Summary Introduction to Process Control

Size: px
Start display at page:

Download "Summary Introduction to Process Control"

Transcription

1 Suy todutio to Po otol Rf iut Fdbk otol hoy Fowd oto Fdbk oto tuto o ditub Plt Zhyu Yg otol yt obl: Albog Uivity Ebjg A lt: hyil yt dd to b otolld Sifitio: did yt fo DE5 Fll 4 A thodology: to dig otoll uh tht th lodloo (fdbk otol yt tifi th ifitio htt://uudk/~yg/ou/4fll/ fdbk otol thoy o4htl /6/4 todutio to Po otol /6/4 todutio to Po otol lil otol thoy (fquy doi Fdbk otol Sifi toi (itodutio to dvd otol od otol thoy (tt doi obut i dly oli O /6/4 todutio to Po otol 3 Wht you ld though 5 5 : 5: hitoy of fdbk otol 4: blok dig fo yt odlig tt 678: Bi oti of fdbk ll : 63: tidoi ifitio 7985: PD otoll b : tdytt tkig d yt ty & 3: : fquy o (Bod lo S : Gi d h gi ii : Dyi otio u 4: 44: dyi otio ll 3: Stbility ii 5: 36375: yquit tbility itio k /6/4 todutio to Po otol 4 Sod t: 6: odllig u d otol Sifitio 7: PD otol d Exl 8: Fquy Ro thod d Exl 9:Root lou thod od otol thoy (Stt( thod : todutio to tt thod : otol Dig fo Full Stt Fdbk : otol dig uig tito 3: todutio of Rf ut 4: tgl otol, Robut kig d LQR otol 5: uy /6/4 todutio to Po otol 5 ott: lil otol thoy thtil odl of L yt: F, ZP, ODE L yt ly: fquy oti, iul, t, bod, yquit, tbility, otol yt dig Root lou dig Fquy o dig Digitl otol t Dit quivl Slig tho ASD tlb/siulik /6/4 todutio to Po otol 6

2 otio Blok Dig Rf iut Fowd oto Fdbk oto tuto o ditub Plt D( A(S P( F( S( /6/4 todutio to Po otol 7 w otiuou L Syt odl Difftil qutio y ω y ω y f futio ud fo Y ( b b G ( U ( Zool fo Y ( G ( U ( i u Ptil ftio xio i ( z ( L b L b i i g, X FX Y HX g, GU JU G ( /6/4 todutio to Po otol 8, G ( ( (, ω ± ω ω ω i doi lyi ul/t o Dyi Syt Alyi good tit o: Ri ti t, Sttlig ti t, Ovhoot, Pk ti t good tdytt o: Poitioo ott (ty ; Vloity ott (ty ; Altio ott (ty Stbility: h(/h[] i bolutly ubl Fquy doi lyi Bdwidth d ot k: bod lot Pol d zo lotio lyi yquit lot: G, P Routh tbility itio tlb: L Viw /6/4 todutio to Po otol 9 lodloo loo tbility BBO tbility otiuou yt h( Dit yt h[] Pol lotio Stbility Alyi otiuou yt LHP l dit yt uit il zl Routh thod gtiv oot of olyoil: Routh y yquit itio ZP Gi d h gi otiuou yt gi(y Dit yt gi(yd /6/4 todutio to Po otol otol Syt Dig otol gt: Good od o lodloo tbility Ditub ttutio Robut otol Dig thodology: lil thiqu (fquy thod Root lou (Ev 95 fquy o dig (Bod lot PD otol od thiqu (tt thod Pol igt Etto bd dig LQR otil dig /6/4 todutio to Po otol Syt Sifitio: Good Ro Good od o Good tit o Ri ti t Sttlig ti t Ovhoot Pk ti t Good tdytt o Poitioo ott Vloity ott Altio ott ω H ( ω ω : dig tio ω : tul 8 t ω fquy Good l fquy fo dit yt yilly, th l fquy hould b ho to b to 35 ti th lod loo tul fquy t t otiu /6/4 todutio to Po otol 4 ω π ω d uity v , %, fdbk li li %, li %, 4 ω G G σ o d ( o G 6 ( o ( ω y v

3 Bdwidth (fo lodloo yt h xiu fquy ω B oodig to 3dB i th lodloo gitud Bod lot ω B ω fo P9; ω B ω fo P45 (ω : oloo oov fquy Ro k G(jω /(ξ t ω ω Gi gi d Ph gi (fo oloo yt G: u of how lo th yquit lot i to il th P: u of how uh dditiol h lg (ti dly b toltd Dg foul: ξ P/, d ω ω B ω D( G( otiu /6/4 todutio to Po otol 3 /6/4 todutio to Po otol 4 PD Fdbk otoll PD : P: Pootiol (otol : tgl (otol D: Divtiv (otol PD otol Syt Stutu: d otol ( ( PD otoll htiti Stdy tt offt/o obl Ditub jtio obl Good tit o ( t ( d τ τ t & ( Plt G( /6/4 todutio to Po otol 5 D y( Piil: uig th PD otoll t ( ( ( d D( τ τ & t U( D( ( D E( ig d / td to du yt o ig D td to iov tbility Ziglihol uig thod(94943 Qut dy tio thod: Slo t R/τ, Lg L Ultit Sitivity thod ul o Ultit gi: u Ultit iod: P u /6/4 todutio to Po otol 6 tgto Atiwidu otivtio: tuto tutio ho itgtio itgto widu Atiwidu thiqu: u off th itgl tio oo th tuto tut lt with dd zo lt with oliity FquyRo Dig thod Fquyo dig thod ot oul i iduty hy ovid good dig i f of utity i th lt odl hy y to oot with xitl ifotio hy oft th ot otfftiv thod Fquyo dig tool f futio Bod lot: Gi, h lot, G, P, tbility yquit lot: tbility /6/4 todutio to Po otol 7 /6/4 todutio to Po otol 8 3

