The automatic optimal control process for the operation changeover of heat exchangers

Size: px
Start display at page:

Download "The automatic optimal control process for the operation changeover of heat exchangers"

Transcription

1 Te aua pal rl pre fr e pera agever f ea exager K. L. Lu B. eeyer 4 & M. L very f e Feeral Are Fre Haburg Geray very f Saga fr See & Telgy P. R. Ca Tg J very P. R. Ca 4 GKSS Reear Cere Geray Abra Crl prble ex wely e appla f ea exager. A ew eay pera ae f a ea exager a be aeve by ajug e le paraeer f e exager a gve eay pera ae w a ya pre. Te ajug pre uually exeue e ba f a aua rl prple. I e paper e aua pal rl el apple aeve e arge eay pera ae f e exager w e rl ajue are eere arg e ae paraeer f e exager ye; a raal aua rl el e rl ajue are eere arg e upu paraeer f e exager. Cpare w e raal aua rl el e rl pre f e aua pal rl el beer. A exaple ue. Keywr: Te aua pal rl el e pera agever ea exager ae paraeer pal feeba. Iru Te raal aua rl e a -alle frequey-a e urg e rl pre e ajue f pu paraeer are eere arg e real-e upu paraeer f e ya ye []. Hwever a lle fful fr e be apple e ulpu ul-upu ye a e-vara ye a rl pre afary. é Hea Trafer III B. Su C. A. Brebba & A. Mee Er 4 WIT Pre ISB

2 4 Hea Trafer III Te er aua pal rl e a ae-pae e w e ajue are eere arg e ae paraeer f e ya ye. Te ae paraeer lue ly e upu paraeer bu al e er paraeer fr exaple e vara rae f e upu paraeer f e ya ye. Te pa arge f e rl pre ay be u e u e. Dya ye a ave e ae rafer fu r rafer fu arx ay ave ffere er ae ru erefre a g rl e ul er e er araer f e ya ye. Te aua pal rl e ae era e relap ag e pu paraeer e er ae paraeer a e upu paraeer. I e e e feeba f e ae paraeer ly e feeba f e upu paraeer a eere e rl pre. I paper e aua pal rl pre fr e pera agever f ea exager ue. Te a a are w eere e ae paraeer a e ae equa f e exager ye w eere e pal rl bje a w eere e feeba fr rl ajue. Te ya beavur f ea exager Te ya beavur f a ea exager u be eere e up aua pal rl el. Aug a e a flw rae f e l rea a uer flw w-rea ea exager age e ya beavur f ule eperaure a be eue fr e fllwg expre Q C p[ ] M C p C p[ ] Q M C p [ ] [ ] Q F K l[ ] a 4 K [ ] b Here e lg ea eperaure fferee apple w re aurae a e are ea eperaure fferee ue leraure [4]. Eq. a a be raferre a fllw by rug eq. a 4 a rug learza Hea Trafer III B. Sué C. A. Brebba & A. Mee Er 4 WIT Pre ISB

3 ] [ 5 ] [ 4 6 g e Laplae rafr e e rafer fu a be bae a H F p p a ξ 7 H F p p a ξ 8 were 4 H 4 H 4 H a H a / ] [ p / ] [ ξ Slarly e ya beavur aue by er le paraeer a al be bae ey are al e fr f eq. 7 a 8. Te ae equa f e ya exager ye. Oe-pu u a e-upu y lear ye Te ya exager ye a a e rafer fu f eq. 7 r 8 a be erbe by e fllwg ffereal equa e e a: u b u b u b u b y a y a y a y a 9 w al : y j j u j é Hea Trafer III B. Su C. A. Brebba & A. Mee Er 4 WIT Pre ISB Hea Trafer III 5

4 6 Hea Trafer III were u efe a e pu paraeer ajue paraeer f e ya exager ye a y e upu paraeer arge paraeer. Te ree expre f e ffereal equa a be gve a: y a y a y bu bu bu Le x y µ u x x µ u x x µ u Te ae equa f e ya exager ye e ree expre wll be wre a: A Bu y C Du were e ver f ae paraeer f ya ye a e effe are are expree repevely a µ µ A B µ a a a a µ C [ ] D µ rally e effe D equal zer; erwe e pu paraeer wll be rely raferre e upu paraeer.. Mul-pu a e-upu y lear ye Te ree expre f e ffereal equa fr a ul-pu a eupu lear ye a be wre a: y a y a y a B B B Le x y M x x M x x M Hea Trafer III B. Sué C. A. Brebba & A. Mee Er 4 WIT Pre ISB

5 Hea Trafer III 7 Tu e ae equa f e ya exager ye wll be gve a: A B a y C D a Slarly e ae equa f a ul-pu a ul-upu lear ye a be bae a: A B b Y C D b were Y e ver f upu paraeer f ya ye. 4 Te aua pal rl el Te e f ya prgrag rally ue lve e ul-per e pre. I e e e wle pre ve ay per a e pal e fr ea per ee be eere beaue ere ay ex re a e pble e u a ere f pal e fr ul-per wll eure a e wle pre pal. I e paper e e f ya prgrag apple ba e aua pal rl el fr e pera agever f ea exager. 4. Te aeaal erp Aue a e wle rl pre ve per. Te ree expre f e ae equa f a lear e-vara ye wre a: Φ Γ Y H 4 were Φ Γ a H are effe are. Fr a ya exager ye ubje e abve ree expre a w al value f ae * paraeer a e f pal rl ajue ee be eere w e rl aeble Ω w ae e fal ae paraeer f e exager ye be w er ae aeble.e. S a e bjeve fu be u. * * * J J 5 u Ω * T e f pal rl ajue alle e pal rl aeble. Fr u eva f e upu paraeer fr er ew arge eay value a u ajue eergy up f e pu paraeer f e exager e egrae bjeve fu wll be elee a: J Σ W 6 Hea Trafer III B. Sué C. A. Brebba & A. Mee Er 4 WIT Pre ISB

6 were a W are wegg are repevely v v v r w w w W 4. Te eera f pal rl ajue Te pal rl ajue fr ea per wll be eere repevely. Geerally fr a per f e pre w al ae paraeer e pal rl ajue f pu paraeer * ee be eere w ae e fllwg bje fu be a u: W R Cerg e rafer prple f ae paraeer Γ Φ Le R Te pal rl ajue * a be eere a Φ Λ * 7 were Γ Γ Γ Λ W a e bje fu wll be f Φ Φ ~ 8 were ~ Λ Γ ~ Φ Φ Tu e pal l f ae paraeer a upu paraeer y Y a be bae uquely. Fr a a ye a e ya exager ye aalye paper e are Φ Γ Λ a H are all a effe are e aua pal rl el bee ple. é Hea Trafer III B. Su C. A. Brebba & A. Mee Er 4 WIT Pre ISB Hea Trafer III

