Outline. CSE 473: Artificial Intelligence Spring Types of Agents

Size: px
Start display at page:

Download "Outline. CSE 473: Artificial Intelligence Spring Types of Agents"

Transcription

1 9/9/7 CE 7: Atiiil Intllign ing 07 Polms Outlin Polm s & Dit Fox Uninom Mtos Dt-Fist Bt-Fist Uniom-Cost Wit slis om Dn Wl, Pit Al, Dn Klin, tut Russll, Anw Moo, Luk Zttlmoy Agnt vs. Envionmnt Tys o Agnts Rlx An gnt is n ntity tt ivs n ts. A tionl gnt slts tions tt mximiz its utility untion. Ctistis o t ts, nvionmnt, n tion s itt tnius o slting tionl tions. Agnt nsos? Atutos Pts Ations Envionmnt ol oint Utility-s Pln Ask wt i ol Bs Agnts Disions s on (yotsiz) onsuns o tions Must v mol o ow t wol volvs in sons to tions At on ow t wol WOULD BE tu Polm (k tt ) Inut: t o stts Otos [n osts] tt stt ol stt [tst] Outut: Pt: stt [My ui sotst t] stt stisying gol tst [omtims just n stt tt sss tst]

2 9/9/7 Exml: Tvling in Romni Exml: imlii P-Mn tt s: Citis usso untion: Ros: o to jnt ity wit ost = istn tt stt: A ol tst: Is stt == Bust? olution? Inut: A stt s A susso untion A stt stt A gol tst Outut: N,.0 E,.0 tt izs? tt s Polm: Et ll o t oo Pmn ositions: 0 0 x x = = 0 0 Pmn ing: u, own, lt, igt Foo onigutions: 0 ost ositions: ost ositions: 0 tt s g: E no is stt T susso untion is snt y s Egs my ll wit osts In s g, stt ous only on! W n ly uil tis g in mmoy (so w on t) Riiulously tiny s g o tiny s olm 0 x x 0 x x = 6.8 x 0 Ts tt s vs. Ts N,.0 A s t: tt stt t t oot no E,.0 Ciln oson to sussos Nos ontin stts, oson to PLAN to tos stts Egs ll wit tions n osts Tis is now / stt Possil utus Fo most olms, w n nv tully uil t wol t tt E NODE in in t s t is n nti PATH in t stt s g. W onstut ot on mn n w onstut s littl s ossil. T

3 9/9/7 tt s vs. Ts T Consi tis -stt g: How ig is its s t (om )? Imotnt: Lots o t stutu in t s t! Exml: Romni ing wit T : Exn out otntil lns (t nos) Mintin ing o til lns un onsition Ty to xn s w t nos s ossil nl T Dt-Fist Imotnt is: Fing Exnsion Exlotion sttgy Min ustion: wi ing nos to xlo?

4 9/9/7 Dt-Fist Dt-Fist ttgy: xn st no ist Imlmnttion: Fing is LIFO stk ttgy: xn st no ist Imlmnttion: Fing is LIFO stk Algoitm Potis Algoitm Potis Comlt: unt to in solution i on xists? Otiml: unt to in t lst ost t? Tim omlxity? omlxity? Ctoon o s t: is t ning to m is t mximum t solutions t vious ts Num o nos in nti t? m = O( m ) m tis no nos nos m nos Dt-Fist (DF) Potis Bt-Fist Wt nos os DF xn? om lt ix o t t. Coul oss t wol t! I m is init, tks tim O( m ) m tis How mu s os t ing tk? Only s silings on t to oot, so O(m) Is it omlt? m oul ininit, so only i w vnt yls Is it otiml? No, it ins t ltmost solution, glss o t o ost no nos nos m nos

