Linear System Review. Linear System Review. Descriptions of Linear Systems: 2008 Spring ME854 - GGZ Page 1

Size: px
Start display at page:

Download "Linear System Review. Linear System Review. Descriptions of Linear Systems: 2008 Spring ME854 - GGZ Page 1"

Transcription

1 8 Sprg ME854 - Z Pg r Sym Rvw r Sym Rvw r Sym Rvw crpo of r Sym: p m R y R R y FT : & U Y Trfr Fco : y or : & : d y d

2 r Sym Rvw orollbly d Obrvbly: fo 3.: FT dymc ym or h pr d o b corollbl f y l > d fl hr pcw coo p ch h h olo of h FT f. Ohrw h ym d o b corollbl. fo 3.3: FT dymc ym or h pr d o b blzbl f hr fdbck F ch h h ym bl.. F bl or RF <. ohr word ll corollbl mod r bl. 8 Sprg ME854 - Z r Sym Rvw Pg

3 r Sym Rvw Thorm 3.: Th followg r qvl: corollbl. Th mr pov df for y >. Th corollbly mr h fll row rk. W v Th mr [ - ] h fll row rk for ll. d [ ] v d b y gvl d y corrpodg lf gvcor of.. ; h v Th gvl of F c b frly gd wh h rrco h compl gvl r cojg pr by bl choc of F. 8 Sprg ME854 - Z r Sym Rvw Pg 3

4 8 Sprg ME854 - Z Pg 4 r Sym Rvw r Sym Rvw r Sym Rvw : Proof by cordco [ ] Th d df p for om Sppo W d d W W W c c c > >. w hv w hv ] [ ch h vcor rl hr for y Sc. glr for om corollbl d m h > v v v d v v v R v W :

5 r Sym Rvw Thorm 3.: Th followg r qvl: blzbl. v Th mr [ - ] h fll row rk for ll R. v d b y gvl d y corrpodg lf gvcor of.. ; h for ll R v Thr mr F ch h F bl 8 Sprg ME854 - Z r Sym Rvw Pg 5

6 r Sym Rvw orollbly d Obrvbly: fo 3.4: FT dymc ym or h pr d o b obrvbl f for y > h l c b drmd from h hory of h p d h op y h rvl of [ ]. Ohrw h ym d o b obrvbl. fo 3.5: FT dymc ym or h pr d o b dcbl f hr mr ch h bl or R <. ohr word ll obrvbl mod r bl. 8 Sprg ME854 - Z r Sym Rvw Pg 6

7 r Sym Rvw Thorm 3.3: Th followg r qvl: obrvbl. Th mr pov df for y >. Th obrvbly mr O h fll row rk. W O v Th mr [ - ] h fll row rk for ll. d v d y b y gvl d y corrpodg rgh gvcor of.. y y; h y [ ] v Th gvl of c b frly gd wh h rrco h compl gvl r cojg pr by bl choc of. 8 Sprg ME854 - Z r Sym Rvw Pg 7

8 r Sym Rvw Thorm 3.4: Th followg r qvl: dcbl. v Th mr [ - ] h fll row rk for ll R. v d y b y gvl d y corrpodg rgh gvcor of.. y y; h y for ll R v Thr mr ch h bl v blzbl fo 3.6: b gvl of or qvlly mod of h ym. Th h mod d o b corollbl obrvbl f y for ll lf rgh gvcor of ocd wh ; h y y d y. Ohrw h mod d corollbl obrvbl. 8 Sprg ME854 - Z r Sym Rvw Pg 8

9 8 Sprg ME854 - Z Pg 9 r Sym Rvw r Sym Rvw r Sym Rvw Empl: β α blzbl No wh f corollbl 3 α α o dcbl No wh f obrvbl 3 3 y y β β

10 r Sym Rvw Obrvr d Obrvr-d orollr Thorm 3.5: obrvr ff dcbl. Frhr f obrvbl h fll ordr brgr obrvr gv by whr y mr ch h bl. ˆ& yˆ ˆ ˆ yˆ y 8 Sprg ME854 - Z r Sym Rvw Pg

11 r Sym Rvw Obrvr d Obrvr-d orollr Sppo h blzbl d l F b h blzo fdbck g F. odr h followg obrvr-bd corollr & ˆ Fˆ Th h ol ym qo : ˆ h & ˆ& & ˆ& ˆ F F ˆ F ˆ y lod loop pol: d F Sbl clod loop ym 8 Sprg ME854 - Z r Sym Rvw Pg

12 r Sym Rvw Obrvr d Obrvr-d orollr Obrvr-bd corollr K y K F F F No h h obrvr-bd corollr lf my o b bl. No: grl f h ym blzbl hrogh fdg bck h op y h d o b op blzbl. clr h h ym op blzbl f d oly f h dcbl d blzbl 8 Sprg ME854 - Z r Sym Rvw Pg

13 r Sym Rvw Obrvr d Obrvr-d orollr Empl: d [ ] Wh w plc F d {- -3} d {- -} rpcvly. Th F plc [ 3] plc [ ] [ 6 8 ] [ 5] lod loop pol for h ym r { } bl ym b w hv bl corollr c K Sprg ME854 - Z r Sym Rvw Pg 3

14 8 Sprg ME854 - Z Pg 4 r Sym Rvw r Sym Rvw r Sym Rvw Opro o Sym Th rl d ccd coco y y & & & & odr wo ym:

