INF5820 MT 26 OCT 2012

Size: px
Start display at page:

Download "INF5820 MT 26 OCT 2012"

Transcription

1 INF582 MT 26 OCT 22 H22 Jn Tor Lønnng Tody Ssl hn rnslon: Th nosy hnnl odl Word-bsd IBM odl Trnng

2 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 prprd.5 our.2 o.2 brly. onsrud.2 dsh. ood.5 ours.7 Slrly or: pos -2 2x3 pos -3 pos 2-4 pos 3-5 4x5 pos 6-8 os4 pos 6 x3x3 3 ny os5 pos 7 5x3x3 3 ny rgh wh 2.7x -2 rgh wh buldng.7x -8 rgh o.5x - rgh wh onsruon 5.4x -8 rgh by 9.7x -2 rgh wh brly 8.7x -9 ours o.5x -4 ours o brly.5x -6 2

3 Algnn Lngh o Englsh srng: =7 Lngh o orgn srng: =9 An lgnn s vor o lngh h nry An lgnn s vor o lngh h nry nubr bwn nd Th xpl: < 2 9 > = < > 3

4 4 Algnn Arl rsrons Arl rsrons: Svrl orgn words y b lgnd wh h s E word A orgn word nno b lgnd o or hn on E word IBM Modl Consdr ll possbl lgnns : For h lgnn us h gnrv odl: Sply h odl ssupons

5 5 Fgur Th gnrv odl: Ch h l h h Choos h lngh o h orgn srng Whh E word rnsls o h rs F word Wh s h rnslon o hs word? Whh E word rnsls o h -h F d h h F word gvn h hos so r Wh s h rnslon o hs word gvn h hos so r

6 6 Assupons pproxons s onsn ndpndn o nd E ll lgnns h s probbly dds o h word rnslon probbly only dpnds on sour word IBM odl Spls o s norlson or Forul 4.7 n h SMT boo Th boo gos no

7 rr son I h rnng orpus ws lgnd h odl ould b lrnd by ounng: C C I w hd nown h rnslon probbls w ould hv ound h os probbl lgnn. W nhr now word probbls nor lgnn: Chn nd gg probl EM-lgorh: w y lrn h wo sulnously Trnng h d. Inlz h prr vlus. Wh no no s h unorly 2. Assgn probbls o ll possbl lgnns Clld h xpon sp pply odl o d 3. Coll ronl ouns C : How ny s s rnsld s wghd wh h vrous lgnns 4. Norlz C o g Clld h xzon sp s odl ro ouns 5. Rp ro 2 s long s you l 7

8 8 Assgn probbls o lgnns sp 2 xpon Gol: opu Sn w hv W now W now Nssry splon Ths quls Bus Rdus h probl ro h ordr +^ o roughly *

9 Too ny lgnns Words= Algn ll bllons Gnrl d W wn o s how probbl snn s gvn snn W now h rnslon probbls o h word pr W ould onsdr: On lgnn Clul h probbly or h lgnn Su ovr ll lgnns Bu w do nsd For h word n s: How probbl s h hs s rnslon o on o h words n Mulply h probls ovr h words n 9

10 ung hs oghr So r Hn Forul 4. Mxzon sp Counng or on snn Subsung n or p nd dong so non-rvl lulon: p ; Counng ovr h whol orpus nd norlz ; ;

11 Obsrv Th oruls gh b rghnng bu Th d s or nuv: Unor nlzon hunddog = /3 bdog = /3 bdog = /3 hundb = /3 bb = /3 bb = /3 hundbrd = /3 bbrd = /3 bbrd = /3 hund = /3 b = /3 b = / Dog b dog Hund b hund hunddog= bdog = hundb = bb = hund = b = Dog brd Hund b hunddog= bdog = hundbrd = bbrd = hund = b =

12 Dog b dog Hund b hund Dog brd Hund b hunddog= bdog = /2 hundb = ½ bb = /4 hund = /2 b = /4 hunddog= /3 bdog = /3 hundbrd = /3 bbrd = /3 hund = /3 b = /3 ; ; ' ' hund dog ' ' { hund b b} hunddog = bdog = bdog = hundb = bb = bb = hundbrd = bbrd = bbrd = hund = b = b = ; ; ' ' hund dog ' ' { hund b b} hunddog = +/3 bdog = /2 bdog = /3 hundb = ½ bb = ¼ bb = hundbrd = /3 bbrd = bbrd = /3 hund = ½+/3 b = /3+/4 b = /3 hund dog = 4/3/4/3+/2+/3=8/ hunddog = bdog = bdog = hundb = bb = bb = hundbrd = bbrd = bbrd = hund = b = b = 2