7 Hea Trafer III 9 5 Cae uy Here a w-rea ea exager ye ue. Waer ae a wrg flu a e aa f e exager a eg p are le Table. I ay be e a f e ajue f e le paraeer f e exager are le a % f er al value a e eg p repevely e ya exager ye a be ae a a lear ye [5]. Table : Te aa f e w-rea ea exager a eg p. u u KF K Kw/ C C C C C Kw/ C Kw/ C Kw/ C Fgure : Te alula agra f e aua pal rl el. 5. Oe-pu u a e-upu y lear ya pre Suppe e exager perae ealy a eg p. If e ule eperaure f e rea u ee be age up a ew eay arge value 7.4 C w we wa w w eere e pal rl ajue f e a flw rae f e l rea fulfl e a w bee a prble f aua pal rl. Hea Trafer III B. Sué C. A. Brebba & A. Mee Er 4 WIT Pre ISB

8 Hea Trafer III Te a flw rae f e l rea ere be e pu paraeer u f e ya exager ye a e ule eperaure f e rea ere be e upu paraeer y. Te ae belg e e-pu a e-upu ye. Te ya exager ye ere be a a ye e ae equa f ya pre are e fr f eq.. Te alula agra f e aua pal rl el w Fg. w e pal feeba effe arx Λ a a effe arx a be ffle-alulae a elee are le Table. Te pal rl ajue f e pu paraeer e a flw rae f e l rea urg e rl pre are w Fg. w are w e lear reg f e exager. Table : Te elee f pal feeba effe arx Λ ]. [ Ierave uber Ma flwrae f l rea Kg/ Te S Oupu eva C Te S Fgure : Te pal rl ajue. Fgure : Te pal eva. Te pal eva f e upu paraeer e ule eperaure f rea are w Fg.. Te wegg are W are eere expereally e ae ere ay ex e pee f ver- Hea Trafer III B. Sué C. A. Brebba & A. Mee Er 4 WIT Pre ISB

9 Hea Trafer III ajue.e. e ule eperaure f e rea Fg. ay exee ew arge eay value fr e e befre reae eay value. 5. Mul-pu a e-upu y lear ya pre Suppe e ule eperaure f e rea ee be age up a ew eay arge value 4. C w we wa w w eere e pal rl ajue f b e a flw rae f e l rea a e a flw rae f e rea fulfl e a. Here e a flw rae f e l rea a rea are ere be e pu paraeer f e ya exager ye a e ule eperaure f e rea ere be e upu paraeer. Te ae belg e w-pu a e-upu lear ye. Table : Te elee f pal feeba effe arx Λ. Ierave uber Ma flwrae f l rea Kg/ Te S Ma flwrae f rea Kg/ Te S Fgure 4: Te pal rl ajue. Fgure 5: Te pal rl ajue. Hea Trafer III B. Sué C. A. Brebba & A. Mee Er 4 WIT Pre ISB

10 Hea Trafer III Te elee f e pal feeba effe arx are bae by ffle erave alula a w Table. Te pal rl ajue f e pu paraeer urg e rl pre are w Fg.4 a Fg.5 wle e pal eva f e ule eperaure f e rea fr arge value are w Fg Oupu eva C Te S Fgure 6: Te pal eva fr e arge eperaure. Te reul w a e pal rl ajue f b e a flwrae f l rea a rea are w e lear reg f ya exager ye a ere ex ver-ajue 6 Clu Te pera agever f ea exager a be aeve by e aua pal rl eque. Cpare w e raal aua rl el rl pre beer a prple re reaable e e e e rl ajue are eere arg e ae paraeer f exager w lue ly e upu paraeer bu al e er paraeer fr exaple e vara rae f e upu paraeer f exager ye. Te ue exaple w e eque praable. Awlegee Te pree reear wr belg e prje Opal eg flexbly aaly a ya ula f ulrea ea exager ewr Hea Trafer III B. Sué C. A. Brebba & A. Mee Er 4 WIT Pre ISB

11 Hea Trafer III.RO94/9 uppre by e Deue Fruggeeaf DFG a e prje Fel yerge a rl f ea rafer pree w ulple rea.g6 uppre by e aal Develpe Prgra f Ca fr Key Fuaeal Reeare. Referee [] L. e Gexag Huag Mel algr a aae rl fr furrea plae-f ea exager J. very f Saga fr See a Telgy l.. pp [] Te Maea Depare Teaer-rag very f Ea Ca Iru e Mer Crl Tere Te Pre f Saga See a Telgy pp [] F.E. Re Trae repe f e uerflw Hea Exager J. f Hea Trafer l.6. pp [4] F.E. Re Trae repe f e parallel-flw Hea Exager J. f Hea Trafer l.7. pp [5] Y.-F. u Z.-H.Ca M.-L. L a A.-J. L Lup paraeer el fr ya perfrae f w-rea plae-f ea exager J. f Ceal Iury a Egeerg Ca l.48.6 pp Hea Trafer III B. Sué C. A. Brebba & A. Mee Er 4 WIT Pre ISB

The stress transfer calculations presented in the main text reports only our preferred

The stress transfer calculations presented in the main text reports only our preferred GS R ITEM 214377 L.S. Wlh e l. GS T REPOSITORY COULOM STRESS CHNGE PRMETER INPUT TESTS The re rfer lul preee he e repr ly ur preferre el. lhugh he geerl per ue re rbu, he el f he reul ul hge f el preer

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

ON THE EXTENSION OF WEAK ARMENDARIZ RINGS RELATIVE TO A MONOID

ON THE EXTENSION OF WEAK ARMENDARIZ RINGS RELATIVE TO A MONOID wwweo/voue/vo9iue/ijas_9 9f ON THE EXTENSION OF WEAK AENDAIZ INGS ELATIVE TO A ONOID Eye A & Ayou Eoy Dee of e Nowe No Uvey Lzou 77 C Dee of e Uvey of Kou Ou Su E-: eye76@o; you975@yooo ABSTACT Fo oo we

More information

Integrated Optical Waveguides

Integrated Optical Waveguides Su Opls Faha Raa Cll Uvs Chap 8 Ia Opal Wavus 7 Dl Slab Wavus 7 Iu: A va f ff a pal wavus a us f a u lh a hp Th s bas pal wavu s a slab wavus shw blw Th suu s uf h - Lh s u s h b al al fl a h -la fas Cla

More information

Modeling Micromixing Effects in a CSTR

Modeling Micromixing Effects in a CSTR delig irixig Effes i a STR STR, f all well behaved rears, has he wides RTD i.e. This eas ha large differees i perfrae a exis bewee segregaed flw ad perais a axiu ixedess diis. The easies hig rea is he

