Copyright A.Milenin, 2017, AGH University of Science and Technology

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1 Fn lmn nl for Ml Formng n Mrl ngnrng rof. r h. nż. nr Mlnn G nr of n n hnolog Krów oln -ml: mlnn@gh..l nnoon h fn lmn mho (FM) wl n ml formng n mrl ngnrng. h mho n rom mho h' wh rr h of horl rnng. h followng on r onr n h or.. Fnmnl of h FM.. olng hrml rolm.. olng rolm n h hor of l n l.. rnl n rl of rng ofwr on h FM.. Rw of ng ommrl rogrm. h mn r of h l orl r o h lomn of FM o o ml rolm n mrl rong. nl rrmn for n. Fnmnl of rogrmmng h of h rnfr mhn nmrl mho h fnmnl of mrl ngnrng n ml formng. r.nroon o FM. or of FM. g FM n ml formng n mrl ngnrng nrl ml. onon of FM. nrolon n FM fnon of h fnon..fm hn. Fn lmn of hghr orr. ormr rnformon. o mr. mrl ngron.. olng h h flow rolm FM. n non h flow rolm. on for ffn mr n lo or. wo mnonl FM o for mlon of h flow..olon of l rolm FM. of hor of l. ron rnl. on for ffn mr n lo or. ml of FM o for olng ln rn rolm FM..olon of rg l rolm FM. hor of l on non omrl mrl. ron rnl. on for ffn mr n lo or. ml of FM o for mlon of ln rn rolm n flow formlon. nlog wn flow nm n hor of l n flow formlon. 6. Commrl FM o form for mlon of ho ml formng ro. horl of form FM rogrm. rr n nrf of form. mlon of forgng h rollng n ron n form. mlmnon of n mrl mol n form. r n form. mlmnon of flow r n frr mol n form. rr. O.C.Znw R..lor h Fn lmn Mho // rworh nmnn ol -h on onon. K.. h Fn lmn ror n ngnrng nl rn ll n.. grln.. l Fn lmn nl //. l & on w or Koh. Oh.. ln. Ml Formng n h Fn lmn Mho Ofor nr r w or Ofor 99.. nr.g. r M. Cr. Mhml n hl mlon of h ror of o Roll ro lr mrm h://form.r 7. Fn lmn ror for ol n rr (M On Ror) 9.. Mlnn ow M. Zgnn rmomhnn // G Krów 7.mmr of or. nrl ml of g FM n rrh for ml formng n mrl ngnrng. h r. nroon o FM. or of FM. g FM n ml formng n mrl ngnrng nrl ml. onon of FM. nrolon n FM fnon of h fnon. orl gron. FM now wl rrl ngnrng rolm.. n l ronl mhnl mnng mllrgl omhnl ngnrng.. now lon n ml formng n mrl ngnrng.. ro omr rogrm r ll n gnfn (form.) Rhr Krn R. Krn RO MO FOR OO OF ROM OF RM RO 9 lhr R. R r n n Mho r ong gwr ronrolm r mhmhn h. Rn ngw. Mh. ol. (9);

2 FM o. h ro of nl hl rolm (gn gn) Chng of hl rolm FM o. Omon of ml formng ro (rogrm Form) Mhml mol FM olon of mol nrron of rl mro mol Rfn nl gn mromn Mnfr of rlw whl (Forg) h w who FM mlon ng of mrl (Form) Omon of rollng ro (rogrm Rollng)

3 rr n rolm of FM mlon FM mlon of mrl on G mhn Formlon of onr rolm of FM hn nl of rl M n formlon of onr rolm rong ho of of F olon mho. M n nrron of rl FM - h no h mho!!! lgorhm of FM for r m. nl of m of rg r nronn rng.. lrm rrmn.. nronnon rrmn.. Coml rrmn. R R R. lrm rrmn of h rng (Fn lmn) F F F F F F F F *K.. h Fn lmn ror n ngnrng nl rn ll n. h:// F F F F mlg ro. r ffn mho F F F F. lmn nronnon rrmn. F F F F R F F F R F F R F F F F. Coml rrmn. K R R R R R K

4

5 lrn roh - ronl formlon of h rolm: K rmm formlon: K R K R R K K R Mn onon of FM for onn m Conn o -> r mol lgorhm FM (for h rnfr rolm). n h onnm w r ng lm nmr of on (no).. h l of mrr n h no fn rmr whh w gn.. Zon gnon of mrr (olm) omo of lm nmr of on whh r ll fn lmn. On-mnonl ml: ron. h mrr rom for h F ng h olnoml whh gn ng nol mrr.. l of mrr on no m l n h w o nr h romon o h l fl mrr. h lon rform mn of mnmng fnonl whh orron o oh h on onon of h. mrr ron n r ron Fn lmn o l of mrr. Zon gnon of mrr omo of lm nmr of on whh r fn lmn.. h mrr rom for h F ng h olnoml whh gn ng nol mrr.. n h onnm w r ng lm nmr of on (no).. h l of mrr on h no fn rmr whh w gn. romon of mrr n wo n of F

6 6 Glol nrolon of mrr - fn lmn for for h fnon ; n Fn lmn ml fn lmn h fnon of ml lmn for for for А r of F

7 7 h fnon of ml lmn rolm: = M = mm = mm = M = mm =. mm = 6 M = mm = mm = mm =. mm =? rl ml ) ( ) ( ) ( rl ml oorn (nrl oorn) h h oorn (nrl oorn) 6 no F 6