13 Ar so rons s r. 2nd r. 5h r. 25h r h hund b.7647 b dog hund dog b dog b b hund b b brd hund.5 brd b.5 Ar so rons s r. 2nd r. 5h r. 25h r h hund b b dog hund dog b dog b b hund b b brd hund brd b

INF5820/INF9820 LANGUAGE TECHNOLOGICAL APPLICATIONS. Jan Tore Lønning, Lecture 4, 14 Sep

INF5820/INF9820 LANGUAGE TECHNOLOGICAL APPLICATIONS. Jan Tore Lønning, Lecture 4, 14 Sep INF5820/INF9820 LANGUAGE TECHNOLOGICAL ALICATIONS Jn Tor Lønning Lctur 4 4 Sp. 206 tl@ii.uio.no Tody 2 Sttisticl chin trnsltion: Th noisy chnnl odl Word-bsd Trining IBM odl 3 SMT xpl 4 En kokk lgd n rtt

More information

INF5820/INF9820 LANGUAGE TECHNOLOGICAL APPLICATIONS. Jan Tore Lønning, Lecture 4, 10 Sep.

INF5820/INF9820 LANGUAGE TECHNOLOGICAL APPLICATIONS. Jan Tore Lønning, Lecture 4, 10 Sep. INF5820/INF9820 LANGUAGE TECHNOLOGICAL ALICATIONS Jn Tor Lønning Lctur 4 0 Sp. tl@ii.uio.no Tody 2 Sttisticl chin trnsltion: Th noisy chnnl odl Word-bsd Trining IBM odl 3 SMT xpl 4 En kokk lgd n rtt d

More information

The Mathematics of Harmonic Oscillators

The 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 information

SYMMETRICAL COMPONENTS

SYMMETRICAL 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 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

Appendix. In the absence of default risk, the benefit of the tax shield due to debt financing by the firm is 1 C E C

Appendix. 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 information

P a g e 5 1 of R e p o r t P B 4 / 0 9

P a g e 5 1 of R e p o r t P B 4 / 0 9 P a g e 5 1 of R e p o r t P B 4 / 0 9 J A R T a l s o c o n c l u d e d t h a t a l t h o u g h t h e i n t e n t o f N e l s o n s r e h a b i l i t a t i o n p l a n i s t o e n h a n c e c o n n e

More information

The Procedure Abstraction Part II: Symbol Tables and Activation Records

The Procedure Abstraction Part II: Symbol Tables and Activation Records Th Produr Absrion Pr II: Symbol Tbls nd Aivion Rords Th Produr s Nm Sp Why inrodu lxil soping? Provids ompil-im mhnism for binding vribls Ls h progrmmr inrodu lol nms How n h ompilr kp rk of ll hos nms?

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

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

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

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

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

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

More information

( ) ( ) ( ) 0. Conservation of Energy & Poynting Theorem. From Maxwell s equations we have. M t. From above it can be shown (HW)

( ) ( ) ( ) 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 information

NAME: ANSWER KEY DATE: PERIOD. DIRECTIONS: MULTIPLE CHOICE. Choose the letter of the correct answer.

NAME: 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 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

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

Factors 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

Factors 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 information

A Review of Dynamic Models Used in Simulation of Gear Transmissions

A Review of Dynamic Models Used in Simulation of Gear Transmissions ANALELE UNIVERSITĂłII ETIMIE MURGU REŞIłA ANUL XXI NR. ISSN 5-797 Zol-Ios Ko Io-ol Mulu A Rvw o ls Us Sulo o G Tsssos Th vsgo o lv s lu gg g olg l us o sov sg u o pps g svl s oug o h ps. Th pupos o h ols

More information

R. 7.5 E. R. 8 E. ! ( y R. S a Clackamas County. . Sa. Zi gzag R. S almon R. U.S. Forest Service 63. acka m a. Wasco. County. Jefferson. County.

R. 7.5 E. R. 8 E. ! ( y R. S a Clackamas County. . Sa. Zi gzag R. S almon R. U.S. Forest Service 63. acka m a. Wasco. County. Jefferson. County. T 2 N r o T 1 N T 1 T 2 B d r C r lo B L t t dr vr Wh t E Wh o c r C l T 27 ch C r L r c t f C r T 4 Z z t h E T 3 H o od y d Clc l 36 C 4 N t T 3 E C r l E N 17 E H o od u u ll B ull u T 1 B 3 vr M H

More information

The University of Sydney MATH 2009

The University of Sydney MATH 2009 T Unvrsty o Syny MATH 2009 APH THEOY Tutorl 7 Solutons 2004 1. Lt t sonnt plnr rp sown. Drw ts ul, n t ul o t ul ( ). Sow tt s sonnt plnr rp, tn s onnt. Du tt ( ) s not somorp to. ( ) A onnt rp s on n

More information

Single 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.

