Hydrogenlike Atoms. We can separate the center of mass motion from the internal motion by the transformation


 Marshall Griffin
 2 years ago
 Views:
Transcription
1 Hydognik Atos A hydogn ik ato consists of on nucus of chag Z and a sing cton of chag . Th cassica ngy of this syst is th su of th kintic ngis of both patics and thi Couobic attaction' Z E = N & N+ & 4πε N Figu showing position vctos ativ to abitay oigin. W can spaat th cnt of ass otion fo th intna otion by th tansfoation = and n R = + NN / t wh t = + n. Fo ths w gt N = R & = R+ t N t and th ngy bcos Z E = R & t + μ & 4πε N wh μ = + N is th ducd ass. Th cnt of ass ngy is Ec = R = otion. Th ngy du to th ativ otion of th cton and nucus is E & Pc t wh P c is th ina ontu associatd with th cnt of ass t Z p Z int = μ & = 4πε μ 4πε Wh p is th ina ontu associatd with th ativ otion. Th Haitonian fo th two patics is thn J. F. Haison Michigan Stat Univsity
2 ˆ ˆ ˆ ˆ ˆ Pc p Z H = Hc + Hint = + μ 4πε t Wh th cassica onta hav bn pacd by th quantu chanica opatos ˆ P c =ih and ˆp =ih c Th Schoding quation fo th two patic syst is thn ĤΨ= EΨ and bcaus th cnt of ass otion is indpndnt of th intna otion w can wit th wavfunction fo th two patic syst as a poduct Ψ ( R, = φ( R ψ and th tota ngy E can b wittn as th su of th cnt of ass ngy and th intna ngy, E E +E wh = c int ˆ ˆ H φ R = E φ R & H ψ = E ψ and c c c c int int int int ˆ h h Z H = & H = 4πε ˆ c c int t μ In th absnc of an xtna fid, th cnt of ass otion is that of a nuta f patic. If th syst is in f spac (not boundd th wav function is a pan wav and th ngy a continuous function of th patics ontu. ik R h k φ ( R, k = C & Ec = t wh < k <+ Th ngy (in th SI syst associatd with th intna otion is found by soving th ignvau quation Hˆ h Z ψ = ψ = Eintψ μ 4πε int Subjct to th bounday conditions that ψ b finit at th oigin and vanish at. This is don in dtai in any txts and w wi sktch th pocdu and discuss th suts. Not that athough th ngy of th ato is th su of th ngy associatd with th cnt of ass otion and th intna otion on aways assus that th ato is at st J. F. Haison Michigan Stat Univsity
3 and th cnt of ass ngy is zo. W wi ca th intna ngy sipy th ngy and Hˆ Hˆ. int Th kintic ngy opato in sphica poa coodinats is h h h = sinθ + μ μ μ sinθ θ θ sin θ φ And sinc th squa of th obita angua ontu opato ˆL is givn by Lˆ =h sinθ + sinθ θ θ sin θ φ this ay b wittn as h h L = μ μ μ ˆ + Th fist t on th ight is th adia kintic ngy opato whi th scond t is th angua kintic ngy opato. Th ignfunctions of ˆL a w know to b th sphica haonics, Y ( θ, φ with ignvau + ( h ˆ ( θ, φ = ( + h ( θ, φ LY Y Wh is th angua ontu quantu nub and is a positiv intg, < and is th agntic quantu nub and fo a givn is an intg. If w sk a soution to h ˆ L Z (,, E (,, + ψ θφ ψ θφ = μ μ 4πε And wit ψ as a poduct of a adia function and a sphica haaonic, as ψ = R ( Y ( θφ, w find that th adia pat of th wavfunction and th intna ngy a dtind by th diffntia quation h ( + h Z R( ( + = ER μ μ 4πε J. F. Haison Michigan Stat Univsity
4 Lts fist ook at th sphica haonics. Angua Functions Th xpicit fo of Y ( θ, φ is Y with ( θ ( φ ( θ, φ =Θ Φ ( φ Φ = π i φ and ( + ( ( +!! Θ ( θ = δ P θ ( cos P (cosθ is an associatd Lgnd poynoia which ay b wittn in ts of th Lgnd poynoias P ( x as d P ( x = ( P x x dx Th fist fiv Lgnd poynoias a coctd bow. P( x = P( x = x P ( x = (x P ( x = (5x x P x x x = (5 + δ in th dfinition of Θ ( θ is a phas facto which is not univsay agd upon. W wi choos it to b ( whn > and + whn <. This is oftn cad th CondonShoty choic of phas and is sotis wittn as th quint J. F. Haison Michigan Stat Univsity 4
5 ( that Y = ( Y *. Not that th z coponnt of th obita angua ontu Lˆz =ih dpnds ony on φ and whn it acts on Y ( θ, φ ony affcts φ i φ Φ φ = so Y ( θ, φ is aso an ignfunction of L ˆz with ignvau h π ˆ LY ( θ, φ = hy ( θ, φ. z Th fist fw sphica haonics a givn bow aong with thi Catsian psntation obtaind using x= sinθ cosφ y = cosθ sinφ z = cosθ Its coon to idntify an obita angua ontu with a tt cosponding to th obita angua ontu quantu nub. This convntion is of histoica oigin and fs to th natu of th spctoscopic ins in th hydogn ato. Th fist fou w cad shap, piay, diffus and fundanta. Th aining tts continu in squnc with j bing oittd tt s p d f g h i s obitas, = p obitas, = d obitas, = Y = Y 4π z = cosθ = 4π 4π i x iy φ + = = 8π 8π ± ± sinθ Y Y Y Y 5 5 = ( cos θ = 6π 6π ( z x y = 5 ± iφ 5 cosθ sinθ = 8π 8π ( x + ± 5 ± iφ 5 = sin θ = π π ( x+ iy ± iy z J. F. Haison Michigan Stat Univsity 5
6 Th sphica haonics a othonoa in th sns π π '* sinθdθ d φy ( θφ, Y ' ( θφ, = δ' δ ' Radia functions Th adia functions fo a on cton ato a th soutions to th diffntia quation h ( + h Z R( ( + = ER μ μ 4πε and th dtaid soution to this quation is givn in any txt books, Pauing & Wison Th adia functions dpnd on two quantu nubs n&. n is cad th pincipa quantu nub and is a positiv intg btwn and whi is th obita angua ontu quantu nub discussd abov. Fo a givn n, is constaind to b btwn and n. Th gna fo of th adia function is in which Z R n + = L n+ ( n! {( } na n n+! (, and Z = na μ a μ 4πε = μ h and + L ( is an associatd Lagu poynoia. Not that a μ dpnds on th n+ ducd ass of th on cton ato and thus vais fo ato to ato and aong isotops of a givn ato. If w usd th ass of th cton ath than th ducd ass 4πεh of th nucuscton syst a μ woud b th Boh adius a =. Thy a atd by aμ = a +. N J. F. Haison Michigan Stat Univsity 6