8 r. FM hn. - Fn lmn of hghr orr. - ormr rnformon. - o mr. - mrl ngron. of F Moon of g of hghr orr F -no F. rror n romon. rror rng ffrnon ;. ong OF = *+7=7 on = n = OF<on on on h fnon? Rnglr F h fnon: Rnglr F

9 h fnon n lol oorn m of F of F -no ml F no F -no F

10 Z Z Z rnformon of oorn. on mr? ) ( ) ( ) ( rnformon of oorn. Cllon of glol r Z no no ormrl rnformon rmrl ormrl n rrmrl lmn f f f rmrl ormrl rrmrl. 7 6 no no ormrl rnformon

11 ng for F gr mhng mrl ngron n FM f f f n f f... n f f... n f n n For G ngron n wgh of ngron on n+ nmr of ngron on mr of on for ngron n+ G ngron n Rng of l ngr olnoml fnon n= G ngron f n n f n= 7769 f n n f ml of nmrl ngron for rnglr lmn ml of nmrl ngron for rhrl lmn For n= : =/; =/; =/; =/; =; For n= : n= =/; =/; =/; =/. ) =/; =/; =/; = -7/96 ) =/; =/; =/; = /96 ) =/; =/; =/; = /96 ) =/; =/; =/; =/96 =.; =.966; ) = ; =; =; =; =/; ) = ; = ; =; =; =/; ) = ; =; = ; =; =/ ; ) = ; =; =; = ; =/ ; 66

12 O = _ C o_( n _ ); O = ()= ()*_n() + ()*_n() ()= ()*_n() + ()*_n() O; = * (); O = O = n = mk*((n)*() + (n)*())*; (n) = (n) + n; O O O! ******************************************************************! Mlnn nr G mlnn@gh..l! ****************************************************************** RO o_( n _ ); MC O; R* MO() :: n; GR* _ ; R* MO( _) :: ; R* MO() :: ; R* ; ngr* ; _=.; _n=.; O = _() = _()+()*(); _() = _()+()*(); _() = _()+()*(); _() = _()+()*(); O; = _()*_()-_()*_(); =; C n_m( n); RO o_; ml of o r. - olng h h flow rolm FM. - n non h flow rolm. - on for ffn mr n lo or. - wo mnonl FM o for mlon of h flow. ff mrr ron onw onw (/m K); r r (/m K ). ) ( ron n. ) ( w h rl n h orgnl fnonl n n / /. /: Mnmon of fnonl ) ( ) ( ffn mr w ffrn h fnonl or {} n h rl o ro ml: ; ;

13 () () () () () () () () () () () () () () () () () () () () () () () () () ) ( () ; n oon of ffn mr for F nmr Glol ffn mr () () () () () () () () () () () () () () () () () () () () on- onr rolm ff ff ff 77 h rl no nl on ) ( C ff C ff ff ffn mr :

14 r n m C (). l mho: {}={ }. ngron n m C C () C ().. ml mho {}={ } : C C C () M OF FM CO FORMO OF RM ROM whr C C C. FOR MO mgn nl mrr C mm m of ro mm m m_oon mrr of nromn C mlf /Cm m h mm m mm mh nh mh n 7 mc /Cg mk 7 mr ro g/m on..olon of l rolm FM. of hor of l. ron rnl. on for ffn mr n lo or. ml of FM o for olng ln rn rolm FM..

15 r nor. Coh r. ff r (nn). 6 horl of h lnr hor of l rn. ngnr roh. ogrhml rn. ln ln ln ln Ch on (gn o Ch) Ch on n mr form for ln rn Ch on ong' mol. oon' ro.

16 6 oo' lw. / oo' lw n mr form. rnl of rl wor n mr form oo` lw Ch on h rl no fr on: / / / / / m Mrl ror n mr form ln rn ln r rn m m M M m m M rnl of rl wor n mr form ffn mr F K n K K n F F M F K K M F K / ffn mr

17 ffn mr for ln rn rolm ml of FM o for olng ln rn rolm FM. F M 9 on. olon of rg l rolm FM. - hor of l on non omrl mrl. - ron rnl. - on for ffn mr n lo or. - ml of FM o for mlon of ln rn rolm n flow formlon. - nlog wn flow nm n hor of l n flow formlon. h horl fonon of h hor of l flow of nomrl mrl ( ) Mhnl ror of h worl ml rolm: m n n l mn m n mn n m C 7

18 Fr of ng FM o ol rolm n h hor of l flow romon of mn r: 6 F K 7 F ffn mr [K]: o or:. K

19 Grh nrron of lol ffn mr [K]: Grh nrron of glol ffn mr [K]: h h K. 9 l nrolon () n ( ) O(h) / C O(h ) 9 / C O(h ) 6 / C O(h) 6 / ml of FORR o O = l%_ O = Row = ; Row = + ; Row = * + ; O = C = ; C = + ; C = * + ; fm(rowc)=fm(rowc) + m*(*()*()+()*())*; fm(rowc)=fm(rowc) + m*()*()*; f (<=) fm(rowc)=fm(rowc) + ()**(); fm(rowc)=fm(rowc) + m*()*()*; fm(rowc)=fm(rowc) + m*(*()*()+()*())* O(h) / O(h ) 9 / O(h ) 9 / O(h) 6 / f (<=) fm(rowc) = fm(rowc) + ()**(); f (<=) hn fm(rowc) = fm(rowc) + ()**(n); fm(rowc) = fm(rowc) + ()**(n); n f O O O on 6. Commrl FM o form for mlon of ho ml formng ro. horl of form FM rogrm. rr n nrf of form. mlon of forgng h rollng n ron n form. mlmnon of n mrl mol n form. r n form. mlmnon of flow r n frr mol n form. 9

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