Single 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

Chapter 7. Now, for 2) 1. 1, if z = 1, Thus, Eq. (7.20) holds

Chapter 7. Now, for 2) 1. 1, if z = 1, Thus, Eq. (7.20) holds Chapr 7, n, 7 Ipuls rspons of h ovng avrag flr s: h[, ohrws sn / / Is frquny rspons s: sn / Now, for a BR ransfr funon,, For h ovng-avrag flr, sn / W shall show by nduon ha sn / sn / sn /,, Now, for sn

More information

A L A BA M A L A W R E V IE W

A L A BA M A L A W R E V IE W A L A BA M A L A W R E V IE W Volume 52 Fall 2000 Number 1 B E F O R E D I S A B I L I T Y C I V I L R I G HT S : C I V I L W A R P E N S I O N S A N D TH E P O L I T I C S O F D I S A B I L I T Y I N

More information

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

Weighted Graphs. Weighted graphs may be either directed or undirected.

Weighted Graphs. Weighted graphs may be either directed or undirected. 1 In mny ppltons, o rp s n ssot numrl vlu, ll wt. Usully, t wts r nonntv ntrs. Wt rps my tr rt or unrt. T wt o n s otn rrr to s t "ost" o t. In ppltons, t wt my msur o t lnt o rout, t pty o ln, t nry rqur

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

1- I. M. ALGHROUZ: A New Approach To Fractional Derivatives, J. AOU, V. 10, (2007), pp

1- 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 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

Posterior analysis of the compound truncated Weibull under different loss functions for censored data.

Posterior analysis of the compound truncated Weibull under different loss functions for censored data. INRNAIONA JOURNA OF MAHMAIC AND COMUR IN IMUAION Vou 6 oso yss of h oou u Wu u ff oss fuos fo so. Khw BOUDJRDA Ass CHADI Ho FAG. As I hs h Bys yss of gh u Wu suo s os u y II so. Bys sos osog ss hv v usg

More information

Machine Translation. Hiroshi Nakagawa

Machine Translation. Hiroshi Nakagawa Mhn Trnson Hrosh Nkgw Inoron Thnoogy Cnr; Mh Inors Grdu Shoo o Inoron Sn nd Thnoogy; Grdu Shoo o Inrdspnry Inoron Suds Th Unvrsy o Tokyo Ps Mhn Trnson Inpu snn: "w--s h r-n-go wo -b- I n pp. " -> Morphoog

More information

Republic of tlre Ph?lippines OEPARTMENT OF EDUCATION

Republic of tlre Ph?lippines OEPARTMENT OF EDUCATION Repb re Ph?ppnes OPARTMT O DATO Ren V& AABARZO w ss Ds ABYA TORADT TO: ROM SBT: DAT Asssn Shs Dsn Speenen O he Sr emne n Operns Dbn O he nr:m mpemenn Dsbn Pb n Pre emenry, Senry n Senr h Sr es Ahers neme

More information

RAKE Receiver with Adaptive Interference Cancellers for a DS-CDMA System in Multipath Fading Channels

RAKE Receiver with Adaptive Interference Cancellers for a DS-CDMA System in Multipath Fading Channels AKE v wh Apv f Cs fo DS-CDMA Ss Muph Fg Chs JooHu Y Su M EEE JHog M EEE Shoo of E Egg Sou o Uvs Sh-og Gw-gu Sou 5-74 Ko E-: ohu@su As hs pp pv AKE v wh vs og s popos fo DS-CDMA ss uph fg hs h popos pv

More information

Consider a system of 2 simultaneous first order linear equations

Consider 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 information

j '1 ' W W I T H M A L I C E T O W A R D I S T O K T E A N D C H A R I T Y F O R A L L. "

j '1 ' W W I T H M A L I C E T O W A R D I S T O K T E A N D C H A R I T Y F O R A L L. j O R D O K D R O R O O 7 O K OU R 5 97 O O 9 j - j : : 9 (9/» \>» j >- --4 U -U\- - > U 6 9 - O» X j 5 O P R j- O O R O K >/» - >/»/»> / ) -/»» K OOR O j- O ROB O D 9? - B 6 D - B? «K P BK ) P UURR O

More information

HIGHER ORDER DIFFERENTIAL EQUATIONS

HIGHER 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 information

INDUCTANCE OF A PLUNGER-TYPE ELECTROMAGNET

INDUCTANCE 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 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

