1ero - Proyecto Científico 2

 

SWORHKQO AO[ KBHLQÄJBKO [XGLBZHI/LBZHI GÀ [BK@ [XSHWBOW [XSHWBOW  NW@AO5 SWBDHWO GNX KBKIO KO[Q@  @ÐO  @ ÐO IHKQBZO 7370-7377 7370 -7377   Ios hstuab`lths kodprhlahràl quh hi kolsudo ah `ibdhltos s`iua`gihs

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OGEHQBZO AH @SWHLABU@EH5

 

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OGEHQBZO[ H[SHKÄJBKO[5

 

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progihd`s nhlhr`aos por i` j`it` ah hehrkbkbo, i` hxposbkbûl ` i` kolt`dbl`kbûl `dgbhlt`i y hi kolsudo ah `ibdhltos kolt`dbl`aos, rhkolokbhlao rhkolokbh lao hi v`ior lutrbkbol`i ah ios `ibdhltos ah uso kotbab`lo.  kotbab`lo.     B.KL.P.8.7.0 @l`ibz` i` hstruktur` ahi àtodo kodp`r`lao i`s thorä`s `tûdbk`s ah Gomr (hxpibk` ios hsphktros ah ios hihdhltos quädbkos), Ahdûkrbto, A`itol, Qmodpsol y Wutmhrjora, y rh`ibz` hehrkbkbos ah i` koljbnur`kbûl hihktrûlbk` ahsah hi doahio dhkàlbko-kuàltbko ah i` d`thrb`. (B.7).  (B.7).     Ogtbhlh d`nlbtuahs kblhdàtbk`s ahi DWXZ kol ul hljoquh vhktorb`i5 posbkbûl, vhiokba`a, vhiokba`a dhab` h blst`ltàlh`, y ahspi`z`dbhlto ` g`sh ah rhprhshlt`kbolhs nràjbk`s ah ul ogehto quh sh duhvh hl aos abdhlsbolhs. WHJ. KL.J.8.7.0   B.KL.J.8.:.0. @l`ibz` i` vhiokba`a, àlnuio ah i`lz`dbhlto, `khihr`kbûl, `ik`lkh, `itur` dàxbd`, tbhdpo ah vuhio, vu hio, `khihr`kbûl lord`i y khlträpht` hl hi dovbdbhlto ah proyhktbihs, hl julkbûl ah i` l`tur`ihz` vhktorb`i ah i` shnula` ihy ah Lhwtol.   B.D.8.:.0. Nr`jbk` vhktorhs hl hi pi`lo6 m`ii` su dûauio y rh`ibz` ophr`kbolhs ah sud`, rhst` y proaukto por ul hsk`i`r6 rhsuhivh progihd`s `pibk`aos ` i` Nhodhträ` y ` i` Jäsbk`.   B.HJI.;.7.0. Ih`rlhrs k`l s`y w`ys to t`fh k`rh oj tmh mh`itm `la olh‒s surroulablns. Ih`rlhrs k`l bahltbjy `la hxmbgbt sokb`iiy rhspolsbgih ghm`vbors `t modh, `t skmooi `la tow`ras tmh hlvbroldhlt. (E.;, [.0)   Bahltbjbk` i`s ahd`la`s ah i`s pràktbk`s korpor`ihs y i`s rhi`kbol` kol hi bdp`kto hl i` s`iua. WHJ. B.HJ.8.=.0.  B.HJ.8.=.0.    KH.HN.8.0 Xtbibz` ios kolkhptos gàsbkos kolt`gihs p`r` kolokhr hi juturo jbl`lkbhro ah ul hdprhlabdbhlto y ahthrdbl`r hi k`pbt`i ah tr`g`eo lhkhs`rbo.

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BLABK@AOWH[ AH HZ@IX@KBÛL5

kodgbl`aos kol màgbtos sosthlbgihs j`vorhkh i` tod` ah ahkbsbolhs `khrt`a`s p`r` d`lthlhr i` s`iua blthnr`i, kodulbk`lao rhkodhla`kbolhs ah jord` `shrtbv` hl hi kolthxto hl quh sh hlkuhltrh. Kolkbhltbz`r ` i` kodulba`a hauk`tbv` sogrh i` bdport`lkb` ah ul` guhl` `ibdhlt`kbûl p`r` thlhr ul` vba` s`iua`gih. Srodovhr màgbtos ah kolsudo sosthlbgih y s`iua`gih hl i` kodulba`a hauk`tbv` p`r` hi dheor`dbhlto ah ul hstbio ah vba` Blkhltbv`r hi màgbto ah `ktbvba`a jäsbk` p`r` hi ghlhjbkbo ah i` s`iua blthnr`i B.KL.G.8.=.0. Hi`gor` ul pi`l ah s`iua blthnr`i, ` p`rtbr ah i` kodprhlsbûl ah i`s hljhrdha`ahs, ahsûrahlhs `ibdhltbkbos y hjhktos ahi kolsudo ah `ikomoi y i`s aron`s quh `jhkt`l `i sbsthd` lhrvboso y hlaokrblo, `sä kodo ah ios

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  Ahskrbgh proyhkkbolhs jbl`lkbhr`s y hi k`pbt`i ah tr`g`eo ah ul hdprhlabdbhlto g`sàlaosh hl kolkhptos jbl`lkbhros gàsbkos. (Whj.B.HN.8.0.0.) (Whj.B.HN.8.0. 0.) (B.0., B.1.)   KH.HN.8.0 Xtbibz` ios kolkhptos gàsbkos kolt`gihs p`r` kolokhr hi juturo jbl`lkbhro ah ul hdprhlabdbhlto y ahthrdbl`r hi k`pbt`i ah tr`g`eo lhkhs`rbo.   Ahskrbgh proyhkkbolhs jbl`lkbhr`s y hi k`pbt`i ah tr`g`eo ah ul hdprhlabdbhlto g`sàlaosh hl kolkhptos jbl`lkbhros gàsbkos. (Whj.B.HN.8.0.0.) (Whj.B.HN.8.0. 0.) (B.0., B.1.)   Kopb`, kort` y hibdbl` aokudhltos utbibz`lao hi hxpior`aor ah ^blaows. KOL @IBDHLQ@KBÛL [@IXA@GIH… I@WN@ ZBA@ QHLAWÀ[

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SWORHKQO5

  [h propolh ul proyhkto, rhi`kbol`ao kol ul ogehtbvo ah `prhlabz`eh. Hi proyhkto blkiuyh `ktbvba`ahs p`r` k`a` shd`l`, quh poaràs rh`ibz`r blabvbau`idhlth o kol hi `poyo ah tu j`dbib`. Qh rhkodhla`dos tr`g`e`r hl tu proyhkto aur`lth `i dhlos :3 dblutos ab`rbos.   Hl ios proyhktos, i`s `ktbvba`ahs pi`lth`a`s p`r` k`a` shd`l` lo rhqubhrhl ah d`thrb`i bdprhso. Qr`g`e` kol ios rhkursos abspolbgihs hl k`s`.   S`r` kolsuit`r bljord`kbûl y jort`ihkhr tus `prhlabz`ehs, utbibz` ios thxtos hskoi`rhs ah hsth `ðo o ah `ðos `lthrborhs. Ios thxtos ah hsth `ðo hskoi`r ios mttps5//rhkursos7.hauk`kbol.nog.hk/thxtos/   puhahs hlkoltr`r hl5  hl5 mttps5//rhkursos7.hauk`kbol.nog.hk/thxtos/

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  [bnuh ul` rutbl`, kol mor`rbos rhnui`rhs p`r` tus `ktbvba`ahs ah `prhlabz`eh, y t`dgbâl p`r` ios euhnos, i` rhkrh`kbûl, i`s t`rh`s ahi mon`r y hi ahsk`lso.   Iihv` ul rhnbstro ah tus `ktbvba`ahs y nu`ra` i`s hvbahlkb`s hl tu port`joibo. Hsth port`joibo sh utbibz`rà p`r` hv`iu`r tu proyhkto. pro yhkto.   Hi proaukto jbl`i shrà i` hi`gor`kbûl ah ul` pbràdbah `ibdhltbkb`.

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BLABK@KBOLH[5

Suhahs us`r ios sbnubhlths rhkursos y d`thrb`ihs        

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S`phi o d`thrb`i rhutbibz`ao Iàpbkhs ah koior. Iàpbz, hsjhro y gorr`aor. Euhno nhodâtrbko.

 

 

@[BNL@QXW@[5 Gboionä`, Puädbk` Puädbk`,, Jäsbk`, D`thdàt D`thdàtbk`, bk`, Blniâs, Hauk`kbûl Jäsbk`, Hdprhlabdbhlt Hdprhlabdbhlto oy Nhstbûl, Bljordàtbk`.

 @KQBZBA@AH[  @ KQBZBA@AH[ S@W@ I @ [HD@L@ 0

GBOIONÄ@ QHD@5 SI@LH[ S@W@ D@LQHLHW I@ [@IXA BLQHNW@I

0.  @l`ibkh i` sbnubhlth ihktur` ¿Puâ hs ul pi`l? I` p`i`gr` pi`l p`i`gr`  pi`l puhah  puhah ahjblbrsh kodo ul koleulto ah dhaba`s quh `inubhl proyhkt` rh`ibz`r hl dbr`s ` kudpibr ul ogehtbvo. ¿Puâ hs i` s`iua blthnr`i y kûdo kolshnubri`? Ah toaos hs s`gbao quh i` dhabkbl` m` mhkmo nr`lahs `v`lkhs y quh hi pronrhso kbhltäjbko los phrdbth iihv`r ul` vba` dukmo dàs iolnhv` y shnur`. [bl hdg`rno, ¿hs âsth hi õlbko tbpo ah a h s`iua ahi quh ahghdos okup`rlos hl luhstro aä` ` aä`? Q`i vhz lulk` m`y`s oäao m`gi`r ahi târdblo s`iua blthnr`i , phro shnuro quh s`ghs io quh hs5 i` s`iua blthnr`i hs hi kodphlabo ah luhstr` s`iua jäsbk`, luhstr` s`iua dhlt`i y luhstr` s`iua `lädbk`. I`  I` OD[ OD[  (Orn`lbz`kbûl Dulab`i ah i` [`iua) krhû hsth târdblo m`kbhlao rhjhrhlkb` ` i` tot`iba`a tot` iba`a ahi gbhlhst`r ahi shr mud`lo. I`s phrsol`s hst`dos k`a` vhz dàs kolkbhlkb`a`s ah i` bdport`lkb` ah kuba`rlos y ah prhshrv`r luhstro gbhlhst`r por hlkbd` ah toa`s i`s kos`s6 por hiio, luhstr` sokbha`a sh m` voik`ao hl hxpior`r dâtoaos y rutbl`s quh los `yuahl ` iihv`r ul` vba` s`l`6 pruhg` ah hiio hs luhstro krhkbhlth blthrâs por i`s rhkht`s s`l`s, i` gõsquha` ah rutbl`s ah hehrkbkbo hl Blthrlht, o hi nr`l âxbto ah ios ibgros ah `uto `yua`.

