Design of a Three Phase Active Power Filter with Sliding Mode Control and Energy Feedback

Size: px
Start display at page:

Download "Design of a Three Phase Active Power Filter with Sliding Mode Control and Energy Feedback"

Transcription

1 Deg f Three Phe Ate Pwer Flter wth lg Me trl Eergy Feek M. Nyerr, T. Nk Atrt Nler le l three he etwrk rete hr le. Ate e flter re e fr elt r ret f thee effet. Pe flter he e ltt. Fr exle, they re ege ly fr ef freey they y e t ree the etwrk t the t f lg. The ther rwk f e flter tht the ze f rere eleet re rlly lrge. The te flter re e f ltt f e flter fr exle; they elte re th e hr 't e ree the etwrk. I th er erter ly he ee e ltely three he the ee f the le he ee ere. A lg e trl e eergy feek f tr elye the eg wth th eth, the y ee f the flter re effetely hr l le etg kly. Atrt ht te flter, hr, erter, lg e trl, eergy feek. I. INTODTION ONNETION f ler l t the etwrk, e t er f rret ltge hr flly ree the wer le. By g rret re rllel wth the l, rere hr rret e re fr the ler l. ht te flter wth PWM erter re rlly e fr th re. A D tr e wth erter tht hrge wth t rllel e hw Fg.. I th er, r eft f Eletr wer re frt e el e -x ere fr wer et. I rer t tke the hrgg f tr y t- rllel e t t, three-he el f the etwrk ere. Al lg e erter wth eergy feek elye t trk referee rret wth ft y. II. DEFINITION OF EETI POWE There re r eft fr -l tret t, th te freey [, ]. The t rtt eft te freey Fryze Be reetely []. Te e trl lgrth re fter th freey th er we e te. V V Fg. ht te wer flter A. Freey D Deft f Eletr Pwer Fr the frt te the wer eft freey tre y Be. Th eft wrk tey tte e hr tt fr eh freey. M ltge: V t V T Where V the M le f -th hr ltge the et fr M rret l lr t e et. The ret wer, te rete wer efe : VI P V I ϕ Q V I ϕ I th eth, the rerl effet f hr re t ere fr lg f wer, the hr wer efe : D It w ler tht g f th eth fr te r e flter w t rrte ee the effet f ltge rret hr wth eh ther t ere.

2 B. Te D Deft f Eletr Pwer Fr the frt te the wer eft te tre y Fryze. The ret wer, te rete wer efe : VI P t t t VI w T Q P ete wer rt f tte wer whh e t trte t te wer. zrek re th eft y g the rete wer t fr fferet rt e ther hyl rg. Ate rete wer eft Frze e re the e. It t e ere tht Fryze eft, f the wer ftr el e l e, the the ltge rret wll e he the wer trt wll e tl. Hweer, t t rret -l e.. Deft f Eletr Pwer Three-Phe yte I gle-he yte, the tte wer el t rt f tte ltge rret. Al the te wer el t erge wer flly the rete wer el t the rt f the tte wer whh e t trte t te wer. The tte te three-he wer efe : t t t t t t t The erge f t P el t te wer whh trt fr re t l t erge wer el t lltry wer P ~ whh llte etwee re l t erge el t zer. The three he rete wer rt f eletr wer, whh e t trte t three he tte te wer. I ft, rete wer rlte etwee three he f yte. Fr llt f te rete wer et, t rere t e eh he rret t te rete et ze the grge ft f the. w ϕ μ 9 μ We rewrte e et :, Iω k Ge k ; K, The lt relt fr te rete three he rret wth l ltge wth lte el t -l rret wth t, r, th 7 th hr wth lte el t ere f hr rer, /, /, /7 reetely hw Fg.. The tte wer tw e wth wtht et hw Fg. [-]. he he w μ μ,, μ μ 6 Wth the trt f: Φ μ, μ, μ μ μ μ 7 Flly, we he: μ ϕ μ 8 μ he Fg. Phe ltge rret te et f rret ete

3 Fg. Itte l wer : w w w t D. Itte Pwer -Ax The ltge rret x e te fr x y lrk trfrt: Phe ltge x l e te y lr et. Itte wer el t.. P Al we he: { }.. ϕ ϕ We rewrte the e et :. Oe f the eeft f tht we ete the, lly. If we wt t ete,, ~ the: ~ 6 Wth ere lrk trfrt, we f referee rret fr te flter. 7 III. DEIGN OF ATIVE POWE FITE The three he te flter hw Fg. t tw rt:. Pwer rt PWM erter. trl rt rret re r ltge re erter e e wer rt. I th er, ltge re erter wth rret trl elye. g lt tr D e f erter, the zer eee f rret e ete. Al f the ltge re t yetrl, we f the fetl te eee ltge y g P the f the referee rret y et 6 7 []. The trl rt t exterl lg e trl l fr erter trl terl eergy feek l fr D ltge reglt []. A. Pwer rt PWM Ierter It rere tht the erter three he rret f f f,,, trk the referee rret,,, wth ft y ree. Oe f the erter leg hw Fg.. By lg the wth T, f etg rret egte f <, wll hrge f /t < f the rret te f >, wll hrge f /t >. Al By lg the wth T, f etg rret te f >, wll hrge f /t < f the rret egte f <, wll hrge f /t >. Tkg the ltge f tr three he rret tte rle, the effet f three he hrge hrge f tr e tke t t.,, re the trl rle f three he wthe. If trl rle el t -, the er wth f the reete he le. If t el t the lwer wth f the reete he, t. If the trl rle el t zer th wthe re e.

