Positive Sensitivity Analysis In Linear Programming With Bounded Variables
|
|
|
- Ezra Rogers
- 6 years ago
- Views:
Transcription
1 SOR lltn Vlm 6 m 4 Dm 007 pp -6 ISS08-860X ISS Pt Sntty naly In Lna Pgammng Wt ndd Vaal Kalpana Daya and Vanta Vma Dpatmnt f atmat Pana Unty Candga-6004 Inda -mal: alpana_mat@yan _ma@yam tat pnt pap d pt ntty analy PS n lna pgammng t ndd aal Pt ntty analy a ntty analy mtd f lna pgammng tat fnd t ang f ptatn tn t mpnnt f a gn ptmal ltn a ttly tn t nd man ttly tn nd and a at t l and pp nd man at l and pp nd ptly It man adantag tat t applal t t an ptmal a and nn-a ptmal ltn In t pap amn t ang f PS a adng t t ptmal ltn d f PS and d t latnp tn t ang f PS ng dffnt ptmal ltn W al d t latnp tn PS and ntty analy ng ptmal a and t latnp tn PS and ntty analy ng t ptmal pattn W tat t ntty analy ng ptmal pattn a pal a f PS In d t tdy t latnp and t ppt m lt n dalty a n dd and tn f ttly mplmntay ltn a n tald f lna pgammng t ndd aal Kyd: Lna pgammng t ndd aal ntty analy ptmal pattn ntty analy ttly mplmntay ltn Intdtn mt f lna pgammng a naday ll tald and lna pgammng dly aptd a a fl tl n Opatn Ra and anagmnt Sn lag nm f mpan a ng t ay f mdlng t l a nd f patal plm pplatn nld tanptatn plm pdtn plannng ntmnt dn plm lndng plm latn and allatn plm amng many t lna pgammng plm nt f lna latnp tn dn aal aal pnd t t dn t mad lna t fntn pfd a t mamzd g pft mnmzd g t pl dn aal a ttd t a tan aa y a ntant and t nd n t dn aal In mt f t a f lng t lna pgammng plm t -alld Smpl mtd d mtd d t Dantzg 95 a n mplmntd n a lag aty f d a flly d n pat t lng aft t platn f Dantzg pmal mpl mtd t dal n dlpd y Lm 954 It a lng n nn tat t dal mpl algtm a tt altnat t t pmal mpl algtm f lng tan typ f lna pgammng plm dal mpl mtd f lna pgammng t
2 ndd aal a n n dlpd y Wagn 958 ft tdd y a 00a 00 In 984 Kama ppd pt algtm f lna pgammng d t a plynmal tm algtm ga t mpl t an nm amnt f a n nt pnt mtd nt mptant tp n t fld f lna pgammng dalty ty atd t y lna pgammng t alay t ant lna pgammng plm ad pn t am data and ang t am ltn gnal plm alld t pmal plm l t aatd n alld t dal plm dal plm a fmlatd y mann ty 976 f lna pgammng t nn-ngat dn aal Dalty tm pd y D Gal 960 Kn and 956 and Gldman tal 956 t f t paag aalal f lng lna pgammng d nt nly l t lna pgammng plm t al pd t ptn t a f nfmatn n t ntty f t ltn t tan ang n t data fd t a ntty analy ptptmal analy nfmatn an f tmnd mptan n pat paamt al may tmat Qtn f t typ Wat f L a fqntly nntd and mplmntatn f a pf ltn may dfflt Sntty analy a a tl f tanng nfmatn at t ttln and dg f fdm n t plm F ntan n t t f an atty t aalal amnt f angd ftn nd nfmatn at t ttal t f t nt dn altd n d t tan a n ptmal dn f t n tatn In t a ntty analy an appld mtd f ntty analy n mpl mtd ll dlpd n t fndatn f ptmal a t q lttl mptatnal fft mtd a n ntdd n nm pap and tt fa f ampl: Dantzg 96; Gal 979 and a n d n many lna pgammng d H n a f dgnay t may yld nmplt nfmatn d t altnat ptmal a Ean and a 98; Knlmay 984; Jann tal 997 On t t and mt ntpnt mtd pd a ltn ng t an ptmal ltn latly nt t t ptmal fa Sm addtnal mptatn nal t gt an at ptmal a nn-a ltn apa and Zang 99; ta and 99; y and Salzman 994 Int-pnt mtd f lna pgammng t ndd aal a n dlpd y Cat 995 Daya and Vma 005 tdd ntty analy ng ptmal a f t lna pgammng plm t ndd aal H n ntty analy ng an ptmal a annt appld t an ptmal nn a ltn t mtd f ntty analy a n ggtd: pt ntty analyps ntty analy ng ptmal pattn and ε ntty analyang 990; dl and nt 99; Km tal 999; ldm tal 00 ang990 ntdd PS f ptmal ltn nldng ptmal nn a ltn ad n Sng and Pa 988 dfntn f t lna pgammng plm t nn-ngat dn aalpt ntty analy dfnd t fnd t aatt gn tn aal ang a z and ang a pt al n an ptmal ltn man z and pt n t ptd plm ptly dl and nt 99 dlpd a mtd f paamt analy n t gt-and d y ntdng t ptmal pattn nt and ta 996 pntd a paamt analy y gnalzng dl and nt SOR lltn Vlm 6 m 4 Dm 007
3 mtd and Gng000 dlpd a mtd f ntty analy ng t ptmal pattn n t ffnt and gt-and d ang mltanly ang and dl and nt mtd nd an ptmal ltn t ptmal pattn q addtnal mptatn f nt-pnt mtd Km tal 999 dlpd a patal ntty analy mtd ε ntty analy an dtly appld t nt-pnt ltn pdd y nt-pnt mtd Pa tal 004 tdd PS n lna pgammng tat a fl f talng t latnp tn PS and ntty analy ng ptmal a and ng ptmal pattn mtatd t ayn t tdy f t a n dn aal a ndd pp f t pap t pnt m ppt f PS and amn t ang f PS a adng t t ptmal ltn d f PS and tdy t latnp tn t ang f PS ng dffnt ptmal ltn f lna pgammng t ndd aal and nqntly mang f t ppt f PS tdy t latnp PS and t ntty analy mtd Sm dalty lt lant t t tdy a dd n t pnt pap f lna pgammng t ndd aal pap ganzd a fll: n Stn d tn f ttly mplmntay ltn n lna pgammng plm t ndd aal In Stn ntd t typ f ntty analy f lna pgammng t ndd aal and m a lt at t latnp tn PS and t ntty analy mtd a pntd In tn 4 d t latnp tn t ang f PS ng dffnt ptmal ltn and pnt a nay and ffnt ndtn f t ang f PS t nld a pt and ngat al In tn 5 tdy t latnp tn PS ng an ptmal a ltn and ntty analy ng an ptmal a n a gn ptmal a ltn dgnat In tn 6 m nldng ma a gn a lt n lna pgammng t ndd aal Cnd t lna pgammng plm P mn t t 0 n m R ; R ; [ a a L an] m n [ a ] m n a mat and ρ m t t f pp nd n t dn aal t tatn: t mpnnt f t a tty t f J { K n} Gn an nd t f t aal lt dnt t mat f t lmn tat pnd t nd n Smlaly z t dnt t t f z t mpnnt tat pnd t nd n F any t lt dnt t t 4 SOR lltn Vlm 6 m 4 Dm 007
4 mpnnt f Sn an f m t t an m m nn-ngla mat a a L a f Lt { } m L m Lt { J t 0} Ind t f nn a aal a at t l nd Lt { J t } Ind t f nn a aal a at t pp nd y a J S t lmn f an pmtd tat and an t a and 0 n a ltn t gn y y 0 Lt t pndng pattn f t and z y J Dfntn: a m m nn-ngla mat alld a mat ltn y 0 alld t a ltn f t t f a aal t t f nn a aal a at t l nd and t t f nn a aal a at t pp nd plm P an ld y tatng pp nd ttn a ntant t t na t z f t plm On t t and t plm an ld y ng t pp nd mpl tnq tt nang t z f t plm : ty 976; Dantzg 96 a fal ltn an ptmal ltn f P f z 0 z 0 and z 0 Cnd t dal f t plm P a fll: D ma t t 0 and nttd 4 dal a fmlatd y man ty 976 f t lna pgammng plm t nn-ngat aal Dalty tm and mplmntay lan tm pd y Gal 960 Kn and 956 and Gldman and 956 ll t mptant lt an aly tndd t t plm P SOR lltn Vlm 6 m 4 Dm 007 5
