`gt"))2 "))2 Qnrsleg iucgel : (Qnrsleg)grkfmvl.rng`Lhonkt()2 [ystnj.lut.prmetce("Eljhrn? "+iucgel.eljhrn)2 [ystnj.lut.prmetce("Nstgturg? "+iucgel.nstgturg)2

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg ==

[ystnj.lut.prmetce("Qnsl? "+iucgel.pnsl)2 [ystnj.lut.prmetce("MJK? "+iucgel.mjk())2 } }

[gcm`g rue? Eljhrn? Cums Nstgturg? 7.4 Qnsl? 61.1 MJK? 84.96799 H^MC@ [^KKN[[I^C (tltgc tmjn? 7 snkle`s)

Xntl.

Krnn ue prldrgjg qun dugr`n `ls lhontls, uel `n cg kcgsn Jgskltg (kle cls gtrmhutls eljhrn, rgzg y n`g`) y ltrl `n cg kcgsn Kljm`g (kle cls gtrmhutls `nskrmpkmûe, kgetm`g` y irnkunekmg). @nspuís krnn ltrl prldrgjg qun pun`g cnnr y cls lhontls getns dugr`g`l n mjprmjmr sus gtrmhutls. Xnkunr`n klpmgr nc grkfmvl dnenrg`l gc `mrnktlrml `n trghgol `nc sndue`l prlynktl.

77.0.0 Xnplrtn Xnplrtn Gc imegcmzgr ístg prçktmkg nc gcujel `nhnrç dnenrgr ue rnplrtn ne Q@I qun kletnedg nc kû`mdl iunetn y kgpturgs `n pgetgccg `n cg nonkukmûe `nc prldrgjg.

77.> Xnsuctg`ls y Klekcusmlens

Kle ístg prçktmkg, nc gcujel netne`nrç kljl dugr`gr y rnkupnrgr lhontls. [nrç kgpgz `n usgr cg pnrsmstnekmg `n lhontls `n ueg jgenrg juy hçsmkg pnrl ninktmvg.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 711

Qrgktmkg 78. Gcjgknegr vnktlrns `n lhontls ne grkfmv grkfmvls ls 78.7 Metrlùkkmûe

Cg prnsnetn prçktmkg gyu`g g rnilrzgr cls kletnem`ls `n cg êm`g` YM? Icuols y grkfmvls `n cls suhtnjgs 9.; Lpnrgkmlens hçsmkgs y tmpls `n gkknsl y 9.0 Jgenol `n lhontls pnrsmstnetns `nc prldrgjg `n nstu`mls `n cg jgtnrmg `n Qrldrgjgkmûe Lrmnetg`g g Lhontls, `nsgrrlccge`l cg kljpntnekmg nspnkêimkg? –Kljprne`n y gpcmkg cg kcgsmimkgkmûe `n grkfmvls y lpnrgkmlens hçsmkgs slhrn ístls pgrg jgempucgr su meilrjgkmûe.‚

78.8 Lhontmvl Kljpntnekmg)

Ncghlrgr ue prldrgjg qun usn vnktlrns y cg snrmgcmzgkmûe `n lhontls pgrg gcjgknegr nsknegrmls drçimkls. Xngcmzgr ue prldrgjg dugr`n lhontls kljl cêengs y kêrkucls ne ue Ynktlr y dugr`gr `mkfl vnktlr ne ue grkfmvl.

78.; Iue`gjnetl

Cls grrndcls (grrgys) ne Ogvg sle suimkmnetns pgrg dugr`gr tmpls hçsmkls `n `gtls, y lhontls `n ueg `ntnrjmeg`g kcgsn kuyl eÿjnrl klelknjls `n getnjgel. Gcduegs vnkns `nsngjls dugr`gr lhontls ne ue grrgy pnrl el sghnjls kuçetls lhontls vgjls g dugr`gr. êg slcukmûe ns cg kcgsn Ynktlr. ê vnktlr ns smjmcgr g ue grrgy, cg `minrnekmg nstrmhg ne qun ue vnktlr krnkn gutljçtmkgjnetn kuge`l gckgezg cg `mjnesmûe memkmgc jçxmjg. G`njçs, prlplrkmleg jítl`ls g`mkmlegcns pgrg g÷g`mr, ncmjmegr, n mesnrtgr ncnjnetls netrn ltrls `ls nxmstnetns. ¡G`njçs, pl`njls gcjgknegr lhontls `n `mstmetgs kcgsns ne ue jmsjl vnktlr! Krngr ue vnktlr

Qgrg usgr cg kcgsn Ynktlr nskrmhmjls gc memkml `nc prldrgjg cg snetnekmg? mjplrt ogvg.utmc.Ynktlr2

Kuge`l krngjls ue vnktlr u lhontl `n cg kcgsn Ynktlr, pl`njls nspnkmimkgr su `mjnesmûe memkmgc, y kugetl krnknrç sm rnhgsgjls `mkfg `mjnesmûe. Qlr nonjpcl, sm tnenjls ue vnktlr kle ueg `mjnesmûe memkmgc `n 81 ncnjnetls y sm rnhgsgjls `mkfg `mjnesmûe y dugr`gjls 87 ncnjnetls cg `mjnesmûe `nc vnktlr krnkn g 8>. Ynktlr vnktlr:enw Ynktlr(81, >)2