15 8 Sprg ME854 - Z Pg 5 r Sym Rvw r Sym Rvw r Sym Rvw Opro o Sym or : T Prlll coco: Trpo of : ojg of : ~ or : T

16 8 Sprg ME854 - Z Pg 6 r Sym Rvw r Sym Rvw r Sym Rvw Opro o Sym vr of rfr mr ˆ qr d vrbl.sppo ˆ ˆ f clld vr of ˆ rfr mr rol rl ˆ T

17 r Sym Rvw S Spc Rlzo for Trfr mrc f cll -pc modl ch h rl rol rfr mr h propr.th w rlzo of fo 3.9:. -pc rlzo of d o b mml rlzo of f h h mll pobl dmo. Thorm 3.6: -pc rlzo of mml f d oly f corollbl d obrvbl. 8 Sprg ME854 - Z r Sym Rvw Pg 7

18 8 Sprg ME854 - Z Pg 8 r Sym Rvw r Sym Rvw r Sym Rvw S Spc Rlzo for Trfr mrc wh Th op rfr fco wh b colm vcor of d b R d d p p β β β β β orollbl ocl Form SMO [ ] b β β β β : : : M M M O M M

19 8 Sprg ME854 - Z Pg 9 r Sym Rvw r Sym Rvw r Sym Rvw S Spc Rlzo for Trfr mrc wh Th p rfr fco wh of b row vcor d c R d d m m η η η η η Obrvbl ocl Form MSO [ ] : : : M M O M M M b η η η η

20 8 Sprg ME854 - Z Pg r Sym Rvw r Sym Rvw r Sym Rvw S Spc Rlzo for Trfr mrc Th 34 block rfr fco b MMO o mml rlzo

21 8 Sprg ME854 - Z Pg r Sym Rvw r Sym Rvw r Sym Rvw S Spc Rlzo for Trfr mrc Th ch h d rk rfr mr h followg form b r W R R W k d W d N m p r r k k k k p m k r r r M O MMO lbr rlzo

22 8 Sprg ME854 - Z Pg r Sym Rvw r Sym Rvw r Sym Rvw S Spc Rlzo for Trfr mrc rlzo Mml MMO lbr rlzo mpl

23 r Sym Rvw Mlvrbl Sym Pol d Zro fo 3.: Q b p m polyoml mr or rfr fco of. Th h orml rk of Q dod orml rkq h mmlly pobl rk of Q for l o. Q ormlrk Q c rk Q Th pol d zro of rfr of pc rlzo. fco r chrcrzd rm 8 Sprg ME854 - Z r Sym Rvw Pg 3

24 r Sym Rvw Mlvrbl Sym Pol d Zro fo 3.: Th gvl of r clld h pol of rlzo. No: Pol r rlzo dpd. odr h followg ym mr fo 3.: compl mbr rlzo f rk z z f Q < clld vr zro of orml rk h ym 8 Sprg ME854 - Z r Sym Rvw Pg 4

25 r Sym Rvw Mlvrbl Sym Pol d Zro vr zro r o chgd by co fdbck F z z z rk rk F rk mm 3.7: Sppo of rlzo f d oly f Morovr f No h wh h fll - colm orml rk.th z h z hr z lo oobrvbl mod. z vr zro d ch h 8 Sprg ME854 - Z r Sym Rvw Pg 5 m

26 8 Sprg ME854 - Z Pg 6 r Sym Rvw r Sym Rvw r Sym Rvw Mlvrbl Sym Pol d Zro. h zro of f prclr. d h l h h op d o h p rbrry co vcor d pol of o whr h form of h ym p f rlzo. mml b rfr fco d l b y y m p R m P mm 3.: Proof of mm 3.: y U U Y ] [

27 8 Sprg ME854 - Z Pg 7 r Sym Rvw r Sym Rvw r Sym Rvw Mlvrbl Sym Pol d Zro Empl 3.3: z. >> pck zzro % or >> zzro [ ] z v y >> ll[ - zy3 ;] v y

Introduction to Laplace Transforms October 25, 2017

Introduction to Laplace Transforms October 25, 2017 Iroduco o Lplc Trform Ocobr 5, 7 Iroduco o Lplc Trform Lrr ro Mchcl Egrg 5 Smr Egrg l Ocobr 5, 7 Oul Rvw l cl Wh Lplc rform fo of Lplc rform Gg rform b gro Fdg rform d vr rform from bl d horm pplco o dffrl

More information

Chapter4 Time Domain Analysis of Control System

Chapter4 Time Domain Analysis of Control System Chpr4 im Domi Alyi of Corol Sym Rouh biliy cririo Sdy rror ri rpo of h fir-ordr ym ri rpo of h cod-ordr ym im domi prformc pcificio h rliohip bw h prformc pcificio d ym prmr ri rpo of highr-ordr ym Dfiiio

More information

x xi r 0. The most popular RBFs are given as follows: IUST International Journal of Engineering Science, Vol. 19, No.5-2, 2008, Page 21-26

x xi r 0. The most popular RBFs are given as follows: IUST International Journal of Engineering Science, Vol. 19, No.5-2, 2008, Page 21-26 IST Iol Jol of Egg S Vol 9 o5-8 Pg -6 O THE MERICAL SOLTIO OF OE IMESIOAL SCHROIGER EQATIO WITH OARY COITIOS IVOLVIG FRACTIOAL IFFERETIAL OPERATORS Jzb & M Mo Ab: I pp w y of olloo mo w Rl Fo o olv o mol

