Exponential Stability Analysis of a System Comprised of a Robot and its Associated Safety Mechanism
|
|
- Belinda Kelley
- 6 years ago
- Views:
Transcription
1 rongs of nnul onfrn of hn nsu of ommunons Eponnl Sbl nlss of Ssm omprs of obo n s sso Sf Mhnsm Whu GUO ng YNG prmn of Mhms n nforms sn Zhngzhou Unvrs of lgh nusr Zhngzhou hn; E-ml: whguosr@hooomn; ngp66@hoon bsr: Th ssm omprs of robo n s sso sf mhnsm s su n h ppr h mho of srong onnuous sm-group h ppr nlzs h rsron of ssnl sprl growh boun of h ssm opror Th ssnl sprl rus of h ssm opror s lso suss bfor n fr prurbon Th rsuls show h h nm soluon of h ssm s ponnl sbl n ns o h s soluon of h ssm K wors: robo; srl omnn gnvlu; ssnl sprum; surbn; ponnl sbl nrouon Wh rp vlopmn of sn n hnolog h pplon of robos hs nrs n mprssv r n h r of nusrl sor onsruon fr prvnon unrwr ploron our sp ploron n mn Unoubl robo wll b houshol goo s norml h nrs fuur Hn robo sf n rlbl hs bom n mporn for Th uhors sblsh h mhm mols of h ssm onssng of obo sso sf mhnsm s ssm n su h s soluon of h ssm b h mho of plrnsform [] usng h lnr opror hor n nh sp h uhors prov h h soluon of h ssm s smpo sbl n s s soluon s h gnvor whh s orrsponng o h gnvlu of h ssm opror [] n hs ppr unr mor norml ssumpons w wll prov h sn of rgorous omnn gnvlu n nlz h rsron of ssnl sprl growh boun of h ssm opror n h hng of h ssnl sprl rus fr prurbon Th rsuls show h h nm soluon of h ssm s ponnl sbl n ns o h s soluon of h ssm Th s ssumpons n Mhm Mol of h Ssm Th s ssumpons Th followng ssumpons r sso wh h nlss prsn n hs rl: Th ssm s ompos of wo ms: robo n s sso sf mhnsm ssm Flurs r ssll npnn Nur Sn Fun of Hnn rovnl Thnolog prmn 97 Tms o flur ohr hn h of ommon-us flurs r ponnll srbu Ssm fls whn h robo fls Th rpr robo or s sso sf mhnsm s s goo s nw 6 Th fl ssm rpr ms r rbrrl srbu 7 Th prll fl ssm rpr ms r ponnll srbu 8 Th pplon of h v of sgs mho m nvolv som ppromon 9 ommon-us flur ms r gmm srbu Th followng smbols r sso wh Fgur or s rl nlss: m h s of h ssm: = obo n s sso sf mhnsm worng normll =l obo worng normll sf mhnsm fl = obo fl wh n nn = obo fl sfl = obo fl sf ssm oprng normll = obo fl u o ommon-us flur = umm s onsn flur r of h sf mhnsm / ssm onsn flur r of h robo flng wh n nn onsn flur r of h robo flng sfl onsn flur r of h robo rmrs sso wh ommon-us flurs onsn rpr r from s ; = Tm-pnn rpr r whn h fl Ss
2 ssm s n s n hs n lps rpr m of ; for = robbl h h robo s n s m ; = p [ Th probbl h m h fl ssm s n s n h lps rpr m ls n h nrvl ; for = ] Th s-sp grm of h ssm s shown n Fgur Fgur S sp grm of h ssm onnng robo n s sso sf mhnsm Th Mhml Mol n h ssumpons s bfor b supplmnr vrbls w n g h followng ngrl ffrnl quon group whh srbs h ssm Th rpr funon s ssum o b boun [] So whn w suss h ssm som prl ul mnng n som goo proprs wll b los n f n h prl pplon s unboun gnrll n orr o prf h ssm w ssum ; sup nf ssum s sp s followng For h norm of s fn Obvousl s nh sp no n w fn opror g h fn rgon of b } { fn opror n : T ; Th ssm n b srb s n bsr uh problm: Th S Soluon of h Ssm Frsl w su h nonzro soluon s sn bou whr Th quon n b prss b solvng w n g Ss rongs of nnul onfrn of hn nsu of ommunons