5 9/9/7 Bt-Fist Bt-Fist (BF) Potis ttgy: xn sllowst no ist Imlmnttion: Fing is FIFO uu Wt nos os BF xn? Posss ll nos ov sllowst solution Lt t o sllowst solution tks tim O( ) tis How mu s os t ing tk? Hs ougly t lst ti, so O( ) no nos nos nos Tis Is it omlt? must init i solution xists, so ys! Is it otiml? Only i osts ll (mo on osts lt) m nos DF vs BF Algoitm Comlt Otiml Tim DF BF w/ Pt Cking N unlss init N O( m ) O(m) Y Y O( ) O( ) Mmoy Limittion? uos: Hz CPU B min mmoy 00 instutions / xnsion 5 yts / no 0 M xnsions / s Mmoy ill in 60 s min Ittiv Dning Ittiv ning uss DF s suoutin:. Do DF wi only ss o ts o lngt o lss.. I il, o DF wi only ss ts o lngt o lss.. I il, o DF wi only ss ts o lngt o lss..n so on. Algoitm Comlt Otiml Tim DF BF ID w/ Pt Cking Y N O( m ) O(m) Y Y O( ) O( ) Y Y O( ) O() BF vs. Ittiv Dning Fo = 0, = 5: BF = , , ,000 =, ID = , , ,000 =,56 Ov = (,56 -,) /, = % Mmoy BF: 00,000; ID:

6 9/9/7 Costs on Ations Uniom Cost TART 5 8 Noti tt BF ins t sotst t in tms o num o tnsitions. It os not in t lst-ost t. 9 8 OAL Exn st no ist: Fing is ioity uu TART OAL ttgy: xn st no ist: Fing is ioity uu (ioity: umultiv ost) Cost ontous Uniom Cost Uniom Cost (UC) Potis Wt nos os UC xn? Posss ll nos wit ost lss tn st solution! I tt solution osts C* n s ost t lst ε, tn t tiv C t is ougly C*/ε C*/ε C Tks tim O( C*/ε ) (xonntil in tiv t) tis C How mu s os t ing tk? Hs ougly t lst ti, so O( C*/ε ) Is it omlt? Assuming st solution s init ost n minimum ost is ositiv, ys! Is it otiml? Ys! Uniom Cost ttgy: xn lowst t ost T goo: UC is omlt n otiml! T : Exlos otions in vy ition No inomtion out gol lotion tt ol Uniom Cost Algoitm Comlt Otiml Tim DF BF UC w/ Pt Cking C*/ε tis Y N O( m ) O(m) Y Y O( ) O( ) Y* Y O( C*/ε ) O( C*/ε ) 6

7 9/9/7 Uniom Cost: P-Mn Cost o o tion Exlos ll o t stts, ut on All ts s lgoitms t sm xt o ing sttgis T On Quu Contully, ll ings ioity uus (i.. olltions o nos wit tt ioitis) Ptilly, o DF n BF, you n voi t log(n) ov om n tul ioity uu, y using stks n uus Cn vn o on imlmnttion tt tks vil uuing ojt To Do: Look t t ous wsit: tt:// Do t ings (C ) Do P0 i nw to Pyton tt P, wn it is ost 7

CS 188: Artificial Intelligence

CS 188: Artificial Intelligence C 188: Atiiil Intllign Toy Agnts tt Pln A Polms Instuto: Mo Alvz Univsity o Ro Isln (Ts slis w t/moii y Dn Klin, Pit Al, An Dgn o C188 t UC Bkly) Uninom Mtos Dt-Fist Bt-Fist Uniom-Cost Agnts tt Pln Rlx

More information

Today. CS 232: Ar)ficial Intelligence. Search. Agents that Plan. September 3 rd, 2015 Search Problems. Uninformed Search Methods

Today. CS 232: Ar)ficial Intelligence. Search. Agents that Plan. September 3 rd, 2015 Search Problems. Uninformed Search Methods 1 C 232: A)iil Intllign Toy tm 3, 2015 Agnts tt Pln A Polms Uninom Mtos Dt- Fist Bt- Fist Uniom- Cost [Ts slis w t y Dn Klin n Pit Al o C188 Into to AI t UC Bkly. All C188 mtils vill t M://i.kly.u.] Agnts

More information

Announcements. CS 188: Artificial Intelligence Fall Today. Reflex Agents. Goal Based Agents. Search Problems

Announcements. CS 188: Artificial Intelligence Fall Today. Reflex Agents. Goal Based Agents. Search Problems C 88: Atiiil Intllign Fll 009 Ltu : Quu-Bs 9//009 Dn Klin UC Bkly Multil slis om tut Russll, Anw Moo Announmnts Pojt 0: Pyton Tutoil Du tomoow! T is l tomoow om m-3m in o 75 T l tim is otionl, ut P0 itsl