More information

AE57/AC51/AT57 SIGNALS AND SYSTEMS DECEMBER 2012

AE57/AC51/AT57 SIGNALS AND SYSTEMS DECEMBER 2012 AE7/AC/A7 SIGNALS AND SYSEMS DECEMBER Q. Drmi powr d rgy of h followig igl j i ii =A co iii = Solio: i E P I I l jw l I d jw d d Powr i fii, i i powr igl ii =A cow E P I co w d / co l I I l d wd d Powr

More information

counting statistics in thermal transport in nanojunctions

counting statistics in thermal transport in nanojunctions rs bhvor d fll cog sscs hrml rspor ojcos J-Shg Wg Dp PhysNUS Ol of h lk rodco Mhod of oqlbrm r s fcos Applcos hrml crrs D ch d obs rs problm Fll cog sscs MS workshop Forr s lw for h codco J [ ] f f d Forr

More information

EE Control Systems LECTURE 11

EE Control Systems LECTURE 11 Up: Moy, Ocor 5, 7 EE 434 - Corol Sy LECTUE Copyrigh FL Lwi 999 All righ rrv POLE PLACEMET A STEA-STATE EO Uig fc, o c ov h clo-loop pol o h h y prforc iprov O c lo lc uil copor o oi goo y- rcig y uyig

More information

U1. Transient circuits response

U1. Transient circuits response U. Tr crcu rpo rcu ly, Grdo Irí d omucco uro 6-7 Phlp Sm phlp.m@uh. Dprmo d Torí d l Sñl y omucco Idx Rcll Gol d movo r dffrl quo Rcll Th homoou oluo d d ordr lr dffrl quo Exmpl of d ordr crcu Il codo

More information

Exterior Building Renovations

Exterior Building Renovations xterior Building enovations Fifth treet Henderson, 0 Project : 0-0 ate: J, 0 OPL O L H F O O P L uite 00 outheast hird treet vansville, ndiana 0- :.. F:.. H POJ LOO HH VH OMMOWLH JFF J XH M V OH M FFH

More information

Boyce/DiPrima 9 th ed, Ch 7.6: Complex Eigenvalues

Boyce/DiPrima 9 th ed, Ch 7.6: Complex Eigenvalues BocDPm 9 h d Ch 7.6: Compl Egvlus Elm Dffl Equos d Boud Vlu Poblms 9 h do b Wllm E. Boc d Rchd C. DPm 9 b Joh Wl & Sos Ic. W cosd g homogous ssm of fs od l quos wh cos l coffcs d hus h ssm c b w s ' A

More information

Applications of semi-markov processes in reliability

Applications of semi-markov processes in reliability rbk Alco o m-mrko roc rlbl - TA # 3-4 7 Dcmbr - Scl I rbk rczk Nl Ur d old Alco o m-mrko roc rlbl Kword m-mrko roc rlbl rdom lr r cold db m wh rr Abrc Th bc do d horm rom h m-mrko roc hor r dcd h r Th

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

Mathematical Statistics. Chapter VIII Sampling Distributions and the Central Limit Theorem

Mathematical Statistics. Chapter VIII Sampling Distributions and the Central Limit Theorem Mahmacal ascs 8 Chapr VIII amplg Dsrbos ad h Cral Lm Thorm Fcos of radom arabls ar sall of rs sascal applcao Cosdr a s of obsrabl radom arabls L For ampl sppos h arabls ar a radom sampl of s from a poplao

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

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

More information

Let's revisit conditional probability, where the event M is expressed in terms of the random variable. P Ax x x = =

Let's revisit conditional probability, where the event M is expressed in terms of the random variable. P Ax x x = = L's rvs codol rol whr h v M s rssd rs o h rdo vrl. L { M } rrr v such h { M } Assu. { } { A M} { A { } } M < { } { } A u { } { } { A} { A} ( A) ( A) { A} A A { A } hs llows us o cosdr h cs wh M { } [ (

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

EEE 303: Signals and Linear Systems

EEE 303: Signals and Linear Systems 33: Sigls d Lir Sysms Orhogoliy bw wo sigls L us pproim fucio f () by fucio () ovr irvl : f ( ) = c( ); h rror i pproimio is, () = f() c () h rgy of rror sigl ovr h irvl [, ] is, { }{ } = f () c () d =

More information

Major: All Engineering Majors. Authors: Autar Kaw, Luke Snyder

Major: All Engineering Majors. Authors: Autar Kaw, Luke Snyder Nolr Rgrsso Mjor: All Egrg Mjors Auhors: Aur Kw, Luk Sydr hp://urclhodsgusfdu Trsforg Nurcl Mhods Educo for STEM Udrgrdus 3/9/5 hp://urclhodsgusfdu Nolr Rgrsso hp://urclhodsgusfdu Nolr Rgrsso So populr

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

Overview. Splay trees. Balanced binary search trees. Inge Li Gørtz. Self-adjusting BST (Sleator-Tarjan 1983).