3 So h frs quon of bom 7 hn w hv quon group s followng 8 no h offn rmnn of 8 b n hn w hv Whn n s n gnvlu of hn n urn f n ssfs hn h quon group 8 hs nonzro soluon hn n s soluon of Spll whn hn So s n gnvlu of h opror n s ln vor hs h followng omponns: 9 hn w hv For n w hv hn s n smpl gnvlu of h opror * Hn w n g h s posv soluon of h ssm ˆ whr p p r prss s n 9 Th Eponnl Sbl of h Soluon of Ssm Th uhors hv prov h h soluon of ssm s h mol s progrssvl sn s smpl gnvlu of h opror of h ssm [] n hs son w wll llumn h wh h mor srongl onons h ssm hs mor wll sbl Thorm [] s smpl gnvlu of h opror ; { } : Thorm Suppos h s fn s bfor n hr s posv numbr ssf } mn{ Thn whn w hv n roof Whn for n gvn w onsr h rsolvn quon whr Ss rongs of nnul onfrn of hn nsu of ommunons
4 rongs of nnul onfrn of hn nsu of ommunons Th nl prsson of h rsolvn quon s s followng Whn w hv solvng w hv Snorng o h nfrn [] w hv p o llumns h whn : s boun hn n orng o h umr-hlps horm [] w n onlu h followng nfrn nfrn Suppos h n s fn s bfor hn h omprsson sm-group S spnn b opror s ponnll grssv nml for n hn S Sn h opror s fn rn opror n hn s omp opror orng o h opror sm-group horm n omp prurbon of sm-groupw hv h followng onluson Thorm Suppos h n s fn s bfor hn h omprsson sm-group T whh s spnn b + posssss h proprs s follow Whn w hv ; Suppos h for n { } whr N hn w hv s rgorous omnn gnvlu Suppos h ˆ s h s soluon of h ssm n hn for n hr ss onsn M suh h T ˆ whr roof Whn orng o h horm w hv Sn s hr orr rn opror hn s omp opror hn f n onl f s no n gnvlu of So whn w hv Sn s n nl funon hn mos hr r fn zro pons n hr s no umulon pon n fn rgon Suppos h hn w hv { } Whr N orng o h srnss of gnvlu n horm w hv Sn h gnfunon h orrsponng o s posv hn w hv s rgorous omnn gnvlu Fnll b h prurbon horm of sm-group omp prurbon os no hng h ssnl sprum boun of h sm-grouphn h sm-group T spnn b + n sm-group S spnn b hv h sm h ssnl sprum boun [-6] Hn for h ssnl sprum boun of T w hv Suppos h ˆ s fn s n n orng o h fn pnson Ss 8
5 rongs of nnul onfrn of hn nsu of ommunons horm of sm-groupw hv h followng onluson For n hr ss onsn M suh h T ˆ M whr Th bov onlusons show h unr som fn onons h nm soluon of h ssm s ponnl sbl n ns o h s soluon of h ssm frns [] HON S FSHN M obo Ssms robbls nlss [J] Mrolron lb 997 7: - [] Guo Whu u Gnq Sbl nlss of h Ssm onssng of obo n s sso Sf Mhnsm [J] Mhms n r n Thor 9: 6- [] GUO WhuEponnl Sbl nlss of rll prbl Ssm wh Two Non-nlUn[J] Mhms n rn Thor 99: 8- [] z Smgroup of nr Oprors n pplons o rl ffrnl Equons [M] Sprngr Nw Yor 98 [] u Gnq rurbon Thorm for us of Srong onnuous Sm-group Essnl Sprum [J] T mhm Sn99 6:77-76 [6] u Gnq Th Esmon of Srongl onnuous _ Sm-group rurbon Essnl Sprum [J] T Mhm Sn99 6: Ss
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 informationThe Mathematics of Harmonic Oscillators
Th Mhcs of Hronc Oscllors Spl Hronc Moon In h cs of on-nsonl spl hronc oon (SHM nvolvng sprng wh sprng consn n wh no frcon, you rv h quon of oon usng Nwon's scon lw: con wh gvs: 0 Ths s sos wrn usng h
More informationWave 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 informationConsider a system of 2 simultaneous first order linear equations
Soluon of sysms of frs ordr lnar quaons onsdr a sysm of smulanous frs ordr lnar quaons a b c d I has h alrna mar-vcor rprsnaon a b c d Or, n shorhand A, f A s alrady known from con W know ha h abov sysm
More informationCanonical 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 informationAppendix. In the absence of default risk, the benefit of the tax shield due to debt financing by the firm is 1 C E C