7 Th fist fw associatd Lagu poynoias a n = = L ( x = n = = L = L n = = L!( = L 4 = L 5 5 n = 4 = L 4 4!(4 6 6 = L 5 5!( 5 = L 5 6 = L 7 7 and th fist fw adia functions a shown bow. n =, K sh: n =, L sh: n =, M sh: =, s R = Z a μ ( Zaμ ( Zaμ ( =, s R = =, p R = 6 ( Zaμ ( Zaμ ( Zaμ ( =, s R = =, p R = =, d R = 9 J. F. Haison Michigan Stat Univsity 7
8 Ths functions a a noaizd to R n d = and a othogona within a paticua ' n = ' n nn R R d δ This ans that a of th s functions, a of th p functions, tc a utuay othogona but fo xap R ( s is not othogona to R ( p. Ths adia functions a pottd bow fo Z=. Th a sva fatus of th adia functions that dsv ou attntion and a iustatd in ths pots. Fist, ony th s functions a nonzo at th oigin. Scond, a givn adia function Rn ( has n nods btwn and. Thid, functions shaing th sa pincipa quantu nub n hav copaab agnituds and spatia xtnsions...5 Hydogn ato s adia function R ((au (a.8.6 Hydogn Ato s & p adia functions R (.4. R s ( R p ( (a J. F. Haison Michigan Stat Univsity 8
9 .4. Hydogn ato s, p & d adia functions R ( (au.. R s ( R p ( R d ( (a Radia Distibution Function Th adia distibution function fo an obita is dfind as th pobabiity of finding an cton on th sufac of a sph of adius with th nucus as th oigin. W can div it by fist considing th pobabiity of an cton in th stat ψ n bing found in th vou ncosd by a sph o adius. Dnoting this as P ( and noting that th sphica haonics a noaizd to w hav P d d sin d R = = ( d π π * φ θ θψ nψ n n Thn th pobabiity of finding it within a sph of adius + δ is P ( + δ so th pobabiity of finding th cton in th vou btwn th two sphs is givn by th diffnc δ + δ n n P ( + P = R ( d R ( δ and th adia distibution P ( + δ P ( function is obtaind as i = R n (. Not that ach obita has a δ δ adia distibution function (RDF that dpnd on n& but not. W pot ths fist fw RDF s bow.. J. F. Haison Michigan Stat Univsity 9
10 .6 Hydogn ato s adia distibution function.5.4 R ( (a. Hydogn ato s & p adia distibution functions.5 p s R ( (a. Hydogn ato s, p & d adia distibution functions..8 d p s R ( (a Sva ipotant fatus of th adia distibution function a iustatd in ths pots. Fist, th RDF of ψ n hav n axia. Scond, th hight of th agst axiu fo a givn n dcass as dcass. Thid, within a givn n th spatia xtnsion incass as dcass. Fouth, th spatia xtnsion incass with incasing n J. F. Haison Michigan Stat Univsity
11 Engy and Dgnacy Whi th adia wavfunctions dpnd on n& th ngy ignvau E, givn by Z E n =, and dpnds ony on n. This is a consqunc of th Couob 8πε an μ potntia. Futho sinc th tota wavfunction ψ n dpnds on n, & w ay hav sva diffnt wavfunctions with th sa ngy. An individua wavfunction ψ n dfins a stat whi an ngy E n dfins a v and diffnt stats having th sa ngy a said to b dgnat. Th nub of stats in a givn ngy v is cad th dgnacy of th v. Bcaus of th constaints on th quantu nubs &, n and th dgnacy of th v En is (+ = n. Copaison with xpint Sinc w hav th ngy vs of th atos w can copa th thotica tansition ngis with xpint. Lt s fist ook at th tansition fo th gound v to th continuu o th ionization ngy. To btt undstand th ffct of th ducd ass w wi wit a a / μ = γ wh γ = + γz γz and so En = = R wh N 8πε an n R = adius 8πε a is cad th Rydbg. Th subscipt ans that w hav usd th Boh in th dfinition. Occasionay on wi s th Rydbg dfind as a n = R μ = 8πε a so th two a at though th ducd ass γ R = R in cton vots quas γ Z V and so E n= V and th ionization ngy is n IP=E = γ Z V. If th nuca ass was infinit, γ =, and a isotops of an nt woud hav th sa IP. W s fo th foowing tab that th is a sa but asiy asuab dpndnc of th IP on th isotop of a givn nt. Ato Z Mass (u IP(xp IP ( γ = V γ IP ( γ V Δ IP ( γ = V ΔIP ( γ H H H H R μ μ 4 H Li Li B J. F. Haison Michigan Stat Univsity
12 Th figu bow pots th diffnc btwn th xpinta IP and that cacuatd with (d and without (back th cnt of ass coction B + (IP(xpIP(cac V H H H + H 4 H + IP(xpintIP(γ 7 Li + 6 Li + H + IP(xpintIP(γ= Mass (u Th o is a bit atic if w ngct th cnt of ass coction (back cuv but bcos vy ody whn this coction is incudd (d cuv and th o btwn th xpinta and cacuatd IP is ssntiay th sa fo a isotops of a givn nt. This ans that th o ust dpnd on th atoic nub Z. A itt 4 nuica xpintation suggsts that th o dpnds on Z and ths data suggst 4 4 that th coction is ΔIP( γ.5x Z V. W wi s att that th ading t in th ativistic coction to th IP is.8x concusion. ZVin asonab agnt with this 4 4 In addition to th IP w can copa th cacuatd ngy vs with xpint. Th owst tansition in th Schoding thoy is n= n= which cosponds to th ngy E E =.46895γ Z V which fo th H ato is V o 8,58.58 c . Expintay howv instad of a sing v with this ngy w s th cosy spacd vs a within a wavnub of th Schoding pdiction as shown bow. J. F. Haison Michigan Stat Univsity