Overview. Splay trees. Balanced binary search trees. Inge Li Gørtz. Self-adjusting BST (Sleator-Tarjan 1983). Ovrvw B r rh r: R-k r -3-4 r 00 Ig L Gør Amor Dm rogrmmg Nwork fow Srg mhg Srg g Comuo gomr Irouo o NP-om Rom gorhm B r rh r -3-4 r Aow,, or 3 k r o Prf Evr h from roo o f h m gh mr h E w E R E R rgr h

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

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

Special Curves of 4D Galilean Space

Special Curves of 4D Galilean Space Irol Jourl of Mhml Egrg d S ISSN : 77-698 Volum Issu Mrh hp://www.jms.om/ hps://ss.googl.om/s/jmsjourl/ Spl Curvs of D ll Sp Mhm Bkş Mhmu Ergü Alpr Osm Öğrmş Fır Uvrsy Fuly of S Dprm of Mhms 9 Elzığ Türky

More information

Approximate Integration. Left and Right Endpoint Rules. Midpoint Rule = 2. Riemann sum (approximation to the integral) Left endpoint approximation

Approximate Integration. Left and Right Endpoint Rules. Midpoint Rule = 2. Riemann sum (approximation to the integral) Left endpoint approximation M lculus II Tcqus o Igros: Approm Igro -- pr 8.7 Approm Igro M lculus II Tcqus o Igros: Approm Igro -- pr 8.7 7 L d Rg Edpo Ruls Rm sum ppromo o grl L dpo ppromo Rg dpo ppromo clculus ppls d * L d R d

More information

TABLES AND INFORMATION RETRIEVAL

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

More information

Chapter 5 Transient Analysis

Chapter 5 Transient Analysis hpr 5 rs Alyss Jsug Jg ompl rspos rs rspos y-s rspos m os rs orr co orr Dffrl Equo. rs Alyss h ffrc of lyss of crcus wh rgy sorg lms (ucors or cpcors) & m-ryg sgls wh rss crcus s h h quos rsulg from r

More information

Inner Product Spaces INNER PRODUCTS

Inner Product Spaces INNER PRODUCTS MA4Hcdoc Ir Product Spcs INNER PRODCS Dto A r product o vctor spc V s ucto tht ssgs ubr spc V such wy tht th ollowg xos holds: P : w s rl ubr P : P : P 4 : P 5 : v, w = w, v v + w, u = u + w, u rv, w =

More information

Convergence tests for the cluster DFT calculations

Convergence tests for the cluster DFT calculations Covgc ss o h clus DF clculos. Covgc wh spc o bss s. s clculos o bss s covgc hv b po usg h PBE ucol o 7 os gg h-b. A s o h Guss bss ss wh csg s usss hs b us clug h -G -G** - ++G(p). A l sc o. Å h c bw h

More information

Lecture 12: Introduction to nonlinear optics II.

Lecture 12: Introduction to nonlinear optics II. Lcur : Iroduco o olar opcs II r Kužl ropagao of srog opc sgals propr olar ffcs Scod ordr ffcs! Thr-wav mxg has machg codo! Scod harmoc grao! Sum frqucy grao! aramrc grao Thrd ordr ffcs! Four-wav mxg! Opcal

More information

CONSTACYCLIC CODES OF LENGTH OVER A FINITE FIELD

CONSTACYCLIC CODES OF LENGTH OVER A FINITE FIELD Jorl o Algbr Nbr Tory: Ac Alco Vol 5 Nbr 6 Pg 4-64 Albl ://ccc.co. DOI: ://.o.org/.864/_753 ONSTAYLI ODES OF LENGTH OVER A FINITE FIELD AITA SAHNI POONA TRAA SEHGAL r or Ac Sy c Pb Ury gr 64 I -l: 5@gl.co

More information

Vr Vr

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

More information

On the Hubbard-Stratonovich Transformation for Interacting Bosons

On the Hubbard-Stratonovich Transformation for Interacting Bosons O h ubbrd-sroovh Trsformo for Irg osos Mr R Zrbur ff Fbrury 8 8 ubbrd-sroovh for frmos: rmdr osos r dffr! Rdom mrs: hyrbol S rsformo md rgorous osus for rg bosos /8 Wyl grou symmry L : G GL V b rrso of

More information

Advanced Engineering Mathematics, K.A. Stroud, Dexter J. Booth Engineering Mathematics, H.K. Dass Higher Engineering Mathematics, Dr. B.S.

Advanced Engineering Mathematics, K.A. Stroud, Dexter J. Booth Engineering Mathematics, H.K. Dass Higher Engineering Mathematics, Dr. B.S. Rfrc: (i) (ii) (iii) Advcd Egirig Mhmic, K.A. Sroud, Dxr J. Booh Egirig Mhmic, H.K. D Highr Egirig Mhmic, Dr. B.S. Grwl Th mhod of m Thi coi of h followig xm wih h giv coribuio o h ol. () Mid-rm xm : 3%

More information

Hence, Consider the linear, time-varying system with state model. y( t) u(t) H(t, )

Hence, Consider the linear, time-varying system with state model. y( t) u(t) H(t, ) Df. h mpul rpo mar of a lar, lumpd, m-varyg ym a mar map H, : RR R rm gv by H, = [h,,, h m, ], whr ach colum h, rpr h rpo of h ym o h mpulv pu u = -, R m, = [ ] occur a h h compo, h m of applcao of h pu

More information

Chapter 2 Reciprocal Lattice. An important concept for analyzing periodic structures

Chapter 2 Reciprocal Lattice. An important concept for analyzing periodic structures Chpt Rcpocl Lttc A mpott cocpt o lyzg podc stuctus Rsos o toducg cpocl lttc Thoy o cystl dcto o x-ys, utos, d lctos. Wh th dcto mxmum? Wht s th tsty? Abstct study o uctos wth th podcty o Bvs lttc Fou tsomto.