4 Dyi oto Dig Objtiv: f tiftoy o dyi ot b obtid by gi djutt lo, o odifitio o otio of th o dyi i dd D(G( ool: bod lot P, G, oov fquy, Ld d lg otio Ld otio: t ily to low i ti d d th tit ovhoot: D((/(α, α < Lg otio: t ily to iov th tdytt uy: D((α/(, α < otioi tyilly ld i i with th lt i th fdfowd th otoll D( Plt G( /6/4 todutio to Po otol 9 Ld oto Dig F396 F Ld otio: D((/(α, α < Ld oto i high filt (PD otol t i ud whv ubttil iovt i dig i quid Dig odu: St : Dig th low fquy gi with t to th tdytt o ifitio St : Dti th dd h ld St 3: Dti i β x i 45 α 76 i β x i 45 St 4: Dti 548 ω α ( ω / α 9 α x St 6: tt o th dig util ll ifitio t /6/4 todutio to Po otol Root Lou Dig thod Root lou i th t of vu of fo whih G( hold fo o oitiv l vu of G( htiti: Show how hg i th yt fdbk htiti d oth t iflu th ol lotio By tudyig th fft of dditiol ol d zo, th dig of dyi otio lo b odd h fft of zo i to ov th lou to th lft h fft of th ol i to th lou towd th ight Dig of ld d lg oto D((z/( with z <, D((z/( with z > /6/4 todutio to Po otol Pkowldg: Li lgb tix outtio Ltu: : todutio to Stt S Dig : otol Dig fo Full Stt Fdbk 3: Etito Dig 4: todutio of th Rf ut 5: tgl otol d Robut kig od otol thoy (tt doi ott: thtil odl of L yt: SS, SSF Pol igt though full tt fdbk: otollbility, otol oil fo, Stt Etito dig: obvbility, otol dig bd o tito: tio iil todutio of f iut: Zo igt tito, utooou tito, tkig o tito tgl otol ASD tlb/siulik /6/4 todutio to Po otol f Futio fo Stt Equtio fo futio X AX BU Y X DU Y ( G ( ( A U ( Stt ditio X AX BU Y X DU Eigvlu of A ig(a iio zo tzo(a,b,,d [A,B,,D] tf(u,de [U,DE] tf(a,b,,d A B dt D G ( dt( A B D fquy o ditio Pol of G( oot(doito Zo of G( oot(uto /6/4 todutio to Po otol 3 otollbility A L yt i otollbl if d oly if [B AB A B A B ] i full ow k Ftu of otollbility f th yt i otollbl, th th yt b tfod ito otol oil fo; oigul li tfotio do ot hg th yt otollbility; otollbility ot b didd fo th tf futio; f th yt i otollbl, th th lodloo yt ol b ut i y bity lotio though tt fdbk; ol igt /6/4 todutio to Po otol 4 4

5 Pol Plt though Stt Fdbk Poditio: h oidd yt i otollbl Au th did htiti qutio of th lodloo G ( ( d ( L( St : otut olyoil of tix vibl σ ( A A α A α A L α St : lult th otollbility tix [B AB A B A B ] α α L St 3: lult th gi vto [ k k k ] though XAXBu [ L ] σ ( A X ( A B X BU ux Y X dt( ( A B /6/4 todutio to Po otol 5 α k k(a,b, l(a,b,; Objtiv Etit th yt tt though th outut d iut igl Etito Stutu l A Bu L( y wh L, d X AX BU Y X l (A,B (A,B Eo Equtio Etito Dig X( L Y( ~ ~ X ( A L X, dt( ( A L /6/4 todutio to Po otol 6 Obvbility Obvbility h oidd yt i lld obvbl if d oly if th obvbility tix i full olu k: obvbil ity tix A : O A Etito Gi Dig (Ak tito foul St : otut olyoil of tix vibl σ ( A A α A α A L α St : lult th obvbility tix St 3: lult th gi vto L [ l l l ] though σ ( A O /6/4 todutio to Po otol 7 A O A Dulity of Etitio d otol otol obl to lt ow tix fo tifoty lt of th ol of th yt tix AB otollbility tix [B AB A B A B ] Ak otol foul [ L ] σ ( A Etitio obl to lt olu tix L fo tifoty lt of th ol of th yt tix AL A Obvbility tix O O A Ak tito foul L σ ( A O Dulity: otol obl: A, A, B, B, Etitio ol: A,,,, B Lk(A,, /6/4 todutio to Po otol 8 obid otol Lw d Etito todutio of th Rf ut Plt X AX Bu So YX XAXBu y otoll Etito A Bu L( y A B x x A B D u u D u u ( X x X ( u x X lod loo yt d ol X A B B X ~ ~ Stio iil X A L X ( A B B dt( dt( ( dt( ( ( A B A L A L /6/4 todutio to Po otol 9 Plt X & AX Bu otoll So YX Etito X ( A B L Ly /6/4 todutio to Po otol 3 ˆ 5

6 How to dti th t,? Zo igt tito: Objtiv: ll zo of th lod loo b igd Poditio: (ABL, i obvbl Y ( γ ( b( f futio: ( R( α( α( α( : olyoil ult i tito gi L, i, dt (AL α( : olyoil ult i otol gi, i, dt (AB b( : ogil lt zo olyoil γ ( : did zo olyoil γ ( dt( ( A B L : totl yt gi Autooou tito: Etito o i iddt of Y ( b( ( R( α ( B Plt X AX Bu otoll So YX Etito X ( A L Bu Ly /6/4 todutio to Po otol 3 ˆ How to dti th t,? kigeo Etito : otol dig wh th o u oly th outut o Stutu: Ld oto i th fowd th f futio: zo dd o th ltio of d L, L Plt X AX Bu otoll Y ( γ ( b( ( R( α ( α ( ( A B L L dt( γ ( So YX Etito ( A B L L( y /6/4 todutio to Po otol 3 / ugtl tt qutio with itgl fdbk lw with itgl otol : u tgl otol XAXBu f X& otol : X& X [ f ] X X u A X B htiti: obut h lod loo yt tk odyig iut with zo tttt o d jt odyig ditub with zo tdytt o y LQR Otil otol Li Qudti Rgultig (LQR otil otol Otil idx: ij( U ( X QX U RU dt U Otil otol: U( X( R BPX( Algbi Riti q: PA A P PBR B P Q [,S,] lq(a,b,q,r lult th otil gi tix uh tht th ttfdbk ux, iiiz th qudti ot futio XAXBu ux /6/4 todutio to Po otol 33 /6/4 todutio to Po otol 34 otol utoil fo tlb htt://wwwgiuihdu/gou/ t/hotxthtl /6/4 todutio to Po otol 35 6

Chapter 3 Higher Order Linear ODEs

Chapter 3 Higher Order Linear ODEs ht High Od i ODEs. Hoogous i ODEs A li qutio: is lld ohoogous. is lld hoogous. Tho. Sus d ostt ultils of solutios of o so o itvl I gi solutios of o I. Dfiitio. futios lld lil iddt o so itvl I if th qutio

More information

Chapter 6 Perturbation theory

Chapter 6 Perturbation theory Ct 6 Ptutio to 6. Ti-iddt odgt tutio to i o tutio sst is giv to fid solutios of λ ' ; : iltoi of si stt : igvlus of : otool igfutios of ; δ ii Rlig-Södig tutio to ' λ..6. ; : gl iltoi ': tutio λ : sll

More information

Three Phase Asymmetrical Load Flow for Four-Wire Distribution Networks

Three Phase Asymmetrical Load Flow for Four-Wire Distribution Networks T Aytl Lo Flow o Fou-W Dtuto Ntwo M. Mo *, A. M. Dy. M. A Dtt o Eltl E, A Uvty o Toloy Hz Av., T 59, I * El: o8@yoo.o Att-- Mjoty o tuto two ul u to ul lo, yty to l two l ut. T tt o tuto yt ult y o ovt

More information

264m. Raggengill Gilkerscleuch. Abington. 250m. Cottage. Iss. Mast. 246m. TER R AC E 240m OO KE TE H U N TE COLEBROOKE. Over Abington STATION.

