GMP. Strand Tensionmeter Operation and Maintenance Manual. P/N Date:071017

Size: px
Start display at page:

Download "GMP. Strand Tensionmeter Operation and Maintenance Manual. P/N Date:071017"

Transcription

1 GMP Strad Timtr Oprati ad Maitac Maual 1 P/N Dat:071017

2 2

3 Tabl f ctt Gral Gral 3 Prcauti 5 Calibrati Chart 6 Tmpratur Cmpati Chart 8 Dial 16 Uig th Timtr 16 Accry Saddl 18 R-calibrati 19 A itiv tudy by th Natial Elctric Safty Cd Clarac Subcmmitt ha rultd i a cmpltly w "Uifrm Sytm f Clarac" adptd i th 1990 ad ubqut diti f th NESC. Thi rvii plac rwd mphai utiliti' practic fr girig ad trigig f arial cabl t maitai prpr cabl clarac udr th variu pcifid cditi. Th ability t accuratly maur trad ti i th fild i tial fr cmpliac with th cd. Th GMP Strad Timtr, al calld a B Strad Dyammtr, i a prcii itrumt digd t maur th ti f crtai pcific zic-catd guy wir ad mgr cabl pr ASTM A-475. Th pcific iz ad typ() f cabl() with which thi uit i cmpatibl ar litd i th calibrati chart which ha b prpard fr thi pcific rial umbrd timtr ad which bar that idtical rial umbr. 3

4 Th fllwig lit hw th variu iz, typ ad digati f mgr cabl fr which th tl ca b calibratd: Nmial Diamtr Ich mm Digati Dcripti 1/ M 1 X 7 EHS 5/ M 1 X 7 Utility Grad 5/ M 1 X 7 EHS 3/ M 1 X 7 Utility Grad 7/ M 1 X 7 EHS 7/ M 1 X 7 Utility Grad T btai a accurat maurmt it i imprativ that th trad t b maurd b pitivly idtifid a t it actual diamtr ad it grad, ithr Utiliti Grad r Extra-High Strgth. Scdly, th Strad Timtr t b ud mut hav a currt calibrati chart with a crrpdig rial umbr which ha a calibrati fr th pcific trad yu hav idtifid. Th Timtr maur th frc rquird t dflct th trad t a ut-f-li piti ad rgitr th amut f frc rquird th itgral dial. Th actual trad ti i th dtrmid by rfrrig t th calibrati chart pcifically prpard fr ad furihd with ach Timtr, which cvrt th dial idicatr radig it th actual ti valu. Th itrumt maur ti i pud frc t withi a accuracy f thr prct (± 3%) r ± 150 pud, whichvr i gratr. 4

5 Th Timtr i primarily mad frm icklplatd tl ad i furihd i a hard hll platic carryig ca; th itrir i cuhid with fam fr uit prtcti. Each Timtr ha a rgitrd rial umbr tampd th uit. Prcauti D t maur ti f 1/2" diamtr trad with th cabl i plac; th ti valu uually xcd 10,000 pud. D t drp r jar th Timtr. Rai ad lwr th itrumt with a had li. Kp th dvic away frm dirt, gra, ad r watr. Kp frig matrial frm damagig th dial r plugr. Maitai th uit i th carryig ca whvr pibl. Mak crtai that th crrct calibrati chart i alway kpt i th carryig ca. U th Timtr ly trad typ ad iz hw th calibrati chart. D t u thi dvic trad tiig applicati xcdig 10,000 pud. 5

6 Calibrati Chart Icludd with ach Timtr i a calibrati chart rgitrd udr th am rial umbr a th Timtr. Thi chart i t b ud fr itrprtig th radig fr that pcific itrumt ly. N thr chart huld b ud. N thr typ f trad huld b ud. Th tabl acr th tp f th chart lit th cmmly ud trad iz fr which th Timtr wa calibratd, a wll a th hadl piti fr ach typ f trad. Th data i th chart idicat th dial radig f th Timtr crrpdig t th amut f trad ti i 100 pud icrmt fr th rmal ti rag f ach trad iz. Th chart idicat th dat wh th iitial calibrati wa mad. If th chart i lt, th Timtr mut b rturd fr r-calibrati. Tmpratur Cmpati Chart Strad ti i affctd by ambit tmpratur. Grally pakig, trad ti icra a tmpratur dcra du t th trad ctracti ad, cvrly, trad ti dcra a tmpratur ri, du t xpai. Th Strad Timtr will maur th actual ti at th ambit tmpratur at th tim f th maurmt. Yu huld cult with th Outid Plat Faciliti Egir a t th prpr trad ti fr th ambit tmpratur at th tim f maurmt. 6

7 Tmpratur Cmpati Chart (ctiud) Li chart ar prvidd i th itructi i rdr fr th ur t dtrmi hw t cmpat fr chag i ambit tmpratur. Th chart ar drivd frm th rcmmdd valu xprd i th rfrcd idutry tadard practic. Thy ar t itdd t uprd ay ti calculati which might b prvidd t th ur by th utility' plat girig dpartmt. Fr xampl, aum that th girig pcificati fr tiig a crtai 300 ft. pa f 1/4" Extra-High Strgth trad (i.. Bll Sytm 6.6M) call fr th trad t b at 600 lb. at 60 dgr F. Wh yu ar at th wrk it, yur thrmmtr idicat a ambit tmpratur f 86 dgr. Rfrrig t th Tmpratur Cmpati Chart fr that pcific trad, yu will thr li. Fid th which crrpd t pa ft. Ntic that 600 pud th vrtical axi crrpd t 60 dgr th hriztal axi. Nw ctiu right alg th hriztal axi t 86 dgr. With a traight dg, fllw frm that pit vrtically util yu itrct with th ft. li. 86 dgr crrpd t jut vr 500 pud. That i th trad ti cmpatd fr 86 dgr ambit. O th Timtr Calibrati Chart fr 1/4" EHS, lcat 500 Ib. ad cvrt t th dial idicatr radig. That i th dial idicatr umbr t ht fr wh tiig thi particular trad. A aalg thrmmtr i prvidd i ach Strad Timtr trag ca fr th purp f accuratly dtrmiig th ambit tmpratur at th tim f th maurmt. B ur t hld th thrmmtr by th dial ad t by th ig tm ad t allw at lat tw miut fr th thrmmtr t tabiliz itlf. 7

8 1/4 Extra High Strgth Tmpratur Cmpati Chart Pr BSP i r c F d u P i T Tmpratur F SPANS < 250' SPANS ' SPANS >450' 8

9 1/4 Extra High Strgth Tmpratur Cmpati Chart Pr GTEP i r c 1200 F d u 1150 P i T Tmpratur F SPANS < 250' SPANS ' SPANS >450' 9

10 5/16 Extra High Strgth Tmpratur Cmpati Chart Pr GTEP i c2200 r F d u P2100 i T T mpratur F SPANS <400 SPANS >400 10

11 7/16 Extra-High Strgth Tmpratur Cmpati Chart Pr GTEP i rc F d u P i T Tmpratur F ALL SPANS 11