More information

EXERCISE - 01 CHECK YOUR GRASP

EXERCISE - 01 CHECK YOUR GRASP DEFNTE NTEGRATON EXERCSE - CHECK YOUR GRASP. ( ) d [ ] d [ ] d d ƒ( ) ƒ '( ) [ ] [ ] 8 5. ( cos )( c)d 8 ( cos )( c)d + 8 ( cos )( c) d 8 ( cos )( c) d sic + cos 8 is lwys posiiv f() d ( > ) ms f() is

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

glo beau bid point full man branch last ior s all for ap Sav tree tree God length per down ev the fect your er Cm7 a a our

glo beau bid point full man branch last ior s all for ap Sav tree tree God length per down ev the fect your er Cm7 a a our SING, MY TONGU, TH SAVIOR S GLORY mj7 Mlod Kbd fr nd S would tm flsh s D nd d tn s drw t crd S, Fth t So Th L lss m ful wn dd t, Fs4 F wd; v, snr, t; ngh, t: lod; t; tgu, now Chrst, h O d t bnd Sv God

More information

Opening. Monster Guard. Grades 1-3. Teacher s Guide

Opening. Monster Guard. Grades 1-3. Teacher s Guide Tcr Gi 2017 Amric R Cr PLEASE NOTE: S m cml Iiii ci f Mr Gr bfr y bgi i civiy, i rr gi cc Vlc riig mii. Oig Ifrm y r gig lr b vlc y f vlc r. Exli r r vlc ll vr rl, i Ui S, r, iclig Alk Hii, v m civ vlc.

More information

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.

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

More information

Wave Phenomena Physics 15c

Wave Phenomena Physics 15c Wv hnon hyscs 5c cur 4 Coupl Oscllors! H& con 4. Wh W D s T " u forc oscllon " olv h quon of oon wh frcon n foun h sy-s soluon " Oscllon bcos lr nr h rsonnc frquncy " hs chns fro 0 π/ π s h frquncy ncrss

More information

I-1. rei. o & A ;l{ o v(l) o t. e 6rf, \o. afl. 6rt {'il l'i. S o S S. l"l. \o a S lrh S \ S s l'l {a ra \o r' tn $ ra S \ S SG{ $ao. \ S l"l. \ (?

I-1. rei. o & A ;l{ o v(l) o t. e 6rf, \o. afl. 6rt {'il l'i. S o S S. ll. \o a S lrh S \ S s l'l {a ra \o r' tn $ ra S \ S SG{ $ao. \ S ll. \ (? >. 1! = * l >'r : ^, : - fr). ;1,!/!i ;(?= f: r*. fl J :!= J; J- >. Vf i - ) CJ ) ṯ,- ( r k : ( l i ( l 9 ) ( ;l fr i) rf,? l i =r, [l CB i.l.!.) -i l.l l.!. * (.1 (..i -.1.! r ).!,l l.r l ( i b i i '9,

More information

Colby College Catalogue

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

More information

Chapter 8: Propagating Quantum States of Radiation

Chapter 8: Propagating Quantum States of Radiation Quum Opcs f hcs Oplccs h R Cll Us Chp 8: p Quum Ss f R 8. lcmc Ms Wu I hs chp w wll cs pp quum ss f wus fs f spc. Cs h u shw lw f lcc wu. W ssum h h wu hs l lh qul h -c wll ssum l. Th lcc cs s fuc f l

More information

Quantum Properties of Idealized GW Detector

Quantum Properties of Idealized GW Detector Qm Prors of Idlzd GW Dor Sg Pyo Km Ks N l Uvrsy Osk Uvrsy J 3 Th 4 h Kor-J Worksho o KAGRA Ol Idlzd Dor for Grvol Wvs Qm Thory for Dsso Wgr Fo of Tm-Dd Osllor Dmd Osllor Drv by Erl Fors Colso Idlzd Dor

More information

Binary Choice. Multiple Choice. LPM logit logistic regresion probit. Multinomial Logit

Binary Choice. Multiple Choice. LPM logit logistic regresion probit. Multinomial Logit (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty 3 Bary Choc LPM logt logstc rgrso probt Multpl Choc Multomal Logt (c Pogsa Porchawssul,

More information

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

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

More information

STATE SPACE CONTROL. Prof. Ing. Miluše Vítečková, CSc. Prof. Ing. Antonín Víteček, CSc., Dr.h.c.

STATE SPACE CONTROL. Prof. Ing. Miluše Vítečková, CSc. Prof. Ing. Antonín Víteček, CSc., Dr.h.c. VŠB h Uvr f Orv F f Mh Egrg Dpr f Cr S r Czh Rp SE SPCE CONROL Prf g Mš Víčvá CS Prf g í Víč CS Drh Orv 6 Rvr: D g M Hgr CS Cprgh : Prf g Mš Víčvá CS Prf g í Víč CS Drh SE SPCE CONROL SBN 978-8-8-979-

More information

page 11 equation (1.2-10c), break the bar over the right side in the middle

page 11 equation (1.2-10c), break the bar over the right side in the middle I. Corrctios Lst Updtd: Ju 00 Complx Vrils with Applictios, 3 rd ditio, A. Dvid Wusch First Pritig. A ook ought for My 007 will proly first pritig With Thks to Christi Hos of Swd pg qutio (.-0c), rk th

More information

Ch. 22: Classical Theory of Harmonic Crystal

Ch. 22: Classical Theory of Harmonic Crystal C. : Clssl Toy o mo Cysl gl o ml moo o o os l s ld o ls o pl ollowg:. Eqlbm Pops p o ls d Islos Eqlbm sy d Cos Egs Tml Epso d lg. Tspo Pops T pd o lo Tm Fl o Wdm-Fz Lw pody Tml Cody o Islos Tsmsso o od.