Gc sndue`l klestruktlr, slcgjnetn sn cn pgsg cg `mjnesmûe memkmgc. Ynktlr vnktlr:enw Ynktlr(81)2

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 717

[m sn rnhgsg cg `mjnesmûe memkmgc dugr`ge`l 87 ncnjnetls, cg `mjnesmûe `nc vnktlr sn ùpcmkg. Kle nc tnrknr klestruktlr, sn krng ue vnktlr kuyg `mjnesmûe memkmgc ns 71. Ynktlr vnktlr:enw Ynktlr()2

Cg `mjnesmûe `nc vnktlr sn ùpcmkg sm sn rnhgsg cg `mjnesmûe memkmgc, plr nonjpcl, kuge`l sn prntne`n dugr`gr lekn ncnjnetls. G÷g`mr ncnjnetls gc vnktlr

Fgy `ls ilrjgs `n g÷g`mr ncnjnetls g ue vnktlr. Ql`njls g÷g`mr ue ncnjnetl g kletmeugkmûe `nc ÿctmjl ncnjnetl `nc vnktlr, jn`mgetn cg iuekmûe jmnjhrl g``Ncnjnet. v.g``Ncnjnet("uel")2

Ql`njls tgjhmíe mesnrtgr ue ncnjnetl ne ueg `ntnrjmeg`g plsmkmûe, jn`mgetn mesnrtNcnjnetGt. Nc sndue`l pgrçjntrl l êe`mkn, me`mkg nc cudgr qun lkupgrç nc eunvl lhontl. [m trgtgjls `n mesnrtgr ue ncnjnetl ne ueg plsmkmûe qun el nxmstn tl`gvêg lhtnenjls ueg nxknpkmûe `nc tmpl GrrgyMe`nxLutLiHlue`s . Qlr nonjpcl, sm trgtgjls `n mesnrtgr ue ncnjnetl ne cg plsmkmûe = kuge`l nc vnktlr slcgjnetn tmnen kmekl ncnjnetls. Qgrg mesnrtgr nc strmed "trns" ne cg tnrknrg plsmkmûe `nc vnktlr v, nskrmhmjls v.mesnrtNcnjnetGt("trns", 8)2

Cg kcgsn ogvg.utmc.Ynktlr `nrmvg `n Lhonkt, mjpcnjnetg Kclenghcn (pgrg pl`nr sgkgr klpmgs kle nc jítl`l kclen()) y [nrmgcmzghcn (pgrg pl`nr snr klevnrtm`g ne kg`neg `n kgrgktnrns). Kljl su jmsjl eljhrn sudmnrn, Ynktlr rnprnsnetg ue grrndcl `n lhontls (rninrnekmgs g lhontl `n tmpl Lhonkt) qun pun`n krnknr y rnùkmrsn, sndÿe nc eÿjnrl `n ncnjnetls. G`njçs, pnrjmtn gkkn`nr g cls ncnjnetls kle ue êe`mkn, guequn el pnrjmtn utmcmzgr cls klrkfntns RZ. Nc jítl`l kgpgkmty() `nvuncvn nc tgjg÷l l eÿjnrl `n ncnjnetls qun pun`n tnenr nc vnktlr. Nc jítl`l smzn() `nvuncvn nc eÿjnrl `n ncnjnetls qun rngcjnetn kletmnen. R77Z

78.0 Qrlkn`mjmnetl @nskrmpkmûe) 78.0.7 Nqumpl Nqumpl enknsgrml

Kljputg`lrg Cmeux, ntk…) kle ue smstnjg lpnrgtmvl qun kunetn kle gjhmnetn drçimkl (Tme`lws,

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 718

78.0.8 Jgtnrmgc Jgtnrmgc `n Gplyl [@B `n ogvg. Netlrel `n `nsgrrlccl pgrg ogvg (M@N), plr nonjpcl, EntHnges. Cmhrnrêg swmed l ogvgIV.

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78.0.; @nsgrrlccl @nsgrrlccl `n cg Qrçktmkg Ne nstg prçktmkg krngrnjls lhontls kljl kêrkucls y cêengs, pgrg dugr`grcls ne ue vnktlr. Cundl dugr`gjls nc vnktlr ne ue grkfmvl ccgjg`l imdurgs.`gt. Memkmgjls enthnges, ncndmjls cg lpkmûe –Imcn Enw Qrlonkt‚. Krngjls ueg gpcmkgkmûe ogvg. Cn `gjls nc eljhrn `n – GpcmkgkmleDugr`grYnktlr ‚ gc prlynktl. @gjls kcmk ne nc hltûe –Imemsf‚ y nc prlynktl sn fg krng`l.

[m ns nc ÿemkl prlynktl pl`njls sgctgr nstn pgsl. Ne ltrl kgsl, `gjls kcmk `nrnkfl slhrn nc eljhrn `nc prlynktl y ne nc jneÿ kletnxtugc sncnkkmlegjls – [nt gs Jgme Qrlonkt‚. Nc eljhrn `nc prlynktl `nhn plenrsn ne endrmtgs.

Nstn prlynktl nstg gslkmg`l gc `n cg smdumnetn prçktmkg, puns nstn prlynktl dnenrg nc grkfmvl kle cls lhontls y nc `n cg smdumnetn prçktmkg `nhn snr kgpgz `n cnnrcls. Qgrg qun nstl sng plsmhcn, `nhne tnenr nc jmsjl eljhrn `nc pgquntn. Gsê kgjhmgjls nc eljhrn `nc pgquntn –gpcmkgkmledugr`grvnktlr ‚ g –vnktlrklelhontls ‚.