12 5/16 Utiliti Grad Tmpratur Cmpati Chart Pr BSP i r c F d u P 1200 i T Tmpratur F SPANS < 250' SPANS ' SPANS >450' 12

13 3/8 Utiliti Grad Tmpratur Cmpati Chart Pr BSP i r c 2300 F d u P 2200 i T Tmpratur F SPANS <400 SPANS >400 13

14 7/16 Utiliti Grad Tmpratur Cmpati Chart Pr BSP i r c F d 3800 u P 3600 T Tmpratur F ALL SPANS 14

15 1/2 Utiliti Grad Tmpratur Cmpati Chart Pr BSP i r c 8400 F d u8200 P 8000 T Tmpratur F ALL SPANS 15

16 Dial Th calibratd dial rad 0 t 100. Th majrity f rcrdd maurmt will b withi thi rag ad ar radjut a th graduati appar th dial. Hwvr, high lad maurmt, it i pibl fr th dl t mak cmplt rvluti pat zr. Fr th radig, it i cary t add 100 t th graduati idicatd by th dl. Uig th Timtr Accurat trad ti maurmt rquir that a cti f trad b at lat twty ft lg ad fr frm damag r crri. If cabl i i plac, rmv rig r cabl upprt r u-lah ufficitly t btai abut tw ft f ubtructd trad. Supd th itrumt th trad by th hk lcatd at ach d f th ti bar with th hadl prjctig dwward. With th uit i piti, alway chck t mak crtai that th dial idicatr rad zr. If th dial idicatr d t rad zr, l th lttd crw lcatd i th dial hrud. Rtat th dial lightly util th dial idicatr rad zr ad rtight th crw. A a altrat t "r-zrig" th uit ach tim th italld piti f th Timtr i chagd, plac th uit i th piti i which it i t b ud ad t th umbr f graduati abv r blw th zr mark. Oc th Timtr i italld ad t, add r ubtract th graduati t/frm th dial radig bfr rfrrig t th chart. 16

17 Uig th Timtr (ctiud) Lcat th clum th calibrati chart fr th grad ad diamtr f trad t b ttd ad t th crrct hadl piti. (A atrik algid f th hadl piti umbr ma that th accry addl mut b ud.* S th xt cti titld Accry Saddl bfr prcdig.) Pull th hadl dw util th bttm dg f th cam plugr mv upward ad tp at th crrct piti umbrd th cam ca. Th trad will b dflctd btw th upi hk wh th hadl gag it th dtt at th crrct umbrd piti. Rad ad rcrd th dial idicatr umbr. IMPORTANT: Th calibratd dial rad 0 t 100. Th majrity f rcrdd maurmt will b withi thi rag ad ar rad xactly a th umbr appar th dial. O high lad maurmt, hwvr, it i pibl fr th dl t mak cmplt rvluti pat zr. Fr th radig, it i cary t add 100 t th umbr idicatd by th dl. Tak tw additial radig mvig th Timtr apprximatly 1/4" alg th trad fr ach radig. Rad ad rcrd ach dial idicatr umbr. Dicard th high ad lw radig ad u ly th itrmdiat radig a th crrct valu. Rfr t th calibrati chart udr th pcific trad diamtr ad lcat th dial radig clt t th brvd radig. Mv t th lft clum hwig th crrpdig amut f ti i pud frc. * crtai ldr dig uit 17

18 Accry Saddl Crtai Strad Timtr maufacturd ad ld btw Ja ad July 1992 had cam plugr f a diffrt dig tha ithr th AT&T uit which prcdd thm r th currt GMP dig which fllw thm. Th uit bar rial umbr i th rag tampd th hadl. Wh chckig th ti 1/4, 5/16 r 3/8 diamtr trad, a part calld th accry addl blck mut b ud t achiv dial idicatr mvmt ad a crrct ti radig. Thi accry addl blck i a rctagular tl blck which mut tp f th cam plugr ad i hld i plac by tw 7/16" had hx crw. Th calibrati chart furihd with th uit hav a atrik (*) algid th hadl piti umbr fr th trad iz whr th accry addl mut b ud. A hadl piti umbr with atrik ma that th accry addl mut t b ud. Th accry addl appli ly t th uit dcribd abv ad d t apply t AT&T uit, r d it apply t GMP uit with 5 digit rial umbr. 18

19 Rcalibrati T maitai ptimum rvic, th Timtr huld b r-calibratd pridically. With mdrat t havy u, a calibrati chck huld b prfrmd vry yar. Th iitial calibrati dat i hw ach calibrati chart. N attmpt huld b mad t diambl, rpair r rcalibrat i th fild. If a uit i t rpdig t rmal u, it huld b placd i th carryig ca with th calibrati chart ad rturd t Gral Machi Prduct (KT), LLC fr rvic. Pla upply a ctact am, addr, ph umbr ad a ra fr rtur. Calibrati Dat 19

20 Gral Machi Prduct (KT), LLC 3111 Old Licl Highway Trv, PA USA TEL: FAX: WEB: GMP rrv th right, withut tic, t mak chag i quipmt dig r cmpt a prgr i girig r maufacturig mthd may warrat. All ctt 2017 GMP 20

ELEC 372 LECTURE NOTES, WEEK 11 Dr. Amir G. Aghdam Concordia University

ELEC 372 LECTURE NOTES, WEEK 11 Dr. Amir G. Aghdam Concordia University ELEC 37 LECTURE NOTES, WEE Dr Amir Aghdam Cncrdia Univrity Part f th nt ar adaptd frm th matrial in th fllwing rfrnc: Mdrn Cntrl Sytm by Richard C Drf and Rbrt H Bihp, Prntic Hall Fdback Cntrl f Dynamic

More information

Lectur 22. RF and Microwave Circuit Design Γ-Plane and Smith Chart Analysis. ECE 303 Fall 2005 Farhan Rana Cornell University

Lectur 22. RF and Microwave Circuit Design Γ-Plane and Smith Chart Analysis. ECE 303 Fall 2005 Farhan Rana Cornell University ctur RF ad Micrwav Circuit Dig -Pla ad Smith Chart Aalyi I thi lctur yu will lar: -pla ad Smith Chart Stub tuig Quartr-Wav trafrmr ECE 33 Fall 5 Farha Raa Crll Uivrity V V Impdac Trafrmati i Tramii i ω

More information

Even/Odd Mode Analysis of the Wilkinson Divider

Even/Odd Mode Analysis of the Wilkinson Divider //9 Wilkinn Dividr Evn and Odd Md Analyi.dc / Evn/Odd Md Analyi f th Wilkinn Dividr Cnidr a matchd Wilkinn pwr dividr, with a urc at prt : Prt Prt Prt T implify thi chmatic, w rmv th grund plan, which

More information

ANOVA- Analyisis of Variance

ANOVA- Analyisis of Variance ANOVA- Aalii of Variac CS 700 Comparig altrativ Comparig two altrativ u cofidc itrval Comparig mor tha two altrativ ANOVA Aali of Variac Comparig Mor Tha Two Altrativ Naïv approach Compar cofidc itrval

More information

H2 Mathematics Arithmetic & Geometric Series ( )

H2 Mathematics Arithmetic & Geometric Series ( ) H Mathmatics Arithmtic & Gomtric Sris (08 09) Basic Mastry Qustios Arithmtic Progrssio ad Sris. Th rth trm of a squc is 4r 7. (i) Stat th first four trms ad th 0th trm. (ii) Show that th squc is a arithmtic

More information

Worksheet: Taylor Series, Lagrange Error Bound ilearnmath.net

Worksheet: Taylor Series, Lagrange Error Bound ilearnmath.net Taylor s Thorm & Lagrag Error Bouds Actual Error This is th ral amout o rror, ot th rror boud (worst cas scario). It is th dirc btw th actual () ad th polyomial. Stps:. Plug -valu ito () to gt a valu.