nx. Dvon o h n wh In h sn o ul sk h n o h x shl u o nnng y h m s s h ol ouon s h num o ssus s h oo nom x s h sonl nom x n s h v x on quy whh s wgh vg o vn n l gns x s. In hs s h o sonl nom xs on h x shl
More informationSpecial 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 information1- I. M. ALGHROUZ: A New Approach To Fractional Derivatives, J. AOU, V. 10, (2007), pp
Jourl o Al-Qus Op Uvrsy or Rsrch Sus - No.4 - Ocobr 8 Rrcs: - I. M. ALGHROUZ: A Nw Approch To Frcol Drvvs, J. AOU, V., 7, pp. 4-47 - K.S. Mllr: Drvvs o or orr: Mh M., V 68, 995 pp. 83-9. 3- I. PODLUBNY:
More informationSummary: Solving a Homogeneous System of Two Linear First Order Equations in Two Unknowns
Summary: Solvng a Homognous Sysm of Two Lnar Frs Ordr Equaons n Two Unknowns Gvn: A Frs fnd h wo gnvalus, r, and hr rspcv corrspondng gnvcors, k, of h coffcn mar A Dpndng on h gnvalus and gnvcors, h gnral
More informationGeneralized 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( ) ( ) ( ) 0. Conservation of Energy & Poynting Theorem. From Maxwell s equations we have. M t. From above it can be shown (HW)
8 Conson o n & Ponn To Fo wll s quons w D B σ σ Fo bo n b sown (W) o s W w bo on o s l us n su su ul ow ns [W/ ] [W] su P su B W W 4 444 s W A A s V A A : W W R o n o so n n: [/s W] W W 4 44 9 W : W F
More informationCopyright A.Milenin, 2017, AGH University of Science and Technology
Fn lmn nl for Ml Formng n Mrl ngnrng rof. r h. nż. nr Mlnn G nr of n n hnolog Krów oln -ml: mlnn@gh..l nnoon h fn lmn mho (FM) wl n ml formng n mrl ngnrng. h mho n rom mho h' wh rr h of horl rnng. h followng
More informationt the propensity to consume the resource good. Maximizing U t in (9) subject to the budget constraint (8) yields
ISB 978-9-84468-8-5 Innaonal Confn on Issus n Busnss onoms Mang an Mamas (IBMM-6) Sngapo 5-6 6 Busnss Cls Capal nvonmn an Rnabl Rsous W-Bn Zang Rsuman Asa Paf Unvs Bppu-s Japan Absa: Ts pap nfs busnss
More informationControl Systems (Lecture note #7)
6.5 Conrol Sysms (Lcur no #7) Ls Tm: Gnrlz gnvcors Jorn form Polynoml funcons of squr mrx bg pcur: on brnch of h cours Vcor spcs mrcs lgbrc quons Egnvlus Egnvcors Dgonl form Cnoncl form Soluons o : x x
More informationSingle Correct Type. cos z + k, then the value of k equals. dx = 2 dz. (a) 1 (b) 0 (c)1 (d) 2 (code-v2t3paq10) l (c) ( l ) x.
IIT JEE/AIEEE MATHS y SUHAAG SIR Bhopl, Ph. (755)3 www.kolsss.om Qusion. & Soluion. In. Cl. Pg: of 6 TOPIC = INTEGRAL CALCULUS Singl Corr Typ 3 3 3 Qu.. L f () = sin + sin + + sin + hn h primiiv of f()
More information(2) If we multiplied a row of B by λ, then the value is also multiplied by λ(here lambda could be 0). namely
. DETERMINANT.. Dtrminnt. Introution:I you think row vtor o mtrix s oorint o vtors in sp, thn th gomtri mning o th rnk o th mtrix is th imnsion o th prlllppi spnn y thm. But w r not only r out th imnsion,
More informationPR 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 informationINDUCTANCE OF A PLUNGER-TYPE ELECTROMAGNET
NDUCTANCE OF A PUNGER-TYPE EECTROMAGNET Grgor A. CVDJAN, Aln DOAN, Vor CMOV, Al hsn CANAKOGU * Unvrsy of Crov, Ron, * Dlpnr Unvrsy, Khy, Try ps 5, RO- Crov, Tl: +45/4574, E-l : gvdjn@lh.v.ro Asr n h ppr,
More informationThe Variance-Covariance Matrix
Th Varanc-Covaranc Marx Our bggs a so-ar has bn ng a lnar uncon o a s o daa by mnmzng h las squars drncs rom h o h daa wh mnsarch. Whn analyzng non-lnar daa you hav o us a program l Malab as many yps o