More information

Announcements. CS 188: Artificial Intelligence Fall Reflex Agents. Today. Goal Based Agents. Search Problems

Announcements. CS 188: Artificial Intelligence Fall Reflex Agents. Today. Goal Based Agents. Search Problems Announmnts Pojt 0: Pyton Tutoil Du tomoow! T is l Wnsy om 3m-5m in o 75 T l tim is otionl, ut P0 itsl is not On sumit, you soul gt mil om t utog Pojt : On t w toy tt ly n sk ustions. It s long tn most!

More information

CS 188: Artificial Intelligence Fall Announcements

CS 188: Artificial Intelligence Fall Announcements C 188: Atiiil Intllign Fll 2009 Ltu 2: Quu-Bs 9/1/2009 Dn Klin UC Bkly Multil slis om tut Russll, Anw Moo Announmnts Pojt 0: Pyton Tutoil Du tomoow! T is l tomoow om 1m-3m in o 275 T l tim is otionl, ut

More information

CS 188: Artificial Intelligence Fall 2011

CS 188: Artificial Intelligence Fall 2011 Announmnts Pojt 0: Pyton Tutoil Du tomoow! T is l Wnsy om 3m-5m in o 275 T l tim is otionl, ut P0 itsl is not On sumit, you soul gt mil om t utog Pojt 1: On t w toy tt ly n sk ustions. It s long tn most!

More information

CS 188: Artificial Intelligence Fall Announcements

CS 188: Artificial Intelligence Fall Announcements C 188: Atiiil Intllign Fll 007 Ltu : Quu-Bs 8/31/007 Dn Klin UC Bkly Mny slis om it tut Russll o Anw Moo Announmnts Nxt wk Nw oom is 105 Not Gt, stts Tusy Ck w g o stions (nw oming) L Fiy 10m to 5m in

More information

CS 188: Artificial Intelligence Spring Announcements

CS 188: Artificial Intelligence Spring Announcements C 188: Atiiil Intllign ing 2006 Ltu 2: Quu-Bs 8/31/2006 Dn Klin UC Bkly Mny slis om it tut Russll o Anw Moo Announmnts L Fiy 1-5m in o 275 Ln Pyton tt on Pojt 1.1: Mzwol Com o wtv tims you lik No stions

More information

Announcements. CS 188: Artificial Intelligence Spring More Announcements. Today. From Last Time: Reflex Agents.

Announcements. CS 188: Artificial Intelligence Spring More Announcements. Today. From Last Time: Reflex Agents. C 88: Atiiil Intllign ing 009 Ltu : Quu-Bs //008 Jon DNo UC Bkly Mny slis om Dn Klin, tut Russll o Anw Moo Announmnts Pojt 0: Pyton Tutoil Post onlin now Du nxt Wnsy, Jn 8 T is l toy om m-3m in o 75 T

More information

CS 188: Artificial Intelligence Spring Announcements

CS 188: Artificial Intelligence Spring Announcements C 188: Atiiil Intllign ing 2010 Ltu 2: Quu-Bs 1/21/2010 Pit Al UC Bkly Mny slis om Dn Klin Announmnts Pojt 0: Pyton Tutoil Out toy. Du nxt wk Tusy. L sssions in 271 o: Mony 2-3m Wnsy 4-5m T l tim is otionl,

More information

CS 188: Artificial Intelligence Spring 2009

CS 188: Artificial Intelligence Spring 2009 C 188: Atiiil Intllign ing 009 Ltu : Quu-Bs 1//008 Jon DNo UC Bkly Mny slis om Dn Klin, tut Russll o Anw Moo Announmnts Pojt 0: Pyton Tutoil Post onlin now Du nxt Wnsy, Jn 8 T is l toy om 1m-3m in o 75

More information

CS 188: Artificial Intelligence Spring Announcements

CS 188: Artificial Intelligence Spring Announcements CS 188: Atiiil Intllign Sing 2011 Ltu 2: Quu-Bs S 1/24/2010 Pit Al UC Bkly Mny slis om Dn Klin Announmnts Pojt 0: Pyton Tutoil Du Fiy 5m. L sssion Wnsy 3-5m in 271 So T l tim is otionl, ut P0 itsl is not