264m. Raggengill Gilkerscleuch. Abington. 250m. Cottage. Iss. Mast. 246m. TER R AC E 240m OO KE TE H U N TE COLEBROOKE. Over Abington STATION. I 4 4 I I L KY t lttio F 9 ott v bito 4 4 F L ii 3 lui 1 p F L F I I 9 F L I LK i i tip i 9 6 v bito U l K L 6 ott bito i 5 1 5 9 i oo 8 4 6 otl it o ov b i o 116-3 ott 6 i i ollt u o v bito 4 lo i 6 v

More information

MM1. Introduction to State-Space Method

MM1. Introduction to State-Space Method MM Itroductio to Stt-Spc Mthod Wht tt-pc thod? How to gt th tt-pc dcriptio? 3 Proprty Alyi Bd o SS Modl Rdig Mtril: FC: p469-49 C: p- /4/8 Modr Cotrol Wht th SttS tt-spc Mthod? I th tt-pc thod th dyic

More information

INSTITUTIONAL DEVELOPMENT PLAN & LAWRENCE PUBLIC LIBRARY EXPANSON 707 VERMONT STREET LAWRENCE, KS SITE PLAN FOR LOCATION MAP SP-1

INSTITUTIONAL DEVELOPMENT PLAN & LAWRENCE PUBLIC LIBRARY EXPANSON 707 VERMONT STREET LAWRENCE, KS SITE PLAN FOR LOCATION MAP SP-1 OTIO -1 ITITUTIO VOT & IT O UI IY XO 0 VOT TT, -2 0 VOT TT, UI IY XO O ITITUTIO VOT & IT IT TI IITIO - ITITUTIO VOT & IT O UI IY XO 0 VOT TT, V '0" + 1' '0" '0" O " I YO IT TI, 20, V 2 '0" O, I U, I OTIU

More information

Noise in electronic components.

Noise in electronic components. No lto opot5098, JDS No lto opot Th PN juto Th ut thouh a PN juto ha fou opot t: two ffuo ut (hol fo th paa to th aa a lto th oppot to) a thal at oty ha a (hol fo th aa to th paa a lto th oppot to, laka

More information

Easy Steps to build a part number... Tri-Start Series III CF P

Easy Steps to build a part number... Tri-Start Series III CF P ulti-l i Oti iul ( oto) ow to O ol os sy ts to uil t u... i-tt is 1. 2 3 4. 5. 6. oto y til iis ll tyl ll iz- st t ott y & y/ ywy ositio 50 9 0 17-08 ol ulti-l i oti otos o us wit ulti-o sil o tii o y

More information

Classical Theory of Fourier Series : Demystified and Generalised VIVEK V. RANE. The Institute of Science, 15, Madam Cama Road, Mumbai

Classical Theory of Fourier Series : Demystified and Generalised VIVEK V. RANE. The Institute of Science, 15, Madam Cama Road, Mumbai Clssil Thoy o Foi Sis : Dmystii Glis VIVEK V RANE Th Istitt o Si 5 Mm Cm Ro Mmbi-4 3 -mil ss : v_v_@yhoooi Abstt : Fo Rim itgbl tio o itvl o poit thi w i Foi Sis t th poit o th itvl big ot how wh th tio

More information

fo=^i^oj=i mlto=i `ljjrf`^qflp=i o^i=lqp YOL TO H T xx xx xx xx L UO/UL UTO, OUT T +7'-0" O 6" LOW H L, WHH LOW. UT U T TO L T. L UL TO UTO, OUT T +7'-0" O 6" LOW H L, WHH LOW. UT U T TO L T. L UO/UL UTO,

More information

176 5 t h Fl oo r. 337 P o ly me r Ma te ri al s

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

More information

JHC series electrical connector

JHC series electrical connector i lil oo i iouio oli wi I-- Ⅲ i i- ui ouli wi i-looi i ll iz, li i wi, i o iy I/I ili ovl i o, oo-oo i ii i viio u i u, li i vio li wi,, oi,. liio: i il ii [il] oui: luiu lloy, il l li: - y iu li lol il

More information

IJRET: International Journal of Research in Engineering and Technology eissn: pissn:

IJRET: International Journal of Research in Engineering and Technology eissn: pissn: IJRE: Iiol Joul o Rh i Eii d holo I: 39-63 I: 3-738 VRIE OF IME O RERUIME FOR ILE RDE MOWER EM WI DIFFERE EO FOR EXI D WO E OF DEIIO VI WO REOLD IVOLVI WO OMOE. Rvihd. iiv i oo i Mhi R Eii oll RM ROU ih

More information

VICTORIA AVE. Chip pawa- Gra ss Isl and Pool. Ice Dam Niagara Falls WTP and Intake. Chippawa. Cree

VICTORIA AVE. Chip pawa- Gra ss Isl and Pool. Ice Dam Niagara Falls WTP and Intake. Chippawa. Cree 656 g 477 Y EL IZ B H Y GRN ILN 476 476 B E w R N OOM R MONROE R EE NI G NIGR FLL l 9 E R R E IN EK w l l d Riv RE Nv Ic m g Fll P d It E N ip pw- G Il d Pool Riv NIE MLEO R PK u t o-i pp w Po w l 477

More information

T h e C S E T I P r o j e c t

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

More information

30th 30th 29th 28th. 27th. Easte Rail. Howard. 25th. 2th. river Whiteriv Wh. Aca. 21st. 18th. 16th Anvil View. Prefontaine. Rif. Rifle.

30th 30th 29th 28th. 27th. Easte Rail. Howard. 25th. 2th. river Whiteriv Wh. Aca. 21st. 18th. 16th Anvil View. Prefontaine. Rif. Rifle. RFTA REGIOAL IYLE, EDETRIA AD TRAIT AE LA Ri Til vi imtt li ug tw 3 Rifl Rifl w li t ill ilt Rig F Ttti Auit iccl ti t l D 3 3 2 2 t R Et Ril il t 2t v i w 2 ci Ac t v 2 iv itiv F t w 2 24 Rifl ig cl cl

More information

SCHEMATIC SYMBOLS AMP METER MASTER RESCUE ASSISTANCE INTERCOM SYSTEM STATION CIRCUIT BREAKER CIRCUIT BREAKER (GFI) GFI CONTACT (N.C.) CONTACT (N.O.

SCHEMATIC SYMBOLS AMP METER MASTER RESCUE ASSISTANCE INTERCOM SYSTEM STATION CIRCUIT BREAKER CIRCUIT BREAKER (GFI) GFI CONTACT (N.C.) CONTACT (N.O. YO & VITIO I YO ITO (I) OTO OO O TTO O IT TTO O OTO T TTO I T IT ITO YT TTIO O I IT TTIO OTOIZ OTO OTT Y O TTO O TTO (T) T TTO I 000 TI YO T IIT IIT (I) OTT (..) OTT (.O.) OTT (OT,..) OTT (OT,.O.) IOT

More information

TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS

TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS UNIT-I PARTIAL DIFFERENTIAL EQUATIONS PART-A. Elimit th ritrry ott & from = ( + )(y + ) Awr: = ( + )(y + ) Diff prtilly w.r.to & y hr p & q y p = (y + ) ;

More information

Daily Skill Practice

Daily Skill Practice G CD-0 Dily Skill Pti 00 Wkk ## W i t it Eh. gh y w m y il A ll? + = 8 Dy 8= 0. =. Nm. C h l lit tl k ty i g. I h hi ty w ig h, m y hw hi g w ig h?. W Wkk ##00 A A = t, >, = W it < t t m t m k t. Dy Dy

More information

Relation of Finite Mellin Integral Transform. with Laplace and Fourier Transforms

Relation of Finite Mellin Integral Transform. with Laplace and Fourier Transforms Cotmpo Egiig Si Vol. 4 o. 6 69-88 Rltio o Fiit Mlli Itgl Tom with Lpl d Foui Tom S. M. Khi R. M. Pi* d J. N. Sluk** Dptmt o Mthmti Mhht Adm o Egiig Aldi-45Pu Idi mkhi7@gmil.om *Dptmt o Mthmti (A.S.&H.