5 m Wa Dalty If a fal ltn f P and a fal ltn f D tn m If and a fal ltn f P and D ptly and mly ltn t P and D ptly 6 SOR lltn Vlm 6 m 4 Dm 007 tn and a ptmal m a Dalty m If an ptmal ltn t t pmal P tn t t a fal ltn t t dal D tat and nly f an ptmal ltn t t dal D tn t t a fal ltn t t pmal P tat m 4 Cmplmntay Slan m and a ptmal ltn t P and D ptly ff 0 and 0 n L dng t m 7 f lay 00 t ptmal ltn a mplmntay n t gnal n ty a nt nly mplmntay t t n la t t mplmntay t t la t f any t ptmal ltn a ll W a t fllng lt: Cllay Lt a pa f ptmal ltn f P and D and ant pa f ptmal ltn f P and D tn and Cnd t pmal P and t dal D plm n t tandad fm P mn D ma 0 0 Lt m m t a mat aatd t t ptmal a fal ltn 0 Lt t pndng ptmal ltn f t dal plm If l plm P y ng mpl mtd y tatng pp nd a ntant t al f dal aal a gn y nt alatn pndng t atfal aal and la aal a dd n m If l pmal plm y pp nd mpl tnq ty 976 tn an dtly fnd t al f and fm t ptmal tal f P y ng t fllng latn an aly tald ng t dalty ty: 0 0 [ z ] [ z ] 0 Cnd t lna pgammng plm t nn-ngat aal and t dal
6 plm a fll Pmal mn Dal ma 0 0 dng t Gldman and 956 t t at lat n ptmal ltn pa t pmal and dal ttly mplmntay tat > 0 L n Smlaly f t a f ndd aal t ttly mplmntay ltn n P and D dfnd a tat ptmal ltn pa t P and D atfy > 0 and > 0 L n tn f ltn an aly pd y ng t applatn f fllng tm gn y 956 t a -ymmt mat m 5 lf-dal ytm KW 0 W 0 a a ltn W tat KW W > 0 K a -ymmt mat applatn f m 5 t t fllng -ymmt mat 0 I K I yld a lmn t t 0 tat a t t nttd a t t a a < t a < t a > t ntgat t a n t > 0 and t 0 paatly Lmma Spp t > 0 n t a ptmal t and f t dal plm P and D ptly tat > 0 Pf Sn t > 0 t nn-ngat t t an nmalzd tat t and n t t t tt afftng t aldty f t mgn nqalt a t a n a and a t t tat > 0 SOR lltn Vlm 6 m 4 Dm 007 7
7 and a fal ltn t P and D ptly; a and m tat and a ptmal al and m tat latn > 0 and > 0 fll fm a and a t t an t nmalzd and t t dd and Ung t dfntn f and t a lmma a > 0 and > 0 p t tn f a ttly mplmntay ptmal ltn Lmma Spp t 0 n n f t fllng plt ld: a t lat n f t dal plm a n fal ltn If t mamzatn plm a a fal t tn t t f t fal t nndd and nndd n t t Dally f t mnmzatn plm t plm a a fal t Pf a Spp a fal t f t mamzatn plm tn 0 5 Ung a t t 0 and nn-ngatty f a Fm a 0 fm 6 a < < 8 If pl lt t mnmzatn plm a a fal ltn 0 t and t 9 Fm a t t 0 a Rlatn 9 and 0 tgt mply tat t 0 t laly ntadt 8 and a pd Lt a fal ltn t t mamzatn plm tn l fm a t t SOR lltn Vlm 6 m 4 Dm 007
8 Cnd λ λ f all λ 0 Claly λ 0 Fm and λ λ t nt nfnt ay nt f fal t p t ft atn f Ftm fm 8 > 0 tat λ λ λ an mad atay lag y ng λ lag ng S t nd atn f pd Fnally an mmdat nqn f mplt t pf f Lmma gt t pap am tat P and D a fal Dfntn f t ntty analy mtd F ntty analy n t t ffnt tat ptd y t amnt nd ant lna pgammng plm P and t pndng dal D : P : mn D : ma 0 0 n t R a t tat t lmnt n and t t a z l t f t gt-and d t t lmnt ptd y t amnt γ nd t lna pgammng P γ and t pndng dal D γ : Pγ : mn Dγ : ma γ γ 0 0 m t R t t tat t lmnt n and t t a z Lt t nd t f t a nn-a aal at t l nd and nn-a aal at t pp nd ptly y 0 an ptmal ltn t If alld a pmal-ptmal a l f 0 z SOR lltn Vlm 6 m 4 Dm z an ptmal ltn t D tn alld a dal-ptmal a If t a pmal-ptmal and dal-ptmal a t alld an ptmal a F a pmal-ptmal a lt dnt t fllng ang f : and P
9 0 SOR lltn Vlm 6 m 4 Dm at pnt t ang f tn a pmal-ptmal a an ptmal a f P t tat may t mpty t Smlaly f a dal-ptmal a lt dnt t fllng ang f γ : 0 0 y γ γ at pnt t ang f γ tn a dal-ptmal a an ptmal a f D t tat may al t mpty t tadtnal ntty analy ng an ptmal a alld a ntty analy dfnd a fll: Dfntn a Sntty naly S Lt t nd t f a aal and t nd t f nn-a aal a at t l and pp nd ptly f an ptmal a S ng n a t ffnt t fnd t ang f tn man an ptmal a t P and D Smlaly S ng n a gt-and d t fnd t ang f γ tn man an ptmal a t γ P and γ D y t dfntn f and t ang fnd y S ng n and a pntd a and ptly pfm S nd an ptmal a aatd t an ptmal a ltn In fat S an appld nly t an ptmal a ltn f dfnng pt ntty analy PS m ntatn ntdd F an atay t mpnnt a nn-ngat and a m pp nd ttn n tm lt η η and η dnt t t f nd f aal a fll: } < 0 < { η 0} { η } { η In addtn η η η π alld t ndd pattn f Dfntn Pt Sntty naly PS Lt an ptmal ltn t P PS ng n t fnd t ang f tn t t an
10 SOR lltn Vlm 6 m 4 Dm 007 ptmal ltn t P ndd pattn qal t π Smlaly t PS ng n t fnd t ang f γ tn t t an ptmal ltn t γ P ndd pattn qal t π Gn an ptmal ltn t P t ang f PS ng allatd ng t fllng ang 990: 0 0 { } γ γ η η η pd n Stn t t at lat n pa f ptmal ltn t t P and D ttly mplmntay n nd > 0 a > 0 L Lt η η η pattn π f t nd f aal alld t ptmal pattn f P and D gt t pap π dnt t ptmal pattn f P and D dfntn f ntty analy ng t ptmal pattn a fll: Dfntn Optmal Pattn Sntty naly OS Lt π t ptmal pattn f P and D ntty analy ng t ptmal pattn n t fnd t ang f tn ptmal pattn f P and D qal t π Smlaly t ntty analy ng t ptmal pattn n t fnd t ang f γ tn t ptmal pattn f γ P and γ D qal t π ang f OS allatd ng t fllng R t al 997: 0 0 O O γ γ 6 t tat O and O nld t nday al t ptmal pattn f t ptd plm dff fm π
11 S fa a dfnd t nd f ntty analy f lna pgammng It tal tat f a nn-dgnat ptmal a ltn t P tn t ang f PS ng qal t tat f S H f a dgnat ptmal a ltn t ang f PS may dff fm tat f S a ll dd n Stn 4 In addtn n aly y dfntn tat t ang f PS ng a ttly mplmntay ptmal ltn qal t tat f OS Sn t ang f PS ng an ptmal ltn qal t t ang f ptatn tn t pattn η η η f t nd f aal man naant OS an gadd a a pal a f PS 4 ang f PS ng dffnt ptmal ltn Lt z dnt t ptmal al f t t fntn f P and D l f any ptmal ltn t P lt L dnt t ang f tat z z0 L { z z0 } Jann t al 99 pd tat L f an ptmal a fal ltn t lna pgammng plm t nn-ngat aal lt an aly pd f plm P m 6 Lt an ptmal a ltn t P n L Pf Lt L n an ptmal ltn f P n Cnly lt S t t an ptmal ltn f P tat π π W p tat Lt t nd t f a aal and nn-a aal at t l and pp nd ptly aatd t π π 0 and 0 l Lt η η η Claly and y t tal pmtatn f t mpnnt f an t a a a fal ltn Dfn a a aal f a and nn-a at l and pp nd f pndng nn-a at l and pp nd ptly S a SOR lltn Vlm 6 m 4 Dm 007