13 N vs of th Hydogn ato ΔE(c c  P / S / P / Lab shift.5 c N= Schoding Onc again w s that th Schoding quation is akaby accuat, th o in th tansition ngy bing about c  out of 8,59 c  and ost of this o is du to ativistic ffcts which w wi not discuss. Howv th fist od ativistic coction fo th o in th ionization ngy is shown in th foowing figu and indd it aks a significant ipovnt. Th aind of th o is du to th ngct of th couping btwn th adiation fid and th ato (quantu ctodynaics. In what foows w wi consid ony th consquncs of th Schoding thoy and whi it is not pfct ths sut show that it is vy, vy good. IP(xpintIP(cacuatd V Eo in th cacuatd Ionization ngy H H H + 4 H + H Schoding 6 Li + 7 Li + Paui (ativistic 9 B + 9 B Mass (u J. F. Haison Michigan Stat Univsity
14 Spin Whn spin is takn into account th hydognic wavfunctions a ψ nα & ψnβ and sinc th Schoding Haitonian dosn t contain spin both hav th sa ngy and th dgnacy of th v with pincip quantu nub n has bn doubd fo n to n. W wi s that spin has a pofound ffct on atos and ocus with o o ctons. Atoic Units It is usuay o convnint to xpss th ngy in atoic units ath than in th SI syst. In th atoic syst ngths a xpssd as utips of th Boh adius 4πε h a = = M which diffs fo a μ in that th cton ass has pacd th ducd ass. Th Lapacian bcos = au which suts in th a Haitonian fo th intna otion bcoing Hˆ h Z h Z = = = μ 4πε γ ˆ au au H au a aua a au a h wh γ = + accounts fo th fact that th cnt of ass is not pcisy at th N nucus. It s sast fo th hydogn ato, γ H = and appoachs as th nuca ass incass. Th Schoding quation is thn h Hˆ au ψ = Eψ o a Hˆ Ea h au ψ = E au ψ wh E au =. quas x 8 J o 7.8 h a V and is th aount of ngy cosponding to atoic unit. This ngy unit is oftn cad a Hat and psntd as E H o sipy th atoic unit of ngy. Sinc th Z aowd vaus fo th intna ngy a En = th ignvaus in Hats 8πε an γ Z γ Z a En =. Not that E = is th ionization ngy of th ato. n Sinc in what foows w wi usuay us atoic units w wi dop th au fo th ngy and vaious ngths and assu a nuci a assiv ativ to th cton so that γ =. This is an xcnt appoxiation fo ost puposs. Accodingy th on μ J. F. Haison Michigan Stat Univsity 4
15 cton Haitonian wi b wittn as Z a H ik ato is thn Hats. Hˆ Z = and th gound stat ngy fo Ra Sphica Haonics Bcaus th ngy of a hydogn ik ato is indpndnt of & w can tak ina cobinations of th dgnat ignfunctions and sti hav a vaid soution to th Schoding quation. A vy coon choic is to tak ina cobinations of th copx sphica haonics so that th angua ignfunctions a a and sti ignfunctions of ˆL but not of ˆL z. Sinc Y a aady a ths don t chang but w wi ist th again fo coptnss: s obita, = 4π p obitas, = p z = cosθ 4π + Y Y px = = sinθ cosφ 4π + Y + Y py = = sinθ sinφ i 4π d obitas, = 5 d = Y z = cos 6π + ( θ + Y Y 5 dxz = = sinθcosθcosφ 4π + Y + Y 5 dxz = = sinθcosθ sinφ i 4π d xy Y = Y i 5 5 = sin θ sinφcosφ = sin θ sin φ 4π 6π Y + Y 5 5 = = = φ 6π 6π + d sin θ x y ( sin φ cos φ sin θcos J. F. Haison Michigan Stat Univsity 5
16 Paiing an angua and a adia function suts in a vaid hydognik obita. Fo xap Z ( s = R ( Y = 4π and Za 5 dxy = R (d xy ( θ, φ = sin θ sinφ 9 6π J. F. Haison Michigan Stat Univsity 6
17 Mo Hydognik Wav Functions Fo convninc w tabuat th hydognic wavfunctions fo n=,,, 4, 5 & 6 and =,,,, 4, & 5. (s though h obitas ψ (, θφ, = R ( Y ( θφ, = R ( Θ ( θ ( φ n n n Φ with th sphica haonic wittn as a poduct of Θ ( θ & Φ ( φ Y ( θ ( φ ( θ, φ =Θ Φ Th functions in, θ, and φ a spaaty noaizd to unity and utuay othogona π * Φ φ Φ φ dφ = π Θ sin θ θdθ = R n d = π π * d sin θdθ ψ (,, (,, n θ φ ψn θ φ dφ = δnn δ δ vanishing, xcpt fo n= n, =, and =. =, s obitas: =, p obitas: ( θ Θ = ± ( θ Θ = ( θ Θ = 6 cos θ sin θ Th Functions Θ ( θ J. F. Haison Michigan Stat Univsity 7
18 =, d obitas: =, f obitas: = 4, g obitas: ± ( θ ( cos θ Θ = 4 5 Θ ± ( θ = sin θ cos θ ( θ Θ = ± ( θ 5 sin 4 θ 4 ( θ sin ϑ( 5cos θ ( θ 4 5 cos cos Θ = θ 4 Θ ± = 8 5 sin cos Θ ± θ = θ θ 4 Θ = 4± 4 7 sin 8 θ θ 5 ( θ sin θ( 7cos θ ( θ 9 5 cos 4 cos Θ 4 ( θ = θ θ Θ 4± ( θ = sinθ cos θ cosθ 8 Θ 4± = 8 7 sin cos Θ 4± θ = θ θ 8 Θ = 5 sin 6 4 θ J. F. Haison Michigan Stat Univsity 8
19 = 5, h obitas: Θ 5 ( θ = cos θ cos θ + cosθ 6 5 5± ( θ sin θ( cos θ 4cos θ + Θ 5 ± = 6 55 ( θ sin θ( cos θ cos θ Θ 5± = 8 77 ( θ sin θ( 9cos θ Θ 5± = ( θ 85 sin 4 cos Θ 5± 4θ = θ θ 6 Θ = 54 sin 5 θ Th Hydogn ik Radia Wav Functions Kp in ind Z = na n =, K sh: n =, L sh: n =, M sh: =, s R = Z a ( =, s R = =, p R = 6 ( =, s R = =, p R = =, d R = 9 J. F. Haison Michigan Stat Univsity 9
20 n = 4, N sh: n = 5, O sh: ( =, 4s R4 = =, 4 p R4 = + 5 = 4, d R4 = = 4, f R4 = ( =, 5s R5 = =, 5 p R5 = =, 5d R5 = = 5, f R5 = = 45, g R54 = 9 7 J. F. Haison Michigan Stat Univsity
21 n = 6, P sh: ( ( Za = 46, g R ( = ( =, 6s R6 = =, 6 p R6 = =, 6d R6 = = 6, f R6 = = 56, h R65 = J. F. Haison Michigan Stat Univsity
Handout 3. Free Electron Gas in 2D and 1D
Handout 3 F lcton Gas in D and D In this lctu ou will lan: F lcton gas in two dinsions and in on dinsion Dnsit o Stats in spac and in ng in low dinsions C 47 Sping 9 Fahan Rana Conll Univsit lcton Gass
More informationProblem Solving Session 1: Electric Dipoles and Torque