More information

NO REGISTRATION FOR U.S. REDS TONIGHT IN FEE

NO REGISTRATION FOR U.S. REDS TONIGHT IN FEE H ' f l f J l l : l - -G I H IG U IV I Y L Vl 8 l L : l «GII U D IGH I V I Y U l l f ffl U l J f l f f U " ll ff f ll l x f ffl " ff l f f I " I l l ffl ff " " f l f ll " " I l f f l J ff l " " I f ll

More information

Order Reduction of Linear High-Order Discrete Time Systems Using Polynomial Differentiation Technique in w-domain and PID Controller Design

Order Reduction of Linear High-Order Discrete Time Systems Using Polynomial Differentiation Technique in w-domain and PID Controller Design Ittiol Joul of Eltoi Eltil Egiig ISSN 97-7 Volum 5, Num, pp 7-5 Ittiol Rsh Pulitio Hous http://iphousom O Rutio of Li High-O Dist Tim Systms Usig Polyomil Difftitio Thiqu i -Domi PID Cotoll Dsig B Stish

More information

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 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

More information

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 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

More information

Call for Applications

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

More information

The Reign of Grace and Life. Romans 5:12-21 (5:12-14, 17 focus)

The Reign of Grace and Life. Romans 5:12-21 (5:12-14, 17 focus) Th Rig of Gc d Lif Rom 5:12-21 (5:12-14, 17 focu) Th Ifluc of O h d ud Adolph H J o ph Smith B i t l m t Fid Idi Gdhi Ci Lu Gu ich N itz y l M d i M ch Nlo h Vig T L M uhmmd B m i o t T Ju Chit w I N h

More information

Beechwood Music Department Staff

Beechwood Music Department Staff Beechwood Music Department Staff MRS SARAH KERSHAW - HEAD OF MUSIC S a ra h K e rs h a w t r a i n e d a t t h e R oy a l We ls h C o l le g e of M u s i c a n d D ra m a w h e re s h e ob t a i n e d

More information

KEB INVERTER L1 L2 L3 FLC - RELAY 1 COMMON I1 - APPROACH CLOSE 0V - DIGITAL COMMON FLA - RELAY 1 N.O. AN1+ - ANALOG 1 (+) CRF - +10V OUTPUT

KEB INVERTER L1 L2 L3 FLC - RELAY 1 COMMON I1 - APPROACH CLOSE 0V - DIGITAL COMMON FLA - RELAY 1 N.O. AN1+ - ANALOG 1 (+) CRF - +10V OUTPUT XT SSMLY MOL 00 (O FS) 00 (I- PT) 00 (SIGL SLI) WG O 0 0-0 0-0-0 0.0. 0 0-0 0-0-0 0 0-0 0-0-0 VOLTG F.L...0..0..0.0..0 IIG POW FOM US SUPPLI ISOT (S TL) US OP OUTOS T T 0 O HIGH H IUIT POTTIO OT: H IUIT

More information

National Survey of Student Engagement, Spring 2011 The University at Albany, SUNY

National Survey of Student Engagement, Spring 2011 The University at Albany, SUNY Ntil uvy f tudt Eggt, pig 11 T Uivity t Alby, UNY EXECUTIVE UMMARY Jl D. Bl, P.D. Dit f Adi At & uvy R I Fbuy d M 11, T Uivity t Alby ptiiptd i t Ntil uvy f tudt Eggt (NE) f t d ti, fllwig up u pviu ptiipti

More information

Gavilan JCCD Trustee Areas Plan Adopted November 10, 2015

Gavilan JCCD Trustee Areas Plan Adopted November 10, 2015 Gvil JCCD Tust A Pl Aopt Novmb, S Jos US p Ls Pl Aopt // Cit/Csus Dsigt Plc ighw Cit Aom ollist igm S Jos Ts Pios c Ps 4 ut S Bito ut ils Aom ollist igm Ts Pios S Bito ut Lpoff & Goblt Dmogphic sch, Ic.

More information

ROUTH-HURWITZ CRITERION

ROUTH-HURWITZ CRITERION Automti Cotrol Sytem, Deprtmet of Mehtroi Egieerig, Germ Jordi Uiverity Routh-Hurwitz Criterio ite.google.om/ite/ziydmoud 7 ROUTH-HURWITZ CRITERION The Routh-Hurwitz riterio i lytil proedure for determiig

More information

TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS

TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS UNIT-I PARTIAL DIFFERENTIAL EQUATIONS PART-A. Elimit th ritrry ott & from = ( + )(y + ) = ( + )(y + ) Diff prtilly w.r.to & y hr p & q p = (y + ) ; q = ( +

More information

CBSE SAMPLE PAPER SOLUTIONS CLASS-XII MATHS SET-2 CBSE , ˆj. cos. SECTION A 1. Given that a 2iˆ ˆj. We need to find

CBSE SAMPLE PAPER SOLUTIONS CLASS-XII MATHS SET-2 CBSE , ˆj. cos. SECTION A 1. Given that a 2iˆ ˆj. We need to find BSE SMLE ER SOLUTONS LSS-X MTHS SET- BSE SETON Gv tht d W d to fd 7 7 Hc, 7 7 7 Lt, W ow tht Thus, osd th vcto quto of th pl z - + z = - + z = Thus th ts quto of th pl s - + z = Lt d th dstc tw th pot,,

More information

VICTORIA AVE. Chippawa. Cree

VICTORIA AVE. Chippawa. Cree 656 Nig MLEOD RD 477 Riv AE ANA ip pw- G Il d Pool Nv Ic Dm Nig Fll P d It NIE D w l l d Riv EL IZ AB H AY 476 476 B E GRAND ILAND N Y A EE w AR NI AG ODOM RD MONROE RD NIAGARA FALL l 9 E A R RD E IN EK

More information

Parametric Methods. Autoregressive (AR) Moving Average (MA) Autoregressive - Moving Average (ARMA) LO-2.5, P-13.3 to 13.4 (skip

Parametric Methods. Autoregressive (AR) Moving Average (MA) Autoregressive - Moving Average (ARMA) LO-2.5, P-13.3 to 13.4 (skip Pmeti Methods Autoegessive AR) Movig Avege MA) Autoegessive - Movig Avege ARMA) LO-.5, P-3.3 to 3.4 si 3.4.3 3.4.5) / Time Seies Modes Time Seies DT Rdom Sig / Motivtio fo Time Seies Modes Re the esut

More information

P a g e 3 6 of R e p o r t P B 4 / 0 9

P a g e 3 6 of R e p o r t P B 4 / 0 9 P a g e 3 6 of R e p o r t P B 4 / 0 9 p r o t e c t h um a n h e a l t h a n d p r o p e r t y fr om t h e d a n g e rs i n h e r e n t i n m i n i n g o p e r a t i o n s s u c h a s a q u a r r y. J

More information

fur \ \,,^N/ D7,,)d.s) 7. The champion and Runner up of the previous year shall be allowed to play directly in final Zone.