More information

LECTURE 13 Filling the bands. Occupancy of Available Energy Levels

LECTURE 13 Filling the bands. Occupancy of Available Energy Levels LUR 3 illig th bads Occupacy o Availabl rgy Lvls W hav dtrmid ad a dsity o stats. W also d a way o dtrmiig i a stat is illd or ot at a giv tmpratur. h distributio o th rgis o a larg umbr o particls ad

More information

Lecture 4: Parsing. Administrivia

Lecture 4: Parsing. Administrivia Adminitrivia Lctur 4: Paring If you do not hav a group, pla pot a rqut on Piazzza ( th Form projct tam... itm. B ur to updat your pot if you find on. W will aign orphan to group randomly in a fw day. Programming

More information

EE 119 Homework 6 Solution

EE 119 Homework 6 Solution EE 9 Hmwrk 6 Slutin Prr: J Bkr TA: Xi Lu Slutin: (a) Th angular magniicatin a tlcp i m / th cal lngth th bjctiv ln i m 4 45 80cm (b) Th clar aprtur th xit pupil i 35 mm Th ditanc btwn th bjctiv ln and

More information

Source code. where each α ij is a terminal or nonterminal symbol. We say that. α 1 α m 1 Bα m+1 α n α 1 α m 1 β 1 β p α m+1 α n

Source code. where each α ij is a terminal or nonterminal symbol. We say that. α 1 α m 1 Bα m+1 α n α 1 α m 1 β 1 β p α m+1 α n Adminitrivia Lctur : Paring If you do not hav a group, pla pot a rqut on Piazzza ( th Form projct tam... itm. B ur to updat your pot if you find on. W will aign orphan to group randomly in a fw day. Programming

More information

ELG3150 Assignment 3

ELG3150 Assignment 3 ELG350 Aigmt 3 Aigmt 3: E5.7; P5.6; P5.6; P5.9; AP5.; DP5.4 E5.7 A cotrol ytm for poitioig th had of a floppy dik driv ha th clodloop trafr fuctio 0.33( + 0.8) T ( ) ( + 0.6)( + 4 + 5) Plot th pol ad zro

More information

They must have different numbers of electrons orbiting their nuclei. They must have the same number of neutrons in their nuclei.

They must have different numbers of electrons orbiting their nuclei. They must have the same number of neutrons in their nuclei. 37 1 How may utros ar i a uclus of th uclid l? 20 37 54 2 crtai lmt has svral isotops. Which statmt about ths isotops is corrct? Thy must hav diffrt umbrs of lctros orbitig thir ucli. Thy must hav th sam

More information

6. Negative Feedback in Single- Transistor Circuits

6. Negative Feedback in Single- Transistor Circuits Lctur 8: Intrductin t lctrnic analg circuit 36--366 6. Ngativ Fdback in Singl- Tranitr ircuit ugn Paprn, 2008 Our aim i t tudy t ffct f ngativ fdback n t mall-ignal gain and t mall-ignal input and utput

More information

ALOHA Product no.: 03007

ALOHA Product no.: 03007 EN s l d m S vrsatil, s yu! Yur styl is vry prsal as is yur MySpdy. Attach f ths trdy spdmtrs t yur bik ad shw vry wh yu rally ar. Satch up yur favrit dsig ad xprss yur idividuality mr tha vr wh ut ad

More information

Cthulhu Through The Ages. Sample file

Cthulhu Through The Ages. Sample file Cthulhu Thrugh Th Ag Sampl fil h t i g d p CREDITS Writt By Mik Ma, Pdr Ziviai, Jh Frch, ad Chad Bwr Editig ad Dvlpmt by Mik Ma ad Duti Wright Cvr Art Paul Carrick Itrir Art Stv Gilbrt, Sam Lamt, Flria

More information

The Language of SOCIAL MEDIA. Christine Dugan

The Language of SOCIAL MEDIA. Christine Dugan Th Languag f SOCIAL MEDIA Christin Dugan Tabl f Cntnts Gt th Wrd Out...4 A Nw Kind f Languag...6 Scial Mdia Talk...12 Cnncting with Othrs...28 Changing th Dictinary...36 Glssary...42 Indx...44 Chck It

More information

User s Guide. Electronic Crossover Network. XM66 Variable Frequency. XM9 24 db/octave. XM16 48 db/octave. XM44 24/48 db/octave. XM26 24 db/octave Tube

User s Guide. Electronic Crossover Network. XM66 Variable Frequency. XM9 24 db/octave. XM16 48 db/octave. XM44 24/48 db/octave. XM26 24 db/octave Tube U Guid Elctnic Cv Ntwk XM66 Vaiabl Fquncy XM9 24 db/ctav XM16 48 db/ctav XM44 24/48 db/ctav XM26 24 db/ctav Tub XM46 24 db/ctav Paiv Lin Lvl XM126 24 db/ctav Tub Machand Elctnic Inc. Rcht, NY (585) 423

More information

PREPARATORY MATHEMATICS FOR ENGINEERS

PREPARATORY MATHEMATICS FOR ENGINEERS CIVE 690 This qusti ppr csists f 6 pritd pgs, ch f which is idtifid by th Cd Numbr CIVE690 FORMULA SHEET ATTACHED UNIVERSITY OF LEEDS Jury 008 Emiti fr th dgr f BEg/ MEg Civil Egirig PREPARATORY MATHEMATICS

More information

Continuous-Time Fourier Transform. Transform. Transform. Transform. Transform. Transform. Definition The CTFT of a continuoustime

Continuous-Time Fourier Transform. Transform. Transform. Transform. Transform. Transform. Definition The CTFT of a continuoustime Ctiuus-Tim Furir Dfiiti Th CTFT f a ctiuustim sigal x a (t is giv by Xa ( jω xa( t jωt Oft rfrrd t as th Furir spctrum r simply th spctrum f th ctiuus-tim sigal dt Ctiuus-Tim Furir Dfiiti Th ivrs CTFT

More information

(1) Then we could wave our hands over this and it would become:

(1) Then we could wave our hands over this and it would become: MAT* K285 Spring 28 Anthony Bnoit 4/17/28 Wk 12: Laplac Tranform Rading: Kohlr & Johnon, Chaptr 5 to p. 35 HW: 5.1: 3, 7, 1*, 19 5.2: 1, 5*, 13*, 19, 45* 5.3: 1, 11*, 19 * Pla writ-up th problm natly and

More information

[ ] 1+ lim G( s) 1+ s + s G s s G s Kacc SYSTEM PERFORMANCE. Since. Lecture 10: Steady-state Errors. Steady-state Errors. Then

[ ] 1+ lim G( s) 1+ s + s G s s G s Kacc SYSTEM PERFORMANCE. Since. Lecture 10: Steady-state Errors. Steady-state Errors. Then SYSTEM PERFORMANCE Lctur 0: Stady-tat Error Stady-tat Error Lctur 0: Stady-tat Error Dr.alyana Vluvolu Stady-tat rror can b found by applying th final valu thorm and i givn by lim ( t) lim E ( ) t 0 providd

More information

Bohr type models of the atom give a totally incorrect picture of the atom and are of only historical significance.