More information

FL/VAL ~RA1::1. Professor INTERVI of. Professor It Fr recru. sor Social,, first of all, was. Sys SDC? Yes, as a. was a. assumee.

FL/VAL ~RA1::1. Professor INTERVI of. Professor It Fr recru. sor Social,, first of all, was. Sys SDC? Yes, as a. was a. assumee. B Pror NTERV FL/VAL ~RA1::1 1 21,, 1989 i n or Socil,, fir ll, Pror Fr rcru Sy Ar you lir SDC? Y, om um SM: corr n 'd m vry ummr yr. Now, y n y, f pr my ry for ummr my 1 yr Un So vr ummr cour d rr o l

More information

(A) 1 (B) 1 + (sin 1) (C) 1 (sin 1) (D) (sin 1) 1 (C) and g be the inverse of f. Then the value of g'(0) is. (C) a. dx (a > 0) is

(A) 1 (B) 1 + (sin 1) (C) 1 (sin 1) (D) (sin 1) 1 (C) and g be the inverse of f. Then the value of g'(0) is. (C) a. dx (a > 0) is [STRAIGHT OBJECTIVE TYPE] l Q. Th vlu of h dfii igrl, cos d is + (si ) (si ) (si ) Q. Th vlu of h dfii igrl si d whr [, ] cos cos Q. Vlu of h dfii igrl ( si Q. L f () = d ( ) cos 7 ( ) )d d g b h ivrs

More information

Mat e h a m t c i a lmo e il of a r T a v n er e s e S ar Defor a m t o i k S e h l T ory 2. M T T E si ce e m t n Mo e d sl. 30 www. jier.

Mat e h a m t c i a lmo e il of a r T a v n er e s e S ar Defor a m t o i k S e h l T ory 2. M T T E si ce e m t n Mo e d sl. 30 www. jier. rol Jl grg r g J SS : 9-8 Vol- - Oobr l olg Trr fo T Sll Ty Sr OH ZO OH TU br Tr- ol y ly rlr o ploy o r r r rbo l rf opo ll r ro oprg oo T o oo r r by g rlop b f o r pl ll g Hlo prpl rgy T ry l po r o

More information

n

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

More information

Right Angle Trigonometry

Right Angle Trigonometry Righ gl Trigoomry I. si Fs d Dfiiios. Righ gl gl msurig 90. Srigh gl gl msurig 80. u gl gl msurig w 0 d 90 4. omplmry gls wo gls whos sum is 90 5. Supplmry gls wo gls whos sum is 80 6. Righ rigl rigl wih

More information

LECTURE 6 TRANSFORMATION OF RANDOM VARIABLES

LECTURE 6 TRANSFORMATION OF RANDOM VARIABLES LECTURE 6 TRANSFORMATION OF RANDOM VARIABLES TRANSFORMATION OF FUNCTION OF A RANDOM VARIABLE UNIVARIATE TRANSFORMATIONS TRANSFORMATION OF RANDOM VARIABLES If s a rv wth cdf F th Y=g s also a rv. If w wrt

More information

Canonical Quantizing of Spinor Fields: Anti-Commutation Relations

Canonical Quantizing of Spinor Fields: Anti-Commutation Relations JOURNA ON POTONICS AND SPINTRONICS VO.5 NO. MAY 6 ISSN - 857 Prn ISSN - 858 Onln h://www.rrh.org/jornl/j/j.hml Cnonl Qnzng of Snor Fl: An-Common Rlon D. Grn PhD Unvr of Brln* Ar Nw mg of hr nor ro on h

More information

TOPIC 5: INTEGRATION

TOPIC 5: INTEGRATION TOPIC 5: INTEGRATION. Th indfinit intgrl In mny rspcts, th oprtion of intgrtion tht w r studying hr is th invrs oprtion of drivtion. Dfinition.. Th function F is n ntidrivtiv (or primitiv) of th function

More information

{ } [ ] { } { } 1. The simple Wright-Fisher model. Mathematics Population Genetics. n-step transition probabilities eqn(11)

{ } [ ] { } { } 1. The simple Wright-Fisher model. Mathematics Population Genetics. n-step transition probabilities eqn(11) Mhmcs Polo Gcs Corll Uvrsy J Jly 6 Wrr J ws Th sml Wrgh-shr modl q6 -s rso robbls q { } { }? r o r q { } { } { } { } } Prob{ δ δ δ δ δ δ { } [ ] / 4 gvs Ths. / - shr modl or h sml Wrgh δ δ M ms dffso romo

More information

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 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

More information

ERDOS-SMARANDACHE NUMBERS. Sabin Tabirca* Tatiana Tabirca**

ERDOS-SMARANDACHE NUMBERS. Sabin Tabirca* Tatiana Tabirca** ERDO-MARANDACHE NUMBER b Tbrc* Tt Tbrc** *Trslv Uvrsty of Brsov, Computr cc Dprtmt **Uvrsty of Mchstr, Computr cc Dprtmt Th strtg pot of ths rtcl s rprstd by rct work of Fch []. Bsd o two symptotc rsults