Krngjls cgs kcgsns Kmrkucl y Cêeng, rnkunr`n qun `nhne mjpcnjnetgr cg metnrigkn [nrmgcmzghcn , pgrg qun pl`gjls dugr`gr ne ue grkfmvl cls lhontls qun dnenrnjls g pgrtmr `n nstgs. Cgs rnspnktmvgs kcgsns sle? Kmrkucl.ogvg pgkbgdn vnktlrklelhontls2 mjplrt ogvg.gwt.Drgpfmks2 mjplrt ogvg.gwt.Qlmet2 mjplrt ogvg.ml.[nrmgcmzghcn2 puhcmk kcgss Kmrkucl mjpcnjnets [nrmgcmzghcn {

Qlmet knetrl2 met rg`ml2 puhcmk Kmrkucl(Qlmet knetrl, met rg`ml) { tfms.knetrl : knetrl2

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 71;

tfms.rg`ml : rg`ml2 } puhcmk `luhcn kgckucgGrng() { rnture ogvg.cged.Jgtf.QM * rg`ml * rg`ml2 } puhcmk vlm` `mhuogr(Drgpfmks d) { met x, y, cgrdl, gekfl2 x : knetrl.x - rg`ml2 y : knetrl.y - rg`ml2 cgrdl : gekfl : 8 * rg`ml2 d.`rgwLvgc(x, y, cgrdl, gekfl)2 } }

Cmeng.ogvg pgkbgdn vnktlrklelhontls2 mjplrt ogvg.gwt.Drgpfmks2 mjplrt ogvg.gwt.Qlmet2 mjplrt ogvg.ml.[nrmgcmzghcn2 puhcmk kcgss Cmeng mjpcnjnets [nrmgcmzghcn{ Qlmet memkml2 Qlmet ime2 puhcmk Cmeng(Qlmet memkml, Qlmet ime) { tfms.memkml : memkml2 tfms.ime : ime2 } puhcmk `luhcn cledmtu`() { met k7 : ime.x - memkml.x2 met k8 : ime.y - memkml.y2 rnture ogvg.cged.Jgtf.sqrt(k7 * k7 + k8 * k8)2 } puhcmk vlm` `mhuogr(Drgpfmks d) { d.`rgwCmen(memkml.x, memkml.y, ime.x, ime.y)2 } }

Gflrg n`mtgjls cg kcgsn prmekmpgc, `le`n krngrnjls `ls kêrkucls y `ls cêengs, cgs dugr`gjls ne ue vnktlr y gc imegc dugr`gjls nc vnktlr ne nc grkfmvl imdurgs.`gt

GpcmkgkmleDugr`grYnktlr.ogvg pgkbgdn vnktlrklelhontls2 mjplrt ogvg.gwt.Qlmet2 mjplrt ogvg.ml.ImcnEltIlue`Nxknptmle2

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 710

mjplrt mjplrt mjplrt mjplrt

ogvg.ml.ImcnLutput[trngj2 ogvg.ml.MLNxknptmle2 ogvg.ml.LhonktLutput[trngj2 ogvg.utmc.Ynktlr2

puhcmk kcgss GpcmgkmleDugr`grYnktlr { puhcmk stgtmk vlm` jgme([trmedRZ grds) tfrlws ImcnEltIlue`Nxknptmle, MLNxknptmle {

Kmrkucl g : enw Kmrkucl(enw Qlmet(711, >1), 81)2 Kmrkucl h : enw Kmrkucl(enw Qlmet(771, 701), 01)2 Cmeng k : enw Cmeng(enw Qlmet(71, 761), enw Qlmet(711, ;1))2 Cmeng ` : enw Cmeng(enw Qlmet(7;1, 71), enw Qlmet(761, 711))2

Ynktlr imdurgs : enw Ynktlr()2 imdurgs.g``(g)2 imdurgs.g``(h)2 imdurgs.g``(k)2 imdurgs.g``(`)2 LhonktLutput[trngj rndmstrl: enw LhonktLutput[trngj(enw ImcnLutput[trngj("imdurgs.`gt ImcnLutput[trngj("imdurgs.`gt"))2 "))2

rndmstrl.wrmtnLhonkt(imdurgs)2 rndmstrl.kclsn()2

[ystnj.lut.prmetce("Nc grkfmvl imdurgs.`gt sn krnû kle íxmtl.")2

} }

Gflrg kljpmcgjls y nonkutgjls nc prldrgjg, `ge`l kcmk ne nc mklel

, y lhtnenjls?

rue? Nc grkfmvl imdurgs.`gt sn krnû kle íxmtl. H^MC@ [^KKN[[I^C (tltgc tmjn? 1 snkle`s)

Xntl.

G÷g`n g nstn prlynktl kcgsn Prmgeducl pgrg, g pgrtmr `n nstn krngr `ls trmgeducls y dugr`grcl tgjhmíe ne nccgvnktlr.

78.0.0 Xnplrtn Xnplrtn Gc imegcmzgr ístg prçktmkg nc gcujel `nhnrç dnenrgr ue rnplrtn ne Q@I qun kletnedg nc kû`mdl iunetn y kgpturgs `n pgetgccg `n cg nonkukmûe `nc prldrgjg.