Bohr type models of the atom give a totally incorrect picture of the atom and are of only historical significance. VISUAL PHYSICS ONLIN BOHR MODL OF TH ATOM Bhr typ mdls f th atm giv a ttally icrrct pictur f th atm ad ar f ly histrical sigificac. Fig.. Bhr s platary mdl f th atm. Hwvr, th Bhr mdls wr a imprtat stp

More information

ARC Window System. General Information: Determine your window type and turn to the specific pages for the. Type #1 Arc. Windows. Type #2 Arc Windows

ARC Window System. General Information: Determine your window type and turn to the specific pages for the. Type #1 Arc. Windows. Type #2 Arc Windows I-1 ARC Wid Systm This systm quis a additial tip t th jb sit ad cdiati bt th km ad th istall. Tip #1- Masu th id. Tip #2- Fi-tu th fit t th id, th s th tatmt. Tip #3- Istall fial tatmt. As ith ay typ f

More information

MONTGOMERY COLLEGE Department of Mathematics Rockville Campus. 6x dx a. b. cos 2x dx ( ) 7. arctan x dx e. cos 2x dx. 2 cos3x dx

MONTGOMERY COLLEGE Department of Mathematics Rockville Campus. 6x dx a. b. cos 2x dx ( ) 7. arctan x dx e. cos 2x dx. 2 cos3x dx MONTGOMERY COLLEGE Dpartmt of Mathmatics Rockvill Campus MATH 8 - REVIEW PROBLEMS. Stat whthr ach of th followig ca b itgratd by partial fractios (PF), itgratio by parts (PI), u-substitutio (U), or o of

More information

1985 AP Calculus BC: Section I

1985 AP Calculus BC: Section I 985 AP Calculus BC: Sctio I 9 Miuts No Calculator Nots: () I this amiatio, l dots th atural logarithm of (that is, logarithm to th bas ). () Ulss othrwis spcifid, th domai of a fuctio f is assumd to b

More information

section 1 Influencing Change Toolkit How to: Influence People

section 1 Influencing Change Toolkit How to: Influence People Influncing Chang Tlkit Hw t: Influnc Ppl Influncing ppl mans having an ffct n thm, changing r mdifying thir viw. In rdr t influnc chang, w nd t influnc th ppl wh ar in a psitin t mak that chang happn.

More information

Chapter (8) Estimation and Confedence Intervals Examples

Chapter (8) Estimation and Confedence Intervals Examples Chaptr (8) Estimatio ad Cofdc Itrvals Exampls Typs of stimatio: i. Poit stimatio: Exampl (1): Cosidr th sampl obsrvatios, 17,3,5,1,18,6,16,10 8 X i i1 17 3 5 118 6 16 10 116 X 14.5 8 8 8 14.5 is a poit

More information

Chapter 2 Infinite Series Page 1 of 11. Chapter 2 : Infinite Series

Chapter 2 Infinite Series Page 1 of 11. Chapter 2 : Infinite Series Chatr Ifiit Sris Pag of Sctio F Itgral Tst Chatr : Ifiit Sris By th d of this sctio you will b abl to valuat imror itgrals tst a sris for covrgc by alyig th itgral tst aly th itgral tst to rov th -sris

More information

Acid Base Reactions. Acid Base Reactions. Acid Base Reactions. Chemical Reactions and Equations. Chemical Reactions and Equations

Acid Base Reactions. Acid Base Reactions. Acid Base Reactions. Chemical Reactions and Equations. Chemical Reactions and Equations Chmial Ratins and Equatins Hwitt/Lyns/Suhki/Yh Cnptual Intgratd Sin During a hmial ratin, n r mr nw mpunds ar frmd as a rsult f th rarrangmnt f atms. Chaptr 13 CHEMICAL REACTIONS Ratants Prduts Chmial

More information

If σis unknown. Properties of t distribution. 6.3 One and Two Sample Inferences for Means. What is the correct multiplier? t

If σis unknown. Properties of t distribution. 6.3 One and Two Sample Inferences for Means. What is the correct multiplier? t /8/009 6.3 Oe a Tw Samle Iferece fr Mea If i kw a 95% Cfiece Iterval i 96 ±.96 96.96 ± But i ever kw. If i ukw Etimate by amle taar eviati The etimate taar errr f the mea will be / Uig the etimate taar

More information

ECEN620: Network Theory Broadband Circuit Design Fall 2014

ECEN620: Network Theory Broadband Circuit Design Fall 2014 ECE60: work Thory Broadbad Circui Dig Fall 04 Lcur 6: PLL Trai Bhavior Sam Palrmo Aalog & Mixd-Sigal Cr Txa A&M Uivriy Aoucm, Agda, & Rfrc HW i du oday by 5PM PLL Trackig Rpo Pha Dcor Modl PLL Hold Rag

More information

Registered Sex Offenders

Registered Sex Offenders gitrd x ffdr victd x ffdr r rquird by tt lw t rgitr wit t lw frct gcy vig juridicti vr wr ty rid cwll lic prtt tctiv igd t ti prc t ur rgitrti d cplic wit t rquirt t frt udr t lw fllwig pg w ll currtly

More information

(Reference: sections in Silberberg 5 th ed.)

(Reference: sections in Silberberg 5 th ed.) ALE. Atomic Structur Nam HEM K. Marr Tam No. Sctio What is a atom? What is th structur of a atom? Th Modl th structur of a atom (Rfrc: sctios.4 -. i Silbrbrg 5 th d.) Th subatomic articls that chmists

More information

The Phase Probability for Some Excited Binomial States

The Phase Probability for Some Excited Binomial States Egypt. J. Sl., Vl. 5, N., 3 Th Pha Prbability fr S Excitd Biial Stat. Darwih Faculty f Educati, Suz Caal Uivrity at Al-Arih, Egypt. I thi papr, th pha prprti i Pgg-Bartt frali ar cidrd. Th pha ditributi

More information

Chapter 15: Mathematics More Fun With

Chapter 15: Mathematics More Fun With Pg 5 Chpt 15: Mthmtic M Fu With Numb. I thi chpt w will lk t m dditil mthmticl pt d fucti tht wk with umb. Tpic will b bk dw it fu cti: 1) w pt; ) w itg fucti, 3) w fltig pit fucti, d 4) tigmtic fucti.