THIS PAGE DECLASSIFIED IAW EO 12958

THIS PAGE DECLASSIFIED IAW EO 12958 THIS PAGE DECLASSIFIED IAW EO 2958 THIS PAGE DECLASSIFIED IAW EO 2958 THIS PAGE DECLASSIFIED IAW E0 2958 S T T T I R F R S T Exhb e 3 9 ( 66 h Bm dn ) c f o 6 8 b o d o L) B C = 6 h oup C L) TO d 8 f f

More information

MATHEMATICS FOR MANAGEMENT BBMP1103

MATHEMATICS FOR MANAGEMENT BBMP1103 Objctivs: TOPIC : EXPONENTIAL AND LOGARITHM FUNCTIONS. Idntif pnntils nd lgrithmic functins. Idntif th grph f n pnntil nd lgrithmic functins. Clcult qutins using prprtis f pnntils. Clcult qutins using

More information

J = 1 J = 1 0 J J =1 J = Bout. Bin (1) Ey = 4E0 cos(kz (2) (2) (3) (4) (5) (3) cos(kz (1) ωt +pπ/2) (2) (6) (4) (3) iωt (3) (5) ωt = π E(1) E = [E e

J = 1 J = 1 0 J J =1 J = Bout. Bin (1) Ey = 4E0 cos(kz (2) (2) (3) (4) (5) (3) cos(kz (1) ωt +pπ/2) (2) (6) (4) (3) iωt (3) (5) ωt = π E(1) E = [E e ) ) Cov&o for rg h of olr&o for gog o&v r&o: - Look wv rog&g owr ou (look r&o). - F r wh o&o of fil vor. - I h CCWLHCP CWRHCP - u &l & hv oo g, h lr- fil vor r ou rgh- h orkrw for RHCP! 3) For h followg

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

Control Systems. Modelling Physical Systems. Assoc.Prof. Haluk Görgün. Gears DC Motors. Lecture #5. Control Systems. 10 March 2013

Control Systems. Modelling Physical Systems. Assoc.Prof. Haluk Görgün. Gears DC Motors. Lecture #5. Control Systems. 10 March 2013 Lcur #5 Conrol Sy Modlling Phyicl Sy Gr DC Moor Aoc.Prof. Hluk Görgün 0 Mrch 03 Conrol Sy Aoc. Prof. Hluk Görgün rnfr Funcion for Sy wih Gr Gr provid chnicl dvng o roionl y. Anyon who h riddn 0-pd bicycl

More information

Inverse Fourier Transform. Properties of Continuous time Fourier Transform. Review. Linearity. Reading Assignment Oppenheim Sec pp.289.

Inverse Fourier Transform. Properties of Continuous time Fourier Transform. Review. Linearity. Reading Assignment Oppenheim Sec pp.289. Convrgnc of ourir Trnsform Rding Assignmn Oppnhim Sc 42 pp289 Propris of Coninuous im ourir Trnsform Rviw Rviw or coninuous-im priodic signl x, j x j d Invrs ourir Trnsform 2 j j x d ourir Trnsform Linriy

More information

Minimum Spanning Trees

Minimum Spanning Trees Mnmum Spnnng Trs Spnnng Tr A tr (.., connctd, cyclc grph) whch contns ll th vrtcs of th grph Mnmum Spnnng Tr Spnnng tr wth th mnmum sum of wghts 1 1 Spnnng forst If grph s not connctd, thn thr s spnnng

More information

CE427 - CHEMICAL ENGINEERING LABORATORY III FALL 2005 MATHEMATICAL MODELLING OF TANK DRAINING

CE427 - CHEMICAL ENGINEERING LABORATORY III FALL 2005 MATHEMATICAL MODELLING OF TANK DRAINING CE47 - CEMICA ENGINEERING ABORATORY III FA 005 MATEMATICA MODEING OF TANK DRAINING Ojvs: Dvlop r mml modls o vryng omplxy o prd m rqurd o drn vrl ylndrl nk nd ompr modls w xprmnl d. Sysm: Two nks lod n

More information

Having a glimpse of some of the possibilities for solutions of linear systems, we move to methods of finding these solutions. The basic idea we shall

Having a glimpse of some of the possibilities for solutions of linear systems, we move to methods of finding these solutions. The basic idea we shall Hvn lps o so o t posslts or solutons o lnr systs, w ov to tos o nn ts solutons. T s w sll us s to try to sply t syst y lntn so o t vrls n so ts qutons. Tus, w rr to t to s lnton. T prry oprton nvolv s

More information

ADORO TE DEVOTE (Godhead Here in Hiding) te, stus bat mas, la te. in so non mor Je nunc. la in. tis. ne, su a. tum. tas: tur: tas: or: ni, ne, o:

ADORO TE DEVOTE (Godhead Here in Hiding) te, stus bat mas, la te. in so non mor Je nunc. la in. tis. ne, su a. tum. tas: tur: tas: or: ni, ne, o: R TE EVTE (dhd H Hdg) L / Mld Kbrd gú s v l m sl c m qu gs v nns V n P P rs l mul m d lud 7 súb Fí cón ví f f dó, cru gs,, j l f c r s m l qum t pr qud ct, us: ns,,,, cs, cut r l sns m / m fí hó sn sí

More information

x, x, e are not periodic. Properties of periodic function: 1. For any integer n,

x, x, e are not periodic. Properties of periodic function: 1. For any integer n, Chpr Fourir Sri, Igrl, d Tror. Fourir Sri A uio i lld priodi i hr i o poiiv ur p uh h p, p i lld priod o R i,, r priodi uio.,, r o priodi. Propri o priodi uio:. For y igr, p. I d g hv priod p, h h g lo

More information

How to Make a Zia. (should you ever be inclined to do such a thing)

How to Make a Zia. (should you ever be inclined to do such a thing) H Mk Z (hud yu vr b d d uh hg) h Z? Th Z r dgu rb rd Z Pub, Id rrv N Mx, U..A.. Th Z r k fr hr pry d u f h u ymb. Th pp r brh f h rg Pub mmuy. N Mx' dv g h Z u ymb, hh rgd h h Id f Z Pub m. I dg rf hr

More information

Relation between Fourier Series and Transform

Relation 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 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

Ch 1.2: Solutions of Some Differential Equations

Ch 1.2: Solutions of Some Differential Equations Ch 1.2: Solutions of Som Diffrntil Equtions Rcll th fr fll nd owl/mic diffrntil qutions: v 9.8.2v, p.5 p 45 Ths qutions hv th gnrl form y' = y - b W cn us mthods of clculus to solv diffrntil qutions of

More information

t=0 t>0: + vr - i dvc Continuation

t=0 t>0: + vr - i dvc Continuation hapr Ga Dlay and rcus onnuaon s rcu Equaon >: S S Ths dffrnal quaon, oghr wh h nal condon, fully spcfs bhaor of crcu afr swch closs Our n challng: larn how o sol such quaons TUE/EE 57 nwrk analys 4/5 NdM

More information

Summary: Solving a Homogeneous System of Two Linear First Order Equations in Two Unknowns

Summary: 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 information

Bag for Sophia by Leonie Bateman and Deirdre Bond-Abel

Bag for Sophia by Leonie Bateman and Deirdre Bond-Abel Bag for Sopha 2012 by Leone Baeman and Derdre Bond-Abel Ths bag was desgned o go wh he beauful feled wool scarf of our book Elegan Quls, Counry Charm. Make boh and you ll have he perfec ensemble o wear

More information

w a s t h e t a r g e t f o r b i t t e r Gear* e d m y p o s i t i o n and. I s h a l l a c c e p t will ^travel a r o u n d t h e c o u n t r y, ;

w a s t h e t a r g e t f o r b i t t e r Gear* e d m y p o s i t i o n and. I s h a l l a c c e p t will ^travel a r o u n d t h e c o u n t r y, ; M M KER xor z > &5W3-> --1>-««K-U- - W - - - - ~ - -~-- >N!V- ---- - -> GENEROR MM GENE q - O F L N ; / U W 4 K -W RLPH GENZURG GERR RNGUHEO N F N L G H O - P -UM UN F - M W P W G

More information

An action with positive kinetic energy term for general relativity. T. Mei

An action with positive kinetic energy term for general relativity. T. Mei An ton wt post nt ny t fo n tty T (Dptnt of Jon Cnt Cn o Unsty Wn H PRO Pop s Rp of Cn E-: to@nn tow@pwn ) Astt: At fst w stt so sts n X: 7769 n tn sn post nt ny oont onton n y X: 7769 w psnt n ton wt

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

2mm Pitch 2 Piece Battery Connector for Litium-ion / Litium-polymer GF SERIES E-9

2mm Pitch 2 Piece Battery Connector for Litium-ion / Litium-polymer GF SERIES E-9 2mm Pitch 2 Piece Battery Connector for Litium-ion / Litium-polymer GF SERIES E-9 E-10 Horizontal Mating GF SERIES Mating Variation PLUG : GF 01-1 F PLUG : GF 02-1 F PLUG : GF 21 - -1F PLUG RECEPTACLE