4 If V T T V V f f f If the er wth f he,. : Fg. Oe erter leg wth D e tr If ly e f the er wthe t, fr exle T, the we he: f t f If ll er wthe t: t f 8 If the lwer wth : Χ Χ Χ lr exre e wrtte fr ther he. Fr he f: f t f f t 9 A f: 6 A f ll lwer wthe t: t f f f t Nw exle, f the lwer wth f he. er wth f he. he. re, we he: f f, t f t tte rle re efe : A fr he f: A f: 7 8 If ll er wthe re : 9 A f ll lwer wthe re :

5 We rewrte ll f the e et the fr f et flly. B A Et re the geerl fr f et ere [] [] []. I referee [-] gle he rret ere the tte rle, the rete f trfrer eglete. If we er e f the he rret eglet the rete f trfrer, the we he : B. lg Me trl The lg rfe re el t the errr f tte rle, whh e exre : I the tte rle etr whh efe * the tte rle referee etr, ] [ re the lg rfe eg tt The th th l f the e trx etere y the wthe t. Th, te g fr te egte g fr egte hlf yle f A t ltge, whe ete t erter tr. By relg we he: effet whh, f el t e, the tte feek [] f, el t tw, the eergy feek f tr e. Th wll elrte the ext et. trl t efe : e 7 I lg rfe g ft, whh fre the tte rle t lg rfe: [ ] g g g 8 e the trl t, whh fre the tte rle t the rg zer errr the lg rfe. I ft, trl wll fre the tte rle t trk ther reete referee. If we re t f lg rfe, wll e r - wth reet t lg rfe g. Th efe whh wth leg t e r ff. I th t e wll e zer ee we t reh lg rfe yet. Whe we reh the lg rfe, trller wll fre the errr t zer ttely. lg rfe tlty trt : t 9 O the ther h: e B B A B A Wth reet t e eft: A x B e The lft f : B

6 Fr 9,, 7, we wll he: t g g g g g g g g g If three l e-he lye re erfre, we t flly he []: It ler tht tfyg et e t eerly tfy, trt, le,, re elete lrge egh, whh wll ree the ee f y ree f le l yte. Th ehze the rte f three he ly whh ke t le t f ll,, eetly fter y ee ree hee. If et tfe, the tlty grtee. f three gle he ly re e, effet f,, t e he lrge t hee tlty. erg the lrty f frt ter wth r ter et, f we e the frt ter y g, we he: g g g g Bee the f tw tr ltge lwy te, the f we er t e hgh, the the e et wll e tfe the tlty wll e grtee.. The trl fr Vltge eglt f tr I et 6 f the trl l fr ltge reglt ft tte feek []. I th er, we et el t e tr eergy feek l t tlze the tr ltge e t te wer llt zer eee wer trt. The lk gr f trl yte hw Fg.. I th trl yte, the three he ltge rret wll e ere et wll e ere y lrk trfrt. The y llt f eletr wer, whh t e ete, the referee rret re llte. The referee rret the tte rle re the fe t the lg e trller. The ltge reglt l l ere the tr ltge re th le wth referee tr ltge. Th, the rere ze f eergy te fe t the lg e trller thrgh PI trller. A hgh flter wth tff freey el t HZ w e rllel wth the te flter, whh elte hgh freey hr rete y wthg. lg rfe trler I V V I g g g Fg. Blk gr f trller Ate Pwer Flter IV. IMATION ET lt relt re hw Fg. 6 t Fg.. The lt reter re el t:.h, μf V.,., The re rret THD el t 8.6% efre et fter et the re rret wll e l wth THD el t.. The re rret ltge l he. I Fg. 7, the lt relt fr tr ltge whh te y lg e trl wth eergy feek wth three he ly re wth the lt relt f etl trller wth gle-he ly. It ler tht y g eergy feek fr ltge trl threehe ly, the ltge reglt etter. The l rret, etg rret re rret hw Fg. 8 tret t. Fr gle-he ly, the re rret THD el t 7.9% efre et 7.7% fter et. I V V V

7 Fg. 6 rret, etg rret, re rret he ltge fter et Fg. Errr etwee referee rret te wer flter rret Fg. 9 rereet the tr ltge whe the three he te flter ete t gle-he rge retfer. Dy ree ltge reglt wll e etter re wth the ther eth. The errr etwee etg referee rret wth lg e trl eergy feek hw Fg.. The errr rhe zer eh wthg terl, ery ft. Fg. 7 tr ltge te wer flter Fg. 8 gle he retfer rret V. ONION I th er, t w hw tht etter erfre e hee, g three he ly te f three gle he ly, erg the rete f trfrer wth eergy feek fr ltge reglt. Al g fr-wre yte eth fr trl, we ete the llt f te wer zer eee wer three-he yte. Whe g three-he ly lg e trl, the tlty trt wll e lte. It e tht y g three lg rfe, the tlty trt wll e ller, whh e fter y ee ree e hee. Fg. 8 Three he rret f te wer flter EFEENE [] M. Aree, Ate Pwer e ter, Ph.D. The, Ittt fr Allgeee Elektrtehk, Tehl erty f Berl, 996. [] M.. Beh,. te, New trl Arh Fr Fr-Wre Ate Pwer Flter Be O The e f yhr efere Fre, Eletr Pwer yte eerh, l. 7,. -6,. [] N. Mrk, F. Fjeh, lg Me trl f A -Phe-ht Ate Pwer Flter, Pr. IIT,. 97-6,. [] J. Mret,. rz, A le lg Me trl f Ate Pwer Flter, r.f IEEE Pwer Eletr elt feree,. -6,. [] H. h-ye, W. Hrg-Y, A New gle-phe Ate Pwer Flter Wth ee Eergy trge tr, r. IEEE Pwer Eletr elt feree,. -8,9. Mj Nyerr w r 97. He reee h B.. egree eletr Eg. fr Gl erty M. egree Eletrl Eg. fr Efh erty f Tehlgy PhD egree Eletrl Eg. fr Trt Mre erty, Tehr, Ir. rretly, he Att Prfer wth the hrz erty f Tehlgy. H reerh teret le FAT ee, Pwer Qlty. Fg. 9 Vltge tr f te wer flter fr gle-he retfer l 6

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

AN ALGEBRAIC APPROACH TO M-BAND WAVELETS CONSTRUCTION

AN ALGEBRAIC APPROACH TO M-BAND WAVELETS CONSTRUCTION AN ALGEBRAIC APPROACH TO -BAN WAELETS CONSTRUCTION Toy L Qy S Pewe Ho Ntol Lotoy o e Peeto Pe Uety Be 8 P. R. C Att T e eet le o to ott - otool welet e. A yte of ott eto ote fo - otool flte te olto e o

More information

CS 4758 Robot Kinematics. Ashutosh Saxena

CS 4758 Robot Kinematics. Ashutosh Saxena CS 4758 Rt Kemt Ahuth Se Kemt tude the mt f de e re tereted tw emt tp Frwrd Kemt (ge t pt ht u re gve: he egth f eh he ge f eh t ht u fd: he pt f pt (.e. t (,, rdte Ivere Kemt (pt t ge ht u re gve: he