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Dpatmnt of Physics 8.02 Poblm Solving Sssion 1: Elctic Dipols and Toqu Sction Tabl (if applicabl) Goup Mmbs Intoduction: In th fist poblm you will lan to apply Coulomb
More informationA Model for AntennaPlasma Wave Coupling towards Control of Uniformity in SlotExcited Microwave Discharges
J. Plasa Fusion Rs. SERIES, Vol. 9 () A Modl fo AntnnaPlasa Wav Couling towads Contol of Unifoity in SlotExcitd Micowav Dischags Daichi SAWADA, Akihio TSUJI, Takanoi KITSUDO, Yasuyoshi YASAKA, and Hioasa
More informationHEAT TRANSFER ANALYSIS OF LNG TRANSFER LINE
Scintific Jounal of Impact Facto(SJIF): 3.34 Intnational Jounal of Advanc Engining and sach Dvlopmnt Volum,Issu, Fbuay 05 HEAT TANSFE ANALYSIS OF LNG TANSFE LINE J.D. Jani ISSN(O): 3484470 pissn(p):
More informationReach Versus Competition in Channels with Internet and Traditional Retailers
Rach Vsus Comptition in Channls with Intnt and Taditional Rtails Bai R Nault Haskayn School of Businss, Univsity of Calgay, Calgay, Albta, Canada, nault@ucalgayca Mohammad S Rahman Haskayn School of Businss,
More informationPHYSICS 206a HOMEWORK #11 SOLUTIONS
PHYSICS 0a HOEWORK # SOLUTIONS. Using Nwton s law of gavitation, div th acclation du to gavity xpincd by an objct of ass at th sufac of th Eath. Show that this acclation is indpndnt of th ass of th objct.
More informationChapter 3. Electric Potential
Chapt 3 Elctic Potntial 3.1 Potntial and Potntial Engy...33. Elctic Potntial in a Unifom Fild...35 3.3 Elctic Potntial du to Point Chags...36 3.3.1 Potntial Engy in a Systm of Chags...38 3.4 Continuous
More informationGravity and the Earth Newtonian Gravity and Earth Rotation Effects
Gavity and th Eath Nwtonian Gavity and Eath Rotation Effcts Jams R. Clynch, 003 I. Nwtonian Gavity A. Nwtonian Gavitational Foc B. Nwtonian Gavitational Fild C. Nwtonian Gavitational Potntial D. Gavity
More informationDEGRADATION MODEL OF BREAST IMAGING BY DISPERSED RADIATION
THE PUBLISHING HOUSE PROCEEDINGS OF THE ROMANIAN ACADEMY, Sis A, OF THE ROMANIAN ACADEMY Volum 1, Numb 4/011, pp. 347 35 DEGRADATION MODEL OF BREAST IMAGING BY DISPERSED RADIATION Migul BUSTAMANTE 1, Gastón
More informationME 612 Metal Forming and Theory of Plasticity. 6. Strain
Mtal Forming and Thory of Plasticity mail: azsnalp@gyt.du.tr Makin Mühndisliği Bölümü Gbz Yüksk Tknoloji Enstitüsü 6.1. Uniaxial Strain Figur 6.1 Dfinition of th uniaxial strain (a) Tnsil and (b) Comprssiv.
More informationPhysics. Lesson Plan #9 Energy, Work and Simple Machines David V. Fansler Beddingfield High School
Physics Lsson Plan #9 Engy, Wok an Simpl Machins Davi V. Fansl Bingfil High School Engy an Wok Objctivs: Dscib th lationship btwn wok an ngy; Display an ability to calculat wok on by a foc; Intify th foc
More informationHigh Voltage Cables. Figure 5.1  Layout of three, singlecore cables
High oltag Cabls 5.0 High oltag Cabls High oltag Cabls a usd whn undgound tansmission is quid. Ths cabls a laid in ducts o may b buid in th gound. Unlik in ovhad lins, ai dos not fom pat of th insulation,
More informationAn AnyLogic Simulation Model for Power and Performance Analysis of Data Centres
An AnyLogic Simulation Modl fo Pow and Pfomanc Analysis of Data Cnts Bjön F. Postma and Boudwijn R. Havkot Cnt fo Tlmatics and Infomation Tchnology, Univsity of Twnt, th Nthlands {b.f.postma, b..h.m.havkot}@utwnt.nl
More informationDesign of Extended Warranties in Supply Chains. Abstract
Dsign of Extndd Waantis in Supply Chains Kunpng Li Univsity of Illinois at Ubana Champaign, Collg of Businss Dilip Chhajd Univsity of Illinois at Ubana Champaign, Collg of Businss Suman Mallik Univsity
More informationInstruction: Solving Exponential Equations without Logarithms. This lecture uses a fourstep process to solve exponential equations:
49 Instuction: Solving Eponntil Equtions without Logithms This lctu uss foustp pocss to solv ponntil qutions: Isolt th bs. Wit both sids of th qution s ponntil pssions with lik bss. St th ponnts qul to
More informationEnergy Density / Energy Flux / Total Energy in 3D
Lecture 5 Phys 75 Energy Density / Energy Fux / Tota Energy in D Overview and Motivation: In this ecture we extend the discussion of the energy associated with wave otion to waves described by the D wave
More informationSale Mode Choice of Product Extended Warranty based on the Service Level
Intnational Jonal of  and  Svic, Scinc and Tchnology Vol8, No 8 (015, pp11 http://dxdoiog/101457/ijnsst0158801 Sal od Choic of Podct Extndd Waanty basd on th Svic Lvl Li Ji School of Infoation Tchnology,
More informationSuperconducting gravimeter calibration by colocated gravity observations results from GWR C025
Supconducting gavimt calibation by colocatd gavity obsvations sults fom GWR C25 B. us Dpatmnt of toology and Gophysics, Univsity of Vinna, Althanstass 19, A 19 Win, Austia. Cospondnc should b addssd
More informationMechanics 1: Motion in a Central Force Field
Mechanics : Motion in a Cental Foce Field We now stud the popeties of a paticle of (constant) ass oving in a paticula tpe of foce field, a cental foce field. Cental foces ae ve ipotant in phsics and engineeing.