 

 

I` s`iua blthnr`i hs gàsbk` p`r` poahr iihv`r ul` vba` pihl`. Kolozk`dos i`s trhs vä`s hxbsthlths p`r` kuba`r y dheor`r luhstr` s`iua. ❚ 

[`iua jäsbk`

Gusk`r orbhlt`kbûl hl ku`lto `ibdhlt`kbûl y abht`s hs `ino k`a` vhz dàs kodõl, blkiuso sbl sujrbr progihd`s ah sogrh phso6 hs duy rhkodhla`gih vbsbt`r ` ul abhtbst` quh los todh luhstro phso y dhaba`s p`r` poahr koljhkkbol`r ul` abht` ` dhaba` p`r` luhstro kuhrpo y dht`goibsdo. Lo ahghdos oivba`r quh k`a` kuhrpo hs abjhrhlth6 hs guhlo kolokhrio hl aht`iih p`r` a`rih hx`kt`dhlth io quh lhkhsbt`. Q`dgbâl hs duy rhkodhla`gih m`khr hehrkbkbo kol rhnui`rba`a aur`lth i` shd`l`5 s`ibhlao ` korrhr, k`dbl`lao ul` mor` `i aä` o yhlao ` ul nbdl`sbo6 ahghdos rodphr luhstr` rutbl` shahlt`rb` hl `inõl dodhlto ahi aä`. D`ltâl tu kuhrpo hl jord` y th rhkodphls`rà kol ul dheor hst`ao ah s`iua, dukm`s dhlos aoihlkb`s y ul` nr`l shls`kbûl ah vbt`iba`a y s`tbsj`kkbûl. ❚ 

[`iua dhlt`i

M`y quh prhst`r `thlkbûl ` luhstr` s`iua dhlt`i. I`s hljhrdha`ahs dhlt`ihs o ios tr`storlos hstàl hl vä`s ah shr rhkolokbaos kodo hst`aos ah kolv`ihkhlkb` sujbkbhlths p`r` `ushlt`rsh ahi tr`g`eo dbhltr`s aurhl. Hi hqubibgrbo ah luhstr` dhlth hs `ino jrànbi y duy v`iboso5 hi khrhgro hs hi dotor ah luhstro kuhrpo. @ dhluao i` ahprhsbûl, i` `lsbha`a o ios phls`dbhltos tûxbkos sol kolsbahr`aos hst`aos ah àlbdo, phro hstàl rhkolokbaos por i` dhabkbl` kodo tr`storlos quh ahghl tr`t`rsh kol i` `yua` ah hsphkb`ibst`s o ah dhabk`kbûl. @ktu`idhlth sol i` aoihlkb` dàs kodõl hl i`s phrsol`s ahi prbdhr dulao5 luhstro `khihr`ao doao ah vba` puhah iihn`r ` ahsn`st`r luhstr` dhlth, y ahghdos a`rih ahsk`lsos (o kuba`aos blthlsbvos) ku`lao ios lhkhsbth. @ahdàs ah hsto, `sbstbr ` ul psbkûiono ah jord` rhnui`r hs `ino duy rhkodhla`gih, ah i` dbsd` jord` quh soibkbt`dos rhvbsbolhs phrbûabk`s ` luhstro dâabko ah k`ghkhr`. ❚ 

[`iua `lädbk` o psäqubk`

Lulk` ahghdos oivba`r luhstr` s`iua `lädbk`. Ios `dgbhlths o hltorlos quh lo los `port`l kos`s posbtbv`s, `sä kodo i`s phrsol`s quh los m`khl a`ðo ahghl quha`r juhr` ah luhstr`s vba`s. Hsth `sphkto m` sbao `dpib`dhlth `gora`ao por ios ibgros ah `uto `yua`, ` luhstro `ik`lkh hl ku`iqubhr ibgrhrä` o khltro kodhrkb`i. Hs guhlo `thlahr ` ios kolsheos ah hsphkb`ibst`s y iihv`r ` k`go phquhðos hehrkbkbos ab`rbos, kodo kort`r rhi`kbolhs tûxbk`s o `p`rt`r d`i`s d `i`s bljiuhlkb`s ah luhstr` vba`. Hs bdport`lth roah`rsh õlbk`dhlth ah phrsol`s quh `dhl ah jord` sblkhr`, sbl bdposbkbolhs lb km`lt`ehs hdokbol`ihs6 tr`g`e`r hi `dor propbo y thlhr rhi`kbolhs s`l`s d`lthlarà luhstr` s`iua `lädbk` hl pihl` jord`. Kodo vhs, i` s`iua blthnr`i hs hshlkb`i hl hst` luhstr` vba` p`r` ahshdp`ð`r hi tr`g`eo, p`r` kodp`rtbr nr`lahs pi`lhs kol tus shrhs quhrbaos o p`r` vb`e`r y kolokhr luhvos iun`rhs. ¡I` vba` m`y quh vbvbri` kol pihlbtua! Gusk` tu gbhlhst`r hl toao dodhlto6 s`gbhlao kuba`r ah tb `prhlahràs kûdo kuba`r toao `quhiio quh th bdport`. Whkuphr`ao ah5 Hahl ’31/3>/7370— 

mttps5//www.`nu`h mttps5//www.`nu`hahl.hs/gion/q ahl.hs/gion/quh-hs-i`-s`iua-blthnr`i-y-kod uh-hs-i`-s`iua-blthnr`i-y-kodo-kolshnubri` o-kolshnubri`   mttps5//www.youtugh.kod/w`tkm?v4;M0z;E[PGUo   7.  Ogshrv` hi sbnubhlth vbaho  vbaho  mttps5//www.youtugh.kod/w`tkm?v4;M0z;E[PGUo

   

;.  @ktbvba`ahs `. `.   g. g.   k. k.   a. a.   h.  h. 

Dhab`lth ul orn`lbz`aor hxpibquh ios `sphktos ah i` s`iua blthnr`i. Hskrbg` aos abjhrhlkb`s hltrh s`iua dhlt`i y s`iua `lädbk`. Hxpibquh quâ hs s`iua blthnr`i. Sropoln` trhs dhaba`s prhvhltbv`s quh ahghdos `aopt`r p`r` ionr`r ul` s`iua s `iua blthnr`i. Lo oivbah abgue`r ios `ibdhltos ah i` pbràdbah `ibdhltbkb`.

PXÄDBK@ QHD@5 KOLJBNXW@KBÛL HIHKQWÛLBK@

I` quädbk` y ios `ibdhltos Xl `ibdhlto hs toa` sust`lkb` lo vhlhlos`, kodhstbgih o ghgbgih quh kolst` ah kodpolhlths quh puhahl blnhrbrsh, `gsorghrsh y utbibz`rsh por hi orn`lbsdo p`r` su d`lthlbdbhlto y ahs`rroiio. Ahsah ul pulto ah vbst` quädbko, ios `ibdhltos tbhlhl i` sbnubhlth kodposbkbûl (hl tbpos ah kodpuhstos quädbkos)5 Mbar`tos ah k`rgolo o sus kolstbtuyhlths, nr`s`s o sus kolstbtuyhlths, prothäl`s o sus kolstbtuyhlths, vbt`dbl`s o prhkursorhs kol ios quh hi orn`lbsdo puhah hi`gor`ri`s, s`ihs dblhr`ihs, `nu`. Sor io t`lto, toao io i o quh kodhdos hs ul` dhzki` ah kodpuhstos quädbkos.

0. Ih` `thlt`dhlth i` sbnubhlth bljord`kbûl Lõdhros kuàltbkos K`a` hihktrûl ahi àtodo hstà rhprhshlt`ao por ku`tro lõdhros kuàltbkos5 l5 lõdhro l5 lõdhro kuàltbko prblkbp`i. i5 lõdhro i5 lõdhro kuàltbko orgbt`i o ah dodhlto `lnui`r. di5 lõdhro di5  lõdhro kuàltbko d`nlâtbko. ds5 lõdhro ds5  lõdhro kuàltbko ah spbl.

Lõdhro kuàltbko prblkbp`i (l). - Hi lõdhro kuàltbko prblkbp`i prblkbp`i (l) soio puhah tod`r v`iorhs l`tur`ihs 0, 7, ;, 1... K`a` v`ior ahsbnl` ul lbvhi, hi ku`i hstà rhi`kbol`ao kol hi t`d`ðo y i` hlhrnä` ahi orgbt`i. @ d`yor v`ior ah l, d`yor hs i` abst`lkb` prodhabo ahi hihktrûl rhsphkto `i lõkiho. Hi prbdhr lbvhi hs hi ah dhlor hlhrnä`, y ios sbnubhlths, k`a` vhz dàs `ihe`aos ahi lõkiho, tbhlhl hlhrnä`s d`yorhs.

 

  Lõdhro kuàltbko shkula`rbo (i). - Hi lõdhro kuàltbko shkula`rbo tod` v`iorhs hlthros (i4l-0)5

[uglbvhi s p a j

Z`ior ah ah i   i   3 0 7 ;

L³ ah hihktrolhs por suglbvhi 7 : 03 01

Hsth lõdhro hstà rhi`kbol`ao kol i` jord` ahi orgbt`i quh okup` hi hihktrûl. Xl orgbt`i `tûdbko hs ul` rhnbûl ahi hsp`kbo, hl torlo `i lõkiho, aolah i` prog`gbiba`a ah hlkoltr`r hi hihktrûl kol ul` ahthrdbl`a` hlhrnä` hs duy nr`lah.

Lõdhro kuàltbko d`nlâtbko (di). - [us - [us v`iorhs ahphlahl ahi v`ior ah i, ah d`lhr` quh puhah tod`r toaos ios v`iorhs hlthros kodprhlabaos hltrh ∗i y +i, blkiubao hi khro. Hstà rhi`kbol`ao r hi`kbol`ao kol i` orbhlt`kbûl ahi orgbt`i hl hi hsp`kbo.

i

3

0

di

3

Qbpo ah orgbt`i

s

p

a

j

Ahlodbl`kbûl ah ios orgbt`ihs

ls

lp

la

lj

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0, 3, +0

7 ∗

7, ∗0, 3, +0, +7

; ∗

;, ∗7, ∗0, 3, +0, +7, +;

Lõdhro kuàltbko spbl (ds). - [oio puhah tod`r ios v`iorhs + ´ y -´. Hstà rhi`kbol`ao kol hi nbro ahi hihktrûl rhsphkto ` su heh, io quh nhlhr` n hlhr` ul k`dpo d`nlâtbko kol aos posbgihs orbhlt`kbolhs, shnõl hi shltbao ahi nbro.

Xl` vhz ahskrbtos ios ku`tro lõdhros kuàltbkos, hs jàkbi kodprhlahr quh k`a` orgbt`i `tûdbko hstà rhprhshlt`ao por ios trhs lõdhros kuàltbkos l, i y di, quh suhihl ahsbnl`rsh por ul lõdhro (hi lbvhi) y ul` ihtr` (hi suglbvhi) dbhltr`s quh i` ahskrbpkbûl ah k`a` hihktrûl hl hi àtodo rhqubhrh, `ahdàs, ahi ku`rto lõdhro kuàltbko, ds.

 

  I` t`gi` sbnubhlth duhstr` i` abstrbgukbûl ah ios hihktrolhs por lbvhihs y orgbt`ihs. Abstrbgukbûl ah hihktrolhs por lbvhihs y orgbt`ihs Lbvhi ah hlhrnä` (l) 0 7 ; 7 Lõdhro tot`i ah orgbt`ihs (l ) 0 1 2 Qbpo ah orgbt`ihs s s p s p a Lõdhro ah orgbt`ihs ah k`a` tbpo 0 0 ; 0 ; 8 Ahlodbl`kbûl ah ios orgbt`ihs 0s 7s 7p ;s ;p ;a Lõdhro dàxbdo ah hihktrolhs hl 7 7 : 7 : 03 ios orgbt`ihs Lõdhro dàxbdo ah hihktrolhs por 7 = 0= lbvhi (7l7)

1 0: s 0 1s

p ; 1p

a 8 1a

j > 1j

7

:

03

01

;7

Zh`dos ` koltblu`kbûl kodo sh abstrbguyhl ios hihktrolhs hl i` korthz`. •  Ios hihktrolhs sh hlkuhltr`l hl orgbt`ihs. Hl k`a` ulo ah hiios k`gh ul

dàxbdo ah aos hihktrolhs. •  Ios orgbt`ihs sh `nrup`l hl sbhth lbvhihs hlhrnâtbkos. •  K`a` lbvhi ah hlhrnä` poshh ulo o v`rbos orgbt`ihs, abjhrhlths, ahlodbl`aos

s, p, a, y j. Hi lõdhro ah orgbt`ihs ah k`a` tbpo, y hi lõdhro ah hihktrolhs quh k`ghl hl k`a` ulo ah hiios, sol ios sbnubhlths5 Qbpo ah orgbt`i

s

p

a

j

Lõdhro ah orgbt`ihs

0

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8

>

K`p`kba`a ah hihktrolhs

7

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03

01

S`r` ahlodbl`r ul orgbt`i ah ul lbvhi kolkrhto, blabk`dos hi lõdhro ahi lbvhi y, ` koltblu`kbûl, i` ahlodbl`kbûl ahi tbpo. @sä, por hehdpio, `i ahkbr 1 p, hst`dos rhjbrbâlaolos ` ios trhs orgbt`ihs ahi tbpo p quh sh hlkuhltr`l hl hi lbvhi 1, hl ios quh k`ghl shbs hihktrolhs.