More informationAn Inventory Model for Deteriorating Items with Quadratic Demand and Partial Backlogging
Brsh Journl of Appl Sn & hnology (): - 0 SCIECEDOMAI nrnonl wwwsnomnorg An Invnory Mol for Drorng Ims wh Qur Dmn n Prl Bkloggng R Bgum S K Shu n R R Shoo Dprmn of Mhms Pmn Collg of Engg Rourkl-76900 Osh
More informationChapter 8 Theories of Systems
~~ 7 Char Thor of Sm - Lala Tranform Solon of Lnar Sm Lnar Sm F : Conr n a n- n- a n- n- a a f L n n- ' ' ' n n n a a a a f Eg - an b ranform no ' ' b an b Lala ranform Sol Lf ]F-f 7 C 7 C C C ] a L a
More informationAdvanced Queueing Theory. M/G/1 Queueing Systems
Advand Quung Thory Ths slds ar rad by Dr. Yh Huang of Gorg Mason Unvrsy. Sudns rgsrd n Dr. Huang's ourss a GMU an ma a sngl mahn-radabl opy and prn a sngl opy of ah sld for hr own rfrn, so long as ah sld
More informationFluctuation-Electromagnetic Interaction of Rotating Neutral Particle with the Surface: Relativistic Theory
Fluuaon-lroagn Inraon of Roang Nural Parl w Surfa: Rlavs or A.A. Kasov an G.V. Dov as on fluuaon-lroagn or w av alula rar for of araon fronal on an ang ra of a nural parl roang nar a polarabl surfa. parl
More informationn 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
More informationA Study of the Solutions of the Lotka Volterra. Prey Predator System Using Perturbation. Technique
Inrnionl hmil orum no. 667-67 Sud of h Soluions of h o Volrr r rdor Ssm Using rurion Thniqu D.Vnu ol Ro * D. of lid hmis IT Collg of Sin IT Univrsi Vishnm.. Indi Y... Thorni D. of lid hmis IT Collg of
More informationJonathan Turner Exam 2-10/28/03
CS Algorihm n Progrm Prolm Exm Soluion S Soluion Jonhn Turnr Exm //. ( poin) In h Fioni hp ruur, u wn vrx u n i prn v u ing u v i v h lry lo hil in i l m hil o om ohr vrx. Suppo w hng hi, o h ing u i prorm
More informationPreparred by A.Immanuvel Maduram Thangiah, St. John s HSS, Palayamkottai Key for March 2015 Maths Questions Pl.visit 12th-maths-key.weebly.
www.pdsl.n Prprrd A.Immnuvl Mdurm Thngh, S. John s HSS, Plmo K for Mrh 5 Mhs Qusons Pl.vs h-mhs-.wl.om Mrh 5 Hghr Sondr Mhms A I Answr ll h Qusons. =. Answr :. Infnl mn soluon. Answr : d. ll h ov. Answr
More informationl 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 informationOn 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 information2011/49. Sustainable Growth and Modernization Under Environmental Hazard and Adaptation. Natali HRITONENKO Yuri YATSENKO
0/49 Susnbl Growh n Mornzon Unr Envronmnl Hzr n Apon Nl HRIONENKO Yur YASENKO CORE DISCUSSION PAPER 0/5 Susnbl growh n mornzon unr nvronmnl hzr n pon Nl HRIONENKO n Yur YASENKO Jun 0 Absr W vlop n ggrg
More informationDynamic Safety Margin in Fault-Tolerant Predictive Controller
Pongs of h 5 IEEE onfn on onol pplons oono, n, gs 8-, 5 n Sf Mgn n Fl-oln Pv onoll M l-gll, E n, G oon L, Unvs of Mnnh, Gn lgll@n-nnh, n@n-nnh, g@n-nnh s n sf gn SM s nw pfon n s o s h sn wn pfn sf on
More informationOverview. Splay trees. Balanced binary search trees. Inge Li Gørtz. Self-adjusting BST (Sleator-Tarjan 1983).
Ovrvw Bn nr rh r: R-k r n -- r 00 Ing L Gør Amor n Dnm rogrmmng Nwork fow Srng mhng Srng nng Comuon gomr Inrouon o NP-omn Rnom gorhm Bn nr rh r -- r. Aow,, or k r no Prf n. Evr h from roo o f h m ngh.