More information

An Introduction to Robot Kinematics. Renata Melamud

An Introduction to Robot Kinematics. Renata Melamud A Itrdut t Rt Kemt Ret Memud Kemt tude the mt f de A Empe -he UMA 56 3 he UMA 56 hsirevute t A revute t h E degree f freedm ( DF tht defed t ge 4 here re tw mre t the ed effetr (the grpper ther t Revute

More information

Discrete random walk with barriers on a locally infinite graph

Discrete random walk with barriers on a locally infinite graph Drete rdo wl wth rrer o loll fte grh Theo Ue Aterd Shool of Teholog Weeerde 9 97 DZ Aterd The etherld El: te@hl Atrt We ot eeted er of rrl orto rolte d eeted te efore orto for etr drete rdo wl o loll fte

More information

K E L LY T H O M P S O N

K E L LY T H O M P S O N K E L LY T H O M P S O N S E A O LO G Y C R E ATO R, F O U N D E R, A N D PA R T N E R K e l l y T h o m p s o n i s t h e c r e a t o r, f o u n d e r, a n d p a r t n e r o f S e a o l o g y, a n e x

More information

St Peter's Anglican Primary School is offering HoLiday Care during JuLy 2016 school holidays.

St Peter's Anglican Primary School is offering HoLiday Care during JuLy 2016 school holidays. I?? 11 T. ptvs G.2. Prry?? OH HOLIDY R Ly26 rlet Fr :4t e 216 Der Prets / rers t Peter's Prry s ffer HLdy re dr Ly 216 s dys. re s vbe fr Mdy, 4f y 216 Trsdy, 21s' (y 216. Te st w be 522 per dy per Ld.

More information

Moments of Generalized Order Statistics from a General Class of Distributions

Moments of Generalized Order Statistics from a General Class of Distributions ISSN 684-843 Jol of Sttt Vole 5 28. 36-43 Moet of Geelzed Ode Sttt fo Geel l of Dtto Att Mhd Fz d Hee Ath Ode ttt eod le d eel othe odel of odeed do le e ewed el e of geelzed ode ttt go K 995. I th e exlt

More information

fur \ \,,^N/ D7,,)d.s) 7. The champion and Runner up of the previous year shall be allowed to play directly in final Zone.

fur \ \,,^N/ D7,,)d.s) 7. The champion and Runner up of the previous year shall be allowed to play directly in final Zone. OUL O GR SODRY DUTO, ODS,RT,SMTUR,USWR.l ntuctin f cnuct f Kbi ( y/gil)tunent f 2L-Lg t. 2.. 4.. 6. Mtche hll be lye e K ule f ene f tie t tie Dutin f ech tch hll be - +0 (Rece)+ = M The ticint f ech Te

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

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

l-h Refer 83 a> Oomm on- fe ft ft j fc fc PL a. a. CL d -3 ^3 > PS c 03 rd c a O - 4 a r c ^!E -e P g k 03 C3 O E p p 03 c P ^ss «gp- f P3^«a s Z S

l-h Refer 83 a> Oomm on- fe ft ft j fc fc PL a. a. CL d -3 ^3 > PS c 03 rd c a O - 4 a r c ^!E -e P g k 03 C3 O E p p 03 c P ^ss «gp- f P3^«a s Z S !? Refer "* Tble f Generl rnne - m W - - T E - - Dm w V - 0 J 09 r JW! rk " J; " 0 " 4 -T f " fr "! * 0 N - -, - r l 4 Tf TT rr J ( ( - * - *» - - -T -rt J +- B% X K - f! - X -» *» l-h w w (h 8 " r " -

More information

National Parks and Wildlife Service

National Parks and Wildlife Service I - til rk Willif i ti jti ri llitrly rl J Vi f til rk Willif i, rtt f ltr, Hrit t Gltt, ly l, li, Irl. W www.w.i -il tr.ti@..i itti W () ti jti llitrly rl. Vi. til rk Willif i, rtt f ltr, Hrit t Gltt.

More information

The Z-Transform in DSP Lecture Andreas Spanias

The Z-Transform in DSP Lecture Andreas Spanias The Z-Trsform DSP eture - Adres Ss ss@su.edu 6 Coyrght 6 Adres Ss -- Poles d Zeros of I geerl the trsfer futo s rtol; t hs umertor d deomtor olyoml. The roots of the umertor d deomtor olyomls re lled the

More information

--- Deceased Information. A1ry't (Ay't olll n5. F\ease turn page ) lslamic Community Center of Tempe. Please print all information clearly.

--- Deceased Information. A1ry't (Ay't olll n5. F\ease turn page ) lslamic Community Center of Tempe. Please print all information clearly. A1y't (Ay't lll l uty ete ee lese t ll t lely. Deese t st e Mle e s t\e Lee De Bth Age Dte Seultv t\ube h :;;"' :;...".::.."'t ' ' ue uetttte ube use Deth Heste Als ( y); he t vle hve lll be use t etg

More information

Adver-isemen- suliber, 8 nries) PLAIN AND FANCT. forrip Sailora. starts, gtorlling5,'tv.to 'gtl. Waikiihalulu Water Lots! LARGE AND COMMODI- -,

Adver-isemen- suliber, 8 nries) PLAIN AND FANCT. forrip Sailora. starts, gtorlling5,'tv.to 'gtl. Waikiihalulu Water Lots! LARGE AND COMMODI- -, E E ERER RER p p p p x p $ p 0 p xp p p p p p p E p q 0 $ p 8 p $ 0 $ E EEER Y R ER 8 E 8 8 p EERE p p p REEREE q 8 Y p p p REEREE x E p Eq R p RE ER ER p x q EE p E E GR G p p 0 0 0 0 p x x p x p q EER

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

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

CHAPTER 5 Vectors and Vector Space

CHAPTER 5 Vectors and Vector Space HAPTE 5 Vetors d Vetor Spe 5. Alger d eometry of Vetors. Vetor A ordered trple,,, where,, re rel umers. Symol:, B,, A mgtude d dreto.. Norm of vetor,, Norm =,, = = mgtude. Slr multplto Produt of slr d

More information

(ril"s::lli '*Y, ,dr4{n. w.j. ",;:ii:{..._, I i,ai I. AOEP'IIICKOTO MyHI4TIUIIA.JTbHO O PAI,rOrrA nepmckoto KpA.fl TIOCTAHOBJTEHPIE