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

More information

Handout on. Crystal Symmetries and Energy Bands

Handout on. Crystal Symmetries and Energy Bands dou o Csl s d g Bds I hs lu ou wll l: Th loshp bw ss d g bds h bs of sp-ob ouplg Th loshp bw ss d g bds h ps of sp-ob ouplg C 7 pg 9 Fh Coll Uvs d g Bds gll hs oh Th sl pol ss ddo o h l slo s: Fo pl h

More information

2.Decision Theory of Dependence

2.Decision Theory of Dependence .Deciio Theoy of Depedece Theoy :I et of vecto if thee i uet which i liely depedet the whole et i liely depedet too. Coolly :If the et i liely idepedet y oepty uet of it i liely idepedet. Theoy : Give

More information

CBSE , ˆj. cos CBSE_2015_SET-1. SECTION A 1. Given that a 2iˆ ˆj. We need to find. 3. Consider the vector equation of the plane.

CBSE , ˆj. cos CBSE_2015_SET-1. SECTION A 1. Given that a 2iˆ ˆj. We need to find. 3. Consider the vector equation of the plane. CBSE CBSE SET- SECTION. Gv tht d W d to fd 7 7 Hc, 7 7 7. Lt,. W ow tht.. Thus,. Cosd th vcto quto of th pl.. z. - + z = - + z = Thus th Cts quto of th pl s - + z = Lt d th dstc tw th pot,, - to th pl.

More information

The tight-binding method

The tight-binding method Th tight-idig thod Wa ottial aoach: tat lcto a a ga of aly f coductio lcto. ow aout iulato? ow aout d-lcto? d Tight-idig thod: gad a olid a a collctio of wa itactig utal ato. Ovla of atoic wav fuctio i

More information

LOWELL LEDGER. INDEPEMDEWT-MOT NEUTRAL, EDELNANN & NERRETER

LOWELL LEDGER. INDEPEMDEWT-MOT NEUTRAL, EDELNANN & NERRETER \ ^K H LOLL LDG X U DD-O UL F VOL X O 7 OFFL LOLL HG HU OO 2 905 V G ULO X 9 0 4 3 5 9 HLL & O H «- 50( K Y D Q - q O ^ - Y - Y F 8 2 H U H O H 4 2 4 U L V O - F 0 L O ( j L O GUH H HO HO H x q L - D OLV

More information

c. What is the average rate of change of f on the interval [, ]? Answer: d. What is a local minimum value of f? Answer: 5 e. On what interval(s) is f

c. What is the average rate of change of f on the interval [, ]? Answer: d. What is a local minimum value of f? Answer: 5 e. On what interval(s) is f Essential Skills Chapter f ( x + h) f ( x ). Simplifying the difference quotient Section. h f ( x + h) f ( x ) Example: For f ( x) = 4x 4 x, find and simplify completely. h Answer: 4 8x 4 h. Finding the

More information

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! 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

More information

Control Systems. Lecture 8 Root Locus. Root Locus. Plant. Controller. Sensor

Control Systems. Lecture 8 Root Locus. Root Locus. Plant. Controller. Sensor Cotol Syt ctu 8 Root ocu Clacal Cotol Pof. Eugo Schut hgh Uvty Root ocu Cotoll Plat R E C U Y - H C D So Y C C R C H Wtg th loo ga a w a ttd tackg th clod-loo ol a ga va Clacal Cotol Pof. Eugo Schut hgh

More information

Grilled it ems are prepared over real mesquit e wood CREATE A COMBO STEAKS. Onion Brewski Sirloin * Our signature USDA Choice 12 oz. Sirloin.

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

More information

OVER 150 J-HOP To Q JCATS S(MJ) BY NOON TUESDAY CO-ED S LEAGUE HOLDS MEETING

OVER 150 J-HOP To Q JCATS S(MJ) BY NOON TUESDAY CO-ED S LEAGUE HOLDS MEETING F F V à y y > * y y y! F! * * F k y è 2 3 U D Y F B U Y 3 * 93 G U P B PU FF; JH H D V 50 JHP QJ (J) BY UDY P G y D; P U F P 0000 GUU VD PU F B U q F' yyy " D Py D x " By ; B x; x " P 93 ; Py y y F H j

More information

LLOQ=UWQOW=^j @ LOW O LOO O U L U LO U O OOLL L L LOW U O O LO OUU O OOLL U O UO UO UX UXLY UL UOO Y Y U O OOLL O Y OUU O OOLL U L U U L U OU OO O W U O W ULY U U W LL W U W LL W ULY ULO K U L L L OOL

More information

The Performance of Feedback Control Systems

The Performance of Feedback Control Systems The Performace of Feedbac Cotrol Sytem Objective:. Secify the meaure of erformace time-domai the firt te i the deig roce Percet overhoot / Settlig time T / Time to rie / Steady-tate error e. ut igal uch

More information

LWC 434 East First Street 4440 Garwood Place

LWC 434 East First Street 4440 Garwood Place //0 :: UI IXTUS TO US IIT TOS O T IST UTU I TOY IST OW - ITIO UTUS IST I TSIS. I ST (O, ZU). cui (, ZU). TOTO (OI, O). SO (ZU, Y). TUO (SO, ZU). TOTO (O US). IS (OSOIT, U). UST (ST WIIS, ZU). Y (T&S SS,

More information

New Advanced Higher Mathematics: Formulae

New Advanced Higher Mathematics: Formulae Advcd High Mthmtics Nw Advcd High Mthmtics: Fomul G (G): Fomul you must mmois i od to pss Advcd High mths s thy ot o th fomul sht. Am (A): Ths fomul giv o th fomul sht. ut it will still usful fo you to

More information

fnm 'et Annual Meeting

fnm 'et Annual Meeting UUVtK Ht.t, A 0 8 4 S.. Rittin Nub t, n L Y t U N i, n ' A N n, t\ V n b n k pny' ull N) 0 R Z A L A V N U X N S N R N R H A V N U R A P A R K A L A N Y Buin Add. N. Stt ity wn / Pvin) Ali l) lil tal?l

More information

Chapter 1 Fundamentals in Elasticity

Chapter 1 Fundamentals in Elasticity Fs s ν . Po Dfo ν Ps s - Do o - M os - o oos : o o w Uows o: - ss - - Ds W ows s o qos o so s os. w ows o fo s o oos s os of o os. W w o s s ss: - ss - - Ds - Ross o ows s s q s-s os s-sss os .. Do o ..