More informationNewton s Law of Gravitation
Physics 106 Lctu 9 Nwton s Law of Gavitation SJ 7 th Ed.: Chap 1.1 to, 1.4 to 5 Histoical ovviw Nwton s invssqua law of avitation i oc Gavitational acclation Supposition Gavitation na th Eath s sufac
More informationGrade 5 Geography Program
Gad 5 Gogaphy Poga OPIC IME FRAME 1. Gogaphy: ools and Concpt h Gogaph s ools Sptb Octob Quiz 1: Globs & Maps, Map Pojctions, Map Pats st 1: Fiv ths of Gogaphy, Globs & Maps, Map Pojctions, Map Pats Quiz
More informationThe Matrix Exponential
Th Matrix Exponntial (with xrciss) 92.222  Linar Algbra II  Spring 2006 by D. Klain prliminary vrsion Corrctions and commnts ar wlcom! Th Matrix Exponntial For ach n n complx matrix A, dfin th xponntial
More informationB y R us se ll E ri c Wr ig ht, DV M. M as te r of S ci en ce I n V et er in ar y Me di ca l Sc ie nc es. A pp ro ve d:
E ff ec ts o f El ec tr ic al ly S ti mu la te d Si lv er C oa te d Im pl an ts a nd B ac te ri al C on ta mi na ti on i n a Ca ni ne R ad iu s Fr ac tu re G ap M od el B y R us se ll E ri c Wr ig ht,
More informationG ri d m on i tori n g w i th N A G I O S (*) (*) Work in collaboration with P. Lo Re, G. S av a and G. T ortone WP3I CHEP 2000, N F N 10.02.2000 M e e t i n g, N a p l e s, 29.1 1.20 0 2 R o b e r 1
More informationFactors that Influence Memory
Ovlaning Factos that Influnc Mmoy Continu to study somthing aft you can call it pfctly. Psychology 390 Psychology of Laning Stvn E. Mi, Ph.D. Listn to th audio lctu whil viwing ths slids 1 2 Oganization
More informationfiziks Institute for NET/JRF, GATE, IIT JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES NUCLEAR AND PARTICLE PHYSICS NET/JRF (JUNE2011)
Institut fo NET/JRF, GTE, IIT JM, JEST, TIFR and GRE in PHYSICL SCIENCES Had offic fiziks, H.No., G.F, Jia Saai, Na IIT, Hauz Khas, Nw Dlhi 6 Phon: 6865455/9 98745498 NUCLER ND PRTICLE PHYSICS NET/JRF
More informationSHAPES AND SHAPE WORDS!
1 Pintbl Activity Pg 1 SAPES AND SAPE WORDS! (bst fo 1 o plys) Fo ch child (o pi of childn), you will nd: wo copis of pgs nd Cyons Scissos Glu stick 10 indx cds Colo nd Mk Shp Cds! Giv ch child o pi of
More informationShould I Stay or Should I Go? Migration under Uncertainty: A New Approach
Should Stay o Should Go? Migation und Unctainty: A Nw Appoach by Yasmn Khwaja * ctob 000 * patmnt of Economics, School of intal and Afican Studis, Unisity of ondon, Thonhaugh Stt, Russll Squa, ondon WC
More information11  KINETIC THEORY OF GASES Page 1
 KIETIC THEORY OF GASES Page Introduction The constituent partices of the atter ike atos, oecues or ions are in continuous otion. In soids, the partices are very cose and osciate about their ean positions.
More informationPhysics 106 Lecture 12. Oscillations II. Recap: SHM using phasors (uniform circular motion) music structural and mechanical engineering waves
Physics 6 Lctur Oscillations II SJ 7 th Ed.: Chap 5.4, Rad only 5.6 & 5.7 Rcap: SHM using phasors (unifor circular otion) Physical pndulu xapl apd haronic oscillations Forcd oscillations and rsonanc. Rsonanc
More informationThe Fourier Transform
Th Fourir Transfor Larning outcos Us th Discrt Fourir Transfor to prfor frquncy analysis on a discrt (digital) signal Eplain th significanc of th Fast Fourir Transfor algorith; Eplain why windowing is
More informationNonHomogeneous Systems, Euler s Method, and Exponential Matrix
NonHomognous Systms, Eulr s Mthod, and Exponntial Matrix W carry on nonhomognous firstordr linar systm of diffrntial quations. W will show how Eulr s mthod gnralizs to systms, giving us a numrical approach
More informationNew Basis Functions. Section 8. Complex Fourier Series
Nw Basis Functions Sction 8 Complx Fourir Sris Th complx Fourir sris is prsntd first with priod 2, thn with gnral priod. Th connction with th ralvalud Fourir sris is xplaind and formula ar givn for convrting
More informationAngles formed by 2 Lines being cut by a Transversal
Chapter 4 Anges fored by 2 Lines being cut by a Transversa Now we are going to nae anges that are fored by two ines being intersected by another ine caed a transversa. 1 2 3 4 t 5 6 7 8 If I asked you
More informationExamples. Epipoles. Epipolar geometry and the fundamental matrix
Epipoar gomtry and th fundamnta matrix Epipoar ins Lt b a point in P 3. Lt x and x b its mapping in two imags through th camra cntrs C and C. Th point, th camra cntrs C and C and th (3D points corrspon
More informationAdverse Selection and Moral Hazard in a Model With 2 States of the World
Advrs Slction and Moral Hazard in a Modl With 2 Stats of th World A modl of a risky situation with two discrt stats of th world has th advantag that it can b natly rprsntd using indiffrnc curv diagrams,
More informationA Mathematical Optimization Approach for Resource Allocation in Large Scale Data Centers
A Mathmatica Optimization Appoach fo Rsouc Aocation in Lag Sca Data Cnts Cipiano Santos, Xiaoyun Zhu, Haan Cowd Intignt Entpis chnoogis Laboatoy HP Laboatois Pao Ato HPL200264 (R.1) Dcmb 12 th, 2002
More information%UHDNGRZQRI *DVHRXV,QVXODWLRQ
1.1 Ionisation of ass %UHDNRZQRI *DVHRXV,QVXODWLRQ Elctical Insulating Matials (o Dilctics) a matials in which lctostatic filds can main almost indfinitly. Ths matials thus off a vy high sistanc to th
More information1. L a m e j o r o p c ió n e s c l o na r e l d i s co ( s e e x p li c a r á d es p u é s ).