More information

NEW VERSION OF SZEGED INDEX AND ITS COMPUTATION FOR SOME NANOTUBES

NEW VERSION OF SZEGED INDEX AND ITS COMPUTATION FOR SOME NANOTUBES Digst Joural of Naomatrials ad Biostructurs Vol 4, No, March 009, p 67-76 NEW VERSION OF SZEGED INDEX AND ITS COMPUTATION FOR SOME NANOTUBES A IRANMANESH a*, O KHORMALI b, I NAJAFI KHALILSARAEE c, B SOLEIMANI

More information

Reliability of time dependent stress-strength system for various distributions

Reliability of time dependent stress-strength system for various distributions IOS Joural of Mathmatcs (IOS-JM ISSN: 78-578. Volum 3, Issu 6 (Sp-Oct., PP -7 www.osrjourals.org lablty of tm dpdt strss-strgth systm for varous dstrbutos N.Swath, T.S.Uma Mahswar,, Dpartmt of Mathmatcs,

More information

Helping you learn to save. Pigby s tips and tricks

Helping you learn to save. Pigby s tips and tricks Hlpg yu lan t av Pigby tip and tick Hlpg vy littl av Pigby ha bn tachg hi find all abut ny and hw t av f what ty want. Tuffl i avg f a nw tappy bubbl d and Pi can t wait t b abl t buy nw il pat. Pigby

More information

Fig. 2. RC beam web: a) axonometric view of the adopted schematization and b) shear loading process.

Fig. 2. RC beam web: a) axonometric view of the adopted schematization and b) shear loading process. FIGURE CAPTIONS Fig. 1. Pib faiur md f a NSM FRP ip: (a) dbdig, (b) amiat ti ruptur, (c) ccrt mi-cica fractur, (d) mid haw mi-c pu dbdig. Fig. 2. RC bam wb: a) amic viw f th adptd chmatizati ad b) har

More information

Lectures 9 IIR Systems: First Order System

Lectures 9 IIR Systems: First Order System EE3054 Sigals ad Systms Lcturs 9 IIR Systms: First Ordr Systm Yao Wag Polytchic Uivrsity Som slids icludd ar xtractd from lctur prstatios prpard by McCllla ad Schafr Lics Ifo for SPFirst Slids This work

More information

Review Exercises. 1. Evaluate using the definition of the definite integral as a Riemann Sum. Does the answer represent an area? 2

Review Exercises. 1. Evaluate using the definition of the definite integral as a Riemann Sum. Does the answer represent an area? 2 MATHEMATIS --RE Itgral alculus Marti Huard Witr 9 Rviw Erciss. Evaluat usig th dfiitio of th dfiit itgral as a Rima Sum. Dos th aswr rprst a ara? a ( d b ( d c ( ( d d ( d. Fid f ( usig th Fudamtal Thorm

More information

Coulomb s Law Worksheet Solutions

Coulomb s Law Worksheet Solutions PHLYZIS ulb Law Wrkht Slutin. w charg phr 0 c apart attract ach thr with a frc f 3.0 0 6 N. What frc rult fr ach f th fllwing chang, cnir paratly? a Bth charg ar ubl an th itanc rain th a. b An uncharg,

More information

. This is made to keep the kinetic energy at outlet a minimum.

. This is made to keep the kinetic energy at outlet a minimum. Runnr Francis Turbin Th shap th blads a Francis runnr is cmplx. Th xact shap dpnds n its spciic spd. It is bvius rm th quatin spciic spd (Eq.5.8) that highr spciic spd mans lwr had. This rquirs that th

More information

O QP P. Limit Theorems. p and to see if it will be less than a pre-assigned number,. p n

O QP P. Limit Theorems. p and to see if it will be less than a pre-assigned number,. p n Limit Trms W ft av t d fr apprximatis w gts vry larg. Fr xampl, smtims fidig t prbability distributis f radm variabls lad t utractabl matmatical prblms. W ca s tat t distributi fr crtai fuctis f a radm

More information

Narayana IIT Academy

Narayana IIT Academy INDIA Sc: LT-IIT-SPARK Dat: 9--8 6_P Max.Mars: 86 KEY SHEET PHYSIS A 5 D 6 7 A,B 8 B,D 9 A,B A,,D A,B, A,B B, A,B 5 A 6 D 7 8 A HEMISTRY 9 A B D B B 5 A,B,,D 6 A,,D 7 B,,D 8 A,B,,D 9 A,B, A,B, A,B,,D A,B,

More information

5.1 The Nuclear Atom

5.1 The Nuclear Atom Sav My Exams! Th Hom of Rvisio For mor awsom GSE ad lvl rsourcs, visit us at www.savmyxams.co.uk/ 5.1 Th Nuclar tom Qustio Papr Lvl IGSE Subjct Physics (0625) Exam oard Topic Sub Topic ooklt ambridg Itratioal

More information

LECTURE 5 Guassian Wave Packet

LECTURE 5 Guassian Wave Packet LECTURE 5 Guassian Wav Pact 1.5 Eampl f a guassian shap fr dscribing a wav pact Elctrn Pact ψ Guassian Assumptin Apprimatin ψ As w hav sn in QM th wav functin is ftn rprsntd as a Furir transfrm r sris.

More information

Solution to 1223 The Evil Warden.

Solution to 1223 The Evil Warden. Solutio to 1 Th Evil Ward. This is o of thos vry rar PoWs (I caot thik of aothr cas) that o o solvd. About 10 of you submittd th basic approach, which givs a probability of 47%. I was shockd wh I foud

More information

Lecture 27: The 180º Hybrid.

Lecture 27: The 180º Hybrid. Whits, EE 48/58 Lctur 7 Pag f 0 Lctur 7: Th 80º Hybrid. Th scnd rciprcal dirctinal cuplr w will discuss is th 80º hybrid. As th nam implis, th utputs frm such a dvic can b 80º ut f phas. Thr ar tw primary

More information

APPENDIX: STATISTICAL TOOLS

APPENDIX: STATISTICAL TOOLS I. Nots o radom samplig Why do you d to sampl radomly? APPENDI: STATISTICAL TOOLS I ordr to masur som valu o a populatio of orgaisms, you usually caot masur all orgaisms, so you sampl a subst of th populatio.

More information

For wood, the natural choice!

For wood, the natural choice! Fr wd, th atural chic! Prducd by h rsistat t saliva ad swat i cfrmity wit I l g y Hardwax-il Classic Flrsrvic hardwax-ils hav built up a xcllt rputati. Th Flrsrvic hardwax-ils sur vry wd flr a lastig atural

More information

Topic 5:Discrete-Time Fourier Transform (DTFT)

Topic 5:Discrete-Time Fourier Transform (DTFT) ELEC64: Sigals Ad Systms Tpic 5:Discrt-Tim Furir Trasfrm DTFT Aishy Amr Ccrdia Uivrsity Elctrical ad Cmputr Egirig Itrducti DT Furir Trasfrm Sufficit cditi fr th DTFT DT Furir Trasfrm f Pridic Sigals DTFT

More information

Another Explanation of the Cosmological Redshift. April 6, 2010.