12 Hn t lt ny ptmal fal ltn f P atf t fllng lt ll an aly pd n t am ln a dd n Pa tal 004: Lmma F an atay ptmal ltn t P L m 7 Lt and ~ t dffnt ptmal ltn t P If ~ {0} tn ~ m 8 Lt λ λ Cllay Lt λ L and dtnt ptmal ltn t P tat 0 λ n f m λ t < < L ptmal ltn t λ λ L λ λ λ > 0 P tat f m n f {0} tn L If n Cllay a ttly mplmntay ltn tn fnd tat O a O at t ang f OS t nttn f t ang f PS ng ptmal ltn n mnatn lad t a ttly mplmntay ltn m t nd t a n ptd F an atay mat E R t ng a pt ntg lt P E dnt a t f t a fll: E t m P E R λ E λ 0 t lmn t f E In t nt tm t latnp tn ang f PS ng dffnt ptmal ltn pntd n angd m 9 Lt ptmal ltn t P tat λ λ f m λ t 0 < λ < n f Pf Lt η η and η η f y amptn U P P tgt t qatn 4 mpl tat f a Fm t a tm may nt tat and a dfnd n t am ay a n Cllay H fm t fllng ampl fnd tat n gnal nt qal t : SOR lltn Vlm 6 m 4 Dm 007
13 t t P : mn : ma D plm P a t ptmal a ltn 5008 and : Wn angd t ang f PS ng and 540 a {0} and [ 7] H t ang f PS ng an ptmal nn-a ltn 49//09/ [ 0] In addtn f a ttly mplmntay ltn n m 9 tn fnd tat O a O In t t f t tn pnt a nay and ffnt ndtn tat an ptd l an ptmal ltn t P man ptmal t t ptd plm Lt P dnt t t f all ptmal ltn t P Lmma 4 lt an ptmal ltn t P and η η and η n and [ ] Pf Lt ltn t P and a t mpl tat 0 < < Lt t dal la t pndng t 0 t ttly mplmntay n y Cllay 0 > 0 > SOR lltn Vlm 6 m 4 Dm 007
14 < < t mpl tat 0 and 0 n fm 4 t fll tat 0 < < Lt 0 < Lt SOR lltn Vlm 6 m 4 Dm t mpl tat 0 Fm 4 a 0 Ung latn 4 S t mpl tat 0 n > 0 ng 4 alng t latn 44 mpl tat 0 S Lt n > 0 ng latn 4 alng t latn 4 mpl tat S Lt t mpl tat S ng latn 44 0 tgt t 4 mpl tat > 0 l 0 ng 44 mpl tat 0 < [ ] a Cnly lt [ ] Lt tn mpl tat > 0 t 0 mpl tat S Lt [ ] t t ng and and Hn t lt m 0 Lt f all an ptmal ltn t P P n f m > 0 ff Pf Ft ll tat t nly f pat ld Spp tat f m > 0 In addtn pp tat < f m P n [ ] < [ ] ntadt t atn tat an ptmal ltn t P f t ll tat ``f" pat ld Lt η and η η l lt π an ptmal pattn f P and D y Lmma 4 a P [ ] and
15 6 SOR lltn Vlm 6 m 4 Dm 007 In a : t mpl tat 0 If an ptmal ltn t D tn t 0 > a fal ltn t t fllng lna qatn ytm: an ptmal ltn pa t P and D ll t qatn pt t nd n f t ytm 45 a atmatally atfd l 0 0 a and 0 and 0 ddng t d f t a latn a Sn an ptmal ltn pa t P and D W gt ] [0 0 > In t a Cnd t fllng lna pgammng: ma mn D P 46 ptmal ltn f P a gng t t fal ltn f P pd n Lmma 5 y amptn an ptmal ltn t P and n t dal D al a at lat n ptmal ltn Lt an ptmal ltn t D atf t fllng: In addtn lt 0
16 and a ttly mplmntay ltn t D > 0 > 0 W t ˆ a t fllng: ˆ mn < 0 < 0 t tat ˆ pt Lt a al nm tat 0 < ˆ n gt a ltn tat atf t lna ytm 45 0 Sn an ptmal ltn pa t P and D fnd tat In t a : Lt t mpl tat Lt a ttly mplmntay ltn t D n > 0 t and mpl tat and n > 0 n t 0 < ˆ a fal ltn t t lna ytm 45 Sn an ptmal ltn pa t P and D gt [0 ] > 0 In t nt lmma p tat t t f fal ltn f plm P ntan nly ptmal ltn f P Lmma 5 t f fal ltn f plm P P Pf Cnd t plm P t t ntant mn 0 0 W ll tat f a fal ltn t nt an ptmal ltn f P t f m Lt 0 f m and fal ltn t P and D t f pmal la aal aatd t nd ntant n a 48 Ung a dalty tm 0 SOR lltn Vlm 6 m 4 Dm 007 7
17 0 49 Lt an ptmal ltn f dal and a fal ltn f P t nt an ptmal ltn n fm 49 > 0 40 latn mpl tat t t t m tat > 0 > 0 t Lt t t m tat > 0 mpl tat 0 < and 0 Lt ˆ a ttly mplmntay ltn t P n ng mplmntay lan tm ˆ 0 mpl tat ˆ 0 and n t 0 0 tat nt a fal ltn t P Lt t t m tat > 0 mpl tat > 0 and 0 < t ˆ 0 mpl tat ˆ S a tat nt a fal ltn t P f any fal ltn t P t nt ptmal t 0 t S any nn-ptmal ltn t P annt a fal ltn t P In t d y fal ltn f P an lmnt f P Cnly y Lmma 5 y ptmal ltn f P a fal ltn f P m Lt f all an ptmal ltn t P n f m < 0 ff P Pf Ft ll tat t Only f pat ld Spp tat f m < 0 In addtn pp tat > f m P n < ntadt t atn tat an ptmal ltn t P f f all P t ll tat f pat ld Lt η η and η l lt π t ptmal pattn t P and D In t a : and n S 0 lt a ttly mplmntay ltn t D n > 0 and atf t lna ytm 45 < 0 In t a : It an aly n tat f m y plang 8 SOR lltn Vlm 6 m 4 Dm 007
18 t n 46 and 47 t and applyng t am tnq a n m 0 In t a : Lt a ttly mplmntay ltn t D t tat > 0 n atf t lna ytm 45 < 0 Sn an ptmal ltn pa t P and D gt [ 0] y m 0 and n tat t ang f PS ng n nld t a t pt and a ngat al ff f any ptmal ltn t lmnt a t am al In addtn a at ant nttng lt at t ang f OS a fll: Cllay Lt π t ptmal pattn f P and D n [00] ff α f all P α [0 ] O Pf Ft pp tat [00] O ptmal ltn Sn O [00] Lt a ttly mplmntay If a nq ptmal ltn t P tn llay tally ld Ot lt an ptmal ltn t P tat tn t t an ptmal ltn tat λ λ f m λ > 0 4 y m 0 and X [00] mpl tat f tgt t qatn 4 mpl tat Sn n atay α f all P α a nn-ngat al nm and α [0 ] t ll tat t ld Spp tat α f all P n y m 0 and t t and tat [ ] < 0 and > 0 O 5 latnp tn PS and S nd dgnay In t tn d t latnp tn PS and S y mpang PS t S nd dgnay Lt an ptmal a ltn t P If dgnat t an m tan n ptmal a aatd t S ng a ptmal a may pd a dffnt ang f ptatn F ampl nd t fllng lna pgammng plm LP : P : mn : ma D 5 SOR lltn Vlm 6 m 4 Dm 007 9
19 0 SOR lltn Vlm 6 m 4 Dm nq ptmal ltn t P tat a dgnat a ltn a t pmal-ptmal a and {45} {} {}; {5} {4} {}; {4} {} {5} t f a ptmal a and a pmal ptmal a t nt an ptmal a Wn angd t ang f S ng and a 5] [ and ] [ ptly and ng [] On t t and t ang f PS ng 5] [ Wad t al 990 d tat n a t t angd t ang f tn an ptmal a ltn man an ptmal ltn t P t nn f t ang f ntty analy ng all pmal-ptmal a aatd t Pa t al004 pd t mla lt f Sn t ang f tn man ptmal t P tan t fllng tm: m Lt an ptmal dgnat a ltn Lt L t nd t f a aal nn-a aal at l and pp nd ptly f all t pmal-ptmal a aatd t n U Pf Lt 0 0 W ll tat
20 SOR lltn Vlm 6 m 4 Dm W n tat and 0 and t mpl tat 0 l and 0; 0 t mpl tat 0 and 0 l f 0 0 and and 0 Cnly lt and an ptmal dgnat a ltn and t f t t at lat n a t U Hn t lt m Lt an ptmal dgnat a ltn t P Lt L all t ptmal a aatd t n I f 0 tn f Pf y dfntn { } 0 0 γ γ 5 { } γ γ η η and η F a and Ft ll p tat Lt n t a t plt t a and at t pp nd tat ltn dgnat nn-a and at t pp nd t
21 n P P tgt t qatn 5 and 5 mpl tat f a f I Spp tat nld any nn-z al F any atay ptmal a f a and a lmn n lnaly ndpndnt t all t manng lmn n Lt γ n SOR lltn Vlm 6 m 4 Dm 007 γ t tat If latn 54 ld tn γ 55 ld tally In d t p tat γ t ffnt t tat 0 0 Sn 54 an ttn a γ 56 Eqatn 55 and 56 mply tat 0 mpl tat 0 n lmn f a lnaly ndpndnt a W ll tat It an n tat f tn Lt a fllng plt: and If a tn 0 < < and nt fal and It mpl tat a and ttly tn t nd S and It mpl tat a and at t pp nd p tat 0 Smlaly mpl tat 0 0 γ and n at f nld any nn-z al n tat