More information

Trader Horn at Strand This Week

Trader Horn at Strand This Week - -N { 6 7 8 9 3 { 6 7 8 9 3 O OO O N U R Y Y 28 93 OU XXXX UO ONR ON N N Y OOR U RR NO N O 8 R Y R YR O O U- N O N N OR N RR R- 93 q 925 N 93; ( 928 ; 8 N x 5 z 25 x 2 R x q x 5 $ N x x? 7 x x 334 U 2

More information

Erlkönig. t t.! t t. t t t tj "tt. tj t tj ttt!t t. e t Jt e t t t e t Jt

Erlkönig. t t.! t t. t t t tj tt. tj t tj ttt!t t. e t Jt e t t t e t Jt Gsng Po 1 Agio " " lkö (Compl by Rhol Bckr, s Moifi by Mrk S. Zimmr)!! J "! J # " c c " Luwig vn Bhovn WoO 131 (177) I Wr Who!! " J J! 5 ri ris hro' h spä h, I urch J J Nch rk un W Es n wil A J J is f

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

A Study of the Solutions of the Lotka Volterra. Prey Predator System Using Perturbation. Technique

A 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 information

On The Fractional Euler Top System with Two Parameters

On The Fractional Euler Top System with Two Parameters Irol OPEN ACCESS Jourl Of Modr Egrg Rsrh IJMER O Th rol Eulr To Sys wh Two Prrs Mh Iv d Ghorgh Iv Ws Uvrsy of Tşor r of Mhs Srul d Gor ş Toolog 4 B-dul V Pârv Tşor Ro Corrsodg Auhor: Mh Iv W rs h dyl hvor

More information

Library Support. Netlist Conditioning. Observe Point Assessment. Vector Generation/Simulation. Vector Compression. Vector Writing

Library Support. Netlist Conditioning. Observe Point Assessment. Vector Generation/Simulation. Vector Compression. Vector Writing hpr 2 uomi T Prn Gnrion Fundmnl hpr 2 uomi T Prn Gnrion Fundmnl Lirry uppor Nli ondiioning Orv Poin mn Vor Gnrion/imulion Vor omprion Vor Wriing Figur 2- Th Ovrll Prn Gnrion Pro Dign-or-T or Digil I nd

More information

A Solution for multi-evaluator AHP

A Solution for multi-evaluator AHP ISAHP Honoll Hw Jly 8- A Solton for lt-vltor AHP Ms Shnohr Kch Osw Yo Hd Nhon Unvrsty Nhon Unvrsty Nhon Unvrsty Iz-cho Nrshno Iz-cho Nrshno Iz-cho Nrshno hb 7-87 Jpn hb 7-87 Jpn M7snoh@ct.nhon-.c.p 7oosw@ct.nhon-.c.p

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

L...,,...lllM" l)-""" Si_...,...

L...,,...lllM l)- Si_...,... > 1 122005 14:8 S BF 0tt n FC DRE RE FOR C YER 2004 80?8 P01/ Rc t > uc s cttm tsus H D11) Rqc(tdk ;) wm1111t 4 (d m D m jud: US

More information

A New Dynamic Random Fuzzy DEA Model to Predict Performance of Decision Making Units

A New Dynamic Random Fuzzy DEA Model to Predict Performance of Decision Making Units Jo o Ozo I Egg 6 75-9 A w D Ro Fzz DEA Mo o P Po o Do Mg U A gho * Mgho A Azoh S Sgh A Poo D o I Egg F o Egg P--oo U Th I Poo D o I Mg Ah T U Th I A Poo D o I Egg F o Egg P--oo U Th I R Oo 4; R 3 J 5;

More information

Telecommunications BUILDING INTERCOM CALL BUTTON WITH 3/4"C AND PULL STRING TO ACCESSIBLE CEILING SPACE. MOUNT 48" AFF.

Telecommunications BUILDING INTERCOM CALL BUTTON WITH 3/4C AND PULL STRING TO ACCESSIBLE CEILING SPACE. MOUNT 48 AFF. 0 NOOY SYMO S N NOOY NOS: NO: his is a standard symbol list and not all items listed may be used. bbreviations () XSN OV NS OO NMW - UNOUN ONU OY ONO UNS ONO NS O ONO UNS OWN NS OX OX U OP SUON UN OO,

More information

S tu d y P la n n e d Leader9s Expulsion Protested

S tu d y P la n n e d Leader9s Expulsion Protested x b 3; 5: D 8 G b 8 0 N U N V R Y 0< 25 965 G 9 x G O k K O N O R N N b N b U x k b b R RRN k V q U q 24 N x U b U 948 Rb 953 b b 25 D D b D b q b N b 954 U '-' jj X '?#»» j k 9 Kj x b j b U " ' b - R