More information

On the convergence of solutions of the non-linear differential equation

On the convergence of solutions of the non-linear differential equation MEMOIRS O F T H E COLLEGE O F SCIENCE, UNIVERSITY OF KYOTO, SERIES A Vol. XXVIII, Mathematics No. 2, 1953. On the convergence of solutions of the non-linear differential equation By Taro YOSHIZAWA (Received

More information

ATTACHMENT 5 RESOLUTION OF THE BOARD OF SUPERVISORS COUNTY OF SANTA BARBARA, STATE OF CALIFORNIA

ATTACHMENT 5 RESOLUTION OF THE BOARD OF SUPERVISORS COUNTY OF SANTA BARBARA, STATE OF CALIFORNIA TTHT 5 I F TH F UI Y F T TT F IFI I TH TT F TI IFI ) I. 15 - T T TH U T F ) TH T Y HI ) : 14-00000-00019 Y TH TI F TH T ) T Y UITY. ) ITH F T TH FI:. 20 1980. 80-566 f U f.. J 20 1993. 93-401 f.. T q f

More information

Helping every little saver

Helping every little saver Spt th diffc d cut hw u c fid I c spt thigs! Hlpig v littl sv Hw d u p i? I ch Just pp it f u chs. T fid u lcl ch just visit s.c.uk/ch If u pig i chqu, it c tk ud 4 wkig ds t cl Ov th ph Just cll Tlph

More information

BLUE LINE TROLLEY STATION IMPROVEMENTS

BLUE LINE TROLLEY STATION IMPROVEMENTS TUT GT DD T T TUT HU GT WTH HG GHT G TZ # - + V Y 0/00 HZ GT WTH HG - + = U& PV-50 #555- P JUT X GHT G & DD. HG GHT D P UT UT Y TW P GT WTH HG GHT G & P DT P UT # - + U& P-50 #500-0 UT Y W/HVY DUTY TT

More information

CONSTRUCTION DOCUMENTS

CONSTRUCTION DOCUMENTS //0 :: 0 0 OV Y T TY O YTO: TY O YTO W # : U.. O OVTO 00 WT V V, OO OTUTO OUT U 0, 0 UTO U U \\d\ayton rojects\ayton nternational irport\.00 Y ustoms acility\\rchitecture\ rocessing enovation_entral.rvt

More information

Rectangular Waveguides

Rectangular Waveguides Rtgulr Wvguids Wvguids tt://www.tllguid.o/wvguidlirit.tl Uss To rdu ttutio loss ig rquis ig owr C ort ol ov rti rquis Ats s ig-ss iltr Norll irulr or rtgulr W will ssu losslss rtgulr tt://www..surr..u/prsol/d.jris/wguid.tl

More information

". :'=: "t',.4 :; :::-':7'- --,r. "c:"" --; : I :. \ 1 :;,'I ~,:-._._'.:.:1... ~~ \..,i ... ~.. ~--~ ( L ;...3L-. ' f.':... I. -.1;':'.

. :'=: t',.4 :; :::-':7'- --,r. c: --; : I :. \ 1 :;,'I ~,:-._._'.:.:1... ~~ \..,i ... ~.. ~--~ ( L ;...3L-. ' f.':... I. -.1;':'. = 47 \ \ L 3L f \ / \ L \ \ j \ \ 6! \ j \ / w j / \ \ 4 / N L5 Dm94 O6zq 9 qmn j!!! j 3DLLE N f 3LLE Of ADL!N RALROAD ORAL OR AL AOAON N 5 5 D D 9 94 4 E ROL 2LL RLLAY RL AY 3 ER OLLL 832 876 8 76 L A

More information

Federal Project No.: To be assigned

Federal Project No.: To be assigned TTE ID FO O TNOTTION.Jl D INII EIINY DETEINTION EQET F, ti, illif tfl f f : -- Fl jt N.: T b i t: T i (T) t t : F: Jff i (xitl. il t f T ) T: Xl (xitl. il t f T ) T : F: xitl. il t f t T: T (xitl. il t

More information

Using the Rational Root Theorem to Find Real and Imaginary Roots Real roots can be one of two types: ra...-\; 0 or - l (- - ONLl --

Using the Rational Root Theorem to Find Real and Imaginary Roots Real roots can be one of two types: ra...-\; 0 or - l (- - ONLl -- Using the Rational Root Theorem to Find Real and Imaginary Roots Real roots can be one of two types: ra...-\; 0 or - l (- - ONLl -- Consider the function h(x) =IJ\ 4-8x 3-12x 2 + 24x {?\whose graph is

More information

The Z transform techniques

The Z transform techniques h Z trnfor tchniqu h Z trnfor h th rol in dicrt yt tht th Lplc trnfor h in nlyi of continuou yt. h Z trnfor i th principl nlyticl tool for ingl-loop dicrt-ti yt. h Z trnfor h Z trnfor i to dicrt-ti yt

More information

MA 201, Mathematics III, July-November 2018, Laplace Transform (Contd.)

MA 201, Mathematics III, July-November 2018, Laplace Transform (Contd.) MA 201, Mathematics III, July-November 2018, Laplace Transform (Contd.) Lecture 19 Lecture 19 MA 201, PDE (2018) 1 / 24 Application of Laplace transform in solving ODEs ODEs with constant coefficients

More information

Chapter #3 EEE Subsea Control and Communication Systems

Chapter #3 EEE Subsea Control and Communication Systems EEE 87 Chter #3 EEE 87 Sube Cotrol d Commuictio Sytem Cloed loo ytem Stedy tte error PID cotrol Other cotroller Chter 3 /3 EEE 87 Itroductio The geerl form for CL ytem: C R ', where ' c ' H or Oe Loo (OL)

More information

CATAVASII LA NAȘTEREA DOMNULUI DUMNEZEU ȘI MÂNTUITORULUI NOSTRU, IISUS HRISTOS. CÂNTAREA I-A. Ήχος Πα. to os se e e na aș te e e slă ă ă vi i i i i

CATAVASII LA NAȘTEREA DOMNULUI DUMNEZEU ȘI MÂNTUITORULUI NOSTRU, IISUS HRISTOS. CÂNTAREA I-A. Ήχος Πα. to os se e e na aș te e e slă ă ă vi i i i i CATAVASII LA NAȘTEREA DOMNULUI DUMNEZEU ȘI MÂNTUITORULUI NOSTRU, IISUS HRISTOS. CÂNTAREA I-A Ήχος α H ris to os s n ș t slă ă ă vi i i i i ți'l Hris to o os di in c ru u uri, în tâm pi i n ți i'l Hris

More information

Crowds of eager worshippers trooping into the venue

Crowds of eager worshippers trooping into the venue LvWld Cv A lld y F uv Fdy m Juy ldg wk Fbuy, ud l gd LvWld Cv A Lg, Ng, l lg mg w P C ggd, Am F Ml Lv. Hly G-dzvu w Ld' y my. Adg P C, dd' ll mg. Ld lly lld m...h d l; w H wd. Cwd g w g vu AN APPNMEN WH

More information

TV Breakaway Fail-Safe Lanyard Release Plug Military (D38999/29 & D38999/30)

TV Breakaway Fail-Safe Lanyard Release Plug Military (D38999/29 & D38999/30) y il- y l l iliy (/9 & /0) O O O -..... 6.. O ix i l ll iz y o l yi oiio / 9. O / i --, i, i- oo. i lol il l li, oi ili i 6@0 z iiio i., o l y, 00 i ooio i oli i l li, 00 o x l y, 0@0 z iiio i.,. &. ll

More information

ADDENDUM NO.1 July 22, The City University of New York Request for Proposals. Student Housing Project Project No. CU