(rils::lli '*Y, ,dr4{n. w.j. ,;:ii:{..._, I i,ai I. AOEP'IIICKOTO MyHI4TIUIIA.JTbHO O PAI,rOrrA nepmckoto KpA.fl TIOCTAHOBJTEHPIE '*Y w.j TOCTOBJTEPE.MCTPU{ OEP'CKOTO MyTU.JTbO O PrOrr EPMCKOTO Kp.fl 26.02.20t3 e387 -l fo uecet Meellf [epe.rer 3eMeJrbbr ycrkb rrperr3ebr r pecrbjreg MferbM cembfl Mr ytbeprme r ctbjrerrem MrcTpr r

More information

t r ès s r â 2s ré t s r té s s s s r é é ér t s 2 ï s t 1 s à r

t r ès s r â 2s ré t s r té s s s s r é é ér t s 2 ï s t 1 s à r P P r t r t tr t r ès s rs té P rr t r r t t é t q s q é s Prés té t s t r r â 2s ré t s r té s s s s r é é ér t s 2 ï s t 1 s à r ès r é r r t ît P rt ré ré t à r P r s q rt s t t r r2 s rtí 3 Pr ss r

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

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

t t t ér t rs r t ét q s

t t t ér t rs r t ét q s rés té t rs té s é té r t q r r ss r t t t ér t rs r t ét q s s t t t r2 sé t Pr ss r rs té P r s 2 t Pr ss r rs té r t r r ss s Pr ss r rs té P r q r Pr ss r t r t r r t r r Prés t r2 r t 2s Pr ss r rs

More information

3. REVIEW OF PROPERTIES OF EIGENVALUES AND EIGENVECTORS

3. REVIEW OF PROPERTIES OF EIGENVALUES AND EIGENVECTORS . REVIEW OF PROPERTIES OF EIGENVLUES ND EIGENVECTORS. EIGENVLUES ND EIGENVECTORS We hll ow revew ome bc fct from mtr theory. Let be mtr. clr clled egevlue of f there et ozero vector uch tht Emle: Let 9

More information

Objective of curve fitting is to represent a set of discrete data by a function (curve). Consider a set of discrete data as given in table.

Objective of curve fitting is to represent a set of discrete data by a function (curve). Consider a set of discrete data as given in table. CURVE FITTING Obectve curve ttg s t represet set dscrete dt b uct curve. Csder set dscrete dt s gve tble. 3 3 = T use the dt eectvel, curve epress s tted t the gve dt set, s = + = + + = e b ler uct plml

More information

10.2 Series. , we get. which is called an infinite series ( or just a series) and is denoted, for short, by the symbol. i i n

10.2 Series. , we get. which is called an infinite series ( or just a series) and is denoted, for short, by the symbol. i i n 0. Sere I th ecto, we wll troduce ere tht wll be dcug for the ret of th chpter. Wht ere? If we dd ll term of equece, we get whch clled fte ere ( or jut ere) d deoted, for hort, by the ymbol or Doe t mke

More information

Current Programmed Control (i.e. Peak Current-Mode Control) Lecture slides part 2 More Accurate Models

Current Programmed Control (i.e. Peak Current-Mode Control) Lecture slides part 2 More Accurate Models Curret Progred Cotrol.e. Pek Curret-Mode Cotrol eture lde prt More Aurte Model ECEN 5807 Drg Mkovć Sple Frt-Order CPM Model: Sury Aupto: CPM otroller operte delly, Ueful reult t low frequee, well uted

More information

Thesis/Dissertation Collections

Thesis/Dissertation Collections Rheter tte f ehlgy R Shlr Wrk hee he/de lle 2995 ret perfre f prllelflw rflw ret trfer type het exhger wth tep tepere hge the pty e fl tre Br D. le Fllw th l wrk t: http://hlrwrk..e/thee Reee t le, Br

More information

Affidavit and Revenue Certification Chimp Haven, Inc. Caddo Parish Keithville, LA

Affidavit and Revenue Certification Chimp Haven, Inc. Caddo Parish Keithville, LA / / / / Affivit Revee Certifiti Chi Hve, I. C Prih Keithville, LA ANNAL WRN FINANCL TATNT AND CRTIFICATIN F RN $0,0 R L (if lible) The l wr fiil tteet re reqire by Lii Revie ttte 24:14 t be file with the

More information

National Parks and Wildlife Service

National Parks and Wildlife Service I -8 til rk Willif i ti jti ri r rl 8 Vi f 8 til rk Willif i, rtt f ltr, Hrit t ltt, ly l, li, Irl. W www.w.i -il tr.ti@..i itti W (8) ti jti r rl. Vi. til rk Willif i, rtt f ltr, Hrit t ltt. ri itr Jffry

More information

Vr Vr

Vr Vr F rt l Pr nt t r : xt rn l ppl t n : Pr nt rv nd PD RDT V t : t t : p bl ( ll R lt: 00.00 L n : n L t pd t : 0 6 20 8 :06: 6 pt (p bl Vr.2 8.0 20 8.0. 6 TH N PD PPL T N N RL http : h b. x v t h. p V l

More information

H NT Z N RT L 0 4 n f lt r h v d lt n r n, h p l," "Fl d nd fl d " ( n l d n l tr l t nt r t t n t nt t nt n fr n nl, th t l n r tr t nt. r d n f d rd n t th nd r nt r d t n th t th n r lth h v b n f

More information

Problem Set 4 Solutions

Problem Set 4 Solutions 4 Eoom Altos of Gme Theory TA: Youg wg /08/0 - Ato se: A A { B, } S Prolem Set 4 Solutos - Tye Se: T { α }, T { β, β} Se Plyer hs o rte formto, we model ths so tht her tye tke oly oe lue Plyer kows tht

More information

DETAIL MEASURE EVALUATE

DETAIL MEASURE EVALUATE MEASURE EVALUATE B I M E q u i t y BIM Workflow Guide MEASURE EVALUATE Introduction We o e to ook 2 i t e BIM Workflow Guide i uide wi tr i you i re ti ore det i ed ode d do u e t tio u i r i d riou dd

More information

MAT 1275: Introduction to Mathematical Analysis

MAT 1275: Introduction to Mathematical Analysis 1 MT 1275: Intrdutin t Mtemtil nlysis Dr Rzenlyum Slving Olique Tringles Lw f Sines Olique tringles tringles tt re nt neessry rigt tringles We re ging t slve tem It mens t find its si elements sides nd

More information

AQUA ACTIVITY POOL WEST TERRACE RESTROOMS. LOBBY LEVEL - 2 nd floor ACTIVE AGING /RECOVERY AZALEA H MIND/ BODY LIBRARY RESTROOMS HOTEL LOBBY ENTRANCE