More information22 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 information46 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 informationSAMPLE 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 informationD 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 informationME 522 PRINCIPLES OF ROBOTICS. FIRST MIDTERM EXAMINATION April 19, M. Kemal Özgören
ME 522 PINCIPLES OF OBOTICS FIST MIDTEM EXAMINATION April 9, 202 Nm Lst Nm M. Kml Özgörn 2 4 60 40 40 0 80 250 USEFUL FOMULAS cos( ) cos cos sin sin sin( ) sin cos cos sin sin y/ r, cos x/ r, r 0 tn 2(
More information9. Simple Rules for Monetary Policy
9. Smpl Ruls for Monar Polc John B. Talor, Ma 0, 03 Woodford, AR 00 ovrvw papr Purpos s o consdr o wha xn hs prscrpon rsmbls h sor of polc ha conomc hor would rcommnd Bu frs, l s rvw how hs sor of polc
More informationHIGHER ORDER DIFFERENTIAL EQUATIONS
Prof Enriqu Mtus Nivs PhD in Mthmtis Edution IGER ORDER DIFFERENTIAL EQUATIONS omognous linr qutions with onstnt offiints of ordr two highr Appl rdution mthod to dtrmin solution of th nonhomognous qution
More informationImproving Union. Implementation. Union-by-size Code. Union-by-Size Find Analysis. Path Compression! Improving Find find(e)
POW CSE 36: Dt Struturs Top #10 T Dynm (Equvln) Duo: Unon-y-Sz & Pt Comprsson Wk!! Luk MDowll Summr Qurtr 003 M! ZING Wt s Goo Mz? Mz Construton lortm Gvn: ollton o rooms V Conntons twn t rooms (ntlly
More informationMA1506 Tutorial 2 Solutions. Question 1. (1a) 1 ) y x. e x. 1 exp (in general, Integrating factor is. ye dx. So ) (1b) e e. e c.
MA56 utorial Solutions Qustion a Intgrating fator is ln p p in gnral, multipl b p So b ln p p sin his kin is all a Brnoulli quation -- st Sin w fin Y, Y Y, Y Y p Qustion Dfin v / hn our quation is v μ
More informationChapter 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 informationFloating Point Number System -(1.3)
Floting Point Numbr Sstm -(.3). Floting Point Numbr Sstm: Comutrs rrsnt rl numbrs in loting oint numbr sstm: F,k,m,M 0. 3... k ;0, 0 i, i,...,k, m M. Nottions: th bs 0, k th numbr o igts in th bs xnsion
More informationFloating Point Number System -(1.3)
Floting Point Numbr Sstm -(.3). Floting Point Numbr Sstm: Comutrs rrsnt rl numbrs in loting oint numbr sstm: F,k,m,M 0. 3... k ;0, 0 i, i,...,k, m M. Nottions: th bs 0, k th numbr o igits in th bs xnsion
More informationTh 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 informationEE243 Advanced Electromagnetic Theory Lec # 10: Poynting s Theorem, Time- Harmonic EM Fields
Appl M Fall 6 Nuruhr Lcur # r 9/6/6 4 Avanc lcromagnc Thory Lc # : Poynng s Thorm Tm- armonc M Fls Poynng s Thorm Consrvaon o nrgy an momnum Poynng s Thorm or Lnar sprsv Ma Poynng s Thorm or Tm-armonc
More information1 Introduction to Modulo 7 Arithmetic
1 Introution to Moulo 7 Arithmti Bor w try our hn t solvin som hr Moulr KnKns, lt s tk los look t on moulr rithmti, mo 7 rithmti. You ll s in this sminr tht rithmti moulo prim is quit irnt rom th ons w
More informationRelation between Fourier Series and Transform
EE 37-3 8 Ch. II: Inro. o Sinls Lcur 5 Dr. Wih Abu-Al-Su Rlion bwn ourir Sris n Trnsform Th ourir Trnsform T is riv from h finiion of h ourir Sris S. Consir, for xmpl, h prioic complx sinl To wih prio
More information4 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
More informationSupplementary Figure 1. Experiment and simulation with finite qudit. anharmonicity. (a), Experimental data taken after a 60 ns three-tone pulse.
Supplmnar Fgur. Eprmn and smulaon wh fn qud anharmonc. a, Eprmnal daa akn afr a 6 ns hr-on puls. b, Smulaon usng h amlonan. Supplmnar Fgur. Phagoran dnamcs n h m doman. a, Eprmnal daa. Th hr-on puls s
More informationINF5820 MT 26 OCT 2012
INF582 MT 26 OCT 22 H22 Jn Tor Lønnng l@.uo.no Tody Ssl hn rnslon: Th nosy hnnl odl Word-bsd IBM odl Trnng SMT xpl En o lgd n r d bygg..9 h.6 d.3.9 rgh.9 wh.4 buldng.45 oo.3 rd.25 srgh.7 by.3 onsruon.33
More information0 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 information9.5 Complex variables
9.5 Cmpl varabls. Cnsdr th funtn u v f( ) whr ( ) ( ), f( ), fr ths funtn tw statmnts ar as fllws: Statmnt : f( ) satsf Cauh mann quatn at th rgn. Statmnt : f ( ) ds nt st Th rrt statmnt ar (A) nl (B)
More information1K21 LED GR N +33V 604R VR? 1K0 -33V -33V 0R0 MUTE SWTH? JA? T1 T2 RL? +33V 100R A17 CB? 1N N RB? 2K0 QBI? OU T JE182 4K75 RB? 1N914 D?