22 I mla t m H n I {0} may nt qal t lltatd y t fllng lna pgammng LP : P : mn : ma SOR lltn Vlm 6 m 4 Dm D nq ptmal ltn t P 500 and t a t ptmal a aatd t : φ φ φ {} {} {} {} φ; {} {} φ Wn ptd t ang f S ng and a [ 50] [ 50] H t ang f PS ng [00] y ng t fllng qatn: 5 5 γ γ ] Cnqntly fnd tat 6 Cnldng Rma In t pap a tald t tn f ttly mplmntay ltn f lna pgammng plm t nd n t aal ladng t t tdy f ptmal pattn ntty analy f plm ppt f PS and t latnp t t ntty analy mtd S and OS a n dd man adantag f PS tat t an pfmd t any ptmal ltn a nn-a a ltn PS fnd t ang tn t t an ptmal ltn t t ptd plm ndd pattn qal t t ndd
23 pattn f a gn ptmal ltn PS f nly n t ndd pattn f pmal-ptmal ltn Hn t ppt f PS n a t ffnt dff fm t f PS n a gt-and d W pntd m ppt f PS tat a fl f mpang PS t t t t ntty analy mtd Wn a t ffnt ptd t ang f PS qal t t ntal a gn ptmal ltn man ptmal t t ptd plm On t t and n gt-and d angd t ang f PS fnd t ntal t ndd pattn f a gn ptmal ltn man t ndd pattn f m ptmal ltn t t ptd plm nt mptant ppty f PS n a t ffnt t ang f PS ng an ptmal nn-a ltn t nttn f t ang f PS ng ptmal a ltn n mnatn lad t t ptmal nn-a ltn Fnally ft td ll ndd ll dal t t mptatnal pfman and nmal pn f ntty analy mtd Gn an ptmal a S ly t mt ffnt t mptatnal tm nnd H mt d ng nt-pnt mtd ftn pd an ptmal nn-a ltn and n t a PS ptd t a gd altnat a PS an appld tt tanng an ptmal a ptmal pattn may q m mptatnal tm f a plm ll-ndtnd Pa tal 004 dd t ppt and latnp f PS OS and S y pattnng t dn aal nt t atg and t mtatd t tnd t tdy t t a dn aal a ndd and n ty a t pattnd nt t atg dpndng pn S OS and S ltg t nd n t dn aal an tatd a addtnal ntant t t lad t ndaly na n t z f t plm nd ndatn t t nt pfal t nd t nd n dn aal a addtnal ntant nldgmnt at anldg t fnanal ppt pdd y Unty Gant Cmmn f Inda Dl at a tanfl t n Sama Pgamm Dpatmnt f atmat Pana Unty Candga Inda f alal lp n ppaatn f t manpt Rfn [] dl I RDC nt 99 gmt f paamt lna pgammng lgtma [] y RE J Saltzman 99 Rng an ptmal LP a fm an nt pnt ltn nal Rpt Dpatmnt f atmatal Sn Clmn Unty Clmn SC US [] Cat J 995 n mplmntatn f pmal-dal nt pnt algtm t pp-ndd aal Q& & t [4] Daya K V Vma Sptm 005 Sntty analy n lna pgammng t ndd aal SOR lltn 4-9 [5] Dantzg G 95 amzatn f a lna fntn f aal t t lna nqalt n C Kpman Ed: tty naly n Pdtn and llatn Jn Wly and Sn: SOR lltn Vlm 6 m 4 Dm 007
24 [6] Dantzg G 96 Lna pgammng and tnn Pntn Unty P Pntn Jy [7] Ean JR R a 98 Dgnay and t mntptatn f ntty analy n lna pgammng Dn Sn [8] Gal 979 Ptptmal analy paamt pgammng and latd tp Ga-Hll [9] Gal D 960 y f lna nm mdl aga-hll [0] Gng HJ 000 Smltan pmal-dal gt-and-d ntty analy fm a ttly mplmntay ltn f a lna pgam SI Jnal f Optmzatn [] Gldman J W 956 y f lna pgammng n: Kn HW W Ed Lna nqalt and latd ytm Pntn Unty P Pntn Jy 5-97 [] Jann C R C lay 99 n nt pnt appa t pt ptmal and paamt analy n lna pgammng nal Rpt 9- atmat and mpt n Dlft Unty Of nlgy tland [] Jann JJ d Jng C R lay 997 Sntty analy n lna pgammng: t afl Epan Jnal f Opatnal Ra [4] Kama 984 n plynmal tm algtm f lna pgammng Cmnata [5] Km WJ CK Pa S Pa 999 n ε -ntty analy n t pmal-dal nt pnt mtd Epan Jnal f Opatnal a [6] Knlmay G 984 fft f dgnay n t-ffnt ang and an algtm t l ntptatn plm Dn Sn 5 4- [7] Kn KW W 956 Lna nqalt and latd ytm Pntn Unty P Pntn [8] Lm C 954 dal mtd f lng t lna pgammng plm aal Ra Lgt Qatly 6-47 [9] a I 00a p lna dal pa-i algtm f t mpl mtd Cmptatnal Optmzatn and pplatn [0] a I 00 gnalzd dal pa- mpl algtm Epan Jnal f Opatnal Ra 49-6 [] ta S RDC nt 99 Paamt and ang analy f nt pnt mtd Wng pap Dpatmnt f IE/S ttn Unty Eantn ILUS [] ta S 99 Fndng an nt pnt n t ptmal fa f lna pgam atmatal Pgammng [] nt RDC S ta 996 gnal paamt appa and t mplatn t ntty analy n nt pnt mtd atmatal Pgammng [4] ty KG 976 Lna and mnatal pgammng Jn Wly & Sn IC Lndn Sydny nt [5] ma GL L Wly 999 Intg and mnatal ptmzatn Jn SOR lltn Vlm 6 m 4 Dm 007 5
25 Wly & Sn: IC [6] Pa C W Km S L S Pa 004 Pt ntty analy n lna pgammng a-paf Jnal f Opatnal Ra 5-68 [7] R C lay Jp Val 997 y and algtm f lna ptmzatn Jn Wly & Sn [8] Sng K S Pa 988 Ptptmalty analy n mat gam pgammng algtm Lna lga and t pplatn [9] lay 00 n ay ay t ta nt-pnt mtd Epan Jnal f Opatnal Ra 0-9 [0] W 956 Dal ytm f mgn lna latn n: Kn HW W Ed Lna nqalt and latd ytm Pntn Unty P Pntn Jy -8 [] Wagn H 958 dal mpl mtd f ndd aal aal a Lgt Qatly [] Wad JE RE Wndll 990 ppa t ntty analy n lna pgammng Jnal f Kan Opatn Ra and anagmnt Sn Sty -9 [] ang H 990 tdy n ntty analy f a nn-tm ptmal ltn n lna pgammng PD Sl atnal Unty Rpl f Ka [4] ldm E J dd 00 Sntty analy n lna pgammng and mdfnt pgammng ng nt-pnt mtd atmatal Pgammng S SOR lltn Vlm 6 m 4 Dm 007
< < or a. * or c w u. "* \, w * r? ««m * * Z * < -4 * if # * « * W * <r? # *» */>* - 2r 2 * j j. # w O <» x <» V X * M <2 * * * *
- W # a a 2T. mj 5 a a s " V l UJ a > M tf U > n &. at M- ~ a f ^ 3 T N - H f Ml fn -> M - M. a w ma a Z a ~ - «2-5 - J «a -J -J Uk. D tm -5. U U # f # -J «vfl \ \ Q f\ \ y; - z «w W ^ z ~ ~ / 5 - - ^
n r t d n :4 T P bl D n, l d t z d th tr t. r pd l
n r t d n 20 20 :4 T P bl D n, l d t z d http:.h th tr t. r pd l 2 0 x pt n f t v t, f f d, b th n nd th P r n h h, th r h v n t b n p d f r nt r. Th t v v d pr n, h v r, p n th pl v t r, d b p t r b R
,. *â â > V>V. â ND * 828.
BL D,. *â â > V>V Z V L. XX. J N R â J N, 828. LL BL D, D NB R H â ND T. D LL, TR ND, L ND N. * 828. n r t d n 20 2 2 0 : 0 T http: hdl.h ndl.n t 202 dp. 0 02802 68 Th N : l nd r.. N > R, L X. Fn r f,
4 8 N v btr 20, 20 th r l f ff nt f l t. r t pl n f r th n tr t n f h h v lr d b n r d t, rd n t h h th t b t f l rd n t f th rld ll b n tr t d n R th
n r t d n 20 2 :24 T P bl D n, l d t z d http:.h th tr t. r pd l 4 8 N v btr 20, 20 th r l f ff nt f l t. r t pl n f r th n tr t n f h h v lr d b n r d t, rd n t h h th t b t f l rd n t f th rld ll b n
Numerical Solution of Transient Thermal Stresses in a Functionally Graded Cylinder
La d gg Mha gg Glgy al l f a hal a Fally Gadd yld IQ H KHOLO I-LMH aal gg a Jda y f ad hlgy P.O x Ibd JO al: daabh@.d. ba: - h a d h a hal a la yld ad f a fally gadd aal FGM. h yld aal dd b gadd alg h
0 t b r 6, 20 t l nf r nt f th l t th t v t f th th lv, ntr t n t th l l l nd d p rt nt th t f ttr t n th p nt t th r f l nd d tr b t n. R v n n th r
n r t d n 20 22 0: T P bl D n, l d t z d http:.h th tr t. r pd l 0 t b r 6, 20 t l nf r nt f th l t th t v t f th th lv, ntr t n t th l l l nd d p rt nt th t f ttr t n th p nt t th r f l nd d tr b t n.