AQUA ACTIVITY POOL WEST TERRACE RESTROOMS. LOBBY LEVEL - 2 nd floor ACTIVE AGING /RECOVERY AZALEA H MIND/ BODY LIBRARY RESTROOMS HOTEL LOBBY ENTRANCE TT K RE EVE - rd floor UY 7-9, 018 KEY EEVTR RESTS U TVTY P RESTS WEST TERRE TVE /REVERY ZE PESE RE/ WTER EER R UTRT PETREE EVE - nd floor U ETURE VY 1 ET/ WEESS VY EE R/ YX UE, R & RESTURT EST TERRE R

More information

Municipality of Central Elgin User Fee Committee Agenda

Municipality of Central Elgin User Fee Committee Agenda ult f etl Elg Use Fee ttee ge Pge 11:.. ttee R # ll t e slsue f Peu Iteest the Geel tue Theef -6 7-18 t f utes t f the utes f eetgs te etebe, 14, Ju 7, 15. suss Ites Reve f the 14 Use Fee heule e Busess

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

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

AGENDA REPORT. Payroll listing conforms to the approved budget except as noted and has been paid WILLIAM A HUSTON CITY MANAGER

AGENDA REPORT. Payroll listing conforms to the approved budget except as noted and has been paid WILLIAM A HUSTON CITY MANAGER Age e 4 AGEDA RERT Reewe ge Fce Dec EETG DATE Al 2 2 T FR A A T T AAGER AEA ARED KG FAE DRETR BET RATFAT F AR AR The cl h e he e f Gee e ec 728 eee he e f f T Reeele Agec blg h e ccce wh he e bge ce e

More information

RESOLUTION NO OVERSIGHT BOARD FOR THE SUCCESSOR AGENCY TO THE REDEVELOPMENT AGENCY OF THE CITY OF SOUTH SAN FRANCISCO

RESOLUTION NO OVERSIGHT BOARD FOR THE SUCCESSOR AGENCY TO THE REDEVELOPMENT AGENCY OF THE CITY OF SOUTH SAN FRANCISCO R. - 1 RG BR R R G RP G R PPRG RG BG P ( RP) R BG R PR 1 RG 17, PR 177( 1). R, elh fe e ei 177( 1), befe eh fil ei, he e ge ile Reeele ge i eqie ee f Regie bligi Pe hele (" RP") h li ll f he bligi h e

More information

The linear system. The problem: solve

The linear system. The problem: solve The ler syste The prole: solve Suppose A s vertle, the there ests uue soluto How to effetly opute the soluto uerlly??? A A A evew of dret ethods Guss elto wth pvotg Meory ost: O^ Coputtol ost: O^ C oly

More information

ADDENDUM NO. 3 TO BID DOCUMENTS FOR LIGHT POLE PAINTING PROJECT FOR THE CITY OF ANN ARBOR, MICHIGAN

ADDENDUM NO. 3 TO BID DOCUMENTS FOR LIGHT POLE PAINTING PROJECT FOR THE CITY OF ANN ARBOR, MICHIGAN DDENDU NO TO BID DOCUENTS FOR LIGHT POLE PINTING PROJECT FOR THE, ICHIGN Th fllw h,, l hll b h B D Pl f Lh Pl P P f h Cy f b, h, B N ITB whh l b v, bf, P y, l, Th f h hll k v h l ll v, h Th Th B kwl f

More information

Colby College Catalogue

Colby College Catalogue Colby College Digital Commons @ Colby Colby Catalogues College Archives: Colbiana Collection 1866 Colby College Catalogue 1866-1867 Colby College Follow this and additional works at: http://digitalcommons.colby.edu/catalogs

More information

22 t b r 2, 20 h r, th xp t d bl n nd t fr th b rd r t t. f r r z r t l n l th h r t rl T l t n b rd n n l h d, nd n nh rd f pp t t f r n. H v v d n f

22 t b r 2, 20 h r, th xp t d bl n nd t fr th b rd r t t. f r r z r t l n l th h r t rl T l t n b rd n n l h d, nd n nh rd f pp t t f r n. H v v d n f n r t d n 20 2 : 6 T P bl D n, l d t z d http:.h th tr t. r pd l 22 t b r 2, 20 h r, th xp t d bl n nd t fr th b rd r t t. f r r z r t l n l th h r t rl T l t n b rd n n l h d, nd n nh rd f pp t t f r

More information

Department of Economics University of Toronto. ECO2408F M.A. Econometrics. Lecture Notes on Simple Regression Model

Department of Economics University of Toronto. ECO2408F M.A. Econometrics. Lecture Notes on Simple Regression Model Deprtmet f Ecmc Uvert f Trt ECO48F M.A. Ecmetrc Lecture Nte Smple Regre Mdel Smple Regre Mdel I the frt lecture we lked t fttg le t ctter f pt. I th chpter we eme regre methd f eplrg the prbbltc tructure

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

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

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

Useful R-norm Information Measure and its Properties

Useful R-norm Information Measure and its Properties IOS Jorl of Eletros Coto Eeer (IOS-JECE) e-issn: 7-34- ISSN: 7-735Vole Isse (No - De 03) PP 5-57 DS oo Keert Uyy DKSr 3 Jyee Uersty of Eeer Teoloy AB o or 4736 Dstt G MP (I) Astrt : I te reset oto ew sefl

More information

,.*Hffi;;* SONAI, IUERCANTII,N I,IMITDII REGD- 0FFICE: 105/33, VARDHMAN GotD[N PLNLA,R0AD No.44, pitampura, DELHI *ffigfk"

,.*Hffi;;* SONAI, IUERCANTII,N I,IMITDII REGD- 0FFICE: 105/33, VARDHMAN GotD[N PLNLA,R0AD No.44, pitampura, DELHI *ffigfk $ S, URCT,,MTD RGD 0C: 10/, VRDM G[ LL,R0D.44, ptmpur, DL114 C: l22ldll98l,c0224gb, eb:.nlmernte.m T, Dte: 17h tber, 201 BS Lmted hre ]eejeebhy Ter Dll Street Mumb 41 The Mnger (Ltng) Delh Stk xhnge /1,

More information

THE WEATHER f. Rain,' colder by night. New Jersey Advocate APPEALING! BENEFK VOL. XVIII. SERIAL NO Among- Those Present SIOUN AUTO CUPS