L P.O. O X 0, N L R. PROROUH, ONRIO N KJ Y PHO N (0) FX (0) 0 WWW.RYSON. ate : Size : 000 File : OVRLL SHMI.Schoc Sheet : 0 of 0 Rev : rawn : 0.0 0K K 0K K 0K0 0K0 0K0 0K0 0K0 00K R K0 R K 0R??? 00N M?
More informationIntroduction 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 information16.512, Rocket Propulsion Prof. Manuel Martinez-Sanchez Lecture 3: Ideal Nozzle Fluid Mechanics
6.5, Rok ropulsion rof. nul rinz-snhz Lur 3: Idl Nozzl luid hnis Idl Nozzl low wih No Sprion (-D) - Qusi -D (slndr) pproximion - Idl gs ssumd ( ) mu + Opimum xpnsion: - or lss, >, ould driv mor forwrd
More informationIntroduction 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:
More informationNEW FLOODWAY (CLOMR) TE TE PIN: GREENS OF ROCK HILL, LLC DB: 12209, PG: ' S67 46'18"E 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 informationOverview. 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 informationCase Study VI Answers PHA 5127 Fall 2006
Qustion. A ptint is givn 250 mg immit-rls thophyllin tblt (Tblt A). A wk ltr, th sm ptint is givn 250 mg sustin-rls thophyllin tblt (Tblt B). Th tblts follow on-comprtmntl mol n hv first-orr bsorption
More informationWalk Like a Mathematician Learning Task:
Gori Dprtmnt of Euction Wlk Lik Mthmticin Lrnin Tsk: Mtrics llow us to prform mny usful mthmticl tsks which orinrily rquir lr numbr of computtions. Som typs of problms which cn b on fficintly with mtrics
More information5/1/2018. Huffman Coding Trees. Huffman Coding Trees. Huffman Coding Trees. Huffman Coding Trees. Huffman Coding Trees. Huffman Coding Trees
/1/018 W usully no strns y ssnn -lnt os to ll rtrs n t lpt (or mpl, 8-t on n ASCII). Howvr, rnt rtrs our wt rnt rquns, w n sv mmory n ru trnsmttl tm y usn vrl-lnt non. T s to ssn sortr os to rtrs tt our
More informationHandout 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 informationAnalytical Study of a Special Case of Complex Canonical Transform
lobl Jornl o Mhmcl Scncs: hory n Prccl Volm, Nmbr 3 00, pp 6--70 Inrnonl Rsrch Pblcon Hos hp://wwwrphoscom Anlycl Sy o Spcl Cs o Complx Cnoncl rnsorm PR Dshmkh n AS h Pro Rm Mgh Ins o chnology & Rsrch,
More informationLINEAR 2 nd ORDER DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS
Diol Bgyoko (0) I.INTRODUCTION LINEAR d ORDER DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS I. Dfiiio All suh diffril quios s i h sdrd or oil form: y + y + y Q( x) dy d y wih y d y d dx dx whr,, d
More informationSeptember 27, Introduction to Ordinary Differential Equations. ME 501A Seminar in Engineering Analysis Page 1. Outline
Introucton to Ornar Dffrntal Equatons Sptmbr 7, 7 Introucton to Ornar Dffrntal Equatons Larr artto Mchancal Engnrng AB Smnar n Engnrng Analss Sptmbr 7, 7 Outln Rvw numrcal solutons Bascs of ffrntal quatons
More information4 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,
More informationMajor: 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 informationChapter 1: Review of Quantum Mechanics. Postulates of Quantum Mechanics: 1-3
Chr : Rw of Qunum Mhns In hs lur you wll lrn..ll h you mgh h forgon: Posuls of qunum mhns Commuon rlons Shrongr n snrg urs Tm lomn Dnsy orors n nsy mrs Dohrn n qunum mhns C 47 Srng 9 Frhn Rn Cornll nrsy
More informationChapter 4 A First Analysis of F edback edbac
Chr 4 A Fr Anly of Fbck 4. h Bc quon of Conrol On-loo ym - Ouu - rror - On-loo rnfr funconolf Clo-loo ym U Uny fbck rucur hr xrnl nu: - : rfrnc h ouu xc o rck - W: urbnc - V : nor no Ouu: ffc by boh nu
More informationChapter 14: Optical Parametric Oscillators
Qunum Oc f Phnc n Olcnc hn n, Cnll Un Ch : Ocl Pmc Ocll. Inucn In h Ch w wll cu n cl mc cll. A mc cll lm lk l. Th ffnc h h cl n n h c cm n fm uln n mum u fm nnln cl mum whch h h cn h h 3 cl nnln. Cn n