More information

Vectors and Matrices

Vectors and Matrices Collg of Egrg d Compur Scc Mchcl Egrg Dprm Egrg Alyss Nos Ls updd: Augus 8, 7 Lrry Cro Vcors d Mrcs Iroduco Ths os provd roduco o h us of vcors d mrcs grg lyss. I ddo, hy provd dscusso of how h smpl cocp

More information

COMPLEX NUMBERS AND ELEMENTARY FUNCTIONS OF COMPLEX VARIABLES

COMPLEX NUMBERS AND ELEMENTARY FUNCTIONS OF COMPLEX VARIABLES COMPLEX NUMBERS AND ELEMENTARY FUNCTIONS OF COMPLEX VARIABLES DEFINITION OF A COMPLEX NUMBER: A umbr of th form, whr = (, ad & ar ral umbrs s calld a compl umbr Th ral umbr, s calld ral part of whl s calld

More information

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

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

More information

Colby College Catalogue

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

More information

1. Introduction and notations.

1. Introduction and notations. Alyi Ar om plii orml or q o ory mr Rol Gro Lyé olyl Roièr, r i lir ill, B 5 837 Tolo Fr Emil : rolgro@orgr W y hr q o ory mr, o ll h o ory polyomil o gi rm om orhogol or h mr Th mi rl i orml mig plii h

More information

Colby College Catalogue

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

More information

On the Existence and uniqueness for solution of system Fractional Differential Equations

On the Existence and uniqueness for solution of system Fractional Differential Equations OSR Jourl o Mhms OSR-JM SSN: 78-578. Volum 4 ssu 3 Nov. - D. PP -5 www.osrjourls.org O h Es d uquss or soluo o ssm rol Drl Equos Mh Ad Al-Wh Dprm o Appld S Uvrs o holog Bghdd- rq Asr: hs ppr w d horm o

More information

Quantum Harmonic Oscillator

Quantum Harmonic Oscillator Quu roc Oscllor Quu roc Oscllor 6 Quu Mccs Prof. Y. F. C Quu roc Oscllor Quu roc Oscllor D S..O.:lr rsorg forc F k, k s forc cos & prbolc pol. V k A prcl oscllg roc pol roc pol s u po of sbly sys 6 Quu

More information

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

More information

,. *â â > V>V. â ND * 828.

,. *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,

More information

INTERQUARTILE RANGE. I can calculate variabilityinterquartile Range and Mean. Absolute Deviation

INTERQUARTILE RANGE. I can calculate variabilityinterquartile Range and Mean. Absolute Deviation INTERQUARTILE RANGE I cn clcul vribiliyinrquril Rng nd Mn Absolu Dviion 1. Wh is h grs common fcor of 27 nd 36?. b. c. d. 9 3 6 4. b. c. d.! 3. Us h grs common fcor o simplify h frcion!".!". b. c. d.

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

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

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

More information

Introduction to Finite Element Method

Introduction to Finite Element Method p. o C d Eo E. Iodo o E Mod s H L p. o C d Eo E o o s Ass L. o. H L p://s.s.. p. o C d Eo E. Cos. Iodo. Appoo o os & o Cs. Eqos O so. Mdso os-es 5. szo 6. wo so Es os 7. os ps o Es 8. Io 9. Co C Isop E.

More information

Generalized Half Linear Canonical Transform And Its Properties

Generalized Half Linear Canonical Transform And Its Properties Gnrlz Hl Lnr Cnoncl Trnorm An I Propr A S Guh # A V Joh* # Gov Vrh Inu o Scnc n Humn, Amrv M S * Shnkrll Khnlwl Collg, Akol - 444 M S Arc: A gnrlzon o h Frconl Fourr rnorm FRFT, h lnr cnoncl rnorm LCT

More information

Control Systems (Lecture note #6)

Control Systems (Lecture note #6) 6.5 Corol Sysms (Lcur o #6 Las Tm: Lar algbra rw Lar algbrac quaos soluos Paramrzao of all soluos Smlary rasformao: compao form Egalus ad gcors dagoal form bg pcur: o brach of h cours Vcor spacs marcs

More information

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

More information

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

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

More information

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

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.

More information

NEW FLOODWAY (CLOMR) TE TE PIN: GREENS OF ROCK HILL, LLC DB: 12209, PG: ' S67 46'18"E APPROX. FLOODWAY NEW BASE FLOOD (CLOMR)

NEW FLOODWAY (CLOMR) TE TE PIN: GREENS OF ROCK HILL, LLC DB: 12209, PG: ' S67 46'18E APPROX. FLOODWAY NEW BASE FLOOD (CLOMR) W LOOWY (LOMR) RVRWLK PKWY ROK HLL, S PPROX. LOOWY W BS LOO (LOMR) lient nformation 4 SS- RM:4 V : PV Pipe V OU: PV Pipe JB SS- RM: V OU: PV Pipe RU R " PV Pipe @. LO SPS OL SSBL GRL ORMO: S OS: M BS LOO

More information

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 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

More information

Years. Marketing without a plan is like navigating a maze; the solution is unclear.