More information

Copyright Birkin Cars (Pty) Ltd

Copyright Birkin Cars (Pty) Ltd e f u:- 5: K360 98AA RADIATOR 5: K360 053AA SEAT MOUNTING GROU 5:3 K360 06A WIER MOTOR GROU 5:4 K360 0A HANDRAKE 5:5 K360 0A ENTRE ONSOE 5:6 K360 05AA RO AGE 5:7 K360 48AA SARE WHEE RADE 5:8 K360 78AA

More information

THE LOWELL LEDGER. X

THE LOWELL LEDGER. X * : V : ~ E E EGER X Y X 22 E Y BK E G U P B - ; * -K R B BY K E BE YU YU RE EE «> BE B F F P B * q UR V BB«56 x YU 88»* 00 E PU P B P B P V F P EPEE EUR E G URY VEBER

More information

Reliability Analysis. Basic Reliability Measures

Reliability Analysis. Basic Reliability Measures elably /6/ elably Aaly Perae faul Πelably decay Teporary faul ΠOfe Seady ae characerzao Deg faul Πelably growh durg eg & debuggg A pace hule Challeger Lauch, 986 Ocober 6, Bac elably Meaure elably:

More information

Laplace Transform. Definition of Laplace Transform: f(t) that satisfies The Laplace transform of f(t) is defined as.

Laplace Transform. Definition of Laplace Transform: f(t) that satisfies The Laplace transform of f(t) is defined as. Lplce Trfor The Lplce Trfor oe of he hecl ool for olvg ordry ler dfferel equo. - The hoogeeou equo d he prculr Iegrl re olved oe opero. - The Lplce rfor cover he ODE o lgerc eq. σ j ple do. I he pole o

More information

LOWELL/ JOURNAL. crew of the schooner Reuben Doud, swept by the West India hurricane I Capt William Lennon alone on the

LOWELL/ JOURNAL. crew of the schooner Reuben Doud, swept by the West India hurricane I Capt William Lennon alone on the LELL/ UL V 9 X 9 LELL E UU 3 893 L E UY V E L x Y VEEL L E Y 5 E E X 6 UV 5 Y 6 x E 8U U L L 5 U 9 L Q V z z EE UY V E L E Y V 9 L ) U x E Y 6 V L U x z x Y E U 6 x z L V 8 ( EVY LL Y 8 L L L < 9 & L LLE

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

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

LONG STAGE MASTER formative laboratory 2011

LONG STAGE MASTER formative laboratory 2011 Davde Pen Aadema & Te ArSudMuran p r e e n LONG STAGE MASTER frmave labrary 2011 exluve pbly lve and wrk n Davde ud fr nly ne eleed uden!! ne upn a me a kd a wa lvng n a mall land durng e afernn f e ummer

More information

dm dt = 1 V The number of moles in any volume is M = CV, where C = concentration in M/L V = liters. dcv v

dm dt = 1 V The number of moles in any volume is M = CV, where C = concentration in M/L V = liters. dcv v Mg: Pcess Aalyss: Reac ae s defed as whee eac ae elcy lue M les ( ccea) e. dm he ube f les ay lue s M, whee ccea M/L les. he he eac ae beces f a hgeeus eac, ( ) d Usually s csa aqueus eeal pcesses eac,

More information

Copyright Birkin Cars (Pty) Ltd

Copyright Birkin Cars (Pty) Ltd E GROU TWO STEERING AND EDAS - R.H.D Aemble clue : K360 043AD STEERING OUMN I u: - : K360 04A STEERING RAK :3 K360 045A EDA OX K360043AD STEERING O UMN Tl eque f embl f u: - mm Alle Ke 3mm Se 6mm Alle

More information

Copyright Birkin Cars (Pty) Ltd

Copyright Birkin Cars (Pty) Ltd WINDSREEN AND WIERS Aemble clue I u: - 7.1 7. 7.3 7. 7.5 K3601 15A K3601 1AA K3601 151AA K3601 18AA K360115AA K3601 08AA WINDSREEN WASHER WIER INKAGE ASSEMY WINDSREEN MOUNTING RAKETS WINDSREEN ASSEMY WIER

More information

700 STATEMENT OF ECONOMIC

700 STATEMENT OF ECONOMIC R RM EME EM ERE H E H E HE E HE Y ERK HE Y P PRE MM 8 PUB UME ER PE Pee e k. ek, ME ER ( ) R) e -. ffe, ge, u ge e ( ue ) -- - k, B, e e,, f be Yu P eu RE) / k U -. f fg f ue, be he. ( ue ) ge: P:. Ju

More information

The Signal, Variable System, and Transformation: A Personal Perspective

The Signal, Variable System, and Transformation: A Personal Perspective The Sgal Varable Syem ad Traformao: A Peroal Perpecve Sherv Erfa 35 Eex Hall Faculy of Egeerg Oule Of he Talk Iroduco Mahemacal Repreeao of yem Operaor Calculu Traformao Obervao O Laplace Traform SSB A

More information

X-Ray Notes, Part III

X-Ray Notes, Part III oll 6 X-y oe 3: Pe X-Ry oe, P III oe Deeo Coe oupu o x-y ye h look lke h: We efe ue of que lhly ffee efo h ue y ovk: Co: C ΔS S Sl o oe Ro: SR S Co o oe Ro: CR ΔS C SR Pevouly, we ee he SR fo ye hv pxel

More information

RAMIFICATIONS of POSITION SERVO LOOP COMPENSATION

RAMIFICATIONS of POSITION SERVO LOOP COMPENSATION RAMIFICATIONS f POSITION SERO LOOP COMPENSATION Gerge W. Yunk, P.E. Lfe Fellw IEEE Indural Cnrl Cnulg, Inc. Fnd du Lac, Wcn Fr many year dural pg er dre dd n ue er cmpena he frward p lp. Th wa referred

More information

β A Constant-G m Biasing

β A Constant-G m Biasing p 2002 EE 532 Anal IC Des II Pae 73 Cnsan-G Bas ecall ha us a PTAT cuen efeence (see p f p. 66 he nes) bas a bpla anss pes cnsan anscnucance e epeaue (an als epenen f supply lae an pcess). Hw h we achee

More information

ROOT-LOCUS ANALYSIS. Lecture 11: Root Locus Plot. Consider a general feedback control system with a variable gain K. Y ( s ) ( ) K

ROOT-LOCUS ANALYSIS. Lecture 11: Root Locus Plot. Consider a general feedback control system with a variable gain K. Y ( s ) ( ) K ROOT-LOCUS ANALYSIS Coder a geeral feedback cotrol yte wth a varable ga. R( Y( G( + H( Root-Locu a plot of the loc of the pole of the cloed-loop trafer fucto whe oe of the yte paraeter ( vared. Root locu