More informationLA PRISE DE CALAIS. çoys, çoys, har - dis. çoys, dis. tons, mantz, tons, Gas. c est. à ce. C est à ce. coup, c est à ce
> ƒ? @ Z [ \ _ ' µ `. l 1 2 3 z Æ Ñ 6 = Ð l sl (~131 1606) rn % & +, l r s s, r 7 nr ss r r s s s, r s, r! " # $ s s ( ) r * s, / 0 s, r 4 r r 9;: < 10 r mnz, rz, r ns, 1 s ; j;k ns, q r s { } ~ l r mnz,
More informationConstructive Geometric Constraint Solving
Construtiv Gomtri Constrint Solving Antoni Soto i Rir Dprtmnt Llngutgs i Sistms Inormàtis Univrsitt Politèni Ctluny Brlon, Sptmr 2002 CGCS p.1/37 Prliminris CGCS p.2/37 Gomtri onstrint prolm C 2 D L BC
More information(A) the function is an eigenfunction with eigenvalue Physical Chemistry (I) First Quiz
96- Physcl Chmstry (I) Frst Quz lctron rst mss m 9.9 - klogrm, Plnck constnt h 6.66-4 oul scon Sp of lght c. 8 m/s, lctron volt V.6-9 oul. Th functon F() C[cos()+sn()] s n gnfuncton of /. Th gnvlu s (A)
More informationChapter 2: Semi-Classical Light- Matter Interaction
Quanum Ops for Phoons and Opolrons (Farhan ana, Cornll Unvrs) Chapr : Sm-Classal Lgh- Mar Inraon. A Two-lvl Ssm Inrang wh Classal Elromagn Fld n h Absn of Dohrn.. Hamlonan for Inraon bwn Lgh and a Two-lvl
More information6 C. Carbon-based materials. Graphene. Graphene applications. Ηλεκτρικές και οπτικές και ιδιότητες γραφενίου
Unvs o Ionnn Dpmn o Mls Sn & nnn Compuonl Mls Sn Cbon-bs mls Ηλεκτρικές και οπτικές και ιδιότητες γραφενίου 6 C los Los Mls Sn & nnn, Unvs o Ionnn, G Gphn Gphn pplons on-om-h pln sh o sp -bon bon oms Pu
More informationFactors Success op Ten Critical T the exactly what wonder may you referenced, being questions different the all With success critical ten top the of l
Fr Su p T rl T xl r rr, bg r ll Wh u rl p l Fllg ll r lkg plr plr rl r kg: 1 k r r u v P 2 u l r P 3 ) r rl k 4 k rprl 5 6 k prbl lvg hkg rl 7 lxbl F 8 l S v 9 p rh L 0 1 k r T h r S pbl r u rl bv p p
More informationTh 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 informationFourier Series and Parseval s Relation Çağatay Candan Dec. 22, 2013
Fourir Sris nd Prsvl s Rlion Çğy Cndn Dc., 3 W sudy h m problm EE 3 M, Fll3- in som dil o illusr som conncions bwn Fourir sris, Prsvl s rlion nd RMS vlus. Q. ps h signl sin is h inpu o hlf-wv rcifir circui
More informationA simple 2-D interpolation model for analysis of nonlinear data
Vol No - p://oog//n Nl Sn A mpl -D npolon mol o nl o nonln M Zmn Dpmn o Cvl Engnng Fl o nolog n Engnng Yo Unv Yo In; m@ml Rv M ; v Apl ; p M ABSRAC o mnon volm n wg o nonnom o n o po vlon o mnng n o ng
More information, each of which is a tree, and whose roots r 1. , respectively, are children of r. Data Structures & File Management
nrl tr T is init st o on or mor nos suh tht thr is on sint no r, ll th root o T, n th rminin nos r prtition into n isjoint susts T, T,, T n, h o whih is tr, n whos roots r, r,, r n, rsptivly, r hilrn o
More informationV. Light amplification & Spontaneous emission
V. Lgh mplfon & Sponnous msson nrgy Lsrs r bsd on onnous msson nd lgh mplfon, hh r nds of qunum phnomnon. Ths hpr qunum mhnlly dsrbs lgh mplfon. nrgy lvl of n om A mr s omposd of oms, nd n om s omposd
More informationFL/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 informationEngineering Circuit Analysis 8th Edition Chapter Nine Exercise Solutions
Engnrng rcu naly 8h Eon hapr Nn Exrc Soluon. = KΩ, = µf, an uch ha h crcu rpon oramp. a For Sourc-fr paralll crcu: For oramp or b H 9V, V / hoo = H.7.8 ra / 5..7..9 9V 9..9..9 5.75,.5 5.75.5..9 . = nh,
More informationCONTINUOUS TIME DYNAMIC PROGRAMMING
Eon. 511b Sprng 1993 C. Sms I. Th Opmaon Problm CONTINUOUS TIME DYNAMIC PROGRAMMING W onsdr h problm of maxmng subj o and EU(C, ) d (1) j ^ d = (C, ) d + σ (C, ) dw () h(c, ), (3) whr () and (3) hold for
More informationChemistry 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.