More information

CSE 573: Artificial Intelligence Autumn Search thru a. Goal Based Agents 9/28/2012. Agent vs. Environment. Example: N Queens

CSE 573: Artificial Intelligence Autumn Search thru a. Goal Based Agents 9/28/2012. Agent vs. Environment. Example: N Queens CE 573: Atiiil Intllign Autumn 0 Intoution & Dn Wl Wit slis om Dn Klin, tut Russll, Anw Moo, Luk Zttlmoy Agnt vs. Envionmnt An gnt is n ntity tt ivs n ts. A tionl gnt slts tions tt mximiz its utility untion.

More information

Reminder. CS 188: Artificial Intelligence. A reflex agent for pacman. Reflex Agent. A reflex agent for pacman (3) A reflex agent for pacman (2)

Reminder. CS 188: Artificial Intelligence. A reflex agent for pacman. Reflex Agent. A reflex agent for pacman (3) A reflex agent for pacman (2) C 88: Atiiil Intllign Ltus n : Rmin Only vy smll tion o AI is out mking omuts ly gms intlligntly Rll: omut vision, ntul lngug, ootis, min lning, omuttionl iology, t. Pit Al UC Bkly Mny slis om Dn Klin

More information

Course Logistics Textbook: Artificial Intelligence: A Modern Approach, Russell and Norvig (3 rd ed) Topics

Course Logistics Textbook: Artificial Intelligence: A Modern Approach, Russell and Norvig (3 rd ed) Topics CE 573: Atiiil Intllign Autumn 0 Intoution & Dn Wl Wit slis om Dn Klin, tut Russll, Anw Moo, Luk Zttlmoy Cous Logistis Txtook: Atiiil Intllign: A Mon Ao, Russll n Novig (3 ) Puisits: Dt tutus (CE 36 o

More information

A search problem. Formalizing a search problem. Our Search Problem. Our Search Problem. Overview

A search problem. Formalizing a search problem. Our Search Problem. Our Search Problem. Overview Sing: Dtministi singl-gnt Atully, tis is otimiztion ov tim wit ist vils Anw W. Moo Posso Sool o Comut Sin Cngi Mllon Univsity www.s.mu.u/~wm wm@s.mu.u -6-7 ot to ot ts n uss o ts slis. Anw woul ligt i

More information

Searching: Deterministic single-agent

Searching: Deterministic single-agent Sing: Dtministi singl-gnt Anw W. Moo Posso Sool o Comut Sin Cngi Mllon Univsity www.s.mu.u/~wm wm@s.mu.u -68-7 ot to ot ts n uss o ts slis. Anw woul ligt i you oun tis sou mtil usul in giving you own ltus.

More information

Announcements. CS 188: Artificial Intelligence Fall Office hours, Section. Today. DFS and BFS. Recap: Search. Lecture 3: A* Search 9/3/2009

Announcements. CS 188: Artificial Intelligence Fall Office hours, Section. Today. DFS and BFS. Recap: Search. Lecture 3: A* Search 9/3/2009 C 88: Atiicil Intllignc Fll 009 Lctu : A* ch 9//009 Pit Al UC Bkly Mny slids om Dn Klin Announcmnts Assignmnts: Pojct 0 (Python tutoil): du Thusdy /8 Wittn (ch): du Thusdy /8 Pojct (ch): to lsd tody, du

More information

Easy Steps to build a part number... Tri-Start Series III CF P

Easy Steps to build a part number... Tri-Start Series III CF P ulti-l i Oti iul ( oto) ow to O ol os sy ts to uil t u... i-tt is 1. 2 3 4. 5. 6. oto y til iis ll tyl ll iz- st t ott y & y/ ywy ositio 50 9 0 17-08 ol ulti-l i oti otos o us wit ulti-o sil o tii o y

More information

Problem solving by search

Problem solving by search Prolm solving y srh Tomáš voo Dprtmnt o Cyrntis, Vision or Roots n Autonomous ystms Mrh 5, 208 / 3 Outlin rh prolm. tt sp grphs. rh trs. trtgis, whih tr rnhs to hoos? trtgy/algorithm proprtis? Progrmming