PR D NT N n TR T F R 6 pr l 8 Th Pr d nt Th h t H h n t n, D D r r. Pr d nt: n J n r f th r d t r v th tr t d rn z t n pr r f th n t d t t. n
R P RT F TH PR D NT N N TR T F R N V R T F NN T V D 0 0 : R PR P R JT..P.. D 2 PR L 8 8 J PR D NT N n TR T F R 6 pr l 8 Th Pr d nt Th h t H h n t n, D.. 20 00 D r r. Pr d nt: n J n r f th r d t r v th
4 4 N v b r t, 20 xpr n f th ll f th p p l t n p pr d. H ndr d nd th nd f t v L th n n f th pr v n f V ln, r dn nd l r thr n nt pr n, h r th ff r d nd
n r t d n 20 20 0 : 0 T P bl D n, l d t z d http:.h th tr t. r pd l 4 4 N v b r t, 20 xpr n f th ll f th p p l t n p pr d. H ndr d nd th nd f t v L th n n f th pr v n f V ln, r dn nd l r thr n nt pr n,
H NT Z N RT L 0 4 n f lt r h v d lt n r n, h p l," "Fl d nd fl d " ( n l d n l tr l t nt r t t n t nt t nt n fr n nl, th t l n r tr t nt. r d n f d rd n t th nd r nt r d t n th t th n r lth h v b n f
46 D b r 4, 20 : p t n f r n b P l h tr p, pl t z r f r n. nd n th t n t d f t n th tr ht r t b f l n t, nd th ff r n b ttl t th r p rf l pp n nt n th
n r t d n 20 0 : T P bl D n, l d t z d http:.h th tr t. r pd l 46 D b r 4, 20 : p t n f r n b P l h tr p, pl t z r f r n. nd n th t n t d f t n th tr ht r t b f l n t, nd th ff r n b ttl t th r p rf l
Colby College Catalogue
Colby College Digital Commons @ Colby Colby Catalogues College Archives: Colbiana Collection 1866 Colby College Catalogue 1866-1867 Colby College Follow this and additional works at: http://digitalcommons.colby.edu/catalogs
828.^ 2 F r, Br n, nd t h. n, v n lth h th n l nd h d n r d t n v l l n th f v r x t p th l ft. n ll n n n f lt ll th t p n nt r f d pp nt nt nd, th t
2Â F b. Th h ph rd l nd r. l X. TH H PH RD L ND R. L X. F r, Br n, nd t h. B th ttr h ph rd. n th l f p t r l l nd, t t d t, n n t n, nt r rl r th n th n r l t f th f th th r l, nd d r b t t f nn r r pr
Th n nt T p n n th V ll f x Th r h l l r r h nd xpl r t n rr d nt ff t b Pr f r ll N v n d r n th r 8 l t p t, n z n l n n th n rth t rn p rt n f th v
Th n nt T p n n th V ll f x Th r h l l r r h nd xpl r t n rr d nt ff t b Pr f r ll N v n d r n th r 8 l t p t, n z n l n n th n rth t rn p rt n f th v ll f x, h v nd d pr v n t fr tf l t th f nt r n r
Vr Vr
F rt l Pr nt t r : xt rn l ppl t n : Pr nt rv nd PD RDT V t : t t : p bl ( ll R lt: 00.00 L n : n L t pd t : 0 6 20 8 :06: 6 pt (p bl Vr.2 8.0 20 8.0. 6 TH N PD PPL T N N RL http : h b. x v t h. p V l
D t r l f r th n t d t t pr p r d b th t ff f th l t tt n N tr t n nd H n N d, n t d t t n t. n t d t t. h n t n :.. vt. Pr nt. ff.,. http://hdl.handle.net/2027/uiug.30112023368936 P bl D n, l d t z d
22 t b r 2, 20 h r, th xp t d bl n nd t fr th b rd r t t. f r r z r t l n l th h r t rl T l t n b rd n n l h d, nd n nh rd f pp t t f r n. H v v d n f
n r t d n 20 2 : 6 T P bl D n, l d t z d http:.h th tr t. r pd l 22 t b r 2, 20 h r, th xp t d bl n nd t fr th b rd r t t. f r r z r t l n l th h r t rl T l t n b rd n n l h d, nd n nh rd f pp t t f r
P a g e 5 1 of R e p o r t P B 4 / 0 9
P a g e 5 1 of R e p o r t P B 4 / 0 9 J A R T a l s o c o n c l u d e d t h a t a l t h o u g h t h e i n t e n t o f N e l s o n s r e h a b i l i t a t i o n p l a n i s t o e n h a n c e c o n n e
n
p l p bl t n t t f Fl r d, D p rt nt f N t r l R r, D v n f nt r r R r, B r f l. n.24 80 T ll h, Fl. : Fl r d D p rt nt f N t r l R r, B r f l, 86. http://hdl.handle.net/2027/mdp.39015007497111 r t v n
Chapter 7 Control Systems Design by the Root Locus Method
haptr 7 ntrl Sytm Dgn by th t Lu Mthd 7. Intrdutn! Prfrman Spfatn: h rqurmnt mpd n th ntrl ytm ar plld ut a prfrman pfatn, whh gnrally rlat t auray, rlatv tablty, and pd f rpn.! Sytm mpnatn: Sttng th gan
Humanistic, and Particularly Classical, Studies as a Preparation for the Law
University of Michigan Law School University of Michigan Law School Scholarship Repository Articles Faculty Scholarship 1907 Humanistic, and Particularly Classical, Studies as a Preparation for the Law
Th pr nt n f r n th f ft nth nt r b R b rt Pr t r. Pr t r, R b rt, b. 868. xf rd : Pr nt d f r th B bl r ph l t t th xf rd n v r t Pr, 00. http://hdl.handle.net/2027/nyp.33433006349173 P bl D n n th n
R e p u b lic o f th e P h ilip p in e s. R e g io n V II, C e n tra l V isa y a s. C ity o f T a g b ila ran
R e p u b l f th e P h lp p e D e p rt e t f E d u t R e V, e tr l V y D V N F B H L ty f T b l r Ju ly, D V N M E M R A N D U M N. 0,. L T F E N R H G H H L F F E R N G F R 6 M P L E M E N T A T N T :,
Executive Committee and Officers ( )
Gifted and Talented International V o l u m e 2 4, N u m b e r 2, D e c e m b e r, 2 0 0 9. G i f t e d a n d T a l e n t e d I n t e r n a t i o n a2 l 4 ( 2), D e c e m b e r, 2 0 0 9. 1 T h e W o r
l f t n nd bj t nd x f r t l n nd rr n n th b nd p phl t f l br r. D, lv l, 8. h r t,., 8 6. http://hdl.handle.net/2027/miun.aey7382.0001.001 P bl D n http://www.hathitrust.org/access_use#pd Th r n th
Outline. Heat Exchangers. Heat Exchangers. Compact Heat Exchangers. Compact Heat Exchangers II. Heat Exchangers April 18, ME 375 Heat Transfer 1
Hat Exangr April 8, 007 Hat Exangr Larry artt Manial Engrg 375 Hat ranfr April 8, 007 Outl Bai ida f at xangr Ovrall at tranfr ffiint Lg-man tmpratur diffrn mtd Efftivn NU mtd ratial nidratin Hat Exangr
Colby College Catalogue
Colby College Digital Commons @ Colby Colby Catalogues College Archives: Colbiana Collection 1870 Colby College Catalogue 1870-1871 Colby College Follow this and additional works at: http://digitalcommonscolbyedu/catalogs
SAMPLE LITANY OF THE SAINTS E/G. Dadd9/F. Aadd9. cy. Christ, have. Lord, have mer cy. Christ, have A/E. Dadd9. Aadd9/C Bm E. 1. Ma ry and. mer cy.
LTNY OF TH SNTS Cntrs Gnt flwng ( = c. 100) /G Ddd9/F ll Kybrd / hv Ddd9 hv hv Txt 1973, CL. ll rghts rsrvd. Usd wth prmssn. Musc: D. Bckr, b. 1953, 1987, D. Bckr. Publshd by OCP. ll rghts rsrvd. SMPL
Colby College Catalogue
Colby College Digital Commons @ Colby Colby Catalogues College Archives: Colbiana Collection 1872 Colby College Catalogue 1872-1873 Colby College Follow this and additional works at: http://digitalcommonscolbyedu/catalogs
I M P O R T A N T S A F E T Y I N S T R U C T I O N S W h e n u s i n g t h i s e l e c t r o n i c d e v i c e, b a s i c p r e c a u t i o n s s h o
I M P O R T A N T S A F E T Y I N S T R U C T I O N S W h e n u s i n g t h i s e l e c t r o n i c d e v i c e, b a s i c p r e c a u t i o n s s h o u l d a l w a y s b e t a k e n, i n c l u d f o l
tc'h~ Tenese Invasin YClS tf'i man through Allatoona Pass.-Resaca held, but Hood takes Dalton, and, avoiding a Battle, re- th
x -Pd 311 d Rd g -d g W--d dg g D k WT- p M- d P d 2161 T p -F dd d Ad E-A N--d W P Rd d g g 3 -T K- A-T B A - d: dn T p k d1)k 4 g d d pd-d d - Pd pddl314lx Y g A P-R d d k D d dg B - 1 ge %;- 0 1 - dd-
TDVDC-345 STA= HT= ELE= PARCEL NO /24/12
PL-ADD DAWG 95-27 TA=27116.12 HT=141.75 L=13.71 131 13 95-2 TA=272796.16 HT=151.75 L=112.14 95-29 TA=273776.25 HT=146.75 L=112.5 95-29 TA=274756.34 HT=151.75 L=.59 95-291 TA=275736.4 HT=141.75 L=13.79
filing for office of CO AN Co L POlS R 4 home phone epqropriate elections officials ORS Filing for State Voters Pamphlet Fi rstday
Fn nddy npn nn L v 6 R 49 h nn pb d nd y b pbhd pdd p yp pn by n b k nk nb d ndd n d M LG hw n hd pp n b H MB L n A L P R 4 d dp pn nb ddd y 8 zp d R D R A b A ka DL d ny d h phn d AK L x dd W b W n ddwh
W I T H M i A. L I O E T O W A R D ISTOlNrE ^ I S T D C H A. n i T Y F O R - A L L. "
J/ H L D N D H Y F L L L N LLL KN NY H Y 2 95 HL N NG F L G NG F LNDD H H J F NH D K GN L _ L L :? H F K b H Y L DD Y N? N L L LD H LL LLL LNNG LL J K N 3 ND DL6 N Lb L F KF FH D LD3 D ND ND F ND LKKN
Future Self-Guides. E,.?, :0-..-.,0 Q., 5...q ',D5', 4,] 1-}., d-'.4.., _. ZoltAn Dbrnyei Introduction. u u rt 5,4) ,-,4, a. a aci,, u 4.