THE WEATHER f. Rain,' colder by night. New Jersey Advocate APPEALING! BENEFK VOL. XVIII. SERIAL NO Among- Those Present SIOUN AUTO CUPS P PBED E EEY RY ERE E EER RY E G R E G D 0 Z R P E R P E E D PPEG BEEF X ER 200 RY Y EDY FER RY 22929 R EYREEE D FR PE GRERE P GR RYD R z BG F x DER G EXGGERE x 3 B 6 / ± P B FREE DEERY RY E RE PPG EER

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

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

GUC (Dr. Hany Hammad) 9/19/2016

GUC (Dr. Hany Hammad) 9/19/2016 UC (Dr. Hny Hmmd) 9/9/6 ecture # ignl flw grph: Defitin. Rule f Reductin. Mn Rule. ignl-flw grph repreenttin f : ltge urce. ive gle-prt device. ignl Flw rph A ignl-flw grph i grphicl men f prtryg the reltinhip

More information

Third Grade Summer Reading Instructions

Third Grade Summer Reading Instructions Thrd Grde Ser Redg Istrts These ssgets re de the rst dy sh, Wedesdy Agst 24'h. Pese be sre yr hd es t sh the rst dy wth ther peted wrk. I the wrk s t retred the rst dy, yr hd w reeve h redt. Fr the bks

More information

Ionization Energies in Si, Ge, GaAs

Ionization Energies in Si, Ge, GaAs Izt erges S, Ge, GAs xtrsc Semcuctrs A extrsc semcuctrs s efe s semcuctr whch ctrlle muts f secfc t r murty tms hve bee e s tht the thermlequlbrum electr hle ccetrt re fferet frm the trsc crrer ccetrt.

More information

Rediscover Your Dream Getaway. handcrafted Pergolas

Rediscover Your Dream Getaway. handcrafted Pergolas R Y D Gwy hf Wl... T O L! R h h f y l. P l j f h k h; hy l f h h yl. Whh y h l f bl ly, y h, y ly lk f jy h b f l, l h w y h b h f. Wh y yl, h l ff l f y. hf W h y w. Thk y ll f h wh h k h w ll hw h jy

More information

Exercise # 2.1 3, 7, , 3, , -9, 1, Solution: natural numbers are 3, , -9, 1, 2.5, 3, , , -9, 1, 2 2.5, 3, , -9, 1, , -9, 1, 2.

Exercise # 2.1 3, 7, , 3, , -9, 1, Solution: natural numbers are 3, , -9, 1, 2.5, 3, , , -9, 1, 2 2.5, 3, , -9, 1, , -9, 1, 2. Chter Chter Syste of Rel uers Tertg Del frto: The del frto whh Gve fte uers of dgts ts del rt s lled tertg del frto. Reurrg ( o-tertg )Del frto: The del frto (No tertg) whh soe dgts re reeted g d g the

More information

National Parks and Wildlife Service

National Parks and Wildlife Service I -4 til Prk Willif i ti jtiv ri wrill H 7 P f til Prk Willif i, Drtt f ltr, Hrit t Gltt, Ki trt rt, Dli 7, D7 7V, Irl. W: www.w.i -il: tr.ti@.v.i itti: PW () ti jtiv: wrill H 7. Vri. til Prk Willif i,

More information

LOW VOLTAGE FROM CABLE TRAY DRAFT 2 37 WAGO END PLATE - -

LOW VOLTAGE FROM CABLE TRAY DRAFT 2 37 WAGO END PLATE - - G KGE 00% FOR REVEW RERVE OE: hese designs and drawings were prepared by Jefferson cience ssociates, LL, hereinafter the ontractor, under ontract o. E00OR with the epartment (OE). ll rights in the designs

More information

n

n p l p bl t n t t f Fl r d, D p rt nt f N t r l R r, D v n f nt r r R r, B r f l. n.24 80 T ll h, Fl. : Fl r d D p rt nt f N t r l R r, B r f l, 86. http://hdl.handle.net/2027/mdp.39015007497111 r t v n

More information

2. Elementary Linear Algebra Problems

2. Elementary Linear Algebra Problems . Eleety e lge Pole. BS: B e lge Suoute (Pog pge wth PCK) Su of veto opoet:. Coputto y f- poe: () () () (3) N 3 4 5 3 6 4 7 8 Full y tee Depth te tep log()n Veto updte the f- poe wth N : ) ( ) ( ) ( )

More information

1) When an object is placed at the center of curvature of a concave mirror, the image is.

1) When an object is placed at the center of curvature of a concave mirror, the image is. ) Whe a bjet is plae at the eter f urature f a ae mirrr, the image is. a) upright a irtual b) ierte a real ) larger a irtual ) Whe a bjet is plae ery far frm the fal pit f a ergig les, the image is. a)

More information

N V R T F L F RN P BL T N B ll t n f th D p rt nt f l V l., N., pp NDR. L N, d t r T N P F F L T RTL FR R N. B. P. H. Th t t d n t r n h r d r

N V R T F L F RN P BL T N B ll t n f th D p rt nt f l V l., N., pp NDR. L N, d t r T N P F F L T RTL FR R N. B. P. H. Th t t d n t r n h r d r n r t d n 20 2 04 2 :0 T http: hdl.h ndl.n t 202 dp. 0 02 000 N V R T F L F RN P BL T N B ll t n f th D p rt nt f l V l., N., pp. 2 24. NDR. L N, d t r T N P F F L T RTL FR R N. B. P. H. Th t t d n t r

More information

n r t d n :4 T P bl D n, l d t z d th tr t. r pd l

n r t d n :4 T P bl D n, l d t z d   th tr t. r pd l n r t d n 20 20 :4 T P bl D n, l d t z d http:.h th tr t. r pd l 2 0 x pt n f t v t, f f d, b th n nd th P r n h h, th r h v n t b n p d f r nt r. Th t v v d pr n, h v r, p n th pl v t r, d b p t r b R

More information

PR D NT N n TR T F R 6 pr l 8 Th Pr d nt Th h t H h n t n, D D r r. Pr d nt: n J n r f th r d t r v th tr t d rn z t n pr r f th n t d t t. n

PR D NT N n TR T F R 6 pr l 8 Th Pr d nt Th h t H h n t n, D D r r. Pr d nt: n J n r f th r d t r v th tr t d rn z t n pr r f th n t d t t. n R P RT F TH PR D NT N N TR T F R N V R T F NN T V D 0 0 : R PR P R JT..P.. D 2 PR L 8 8 J PR D NT N n TR T F R 6 pr l 8 Th Pr d nt Th h t H h n t n, D.. 20 00 D r r. Pr d nt: n J n r f th r d t r v th