Another Explanation of the Cosmological Redshift. April 6, 2010. Anthr Explanatin f th Csmlgical Rdshift April 6, 010. Jsé Francisc García Juliá C/ Dr. Marc Mrncian, 65, 5. 4605 Valncia (Spain) E-mail: js.garcia@dival.s h lss f nrgy f th phtn with th tim by missin f

More information

Chapter 9 Compressible Flow 667

Chapter 9 Compressible Flow 667 Chapter 9 Cmpreible Flw 667 9.57 Air flw frm a tank thrugh a nzzle int the tandard atmphere, a in Fig. P9.57. A nrmal hck tand in the exit f the nzzle, a hwn. Etimate (a) the tank preure; and (b) the ma

More information

Probability & Statistics,

Probability & Statistics, Probability & Statistics, BITS Pilai K K Birla Goa Campus Dr. Jajati Kshari Sahoo Dpartmt of Mathmatics BITS Pilai, K K Birla Goa Campus Poisso Distributio Poisso Distributio: A radom variabl X is said

More information

Topic 5: Discrete-Time Fourier Transform (DTFT)

Topic 5: Discrete-Time Fourier Transform (DTFT) ELEC36: Signals And Systms Tpic 5: Discrt-Tim Furir Transfrm (DTFT) Dr. Aishy Amr Cncrdia Univrsity Elctrical and Cmputr Enginring DT Furir Transfrm Ovrviw f Furir mthds DT Furir Transfrm f Pridic Signals

More information

Session : Plasmas in Equilibrium

Session : Plasmas in Equilibrium Sssio : Plasmas i Equilibrium Ioizatio ad Coductio i a High-prssur Plasma A ormal gas at T < 3000 K is a good lctrical isulator, bcaus thr ar almost o fr lctros i it. For prssurs > 0.1 atm, collisio amog

More information

International Journal of Mathematical Archive-7(5), 2016, Available online through ISSN

International Journal of Mathematical Archive-7(5), 2016, Available online through   ISSN Itratial Jural f athmatial Arhiv-7(5), 06, 60-70 Availabl li thrugh wwwimaif ISSN 9 5046 IDEALS IN ALOST SEILATTICE G NANAJI RAO, TEREFE GETACHEW BEYENE*,Dpartmt f athmatis, Adhra Uivrsity, Visakhpataam,

More information

in dust whoever knee mothers yearning our neigh rest frog sit hour shake full trying

in dust whoever knee mothers yearning our neigh rest frog sit hour shake full trying Wrt a shrt stry. Us as may f ths wrds as yu ca. Crcl ach wrd th wrd b that appars yur stry. dust whvr k mthrs yarg ur gh rst frg st hur shak full tryg Cmplt ach aalgy wth th bst wrd. at ght lgs chckrs

More information

RR-1B. r e Rd W BR O. Wy nd m e RR-1B IX TH. K nol l. r th LR-1A. F arm Rd D A K OTA A VE NG HI LL RD. Long. Lake LR-1A L A KE Y ZA E TR E L IN L UC

RR-1B. r e Rd W BR O. Wy nd m e RR-1B IX TH. K nol l. r th LR-1A. F arm Rd D A K OTA A VE NG HI LL RD. Long. Lake LR-1A L A KE Y ZA E TR E L IN L UC F a c 20 pl a v ac -1B 21 F B faytt -1-1 aag -1-1 iv t ig t P B-4-1-1-1 B P itka Z Bui h aw B B F P B-3 B-4-1B -1B B- PU - ighway cial catial ual idtial -1 - Faily ual idtial - 5 c haig -1-1 - Faily h

More information

Chapter 3.1: Polynomial Functions

Chapter 3.1: Polynomial Functions Ntes 3.1: Ply Fucs Chapter 3.1: Plymial Fuctis I Algebra I ad Algebra II, yu ecutered sme very famus plymial fuctis. I this secti, yu will meet may ther members f the plymial family, what sets them apart

More information

Where k is either given or determined from the data and c is an arbitrary constant.

Where k is either given or determined from the data and c is an arbitrary constant. Exponntial growth and dcay applications W wish to solv an quation that has a drivativ. dy ky k > dx This quation says that th rat of chang of th function is proportional to th function. Th solution is

More information

Outline. Heat Exchangers. Heat Exchangers. Compact Heat Exchangers. Compact Heat Exchangers II. Heat Exchangers April 18, ME 375 Heat Transfer 1

Outline. Heat Exchangers. Heat Exchangers. Compact Heat Exchangers. Compact Heat Exchangers II. Heat Exchangers April 18, ME 375 Heat Transfer 1 Hat Exangr April 8, 007 Hat Exangr Larry artt Manial Engrg 375 Hat ranfr April 8, 007 Outl Bai ida f at xangr Ovrall at tranfr ffiint Lg-man tmpratur diffrn mtd Efftivn NU mtd ratial nidratin Hat Exangr

More information

Lecture contents. Density of states Distribution function Statistic of carriers. Intrinsic Extrinsic with no compensation Compensation

Lecture contents. Density of states Distribution function Statistic of carriers. Intrinsic Extrinsic with no compensation Compensation Ltur otts Dsity of stats Distributio futio Statisti of arrirs Itrisi trisi with o ompsatio ompsatio S 68 Ltur #7 Dsity of stats Problm: alulat umbr of stats pr uit rgy pr uit volum V() Larg 3D bo (L is

More information

CDS 101: Lecture 5.1 Reachability and State Space Feedback

CDS 101: Lecture 5.1 Reachability and State Space Feedback CDS, Lctur 5. CDS : Lctur 5. Rachability ad Stat Spac Fdback Richard M. Murray ad Hido Mabuchi 5 Octobr 4 Goals: Di rachability o a cotrol systm Giv tsts or rachability o liar systms ad apply to ampls

More information

(c) Availability of State Government run similar school / Hostel within 2 km of this school.

(c) Availability of State Government run similar school / Hostel within 2 km of this school. 1. am f Schm: Grant in aid t Vluntary Organizatin wrking fr Schduld Cat (Ridntial n ridntial Schl Htl) 2. Dat f npctin: (i) Tim f cmmncmnt f inpctin: (ii) Tim f cmpltin f inpctin: 3. Cmpitin f th npctin

More information

INTERMEDIATE. mayorsmtbchallenge.org

INTERMEDIATE. mayorsmtbchallenge.org myrmtbchll.r i lcl ti Bik Chll iti crrt w bicyclit i frily lf-cmptiti hihlihti r ivr tr ytm. IDI L ID C L 8.6 y W m c ri D itc C C t rc l ck w i r h l i r trt kk ll rk i t th r r v r v l tiv tiv r r rk

More information

European Business Confidence Survey December 2012 Positive expectations for 2013

European Business Confidence Survey December 2012 Positive expectations for 2013 Dcmbr 2012 Erpa Bsiss Cfic rv Dcmbr 2012 Psitiv xpctatis fr 2013 Lasrp a Ivigrs EMEA hav rctl cmplt thir latst Erpa Bsiss Cfic rv. Th fiigs sggst a psitiv start t 2013 a a mr ptimistic tlk cmpar t that