   

  Juhlth55mttps5//hauk`kbol.nog.hk Juhlth mttps5//hauk`kbol.nog.hk/wp-kolthlt/upio`as/ /wp-kolthlt/upio`as/aowlio`as/730:/32/ibgrosth aowlio`as/730:/32/ibgrosthxto/Qhxto_qubdbk xto/Qhxto_qubdbk`_0_GNX.paj  `_0_GNX.paj   7.- @ktbvba`ahs `)  Blabk` kuàltos suglbvhihs m`y hl hi lbvhi ;. g)  Hlulkb` i` k`p`kba`a ah hihktrolhs ah k`a` ulo ah ios suglbvhihs ahi lbvhi 7. k)  Ahthrdbl` ios lõdhros kuàltbkos ah ios sbnubhlths hihdhltos. Hihdhlto

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i

di

ds

[oabo @rnûl Dhrkurbo Mbhrro

JÄ[BK@ QHD@5 DOZBDBHLQO WHKQBIÄLHO XLBJOWDHDHLQH Z@WB@AO (DWXZ)

0.- Ih` i` sbnubhlth bljord`kbûl  bljord`kbûl   K`dgbos ah vhiokba`a  vhiokba`a  [b `l`ibz`dos ios dovbdbhltos ah ul nbdl`st` hl hi s`ito ah potro, poahdos ogshrv`r quh su vhiokba`a v` k`dgb`lao5 • Ku`lao hi nbdl`st` blbkb` i` k`rrhr`, hi dûauio ah i` vhiokba`a `udhlt`.  • Ku`lao s`it`, i` abrhkkbûl ah i` vhiokba`a k`dgb`. • Ku`lao hi nbdl`st` tod` tbhrr`, hi dûauio ah i` vhiokba`a absdbluyh. 

[bhdprh quh m`y ul k`dgbo hl i` vhiokba`a tbhlh iun`r ul` ul ` `khihr`kbûl.

 

  @khihr`kbûl I` r`pbahz kol quh tbhlh iun`r hi k`dgbo ah vhiokba`a puhah shr d`yor o d dhlor. hlor. Shlshdos, por hehdpio, hl ul `uto quh s`ih ah ul shdàjoro duy ahprbs` y hl otro quh io m`kh a ahsp`kbo. hsp`kbo. @sä kodo i` vhiokba`a los hxprhs` i` r`pbahz hl hi k`dgbo ah posbkbûl, i` d`nlbtua quh los hxprhs` i` r`pbahz hl hi k`dgbo ah vhiokba`a sh ahlodbl` `khihr`kbûl

Xl dûvbi sh ahspi`z` kol dovbdbhlto rhktbiälho ulbjordhdhlth `khihr`ao (DWX@), sb sbnuh ul` tr`yhktorb` rhktbiälh` y su `khihr`kbûl hs kolst`lth y lo lui`.

Hl hi dovbdbhlto rhktbiälho ulbjordhdhlth v`rb`ao sh ulhl t`lto hi `khihr`ao (`udhlt` i` vhiokba`a) y hi rht`ra`ao (absdbluyh i` vhiokba`a)

   

  Hehdpio ah i` vba` kotbab`l` Hi dovbdbhlto ah ul `utogõs hs ul dovbdbhlto rhktbiälho ulbjordh y v`rb`ao, porquh `udhlt` i` vhiokba`a y p`r` quh ahe`r y rhkonhr p`s`ehros absdbluyh i` vhiokba`a @pibk`kbûl ah jûrdui`s p`r` rhsoivhr progihd`s ahi (DWXZ) Xl trhl `udhlt` ulbjordhdhlth i` vhiokba`a vhiokba`a ah 73 d/s ` ;3 d/s hl 03 s. K`ikui`5 `. i` `khihr`kbûl6 g. i` abst`lkb` quh rhkorrh hl hsth tbhdpo6 k. i` vhiokba`a quh thlarà 8s ahspuâs sb d`ltbhlh kolst`lth i` `khihr`kbûl. A`tos55 A`tos Z3 4 73d/s Zj  4  4 ;3d/s t 4 03s ` 4? a 4? Zj 4? sb hi tbhdpo hs ah 8s Jûrdui` `4

∗   

Whhdpi`z`dos ios a`tos hl i` jûrdui`

 ∗ ` 4     ` 4    

`4 0 d/s7 

g) p`r` k`ikui`r i` abst`lkb`  a 4 vb .t +  ª.t7  

a 4 73d/s. 03 s +  0 d/s7. (03s)7  a 4 733d + 83d a 4 783 d k) vhiokba`a ` ios 8 s Zj 4 vo + `.t Zj 4 73 d/s + 0 d/s 7. 8s Zj 4 73d/s + 8d/s Zj 4 78 d/s 7.- @ktbvba`a LOQ@5 rh`ibz`r i`s kolvhrsbolhs ah ulba`ahs ah fd/m ` d/s hl k`a` progihd` 0.- Wh`ibkh ul ku`aro kodp`r`tbvo hltrh dovbdbhlto rhktbiälho `khihr`ao y rht`ra`ao. 7.- Whsuhiv` progihd`s `pibk`lao i`s jûrdui`s ahi DWXZ. `.  `.  K`ikui` i` `khihr`kbûl quh ahgh thlhr ul `uto p`r` `ik`lz`r ul` vhiokba`a ah 03= fd/m hl 03 s sb p`rth ahi rhposo. ‑¿Puâ abst`lkb` rhkorrh hl hsh tbhdpo? g. g.   Xl nuhp`rao phrsbnuh hl iälh` rhkt` ` su prhs` ` :1,= fd/m `aqubrbhlao, ` p`rtbr ah hsth dodhlto, ul` `khihr`kbûl kolst`lth ah 1 d/s 7. K`ikui` i` vhiokba`a y i` abst`lkb` rhkorrba` `i k`go ah = s ah kodhlz`r ` `khihr`r. Whkuhrah abgue`r i` pbràdbah ah `ibdhltos.

     

 

D@QHDÀQBK@ Qhd`5 Zhktorhs hl hi pi`lo. Ahjblbkbûl Ahjblbkbûl ah vhktor vhktor hl hi pi`lo Qh blvbto quh ogshrvhs kol `thlkbûl hi sbnubhlth vbaho, kolkhpto y ahjblbkbûl ah vhktorhs. mttps5//youtu.gh/D8IU0W;I@ps ¿[@GHWH[ SWHZBO[…?  Hl i` `ktu`iba`a, hxbsth ul d`yor tràjbko `ârho6 i`s nr`lahs dhtrûpoibs sol iun`rhs ah ahsphnuh y `thrrbz`eh ah dukm`s `hrol`vhs quh vbhlhl o sh abrbnhl ` abjhrhlths p`rths ahi dulao. S`r` hvbt`r quh ios `vbolhs hl vuhio sh `proxbdhl ahd`sb`ao, vboihl i`s abst`lkb`s dälbd`s ah shnurba`a o koibsbolhl, ` k`a` vuhio sh ih `sbnl` ul vhktor ah vuhio o pi`l ah vuhio quh kolst` ah ul` posbkbûl, vhiokba`a, àlnuio ah abrhkkbûl, tbhdpo, ul` rut` y ul` `itur` hsphkäjbk`.

Zhktorhs hl hi pi`lo.  Ahlot`dos kol Σ ` ul pi`lo. [h ii`d` gbpulto ` toao p`r orahl`ao (@, G) ϸ Σ x Σ. Hi pulto @ ϸ Σ sh ii`d` orbnhl y hi pulto G ϸ Σ, hi hxtrhdo. Abrhdos (@, G) ϸ Σ x Σ hs hi gbpulto ah orbnhl @ y hxtrhdo G I` pbràdbah lutrbkbol`i hs ul` mhrr`dbhlt` ah hauk`kbûl y prodokbûl ah s`iua quh sh duhstr` ah d`lhr` nràjbk` y shlkbii` ` tr`vâs ah abgueos o jotonr`jä`s ah ios `ibdhltos h blabk` quâ k`ltba`ahs m`l ah kolsudbrsh p`r` shnubr ul` `ibdhlt`kbûl s`iua`gih.

Ahjblbkbûl ah ul vhktor hl hi pi`lo. [h` (S, P) ul gbpulto hl hi pi`lo Σ. Hi koleulto ah gbpultos (D, L) hqubpoihlths `i gbpulto (S, P) hs i` ki`sh ah hqubv`ihlkb` ahi gbpulto (S, P) ahlodbl`ao vhktor nhodâtrbkö.

̈ 4 {( (,, ) ∍ ΣΣ Σ/( /(,)~ ,)~( (,, ) )}}  @ahdàs, toaos ios gbpultos (D, L) hqubpoihlths kol (S, P) sol `quhiios quh tbhlhl i` dbsd` abrhkkbûl, iolnbtua (dûauio) y hi dbsdo shltbao quh shltbao quh hi gbpulto (S, P).  P).  

Bnu`ia`a ah Zhktorhs5 ⃞  y ⃞  aos vhktorhs `sokb`aos ` ios gbpultos (@, G) y (K, A). Ahkbdos quh [h`l   ⃞  y  ⃞  sol bnu`ihs, o sh` quh   ⃞  4  ⃞ , sb y soio sb ios shndhltos ah rhkt` V@,   GT y VK, AT tbhlhl hx`kt`dhlth hi dbsdo pulto dhabo  dhabo 

Sropbha`ahs5 ⃞  y S`r` quh m`y` bnu`ia`a ah ios vhktorhs   i`s trhs propbha`ahs sbnubhlths5

⃞, hsto hs,   ⃞  4 ⃞, ahghl vhrbjbk`rsh

 ∨   , y   y   tbhlhl i` dbsd` abrhkkbûl. 0.  I`s 7.  7. V@, G V y VK, A V tbhlhl hi dbsdo shltbao.    shdbrrhkt`s ;.  ;.  Ios shndhltos V@, GT y VK, AT tbhlhl i` dbsd` iolnbtua. @ahdàs, V@, KT || VG, AT

 

  Zhktor Luio. [h` @ ul pulto ahi pi`lo, hi gbpulto (@, @) hs rhprhshlt`lth ahi vhktor ⃞  4 ⃞3  ahsbnl` kol ⃞3 , hs ahkbr,   Lûthsh quh sb G hs ku`iqubhr pulto ahi pi`lo

⃞  , ahlodbl`ao vhktor luio, `i quh sh io  

⃞3 4 {(,) ,)//(, ) ∹ (,)} ,)}  ⃞  4 ⃞3 ⟵  4    [h tbhlh i` sbnubhlth hqubv`ihlkb`5   Abrhkkbûl y shltbao ah vhktorhs lo luios. ⃞ 4 ⃞ , (, ) ∍ ⃞  ,   aos vhktorhs lo luios ahi pi`lo y @, G, K, A ku`tro pultos ahi pi`lo, t`ihs quh ( , ) ∍  [h`l  ⃞ 4    , y   y   ios soporths ah ios gbpultos (@, G) y (K, A). Ahsbnl`dos kol V@, G V i` shdbrrhkt` ah orbnhl @ y quh p`s` por G Hl jord` `làion`, thlhdos VK, A V. Ahjblbkbûl.

I` abrhkkbûl ahi vhktor  ⃞  hs i` abrhkkbûl ah i` rhkt` r hkt`  . Hi shltbao ahi vhktor hs hi shltbao ah i` shdbrrhkt` V@, G V

⃞  

⃞  y   tbhlhl i` dbsd` abrhkkbûl y shltbao sb y soio sb Abrhdos quh ios vhktorhs   ∨   y V@, G V y VK, A V tbhlhl hi dbsdo shltbao

Abrhdos quh ios vhktorhs  ⃞   y    tbhlhl i` dbsd` abrhkkbûl y sol ah shltbao opuhstos sb y soio sb  ∨    y V@, G V y VK, A V tbhlhl shltbaos opuhstos.

Iolnbtua o lord` ah ul vhktor

(, )  ⃞  sh ahlot` kol ‚⃞ ‚ y sh ahjblh kodo ‚⃞ ‚ 4 ( I` iolnbtua o lord` ah ul vhktor  ⃞ ‚ 4 ⃞ 4  (  ,  ) < 3  [h tbhlh quh ‚ [upoln`dos @ ≣ G. Suhsto quh ( , )

vhktorhs

4 ( (,) ,) , sh sbnuh quh ‚⃞ ‚ 4 ⃞  . @ahdàs, @ahdàs, ios

⃞  y  ⃞  tbhlhl i` dbsd` abrhkkbûl, phro sol ah shltbaos opuhstos.  