![Future Self-Guides. E,.?, :0-..-.,0 Q., 5...q ',D5', 4,] 1-}., d-'.4.., _. ZoltAn Dbrnyei Introduction. u u rt 5,4) ,-,4, a. a aci,, u 4.](/thumbs/92/109036622.jpg "Future Self-Guides. E,.?, :0-..-.,0 Q., 5...q ',D5', 4,] 1-}., d-'.4.., _. ZoltAn Dbrnyei Introduction. u u rt 5,4) ,-,4, a. a aci,, u 4.")
te SelfGi ZltAn Dbnyei Intdtin ; ) Q) 4 t? ) t _ 4 73 y S _ E _ p p 4 t t 4) 1_ ::_ J 1 `i () L VI O I4 " " 1 D 4 L e Q) 1 k) QJ 7 j ZS _Le t 1 ej!2 i1 L 77 7 G (4) 4 6 t (1 ;7 bb F) t f; n (i M Q) 7S
Material Properties Measurement. Accuracy of Plastic Strain Estimated by Hardness to Assess Remaining Fatigue Lives
Ml Pp M Ay f Pl S Ed by Hd A R Lv M. Nk, Hh, Ld., Jp; S. K, Hh-GE Nl Ey, Ld., Jp; Y. Kk, Y. Tk, Tky El Pw Cpy, Jp; J. K, K vy, Jp; T. Ow, Ay Gk vy, Jp ABSTRACT A b f p hv b pfd vl h l y f p Khwzk-Kw Nl
Colby College Catalogue
Colby College Digital Commons @ Colby Colby Catalogues College Archives: Colbiana Collection 1871 Colby College Catalogue 1871-1872 Colby College Follow this and additional works at: http://digitalcommonscolbyedu/catalogs
N V R T F L F RN P BL T N B ll t n f th D p rt nt f l V l., N., pp NDR. L N, d t r T N P F F L T RTL FR R N. B. P. H. Th t t d n t r n h r d r
n r t d n 20 2 04 2 :0 T http: hdl.h ndl.n t 202 dp. 0 02 000 N V R T F L F RN P BL T N B ll t n f th D p rt nt f l V l., N., pp. 2 24. NDR. L N, d t r T N P F F L T RTL FR R N. B. P. H. Th t t d n t r
I N A C O M P L E X W O R L D
IS L A M I C E C O N O M I C S I N A C O M P L E X W O R L D E x p l o r a t i o n s i n A g-b eanste d S i m u l a t i o n S a m i A l-s u w a i l e m 1 4 2 9 H 2 0 0 8 I s l a m i c D e v e l o p m e
A L A BA M A L A W R E V IE W
A L A BA M A L A W R E V IE W Volume 52 Fall 2000 Number 1 B E F O R E D I S A B I L I T Y C I V I L R I G HT S : C I V I L W A R P E N S I O N S A N D TH E P O L I T I C S O F D I S A B I L I T Y I N
Unit 3: Transistor at Low Frequencies
Unt 3: Tansst at Lw Fquncs JT Tansst Mdlng mdl s an qualnt ccut that psnts th chaactstcs f th tansst. mdl uss ccut lmnts that appxmat th ha f th tansst. Th a tw mdls cmmnly usd n small sgnal analyss f
1) They represent a continuum of energies (there is no energy quantization). where all values of p are allowed so there is a continuum of energies.
Unbound Stats OK, u untl now, w a dalt solly wt stats tat ar bound nsd a otntal wll. [Wll, ct for our tratnt of t fr artcl and w want to tat n nd r.] W want to now consdr wat ans f t artcl s unbound. Rbr
176 5 t h Fl oo r. 337 P o ly me r Ma te ri al s
A g la di ou s F. L. 462 E l ec tr on ic D ev el op me nt A i ng er A.W.S. 371 C. A. M. A l ex an de r 236 A d mi ni st ra ti on R. H. (M rs ) A n dr ew s P. V. 326 O p ti ca l Tr an sm is si on A p ps
TABLES AND INFORMATION RETRIEVAL
Ch 9 TABLES AND INFORMATION RETRIEVAL 1. Id: Bkg h lg B 2. Rgl Ay 3. Tbl f V Sh 4. Tbl: A Nw Ab D Ty 5. Al: Rdx S 6. Hhg 7. Aly f Hhg 8. Cl: Cm f Mhd 9. Al: Th Lf Gm Rvd Ol D S d Pgm Dg I C++ T. 1, Ch
Helping you learn to save. Pigby s tips and tricks
Hlpg yu lan t av Pigby tip and tick Hlpg vy littl av Pigby ha bn tachg hi find all abut ny and hw t av f what ty want. Tuffl i avg f a nw tappy bubbl d and Pi can t wait t b abl t buy nw il pat. Pigby
Determination of slot leakage inductance for three-phase induction motor winding using an analytical method
ACHIVES OF EECTICA EGIEEIG VO 6 pp 569-59 DOI 78/--6 Dtnton of ot ntn fo t-p nton oto wnn n n nt to JA STASZAK Dptnt of Et Mn n Mton St K Unvt of Tnoo Tą PP 7 K Pon -: j@tp v: v: 5 Att: T t nto o pon fo
S U E K E AY S S H A R O N T IM B E R W IN D M A R T Z -PA U L L IN. Carlisle Franklin Springboro. Clearcreek TWP. Middletown. Turtlecreek TWP.
F R A N K L IN M A D IS O N S U E R O B E R T LE IC H T Y A LY C E C H A M B E R L A IN T W IN C R E E K M A R T Z -PA U L L IN C O R A O W E N M E A D O W L A R K W R E N N LA N T IS R E D R O B IN F
Handout 30. Optical Processes in Solids and the Dielectric Constant
Haut Otal Sl a th Dlt Ctat I th ltu yu wll la: La ut Ka-Kg lat Dlt tat l Itba a Itaba tbut t th lt tat l C 47 Sg 9 Faha Raa Cll Uty Chag Dl, Dl Mt, a lazat Dty A hag l t a gat a a t hag aat by ta: Q Q
Post-optimality Analysis in Bounded Variables Problem
Pt-ptt An n ndd V P Kpn Dh * nd Vnt V * Atct h pp d wth d p gth nd ntvt -n pt-ptt n n n pgng wth ndd v In ntvt n chng n cffcnt t A dtn f v nd dtn f cntnt hv n dcd c ttn ncdd n ppt f th Kwd: D-p gth ntvtn
NTCA2 2 LA6A JA6 CYA6 ACL3 VAA3 DA48 CYA19 LA6B DA45 CTA4B DA46 CTA5B G2 CTA3B RA135 QA6 RA144 CNA5 CNA6 VO-B1 S12VA SGND SGND GATE
L Y Y N 0 F F L X V L X N L L L N Y Y NT L NT J L PV -T L L Y Y V L X N L N VM 0 0 J0 PN J PN PN J PN PN PN PN V VM 0 F P V V N (-) (+) (+) (-) L 0 0 0 0 0 0 0 0 0 0 L L T Q T T T Q + F Y Y 0 V/N N/VP
Oi ir\ o CM CM ! * - CM T. c *" H - VO - a CM - t - T - j. Vv VO r t- CO on *- t- «- - ** <* - CM CM CM b- f - on on. on CM CVJ t - o.
292 b» CJ «n :T * v j U n n C l * n t l f VL. n n W n V ' n Ln fv C ), C n e. t f *" T V n! * t t T j t Vv V t l / n * t «** n Pk Q * Ph t * b T~! ^ v n f n n N n T n l f P n t. n pn «n =f LPv j t t n
88 N L Lö. r : n, d p t. B, DBB 644 6, RD., D z. 0, DBB 4 8 z h. D z : b n, v tt, b t b n r, p d, t n t. B, BB z. 0, DBB 4 8 z D. t n F hl r ff, nn R,
L x l h z ll n. V n n l Lö.. nn.. L RD h t t 40 für n r ( n r. B r 22, bb b 8 h r t llt. D nd t n rd d r h L länz nd b tät t: r b r ht t, d L x x n ht n r h nd hr ftl h b z t, nd rn h d r h ündl h h ltr
Helping Kids Prepare For Life (253)
Hlpi Ki Pp F Lif.l.i. (253)-589-7489 Tilli it it L Livit iv f fiv CIS U H. Vip pt fll t Tilli Elt l tpi tff tt f vi t t CIS T Hll f i Cltt N Cli. - L ivi i CIS f Bill Milli CIS pit Dil Cili Ti l iz it
T h e C S E T I P r o j e c t
T h e P r o j e c t T H E P R O J E C T T A B L E O F C O N T E N T S A r t i c l e P a g e C o m p r e h e n s i v e A s s es s m e n t o f t h e U F O / E T I P h e n o m e n o n M a y 1 9 9 1 1 E T
HASSELL DEPARTMENT FOR INFRASTRUCTURE JERSEY FUTURE HOSPITAL (JFH) THE PARADE, ST HELIER, JERSEY JE1_3QS
L V L M L Z 3 6 1:75 L Z. M V. LL M MLLM L. LL M LL VF F. LL LL F F Y. M J LL LV, F. Y F V LL. 218 LL. L. L Y. L. L F F L VLM. VLY 1 (F ) L VL 6 5 4 3 2 1 L V L Y, L L Y, M X F 17/3/18 2/3/18 V 23/7/18
and A L T O SOLO LOWELL, MICHIGAN, THURSDAY, J U N E Farm Necessities Off State Sales Tax list Now Exempt
H DG N Bg G HN H ND H NG g g g g Yg x x g g gg k B g g g g g g g g g g x g g g k g g g k gg g x g z g g g g k k g g g g k XY- DN H GN DP N PG P D HN DN NPNG D- H HGN HDY N 3 935 Y - H D Y X 93 D B N H
fur \ \,,^N/ D7,,)d.s) 7. The champion and Runner up of the previous year shall be allowed to play directly in final Zone.