More information

MATH Midterm Examination Victor Matveev October 26, 2016

MATH Midterm Examination Victor Matveev October 26, 2016 MATH 33- Midterm Examiati Victr Matveev Octber 6, 6. (5pts, mi) Suppse f(x) equals si x the iterval < x < (=), ad is a eve peridic extesi f this fucti t the rest f the real lie. Fid the csie series fr

More information

10.5 Linear Viscoelasticity and the Laplace Transform

10.5 Linear Viscoelasticity and the Laplace Transform Scn.5.5 Lnar Vclacy and h Lalac ranfrm h Lalac ranfrm vry uful n cnrucng and analyng lnar vclac mdl..5. h Lalac ranfrm h frmula fr h Lalac ranfrm f h drvav f a funcn : L f f L f f f f f c..5. whr h ranfrm

More information

Ordinary Differential Equations

Ordinary Differential Equations Ordiary Diffrtial Equatio Aftr radig thi chaptr, you hould b abl to:. dfi a ordiary diffrtial quatio,. diffrtiat btw a ordiary ad partial diffrtial quatio, ad. Solv liar ordiary diffrtial quatio with fid

More information

ECE602 Exam 1 April 5, You must show ALL of your work for full credit.

ECE602 Exam 1 April 5, You must show ALL of your work for full credit. ECE62 Exam April 5, 27 Nam: Solution Scor: / This xam is closd-book. You must show ALL of your work for full crdit. Plas rad th qustions carfully. Plas chck your answrs carfully. Calculators may NOT b

More information

VII. Quantum Entanglement

VII. Quantum Entanglement VII. Quantum Entanglmnt Quantum ntanglmnt is a uniqu stat of quantum suprposition. It has bn studid mainly from a scintific intrst as an vidnc of quantum mchanics. Rcntly, it is also bing studid as a basic

More information

How many neutrino species?

How many neutrino species? ow may utrio scis? Two mthods for dtrmii it lium abudac i uivrs At a collidr umbr of utrio scis Exasio of th uivrs is ovrd by th Fridma quatio R R 8G tot Kc R Whr: :ubblcostat G :Gravitatioal costat 6.

More information

Engineering Differential Equations Practice Final Exam Solutions Fall 2011

Engineering Differential Equations Practice Final Exam Solutions Fall 2011 9.6 Enginring Diffrntial Equation Practic Final Exam Solution Fall 0 Problm. (0 pt.) Solv th following initial valu problm: x y = xy, y() = 4. Thi i a linar d.. bcau y and y appar only to th firt powr.

More information

Voltage, Current, Power, Series Resistance, Parallel Resistance, and Diodes

Voltage, Current, Power, Series Resistance, Parallel Resistance, and Diodes Lctur 1. oltag, Currnt, Powr, Sris sistanc, Paralll sistanc, and Diods Whn you start to dal with lctronics thr ar thr main concpts to start with: Nam Symbol Unit oltag volt Currnt ampr Powr W watt oltag

More information

Examination No. 3 - Tuesday, Nov. 15

Examination No. 3 - Tuesday, Nov. 15 NAME (lease rit) SOLUTIONS ECE 35 - DEVICE ELECTRONICS Fall Semester 005 Examiati N 3 - Tuesday, Nv 5 3 4 5 The time fr examiati is hr 5 mi Studets are allwed t use 3 sheets f tes Please shw yur wrk, artial

More information

Allowable bearing capacity and settlement Vertical stress increase in soil

Allowable bearing capacity and settlement Vertical stress increase in soil 5 Allwabl barg aaity and ttlmnt Vrtial tr ra il - du t nntratd lad: 3 5 r r x y - du t irularly ladd ara lad:. G t tabl 5..6 Fd / by dtrmg th trm: r/(/) /(/) 3- blw rtangular ladd ara: th t i at th rnr

More information

E o and the equilibrium constant, K

E o and the equilibrium constant, K lectrchemical measuremets (Ch -5 t 6). T state the relati betwee ad K. (D x -b, -). Frm galvaic cell vltage measuremet (a) K sp (D xercise -8, -) (b) K sp ad γ (D xercise -9) (c) K a (D xercise -G, -6)

More information

PD12 21 The Highlands East Sign Package

PD12 21 The Highlands East Sign Package PD12 21 The Highlands ast ign Package March 5, 2013 T T TAT: ALL CHAL LTT MUT B 3 DP (TH G LY) CHAL LTT BY TAT: 3 PFHD Y TU; WHT ACYLC FAC; 1 Y JWLT TM TALLY LLUM. w/wht LD; FT UFAC YL TAT PAL PTD. PAYLAT

More information

GRANITE PEAKS - BUILDING 3 GRADING PLAN ENGINEER SURVEYORS PLANNERS SEGO LILY DRIVE & PETUNIA WAY, SANDY, UTAH NOTES

GRANITE PEAKS - BUILDING 3 GRADING PLAN ENGINEER SURVEYORS PLANNERS SEGO LILY DRIVE & PETUNIA WAY, SANDY, UTAH NOTES T A Utah Corporation G UY PLA 0. Ma in tr eet panish Fork, UT 84660 Phone: 80.798.0555 F a x : 8 0. 7 9 8. 9 9 o f f i c e @ l e i e n g. c o m w w w. l e i e n g. c o m G TD PF o. 808 BA T. GABL T A T

More information

SAFE OPERATION OF TUBULAR (PFR) ADIABATIC REACTORS. FIGURE 1: Temperature as a function of space time in an adiabatic PFR with exothermic reaction.

SAFE OPERATION OF TUBULAR (PFR) ADIABATIC REACTORS. FIGURE 1: Temperature as a function of space time in an adiabatic PFR with exothermic reaction. he 47 Lctu Fall 5 SFE OPERION OF UBULR (PFR DIBI REORS I a xthmic acti th tmatu will ctiu t is as mvs alg a lug flw act util all f th limitig actat is xhaust. Schmatically th aiabatic tmatu is as a fucti

More information

DEPOLOX 3 PLUS RESIDUAL ANALYZER FOR MEASURING CHLORINE, CHLORINE DIOXIDE, OZONE, AND/OR ph OR FLUORIDE BOOK NO. IM CA UA

DEPOLOX 3 PLUS RESIDUAL ANALYZER FOR MEASURING CHLORINE, CHLORINE DIOXIDE, OZONE, AND/OR ph OR FLUORIDE BOOK NO. IM CA UA DEPOLOX 3 PLUS RESIDUAL ANALYZER FOR MEASURING CHLORINE, CHLORINE DIOXIDE, OZONE, AND/OR ph OR FLUORIDE BOOK NO. IM 50.560CA UA ISSUE B EQUIPMENT SERIAL NO. DATE OF START-UP START-UP BY Prmpt srvic availabl

More information

DISCRETE TIME FOURIER TRANSFORM (DTFT)

DISCRETE TIME FOURIER TRANSFORM (DTFT) DISCRETE TIME FOURIER TRANSFORM (DTFT) Th dicrt-tim Fourir Tranform x x n xn n n Th Invr dicrt-tim Fourir Tranform (IDTFT) x n Not: ( ) i a complx valud continuou function = π f [rad/c] f i th digital

More information

INTRODUCTION TO AUTOMATIC CONTROLS INDEX LAPLACE TRANSFORMS

INTRODUCTION TO AUTOMATIC CONTROLS INDEX LAPLACE TRANSFORMS adjoint...6 block diagram...4 clod loop ytm... 5, 0 E()...6 (t)...6 rror tady tat tracking...6 tracking...6...6 gloary... 0 impul function...3 input...5 invr Laplac tranform, INTRODUCTION TO AUTOMATIC

More information

GRAPHS IN SCIENCE. drawn correctly, the. other is not. Which. Best Fit Line # one is which?