Q@IIHW SWÀKQBKO5 0.  0.  [h`l @, G, K, A ku`tro pultos ahi pi`lo, t`i quh ios gbpultos (@, G) y (K, A) sol rhprhshlt`lths ah ios vhktorhs ⃞  y  ⃞   -  `) `)   Wh`ibz` i` rhprhshlt`kbûl nhodâtrbk` ah ⃞  4⃞   ⃞  ah  i` dbsd` abrhkkbûl y iolnbtua, kol shltbao opuhsto ` ⃞ . g) g)   Wh`ibz` i` rhprhshlt`kbûl nhodâtrbk` ah   ⃞  ah i` dbsd` abrhkkbûl y shltbao, kol abjhrhlth iolnbtua ` k) k)   Wh`ibz` i` rhprhshlt`kbûl nhodâtrbk` ah   ⃞  

 

⃞ 4 ⃞   , (, ) ∍ ⃞  ,   aos vhktorhs lo luios ahi pi`lo, t`i quh ( , ) ∍  7.  7.  A`a`s i`s rhkt`s  ∨   y sh`l  ⃞ 4    , ¿kûdo sh ahghl abspolhr ios vhktorhs p`r` quh sh kudpi`l i`s sbnubhlths sbnubhlths kolabkbolhs? `) `)   [h`l ah bnu`i abrhkkbûl y shltbao y ah abjhrhlth iolnbtua. Nr`jbk` g) g)   [h`l ah bnu`i abrhkkbûl y iolnbtua y ah abjhrhlth shltbao Juhlth5 Qhxto blthnr`ao Dblbsthrbo ah Hauk`kbûl prbdhro GNX prbdhr` bdprhsbûl d`rzo 7373

BLNIÂ[ ^HHF OLH ‛ MH@IQMR JOOA NW@DD@W5 [bdpih Srhshlt / [bdpih S`st

7.- ^WBQH 8 [HLQHLKH[ ^BQM MH@IQMR JOOA BL [BDSIH S@[Q. 0.- ………………………………………………………………………………………………………………….  7.- ………………………………………………………………………………………………………………….  ;.- ………………………………………………………………………………………………………………….  1.- ………………………………………………………………………………………………………………….  8.- …………………………………………………………………………………………………………………. 

   

HAXK@KBÛL HAXK@KB ÛL JÄ[BK@ QHD@5 @IBDHLQ@KBÛL [@IXA@GIH (SWOAXKKBÛL R KOL[XDB[DO [O[QHLBGIH) 0.  WH@IBU@ I@[ [BNXBHLQH[ @KQBZBA@AH[.

[ GB [

PX …

@IBDHLQ@KBÛL [O[QHLBGIH R [@IXA@GIH, Hqubibgr`a`, hs ahkbr, quh thln` v`rbha`a ah `ibdhltos, kol prhaodblbo ah `quhiios jrhskos y ah orbnhl vhnht`i. Hl rhi`kbûl kol hsto õitbdo, sol dukmos ios hxphrtos quh koblkbahl hl quh ul` `ibdhlt`kbûl g`s`a` hl mort`ibz`s, vhraur`s, jrut`s, ihnudgrhs, khrh`ihs, nhlhr` dhlor bdp`kto `dgbhlt`i y sogrh i` s`iua, quh ul` g`s`a` hl hi kolsudo ah `ibdhltos ah orbnhl `lbd`i.  `lbd`i.     @a`pt`a` ` i`s k`r`kthrästbk`s blabvbau`ihs, phrsol`ihs, kuitur`ihs y ahi hltorlo.   Kodpiht` hl lutrbhlths, sujbkbhlth hl lhkhsba`ahs y s`tbsj`ktorb`. hkolûdbk`dhlth.   @shqubgih hkolûdbk`dhlth.

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 WHKXHWA@

I@ @IBDHLQ@KBÛL [@IXA@GIH. - Hs - Hs `quhii` quh `port` ` k`a` blabvbauo toaos ios `ibdhltos lhkhs`rbos p`r` kugrbr sus lhkhsba`ahs lutrbkbol`ihs, hl i`s abjhrhlths ht`p`s ah i` vba` (blj`lkb`, `aoihskhlkb`, ha`a `auit` y hlvhehkbdbhlto), hlvhehk bdbhlto), y hl sbtu`kbûl ah s`iua.

7.  S@W@ PXH KOLOUK@[ DÀ[ [OGWH H[QH BDSOWQ@LQH BDS OWQ@LQH QHD@, BLNWH[@ @I [BNXBHLQH HLI@KH [OGWH I@ @IBDHLQ@KBÛL [@IXA@GIH R @KQBZBA@A JÄ[BK@. mttps5//www.youtugh.kod/w`tkm?v4esqOLxbIkRD   mttps5//www.youtugh.kod/w`tkm?v4esqOLxbIkRD mttps5//www.youtugh.kod/w`tkm?v4aEDN;@B[dxP ;.  `)    0.  7.  7. ;.  ;. 

@KQBZBA@AH[ SWÀKQBK@[. Wh`ibz`r ul prhvbo k`ihlt`dbhlto. Wot`kbûl ah 08 shnulaos kolul k`a` p`rth ah su kuhrpo.ahspuâs ah k`a` ulo. Hehrkbkbos 03`rtbkui`kbolhs, rhphtbkbolhs k`a` ulo, us`lao ahsk`lso y rhi`e`kbûl Hstbr`dbhltos, rh`ibz`r ah 08 ` 73 shnulaos k`a` ulo korrhkt`dhlth.

 

  g)  Hehrkbkbos ah vhiokba`a. ➧ 

[fbppbln hl hi propbo thrrhlo5 sh tr`t` ah tr`z`r ul` iälh` hl hi suhio, iuhno rh`ibz`r sfbppbln ahi`lth y `tràs, hl ; shrbhs ah ;3 shnulaos.  shnulaos. 

➧ 

K`rrhr` ah vhiokba`a 08 dhtros5 p`r` hst` `ktbvba`a ahghràs gusk`r ul hsp`kbo hl hi p`tbo ah tu k`s`, ul` k`lkm`, ul p`rquh, tod`lao hl kuhlt` toa`s i`s dhaba`s ah gboshnurba`a, dbah 08 p`sos i`rnos y ugbk` ul` d`rk` hl k`a` hxtrhdo. Iuhno th ugbk`s hl ul pulto, ahghs krolodhtr`r hi tbhdpo p`r` bahltbjbk`r quâ tbhdpo th tod`s hl iihn`r `i otro pulto ` nr`l vhiokba`a.  vhiokba`a. 

1.  @KQBZBA@AH[ S@W@ HI SOWQ@JOIBO. A@QO[ SHW[OL@IH[5 LODGWH5 KXW[O5 JHKM@5 QHD@5 @KQBZBA@A

WH[XIQ@AO (QBHDSO)

K`rrhr` ah vhiokba`a 08 dhtros.

HDSWHLABDBHLQO HDSWHLABD BHLQO R NH[QBÛL 0.  Ihh i` sbnubhlth bljord`kbûl.

QHD@5 KI@[BJBK@KBÛL AH IO[ KO[QO[ R N@[QO[ S`r` ionr`r i` hjbkbhlkb` ah ul` hdprhs` hl io quh sh rhjbhrh ` proaukbr gbhlhs o prhst`r shrvbkbos, sh ahgh ahthrdbl`r kuàlto kuhst` ogthlhr hsh proaukto o nhlhr`r hsh shrvbkbo. Ah hst` d`lhr`, sh poarà hehkut`r ul` pi`lh`kbûl y tod`r ahkbsbolhs. S`r` quh ul ahshdgoiso sh` kolsbahr`ao kosto, sh ahghl ogshrv`r ios sbnubhlths hihdhltos5

 

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abrhktos5  [ol i` d`thrb` prbd` y ios blsudos. I` d`thrb` prbd` hs hi d`thrb`i dàs rhprhshlt`tbvo   D`thrb`ihs abrhktos5

quh koljord` hi proaukto, dbhltr`s ios blsudos sol ios hihdhltos dàs phquhðos. Sor hehdpio, hl ul` k`dbs`, i` d`thrb` prbd` hs i` thi`, y ios blsudos sol hi mbio y ios gotolhs.     D`lo ah ogr` abrhkt`5 [ol ios ahshdgoisos por i` d`lo ah ogr` quh tr`lsjord` i` d`thrb` prbd` o quh rh`ibz` hi shrvbkbo quh ojrhkh i` hdprhs`.    Kostos blabrhktos ah j`grbk`kbûl5 [ol ios ahshdgoisos quh lo tbhlhl rhi`kbûl abrhkt` kol hi proaukto o hi shrvbkbo. [h abvbahl hl5 D`thrb`i blabrhkto (phn`lths), y d`lo ah ogr` blabrhkt` (suphrvbsbûl), (suphrvbs bûl), kostos nhlhr`ihs ah j`grbk`kbûl (shrvbkbos põgibkos). 

mttps5//bd`nh.sibahsm`rhkal.kod/kolk mttps5//bd`nh.sibahsm`rhkal.kod/kolkhptosg`sbkoskostos-03310:011=87-pmp`pp37/28/kolt`g hptosg`sbkoskostos-03310:011=87-pmp`pp37/28/kolt`gbiba`a-ah-kostos-kostos biba`a-ah-kostos-kostos-71->7=.epn?kg40;:0211>1: -71->7=.epn?kg40;:0211>1:  

KI@[BJBK@KBÛL AH IO[ KO[QO[ [hnõl su kodport`dbhlto, ios kostos sh ki`sbjbk`l hl5 jbeos, v`rb`gihs y shdbjbeos. jbeos5 [ol `quhiios rhi`kbol`aos kol i` proaukkbûl, y sh tbhlhl quh `sudbr o k`lkhi`r,   Kostos jbeos5 blahphlabhlthdhlth blahphlabhlth dhlth ahi lbvhi ah proaukkbûl6 hs ahkbr, sh` quh sh proauzk`l dbi ulba`ahs o lblnul`, su p`no sh thlarà quh rh`ibz`r. Hs hi k`so ahi p`no ah `rrhla`dbhlto ah d`qubl`rb`, d`lo ah ogr`, d`lthlbdbhlto, htk.   Kostos v`rb`gihs5 [ol `quhiios rhi`kbol`aos kol i` proaukkbûl, y sol abrhkt`dhlth proporkbol`ihs ` hii`. @sä, ` d`yor proaukkbûl, d`yor kosto y vbkhvhrs`. Sor hehdpio, i`s d`thrb`s prbd`s sol ul kosto v`rb`gih porquh sb quhrhdos proaukbr dàs, sh lhkhsbt`rà kodpr`r dàs ah hii`s. hi i`s.   Kostos shdbjbeos5  shdbjbeos5  [ol ios quh sh k`r`kthrbz`l por shr jbeos p`r` ul ahthrdbl`ao voiudhl ah lhnokbo, phro v`rä`l ` dhaba` quh sh p`s` ah ul r`lno ` otro. Sor hehdpio, `i proaukbr ah 0 ` 0 333 ulba`ahs sh tbhlh ul kosto, phro `i hihv`r hl dàs ah 0 333 3 33 i` proaukkbûl, hi kosto k`dgb` y sh d`ltbhlh m`st` iihn`r ` otr` otr ` k`ltba`a. Xl hehdpio shrä` i` d`lo ah ogr` koltr`t`a` p`r` ul` proaukkbûl dàs nr`lah ah io m`gbtu`i, hl i` quh lo sol sujbkbhlths ios hdpih`aos quh poshh i` hdprhs`. •

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(Qhxto Hdprhlabdbhlto 0hro. G`kmbiihr`to Sàns. 0:, 0>). Juhlth5 mttps5//hauk Juhlth5  mttps5//hauk`kbol.nog.hk/ `kbol.nog.hk/wp-kolthlt/upio`as/ao wp-kolthlt/upio`as/aowlio`as/730:/3=/DBLHAX_ wlio`as/730:/3=/DBLHAX_Ibgro_Hdprhlabdbh Ibgro_Hdprhlabdbhlto-0lto-0GNX.paj  

@KQBZBA@AH[5 `.  @ koltblu`kbûl, blabk` ul dhlõ ah ul ahs`yulo quh kolsudhs y hl i` sbnubhlth t`gi` hlibst` ios sbnubhlths hihdhltos ah ios kostos quh blthrvbhlhl hl tõ ahs`yulo. D@QHWB@IH[ ABWHKQO[

D@LO AH OGW@ ABWHKQ@

KO[QO[ BLABWHKQO[ AH J@GWBK@KBÛL.

 

  g.  Ki`sbjbk` shnõl korrhspola` (kostos jbeos  ‛ J, kostos v`rb`gihs ‛ Z, kostos shdbjbeos ‛ [J)5 

BLJOWDÀQBK@ hlhrnä`   Dbhi p`r` iihl`rth ah hlhrnä` [b gusk`s ul` `ithrl`tbv` s`iua`gih `i `zõk`r ah dhs`, i` dbhi hs ul` nr`l opkbûl. Hltrh sus dõitbpihs propbha`ahs, hsth `ibdhlto hs ul` nr`l juhlth ah hlhrnä` o puhah `yua`rth ` su`vbz`r i` tos. ¡Sruâg`io!  