More information

PROBLEM: Upland Erosion

PROBLEM: Upland Erosion Mdeg Waerhed Er wh CSCD Perre Jue Raa Rja Mark Veeux Jh F. Egad RCEM U. I Ober I r d u PROBLEM: Uad Er Er Pure I r d u PROBLEM: ad De De ure 1 CSCD-SED Rafa 1 S Ifra Er Parg 1 7 Waer, Sedme, ad 1 3 1 De

More information

Continuous Time Markov Chains

Continuous Time Markov Chains Couous me Markov chas have seay sae probably soluos f a oly f hey are ergoc, us lke scree me Markov chas. Fg he seay sae probably vecor for a couous me Markov cha s o more ffcul ha s he scree me case,

More information

A Remark on Generalized Free Subgroups. of Generalized HNN Groups

A Remark on Generalized Free Subgroups. of Generalized HNN Groups Ieraoal Mahemacal Forum 5 200 o 503-509 A Remar o Geeralzed Free Subroup o Geeralzed HNN Group R M S Mahmood Al Ho Uvery Abu Dhab POBo 526 UAE raheedmm@yahoocom Abrac A roup ermed eeralzed ree roup a ree

More information

Fault Tolerant Computing. Fault Tolerant Computing CS 530 Reliability Analysis

Fault Tolerant Computing. Fault Tolerant Computing CS 530 Reliability Analysis Probably /4/6 CS 5 elably Aaly Yahwa K. Malaya Colorado Sae very Ocober 4, 6 elably Aaly: Oule elably eaure: elably, avalably, Tra. elably, T M MTTF ad (, MTBF Bac Cae Sgle u wh perae falure, falure rae

More information

THIS PAGE DECLASSIFIED IAW E

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

More information

2011 8th International Conference on Electrical Engineering, Computing Science and Automatic Control.

2011 8th International Conference on Electrical Engineering, Computing Science and Automatic Control. 211 8 Il C Ell E Cpu S Au Cl Aly Cll I Al G Cl-Lp I Appl Pu DC S k u PD l R 1 F O 1 1 U Plé V Só ó A Nu Tlí S/N Pqu Cí y Tló TECNOTA K C V-S l E-l: @upux 87@l A Uully l ppl y l py ly x l l H l- lp uu u

More information

State-Space Model. In general, the dynamic equations of a lumped-parameter continuous system may be represented by

State-Space Model. In general, the dynamic equations of a lumped-parameter continuous system may be represented by Sae-Space Model I geeral, he dyaic equaio of a luped-paraeer coiuou ye ay be repreeed by x & f x, u, y g x, u, ae equaio oupu equaio where f ad g are oliear vecor-valued fucio Uig a liearized echique,

More information

11. Ideal Gas Mixture

11. Ideal Gas Mixture . Ideal Ga xture. Geeral oderato ad xture of Ideal Gae For a geeral xture of N opoet, ea a pure ubtae [kg ] te a for ea opoet. [kol ] te uber of ole for ea opoet. e al a ( ) [kg ] N e al uber of ole (

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

DC-DC Switch-Mode Converters

DC-DC Switch-Mode Converters - Swich-Mde nverers - cnverers are used : egulaed swich-mde pwer supplies, nrmally wih HF elecrical isla Mr drives, nrmally wihu an isla ransfrmer We will lk a he w basic dc-dc cnverer plgies: Sep-dwn

More information

Ch5 Appendix Q-factor and Smith Chart Matching

Ch5 Appendix Q-factor and Smith Chart Matching Ch5 Appedx -factr ad mth Chart Matchg 5B-1 We-Cha a udwg, F Crcut Deg hery ad Applcat, Chapter 8 -type matchg etwrk w-cmpet Matchg Netwrk hee etwrk ue tw reactve cmpet t trafrm the lad mpedace t the dered

More information

H STO RY OF TH E SA NT

H STO RY OF TH E SA NT O RY OF E N G L R R VER ritten for the entennial of th e Foundin g of t lair oun t y on ay 8 82 Y EEL N E JEN K RP O N! R ENJ F ] jun E 3 1 92! Ph in t ed b y h e t l a i r R ep u b l i c a n O 4 1922

More information

THE LOWELL LEDGER, INDEPENDENT NOT NEUTRAL.

THE LOWELL LEDGER, INDEPENDENT NOT NEUTRAL. E OE EDGER DEEDE O EUR FO X O 2 E RUO OE G DY OVEER 0 90 O E E GE ER E ( - & q \ G 6 Y R OY F EEER F YOU q --- Y D OVER D Y? V F F E F O V F D EYR DE OED UDER EDOOR OUE RER (E EYEV G G R R R :; - 90 R

More information

ERASMUS Application form for entry Please use BLOCK CAPITAL letters.

ERASMUS Application form for entry Please use BLOCK CAPITAL letters. ERSMUS ppl fr fr 2018-19 ery Plee e BLOCK CPITL leer. Plee re ll he fr he he re reflly efre pleg h fr. Frher fr he ppl pre vlle hp://f.le..k/rre-e/erve/er/fr-fr-g-e I el 1. He 2. H epre LSE 3. e f prgre

More information

Collapsing to Sample and Remainder Means. Ed Stanek. In order to collapse the expanded random variables to weighted sample and remainder

Collapsing to Sample and Remainder Means. Ed Stanek. In order to collapse the expanded random variables to weighted sample and remainder Collapg to Saple ad Reader Mea Ed Staek Collapg to Saple ad Reader Average order to collape the expaded rado varable to weghted aple ad reader average, we pre-ultpled by ( M C C ( ( M C ( M M M ( M M M,

More information

2 u Du, k Hu Dv Hu, y H. u Cu j u qu u. Nv. v uy. Cu Hu F A H. qu Cu.. Cu j 1980, u V, v Nu My O k. v u u. A G C. My u v k, 2.5 H v v u / u v u v k y

2 u Du, k Hu Dv Hu, y H. u Cu j u qu u. Nv. v uy. Cu Hu F A H. qu Cu.. Cu j 1980, u V, v Nu My O k. v u u. A G C. My u v k, 2.5 H v v u / u v u v k y H HE 1016 M EEING OF HE ODIE CLU 1,016 Cu 7:30.. D 11, 2007 y W L Uvy. C : Pu A y: Ov 25 x u. Hk, u k MA k D u y Hu, u G, u C C, MN C, Nk Dv Hu, MN, u K A u vu v. W y A Pku G, G u. N EW UINE: D, Cu, 22