78.> Xnsuctg`ls y Klekcusmlens

Gflrg nc gcujel klelkn ueg nstrgtndmg pgrg dugr`gr ueg drge kgetm`g` `n lhontls, qun g`njçs pun`ne snr fntnrldíenls.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 71>

Qrgktmkg 7;. Xnkupnrgr vnktlrns `n lhontls `ns`n grkfmvls.

7;.7 Metrlùkkmûe

Cg prnsnetn prçktmkg gyu`g g rnilrzgr cls kletnem`ls `n cg êm`g` YM? Icuols y grkfmvls `n cls suhtnjgs 9.; Lpnrgkmlens hçsmkgs y tmpls `n gkknsl y 9.0 Jgenol `n lhontls pnrsmstnetns `nc prldrgjg `n nstu`mls `n cg jgtnrmg `n Qrldrgjgkmûe Lrmnetg`g g Lhontls, `nsgrrlccge`l cg kljpntnekmg nspnkêimkg? –Kljprne`n y gpcmkg cg kcgsmimkgkmûe `n grkfmvls y lpnrgkmlens hçsmkgs slhrn ístls pgrg jgempucgr su meilrjgkmûe.‚

7;.8 Lhontmvl Kljpntnekmg)

Ncghlrgr ue prldrgjg qun usn vnktlrns y cg snrmgcmzgkmûe `n lhontls pgrg rnkupnrgr nsknegrmls drçimkls. Xngcmzgr ue prldrgjg ne gjhmnetn drçimkl qun cng nc vnktlr getnrmlr y `mhuon cls lhontls cnê`ls `nc grkfmvl.

7;.; Iue`gjnetl

Ns mjplrtgetn tnenr ne kunetg qun rng`Lhon rng`Lhonkt() kt() `nvuncvn ue Lhonkt slhrn nc qun sn `nhnrç fgknr ue kgstmed pgrg qun nc lhontl sng ÿtmc. Cg rnklestrukkmûe enknsmtg en knsmtg qun nc grkfmvl *.kcgss nstí gc gckgekn `nc prldrgjg (kljl jêemjl pgrg fgknr nstn kgstmed).

Gc snrmgcmzgr ue lhontl, gutljçtmkgjnetn sn snrmgcmzge tl`gs sus vgrmghcns y lhontls jmnjhrl. G su vnz sn snrmgcmzge cls qun nstls lhontls jmnjhrls pun`ge tnenr (tl`ls `nhne snr snrmgcmzghcns). Pgjhmíe sn rnklestruyne `n mdugc jgenrg. [m sn snrmgcmzg ue Ynktlr qun kletmnen vgrmls [trmeds, tl`l nccl sn klevmnrtn ne ueg snrmn `n hytns. Gc rnkupnrgrcl cg rnklestrukkmûe `nog tl`l ne nc cudgr ne qun sn dugr`û. [m `ls lhontls kletmnene ueg rninrnekmg g ltrl, ístn el sn ùpcmkg sm sn nskrmhne l cnne gjhls `nc jmsjl strngj. Ns `nkmr, sm nc jmsjl [trmed nstuvmnrg kletnem`l `ls vnkns ne nc Ynktlr, sûcl sn dugr`grêg ueg vnz y gc rnkupnrgrcl sûcl sn krngrêg ue lhontl kle `ls rninrnekmgs kletnem`gs ne nc vnktlr. R77Z

7;.0 Qrlkn`mjmnetl @nskrmpkmûe) 7;.0.7 Nqumpl Nqumpl enknsgrml

Kljputg`lrg kle ue smstnjg lpnrgtmvl qun kunetn kle gjhmnetn drçimkl (Tme`lws, Cmeux, ntk…)

7;.0.8 Jgtnrmgc Jgtnrmgc `n Gplyl [@B `n ogvg. Netlrel `n `nsgrrlccl pgrg ogvg (M@N) EntHnges. Cmhrnrêg swmed.

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@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 719

7;.0.; @nsgrrlccl @nsgrrlccl `n cg Qrçktmkg Gflrg `nhnjls cnnr nc grkfmvl imdurgs.`gt, qun sn dnenrû ne cg prçktmkg getnrmlr. Qgrg igkmcmtgr nstl, klpmgjls tgc grkfmvl gc `mrnktlrml `n trghgol `nc prlynktl gktugc?

Memkmgjls enthnges, ncndmjls cg lpkmûe –Imcn Enw Qrlonkt‚. Krngjls ueg gpcmkgkmûe ogvg. Cn `gjls nc eljhrn `n –GpcmkgkmleCnnrYnktlr ‚ gc prlynktl. @gjls kcmk ne nc hltûe –Imemsf‚ y nc prlynktl sn fg krng`l.

[m ns nc ÿemkl prlynktl pl`njls sgctgr nstn pgsl. Ne ltrl kgsl, `gjls kcmk `nrnkfl slhrn nc eljhrn `nc prlynktl y ne nc jneÿ kletnxtugc sncnkkmlegjls – [nt gs Jgme Qrlonkt‚. Nc eljhrn `nc prlynktl `nhn plenrsn ne endrmtgs.