Hl hsth proyhkto `prhlahrhdos quâ hs ul [bsthd` Ophr`tbvo, vhrhdos v hrhdos ul poko su mbstorb`. ¿[`ghs quâ hs [bsthd` Ophr`tbvo? @adblbstr` ios rhkursos ahi kodput`aor, hs ahkbr, hi sojtw`rh y m`raw`rh m`raw`rh  ah tu hqubpo. Hs i` hstruktur` quh soport` y d`lhe` toaos ios pronr`d`s y p`rths ah tu kodput`aor. Hi sbsthd` ophr`tbvo hs hi pronr`d` dàs bdport`lth ah i` kodput`aor`.

 

  [bsthd`s Ophr`tbvos p`r` SK Ios dàs us`aos sol5   ^blaows   Xgultu   D`k Os •

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Dbkrosojt ^blaows Dbkrosojt ^blaows hs ^blaows hs ul sbsthd` ophr`tbvo, ophr`tbvo, hs ahkbr, ul koleulto ah pronr`d`s quh posbgbibt` i` `adblbstr`kbûl ah ios rhkursos ah ul` kodput`aor`.. Hsth tbpo ah sbsthd`s hdpbhz` ` tr`g`e`r ku`lao sh kodput`aor` hlkbhlah hi hqubpo p`r` nhstbol`r hi m`raw`rh m`raw`rh `  ` p`rtbr ahsah ios lbvhihs dàs gàsbkos.

Zhrsbolhs ah ^blaows s u `p`rbkbûl hl 0228, vh`dos ` koltblu`kbûl sus vhrsbolhs.  vhrsbolhs.     ^blaows m` thlbao `inul`s `ktu`ibz`kbolhs ahsah su •

 

  @ktbvba`ahs Hst` `ktbvba`a tbhlh ul` k`ibjbk`kbûl ah 03 pultos.  pultos.   hstuab`lth   -  7 pultos hlk`ghz`ao kol a`tos ah i` blstbtukbûl y a`tos ahi hstuab`lth -  7 pultos i` guhl` prhshlt`kbûl, k`ibnr`jä` y ortonr`jä`  ortonr`jä`   prhnult`s   -  : pultos hi ahs`rroiio ah i`s prhnult`s  Nr`jbk`rhdos hi hskrbtorbo ah i` prbdhr` vhrsbûl ah ^blaows kol sus p`rths. Nr`jbquh y ugbquh i`s p`rths ah i` vhlt`l` ahi Hxpior`aor ah ^blaows ^blaows  

 @KQBZBA@  @ KQBZBA@AH[ AH[ S@W@ S@ W@ I @ [HD@ [HD@L@ L@ 7 GBOIONÄ@  QHD@5 HLJHWDHA@AH[ LXQWBKBOL@IH[ LXQWBKBOL@IH[ R AH[ÛWAHLH[ @IBDHLQBKBO[

¿Puâ hs i` `ibdhlt`kbûl sosthlbgih y s`iua`gih? Hs ul doahio ah `ibdhlt`kbûl quh tbhlh kodo ogehtbvo `jrolt`r i`s prhokup`kbolhs ah s`iua y `dgbhlt`ihs `sokb`a`s ` i` proaukkbûl y kolsudo ah `ibdhltos. `ibdhltos . S`r` hiio, `ahdàs ah n`r`ltbz`r i` s`iua ah i`s phrsol`s, gusk` prodovhr i` proaukkbûl y kolsudo rhspols`gihs, nhlhr` ul bdp`kto `dgbhlt`i rhaukbao, iukm` koltr` hi k`dgbo kibdàtbko, rhspht` i` kuitur`, i` gboabvhrsba`a gboabvhrsba`a y  y prothnh ios hkosbsthd`s thrrhstrhs y i` vba` sugd`rbl`. ¿Puâ poahdos m`khr kodo kolsudbaorhs p`r` quh luhstr` `ibdhlt`kbûl sh` dàs sosthlbgih sosth lbgih y s`iua`gih?  s`iua`gih?  Ku`lao `t`ðh ` i` kodba`, ul` prhnult` ahst`k` sbhdprh5 ¿ quâ hs i` `ibdhlt`kbûl s`iua`gih? s`iua`gih? I` rhspuhst` ` hst`,  eulto ` ul` `ib`lz` m`kb` i` sosthlbgbiba`a ahi dhabo `dgbhlth, a` hstos pultos ` thlhr hl kuhlt` hl ul` abht` sosthlbgih55 sosthlbgih 0.  0.  7.  7.  ;.  ;.  1.  1.  8.  8.  :.  :.  >.  >. 

Kodhr dhlos k`rlhs roe`s y prokhs`a`s. Kolsudbr dàs proauktos iok`ihs, ah thdpor`a` y dälbd`dhlth prokhs`aos. @udhlt`r hi kolsudo ah ihnudblos`s y ah jrutos shkos kodo juhlth ah prothäl` vhnht`i. Blkrhdhlt`r hi kolsudo hi kolsudo ah jrut`s y mort`ibz`s.  mort`ibz`s.  Qod`r dàs khrh`ihs y `ibdhltos rbkos hl `idbaûl. D`lthlhr hi kolsudo ah iàkthos. Si`lbjbk`r i`s kodba`s o `provhkm`r i`s sogr`s koltrbguyh `i k`dgbo p`r` hvbt`r hi ahspbij`rro.

 

  Sor io t`lto, `post`r por ul` `ibdhlt`kbûl s`iua`gih y sosthlbgih hs blvhrtbr hl s`iua. Hs bdport`lth prodovhr ul` `ibdhlt`kbûl sujbkbhlth, kodpiht`, hqubibgr`a`, s`tbsj`ktorb`, shnur`, `a`pt`a` `i kodhls`i, `i hltorlo, sosthlbgih y `shqubgih. R hl ahjblbtbv`, tr`g`e`r p`r` tr`lsjord`kbûl niog`i ahi sbsthd` `ibdhlt`rbo. mttps5//kbhlkb`sahi`s`iua.gions.uok.hau/quh-h mttps5//kbhlkb`sahi`s`iua.gions. uok.hau/quh-hs-`ibdhlt`kbol-sosth s-`ibdhlt`kbol-sosthlbgih/ lbgih/   Whkuphr`ao5 [`iua y Kbhlkb` 07/3>/7370 0.Ih` kol `thlkbûl i` bljord`kbûl  bljord`kbûl  I` `ibdhlt`kbûl rhsuit` hshlkb`i p`r` absjrut`r ah ul `ahku`ao hst`ao ah s`iua. Shsh ` hiio, lo sbhdprh hst`dos bljord`aos sogrh hsto. S`r` quh `prhla`s ` kolokhr ul poko po ko dàs hsth dulao ` koltblu`kbûl th dostr`dos kuàihs sol i`s prblkbp`ihs hljhrdha`ahs lutrbkbol`ihs  lutrbkbol`ihs  sogrhphso    Oghsba`a y sogrhphso  [upolh toao io koltr`rbo ` i` ahslutrbkbûl. a hslutrbkbûl. [h tr`t` ahi kolsudo hxkhsbvo ah kodba`, quh sh `k`g` tr`lsjord`lao hl i` `kudui`kbûl ah nr`s` korpor`i quh puhah iihn`r ` orbnbl`r ahshqubibgrbos psbkoiûnbkos y mordol`ihs, hltrh otr`s kos`s. Q`dgbâl blkrhdhlt` i`s posbgbiba`ahs ah p`ahkhr kàlkhr o  o  ab`ghths ah tbpo 7. 7.    Ahslutrbkbûl [h proaukh hst` sbtu`kbûl ku`lao kolsudbdos duy pok` kodba`, m`y progihd`s ah abnhstbûl o abnhstbûl  o los `ibdhlt`dos ah jord` bl`ahku`a`. Hl rh`iba`a, i` blnhst` ah k`iorä`s rhsuit` bljhrbor ` io quh prhkbs` hi orn`lbsdo p`r` julkbol`r korrhkt`dhlth. Guibdb`     Guibdb` I`  I`  guibdb` guibdb`  sh tr`t` ah ul ahsorahl `ibdhltbkbo provok`ao por ul` ogshsbûl por hi phso korpor`i, hi `sphkto jäsbko y i` `lsbha`a. `lsbha`a. @k`rrh` ul kolsudo hihv`ao ah `ibdhltos, k`sb sbl koltroi, p`r` ` koltblu`kbûl vodbt`r o utbibz`r i`x`lths kol abht`s duy hstrbkt`s.   Ab`ghths [h vblkui` kol i` oghsba`a. Kolsbsth hl i` blk`p`kba`a ahi kuhrpo p`r` proaukbr i` sujbkbhlth blsuibl`. blsuibl` . Hsto provok` hl ul` d`i` `gsorkbûl ah niukos` y su `gula`lth prhshlkb` hl hi jiueo s`lnuälho.   @lhdb` `lhdb`  hs ul` hljhrdha`a quh supolh ul` k`äa` bdport`lth hl hi lõdhro ah niûguios roeos. roeos. [h ahgh sogrh toao I`  I` `lhdb` ` ul` d`i` `gsorkbûl ah dblhr`ihs, sogrh toao hi mbhrro. S`r` quh lo ih j`ith mbhrro ` tu orn`lbsdo ahghrä`s blkiubr kol dàs jrhkuhlkb` `ibdhltos kodo hi `tõl, k`rlh ah v`kulo o hi muhvo. mu hvo.   @lorhxb` I` `lorhxb` bdpibk` hi dbhao ` n`l`r phso. Nu`ra` dukm`s sbdbibtuahs kol i` guibdb`. @k`rrh` pâraba`s ah phso duy •

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prolulkb`a`s ahgbao ` i` pràktbk` `gusbv` ah ahporth y ` i`s abht`s t`l rhstrbktbv`s. Hs bdport`lth quh kolozk`s `i prolulkb`a`s ahgbao aht`iih   i`s k`r`kthrästbk`s ah hst`s hljhrdha`ahs lutrbkbol`ihs p`r` lo shr väktbd`s ah hii`s . Lulk` sol gbhl aht`iih rhkbgba`s p`toionä`s ah hsth tbpo, y` quh hl ok`sbolhs sh polh hl euhno luhstr` s`iua. ¿Puâ sol ios tr`storlos tr `storlos `ibdhltbkbos? Ios tr`storlos `ibdhlt`rbos sol `jhkkbolhs nr`vhs ah s`iua dhlt`i. Bdpibk`l progihd`s shrbos sogrh kûdo sh pbhls` sogrh i` kodba` y i` kolaukt` `ibdhltbkb`. [h puhah kodhr dukmo dhlos o dukmo dàs d às ah io lhkhs`rbo. Ios tr`storlos `ibdhltbkbos sol `jhkkbolhs dâabk`s. Lo sol ul hstbio ah vba`. @jhkt`l i` k`p`kba`a ahi kuhrpo p`r` ogthlhr ul` lutrbkbûl `ahku`a`. Hsto puhah provok`r progihd`s ah s`iua kodo hljhrdha`ahs  hljhrdha`ahs k`raä`k`s  k`raä`k`s y rhl`ihs, rhl`ihs, o blkiuso i` duhrth. [bl hdg`rno, m`y tr`t`dbhltos quh puhahl `yua`r.

 

  ¿Kuàihs sol ios tbpos ah tr`storlos `ibdhltbkbos? Ios tbpos kodulhs ah tr`storlos `ibdhltbkbos blkiuyhl5  

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@tr`kolhs ah kodba`5 kodba`5 Hs ahkbr, kodhr sbl koltroi. I`s phrsol`s kol tr`storlo por `tr`kûl sbnuhl kodbhlao blkiuso ahspuâs ah hst`r iihl`s. @ dhluao, kodhl m`st` quh sh sbhlthl duy blkûdoaos. Hl nhlhr`i, ahspuâs tbhlhl shltbdbhltos ah kuip`, vhrnùhlz` y `lnustb`. A`rsh `tr`kolhs ah kodba` kol ahd`sb`a` jrhkuhlkb` puhah k`us`r `udhlto ah phso y  y   oghsba`a. oghsba`a. Hi tr`storlo por `tr`kûl hs hi tr`storlo `ibdhlt`rbo dàs kodõl hl ios Hst`aos Xlbaos

 

Guibdb` lhrvbos`5 lhrvbos`5 I`s phrsol`s kol guibdb` lhrvbos` t`dgbâl tbhlhl phräoaos ah `tr`kolhs. Shro iuhno sh purn`l provokàlaosh vûdbtos o us`lao i`x`lths. Q`dgbâl puhahl m`khr hehrkbkbo hl hxkhso o puhahl `yul`r. I`s phrsol`s kol guibdb` lhrvbos` puhahl thlhr poko phso, phso lord`i o sogrhphso. s ogrhphso.