Years. Marketing without a plan is like navigating a maze; the solution is unclear. F Q 2018 E Mk l lk z; l l Mk El M C C 1995 O Y O S P R j lk q D C Dl Off P W H S P W Sl M Y Pl Cl El M Cl FIRST QUARTER 2018 E El M & D I C/O Jff P RGD S C D M Sl 57 G S Alx ON K0C 1A0 C Tl: 6134821159

More information

DEPARTMENT OF ELECTRICAL &ELECTRONICS ENGINEERING SIGNALS AND SYSTEMS. Assoc. Prof. Dr. Burak Kelleci. Spring 2018

DEPARTMENT OF ELECTRICAL &ELECTRONICS ENGINEERING SIGNALS AND SYSTEMS. Assoc. Prof. Dr. Burak Kelleci. Spring 2018 DEPARTMENT OF ELECTRICAL &ELECTRONICS ENGINEERING SIGNALS AND SYSTEMS Aoc. Prof. Dr. Burak Kllci Spring 08 OUTLINE Th Laplac Tranform Rgion of convrgnc for Laplac ranform Invr Laplac ranform Gomric valuaion

More information

Lecture 21 : Graphene Bandstructure

Lecture 21 : Graphene Bandstructure Fundmnls of Nnolcronics Prof. Suprio D C 45 Purdu Univrsi Lcur : Grpn Bndsrucur Rf. Cpr 6. Nwor for Compuionl Nnocnolog Rviw of Rciprocl Lic :5 In ls clss w lrnd ow o consruc rciprocl lic. For D w v: Rl-Spc:

More information

terms of discrete sequences can only take values that are discrete as opposed to

terms of discrete sequences can only take values that are discrete as opposed to Diol Bgyoko () OWER SERIES Diitio Sris lik ( ) r th sm o th trms o discrt sqc. Th trms o discrt sqcs c oly tk vls tht r discrt s opposd to cotios, i.., trms tht r sch tht th mric vls o two cosctivs os

More information

Improved Exponential Estimator for Population Variance Using Two Auxiliary Variables

Improved Exponential Estimator for Population Variance Using Two Auxiliary Variables Improvd Epoal Emaor for Populao Varac Ug Two Aular Varabl Rajh gh Dparm of ac,baara Hdu Uvr(U.P., Ida (rgha@ahoo.com Pakaj Chauha ad rmala awa chool of ac, DAVV, Idor (M.P., Ida Flor maradach Dparm of

More information

GOVERNMENT OF ANDHRA PRADESH ABSTRACT

GOVERNMENT OF ANDHRA PRADESH ABSTRACT GOVERNMENT OF ANDHRA PRADESH ABSTRACT EDUCATION DEPARTMENT P - S f 10,917 p prpd by SSA (RVM) rqurd udr h RTE A Ordr Iud. ---------------------------------------------------------------------------------------------------

More information

Approximately Inner Two-parameter C0

Approximately Inner Two-parameter C0 urli Jourl of ic d pplid Scic, 5(9: 0-6, 0 ISSN 99-878 pproximly Ir Two-prmr C0 -group of Tor Produc of C -lgr R. zri,. Nikm, M. Hi Dprm of Mmic, Md rc, Ilmic zd Uivriy, P.O.ox 4-975, Md, Ir. rc: I i ppr,

More information

INTEGRALS. Chapter 7. d dx. 7.1 Overview Let d dx F (x) = f (x). Then, we write f ( x)

INTEGRALS. Chapter 7. d dx. 7.1 Overview Let d dx F (x) = f (x). Then, we write f ( x) Chptr 7 INTEGRALS 7. Ovrviw 7.. Lt d d F () f (). Thn, w writ f ( ) d F () + C. Ths intgrls r clld indfinit intgrls or gnrl intgrls, C is clld constnt of intgrtion. All ths intgrls diffr y constnt. 7..

More information

Unbalanced Panel Data Models

Unbalanced Panel Data Models Ubalacd Pal Data odls Chaptr 9 from Baltag: Ecoomtrc Aalyss of Pal Data 5 by Adrás alascs 4448 troducto balacd or complt pals: a pal data st whr data/obsrvatos ar avalabl for all crosssctoal uts th tr

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

Colby College Catalogue

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

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

APPENDIX F WATER USE SUMMARY

APPENDIX F WATER USE SUMMARY APPENDX F WATER USE SUMMARY From Past Projects Town of Norman Wells Water Storage Facltes Exstng Storage Requrements and Tank Volume Requred Fre Flow 492.5 m 3 See Feb 27/9 letter MACA to Norman Wells

More information

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

More information

Linear Algebra Existence of the determinant. Expansion according to a row.

Linear Algebra Existence of the determinant. Expansion according to a row. Lir Algbr 2270 1 Existc of th dtrmit. Expsio ccordig to row. W dfi th dtrmit for 1 1 mtrics s dt([]) = (1) It is sy chck tht it stisfis D1)-D3). For y othr w dfi th dtrmit s follows. Assumig th dtrmit

More information

1 Finite Automata and Regular Expressions

1 Finite Automata and Regular Expressions 1 Fini Auom nd Rgulr Exprion Moivion: Givn prn (rgulr xprion) for ring rching, w migh wn o convr i ino drminiic fini uomon or nondrminiic fini uomon o mk ring rching mor fficin; drminiic uomon only h o

More information

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 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

More information

More on FT. Lecture 10 4CT.5 3CT.3-5,7,8. BME 333 Biomedical Signals and Systems - J.Schesser

More on FT. Lecture 10 4CT.5 3CT.3-5,7,8. BME 333 Biomedical Signals and Systems - J.Schesser Mr n FT Lcur 4CT.5 3CT.3-5,7,8 BME 333 Bimdicl Signls nd Sysms - J.Schssr 43 Highr Ordr Diffrniin d y d x, m b Y b X N n M m N M n n n m m n m n d m d n m Y n d f n [ n ] F d M m bm m X N n n n n n m p

More information