PROCEDIMIENTO DE RECUPERACION Y COPIAS DE SEGURIDAD DEL CORTAFUEGOS LINUX P ar a p od e r re c u p e ra r nu e s t r o c o rt a f u e go s an t e un d es a s t r e ( r ot u r a d e l di s c o o d e l a
More informationVan der Waals Forces Between Atoms
Van dr Waals Forcs twn tos Michal Fowlr /8/7 Introduction Th prfct gas quation of stat PV = NkT is anifstly incapabl of dscribing actual gass at low tpraturs, sinc thy undrgo a discontinuous chang of volu
More informationThe example is taken from Sect. 1.2 of Vol. 1 of the CPN book.
Rsourc Allocation Abstract This is a small toy xampl which is wllsuitd as a first introduction to Cnts. Th CN modl is dscribd in grat dtail, xplaining th basic concpts of Cnts. Hnc, it can b rad by popl
More informationAgilent Basics of Measuring the Dielectric Properties of Materials. Application Note
Agilnt Basics of Masuing th Dilctic Poptis of Matials Application Not Contnts Intoduction...3 Dilctic thoy...4 Dilctic Constant...4 Pmability...7 Elctomagntic popagation...8 Dilctic mchanisms...10 Ointation
More informationThe Food Guide Pyramid
Th Food Guid Pyamid A Guid to Daily Food Choics R s o u c & R f a l H a n d o u t Th Food guid Pyamid is an outlin of what to at ach day basd on th Ditay Guidlins. It s not a igid psciption but a gnal
More informationFEEHELP INFORMATION SHEET FOR DOMESTIC FULL FEE STUDENTS
FEEHELP INFORMATION SHEET FOR DOMESTIC FULL FEE STUDENTS This is n infomtion sht poducd by th Monsh Lw Studnts Socity Juis Docto Potfolio to ssist full f pying studnts (domstic) in undstnding th issus
More informationat 10 knots to avoid the hurricane, what could be the maximum CPA? 59 miles  54 nm STEP 1 Ship s Speed Radius (er) 10 k  1.0 nm every 6 minutes
:1 Navigatio :1 Gal 1 1 1 Rf: P, Huica You a udway o cous T ad you axiu spd is 1 kots. Th y of a huica bas 1 T, ils fo you positio. Th huica is ovig towads T at 1 kots. If you auv at 1 kots to avoid th
More informationParallel and Distributed Programming. Performance Metrics
Paralll and Distributd Programming Prformanc! wo main goals to b achivd with th dsign of aralll alications ar:! Prformanc: th caacity to rduc th tim to solv th roblm whn th comuting rsourcs incras;! Scalability:
More informationLecture 3: Diffusion: Fick s first law
Lctur 3: Diffusion: Fick s first law Today s topics What is diffusion? What drivs diffusion to occur? Undrstand why diffusion can surprisingly occur against th concntration gradint? Larn how to dduc th
More informationG d y n i a U s ł u g a r e j e s t r a c j i i p o m i a r u c z a s u u c z e s t n i k ó w i m p r e z s p o r t o w y c h G d y s k i e g o O r o d k a S p o r t u i R e k r e a c j i w r o k u 2 0
More informationEstablishing Wireless Conference Calls Under Delay Constraints
Establishing Wirlss Confrnc Calls Undr Dlay Constraints Aotz BarNoy aotz@sci.brooklyn.cuny.du Grzgorz Malwicz grg@cs.ua.du Novbr 17, 2003 Abstract A prvailing fatur of obil tlphony systs is that th cll
More informationQuestion 3: How do you find the relative extrema of a function?
ustion 3: How do you find th rlativ trma of a function? Th stratgy for tracking th sign of th drivativ is usful for mor than dtrmining whr a function is incrasing or dcrasing. It is also usful for locating
More information11  KINETIC THEORY OF GASES Page 1. The constituent particles of the matter like atoms, molecules or ions are in continuous motion.
 KIETIC THEORY OF GASES Page Introduction The constituent partices of the atter ike atos, oecues or ions are in continuous otion. In soids, the partices are very cose and osciate about their ean positions.
More informationEvents and Constraints: A Graphical Editor for Capturing Logic Requirements of Programs
Evnts and Constaints: A Gaphical Edito fo Captuing Logic Rquimnts of Pogams Magat H. Smith Bll Laboatois Rm. 2C407 600 Mountain Avnu Muay Hill, NJ 07974 mhs@sach.blllabs.com Gad J. Holzmann Bll Laboatois
More informationA Newer Secure Communication, File Encryption and User Identification based Cloud Security Architecture
A Nw cu Counication, Fil Encyption and Idntification basd Cloud cui Achitctu Tonny hkha Ka 1, M. A. Pavz Mahud 2,hahjadi Hisan Fajana 3,Kaws Wazd Nafi 1, and Bikash Chanda Kaoka 1 Dpatnt Coput cinc and
More informationSaving Through Trailer Tracking
SEE WHAT S HAPPENING. CUT RENTAL COSTS. Losing track of rntal trailrs is on of th worst things that can happn to you, lading to unncssary and costly rntal chargs. A Brkshir Hathaway Copany A Brkshir Hathaway
More informationTraffic Analysis and Simulation of a Prioritized Shared Medium
Taffic Analysis and Simulation of a Pioitizd Shad Mdium Jffy J. Evans Dpatmnt of Elctical and Comput Engining Tchnology Pudu Univsity 401 N. Gant St. Wst Lafaytt, IN 47907 mail: jjvans@tch.pudu.du Cynthia
More informationPrinciples of Humidity Dalton s law
Principls of Humidity Dalton s law Air is a mixtur of diffrnt gass. Th main gas componnts ar: Gas componnt volum [%] wight [%] Nitrogn N 2 78,03 75,47 Oxygn O 2 20,99 23,20 Argon Ar 0,93 1,28 Carbon dioxid
More informationC e r t ifie d Se c u r e W e b
C r t ifi d S c u r W b Z r t ifizi r t Sic h r h it im W b 1 D l gat s N ic o las M ay n c o u r t, C EO, D r am lab T c h n o lo gi s A G M ar c A n d r é B c k, C o n su lt an t, D r am lab T c h n
More informationTank Level GPRS/GSM Wireless Monitoring System Solutions
Tank Lvl GPRS/GSM Wilss Monitoing Systm Solutions HOLYKELL TECHNOLOGY CO.LTD May,2014 Ⅰ. Solution Rquimnts 1. Intoduction Th solution is mainly including: wilss data tansciv tminal, lvl snso and PC sv
More informationI n la n d N a v ig a t io n a co n t r ib u t io n t o eco n o m y su st a i n a b i l i t y
I n la n d N a v ig a t io n a co n t r ib u t io n t o eco n o m y su st a i n a b i l i t y and KB rl iak s iol mi a, hme t a ro cp hm a5 a 2k p0r0o 9f i,e ls hv oa nr t ds eu rmv oedye l o nf dae cr
More informationLecture 09 Nuclear Physics Part 1
Lecture 09 Nuclear Physics Part 1 Structure and Size of the Nucleus Νuclear Masses Binding Energy The Strong Nuclear Force Structure of the Nucleus Discovered by Rutherford, Geiger and Marsden in 1909
More informationHow to Subnet a Network How to use this paper Absolute Beginner: Read all Sections 14 N eed a q uick rev iew : Read Sections 24 J ust need a little h elp : Read Section 4 P a r t I : F o r t h e I P
More informationLINES AND TANGENTS IN POLAR COORDINATES
LINES AND TANGENTS IN POLAR COORDINATES ROGER ALEXANDER DEPARTMENT OF MATHEMATICS 1. Polacoodinate equations fo lines A pola coodinate system in the plane is detemined by a point P, called the pole, and
More informationSPECIAL VOWEL SOUNDS
SPECIAL VOWEL SOUNDS Plas consult th appropriat supplmnt for th corrsponding computr softwar lsson. Rfr to th 42 Sounds Postr for ach of th Spcial Vowl Sounds. TEACHER INFORMATION: Spcial Vowl Sounds (SVS)
More informationIt takes four quantum numbers to describe an electron. Additionally, every electron has a unique set of quantum numbers.