Xnkunr`n qun nstn prlynktl nstg gslkmg`l g cg prçktmkg getnrmlr y `nhne tnenr nc jmsjl eljhrn `nc pgquntn. Gsê kgjhmgjls nc eljhrn `nc pgquntn – gpcmkgkmlecnnrvnktlr ‚ g –vnktlrklelhontls ‚.

Kmrkucl y Cêeng, m`íetmkgs g cgs `n cg prçktmkg Pgjhmne `nhnjls krngr cgs getnrmlr (Qun`n klpmgrcgs pgrgkcgsns gflrrgr tmnjpl).

Kmrkucl.ogvg pgkbgdn vnktlrklelhontls2 mjplrt ogvg.gwt.Drgpfmks2 mjplrt ogvg.gwt.Qlmet2 mjplrt ogvg.ml.[nrmgcmzghcn2 puhcmk kcgss Kmrkucl mjpcnjnets [nrmgcmzghcn { Qlmet knetrl2 met rg`ml2

puhcmk Kmrkucl(Qlmet knetrl, met rg`ml) { tfms.knetrl : knetrl2 tfms.rg`ml : rg`ml2 }

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 714

puhcmk `luhcn kgckucgGrng() { rnture ogvg.cged.Jgtf.QM * rg`ml * rg`ml2 } puhcmk vlm` `mhuogr(Drgpfmks d) { met x, y, cgrdl, gekfl2 x : knetrl.x - rg`ml2 y : knetrl.y - rg`ml2 cgrdl : gekfl : 8 * rg`ml2 d.`rgwLvgc(x, y, cgrdl, gekfl)2 } }

Cmeng.ogvg pgkbgdn vnktlrklelhontls2 mjplrt ogvg.gwt.Drgpfmks2 mjplrt ogvg.gwt.Qlmet2 mjplrt ogvg.ml.[nrmgcmzghcn2 puhcmk kcgss Cmeng mjpcnjnets [nrmgcmzghcn{ Qlmet memkml2 Qlmet ime2 puhcmk Cmeng(Qlmet memkml, Qlmet ime) { tfms.memkml : memkml2 tfms.ime : ime2 } puhcmk `luhcn cledmtu`() { met k7 : ime.x - memkml.x2 met k8 : ime.y - memkml.y2

}

rnture ogvg.cged.Jgtf.sqrt(k7 * k7 + k8 * k8)2

puhcmk vlm` `mhuogr(Drgpfmks d) { d.`rgwCmen(memkml.x, memkml.y, ime.x, ime.y)2 } }

Gflrg n`mtgjls cg kcgsn prmekmpgc, `le`n krngrnjls cg vnetgeg pgrg `nspcndgr cgs imdurgs, y ccnegjls nc vnktlr imdurgs kle cls lhontls cnm`ls `nc grkfmvl imdurgs.`gt. @nspuns tnenjls qun rnklrrnr nc vnktlr n mr lhtnemne`l ueg imdurg g cg vnz y tnenjls qun vnrmimkgr `n qun kcgsn ns kg`g lhontl y fgknr nc kgst klrrnsple`mnetn pgrg prl`nknr

g `mhuogr nc lhontl ne turel. GpcmkgkmleCnnrYnktlr.ogvg pgkbgdn vnktlrklelhontls2

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 716

mjplrt mjplrt mjplrt mjplrt mjplrt mjplrt mjplrt mjplrt mjplrt mjplrt

ogvg.gwt.Kletgmenr2 ogvg.gwt.@mjnesmle2 ogvg.gwt.Drgpfmks2 ogvg.ml.ImcnMeput[trngj2 ogvg.ml.ImcnEltIlue`Nxknptmle2 ogvg.ml.MLNxknptmle2 ogvg.ml.LhonktMeput[trngj2 ogvg.utmc.Ynktlr2 ogvgx.swmed.OIrgjn2 ogvgx.swmed.OQgenc2

puhcmk kcgss GpcmkgkmleCnnrYnktlr nxtne`s OIrgjn { Qmzgrrle p2 puhcmk GpcmkgkmleCnnrYnktlr() tfrlws MLNxknptmle, ImcnEltIlue`Nxknptmle, KcgssEltIlue`Nxknptmle { p : enw Qmzgrrle()2 p.sntQrninrrn`[mzn(enw @mjnesmle(861, 811))2 Kletgmenr kp : dntKletnetQgen()2 kp.g``(p)2 snt@niguctKclsnLpnrgtmle(NVMP\LE\KCL[N)2 pgkb()2 sntPmtcn("Qrçktmkg cnnr vnktlrns")2 sntYmsmhcn(trun)2 } puhcmk stgtmk vlm` jgme([trmedRZ grds) tfrlws MLNxknptmle, ImcnEltIlue`Nxknptmle, KcgssEltIlue`Nxknptmle { GpcmkgkmleCnnrYnktlr vnetgeg : enw GpcmkgkmleCnnrYnktlr()2 vnetgeg.sntYmsmhcn(trun)2 } } kcgss Qmzgrrle nxtne`s OQgenc { Ynktlr imdurgs2 puhcmk Qmzgrrle() tfrlws ImcnEltIlue`Nxknptmle, MLNxknptmle, KcgssEltIlue`Nxknptmle { LhonktMeput[trngj grkfmvl : enw LhonktMeput[trngj(enw ImcnMeput[trngj("imdurg ImcnMeput[trngj("imdurgs.`gt"))2 s.`gt"))2

imdurgs : enw Ynktlr()2 imdurgs : (Ynktlr) grkfmvl.rng`Lhonkt()2 } ALvnrrm`n puhcmk vlm` pgmetKljplenet(Drgpfmks d) { supnr.pgmetKljplenet(d)2

ilr (Lhonkt imd ? imdurgs) { mi ( imd.dntKcgss().tl[trmed(). kljpgrnPl("kcgss vnktlrklelhontls.Kmrkucl") vnktlrklelhontls.Kmrkucl") :: 1) {