More information

Statistical Analysis of Environmental Data - Academic Year Prof. Fernando Sansò

Statistical Analysis of Environmental Data - Academic Year Prof. Fernando Sansò Scl nly of nvronmnl D - cdmc r 8-9 Prof. Frnndo Snò XRISS - PR 5 bl of onn Inroducon... xrc (D mprcl covrnc m)...7 xrc (D mprcl covrnc m)... xrc 3 (D mprcl covrnc m)... xrc 4 (D mprcl covrnc m)...3 xrc

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

Jonathan Turner Exam 2-10/28/03

Jonathan 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 information

Detoxification of wastewater containing As and Sb by hydrothermal mineralization

Detoxification of wastewater containing As and Sb by hydrothermal mineralization P l Sp ETp S 2007, SETS07 2007 Dx ww Sb b hhl lz Tkh k, R S, 2 Hk h 2 ETp S, N Uv, N, Jp 2 Dp ppl h, G Shl E, N Uv, N, Jp b: W h x ww x b hhl lz Th 50200 wh OH 2 w h l ww 2000 p Th w v h pp l l 5 O 4 OH

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

CHARACTERIZATION FROM EXPONENTIATED GAMMA DISTRIBUTION BASED ON RECORD VALUES

CHARACTERIZATION FROM EXPONENTIATED GAMMA DISTRIBUTION BASED ON RECORD VALUES CHARACTERIZATION RO EPONENTIATED GAA DISTRIBUTION BASED ON RECORD VAUES A I Sh * R A Bo Gr Cog o Euo PO Bo 55 Jh 5 Su Ar Gr Cog o Euo Dr o h PO Bo 69 Jh 9 Su Ar ABSTRACT I h r u h or ror u ro o g ruo r

More information

SAN JOSE CITY COLLEGE PHYSICAL EDUCATION BUILDING AND RENOVATED LAB BUILDING SYMBOL LIST & GENERAL NOTES - MECHANICAL

SAN JOSE CITY COLLEGE PHYSICAL EDUCATION BUILDING AND RENOVATED LAB BUILDING SYMBOL LIST & GENERAL NOTES - MECHANICAL S SRUUR OR OORO SU sketch SYO SRPO OO OU O SUPPOR YP SUPPOR O UR SOS OVR SOS (xwx) X W (S) RR RWS U- R R OR ROO OR P S SPR SO S OS OW "Wx00"x0" 000.0, 8/7.0 Z U- R R UPPR ROO S S S SPR SO S OS OW 0"Wx0"x90"

More information

Neutrosophic Hyperideals of Semihyperrings

Neutrosophic Hyperideals of Semihyperrings Nuooph m Vol. 06 05 Uv o Nw Mo Nuooph Hpl o mhpg D Ml Dpm o Mhm j P Moh Collg Up Hooghl-758 mljumh@gml.om A. h pp w hv ou uooph hpl o mhpg o om opo o hm o u oo pop. Kwo: C Pou Compoo l o Nuooph mhpmg.

More information

Engine Thrust. From momentum conservation

Engine Thrust. From momentum conservation Airbrhing Propulsion -1 Airbrhing School o Arospc Enginring Propulsion Ovrviw w will b xmining numbr o irbrhing propulsion sysms rmjs, urbojs, urbons, urboprops Prormnc prmrs o compr hm, usul o din som

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

Chapter 1 Fundamentals in Elasticity

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

More information

Advanced Queueing Theory. M/G/1 Queueing Systems

Advanced 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 information

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

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

More information

Bayesian Estimation of the parameters of the Weibull-Weibull Length-Biased mixture distributions using time censored data

Bayesian Estimation of the parameters of the Weibull-Weibull Length-Biased mixture distributions using time censored data Bys Eso of h s of h Wull-Wull gh-bs xu suos usg so S. A. Sh N Bouss I.S.S. Co Uvsy I.N.P.S. Algs Uvsy shsh@yhoo.o ou005@yhoo.o As I hs h s of h Wull-Wull lgh s xu suos s usg h Gs slg hqu u y I sog sh.