ADDENDUM NO.1 July 22, The City University of New York Request for Proposals. Student Housing Project Project No. CU DDDUM.1 uly 22, 2008 y Uy w Yk u l ud Hug j j. U800008 dddu ud u dg lly llwg du www.uy.du/udug. du : l uly 10, 2008 d l uly 10, 2008. w 10 (Gl d d, ll dd d gd u ly d d d l g. g y ly d y l d d w ud. : Ml

More information

Analytical Evaluation of Multicenter Nuclear Attraction Integrals for Slater-Type Orbitals Using Guseinov Rotation-Angular Function

Analytical Evaluation of Multicenter Nuclear Attraction Integrals for Slater-Type Orbitals Using Guseinov Rotation-Angular Function I. J. Cop. Mh. S Vo. 5 o. 7 39-3 Ay Evuo of Mu u Ao Ig fo S-yp O Ug Guov Roo-Agu uo Rz Y M Ag Dp of Mh uy of uo fo g A-Khj Uvy Kgo of Su A Dp of Mh uy of S o B Auh Uvy Kgo of Su A A. Ug h Guov oo-gu fuo

More information

READ T H E DATE ON LABEL A blue m a r k a r o u n d this notice will call y o u r attention to y o u r LOWELL. MICHIGAN, THURSDAY, AUGUST 29.

READ T H E DATE ON LABEL A blue m a r k a r o u n d this notice will call y o u r attention to y o u r LOWELL. MICHIGAN, THURSDAY, AUGUST 29. B U D D B < / UDY UU 29 929 VU XXXV Y B 5 2 $25 25 25 U 6 B j 3 $8 D D D VD V D D V D B B % B 2 D - Q 22: 5 B 2 3 Z D 2 5 B V $ 2 52 2 $5 25 25 $ Y Y D - 8 q 2 2 6 Y U DD D D D Y!! B D V!! XU XX D x D

More information

Stanford University Medical Center

Stanford University Medical Center tanford University Medical enter VTO TTIO 00 Pasteur rive, tanford, 940 G I I G O T POF T U IO 6 exp /09 I T U I F O 6 IGIGWOO O MTO, IFOI 9864 GI I Y @ MY T TI OT OUTWIGHT IMT IM TW GUII H XITIG VTO XPIO

More information

Exam 2 Solutions. Jonathan Turner 4/2/2012. CS 542 Advanced Data Structures and Algorithms

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

More information

THIS PAGE DECLASSIFIED IAW E

THIS PAGE DECLASSIFIED IAW E THS PAGE DECLASSFED AW E0 2958 BL K THS PAGE DECLASSFED AW E0 2958 THS PAGE DECLASSFED AW E0 2958 B L K THS PAGE DECLASSFED AW E0 2958 THS PAGE DECLASSFED AW EO 2958 THS PAGE DECLASSFED AW EO 2958 THS

More information

For H. S. Athletes. 49 Boy Scouts Initiated Here

For H. S. Athletes. 49 Boy Scouts Initiated Here LD B V L LY L L ( 700 v v v * x Dv L v v B v «v U B v z v v- - - v v v 0 v D U v v v v B X v x v v U v v 0000 v 0000 v x v v U ) YU > v v v v YD L Y x v q -z : v v v v v x v v B L L Y-D LLL Y X L DD UDY

More information

-Z ONGRE::IONAL ACTION ON FY 1987 SUPPLEMENTAL 1/1

-Z ONGRE::IONAL ACTION ON FY 1987 SUPPLEMENTAL 1/1 -Z-433 6 --OGRE::OA ATO O FY 987 SUPPEMETA / APPR)PRATO RfQUEST PAY AD PROGRAM(U) DE ARTMET OF DEES AS O' D 9J8,:A:SF ED DEFS! WA-H ODM U 7 / A 25 MRGOPf RESOUTO TEST HART / / AD-A 83 96 (~Go w - %A uj

More information

St ce l. M a p le. Hubertus Rd. Morgan. Beechwood Industrial Ct. Amy Belle Lake Rd. o o. Am Bell. S Ridge. Colgate Rd. Highland Dr.

St ce l. M a p le. Hubertus Rd. Morgan. Beechwood Industrial Ct. Amy Belle Lake Rd. o o. Am Bell. S Ridge. Colgate Rd. Highland Dr. S l Tu pi Kli 4 Lil L ill ill ilfl L pl hi L E p p ll L hi i E: i O. Q O. SITO UKES Y Bll Sig i 7 ppl 8 Lill 9 Sh 10 Bl 11 ul 12 i 7 13 h 8 10 14 Shh 9 11 41 ill P h u il f uu i P pl 45 Oh P ig O L ill

More information

M5. LTI Systems Described by Linear Constant Coefficient Difference Equations

M5. LTI Systems Described by Linear Constant Coefficient Difference Equations 5. LTI Systes Descied y Lie Costt Coefficiet Diffeece Equtios Redig teil: p.34-4, 245-253 3/22/2 I. Discete-Tie Sigls d Systes Up til ow we itoduced the Fouie d -tsfos d thei popeties with oly ief peview

More information

The Real Hydrogen Atom

The Real Hydrogen Atom T Ra Hydog Ato ov ad i fist od gt iddt of :.6V a us tubatio toy to dti: agti ffts si-obit ad yfi -A ativisti otios Aso av ab sift du to to sfitatio. Nd QD Dia q. ad dds o H wavfutio at sou of ti fid. Vy

More information

MATH 104: INTRODUCTORY ANALYSIS SPRING 2009/10 PROBLEM SET 8 SOLUTIONS. and x i = a + i. i + n(n + 1)(2n + 1) + 2a. (b a)3 6n 2

MATH 104: INTRODUCTORY ANALYSIS SPRING 2009/10 PROBLEM SET 8 SOLUTIONS. and x i = a + i. i + n(n + 1)(2n + 1) + 2a. (b a)3 6n 2 MATH 104: INTRODUCTORY ANALYSIS SPRING 2009/10 PROBLEM SET 8 SOLUTIONS 6.9: Let f(x) { x 2 if x Q [, b], 0 if x (R \ Q) [, b], where > 0. Prove tht b. Solutio. Let P { x 0 < x 1 < < x b} be regulr prtitio

More information

Handout 7. Properties of Bloch States and Electron Statistics in Energy Bands

Handout 7. Properties of Bloch States and Electron Statistics in Energy Bands Hdout 7 Popts of Bloch Stts d Elcto Sttstcs Eg Bds I ths lctu ou wll l: Popts of Bloch fuctos Podc boud codtos fo Bloch fuctos Dst of stts -spc Elcto occupto sttstcs g bds ECE 407 Spg 009 Fh R Coll Uvst

More information

Series III, TV Breakaway Fail-Safe Connectors Quick-Disconnect with an Axial Pull of Lanyard

Series III, TV Breakaway Fail-Safe Connectors Quick-Disconnect with an Axial Pull of Lanyard is, wy il- otos Qui-isot wit xil ull o y ulo ss quo mol i-tt wy il- otos ovi uqul om i viomts quii istt ismt. wy il- oto mily os wi o ltil mil tus: stt ouli m stio omltly itmtl wit st tls (/20 /2) vtoy