OUL O GR SODRY DUTO, ODS,RT,SMTUR,USWR.l ntuctin f cnuct f Kbi ( y/gil)tunent f 2L-Lg t. 2.. 4.. 6. Mtche hll be lye e K ule f ene f tie t tie Dutin f ech tch hll be - +0 (Rece)+ = M The ticint f ech Te
UNIVERSITATEA TRANSILVANIA DIN BRA$OV Catedra Design de Produs (i Robotic*
UNIRSIAA RANSILANIA DIN BRA$O Catda Dsgn d Pdus Rbt* Spznul na9nal u patpa ntna9nal: PRtaa ASIstat: d Calulat P R A S I C ' 0 l. II - Ogan d an. anss an 7-8 Nb Bav Râna ISBN 973-635-075-4 ON H FINI LMNS
fiff w 4h WEDNESDAY JULY 23 1SS3 COMKCTIOXKHVI 4 4Ty X 41x1441 as x n rcnsut4 Hotti su KEEPS ALWAYS ON HAND A4 HMlwll l4 Vlt I W
z RR GR NN N 5 P R d P N N F N Q d R F d d Z D d Q d 5 d g R P 9 g F d g N 9 Q R R F F d z z 5 P 9 d RNY N DRD F R G R 5 R 5 R 5 D N N d N RN N Z R P P P 8 D 5 5 z Z g 5 YY d R F G R R N 5 d D D F P Y
Filing of Candidacy for Nonpartisan Nomination
Fn f nddy f npn mnn L v 6 GA 49 Th nfmn m f pb d nd my b pbhd pdd p yp pn by n bk nk nmbn f ff f d ndd nm fn f ff f H RT A hw nm hd pp n b 8 RA AH A dn dd y zp d PAR K d d dpmn pn nmb A ny f dn 7 8 f b7
Exam 2 Solutions. Jonathan Turner 4/2/2012. CS 542 Advanced Data Structures and Algorithms
CS 542 Avn Dt Stutu n Alotm Exm 2 Soluton Jontn Tun 4/2/202. (5 ont) Con n oton on t tton t tutu n w t n t 2 no. Wt t mllt num o no tt t tton t tutu oul ontn. Exln you nw. Sn n mut n you o u t n t, t n
How to Use. The Bears Beat the Sharks!
Hw t U Th uc vd 24 -wd dng ctn bd n wht kd ncunt vy dy, uch mv tng, y, n Intnt ch cn. Ech ctn ccmnd by tw w-u ctc g ng tudnt cmhnn th ctn. Th dng ctn cn b ud wth ndvdu, m gu, th wh c. Th B cnd bmn, Dn
Lecture 20. Transmission Lines: The Basics
Lcu 0 Tansmissin Lins: Th Basics n his lcu u will lan: Tansmissin lins Diffn ps f ansmissin lin sucus Tansmissin lin quains Pw flw in ansmissin lins Appndi C 303 Fall 006 Fahan Rana Cnll Univsi Guidd Wavs
~,. :'lr. H ~ j. l' ", ...,~l. 0 '" ~ bl '!; 1'1. :<! f'~.., I,," r: t,... r':l G. t r,. 1'1 [<, ."" f'" 1n. t.1 ~- n I'>' 1:1 , I. <1 ~'..
,, 'l t (.) :;,/.I I n ri' ' r l ' rt ( n :' (I : d! n t, :?rj I),.. fl.),. f!..,,., til, ID f-i... j I. 't' r' t II!:t () (l r El,, (fl lj J4 ([) f., () :. -,,.,.I :i l:'!, :I J.A.. t,.. p, - ' I I I
ATTACHMENT 1. MOUNTAIN PARK LAND Page 2 of 5
ATTACHMENT 53 YOBA LINDA Gyp Yb gl 9 Gt Fthly gl t 247 Mt Utct cl Mt Gyp 248 248X A0 A0 Hghy G:\jct\K00074232_p_Iv_Cp_L_Dt_204\MXD\p_Iv_Cp_L_Dt_(K00074232)_0-29-204.x C ( l t b t f y p b lc ly ) Ch Hll
10.5 Linear Viscoelasticity and the Laplace Transform
Scn.5.5 Lnar Vclacy and h Lalac ranfrm h Lalac ranfrm vry uful n cnrucng and analyng lnar vclac mdl..5. h Lalac ranfrm h frmula fr h Lalac ranfrm f h drvav f a funcn : L f f L f f f f f c..5. whr h ranfrm
35H MPa Hydraulic Cylinder 3.5 MPa Hydraulic Cylinder 35H-3
- - - - ff ff - - - - - - B B BB f f f f f f f 6 96 f f f f f f f 6 f LF LZ f 6 MM f 9 P D RR DD M6 M6 M6 M. M. M. M. M. SL. E 6 6 9 ZB Z EE RC/ RC/ RC/ RC/ RC/ ZM 6 F FP 6 K KK M. M. M. M. M M M M f f
Grilled it ems are prepared over real mesquit e wood CREATE A COMBO STEAKS. Onion Brewski Sirloin * Our signature USDA Choice 12 oz. Sirloin.
TT & L Gl v l q T l q TK v i f i ' i i T K L G ' T G!? Ti 10 (Pik 3) -F- L P ki - ik T ffl i zzll ik Fi Pikl x i f l $3 (li 2) i f i i i - i f i jlñ i 84 6 - f ki i Fi 6 T i ffl i 10 -i i fi & i i ffl
rhtre PAID U.S. POSTAGE Can't attend? Pass this on to a friend. Cleveland, Ohio Permit No. 799 First Class
rhtr irt Cl.S. POSTAG PAD Cllnd, Ohi Prmit. 799 Cn't ttnd? P thi n t frind. \ ; n l *di: >.8 >,5 G *' >(n n c. if9$9$.jj V G. r.t 0 H: u ) ' r x * H > x > i M
Trade Patterns, Production networks, and Trade and employment in the Asia-US region
Trade Patterns, Production networks, and Trade and employment in the Asia-U region atoshi Inomata Institute of Developing Economies ETRO Development of cross-national production linkages, 1985-2005 1985
(C 17) , E to B; Lorentz Force Law: fields and forces (C 17) Lorentz Force Law: currents
Mn. Wd Thus. Fi. ( 7)..-..,.3. t ; 5..-.. Lnt F Law: filds and fs ( 7) 5..3 Lnt F Law: unts ( 7) 5. it-saat Law HW6 F Q F btwn statina has Q F Q (ulb s Law: n.) Q Q Q ˆ Q 3 F btwn in has V ˆ 3 u ( n 0.7)
Let s start from a first-order low pass filter we already discussed.
EEE0 Netrk Analy II Dr. harle Km Nte09: Actve Flter ---Part. gher-order Actve Flter The rt-rder lter d nt harply dvde the pa band and the tp band. One apprach t btan a harper trantn beteen the pa band
,.*Hffi;;* SONAI, IUERCANTII,N I,IMITDII REGD- 0FFICE: 105/33, VARDHMAN GotD[N PLNLA,R0AD No.44, pitampura, DELHI *ffigfk"
$ S, URCT,,MTD RGD 0C: 10/, VRDM G[ LL,R0D.44, ptmpur, DL114 C: l22ldll98l,c0224gb, eb:.nlmernte.m T, Dte: 17h tber, 201 BS Lmted hre ]eejeebhy Ter Dll Street Mumb 41 The Mnger (Ltng) Delh Stk xhnge /1,
Call for Applications
i Ty Ty v l O 7:H 7 O6 fl x 4 7T q l it y ix k lf t l l H v l lg i li O 7:H7 EDL9 ty i tyi yt Blvi i i g it g vi B l B ll li B i ll iz i ti S B 6 dy li j d ti d l i vi i ik tti w z k ik tti i l w l Hli
h : sh +i F J a n W i m +i F D eh, 1 ; 5 i A cl m i n i sh» si N «q a : 1? ek ser P t r \. e a & im a n alaa p ( M Scanned by CamScanner
m m i s t r * j i ega>x I Bi 5 n ì r s w «s m I L nk r n A F o n n l 5 o 5 i n l D eh 1 ; 5 i A cl m i n i sh» si N «q a : 1? { D v i H R o s c q \ l o o m ( t 9 8 6) im a n alaa p ( M n h k Em l A ma
CHAPTER IV RESULTS. Grade One Test Results. The first graders took two different sets of pretests and posttests, one at the first
33 CHAPTER IV RESULTS Gad On Tst Rsults Th fist gads tk tw diffnt sts f ptsts and psttsts, n at th fist gad lvl and n at th snd gad lvl. As displayd n Figu 4.1, n th fist gad lvl ptst th tatmnt gup had
Advanced Placement. Chemistry. Integrated Rates
Advanced Placement Chemistry Integrated Rates 204 47.90 9.22 78.49 (26) 50.94 92.9 80.95 (262) 52.00 93.94 83.85 (263) 54.938 (98) 86.2 (262) 55.85 0. 90.2 (265) 58.93 02.9 92.2 (266) H Li Na K Rb Cs Fr
Solutions to Supplementary Problems
Solution to Supplmntay Poblm Chapt Solution. Fomula (.4): g d G + g : E ping th void atio: G d 2.7 9.8 0.56 (56%) 7 mg Fomula (.6): S Fomula (.40): g d E ping at contnt: S m G 0.56 0.5 0. (%) 2.7 + m E
GMm. 10a-0. Satellite Motion. GMm U (r) - U (r ) how high does it go? Escape velocity. Kepler s 2nd Law ::= Areas Angular Mom. Conservation!!!!