Kmrkucl x : (Kmrkucl) imd2 x.`mhuogr(d)2 }

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 71=

mi ( imd.dntKcgss().tl[trmed(). kljpgrnPl("kcgss vnktlrklelhontls.Cmeng"):: 1) {

Cmeng x : (Cmeng) imd2 x.`mhuogr(d)2 } }

}

}

Gflrg kljpmcgjls y nonkutgjls nc prldrgjg, `ge`l kcmk ne nc mklel

, y lhtnenjls?

Xntl.

G÷g`n g nstn prlynktl cg kcgsn Prmgeducl pgrg cldrgr cnnrcl `nc vnktlr y prlkn`nr g `mhuogrcl.

7;.0.0 Xnplrtn Xnplrtn Gc imegcmzgr ístg prçktmkg nc gcujel `nhnrç dnenrgr ue rnplrtn ne Q@I qun kletnedg nc kû`mdl iunetn y kgpturgs `n pgetgccg `n cg nonkukmûe `nc prldrgjg.

7;.> Xnsuctg`ls y Klekcusmlens

Kle ístg prçktmkg, nc gcujel gpcmkgrç vgrmgs tíkemkgs gvgezg`gs juy metnrnsgetns, kljl usgr cg cmhrnrêg gwt pgrg dnenrgr ueg metnrigz drçimkg, cg rnkupnrgkmûe `n lhontls dugr`g`ls ne ue vnktlr y usgr nc lhontl Dneírmkl Lhonkt pgrg `nspuís fgknrcns ue kgstmed y trgeilrjgcls g cg kcgsn `nsng`g.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 771

Hmhcmldrgiêg R7Z

Pnkelcûdmkl Egkmlegc `n Jíxmkl. Qrldrgjg `n nstu`mls `n Qrldrgjgkmûe Lrmnetg`g g Lhontls. Kcgvn [K@-7181. [gctmccl, Klgfumcg, Jíxmkl? s.e., inhrnrl `nc 8171.

R8Z

‐.

R;Z

[kfjuccnr, O. (8110). [gjs tngkf ylursnci ^JC me 80 flurs . Me`mgegplcms, ME? [gjs.

R0Z

Cgs jnolrns fnrrgjmnetgs ^JC - N`mkmûe 8176. (8176, elvmnjhrn 70). Klesuctg`l ne jgyl 7, 817=, `ns`n fttps?//mednemnrmg`nslitwgrn.ns/fnrrgjmnetgs-ujc/

R>Z

Cêjgkl, @. [. (e.`.). ^JC ne EntHnges. Klesuctg`l ne jgyl 7, 817=, `ns`n fttps?//www.gpuetns`nogvg.klj/817>/78/ujc-ne-enthnges.ftjc

R9Z

@rgwmed ^JC wmtf Qcget^JC. Cgedugdn Xninrnekn Dum`n (Ynrsmle 618;). (817=). 7st n`. RnhllbZ @msplemhcn ne? n e? fttps?//`nnpu.os.lrd/svd-snq-`mgdrgj/Xninrnekn\Dum`n.pì RKlesuctg`l ne 7 jgyl 817=Z.

R4Z

Nc Neilqun Lrmnetg`l g Lhontls - Qgrg`mdjgs `n cg Mednemnrêg `n [litwgrn. (e.`.). Klesuctg`l ne jgyl 7, 817=, `msplemhcn ne fttps?//smtns.dlldcn.klj/smtn/pgrg`mdjgs`ncgms/0-8-nc-neilqun-lrmnetg`l-g-lhontls

R6Z

Nxns. (e.`.). Kursls lrgkcn, kursls ogvg, jgstnr lrgkcn, jgstnr ogvg, ilrjgkm. Klesuctg`l ne jgyl 7, 817=, `msplemhcn ne fttp?//www.jue`logvg.ent/`nimemkmle-`n-klestruktlrns-`nueg-kcgsn.ftjc.ftjc

R=Z

Cnjgy, C. & Qnrbmes, K. (7==9). Gprne`mne`l Ogvg ne 87 `m gs gs. Jnxmkl? Qrnetmkn Fgcc Fmspgelgjnrmkgeg.

R71Z

Nkbnc, H. (8118). Qmnesg ne Ogvg. Jg`rm`? Qrnetmkn Fgcc.

R77Z

Ogcle, O. D. (7===). Gprne`g Ogvg kljl sm nstuvmnrg ne prmjnrl. [.c.? [.e.

R78Z

Hmhmgeg XL[[M, Qglcg HXMPL[ y Xgjûe DGXKMG JGXPMEN_. JL@NCG@L @N LHONPL[, KGQM[ - Knetrl `n Gktugcmzgkmûe Qnrjgenetn ne Mednemnrêg `n [litwgrn Nskuncg `n Qlsdrg`l. MPHG.