More information

Exam 2 Solutions. Jonathan Turner 4/2/2012. CS 542 Advanced Data Structures and Algorithms

Exam 2 Solutions. Jonathan Turner 4/2/2012. CS 542 Advanced Data Structures and Algorithms CS 542 Avn Dt Stutu n Alotm Exm 2 Soluton Jontn Tun 4/2/202. (5 ont) Con n oton on t tton t tutu n w t n t 2 no. Wt t mllt num o no tt t tton t tutu oul ontn. Exln you nw. Sn n mut n you o u t n t, t n

More information

Self-Adjusting Top Trees

Self-Adjusting Top Trees Th Polm Sl-jsting Top Ts ynmi ts: ol: mintin n n-tx ost tht hngs o tim. link(,w): ts n g twn tis n w. t(,w): lts g (,w). pplition-spii t ssoit with gs n/o tis. ont xmpls: in minimm-wight g in th pth twn

More information

Search: Cost & Heuristics

Search: Cost & Heuristics 9/9/ CSE 7: Artiiil Intelligene Autumn 0 Pizz? Announements Serh: Cost & Heuristis Dn Wel Projet : Serh online tomorrow ue Mony 0/ ue We / Strt! With slies rom Dn Klein, Sturt Russell, Anrew Moore, Luke

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

Announcements. CS 188: Artificial Intelligence. Costs on Actions. Recap: Search. Lecture 3: A* Search

Announcements. CS 188: Artificial Intelligence. Costs on Actions. Recap: Search. Lecture 3: A* Search Announcmnts Pojcts: Looking fo ojct tns? --- Com to font ft lctu. Ty i ogmming, not divid-nd-conu Account foms vill u font duing k nd ft lctu Assignmnts Looking fo studnts to wok on ssignmnts with? ---

More information

Chapter 6 Perturbation theory

Chapter 6 Perturbation theory Ct 6 Ptutio to 6. Ti-iddt odgt tutio to i o tutio sst is giv to fid solutios of λ ' ; : iltoi of si stt : igvlus of : otool igfutios of ; δ ii Rlig-Södig tutio to ' λ..6. ; : gl iltoi ': tutio λ : sll

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

10.3 The Quadratic Formula

10.3 The Quadratic Formula . Te Qudti Fomul We mentioned in te lst setion tt ompleting te sque n e used to solve ny qudti eqution. So we n use it to solve 0. We poeed s follows 0 0 Te lst line of tis we ll te qudti fomul. Te Qudti

More information

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

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

More information

/99 $10.00 (c) 1999 IEEE

/99 $10.00 (c) 1999 IEEE P t Hw Itt C Syt S 999 P t Hw Itt C Syt S - 999 A Nw Atv C At At Cu M Syt Y ZHANG Ittut Py P S, Uvty Tuu, I 0-87, J Att I t, w tv t t u yt x wt y tty, t wt tv w (LBSB) t. T w t t x t tty t uy ; tt, t x

More information

Problem 1. Solution: = show that for a constant number of particles: c and V. a) Using the definitions of P

Problem 1. Solution: = show that for a constant number of particles: c and V. a) Using the definitions of P rol. Using t dfinitions of nd nd t first lw of trodynis nd t driv t gnrl rltion: wr nd r t sifi t itis t onstnt rssur nd volu rstivly nd nd r t intrnl nrgy nd volu of ol. first lw rlts d dq d t onstnt

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

d e c b a d c b a d e c b a a c a d c c e b

d e c b a d c b a d e c b a a c a d c c e b FLAT PEYOTE STITCH Bin y mkin stoppr -- sw trou n pull it lon t tr until it is out 6 rom t n. Sw trou t in witout splittin t tr. You soul l to sli it up n own t tr ut it will sty in pl wn lt lon. Evn-Count

More information

A TYP A-602 A-304 A-602 A-302 GRADE BEAM SEE 95% COMPACTED STRUCTURAL FILL A '-0"