More information

Parts Manual. EPIC II Critical Care Bed REF 2031

Parts Manual. EPIC II Critical Care Bed REF 2031 EPIC II Critical Care Bed REF 2031 Parts Manual For parts or technical assistance call: USA: 1-800-327-0770 2013/05 B.0 2031-109-006 REV B www.stryker.com Table of Contents English Product Labels... 4

More information

Square law expression is non linear between I D and V GS. Need to operate in appropriate region for linear behaviour. W L

Square law expression is non linear between I D and V GS. Need to operate in appropriate region for linear behaviour. W L MOS Feld-Effec Trassrs (MOSFETs ecure # 4 MOSFET as a Amplfer k ( S Square law express s lear bewee ad. Need perae apprprae reg fr lear behaur. Cpyrgh 004 by Oxfrd Uersy Press, c. MOSFET as a Amplfer S

More information

The Buck Resonant Converter

The Buck Resonant Converter EE646 Pwer Elecrnics Chaper 6 ecure Dr. Sam Abdel-Rahman The Buck Resnan Cnverer Replacg he swich by he resnan-ype swich, ba a quasi-resnan PWM buck cnverer can be shwn ha here are fur mdes f pera under

More information

Data, frameworks, and financial instrument identification

Data, frameworks, and financial instrument identification , fmw, f um f U f h F um Gb f (FG) Rh Rb b57@bmb. ymby uy R, mb L.. F; WW 2017, -RG v f b 17-18, 2017; Wh.. vmb 2-3, 2017; h Gb, -ju, -fu vw Mu f x f f um ff b ; y Ly mb Exhu M ju Fu u (fmb )., m wh Wh

More information

1 Expectation of a continuously distributed random variable

1 Expectation of a continuously distributed random variable OCTOBER 3, 204 LECTURE 9 EXPECTATION OF A CONTINUOUSLY DISTRIBUTED RANDOM VARIABLE, DISTRIBUTION FUNCTION AND CHANGE-OF-VARIABLE TECHNIQUES Expectation of a continuously distributed random variable Recall

More information

T Promotion. Residential. February 15 May 31 LUTRON. NEW for 2019

T Promotion. Residential. February 15 May 31 LUTRON. NEW for 2019 M NEW fr 2019 A e yer brigs fres skig ruiy fr Lur L reverse- dimmers sé sluis, iludig e rdus. Ple rder, e ll el drive sles rug i-sre merdisig rr smlig, el yu mee yur 2019 gls. Mesr L PRO dimmer Our s flexible

More information

IrrItrol Products 2016 catalog

IrrItrol Products 2016 catalog l Ps Valves 205, 200 an 2500 eies Valves M Pa Nmbe -205F 1" n-line E Valve w/ FC - se 2500 eies 3* -200 1" E n-line Valve w/ FC F x F 3-200F 1" n-line Valve w/ FC F x F -2500 1" E Valve w/ FC F x F -2500F

More information

W E S T A N D N E W Y O R K. r NEW YORK > (entral * SYSTEM SYSTEM J. Effective January 14, 1939 Effective January 14, 1939 'IP" -6 " The Direct Route

W E S T A N D N E W Y O R K. r NEW YORK > (entral * SYSTEM SYSTEM J. Effective January 14, 1939 Effective January 14, 1939 'IP -6  The Direct Route e De Rue W N D W N D U W U W N D N D RNGFD N RNGFD N N W Y R N W Y R NW YR (e Y f NWYR (e v Y ffeve u ffeve u F U N N D DNNG R R V Reu e e e bbev D RfD e e; R; Reu e e e e be W U N D N ekek D N uff uff

More information

1. Linear second-order circuits

1. Linear second-order circuits ear eco-orer crcut Sere R crcut Dyamc crcut cotag two capactor or two uctor or oe uctor a oe capactor are calle the eco orer crcut At frt we coer a pecal cla of the eco-orer crcut, amely a ere coecto of

More information

September 10, Addendum 4: Architect responses to RFI s to date as of 18:00 CST, 9/7/2018:

September 10, Addendum 4: Architect responses to RFI s to date as of 18:00 CST, 9/7/2018: eptember, 0 endum : rchitect responses to s to date as of :00, //0: E: the location of Panel as identified on E partial plan has been aed at the upper left of sheet E his panel is shown on sheet 00_ofpdf

More information

Instruction Sheet COOL SERIES DUCT COOL LISTED H NK O. PR D C FE - Re ove r fro e c sed rea. I Page 1 Rev A

Instruction Sheet COOL SERIES DUCT COOL LISTED H NK O. PR D C FE - Re ove r fro e c sed rea. I Page 1 Rev A Instruction Sheet COOL SERIES DUCT COOL C UL R US LISTED H NK O you or urc s g t e D C t oroug y e ore s g / as e OL P ea e rea g product PR D C FE RES - Re ove r fro e c sed rea t m a o se e x o duct

More information

Exam-style practice: A Level

Exam-style practice: A Level Exa-tye practce: A Leve a Let X dete the dtrbut ae ad X dete the dtrbut eae The dee the rad varabe Y X X j j The expected vaue Y : E( Y) EX X j j EX EX j j EX E X 7 The varace : Var( Y) VarX VarX j j Var(

More information

Integral Form of Popoviciu Inequality for Convex Function

Integral Form of Popoviciu Inequality for Convex Function Procees of e Paksa Acaey of Sceces: A. Pyscal a ozaoal Sceces 53 3: 339 348 206 oyr Paksa Acaey of Sceces ISSN: 258-4245 r 258-4253 ole Paksa Acaey of Sceces Researc Arcle Ieral For of Pooc Ieqaly for

More information

Solution. The straightforward approach is surprisingly difficult because one has to be careful about the limits.

Solution. The straightforward approach is surprisingly difficult because one has to be careful about the limits. ose ad Varably Homewor # (8), aswers Q: Power spera of some smple oses A Posso ose A Posso ose () s a sequee of dela-fuo pulses, eah ourrg depedely, a some rae r (More formally, s a sum of pulses of wdh

More information

Solution of Impulsive Differential Equations with Boundary Conditions in Terms of Integral Equations

Solution of Impulsive Differential Equations with Boundary Conditions in Terms of Integral Equations Joural of aheacs ad copuer Scece (4 39-38 Soluo of Ipulsve Dffereal Equaos wh Boudary Codos Ters of Iegral Equaos Arcle hsory: Receved Ocober 3 Acceped February 4 Avalable ole July 4 ohse Rabba Depare

More information

TER T U L OFEREE O URRET TREDS TEHOLOGY O OE [6] G OSYTHETS E P T VEME hv xl lly Gy xvly u k uv hk u l u v wll ly ul ly y lf x ly ul f l lly (F

TER T U L OFEREE O URRET TREDS TEHOLOGY O OE [6] G OSYTHETS E P T VEME hv xl lly Gy xvly u k uv hk u l u v wll ly ul ly y lf x ly ul f l lly (F HMEDBD RM UVERSTY STTUTE OF TEHOLOGY 48 8 08-0 E E D 0 BER M - - y u hv Gxl k lwy y u k k v wll wll ul k fu Bu ly vlv l hl l l l f hh u h hwv hul u y vll l f k hul vlu f ll vlu F l xl ff fv x l v ff l

More information

Mass Linear Momentum Moment of Momentum Energy Putting it all together!