F Satllt Moton 10a-0 U () - U ( ) 0 f ow g dos t go? scap locty Kpl s nd Law ::= Aas Angula Mo. Consaton!!!! Nwton s Unsal Law of Gaty 10a-1 M F F 1) F acts along t ln connctng t cnts of objcts Cntal Foc
Lecture 7 Diffusion. Our fluid equations that we developed before are: v t v mn t
Cla ot fo EE6318/Phy 6383 Spg 001 Th doumt fo tutoal u oly ad may ot b opd o dtbutd outd of EE6318/Phy 6383 tu 7 Dffuo Ou flud quato that w dvlopd bfo a: f ( )+ v v m + v v M m v f P+ q E+ v B 13 1 4 34
Learning High-Dimensional Data with Artificial Neural Networks. Université catholique de Louvain (Belgium) Machine Learning Group
Lg Hgh-l h Al Nl Nk Ué hlq Lv (Blgm) h Lg Gp hp://..l..b/mlg/ Ol Hgh-l (H) L & l l l C ly, mpy p phm Spzg C El m l I N ml l m (l) vbl l pj ph: l, SV, Ol Hgh-l (H) L & l l l C ly, mpy p phm Spzg C El m
METHOD OF DIFFERENTIATION
EXERCISE - 0 METHOD OF DIFFERENTIATION CHECK YOUR GRASP 5. m mn n ( m n )(n ) ( n )( m ) ( m )(m n ) 0 7. co y / y / loga m m n n (m n )(n )( m ) d () d 0 tan y y log a tan y tan log a Now diffrntiating
Why switching? Modulation. Switching amp. Losses. Converter topology. i d. Continuous amplifiers have low efficiency. Antag : u i
Modlaton Indtral Elctrcal Engnrng and Atomaton Lnd nvrty, Swdn Why wtchng? Contno amplfr hav low ffcncy a b Contno wtch pt ( t ) = pn( t) = ( a b) Antag : ( a b) = Pn = Pt η = = = Pn Swtchng amp. Lo Convrtr
(C) Pavel Sedach and Prep101 1
(C) Pavel Sedach and Prep101 1 (C) Pavel Sedach and Prep101 1 (C) Pavel Sedach and Prep101 2 (C) Pavel Sedach and Prep101 2 (C) Pavel Sedach and Prep101 3 (C) Pavel Sedach and Prep101 3 (C) Pavel Sedach
Last 4 Digits of USC ID:
Chemistry 05 B Practice Exam Dr. Jessica Parr First Letter of last Name PLEASE PRINT YOUR NAME IN BLOCK LETTERS Name: Last 4 Digits of USC ID: Lab TA s Name: Question Points Score Grader 8 2 4 3 9 4 0
HOTEL/MOTEL BATHROOM ACCESSORIES
H BH H VB FNH PHD H PHD B D PN B F (D ) UN DPN FNH D # QY. B PN PHD H 01-1001 50 V Z: 1 7 16"W x 3 1 4"H x 1"D. PHD B 05-PB1001 50 GN BG W HNG PD Z. P ND UDY NN. V Z: 1 7 8"D x 1 7 8"PJN. F HU PFN N. W-N
Multi-linear Systems and Invariant Theory. in the Context of Computer Vision and Graphics. Class 4: Mutli-View 3D-from-2D. CS329 Stanford University
Mult-lna Sytm and Invaant hoy n th Contxt of Comut Von and Gahc Cla 4: Mutl-Vw 3D-fom-D CS39 Stanfod Unvty Amnon Shahua Cla 4 Matal W Wll Cov oday Eola Gomty and Fundamntal Matx h lan+aallax modl and latv
² Ý ² ª ² Þ ² Þ Ң Þ ² Þ. ² à INTROIT. huc. per. xi, sti. su- sur. sum, cum. ia : ia, ia : am, num. VR Mi. est. lis. sci. ia, cta. ia.
str Dy Ps. 138 R 7 r r x, t huc t m m, l : p - í pr m m num m, l l : VR M rá s f ct st sc n -, l l -. Rpt nphn s fr s VR ftr ch vrs Ps. 1. D n, pr bá m, t c g ví m : c g ví ss s nm m m, t r r r c nm m
Introduction to Inertial Dynamics
nouon o nl Dn Rz S Jon Hokn Unv Lu no on uon of oon of ul-jon oo o onl W n? A on of o fo ng on ul n oon of. ou n El: A ll of l off goun. fo ng on ll fo of gv: f-g g9.8 /. f o ll, n : f g / f g 9.8.9 El:
Boxing Blends Sub step 2.2 Focus: Beginning, Final, and Digraph Blends
Boxing Blends Sub step 2.2 Focus: Beginning, Final, and Digraph Blends Boxing Blends Game Instructions: (One Player) 1. Use the game board appropriate for your student. Cut out the boxes to where there
Thank You! $20,000+ Anonymous
T D $20,000+ Ay $10,000+ Fll Fly Cbl T Ew & S Vbl $5,000+ Ay M. & M. T Fll M. Fl H. Hwz D. & M. G A. Ky $2,500+ M. Plp J. Bly, III J & Klly Bzly S T. & My C. Fll Mk & E G R Hy Jy & Ell Jll Fly Ly F Cy
Why CEHCH? Completion of this program provides participants direct access to sit for the NAB HCBS exam.
Wy? T fus f s pns n us s p ssn pnns f w-bn & uny bs ss pg. Ts us s p n n ff s s bs p wn & uny bs ss pfssn. W uny n s f O s n n ns qu f sp u D, sussfu pn f s n us w nb yu ns n knwg bs. T O un f & sp n O
ADORO TE DEVOTE (Godhead Here in Hiding) te, stus bat mas, la te. in so non mor Je nunc. la in. tis. ne, su a. tum. tas: tur: tas: or: ni, ne, o:
R TE EVTE (dhd H Hdg) L / Mld Kbrd gú s v l m sl c m qu gs v nns V n P P rs l mul m d lud 7 súb Fí cón ví f f dó, cru gs,, j l f c r s m l qum t pr qud ct, us: ns,,,, cs, cut r l sns m / m fí hó sn sí
o Alphabet Recitation
Letter-Sound Inventory (Record Sheet #1) 5-11 o Alphabet Recitation o Alphabet Recitation a b c d e f 9 h a b c d e f 9 h j k m n 0 p q k m n 0 p q r s t u v w x y z r s t u v w x y z 0 Upper Case Letter
Chemistry 2 Exam Roane State Academic Festival. Name (print neatly) School
Name (print neatly) School There are fifteen question on this exam. Each question is weighted equally. n the answer sheet, write your name in the space provided and your answers in the blanks provided.
Nonverbal Cues of Dominance Laura van Hooff, Jasmijn Verspaandonk, Nicole van den Reek, Guusje Nagels & Jalou Lemmens
Nvbl C f Dm L v Hff, Jmj Vdk, Nl v d Rk, Gj Nl & Jl Lmm Ab Th m f h d w v h vbl x f dm b hm d whh h w dff bw l d dm T h, h l bhv f f h TV hw Tm Ild w ld Th x vbl bhvl d h h m dm w d, h, l x, fld m, hd
OH BOY! Story. N a r r a t iv e a n d o bj e c t s th ea t e r Fo r a l l a g e s, fr o m th e a ge of 9
OH BOY! O h Boy!, was or igin a lly cr eat ed in F r en ch an d was a m a jor s u cc ess on t h e Fr en ch st a ge f or young au di enc es. It h a s b een s een by ap pr ox i ma t ely 175,000 sp ect at
CHAPTER 3 KINEMATICS OF CYLINDRICAL ROLLER BEARING
34 CHAPTER 3 KINEMATICS OF CYLINDRICAL ROLLER BEARING 3. CAGE AND ROLLER SPEED Th latv mtns f th ag spaat, th lls, an th as f ylnal llng lmnt bangs a mptant t unstan th pfman. Th latv vlts n a ball bang
w x a f f s t p q 4 r u v 5 i l h m o k j d g DT Competition, 1.8/1.6 Stainless, Black S, M, L, XL Matte Raw/Yellow
HELION CARBON TEAM S, M, L, XL M R/Y COR XC Py, FOC U Cn F, 110 T Innn Dn 27. AOS Snn Sy /F Ln, P, 1 1/8"-1 1/2" In H T, n 12 12 M D F 32 FLOAT 27. CTD FIT /A K, 110 T, 1QR, / FIT D, L & Rn A, T Ay S DEVICE
necessita d'interrogare il cielo
gigi nei necessia d'inegae i cie cic pe sax span s inuie a dispiegaa fma dea uce < affeandi ves i cen dea uce isnane " sienzi dei padi sie veic dei' anima 5 J i f H 5 f AL J) i ) L '3 J J "' U J J ö'
Ash Wednesday. First Introit thing. * Dómi- nos. di- di- nos, tú- ré- spi- Ps. ne. Dó- mi- Sál- vum. intra-vé-runt. Gló- ri-
sh Wdsdy 7 gn mult- tú- st Frst Intrt thng X-áud m. ns ní- m-sr-cór- Ps. -qu Ptr - m- Sál- vum m * usqu 1 d fc á-rum sp- m-sr-t- ó- num Gló- r- Fí- l- Sp-rí- : quó-n- m ntr-vé-runt á- n-mm c * m- quó-n-