So, quantum mechanics does not define the path that the electron follows; rather, quantum mechanics works by determining the energy of the electron. Once the energy of an electron is known, the probability
More informationC o a t i a n P u b l i c D e b tm a n a g e m e n t a n d C h a l l e n g e s o f M a k e t D e v e l o p m e n t Z a g e bo 8 t h A p i l 2 0 1 1 h t t pdd w w wp i j fp h D p u b l i c2 d e b td S t
More informationGas Exchange Process. Gas Exchange Process. Internal Combustion Engines MAK 493E. Prof.Dr. Cem Soruşbay Istanbul Technical University
Intnal Cbustin Engins MAK 493E Gas Exchang Pcss Pf.D. C Suşbay Istanbul Tchnical Univsity Intnal Cbustin Engins MAK 493E Gas Exchang Pcss Intductin Valv chaniss Inductin in ngins Scavnging in 2stk ngins
More informationA Gas Law And Absolute Zero
A Gas Law And Absolute Zero Equipent safety goggles, DataStudio, gas bulb with pressure gauge, 10 C to +110 C theroeter, 100 C to +50 C theroeter. Caution This experient deals with aterials that are very
More informationMath 447/547 Partial Differential Equations Prof. Carlson Homework 7 Text section 4.2 1. Solve the diffusion problem. u(t,0) = 0 = u x (t,l).
Math 447/547 Partia Differentia Equations Prof. Carson Homework 7 Text section 4.2 1. Sove the diffusion probem with the mixed boundary conditions u t = ku xx, < x
More informationThe Normal Distribution: A derivation from basic principles
Th Normal Distribution: A drivation from basic principls Introduction Dan Tagu Th North Carolina School of Scinc and Mathmatics Studnts in lmntary calculus, statistics, and finit mathmatics classs oftn
More informationPhysics 111 Fall 2007 Electrostatic Forces and the Electric Field  Solutions
Physics 111 Fall 007 Electostatic Foces an the Electic Fiel  Solutions 1. Two point chages, 5 µc an 8 µc ae 1. m apat. Whee shoul a thi chage, equal to 5 µc, be place to make the electic fiel at the
More informationVersion 001 test 1 review tubman (IBII201516) 1
Version 001 test 1 review tuban (IBII01516) 1 This printout should have 44 questions. Multiplechoice questions ay continue on the next colun or page find all choices before answering. Crossbow Experient
More informationINVERSE BORN SERIES FOR SCALAR WAVES * 1. Introduction
Jouna of Computationa Mathematics Vo.3, No.6, 22, 6 64. http://www.gobasci.og/jcm doi:.428/jcm.25m3935 INVERSE BORN SERIES FOR SCALAR WAVES * Kimbey Kigoe Shai Moskow Depatment of Mathematics, Dexe Univesity,
More informationFundamentals: NATURE OF HEAT, TEMPERATURE, AND ENERGY
Fundamntals: NATURE OF HEAT, TEMPERATURE, AND ENERGY DEFINITIONS: Quantum Mchanics study of individual intractions within atoms and molculs of particl associatd with occupid quantum stat of a singl particl
More informationA Systematic Approach to the Comparison of Roles in the Software Development Processes
A Systmatic Appoach to th Compaison of Rols in th Softwa Dvlopmnt Pocsss uat Yilmaz 1, Roy V. O Conno 2 and Paul Clak 1 1 Lo Gaduat School in Softwa Engining, Dublin City Univsity, Iland 2 Lo, th Iish
More informationEcon 371: Answer Key for Problem Set 1 (Chapter 1213)
con 37: Answr Ky for Problm St (Chaptr 23) Instructor: Kanda Naknoi Sptmbr 4, 2005. (2 points) Is it possibl for a country to hav a currnt account dficit at th sam tim and has a surplus in its balanc
More informationIncorporating Statistical Process Control and Statistical Quality Control Techniques into a Quality Assurance Program
Incooating Statistical Pocss Contol and Statistical Quality Contol Tchniqus into a Quality Assuanc Pogam Robyn Sikis U.S. Cnsus Buau Puos Incooat SPC and SQC mthods into quality assuanc ogam Monito and
More informationBasis risk. When speaking about forward or futures contracts, basis risk is the market
Basis risk Whn spaking about forward or futurs contracts, basis risk is th markt risk mismatch btwn a position in th spot asst and th corrsponding futurs contract. Mor broadly spaking, basis risk (also
More informationImplied volatility formula of European Power Option Pricing
Impli volatility fomula of Euopan Pow Option Picing Jingwi Liu * ing hn chool of Mathmatics an ystm cincs, Bihang Univsity, LMIB of th Ministy of Eucation,, Bijing, 009, P.R hina Abstact:W iv th impli
More informationTraffic Flow Analysis (2)
Traffic Flow Analysis () Statistical Proprtis. Flow rat distributions. Hadway distributions. Spd distributions by Dr. GangLn Chang, Profssor Dirctor of Traffic safty and Oprations Lab. Univrsity of Maryland,
More informationA Gas Law And Absolute Zero Lab 11
HB 040605 A Gas Law And Absolute Zero Lab 11 1 A Gas Law And Absolute Zero Lab 11 Equipent safety goggles, SWS, gas bulb with pressure gauge, 10 C to +110 C theroeter, 100 C to +50 C theroeter. Caution
More informationThe (Bad?) Timing of Mutual Fund Investors. Oded Braverman,* Shmuel Kandel,** and Avi Wohl*** First version: February 2005 This version: August 2005
Th (Bad? Timing of Mutual Fund Invstos by Odd Bavman,* Shmul Kandl,** and Avi Wohl*** Fist vsion: Fbuay 2005 This vsion: August 2005 W thank Invstmnt Comany Institut (ICI fo oviding us th mutual fund data
More informationModelling international reverse factoring  and the future of supply chain finance
Eindhovn, Fuay 212 Moding intnationa v actoing  and th utu o uppy chain inanc By Mak van La BSc. Indutia Engining and Managmnt Scinc TU/ 29 Studnt idntity num: TU/: 61366 UvT: 19415 in patia uimnt o th
More information1. Oblast rozvoj spolků a SU UK 1.1. Zvyšování kvalifikace Školení Zapojení do projektů Poradenství 1.2. Financování 1.2.1.