More information

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 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

More information

APPH 4200 Physics of Fluids

APPH 4200 Physics of Fluids APPH 42 Physics of Fluids Problem Solving and Vorticity (Ch. 5) 1.!! Quick Review 2.! Vorticity 3.! Kelvin s Theorem 4.! Examples 1 How to solve fluid problems? (Like those in textbook) Ç"Tt=l I $T1P#(

More information

Design of Digital IIR Filters with the Advantages of Model Order Reduction Technique

Design of Digital IIR Filters with the Advantages of Model Order Reduction Technique Ittiol Joul of Elctoic Egiig Rch ISSN 975-65 Volu Nu 9. 89 Rch Ii Pulictio htt://www.iulictio.co/i.ht Dig of Digitl IIR Filt with th Atg of ol O Ructio Tchiqu K. Rh, A. Nilu 3.uuy Lctu i Dtt of Elcticl

More information

Executive Committee and Officers ( )

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

More information

OPTIMAL CONTROL. Sadegh Bolouki. Lecture slides for ECE 515. University of Illinois, Urbana-Champaign. Fall S. Bolouki (UIUC) 1 / 28

OPTIMAL CONTROL. Sadegh Bolouki. Lecture slides for ECE 515. University of Illinois, Urbana-Champaign. Fall S. Bolouki (UIUC) 1 / 28 OPTIMAL CONTROL Sadegh Bolouki Lecture slides for ECE 515 University of Illinois, Urbana-Champaign Fall 2016 S. Bolouki (UIUC) 1 / 28 (Example from Optimal Control Theory, Kirk) Objective: To get from

More information

/99 $10.00 (c) 1999 IEEE

/99 $10.00 (c) 1999 IEEE P t Hw Itt C Syt S 999 P t Hw Itt C Syt S - 999 A Nw Atv C At At Cu M Syt Y ZHANG Ittut Py P S, Uvty Tuu, I 0-87, J Att I t, w tv t t u yt x wt y tty, t wt tv w (LBSB) t. T w t t x t tty t uy ; tt, t x

More information

5. Identical Particles

5. Identical Particles Phy Qutu Mhi Tt P A Cdti f y t f th ti th tt wi v 5. Idti Pti 5. Tw-Pti yt Ciy Qutu Mhiy i t. t t dd * t t wh dd t. Ct ydg wh th t f th iti hd R wh R R t t. uti f f 5.. B d i Ditiguih ti & i tt d tivy

More information

Example: Two Stochastic Process u~u[0,1]

Example: Two Stochastic Process u~u[0,1] Co o Slo o Coco S Sh EE I Gholo h@h. ll Sochc Slo Dc Slo l h PLL c Mo o coco w h o c o Ic o Co B P o Go E A o o Po o Th h h o q o ol o oc o lco q ccc lco l Bc El: Uo Dbo Ucol Sl Ab bo col l G col G col

More information

ELECTROMAGNETISM, NUCLEAR STRUCTURES & GRAVITATION

ELECTROMAGNETISM, NUCLEAR STRUCTURES & GRAVITATION . l & a s s Vo Flds o as l axwll a l sla () l Fld () l olasao () a Flx s () a Fld () a do () ad è s ( ). F wo Sala Flds s b dd l a s ( ) ad oool a s ( ) a oal o 4 qaos 3 aabls - w o Lal osas - oz abo Lal-Sd

More information

G-001 CHATHAM HARBOR AUNT LYDIA'S COVE CHATHAM ATLANTIC OCEAN INDEX OF NAVIGATION AIDS GENERAL NOTES: GENERAL PLAN A6 SCALE: 1" = 500' CANADA

G-001 CHATHAM HARBOR AUNT LYDIA'S COVE CHATHAM ATLANTIC OCEAN INDEX OF NAVIGATION AIDS GENERAL NOTES: GENERAL PLAN A6 SCALE: 1 = 500' CANADA TR ISL ROR UST 8 O. R-2,4-3 R-4 IX O VITIO IS STT PL ORPI OORITS POSITIO 27698 4-39'-" 88 69-6'-4."W 278248 4-4'-" 8968 69-6'-4"W 27973 4-4'-2" 88 69-6'-"W W MPSIR OOR UUST PORTL MI OR 27 8-OOT OR L -

More information

Creative Office / R&D Space

Creative Office / R&D Space Ga 7th A t St t S V Nss A issi St Gui Stt Doos St Noiga St Noiga St a Csa Chaz St Tava St Tava St 887 itt R Buig, CA 9400 a to Po St B i Co t Au St B Juipo Sa B sb A Siv Si A 3 i St t ssi St othhoo Wa

More information

Fuzzy Reasoning and Optimization Based on a Generalized Bayesian Network

Fuzzy Reasoning and Optimization Based on a Generalized Bayesian Network Fuy R O B G By Nw H-Y K D M Du M Hu Cu Uvy 48 Hu Cu R Hu 300 Tw. @w.u.u.w A By w v wy u w w uy. Hwv u uy u By w y u v w uu By w w w u vu vv y. T uy v By w w uy v v uy. B By w uy. T uy v uy. T w w w- uy.

More information

Available online Journal of Scientific and Engineering Research, 2016, 3(6): Research Article

Available online  Journal of Scientific and Engineering Research, 2016, 3(6): Research Article Av www.. Ju St E R, 2016, 3(6):131-138 R At ISSN: 2394-2630 CODEN(USA): JSERBR Cutvt R Au Su H Lv I y t Mt Btt M Zu H Ut, Su, W Hy Dtt Ay Futy Autu, Uvt Tw, J. Tw N. 9 P, 25136,Wt Sut, I, E-: 65@y. Att

More information

February 12 th December 2018

February 12 th December 2018 208 Fbu 2 th Dcb 208 Whgt Fbu Mch M 2* 3 30 Ju Jul Sptb 4* 5 7 9 Octob Novb Dcb 22* 23 Put ou blu bgs out v d. *Collctios d lt du to Public Holid withi tht wk. Rcclig wk is pik Rcclig wk 2 is blu Th stick

More information

Bayesian Credibility for Excess of Loss Reinsurance Rating. By Mark Cockroft 1 Lane Clark & Peacock LLP

Bayesian Credibility for Excess of Loss Reinsurance Rating. By Mark Cockroft 1 Lane Clark & Peacock LLP By Cly o c o Lo Rc Rg By M Coco L Cl & Pcoc LLP GIRO coc 4 Ac Th pp c how o v cly wgh w po- pc-v o c o lo c. Th po co o Poo-Po ol ch wh po G o. Kywo c o lo c g By cly Poo Po G po Acowlg cl I wol l o h

More information

NEWBERRY FOREST MGT UNIT Stand Level Information Compartment: 10 Entry Year: 2001

NEWBERRY FOREST MGT UNIT Stand Level Information Compartment: 10 Entry Year: 2001 iz oy- kg vg. To. 1 M 6 M 10 11 100 60 oh hwoo uvg N o hul 0 Mix bg. woo, moly low quliy. Coif ompo houghou - WP/hmlok/pu/blm/. vy o whi pi o h ouh fig of. iffiul o. Th o hi i o PVT l wh h g o wll big

More information