 

@lorhxb` lhrvbos`5 lhrvbos`5 I`s phrsol`s kol `lorhxb` lhrvbos` hvbt`l ios `ibdhltos, rhstrblnhl shvhr`dhlth ios `ibdhltos o kodhl k`ltba`ahs duy phquhð`s ah soio `inulos `ibdhltos. Suhahl vhrsh ` sä dbsd`s kol sogrhphso, blkiuso ku`lao hstàl phibnros`dhlth ahin`a`s. I` `lorhxb` lhrvbos` hs hi dhlos kodõl ah ios trhs tr`storlos `ibdhltbkbos, phro ` dhluao hs hi dàs nr`vh. Qbhlh i` t`s` ah a h dort`iba`a dàs `it` ah ku`iqubhr

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tr`storlo dhlt`i ¿Puâ k`us` ios tr`storlos `ibdhltbkbos?  `ibdhltbkbos?  [h ahskolokh i` k`us` hx`kt` ah ios tr`storlos `ibdhltbkbos. Ios blvhstbn`aorhs krhhl quh hst`s `jhkkbolhs sol k`us`a`s por ul` blthr`kkbûl kodpihe` ah j`ktorhs, blkiuyhlao nhlâtbkos, gboiûnbkos, kolauktu`ihs, psbkoiûnbkos y sokb`ihs. ¿Pubâl hstà hl rbhsno ah tr`storlos `ibdhltbkbos? `ibdhltbkbos?   Ku`iqubhr` puhah ahs`rroii`r ul tr`storlo `ibdhltbkbo, phro sol dàs kodulhs hl duehrhs. Hstos tr`storlos `p`rhkhl kol jrhkuhlkb` aur`lth i` `aoihskhlkb` o i` ha`a `auit`, phro t`dgbâl sh puhahl ahs`rroii`r aur`lth i` blj`lkb` o dàs `ahi`lth hl i` vba`. Whkuphr`ao5 Of ab`rbo ah [`iua 3>/3>/7370 mttp mttp5//ofab`rbo.kod/s`iua/prblkbp`ihs-hljhrdha`ahs-lutrbkbol`ihs5//ofab`rbo.kod/s`iua/prblkbp`ihs-hljhrdha`ahs-lutrbkbol`ihs7>23=;3   7>23=;3 Whkuphr`ao5 Dhaiblh Sius3>/3>/7370  Sius3>/3>/7370 mttps5//dhaiblhpius.nov/sp`lbsm/ mttps5//dhaiblhpius.nov/sp`lbsm/h`tblnabsorahrs.mtd h`tblnabsorahrs.mtd   7.@ktbvba`ahs `.  `.  Wh`ibkh ul pi`l ah `ibdhlt`kbûl s`iua`gih p`r` ul aä`. g.  g.  Hst`gihzk` i`s k`us`s ah ios tr`storlos `ibdhltbkbos. k. k.   Dhab`lth ul orn`lbz`aor hxpibquh ios tbpos ah tr`storlos `ibdhltbkbos. a.  ¿Kûdo puhao prhvhlbr o rhtr`s`r i` `p`rbkbûl ah i` ab`ghths tbpo 7? h. h.   Lo oivbah abgue`r ios `ibdhltos ah i` pbràdbah `ibdhltbkb`.

 

PXÄDBK@ QHD@5 KOLJBNXW@KBÛL HIHKQWÛLBK@

I@ PXÄDBK@ R I@ @IBDHLQ@KBÛL Los lutrbdos hxkiusbv`dhlth kol àtodos y doiâkui`s Hsto puhah p`rhkhr sorprhlahlth `i oärio por prbdhr` vhz, phro lo io hs t`lto sb rhkora`dos, por hehdpio, quh hi zudo ah ibdûl hs hshlkb`idhlth àkbao kätrbko, y hi vbl`nrh, àkbao `kâtbko `dgos jord`aos por àtodos ah k`rgolo, oxänhlo h mbarûnhlo, kodgbl`aos hl abjhrhlth lõdhro, proporkbûl y d`lhr`. Q`dgbâl hi `nu` quh blkiubrhdos hltrh ios hihdhltos lhkhs`rbos p`r` luhstr` abht` hs M 7O, hs ahkbr ul` doiâkui` jord`a` por aos àtodos ah mbarûnhlo y ulo ah oxänhlo, y i` s`i hstà jord`a` por kioro y por soabo.

0.  Ih` `thlt`dhlth i` sbnubhlth bljord`kbûl Abstrbgukbûl hihktrûlbk` Srblkbpbos ah orahl`dbhlto. - I` koljbnur`kbûl hihktrûlbk` jula`dhlt`i sh ogtbhlh, hl i` pràktbk`, ` p`rtbr ah trhs rhni`s o prblkbpbos5 rhni` ah i` kolstrukkbûl, prblkbpbo ah hxkiusbûl ah S`uib y rhni` ah i` dàxbd` duitbpibkba`a ah Mula. Whni` ah i` kolstrukkbûl. -I` - I` koljbnur`kbûl hihktrûlbk` jula`dhlt`i sh ogtbhlh koiok`lao ios hihktrolhs ulo ` ulo hl ios orgbt`ihs abspolbgihs ahi àtodo hl orahl krhkbhlth ah hlhrnä`—. Srblkbpbo ah hxkiusbûl ah S`uib. - ’Aos hihktrolhs ah ul dbsdo àtodo lo puhahl thlhr ios ku`tro lõdhros kuàltbkos bnu`ihs—. Kodo k`a` orgbt`i hstà ahjblbao por ios lõdhros kuàltbkos l, i y di di,, soio quha`l aos posbgbiba`ahs, ds4 +0/7 y +0/7 y ds40/7,, quh jäsbk`dhlth quha` rhjihe`ao hl quh k`a` orgbt`i (ahjblbao por l, i y di) puhah kolthlhr ul dàxbdo ah aos 0/7 hihktrolhs, hihktrolh s, y hstos ahghl thlhr spblhs opuhstos (hihktrolhs `p`rh`aos). @grhvb`a`dhlth soihdos hskrbgbr hi lõdhro ah hihktrolhs hl k`a` suglbvhi dhab`lth ul suphrälabkh. Sor hehdpio5 7p; rhprhshlt` quh hl hi koleulto ah orgbt`ihs 7p 7p m`y  m`y trhs hihktrolhs. ’

Whni` ah i` dàxbd` duitbpibkba`a ah Mula.- Ku`lao v`rbos hihktrolhs okup`l orgbt`ihs ahnhlhr`aos, ah i` dbsd` hlhrnä`, io m`ràl hl orgbt`ihs abjhrhlths y kol spblhs spblhs p`r`ihios  p`r`ihios (hihktrolhs ahs`p`rh`aos), dbhltr`s sh` posbgih —.

 

  Sor hehdpio, sb ahghl koiok`rsh trhs hihktrolhs hl orgbt`ihs 7p, io m`ràl ahs`p`rh`aos, hs ahkbr, hl orgbt`ihs abjhrhlths. Hl k`dgbo, sb sh tr`t` ah ku`tro hihktrolhs, aos ah hiios ahghl `p`rh`rsh (sh koiok`l hl hi dbsdo orgbt`i), dbhltr`s quh ios otros aos phrd`lhkhl ahs`p`rh`aos (hl orgbt`ihs abjhrhlths).

7S7  ←  ← 

7S;  ← 

←  ← 

7S1  ←↛  ← 

← 

Ab`nr`d` ah Dohiihr

I` abstrbgukbûl ah ios hihktrolhs ah ul àtodo hl orgbt`ihs rhkbgh hi lodgrh ah koljbnur`kbûl hihktrûlbk`. hihktrûlbk`. Ku`lao hst` hs i` ah dhlor hlhrnä`, sh tr`t` ah i` koljbnur`kbûl hihktrûlbk` jula`dhlt`i jula`dhlt`i.. @ p`rtbr ahi ab`nr`d` ah ios lbvhihs hlhrnâtbkos los a` ` kolokhr i` shkuhlkb` p`r` iihl`r ios orgbt`ihs sbhlao5

0s7 7s7 7p: ;s7 ;p: 1s7 ;a 03 1p: 8s7 1a 03 8p: :s7 1j 01 8a 03 :p: >s7 8j 01 :a 03 >p:  Ios lbvhihs ah hlhrnä` korrhspolahl ` ios lõdhros ahi 0 `i >. Ios suglbvhihs s uglbvhihs sol s, p, a   y j  y j . Ios hxpolhlths, hi lõdhro dàxbdo ah hihktrolhs quh tbhlh k`a` suglbvhi5 s m`st` aos hihktrolhs6 p hihktrolhs6  p m`st`  m`st` shbs6 a  m`st`   m`st` abhz6 y j  y  j  m`st`   m`st` k`torkh hihktrolhs. hihktrolh s. Ios lõdhros nr`lahs ah i` ahrhkm` blabk`l hi lõdhro tot`i ah hihktrolhs por k`a` lbvhi ah hlhrnä`. Ios suglbvhihs sh orahl`l ah `rrbg` m`kb` `g`eo, hl orahl krhkbhlth ah hlhrnä`, kodo sh duhstr` hl i` jbnur`. @ ios orgbt`ihs ios rhprhshlt`dos kol5 @ ios hihktrolhs kol5 ←↛

 

   

 

Hehdpio5 Hi lõdhro `tûdbko ahi hihdhlto los blabk` quh hi lõdhro ah hihktrolhs hs bnu`i `i lõdhro ah protolhs hl ul àtodo lhutro. Ios hihktrolhs sh koiok`l hl ios suglbvhihs hl hi orahl quh blabk` hi ab`nr`d` ah Dohiihr. Hi lõdhro ah hihktrolhs sh blabk` dhab`lth ul suphrälabkh. Ahghdos thlhr hl kuhlt` hi lõdhro dàxbdo ah hihktrolhs quh k`ghl hl ios abstbltos suglbvhihs5 • Oxbnhlo (U 4 =)  

            



Jord`s ah rhprhshlt`kbûl ah ul àtodo Koljbnur`kbûl Àtodo U hihktrûlbk`

Orgbt`ihs

Ib

;

0s7 7s0 

←↛ 

← 

Gh

1

0s7 7s7 

←↛ 

←↛ 

G

8

0s7 7s7 7p0 

←↛ 

←↛ 

← 

K

:

0s7 7s7 7p7 

←↛ 

←↛ 

←  ← 

L

>

0s7 7s7 7p; 

←↛ 

←↛ 

←  ←  ← 

O

=

0s7 7s7 7p1 

←↛ 

←↛ 

←↛  ←  ← 

J

2

0s7 7s7 7p8 

←↛ 

←↛ 

←↛  ←↛  ← 

Lh

03

0s7 7s7 7p: 

←↛ 

←↛ 

←↛  ←↛  ←↛ 

Hst`gbiba`a ah orgbt`i iihlo y shdbokup`ao. - Hi doahio dhk`lo-kuàltbko prhabkh quh ios orgbt`ihs iihlos y shdbokup`aos koljbhrhl `i koleulto ahi àtodo ul` hst`gbiba`a `abkbol`i, io quh supolh `inul` hxkhpkbûl hl i` koljbnur`kbûl hihktrûlbk` hihktrûlbk` ah ios hihdhltos. lt/upio`as/aowlio`as/730:/32/ibgrosthxto/Qhxto_ bgrosthxto/Qhxto_qubdbk`_0_GNX.p qubdbk`_0_GNX.paj  aj   Juhlth55mttps5//hauk`kbol.nog.hk/wp-kolth Juhlth mttps5//hauk`kbol.nog.hk/wp-kolthlt/upio`as/aowlio`as/730:/32/i 7.  7. Ogshrv`r Ogshrv`r hi  hi sbnubhlth vbaho  vbaho mttps5//youtu.gh/1DDvudFdqs1  mttps5//youtu.gh/1DDvudFdqs1 ’Puädbk`. Koljbnur`kbûl hihktrûlbk`— 

 

  ;.;.-   @ktbvba`ahs @ktbvba`ahs   `)  Blabk` hi lõdhro ah orgbt`ihs iihlos, shdbiihlos y v`käos ah ios sbnubhlths hihdhltos5 HIHDHLQO[ OWGBQ@IH[ IIHLO[ OWGBQ@IH[ [HDBIIHLO[ OWGBQ@IH[ Z@KÄO[ [oabo Kogrh Roao g)  Wh`ibkh i` koljbnur`kbûl hihktrûlbk` y ab`nr`d` ah orgbt`ihs ah ios sbnubhlths hihdhltos5  Àtodo

U

K`

73

Sg

=7

[

0:

Ko

7>

@i

0;

Koljbnur`kbûl hihktrûlbk`

Orgbt`ihs

JÄ[BK@ QHD@5 K@BA@ IBGWH

0.- Ih` i` sbnubhlth bljord`kbûl N`ibiho bahû hxphrbdhltos kol pi`los blkibl`aos quh ih phrdbtä`l hstuab`r dàs jàkbidhlth i` k`äa` ibgrh ah ios kuhrpos. Kodprogû quh i` vhiokba`a jbl`i quh `aqubhrh ul kuhrpo `i g`e`r por ul pi`lo blkibl`ao hs i` dbsd` quh sb sh ahe` k`hr ibgrhdhlth hl vhrtbk`i ahsah i` dbsd` `itur` quh hi pi`lo blkibl`ao. Hl `dgos k`sos, hi dûvbi

 

  ahs`rroii` ul DWX@, `ulquh i` `khihr`kbûl hs abstblt`5 hl hi k`so ahi pi`lo, ahphlah ah su blkibl`kbûl6 dbhltr`s quh, hl k`äa` ibgrh, i` `khihr`kbûl v`ih n ≍ 2,= d/s7. 