GRAPHS IN SCIENCE. drawn correctly, the. other is not. Which. Best Fit Line # one is which? 5 9 Bt Ft L # 8 7 6 5 GRAPH IN CIENCE O of th thg ot oft a rto of a xrt a grah of o k. A grah a vual rrtato of ural ata ollt fro a xrt. o of th ty of grah you ll f ar bar a grah. Th o u ot oft a l grah,

More information

Introduction to Arithmetic Geometry Fall 2013 Lecture #20 11/14/2013

Introduction to Arithmetic Geometry Fall 2013 Lecture #20 11/14/2013 18.782 Introduction to Arithmtic Gomtry Fall 2013 Lctur #20 11/14/2013 20.1 Dgr thorm for morphisms of curvs Lt us rstat th thorm givn at th nd of th last lctur, which w will now prov. Thorm 20.1. Lt φ:

More information

07 - SEQUENCES AND SERIES Page 1 ( Answers at he end of all questions ) b, z = n

07 - SEQUENCES AND SERIES Page 1 ( Answers at he end of all questions ) b, z = n 07 - SEQUENCES AND SERIES Pag ( Aswrs at h d of all qustios ) ( ) If = a, y = b, z = c, whr a, b, c ar i A.P. ad = 0 = 0 = 0 l a l

More information

ME 354, MECHANICS OF MATERIALS LABORATORY COMPRESSION AND BUCKLING

ME 354, MECHANICS OF MATERIALS LABORATORY COMPRESSION AND BUCKLING ME 354, MECHANICS OF MATERIALS LABATY COMPRESSION AND BUCKLING 01 January 000 / mgj PURPOSE Th purps f this xrcis is t study th ffcts f nd cnditins, clumn lngth, and matrial prprtis n cmprssiv bhaviur

More information

COHORT MBA. Exponential function. MATH review (part2) by Lucian Mitroiu. The LOG and EXP functions. Properties: e e. lim.

COHORT MBA. Exponential function. MATH review (part2) by Lucian Mitroiu. The LOG and EXP functions. Properties: e e. lim. MTH rviw part b Lucian Mitroiu Th LOG and EXP functions Th ponntial function p : R, dfind as Proprtis: lim > lim p Eponntial function Y 8 6 - -8-6 - - X Th natural logarithm function ln in US- log: function

More information

Chapter 2 Linear Waveshaping: High-pass Circuits

Chapter 2 Linear Waveshaping: High-pass Circuits Puls and Digital Circuits nkata Ra K., Rama Sudha K. and Manmadha Ra G. Chaptr 2 Linar Wavshaping: High-pass Circuits. A ramp shwn in Fig.2p. is applid t a high-pass circuit. Draw t scal th utput wavfrm

More information

W A T E R P R O O F I N G S Y S T E M S

W A T E R P R O O F I N G S Y S T E M S M A X I M A L - R F L C T A N C - M A X I M A L - R F L C T A N C - PRTCTIV CATING W A T R P R F I N G Y T M RI 105 M A X I M A L R F L C T A N C. M A X I M A L R F L C T A N C PRTCTIV CATING Water-based

More information

Outline for Today. A simple data structure for string searching. A compact, powerful, and flexible data structure for string algorithms.

Outline for Today. A simple data structure for string searching. A compact, powerful, and flexible data structure for string algorithms. Suffix Tr Outli fr Tday Rviw frm Lat Tim A quick rfrhr tri. Suffix Tri A impl data tructur fr trig archig. Suffix Tr A cmpact, pwrful, ad flxibl data tructur fr trig algrithm. Gralizd Suffix Tr A v mr

More information

Ordinary Differential Equations

Ordinary Differential Equations Basi Nomlatur MAE 0 all 005 Egirig Aalsis Ltur Nots o: Ordiar Diffrtial Equatios Author: Profssor Albrt Y. Tog Tpist: Sakurako Takahashi Cosidr a gral O. D. E. with t as th idpdt variabl, ad th dpdt variabl.

More information

Multiple Short Term Infusion Homework # 5 PHA 5127

Multiple Short Term Infusion Homework # 5 PHA 5127 Multipl Short rm Infusion Homwork # 5 PHA 527 A rug is aministr as a short trm infusion. h avrag pharmacokintic paramtrs for this rug ar: k 0.40 hr - V 28 L his rug follows a on-compartmnt boy mol. A 300

More information

CDS 101: Lecture 5.1 Reachability and State Space Feedback

CDS 101: Lecture 5.1 Reachability and State Space Feedback CDS, Lctur 5. CDS : Lctur 5. Rachability ad Stat Spac Fdback Richard M. Murray 7 Octobr 3 Goals: Di rachability o a cotrol systm Giv tsts or rachability o liar systms ad apply to ampls Dscrib th dsig o

More information

Chapter Five. More Dimensions. is simply the set of all ordered n-tuples of real numbers x = ( x 1

Chapter Five. More Dimensions. is simply the set of all ordered n-tuples of real numbers x = ( x 1 Chatr Fiv Mor Dimsios 51 Th Sac R W ar ow rard to mov o to sacs of dimsio gratr tha thr Ths sacs ar a straightforward gralizatio of our Euclida sac of thr dimsios Lt b a ositiv itgr Th -dimsioal Euclida

More information

Washington State University

Washington State University he 3 Ktics ad Ractor Dsig Sprg, 00 Washgto Stat Uivrsity Dpartmt of hmical Egrg Richard L. Zollars Exam # You will hav o hour (60 muts) to complt this xam which cosists of four (4) problms. You may us

More information

are given in the table below. t (hours)

are given in the table below. t (hours) CALCULUS WORKSHEET ON INTEGRATION WITH DATA Work th following on notbook papr. Giv dcimal answrs corrct to thr dcimal placs.. A tank contains gallons of oil at tim t = hours. Oil is bing pumpd into th

More information

Equation Sheet Please tear off this page and keep it with you

Equation Sheet Please tear off this page and keep it with you ECE 30L, Exam Fall 05 Equatio Sht Plas tar off this ag ad k it with you Gral Smicoductor: 0 i ( EF EFi ) kt 0 i ( EFi EF ) kt Eg i N C NV kt 0 0 V IR L, D, τ, d d τ c g L D kt I J diff D D µ * m σ (µ +

More information