Mass Linear Momentum Moment of Momentum Energy Putting it all together! inie Cnrl lue nalsis vin fr a Sse a inie Cnrl lue a Linear enu en f enu Ener Puin i all eer! D Cnservain f a B = Tal aun f a in e e b = a er uni a = DB ˆ b b n ˆ n ˆ equain Bu D / =! Cninui Equain a leavin

More information

Analysis of error propagation in profile measurement by using stitching

Analysis of error propagation in profile measurement by using stitching Ay o error propgto proe eureet y ug ttchg Ttuy KUME, Kzuhro ENAMI, Yuo HIGASHI, Kej UENO - Oho, Tuu, Ir, 35-8, JAPAN Atrct Sttchg techque whch ee oger eureet rge o proe ro eer eure proe hg prty oerppe

More information

Abel rings and super-strongly clean rings

Abel rings and super-strongly clean rings An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. N.S. Tomul LXIII, 2017, f. 2 Abel rings and super-strongly clean rings Yinchun Qu Junchao Wei Received: 11.IV.2013 / Last revision: 10.XII.2013 / Accepted: 12.XII.2013

More information

12781 Velp Avenue. West County B Rural Residential Development

12781 Velp Avenue. West County B Rural Residential Development U PL & EET E 28 Vel ee eded 2 P.. ) LL EET T E 2) PPVE E ) ET E ) e e e e eded eebe 2 Plg & g eeg b) Bldg Pe e: eebe ) PUBL FU ( -E TE): g be bg bee e Plg & g eel ll be de ll be e. 5) UEETFEEBK: ) be ll

More information

TBE feahwav *'(:.*&&&& 112, KO.262S. Many Legion Officials-Si^ atuwared City clerk Wilfre

TBE feahwav *'(:.*&&&& 112, KO.262S. Many Legion Officials-Si^ atuwared City clerk Wilfre > ] ( E W R R LR >uf / u )u> N Fu < W N u W E FRDY GD RNNG DEEER 794 F u u F G 5 W 4 7 u D u u N u D q u zu x uu u u u u EQu W u u u R D u u u u u u u u D 8 ) Fz Eu x W u u u u u E R u 4 4 4 W W u Euu

More information

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

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

More information

EECE 301 Signals & Systems Prof. Mark Fowler

EECE 301 Signals & Systems Prof. Mark Fowler EECE 30 Sigal & Sytem Prof. Mark Fowler Note Set #8 C-T Sytem: Laplace Traform Solvig Differetial Equatio Readig Aigmet: Sectio 6.4 of Kame ad Heck / Coure Flow Diagram The arrow here how coceptual flow

More information

African Journal of Science and Technology (AJST) Science and Engineering Series Vol. 4, No. 2, pp GENERALISED DELETION DESIGNS

African Journal of Science and Technology (AJST) Science and Engineering Series Vol. 4, No. 2, pp GENERALISED DELETION DESIGNS Af Joul of See Tehology (AJST) See Egeeg See Vol. 4, No.,. 7-79 GENERALISED DELETION DESIGNS Mhel Ku Gh Joh Wylff Ohbo Dee of Mhe, Uvey of Nob, P. O. Bo 3097, Nob, Key ABSTRACT:- I h e yel gle ele fol

More information

CS344: Introduction to Artificial Intelligence

CS344: Introduction to Artificial Intelligence C344: Iroduco o Arfcal Iellgece Puhpa Bhaacharyya CE Dep. IIT Bombay Lecure 3 3 32 33: Forward ad bacward; Baum elch 9 h ad 2 March ad 2 d Aprl 203 Lecure 27 28 29 were o EM; dae 2 h March o 8 h March

More information

SCOTT PLUMMER ASHTON ANTONETTI

SCOTT PLUMMER ASHTON ANTONETTI 2742 A E E E, UE, AAAMA 3802 231 EE AEA 38,000-cre dversfed federl cmus 41,000 emloyees wth 72+ dfferent gences UE roosed 80-cre mster-lnned develoment 20 home stes 3,000F of vllgestyle retl 100,000 E

More information

GENESIS. God makes the world

GENESIS. God makes the world GENESIS 1 Go me he or 1 I he be Go me he b heve he erh everyh hh p he y. 2 There oh o he e erh. Noh ve here, oh *o ve here. There oy e eep er over he erh. There o h. I very r. The f Spr of Go move over

More information

I M P O R T A N T S A F E T Y I N S T R U C T I O N S W h e n u s i n g t h i s e l e c t r o n i c d e v i c e, b a s i c p r e c a u t i o n s s h o

I M P O R T A N T S A F E T Y I N S T R U C T I O N S W h e n u s i n g t h i s e l e c t r o n i c d e v i c e, b a s i c p r e c a u t i o n s s h o I M P O R T A N T S A F E T Y I N S T R U C T I O N S W h e n u s i n g t h i s e l e c t r o n i c d e v i c e, b a s i c p r e c a u t i o n s s h o u l d a l w a y s b e t a k e n, i n c l u d f o l

More information

R for beginners. 2 The few things to know before st. 8 Index 31

R for beginners. 2 The few things to know before st. 8 Index 31 ; & & & 8 * ( 0 " & 9 1 R f Eu l 1 W R? 3 T fw kw f 5 3-4.1 T

More information

Provider Satisfaction

Provider Satisfaction Prider Satisfaction Prider Satisfaction [1] NOTE: if you nd to navigate away from this page, please click the "Save Draft" page at the bottom (visible to ONLY logged in users). Otherwise, your rpons will

More information

T T V e g em D e j ) a S D } a o "m ek j g ed b m "d mq m [ d, )

T T V e g em D e j ) a S D } a o m ek j g ed b m d mq m [ d, ) . ) 6 3 ; 6 ;, G E E W T S W X D ^ L J R Y [ _ ` E ) '" " " -, 7 4-4 4-4 ; ; 7 4 4 4 4 4 ;= : " B C CA BA " ) 3D H E V U T T V e g em D e j ) a S D } a o "m ek j g ed b m "d mq m [ d, ) W X 6 G.. 6 [ X