. Dovbdbhlto vhrtbk`i ah ios kuhrpos Xl` kuhrpos  Xl` pblz` quh k`h ahi thlahahro ah ul pbso `i p`tbo blthrbor, hi goth ah i` phiot` quh rh`ibz` hi thlbst` `lths ahi s`quh o hi i`lz`dbhlto ah ul` dolha` `i `brh sol hehdpios ah dovbdbhlto vhrtbk`i. I` juhrz` ah nr`vha`a hs i` rhspols`gih ah quh ios kuhrpos khrk` ah i` suphrjbkbh ah i` Qbhrr` k`bn`l kol ul` `khihr`kbûl kolst`lth. Hst` `khihr`kbûl hs i` `khihr`kbûl ah i` nr`vha`a. I` `khihr`kbûl ah i` nr`vha`a hs ul` d`nlbtua vhktorb`i5 • [u dûauio sh ahsbnl` por n y hl pultos prûxbdos ` i` suphrjbkbh suphrjbkbh ah i` Qbhrr` v`ih `proxbd`a`dhlth5 n 4 2,= d/[7 • [u abrhkkbûl hs phrphlabkui`r ` i` suphrjbkbh thrrhstrh.  • [u shltbao hs m`kb` h hii khltro ah i` Qbhrr`. 

Hi dovbdbhlto ah ios kuhrpos sodhtbaos so dhtbaos ` i` `khihr`kbûl ah i` nnr`vha`a r`vha`a quh sh duhvhl hl i` abrhkkbûl phrphlabkui`r phrphlabkui`r ` i` suphrjbkbh ah i` Qbhrr` sh ahlodbl` dovbdbhlto vhrtbk`i5 Hi dovbdbhlto vhrtbk`i hs vhrtbk`i  hs ul DWX@ hl hi quh i` `khihr`kbûl ahi dûvbi hs i` `khihr`kbûl ah i` nr`vha`a [us hku`kbolhs hku`kbolhs ahi dovbdbhlto sol i`s ahi DWX@ kol ` 4  ‛n5

 

 

M`y abjhrhlths tbpos ah dovbdbhlto vhrtbk`i, shnõl i`s kolabkbolhs blbkb`ihs5

SWOGIHD@ 0 [h ahe` k`hr ul` goi` ah pi`stbibl` ahsah io `ito ah ul r`sk`kbhios. K`ikui`r `)  I` abst`lkb`(vhrtbk`i) rhkorrba` hl ; shnulaos g)  I` vhiokba`a ul` vhz rhkorrbao 083d k)  Hi tbhdpo lhkhs`rbo p`r` `ik`lz`r ul` vhiokba`a 78d/s S@[O 0 A@QO[ AHI SWOGIHD@ Z3 4 3 d/s n

4 2,=d/s7 

   

 

S@[O 7 BAHLQBJBK@W I@ JÛWDXI@ D@QHDÀQBK@ R WH[OIZHW IBQHW@I SOW S OW IBQHW@I `)  `)  a 4? t4;s  

a 4 m 4 Z 3 . t + n.t7

rhhdpi`z`dos ios a`tos hl i` jûrdui`  

a 4 m 4 3d/s . ;s + . 2,=d/s7 (;s)7 a 4 m4 3 + 1,2 d/s 7. 2s7  a4m4 11.0 d g)  g)  v 4? a 4 m4 083d

Z 4  7..ℌ 7 ..ℌ 

Z 4  7(2.=) 7(2.=) (083) 

Z 4 ∕ 7213 7213  Z 4 81.77 d/s k) k)   t 4? Zj 4 78d/s

t4

∗   

 ∗ t4   , /

t 4 7,88s Whvbs`r hi thxto blthnr`ao ah Jäsbk` 7GNX pànbl`s ;= y ;2 7.- @ktbvba`a 0.- Hl ul` k`rtuibl` hskrbgbr i`s jûrdui`s ah DWXZ y k`äa` ibgrh (y tbro vhrtbk`i). 7.- @pibk`lao i`s jûrdui`s rhsoivhr ios sbnubhlths progihd`s.

     

  `) [b ul kuhrpo k`h hl 1s p`rtbhlao ahi rhposo, k`ikui`r i` vhiokba`a kol quh iihn` `i suhio y i` `itur` ahi pulto ah p`rtba`5 Whspuhst`. ;2,7 d/s6 >1,=d. g) Kol quâ vhiokba`a ahgh shr i`lz`ao ul kuhrpo quh ku`lao m` sugbao 8kd poshh ul` vhiokba`a blbkb`i ah 7d/s ? ¿Puâ tbhdpo m` hst`ao hst`ao sugbhlao? Whspuhst`5 7,7;d/s 6 3,37;s. k) Ahe`dos k`hr ul ogehto ahsah io `ito ah ul` torrh y dhabdos hi tbhdpo quh t`ra` hl iihn`r `i suhio, quh rhsuit` shr ah 7,1 s. K`ikui` i` `itur` `itur` ah i` torrh5 Whspuhst`5 7=,77 d.

Abgue`r i` pbràdbah `ibdhltbkb`

D@QHDÀQBK@[ Qhd`5 OSHW@KBOLH[ KOL ZHKQOWH[ ZHKQOWH[ HL HI SI@LO SI@LO Qh blvbto quh ogshrvhs kol `thlkbûl ios sbnubhlths vbahos ah ophr`kbolhs kol vhktorhs. mttps5//youtu.gh/fiXe`XN3fPB  mttps5//youtu.gh/fiXe`XN3fPB  mttps5//youtu.gh/D>zLvQ:n-SB mttps5//youtu.gh/D>zLvQ:n-SB   ¿[@GHWH[ SWHZBO[…? 

Moy hl aä` ios sbsthd`s `utod`tbz`aos blabk`l sb aos vhktorhs ah vuhio koblkbahl, hdbtbhlao ul` `i`rd` p`r` quh hi pbioto k`dgbh i` vhiokba`a, hi rudgo o i` `itur`. @sä sh hvbt` quh aos o dàs `vbolhs p`shl por hi dbsdo sbtbo `i dbsdo tbhdpo. Hi koleulto ah toaos ios vhktorhs ahi pi`lo sh ahlot` kol⃞ . [h ahjblhl i`s

⃞  ophr`kbolhs ah `abkbûl y hi proaukto ah hsk`i`rhs por vhktorhs ah  I` pbràdbah lutrbkbol`i hs ul` mhrr`dbhlt` ah hauk`kbûl y prodokbûl ah s`iua quh sh duhstr` ah d`lhr` nràjbk` y shlkbii` ` tr`vâs ah abgueos o jotonr`jä`s ah ios `ibdhltos h blabk` quâ k`ltba`ahs m`l ah kolsudbrsh p`r` shnubr ul` `ibdhlt`kbûl s`iua`gih.

@ABKBÛL AH ZHKQOWH[5 @abkbûl ah vhktorhs5 hs ul` ophr`kbûl hltrh vhktorhs quh rhsuit` ul luhvo vhktor, ii`d`ao i` rhsuit`lth o i` sud` ah ios vhktorhs orbnbl`ihs. ... I` rhsuit`lth shrà hi vhktor kol orbnhl hl hi orbnhl ahi prbdhr vhktor y kol hxtrhdo hl hi hxtrhdo ahi õitbdo.

⃞7. [h ahjblh i`s ⃞7 ophr`kbolhs ah `abkbûl y hi proaukto ah hsk`i`rhs por vhktorhs ah  Hi koleulto ah toaos ios vhktorhs ahi pi`lo sh ahlot` kol

Ahjblbkbûl5 [h`l  ⃞ 0 y ∍ ⃞ 7. Hxbsthl @,G pultos ahi pi`lo, t`i quh (@,G) (@, G) ∍   ⃞ 4 0. @ p`rtbr

⃞   4 ⃞   + . ahghdos ah G kolstrubdos ul pulto K ahi pi`lo, t`i quh   ⃞ y , io ku`i sh ahlot` ⃞  +  , hsto hlj`tbz`r quh hst` sud` ah ios vhktorhs  ⃞   4 ⃞   +  . ahghdos hlj`tbz`r quh hst` sud` hs blahphlabhlth ah i` hs,   shihkkbûl ah sus rhprhshlt`lths. @ahdàs hi gbpulto (@,K) hs ul ⃞  4 ⃞  + . rhprhshlt`lth ahi vhktor 

 

 

⃞  4⃞   Hl i` jbnur` sh duhstr`l hi vhktor v hktor   y trhs gbpultos hqubpoihlths kol hi gbpulto (@,G) kol 

Hl i` jbnur` sh duhstr`l hi vhktor v hktor   y aos pultos hqubpoihlths (K,A) ahi vhktor vhktor ⃞  4   

Hl i` sud`  ⃞  +  , sh hibnh ul rhprhshlt`lth ah ⃞ , por hehdpio (@,G) y ` p`rtbr p `rtbr ahi pulto G sh kolstruyh hi pulto K, ah

⃞  4 ⃞  + . ⃞ 4  . hi gbpulto (@0 , K0) hs ul rhprhshlt`lth ahi vhktor   doao quh (G0 , K0) ∍  Sropbha`ahs ah i` `abkbûl ah vhktorhs5 QHOWHD@ [h vhrbjbk`l i`s sbnubhlths propbha`ahs5

⃞ ,   ∍ ⃞ 7 , ⃞  +   4   + ⃞   0.- Koldut`tbv`, Koldut`tbv`, p`r`  p`r` toao vhktor  7.- @sokb`tbv` @sokb`tbv`,, p`r` toao hi vhktor  ⃞ ,  ,  ⃞  ∍ ⃞ 7, ⃞  + (  +  ⃞ ) 4 ( ⃞  +  ) +  ⃞ 

⃞ 7 , t`i quh p`r` toao ;.- Hxbsthlkb` ah hihdhlto lhutro, lhutro, hxbsth hi vhktor  ∍  ⃞  ∍  ⃞ 7 , ⃞ +   4 ⃞ + ⃞ 4 ⃞   ⃞  ∍ ⃞ 7, hxbsth hi vhktor 1.- Hxbsthlkb` ah opuhstos `abtbvos, `abtbvos , p`r` k`a` vhktor   , ∍ ⃞ 7, t`i quh, ⃞  +   4   + ⃞  4    Hi hihdhlto   sh ii`d` opuhsto `abtbvo ah   y sh ahlot` kol -    Kolsbahr` ` ios vhktorhs

⃞ ,  ,  ⃞  ∍ ⃞ 7, quh sh duhstr` hl i` jbnur` 70=

Jbn. 70=

I` sud` ah vhktorhs  ⃞  +   y   +  ⃞  sh duhstr` hl i` jbnur` 702 Hl i` jbnur` 773 sh duhstr` ios vhktorhs  ⃞  + (  +  ⃞ ) 4 ( ⃞  + ⃞ ) +  ⃞  [h vhrbjbk` i` sbnubhlth propbha`a. ||  ⃞  +   ||≡ || ⃞  ||+ ||  ||, kolokba` kodo i` ahsbnu`ia`a trb`lnui`r.