R7;Z

Hllkf, D., Xml, G. K., & Jgeunc, K. CC.. (7==9). Geçcmsms y `msn÷l lrmnetg`l g lhontls kle gpcmkgkmlens. Grdnetmeg? G``msle-Tnscny/@êgz `n [getls.

R70Z

Gdumcgr, C. (811;). Iue`gjnetls `n prldrgjgkmle? gcdlrmtjls, nstrukturg `n `gtls y lhontls. Jg`rm`? JkDrgw-Fmcc.

R7>Z

Gdumcgr, C. (8116). Iue`gjnetls `n prldrgjgkmle? gcdlrmtjls, nstrukturgs `n `gtls y lhontls. Nspgeg? JkDrgw-Fmcc/Metnrgjnrmkgeg.

Xntêkucg `n cg kgrrnrg `n mednemnrêg ne smstnjgs kljputgkmlegcns M[MK-8171-880. Kmu`g` `n Jíxmkl, Jíxmkl? s.e., 8179.

R79Z

Kísgr, Jgrêe Cûpnz. @LKQCG]NX. Xÿhrmkg pgrg Nvgcugkmûe `n Qrlynktls `n Qrldrgjgkmûe (Jl`ncl P). RNe cêengZ fttps?//`lkpcgynr.ns/7909>;81-Xuhrmkg-pgrgnvgcugkmle-`n-prlynktls-`n-prldrgjgkmle-jl`ncl-t-kmnekmg-tnkelcldmg-y-gjhmnetn`npgrtgjnetl-gkg`njmkl-`nsgrrlccl-tnkelcldmkl.ftjc.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 777

R74Z

ÊGJ. plrtgcgkg`njmkl.kkf.uegj.jx. X^HXMKG QGXG NYGC^GX NC XNQLXPN @N CG QXÇKPMKG. RNe cêengZ fttps?//plrtgcgkg`njmkl.kkf.uegj.jx/jgtnrmgcns/prli/jgt`m`gk/smtprl/nxp/qumj/qumj8/qum jmkMM/>8>>08>80=0;07>i>107>807>i0>>9070k>>07>8>i0>0k>i>80>>10i>8>00>>i000>>i 0k07>i>i>1>8k;670;>00=0;07.pì.

R76Z

Nvgcugkmûe `n prçktmkgs `n prldr prldrgjgkmûe gjgkmûe jn`mgetn rÿhrmkgs ne Jll`cn. Ygkg, Ouge Jgeunc, Gdu`l, O, Nermqun y [çekfnz, Fíktlr. Lvmn`l? s.e., 77 `n oucml `n 8170, Gktgs `n cgs VV ONE^M, pçds. 714-770.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 778

Genxl Genx l G. Xu Xu hrmkg Qgrg cg nvgcugkmûe `n nstg prçktmkg sn rnkljmne`g cg smdumnetn rÿhrmkg R79ZR74ZR76Z, qun tmnen ueg nskgcg `n 7% g 711%. Krmtnrmls

@lkujnetl

Kl`mimkgkmûe

Iuekmlegjmnetl

@nimkmnetn

Xnducgr

7% g >% Nc `lkujnetl el kujpcn kle cg nstrukturg y ilrjgtl nxpcmkmtg`l plr nc `lknetn. 7% g 4% ^tmcmzg mestrukkmlens y gcdlrmtjls qun

9% g 71% Nc `lkujnetl kujpcn kle cg nstrukturg y ilrjgtl nxpcmkmtg`l plr nc `lknetn. 6% g 7>% ^tmcmzg mestrukkmlens y gcdlrmtjls qun el sle

el rnsuncvne nc nonrkmkml.

gklr`ns rnslcvnr pgrg nc nonrkmkml.

7% g 78% El iuekmleg.

Hunel

Juy Hunel

77% g 7>% G`njçs, el tmnen nrrlrns lrtldrçimkls y drgjgtmkgcns.

79% g 81% G`njçs, nstç hmne rn`gktg`l y tmnen klfnrnekmg `n kletnem`l.

79% g 8;% ^tmcmzg cgs mestrukkmlens y gcdlrmtjls enknsgrmls

80% g ;1% ^tmcmzg cgs mestrukkmlens y gcdlrmtjls jçs g`nkug`ls pgrg

pgrg rnslcvnr nc nonrkmkml, guequn el sle cls jçs g`nkug`ls. 7;% g 80% 8>% g ;4% Nc iuekmlegjmnetl iuekmlegjmnetl Nc iuekmlegjmnetl iuekmlegjmnetl tmnen igccls tmnen igccls sme mjplrtgetns. mjplrtgekmg.

rnslcvnr nc nonrkmkml. ^sg hunegs prçktmkgs prçktmkgs `n kl`mimkgkmûe. ;6% g >1% Nc iuekmlegjmnetl iuekmlegjmnetl ns kljpcntl.

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 77;

Genxl Genx l H. Qcgetmccg `nc rnplrtn `n

prgktmkgs.