More informationNAME: ANSWER KEY DATE: PERIOD. DIRECTIONS: MULTIPLE CHOICE. Choose the letter of the correct answer.
R A T T L E R S S L U G S NAME: ANSWER KEY DATE: PERIOD PREAP PHYSICS REIEW TWO KINEMATICS / GRAPHING FORM A DIRECTIONS: MULTIPLE CHOICE. Chs h r f h rr answr. Us h fgur bw answr qusns 1 and 2. 0 10 20
More informationCombinatorial Networks Week 1, March 11-12
1 Nots on March 11 Combinatorial Ntwors W 1, March 11-1 11 Th Pigonhol Principl Th Pigonhol Principl If n objcts ar placd in hols, whr n >, thr xists a box with mor than on objcts 11 Thorm Givn a simpl
More informationMathematical 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,. *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 informationSYMMETRICAL COMPONENTS
SYMMETRCA COMPONENTS Syl oponn llow ph un of volg n un o pl y h p ln yl oponn Con h ph ln oponn wh Engy Convon o 4 o o wh o, 4 o, 6 o Engy Convon SYMMETRCA COMPONENTS Dfn h opo wh o Th o of pho : pov ph
More informationEE 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 informationBoyce/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 informationECE COMBINATIONAL BUILDING BLOCKS - INVEST 13 DECODERS AND ENCODERS
C 24 - COMBINATIONAL BUILDING BLOCKS - INVST 3 DCODS AND NCODS FALL 23 AP FLZ To o "wll" on this invstition you must not only t th riht nswrs ut must lso o nt, omplt n onis writups tht mk ovious wht h
More informationChapter 7 Stead St y- ate Errors
Char 7 Say-Sa rror Inroucon Conrol ym analy an gn cfcaon a. rann ron b. Sably c. Say-a rror fnon of ay-a rror : u c a whr u : nu, c: ouu Val only for abl ym chck ym ably fr! nu for ay-a a nu analy U o
More informationa b c cat CAT A B C Aa Bb Cc cat cat Lesson 1 (Part 1) Verbal lesson: Capital Letters Make The Same Sound Lesson 1 (Part 1) continued...
Progrssiv Printing T.M. CPITLS g 4½+ Th sy, fun (n FR!) wy to tch cpitl lttrs. ook : C o - For Kinrgrtn or First Gr (not for pr-school). - Tchs tht cpitl lttrs mk th sm souns s th littl lttrs. - Tchs th
More informationVerifcaton. Staemnt. Treasur( Oficeholdr, TREASU, Terminato) reasonbl. informat. aplicbe: DIFERNT) knowledg. Contrled Comite: schedul.
hv x x x x / b j ^ Z( _ D w D D D G g Vf NL: h Y x LNG h Y 809 R FX / Lk - L 965 D R 507 HN D/ b g, F Rb f - F H: K - F F F ( 866/ 75 - Z D X L DR f, 6) HN LNG h Y x LNG NY h Z D RU ( ) 8 v - ( F x 0 )
More informationLecture 20: Minimum Spanning Trees (CLRS 23)
Ltur 0: Mnmum Spnnn Trs (CLRS 3) Jun, 00 Grps Lst tm w n (wt) rps (unrt/rt) n ntrou s rp voulry (vrtx,, r, pt, onnt omponnts,... ) W lso suss jny lst n jny mtrx rprsntton W wll us jny lst rprsntton unlss
More informationStatistics Assessing Normality Gary W. Oehlert School of Statistics 313B Ford Hall
Siic 504 0. Aing Normliy Gry W. Ohlr School of Siic 33B For Hll 6-65-557 gry@.umn.u Mny procur um normliy. Som procur fll pr if h rn norml, whr ohr cn k lo of bu n kp going. In ihr c, i nic o know how
More informationPlatform Controls. 1-1 Joystick Controllers. Boom Up/Down Controller Adjustments
Ston 7 - Rpr Prours Srv Mnul - Son Eton Pltorm Controls 1-1 Joystk Controllrs Mntnn oystk ontrollrs t t propr sttns s ssntl to s mn oprton. Evry oystk ontrollr soul oprt smootly n prov proportonl sp ontrol
More information