Jbn702

   

 

v  

 

↗

(    ) ↗ ↗

u + v + w   

+

u  v  

u  w  

w  

u  v + w  

u 

w   v  

↗

(  )

↗

u + v + w  ↗

Jbn. 773



Whst` ah vhktorhs5 Ahjblbkbûl.. Ahjblbkbûl

⃞ ,   ∍ ⃞7. [h ahjblh hi vhktor ⃞  -   ah ⃞ 7 ahi sbnubhlth doao5 ⃞  ‛  4 ⃞  + ( - ) [h`l ios vhktorhs  I` rhst` ah aos vhktorhs sh ahjblh hl târdblos ah i` `abkbûl ah vhktorhs v hktorhs y ahi opuhsto `abtbvo. Hsto hs,  ⃞   ‛‛  sh hxprhs` ⃞  kol hi opuhsto `abtbvo ‛    kodo i` sud` ah  ⃞ 7 , hxbsth - ∍ ⃞ 7 , t`i Ahgbao ` i` hxbsthlkb` ah opuhstos `abtbvos, p`r` k`a` vhktor   ∍  quh   + ( - ) 4    [h`   ∍  ⃞ 7. Kodo ⃞ , -  ∍ ⃞ 7 , sh sbnuh quh ⃞  + ( -  ) ∍ ⃞ 7 . @ hsth hihdhlto sh io m` lot`ao ⃞   ‛‛  . ⃞  , ⃞ , -  y ⃞  ‛  . Hl i` jbnur` 770 sh s h duhstr` ios vhktorhs  Hst` ophr`kbûl lo kudpih kol i`s propbha`ahs koldut`tbv` lb `sokb`tbv`. Q`dpoko poshh hihdhlto lhutro y lo kudpih kol i` hxbsthlkb` ah opuhstos opu hstos p`r` i` ophr`kbûl ’ ‛ ’ 

Jb .

Duitbpibk`kbûl ah ul lõdhro rh`i por ul vhktor ah Z7

⃞ . ⃞  ∍ ⃞    ∍ ℔. @ koltblu`kbûl, sh ahjblh i` duitbpibk`kbûl ahi hsk`i`r   por hi vhktor ⃞ . Hsto hs,  [h`l ios vhktorhs  ⃞ 4 ⃞ . ⃞ , hxbsthl @, G pultos hl hi pi`lo, t`i quh (@, G) ∍   Ahghdos thlhr prhshlth quh a`ao hi vhktor  Ahjblbkbûl5 [h`l ios vhktorhs

⃞ y ` p`rtbr ah G sh kolstruyh hl ⃞  ∍ ⃞   ∍ ℔.. Jbe`ao hl hi pulto @, sh kolstruyh G, t`i quh ⃞  4  

pulto K, t`i quh   4     ⃞ 4  ⃞ . Hi gbpulto ( @, K ) hs rhprhshlt`lth ah ul vhktor   ⃞  ahlodbl`ao proaukto ah  por ⃞  4⃞ . ⃞ , `i quh sh ahlot` ⃞ , hs ahkbr,  ⃞  hs ||⃞   || 4 |   | ||⃞  ||. I` jord` ahi vhktor rhsuit`lth 

⃞  y ⃞  4  ⃞   Hl i` jbnur` 777 sh s h duhstr`l ios vhktorhs  ⃞ 4 

      

  Sroaukto hsk`i`r o proaukto pulto ah aos vhktorhs5 Whkuhra` quh… Soahdos duitbpibk`r ul vhktor por ul hsk`i`r (lõdhro) y hi rhsuit`ao r hsuit`ao shrà otro vhktor. Hl d`thdàtbk`s, hi proaukto hsk`i`r, t`dgbâl kolokbao kodo proaukto blthrlo o proaukto pulto, hs ul` ophr`kbûl `inhgr`bk` quh tod` aos shkuhlkb`s shkuhlkb`s ah lõdhros ah bnu`i iolnbtua (usu`idhlth hl i` jord` ah vhktorhs) y rhtorl` ul õlbko lõdhro. Hehdpio5 Soahdos rhsoivhr ah aos jûrdui`s5 0r` jûrdui`.  jûrdui`.  Kolsbahrhdos ios vhktorhs  hi àlnuio hltrh ios vhktorhs vhktorhs hs hs  ⃞ 4 (;,3)   4 (8,8). @sbdbsdo, hi S`r` k`ikui`r hi proaukto hsk`i`r, prbdhro ahghdos hlkoltr`r hi dûauio ah  ⃞   y   5 Ah hsth doao, hi proaukto hsk`i`r hstà a`ao por5

|u⃞ | 4 ∕ ; + 3   4 ;

|v⃞ | 4 ∕ 8 + 8   4

(18³ 8³)) 4 08 08∕  ⃞ −  4 ; − 8 ∕ 7 − kos(1 ∕ 7 − 7a` jûrdui`. Whphtbrhdos hi hehdpio `lthrbor kol

∕    

4 18³.

∕ 83 4 8∕ 7 4 08 08

⃞ 4 (;,3)   4 (8,8). [bl hdg`rno, `mor` utbibz`rhdos i` otr` jûrdui`5 ⃞ −  4 ; − 8 + 3 − 8 4 08 

Lothdos quh hi rhsuit`ao juh hi dbsdo sbl bdport`r i` jûrdui` quh utbibzàr`dos.   Q@IIHW5 0.  0.  A`aos ios vhktorhs.

 4 (;,1) (;, 1)



⃞ 4 (0,8) 

K`ikui`5 `) Hi proaukto hsk`i`r ah ios aos vhktorhs g) Hi àlnuio quh jord`l k) Xl vhktor lord`i `i vhktor u 7.  7.  [h`l ios vhktorhs.

 4 (0,8)



⃞   4 (;,0) 

K`ikui` x K`ikui`  x h y, ah d`lhr` quh `dgos vhktorhs sh`l phrphlabkui`rhs phrphlabkui`rhs Juhlth5 Nûdhz, N. G. (7373). D@QHDÀQBK@ 0³ GNX. Pubto, GNX. Pubto, Hku`aor5 D@R@ HABKBOLH[ KÄ@. IQA@.

BLNIÂ[  ^HHF Q^O QOSBK5 HKX@AOWB@L JOOA NW@DD@W5 KOOFBLN ZHWG[ 0.- Kmoosh `l Hku`aorb`l absm 7.- ^rbth tmh ibst oj blnrhabhlts ;.- ^rbth tmh sthps oj tmh rhkbph. 1.- Srhp`rh tmh rhkbph. 8.- Q`fh ` pmoto `gout tmh Hku`aorb`l jbsm. :.- [hla to your th`kmhr.

 

HDSWHLABDBHLQO HDSWHLABD BHLQO R NH[QBÛL 0.  Ihh i` sbnubhlth bljord`kbûl.

QHD@5 KI@[BJBK@KBÛL AH IO[ N@[QO[   N`stos `adblbstr`tbvos5 [ol `quhiios quh sh `trbguyhl `i àrh` `adblbstr`tbv` ah ul hdprhlabdbhlto. Sor hehdpio, hi `rrbhlao ah i`s ojbkbl`s, hi suhiao ah ul `sbsthlth ah nhrhlkb`, ios shrvbkbos gàsbkos, htk.

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mttps5//`nhlkb`ahlotbkb`s.ul`i.h ahlotbkb`s.ul`i.hau.ko/typo;thdp/_ au.ko/typo;thdp/_prokhssha_/ksd_@nhlkb prokhssha_/ksd_@nhlkb`Lotbkb` `Lotbkb`s-730>3=78-3;_30_2>h=;ghh=`. s-730>3=78-3;_30_2>h=;ghh=`.epn epn mttps5//`nhlkb`

vhlt`5 [ol n`stos lhkhs`rbos p`r` quh ul kibhlth o usu`rbo `aqubhr` ios proauktos o shrvbkbos. Sor   N`stos ah vhlt`5 [ol hehdpio, ios suhiaos ah ios vhlahaorhs, i` pugibkba`a, i`s kodbsbolhs hl vhlt`s, htk.

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mttps5//tudulaohkolodb`.kod/wp-kolthlt/upio`as/7373/3 mttps5//tudulaohkolodb`.kod/ wp-kolthlt/upio`as/7373/3>/Kodbsbolhs-0.epn >/Kodbsbolhs-0.epn  

Ios n`stos `adblbstr`tbvos y i` d`yorä` ah n`stos ah vhlt` ahghl shr rh`ibz`aos blahphlabhlthdhlth sb sh vhlah ul proaukto o shrvbkbo. Sor hehdpio, hi `rrbhlao ah i`s ojbkbl`s thlarà quh shr k`lkhi`ao, `sä lo m`y` vhlt`s. v hlt`s. (Qhxto Hdprhlabdbhlto 0hro. G`kmbiihr`to Sàn. 0>). mttps5//hauk`kbol.nog.hk/ `kbol.nog.hk/wp-kolthlt/upio`as/ao wp-kolthlt/upio`as/aowlio`as/730:/3=/DBLHAX_ wlio`as/730:/3=/DBLHAX_Ibgro_Hdprhlabdbh Ibgro_Hdprhlabdbhlto-0lto-0Juhlth5  mttps5//hauk Juhlth5 GNX.paj

 

 

@KQBZBA@AH[5 `.  Krh` ul dhlõ s`iua`gih p`r` ul aä`, nuä`th kol i` t`gi` ah `ibdhltos s`iua`gihs. (ahs`yulo, `iduhrzo y dhrbhla`). Hxpiot` tu bd`nbl`kbûl ` i` mor` ah hskonhr ios blnrhabhlths, `ahdàs ahghs blkiubr ios prhkbos ah ios proauktos p`r` s`ghr kuàlto blvbhrths hl k`a` dhlõ.

Dhlõ [`iua`gih A

BLNWHABHLQH[

SWHKBO[ SWOAXKQO[

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  g.  Bd`nbl` quh kol hi dhlõ `lthrbor th polhs ul hdprhlabdbhlto ah ul rhst`ur`lth. ¿Puâ tbpos ah n`stos `adblbstr`tbvos y ah vhlt`s thlaràs?6 aht`ii` ` koltblu`kbûl ios lodgrhs ah tus n`stos. N@[QO[ @ADBLB[QW@QBZO[  _________________  _______ ____________________ _____________ ___  _________________  _______ ____________________ _____________ ___  _________________  _______ ____________________ _____________ ___

N@[QO[ AH ZHLQ@[ ZHLQ@[   _________________ ___________________________ _____________ ___ _________________ ___________________________ _____________ ___ _________________ ___________________________ _____________ ___

k.  Hlkbhrr` hl ul kärkuio ios `ibdhltos `ib dhltos quh utbibz`sth p`r` i` prhp`r`kbûl ahi ahs`yulo s`iua`gih ah tu dhlõ quh sh hlkuhltr` hl hi ibthr`i `, hl i` pbràdbah `ibdhltbkb` y ugbk` ul` htbquht` kol hi prhkbo ah k`a` ulo.

BLJOWDÀQBK@

Hxpior`aor ah ^blaows

Hi Hxpior`aor ah ^blaows hs ul hihdhlto prbdorab`i hl ku`iqubhr sbsthd` ah kûdputo, y` quh su jbl`iba`a hs i` ah orn`lbz`r y koltroi`r ios `rkmbvos y k`rpht`s ah ios abstbltos sbsthd`s ah `id`khl`dbhlto `id`khl`dbh lto quh utbibz`dos. Ku`lao `grbdos hi Hxpior`aor ah ^blaows hlkoltr`dos ul` vhlt`l`, quh hl i` d`yorä` kuhlt` kol v`rbos hihdhltos. Hs prog`gih quh su `sphkto v`räh y hsto sh ahgh ` i`s abstblt`s vhrsbolhs ahi [bsthd` Ophr`tbvo.

 

  Sràktbk` Hxpior`aor ah ^blaows  @grbr hi Hxpior`aor utbibz`lao thki`s `grhvb`a `grhvb`a`s `s   Io ionrâ @ktbvba`a [b

Lo

@grbr hi Hxpior`aor utbibz`lao thki`s `grhvb`a`s Krh`kbûl ah k`rpht`s K`dgb`r lodgrh ah ul` k`rpht` Kopb`r `rkmbvos ahltro ah ul` k`rpht`

Nu`ra`r ul aokudhlto luhvo ah ^ora ahltro ah ul` k`rpht`

Hibdbl`r5 S`phihr` ah rhkbki`eh

KODSWODB[O[5

Dh kodprodhto `5   Qhlhr ul` guhl` `ibdhlt`kbûl p`r` `sä noz`r ah ul` vba` s`iua`gih.   D`lthlhr màgbtos ah kolsudo sosthlbgih y s`iua`gih p`r` dheor`r luhstro hstbio ah vba`.

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  Sr`ktbk`r `ktbvba`ahs jäsbk`s phrd`lhlths, quh ghlhjbkbh luhstr` s`iua blthnr`i.  

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 @XQOHZ@I  @XQ OHZ@I X@KBÛL5

Whvbs` i`s `ktbvba`ahs quh m`s rh`ibz`ao aur`lth hst`s shd`l`s y rhjihxbol` sogrh ios `prhlabz`ehs quh m`s `ik`lz`ao.