1. O b l a s t r o z v o j s p o l k a S U U K 1. 1. Z v y š o v á n í k v a l i f i k a c e Š k o l e n í o S t u d e n t s k á u n i e U n i v e r z i t y K a r l o v y ( d á l e j e n S U U K ) z í
More informationExam 3: Equation Summary
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Depatment of Physics Physics 8.1 TEAL Fall Tem 4 Momentum: p = mv, F t = p, Fext ave t= t f t= Exam 3: Equation Summay total = Impulse: I F( t ) = p Toque: τ = S S,P
More informationPut the human back in Human Resources.
Put the human back in Human Resources A Co m p l et e Hu m a n Ca p i t a l Ma n a g em en t So l u t i o n t h a t em p o w er s HR p r o f essi o n a l s t o m eet t h ei r co r p o r a t e o b j ect
More informationstichting mathematisch centrum
A stichting mathematisch centrum AFDELING INFORMATICA IV 2/73 FEBRUARY L,G.L,Tho MEERTENS and J X V A N VLiE T REPAIRING THE PARENTHESIS SKELETON 15F ALGOL 6 8 PROGRAMS A 2e boerhaavestraat 49 amsterdam
More informationAnswer, Key Homework 7 David McIntyre 45123 Mar 25, 2004 1
Answer, Key Hoework 7 David McIntyre 453 Mar 5, 004 This printout should have 4 questions. Multiplechoice questions ay continue on the next colun or page find all choices before aking your selection.
More informationPhysics 100A Homework 11 Chapter 11 (part 1) The force passes through the point A, so there is no arm and the torque is zero.
Physics A Homework  Chapter (part ) Finding Torque A orce F o magnitude F making an ange with the x axis is appied to a partice ocated aong axis o rotation A, at Cartesian coordinates (,) in the igure.
More information1240 ev nm 2.5 ev. (4) r 2 or mv 2 = ke2
Chapte 5 Example The helium atom has 2 electonic enegy levels: E 3p = 23.1 ev and E 2s = 20.6 ev whee the gound state is E = 0. If an electon makes a tansition fom 3p to 2s, what is the wavelength of the
More informationGravity Chapter 8 Homework answers (Dec. 2009)
Gravity Chaptr 8 Howork answrs (Dc 2009) 1 Givn th valu of littlg at th quator is 97801 /s 2, what is th valu of gravity at th North Pol or South Pol? Gravity varis with latitud according to this Intrnational
More informationTransformations in Homogeneous Coordinates
Tansfomations in Homogeneous Coodinates (Com S 4/ Notes) YanBin Jia Aug, 6 Homogeneous Tansfomations A pojective tansfomation of the pojective plane is a mapping L : P P defined as u a b c u au + bv +
More informationpage 11, Problem 1.14(a), line 1: Ψ(x, t) 2 Ψ(x, t) 2 ; line 2: h 2 2mk B page 13, Problem 1.18(b), line 2, first inequality: 3mk B
Corrections to the Instructor s Soution Manua Introduction to Quantum Mechanics, nd ed by David Griffiths Cumuative errata for the print version corrected in the current eectronic version I especiay thank
More informationFinance 360 Problem Set #6 Solutions
Finance 360 Probem Set #6 Soutions 1) Suppose that you are the manager of an opera house. You have a constant margina cost of production equa to $50 (i.e. each additiona person in the theatre raises your
More informationFrederikshavn kommunale skolevæsen
Frederikshavn kommunale skolevæsen Skoleåret 196970 V e d K: HillersAndersen k. s k o l e d i r e k t ø r o g Aage Christensen f u l d m æ g t i g ( Fr e d e rik sh av n E k sp r e s T ry k k e rie
More informationInductance. Bởi: OpenStaxCollege
Inductance Bởi: OpenStaxCoege Inductors Induction is the process in which an emf is induced by changing magnetic fux. Many exampes have been discussed so far, some more effective than others. Transformers,
More informationAssigning Tasks in a 24Hour Software Development Model
Assigning Tasks in a Hour Software Deveopent Mode Pankaj Jaote, Gourav Jain Departent of Coputer Science & Engineering Indian Institute of Technoogy, Kanpur, INDIA 006 Eai:{jaote, gauravj}@iitk.ac.in
More informationPSTN. Gateway. Switch. Supervisor PC. Ethernet LAN. IPCC Express SERVER. CallManager. IP Phone. IP Phone. Cust DB
M IPCC EXPRESS Product Solution (IPCC  IP Co n t a c t Ce n t e r ) E i n f ü h r u n g Ü b e r h u nd e r t M il l io ne n N u t ze r  P r o g no s e n zu f o l g e w e r d e n e s in d ie s e m J ah
More informationLecture 33: Quantum Mechanical Spin
Lctu 33: Quantu Mcancal pn Py85 Fall 9 Intnc pn Epcally w av foun tat ot patcl av an atonal ntnal g of fo call pn T tnglac pnt 9): Eac typ of patcl a a ct nub of ntnal tat: tat > pn _ 3 tat > pn Etc.
More informationThe Casino Experience
Th Casino Expin with Mahi s authnti Indian uisin Lt us nttain you Th Casino Expin 10 Th Staight Flush Expin 20 p ps If you looking fo a gat night out, a Casino Expin patnd This is a gat intoduti to gaing
More informationCIRCUITS AND ELECTRONICS. Basic Circuit Analysis Method (KVL and KCL method)
6. CIRCUITS AND ELECTRONICS Basic Circuit Analysis Mthod (KVL and KCL mthod) Cit as: Anant Agarwal and Jffry Lang, cours matrials for 6. Circuits and Elctronics, Spring 7. MIT 6. Fall Lctur Rviw Lumpd
More information