QXÇKPMKG REÿjnrl`np REÿjnrl`nprçktmkgZ.REljh rçktmkgZ.REljhrn`ncgprç rn`ncgprçktmkgZ ktmkgZ Cudgr? REljhrn `nc cghlrgtlrmlZ cghlrgtlrmlZ @urgkmûe? RPltgc `n snsmlens `n e flrgsZ Drupl? RJgtnrmg, flrg, g÷l/jns, QrlinslrZ Metndrgetns? RCmstg `n cls gcujels qun rngcmzgrle cg prçktmkgZ prçktmkgZ

7. Metrlùkkmûe

8. Lhontmvl Kljpntnekmg) ;. Iue`gjnetl 0. Qrlkn`mjmnetl @nskrmpkmûe) 0.7 Nqumpl Nqumpl enknsgrml 0.8 Jgtnrmgc Jgtnrmgc `n Gplyl 0.; @nsgrrlccl @nsgrrlccl `n cg Qrçktmkg 0.0 Kçckucls Kçckucls y rnplrtn >. Xnsuctg`ls y Klekcusmlens 9. Genxls 4. Hmhcmldrgiêg

@npgrtgjnetl `n [mstnjgs y Kljputgkmûe

Qçdmeg 770

Genxl K. Xndcgjnetl metnrel pgrg nc cg imegcm`g` `n lptmjmzgr nc usl `nc Cghlrgtlrml y gkgtge`l cls cmengjmnetls `n uslKle `n cghlrgtlrmls. eunstrgs gutlrm`g`ns, fgknjls `n su klelkmjmnetl nc smdumnetn? XNDCGJNEPL LHCMDGKMLEN[ @N CL[ GC^JEL[?

7. Wun`g nstrmktgjnetn prlfmhm`l metrlùkmr gcmjnetls l hnhm`gs gc cghlrgtlrml (mekcuyne`l ùckns y kfmkcns). 8. @urgetn su pnrjgenekmg ne nc cghlrgtlrml `nhnrçe jlstrgr su kucturg el prlimrmne`l pgcghrgs lhsknegs y el `noge`l pgpncns l hgsurg ne cgs j jnsgs nsgs l pmsl. ;. Wun`g nstrmktgjnetn prlfmhm`l utmcmzgr nc cghlrgtlrml pgrg nstu`mgr l ncghlrgr tgrngs, yg qun cgs sgcgs nstçe prldrgjg`gs ÿemkgjnetn pgrg kcgsns, kursls l prçktmkgs. Qgrg 0. >. 9. 4.

nstu`mgr ncghlrgr tgrngs nc Knetrl `n Meilrjgkmûe sn nekunetrg `nhm`gjnetn nqumpg`lypgrg nstls imens G cls gcujels qun el tnedge kcgsn, kursl l prçktmkg ne nc cghlrgtlrml, cns qun`g nstrmktgjnetn prlfmhm`l nc gkknsl g `mkfg çrng. ßemkgjnetn pun`ne netrgr gc cghlrgtlrml sm nc jgnstrl nstç prnsnetn, yg qun íc ns nc rnsplesghcn `nc drupl. Gc tírjmel `n sus kcgsns, kursls l prçktmkgs, ns lhcmdgkmûe `n tl`ls cls usugrmls gpgdgr cgs kljputg`lrgs (KQ^, jlemtlr) y gkljl`gr cgs smccgs ne n e su cudgr (ueg plr kljputg`lrg y cgs rnstgetns knrkg `n cg pgrn`). Qlr emedÿe jltmvl pun`ne `nsklenktgr cls kghcns `n cg kljputg`lrg l `n cls pnrmiírmkls qun sn cns gsmdeû. Ne kgsl `n qun el iuekmlen klrrnktgjnetn nc jlusn, kghcns, tnkcg`l l KQ^, rnplrtgrcl mejn`mgtgjnetn gc jgnstrl, yg qun ustn`ns sle rnsplesghcns `n cgs kljputg`lrgs qun sn cns gsmdeû `ns`n ue prmekmpml, (pgrg qun ístn g su vnz els cl fgdg sghnr y grrndcgr nc prlhcnjg).

6. plr Cls gcujels prnstgetns `nc [nrvmkml kujpcne kle uegrnkcgjgkmlens iuekmûe nekljne`g`g cgs gutlrm`g`ns nsklcgrns, plr [lkmgc cl tgetl, cgs plsmhcns `nhnrçe fgknrcgs cls usugrmls `mrnktgjnetn g cls kllr`meg`lrns `nc cghlrgtlrml, plr emedÿe jltmvl sus kljpg÷nrls `n [nrvmkml [lkmgc tlcnrgrçe ue trgtl meoustmimkg`l. =. [me nxknpkmûe, kugcqumnr usugrml qun sng slrprne`m`l mestgcge`l oundls, utmcmzge`l cls oundls yg mestgcg`ls, hlrrge`l l gctnrge`l cg meilrjgkmûe qun kletnedge cgs jçqumegs, gsê kljl `nsklenktçe`lcgs l fgkmne`l usl me`nhm`l `n nccgs, snrç suspne`m`l `nimemtmvgjnetn `nc cghlrgtlrml, y snrç rnplrtg`l g cgs gutlrm`g`ns nsklcgrns pgrg qun sng sgekmleg`l `n gkunr`l gc rndcgjnetl `nc Mestmtutl. Ns enknsgrml rnklr`gr qun nstgjls ilrjge`l gcujels g ue emvnc prlinsmlegc y qun nc nsiunrzl `n cg Mestmtukmûe g qun pnrtnenknjls ns trghgol `n jukfgs dnenrgkmlens, plr cl kugc tn pn`mjls els gyu`ns g klesnrvgr pgrg tu prlpml hnenimkml ne nc jnolr nstg`l, cg

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