More information

PART NUMBERS ACCESSORIES: Genuine & Optomize

PART NUMBERS ACCESSORIES: Genuine & Optomize PRT NUMRS SSORS: enuine & Optomize V(S) SSORY PRT NUMR V(S) SSORY PRT NUMR R-S TR R TR PTR43-00085 i OOR ST NNMNT PT948-1M160 R-S TR R PS PTR09-18130 im RO NT PT347-12160 t TR O TR PTR43-00082 R-S RPT

More information

Geometric Predicates P r og r a m s need t o t es t r ela t ive p os it ions of p oint s b a s ed on t heir coor d ina t es. S im p le exa m p les ( i

Geometric Predicates P r og r a m s need t o t es t r ela t ive p os it ions of p oint s b a s ed on t heir coor d ina t es. S im p le exa m p les ( i Automatic Generation of SS tag ed Geometric PP red icates Aleksandar Nanevski, G u y B lello c h and R o b ert H arp er PSCICO project h ttp: / / w w w. cs. cm u. ed u / ~ ps ci co Geometric Predicates

More information

Study on Non-linear Responses of Eccentric Structure

Study on Non-linear Responses of Eccentric Structure Th 4 h World ofr o Erh Egrg or -7 8 Bg h Sd o No-lr Rpo of Er Srr Hdz WATANABE oh USUNI Ar TASAI 3 Grd Sd Dpr of Arhr ooh Nol Uvr ooh Jp Ao Profor Dpr of Arhr ooh Nol Uvr ooh Jp ABSTRAT : 3 Profor Dpr

More information

Adrian Sfarti University of California, 387 Soda Hall, UC Berkeley, California, USA

Adrian Sfarti University of California, 387 Soda Hall, UC Berkeley, California, USA Innionl Jonl of Phoonis n Oil Thnolo Vol. 3 Iss. : 36-4 Jn 7 Rliisi Dnis n lonis in Unifol l n in Unifol Roin s-th Gnl ssions fo h loni 4-Vo Ponil in Sfi Unisi of Clifoni 387 So Hll UC Bkl Clifoni US s@ll.n

More information

Beechwood Music Department Staff

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

More information

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

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

More information

Math 3301 Homework Set 6 Solutions 10 Points. = +. The guess for the particular P ( ) ( ) ( ) ( ) ( ) ( ) ( ) cos 2 t : 4D= 2

Math 3301 Homework Set 6 Solutions 10 Points. = +. The guess for the particular P ( ) ( ) ( ) ( ) ( ) ( ) ( ) cos 2 t : 4D= 2 Mah 0 Homwork S 6 Soluions 0 oins. ( ps) I ll lav i o you o vrify ha y os sin = +. Th guss for h pariular soluion and is drivaivs is blow. Noi ha w ndd o add s ono h las wo rms sin hos ar xaly h omplimnary

More information

Theorem 1. An undirected graph is a tree if and only if there is a unique simple path between any two of its vertices.

Theorem 1. An undirected graph is a tree if and only if there is a unique simple path between any two of its vertices. Cptr 11: Trs 11.1 - Introuton to Trs Dnton 1 (Tr). A tr s onnt unrt rp wt no sp ruts. Tor 1. An unrt rp s tr n ony tr s unqu sp pt twn ny two o ts vrts. Dnton 2. A root tr s tr n w on vrtx s n snt s t

More information

CONTINUOUS TIME DYNAMIC PROGRAMMING

CONTINUOUS 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 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

Extension Formulas of Lauricella s Functions by Applications of Dixon s Summation Theorem

Extension Formulas of Lauricella s Functions by Applications of Dixon s Summation Theorem Avll t http:pvu.u Appl. Appl. Mth. ISSN: 9-9466 Vol. 0 Issu Dr 05 pp. 007-08 Appltos Appl Mthts: A Itrtol Jourl AAM Etso oruls of Lurll s utos Appltos of Do s Suto Thor Ah Al Atsh Dprtt of Mthts A Uvrst

More information

_ J.. C C A 551NED. - n R ' ' t i :. t ; . b c c : : I I .., I AS IEC. r '2 5? 9

_ J.. C C A 551NED. - n R ' ' t i :. t ; . b c c : : I I .., I AS IEC. r '2 5? 9 C C A 55NED n R 5 0 9 b c c \ { s AS EC 2 5? 9 Con 0 \ 0265 o + s ^! 4 y!! {! w Y n < R > s s = ~ C c [ + * c n j R c C / e A / = + j ) d /! Y 6 ] s v * ^ / ) v } > { ± n S = S w c s y c C { ~! > R = n

More information

Construction 11: Book I, Proposition 42

Construction 11: Book I, Proposition 42 Th Visul Construtions of Euli Constrution #11 73 Constrution 11: Book I, Proposition 42 To onstrut, in givn rtilinl ngl, prlllogrm qul to givn tringl. Not: Equl hr mns qul in r. 74 Constrution # 11 Th

More information

FOR MORE PAPERS LOGON TO

FOR MORE PAPERS LOGON TO IT430 - E-Commerce Quesion No: 1 ( Marks: 1 )- Please choose one MAC sand for M d a A ss Conro a M d a A ss Consor M r of As an Co n on of s Quesion No: 2 ( Marks: 1 )- Please choose one C oos orr HTML

More information