More information

828.^ 2 F r, Br n, nd t h. n, v n lth h th n l nd h d n r d t n v l l n th f v r x t p th l ft. n ll n n n f lt ll th t p n nt r f d pp nt nt nd, th t

828.^ 2 F r, Br n, nd t h. n, v n lth h th n l nd h d n r d t n v l l n th f v r x t p th l ft. n ll n n n f lt ll th t p n nt r f d pp nt nt nd, th t 2Â F b. Th h ph rd l nd r. l X. TH H PH RD L ND R. L X. F r, Br n, nd t h. B th ttr h ph rd. n th l f p t r l l nd, t t d t, n n t n, nt r rl r th n th n r l t f th f th th r l, nd d r b t t f nn r r pr

More information

4 4 N v b r t, 20 xpr n f th ll f th p p l t n p pr d. H ndr d nd th nd f t v L th n n f th pr v n f V ln, r dn nd l r thr n nt pr n, h r th ff r d nd

4 4 N v b r t, 20 xpr n f th ll f th p p l t n p pr d. H ndr d nd th nd f t v L th n n f th pr v n f V ln, r dn nd l r thr n nt pr n, h r th ff r d nd n r t d n 20 20 0 : 0 T P bl D n, l d t z d http:.h th tr t. r pd l 4 4 N v b r t, 20 xpr n f th ll f th p p l t n p pr d. H ndr d nd th nd f t v L th n n f th pr v n f V ln, r dn nd l r thr n nt pr n,

More information

1. Elementary Electronic Circuits with a Diode

1. Elementary Electronic Circuits with a Diode ecture 1: truct t electrc aal crcut 361-1-3661 1 1. Elemetary Electrc Crcut wth a e Euee Paer, 2008 HE M OF HE COUSE ume lear tme-arat () electrc crcut t re ay lut t the fllw fe tak (ee F. 1), whch are

More information

ECEN 5807 Lecture 26

ECEN 5807 Lecture 26 ECEN 5807 eture 6 HW 8 due v D Frdy, rh, 0 S eture 8 on Wed rh 0 wll be leture reorded n 0 he week of rh 5-9 Sprng brek, no le ody: Conlude pled-dt odelng of hghfrequeny ndutor dyn n pek urrentode ontrolled

More information

Danger of electrical shock, burns or death.

Danger of electrical shock, burns or death. anger of electrical shock, burns or death. lways remove all power sources before a emp ng any repair, service or diagnos c work. Power can be present from shore power, generator, inverter or ba ery. ll

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

D t r l f r th n t d t t pr p r d b th t ff f th l t tt n N tr t n nd H n N d, n t d t t n t. n t d t t. h n t n :.. vt. Pr nt. ff.,. http://hdl.handle.net/2027/uiug.30112023368936 P bl D n, l d t z d

More 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

,. *â â > V>V. â ND * 828.

,. *â â > V>V. â ND * 828. BL D,. *â â > V>V Z V L. XX. J N R â J N, 828. LL BL D, D NB R H â ND T. D LL, TR ND, L ND N. * 828. n r t d n 20 2 2 0 : 0 T http: hdl.h ndl.n t 202 dp. 0 02802 68 Th N : l nd r.. N > R, L X. Fn r f,

More information

A Dynamical Quasi-Boolean System

A Dynamical Quasi-Boolean System ULETNUL Uestăţ Petol Gze Ploeşt Vol LX No / - 9 Se Mtetă - otă - Fză l Qs-oole Sste Gel Mose Petole-Gs Uest o Ploest ots etet est 39 Ploest 68 o el: ose@-loesto stt Ths e oes the esto o ol theoetl oet:

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

m = Mass flow rate The Lonely Electron Example 0a:

m = Mass flow rate The Lonely Electron Example 0a: The Lel Elect Exaple 0a: Mass flw ate l Liea velcit Hw fa ut f ptial eeg iteacti? Hge ucleus Bh --- 93: Uest the etu ccept. Liea etu istace eeg ( l ) l F ( tie ) ( tie ) + Like t use the peples ieas (if

More information

First assignment of MP-206

First assignment of MP-206 irt igmet of MP- er to quetio - 7- Norml tre log { : MP Priipl tree: I MP II MP III MP Priipl iretio: { I { II { III Iitill uppoe tht i tre tte eribe i the referee tem ' i the me tre tte but eribe i other

More information

LARf,DO INDEPENDENT SCHOOL DISTR 904 Juarez Ave.. Laredo, Texas Ph. 956 Tax Office. s7.76%

LARf,DO INDEPENDENT SCHOOL DISTR 904 Juarez Ave.. Laredo, Texas Ph. 956 Tax Office. s7.76% T: Shl Br f Truee re nepenen Shl Dr 1702 Hun Sree re, Te 78040 /) rm: Rlb Snhe. RTA.CSTAlW Drer f T Cllen U V De: Deember 17,2014 m ARf,DO DPDT SCHOO DSTR 904 ure Ave.. re, Te 78040. Ph. 95 T Offe CT 273-1800

More information

Preliminary Examinations: Upper V Mathematics Paper 1

Preliminary Examinations: Upper V Mathematics Paper 1 relmr Emtos: Upper V Mthemtcs per Jul 03 Emer: G Evs Tme: 3 hrs Modertor: D Grgortos Mrks: 50 INSTRUCTIONS ND INFORMTION Ths questo pper sts of 0 pges, cludg swer Sheet pge 8 d Iformto Sheet pges 9 d 0

More information

Years. Marketing without a plan is like navigating a maze; the solution is unclear.

Years. Marketing without a plan is like navigating a maze; the solution is unclear. F Q 2018 E Mk l lk z; l l Mk El M C C 1995 O Y O S P R j lk q D C Dl Off P W H S P W Sl M Y Pl Cl El M Cl FIRST QUARTER 2018 E El M & D I C/O Jff P RGD S C D M Sl 57 G S Alx ON K0C 1A0 C Tl: 6134821159

More information

)ti bo I 9. When a quadratic equation is graphed, it creates this.