More information

IO Gender and natural history

IO Gender and natural history LNA HEBNGER Gede d tul hty The tylu f the fele [plt] the v hle the vulv d the Veu epd t the t Thu the uteu v d vulv ke up the ptl the e tht de btt ve t ll the fele pt f plt A f e e e eed quk lk euh f Ppu

More information

8.6 Order-Recursive LS s[n]

8.6 Order-Recursive LS s[n] 8.6 Order-Recurive LS [] Motivate ti idea wit Curve Fittig Give data: 0,,,..., - [0], [],..., [-] Wat to fit a polyomial to data.., but wic oe i te rigt model?! Cotat! Quadratic! Liear! Cubic, Etc. ry

More information

(V 1. (T i. )- FrC p. ))= 0 = FrC p (T 1. (T 1s. )+ UA(T os. (T is

(V 1. (T i. )- FrC p. ))= 0 = FrC p (T 1. (T 1s. )+ UA(T os. (T is . Yu are repnible fr a reacr in which an exhermic liqui-phae reacin ccur. The fee mu be preheae he hrehl acivain emperaure f he caaly, bu he pruc ream mu be cle. T reuce uiliy c, yu are cniering inalling

More information

F l a s h-b a s e d S S D s i n E n t e r p r i s e F l a s h-b a s e d S S D s ( S o-s ltiad t e D r i v e s ) a r e b e c o m i n g a n a t t r a c

F l a s h-b a s e d S S D s i n E n t e r p r i s e F l a s h-b a s e d S S D s ( S o-s ltiad t e D r i v e s ) a r e b e c o m i n g a n a t t r a c L i f e t i m e M a n a g e m e n t o f F l a-b s ah s e d S S D s U s i n g R e c o v e r-a y w a r e D y n a m i c T h r o t t l i n g S u n g j i n L e, e T a e j i n K i m, K y u n g h o, Kainmd J

More information

R e p u b lic o f th e P h ilip p in e s. R e g io n V II, C e n tra l V isa y a s. C ity o f T a g b ila ran

R e p u b lic o f th e P h ilip p in e s. R e g io n V II, C e n tra l V isa y a s. C ity o f T a g b ila ran R e p u b l f th e P h lp p e D e p rt e t f E d u t R e V, e tr l V y D V N F B H L ty f T b l r Ju ly, D V N M E M R A N D U M N. 0,. L T F E N R H G H H L F F E R N G F R 6 M P L E M E N T A T N T :,

More information

UBI External Keyboard Technical Manual

UBI External Keyboard Technical Manual UI Eer eyor ei u EER IORIO ppiio o Ue ouiio e Eer eyor rie uer 12911 i R 232 eyor iee or oeio o e re o UI Eyoer prier Eyoer 11 Eyoer 21 II Eyoer 41 Eyoer 1 Eyoer 1 e eyor o e ue or oer UI prier e e up

More information

I N A C O M P L E X W O R L D

I N A C O M P L E X W O R L D IS L A M I C E C O N O M I C S I N A C O M P L E X W O R L D E x p l o r a t i o n s i n A g-b eanste d S i m u l a t i o n S a m i A l-s u w a i l e m 1 4 2 9 H 2 0 0 8 I s l a m i c D e v e l o p m e

More information

Econometric modelling and forecasting of intraday electricity prices

Econometric modelling and forecasting of intraday electricity prices E y y Xv:1812.09081v1 [q-.st] 21 D 2018 M Nw Uvy Duu-E F Z Uvy Duu-E D 24, 2018 A I w w y ID 3 -P G Iy Cuu Ey M u. A uv u uy qu-uy u y. W u qu u-- vy - uy. T w u. F u v w G Iy Cuu Ey M y ID 3 -P vu. T

More information

Corrupt the signal waveform Degrade the performance of communication systems

Corrupt the signal waveform Degrade the performance of communication systems Nie Nie : rd luui pwer i ye Crrup he igl wver Degrde he perre uii ye ure Nie: rd wderig ree eler i reir herl ie, rd lw hrge i eidur jui h ie, e. ddiive ie Zer-e Whie Gui-diribued Nie, pwer perl deiy /

More information

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

176 5 t h Fl oo r. 337 P o ly me r Ma te ri al s A g la di ou s F. L. 462 E l ec tr on ic D ev el op me nt A i ng er A.W.S. 371 C. A. M. A l ex an de r 236 A d mi ni st ra ti on R. H. (M rs ) A n dr ew s P. V. 326 O p ti ca l Tr an sm is si on A p ps

More information

On Extensions of Green s Relations in Semi groups

On Extensions of Green s Relations in Semi groups IOSR Journal of Mathematics (IOSRJM) ISSN: 2278-5728 Volume 1, Issue 3 (July-Aug 2012), PP 04-11 On Extensions of Green s Relations in Semi groups 1 D.V.Vijay Kumar and 2 K.V.R.Srinivas Abstract: In this

More information

Chapter 5: Quantization of Radiation in Cavities and Free Space

Chapter 5: Quantization of Radiation in Cavities and Free Space Quu O f Ph Ol Fh R Cll vy Ch 5: Quz f R Cv F S 5 Cll ly 5 Cll Cvy ly Mxwll u f lg J 4 h lv l C fl vy W f h g f h vy Th vy u luly ll W l u h J Cvy F Mxwll u v h wv u Th v u lv h f h fu h vy I w wh h v l

More information

The Poisson Process Properties of the Poisson Process

The Poisson Process Properties of the Poisson Process Posso Processes Summary The Posso Process Properes of he Posso Process Ierarrval mes Memoryless propery ad he resdual lfeme paradox Superposo of Posso processes Radom seleco of Posso Pos Bulk Arrvals ad

More information

Design of Controller for Robot Position Control

Design of Controller for Robot Position Control eign of Conroller for Robo oiion Conrol Two imporan goal of conrol: 1. Reference inpu racking: The oupu mu follow he reference inpu rajecory a quickly a poible. Se-poin racking: Tracking when he reference

More information

Continuous-Time Filters

Continuous-Time Filters tuute Flter.0 Operatal Tracductace Aplfer (OTA Z Z ut (a (b (c (d Fgure. deal all gal equvalet crcut f Sgle eded OTA ad Fully dfferetal OTA pleetat Ug Sgle eded OTA. Fgure (a h the ybl f gle eded OTA.