)ti bo I 9. When a quadratic equation is graphed, it creates this. ALGEBRA 1 Ch 8 Closure - Quadratic Functions Name: il-1-9cabulary: )ial -gr-aphial5lfarxg -vertexeisrnialeting-the,square- -solutions- -steis4u-nstio -elifference-of-se -standar-el-form- -factor- seffeet-setuare4rinanaial-

More information

Technote 6. Op Amp Definitions. April 1990 Revised 11/22/02. Tim J. Sobering SDE Consulting

Technote 6. Op Amp Definitions. April 1990 Revised 11/22/02. Tim J. Sobering SDE Consulting Technte 6 prl 990 Resed /22/02 Op mp Dentns Tm J. Sberng SDE Cnsultng sdecnsultng@pbx.cm 990 Tm J. Sberng. ll rghts resered. Op mp Dentns Pge 2 Op mp Dentns Ths Technte summrzes the bsc pertnl mpler dentns

More information

l~ 0 0 'JL 1. )t\ 1-, 'x,,; 1-r

l~ 0 0 'JL 1. )t\ 1-, 'x,,; 1-r Test 1 Math 2407 Spring 2011 1. (9 points) For each of the following augmented matrices answer the following questions. ~ 1 0 0 5 6] i. [ 0 000 1 X( 1('1 7ty: Number of equations of the corresponding system

More information

Colby College Catalogue

Colby College Catalogue Colby College Digital Commons @ Colby Colby Catalogues College Archives: Colbiana Collection 1872 Colby College Catalogue 1872-1873 Colby College Follow this and additional works at: http://digitalcommonscolbyedu/catalogs

More information

MTH 146 Class 7 Notes

MTH 146 Class 7 Notes 7.7- Approxmte Itegrto Motvto: MTH 46 Clss 7 Notes I secto 7.5 we lered tht some defte tegrls, lke x e dx, cot e wrtte terms of elemetry fuctos. So, good questo to sk would e: How c oe clculte somethg

More information

BACHELOR'S DEGREE PROGRAMME (BDP) Term-End Examination ELECTIVE COURSE : MATHEMATICS MTE-02 : LINEAR ALGEBRA

BACHELOR'S DEGREE PROGRAMME (BDP) Term-End Examination ELECTIVE COURSE : MATHEMATICS MTE-02 : LINEAR ALGEBRA No. of Printed Pages : 8 MTE-021 BACHELOR'S DEGREE PROGRAMME (BDP) Term-End Examination 01-2. 0 6 June, 2016 ELECTIVE COURSE : MATHEMATICS MTE-02 : LINEAR ALGEBRA Time : 2 hours Maximum Marks : 50 (Weightage

More information

m y -I c D n ac r m ó ñ z _ O m x) áñ -1 m co _ Cl) co)

m y -I c D n ac r m ó ñ z _ O m x) áñ -1 m co _ Cl) co) Ìü ehsty _ x) l) z z _ y ) ) (4 ehsty R 5 u l 5 l t l Ç f K=(_ H ÿ Ç "? ( ft ( T S : s s`_ ` < ÿ H H < t t ~: H t + 8 H!S» y + ( y H ( _ + + < Ç v < < \ t S + y ( < + Sj T _ v S f _ t S S * ( S + (? H

More information

42. (20 pts) Use Fermat s Principle to prove the law of reflection. 0 x c

42. (20 pts) Use Fermat s Principle to prove the law of reflection. 0 x c 4. (0 ts) Use Femt s Piile t ve the lw eleti. A i b 0 x While the light uld tke y th t get m A t B, Femt s Piile sys it will tke the th lest time. We theee lulte the time th s uti the eleti it, d the tke

More information

Executive Committee and Officers ( )

Executive Committee and Officers ( ) Gifted and Talented International V o l u m e 2 4, N u m b e r 2, D e c e m b e r, 2 0 0 9. G i f t e d a n d T a l e n t e d I n t e r n a t i o n a2 l 4 ( 2), D e c e m b e r, 2 0 0 9. 1 T h e W o r

More information

Linear Open Loop Systems

Linear Open Loop Systems Colordo School of Me CHEN43 Trfer Fucto Ler Ope Loop Sytem Ler Ope Loop Sytem... Trfer Fucto for Smple Proce... Exmple Trfer Fucto Mercury Thermometer... 2 Derblty of Devto Vrble... 3 Trfer Fucto for Proce

More information

0 t b r 6, 20 t l nf r nt f th l t th t v t f th th lv, ntr t n t th l l l nd d p rt nt th t f ttr t n th p nt t th r f l nd d tr b t n. R v n n th r

0 t b r 6, 20 t l nf r nt f th l t th t v t f th th lv, ntr t n t th l l l nd d p rt nt th t f ttr t n th p nt t th r f l nd d tr b t n. R v n n th r n r t d n 20 22 0: T P bl D n, l d t z d http:.h th tr t. r pd l 0 t b r 6, 20 t l nf r nt f th l t th t v t f th th lv, ntr t n t th l l l nd d p rt nt th t f ttr t n th p nt t th r f l nd d tr b t n.

More information

SPECIFICATION SHEET : WHSG4-UNV-T8-HB

SPECIFICATION SHEET : WHSG4-UNV-T8-HB SPECIFICATION SHEET : WHSG4UNVT8HB ELECTRICAL DATA (120V APPLICATION) INPUT VO LT : 120V ± 10%, 50/60H z LAM P W ATTS/T YPE F17T8 F25T8 F30T8 F 32T8 F32T 8( 25W ) F32T8(28W ) F32T8(30W ) FB31T 8 FB32T8

More information

Humanistic, and Particularly Classical, Studies as a Preparation for the Law

Humanistic, and Particularly Classical, Studies as a Preparation for the Law University of Michigan Law School University of Michigan Law School Scholarship Repository Articles Faculty Scholarship 1907 Humanistic, and Particularly Classical, Studies as a Preparation for the Law

More information

this is the indefinite integral Since integration is the reverse of differentiation we can check the previous by [ ]

this is the indefinite integral Since integration is the reverse of differentiation we can check the previous by [ ] Atervtves The Itegrl Atervtves Ojectve: Use efte tegrl otto for tervtves. Use sc tegrto rules to f tervtves. Aother mportt questo clculus s gve ervtve f the fucto tht t cme from. Ths s the process kow

More information

CH 45 INTRO TO FRACTIONS

CH 45 INTRO TO FRACTIONS CH INTRO TO FRACTIONS Itrotio W e re ot to erk o st of frtios. If o ve erstoo ritheti frtios efore, o ll fi tht lgeri frtios follo the se set of rles. If frtios re still ster, let s ke this the seester

More information