More information

OH BOY! Story. N a r r a t iv e a n d o bj e c t s th ea t e r Fo r a l l a g e s, fr o m th e a ge of 9

OH BOY! Story. N a r r a t iv e a n d o bj e c t s th ea t e r Fo r a l l a g e s, fr o m th e a ge of 9 OH BOY! O h Boy!, was or igin a lly cr eat ed in F r en ch an d was a m a jor s u cc ess on t h e Fr en ch st a ge f or young au di enc es. It h a s b een s een by ap pr ox i ma t ely 175,000 sp ect at

More information

Si Oxidation. SiO 2. ! A method of forming SiO 2

Si Oxidation. SiO 2. ! A method of forming SiO 2 S Oxatn! A met f frmn SO wc ue a Ma (e.., fr n mplantatn) Oxe n MOSFET Surface pavatn! Frm perfect S-SO nterface S S ( ) ( ) O ( ) ( ) SO ( ) H O SO H ( ) ( ) SO S O Oxant ffue tru te SO flm Reactn tae

More information

6-5. H 2 O 200 kpa 200 C Q. Entropy Changes of Pure Substances

6-5. H 2 O 200 kpa 200 C Q. Entropy Changes of Pure Substances Canges f ure Substances 6-0C Yes, because an ternally reversible, adiabatic prcess vlves n irreversibilities r eat transfer. 6- e radiatr f a steam eatg system is itially filled wit supereated steam. e

More information

Fuzzy Reasoning and Optimization Based on a Generalized Bayesian Network

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

More information

Chapter 8 Sections 8.4 through 8.6 Internal Flow: Heat Transfer Correlations. In fully-developed region. Neglect axial conduction

Chapter 8 Sections 8.4 through 8.6 Internal Flow: Heat Transfer Correlations. In fully-developed region. Neglect axial conduction Chapter 8 Sectin 8.4 thrugh 8.6 Internal Flw: Heat Tranfer Crrelatin T v cu p cp ( rt) k r T T k x r r r r r x In fully-develped regin Neglect axial cnductin u ( rt) r x r r r r r x T v T T T T T u r x

More information

Evaluation of The Necessary of Agriculture Public Expenditure for Poverty Reduction and Food Security in Benin

Evaluation of The Necessary of Agriculture Public Expenditure for Poverty Reduction and Food Security in Benin MPRA Mu P RPE Av Evu N Aguu Pu Exu Pv Ru F Su B A C L Zg Uv E Lw O 010 O ://.u.u-u./447/ MPRA P N. 447, 7. Augu 010 0:17 UC qwugjkzxvqw ugjkzxvqwu gjkzxvqwug [ Evu N jkzxvqwugjkzx vqwugjkzxv qwugjkzxvqw

More information

x

x Macmí36 è98-è Solutions Homework è èdue January 6, 998è Exercise Set.. èaè witèplotsè: f:=è-expèxè+*xèè3; f := 3, 3 ex + 3 x?abs plotèabsèfè,x=0..è; 0.6 0. 0. 0. 0.38 0.36 0.3 0 0. 0. 0.6 0.8 x By moving

More information

Concept of Reynolds Number, Re

Concept of Reynolds Number, Re Concept of Reynold Nuber, Re Ignore Corioli and Buoyancy and forcing Acceleration Advection Preure Gradient Friction I II III IV u u 1 p i i u ( f u ) b + u t x x x j i i i i i i U U U? U L L If IV <

More information

On Metric Dimension of Two Constructed Families from Antiprism Graph

On Metric Dimension of Two Constructed Families from Antiprism Graph Mah S Le 2, No, -7 203) Mahemaal Sees Leers A Ieraoal Joural @ 203 NSP Naural Sees Publhg Cor O Mer Dmeso of Two Cosrued Famles from Aprm Graph M Al,2, G Al,2 ad M T Rahm 2 Cere for Mahemaal Imagg Tehques

More information

Analysis of a Stochastic Lotka-Volterra Competitive System with Distributed Delays

Analysis of a Stochastic Lotka-Volterra Competitive System with Distributed Delays Ieraoal Coferece o Appled Maheac Sulao ad Modellg (AMSM 6) Aaly of a Sochac Loa-Volerra Copeve Sye wh Drbued Delay Xagu Da ad Xaou L School of Maheacal Scece of Togre Uvery Togre 5543 PR Cha Correpodg

More information

C o r p o r a t e l i f e i n A n c i e n t I n d i a e x p r e s s e d i t s e l f

C o r p o r a t e l i f e i n A n c i e n t I n d i a e x p r e s s e d i t s e l f C H A P T E R I G E N E S I S A N D GROWTH OF G U IL D S C o r p o r a t e l i f e i n A n c i e n t I n d i a e x p r e s s e d i t s e l f i n a v a r i e t y o f f o r m s - s o c i a l, r e l i g i

More information

ES 330 Electronics II Homework 03 (Fall 2017 Due Wednesday, September 20, 2017)

ES 330 Electronics II Homework 03 (Fall 2017 Due Wednesday, September 20, 2017) Pae1 Nae Soluios ES 330 Elecroics II Hoework 03 (Fall 017 ue Wedesday, Sepeber 0, 017 Proble 1 You are ive a NMOS aplifier wih drai load resisor R = 0 k. The volae (R appeari across resisor R = 1.5 vols

More information

On the energy of complement of regular line graphs

On the energy of complement of regular line graphs MATCH Coucato Matheatcal ad Coputer Chetry MATCH Cou Math Coput Che 60 008) 47-434 ISSN 0340-653 O the eergy of copleet of regular le graph Fateeh Alaghpour a, Baha Ahad b a Uverty of Tehra, Tehra, Ira

More information

S-Y0 U-G0 CANDIDATES

S-Y0 U-G0 CANDIDATES «< «X((«( (V«" j -- Y ? K «: :» V X K j 44 E GVE E E EY Y VE E 2 934 VE EEK E-EE E E 4 E -Y0 U-G0 E - Y - V Y ^ K - G --Y-G G - E K - : - ( > x 200 G < G E - : U x K K - " - z E V E E " E " " j j x V

More information

LM A F LABL Y H FRMA H P UBLCA B LV B ACCURA ALL R PC H WVR W C A AU M RP BLY FR AY C QUC RUL G F RM H U HR F H FRMA C A HR UBJC CHA G WHU C R V R W H

LM A F LABL Y H FRMA H P UBLCA B LV B ACCURA ALL R PC H WVR W C A AU M RP BLY FR AY C QUC RUL G F RM H U HR F H FRMA C A HR UBJC CHA G WHU C R V R W H H R & C C M RX700-2 Bx C LM A F LABL Y H FRMA H P UBLCA B LV B ACCURA ALL R PC H WVR W C A AU M RP BLY FR AY C QUC RUL G F RM H U HR F H FRMA C A HR UBJC CHA G WHU C R V R W H PUBLCA M AY B U CRP RA UCH

More information

Laplace Transformation

Laplace Transformation Univerity of Technology Electromechanical Department Energy Branch Advance Mathematic Laplace Tranformation nd Cla Lecture 6 Page of 7 Laplace Tranformation Definition Suppoe that f(t) i a piecewie continuou

More information