A TYP A-602 A-304 A-602 A-302 GRADE BEAM SEE 95% COMPACTED STRUCTURAL FILL A '-0 W W/TITI -0 X U I I X TITI TY S W TYS TIS X W S SU XISTI -0-0 -0-0 -0-0 ' - " ' - " ' - " ' - " ' - " ' - /" ' - /" ' - " -STUTU I -0 ' - ' - " " ' - " " 0' - " ' - U I S STUT W'S TY UTI W S STUT W'S TY

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

Spanning Trees. BFS, DFS spanning tree Minimum spanning tree. March 28, 2018 Cinda Heeren / Geoffrey Tien 1

Spanning Trees. BFS, DFS spanning tree Minimum spanning tree. March 28, 2018 Cinda Heeren / Geoffrey Tien 1 Spnnn Trs BFS, DFS spnnn tr Mnmum spnnn tr Mr 28, 2018 Cn Hrn / Gory Tn 1 Dpt-rst sr Vsts vrts lon snl pt s r s t n o, n tn ktrks to t rst junton n rsums own notr pt Mr 28, 2018 Cn Hrn / Gory Tn 2 Dpt-rst

More information

Three Phase Asymmetrical Load Flow for Four-Wire Distribution Networks

Three Phase Asymmetrical Load Flow for Four-Wire Distribution Networks T Aytl Lo Flow o Fou-W Dtuto Ntwo M. Mo *, A. M. Dy. M. A Dtt o Eltl E, A Uvty o Toloy Hz Av., T 59, I * El: o8@yoo.o Att-- Mjoty o tuto two ul u to ul lo, yty to l two l ut. T tt o tuto yt ult y o ovt

More information

Trade Patterns, Production networks, and Trade and employment in the Asia-US region

Trade Patterns, Production networks, and Trade and employment in the Asia-US region Trade Patterns, Production networks, and Trade and employment in the Asia-U region atoshi Inomata Institute of Developing Economies ETRO Development of cross-national production linkages, 1985-2005 1985

More information

Series III, TV Breakaway Fail-Safe Connectors Quick-Disconnect with an Axial Pull of Lanyard

Series III, TV Breakaway Fail-Safe Connectors Quick-Disconnect with an Axial Pull of Lanyard is, wy il- otos Qui-isot wit xil ull o y ulo ss quo mol i-tt wy il- otos ovi uqul om i viomts quii istt ismt. wy il- oto mily os wi o ltil mil tus: stt ouli m stio omltly itmtl wit st tls (/20 /2) vtoy

More information

LWC 434 East First Street 4440 Garwood Place

LWC 434 East First Street 4440 Garwood Place //0 :: UI IXTUS TO US IIT TOS O T IST UTU I TOY IST OW - ITIO UTUS IST I TSIS. I ST (O, ZU). cui (, ZU). TOTO (OI, O). SO (ZU, Y). TUO (SO, ZU). TOTO (O US). IS (OSOIT, U). UST (ST WIIS, ZU). Y (T&S SS,

More information

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

Appendix. In the absence of default risk, the benefit of the tax shield due to debt financing by the firm is 1 C E C nx. Dvon o h n wh In h sn o ul sk h n o h x shl u o nnng y h m s s h ol ouon s h num o ssus s h oo nom x s h sonl nom x n s h v x on quy whh s wgh vg o vn n l gns x s. In hs s h o sonl nom xs on h x shl

More information

Solutions for HW11. Exercise 34. (a) Use the recurrence relation t(g) = t(g e) + t(g/e) to count the number of spanning trees of v 1

Solutions for HW11. Exercise 34. (a) Use the recurrence relation t(g) = t(g e) + t(g/e) to count the number of spanning trees of v 1 Solutions for HW Exris. () Us th rurrn rltion t(g) = t(g ) + t(g/) to ount th numr of spnning trs of v v v u u u Rmmr to kp multipl gs!! First rrw G so tht non of th gs ross: v u v Rursing on = (v, u ):

More information

4.1 Interval Scheduling. Chapter 4. Greedy Algorithms. Interval Scheduling: Greedy Algorithms. Interval Scheduling. Interval scheduling.

4.1 Interval Scheduling. Chapter 4. Greedy Algorithms. Interval Scheduling: Greedy Algorithms. Interval Scheduling. Interval scheduling. Cptr 4 4 Intrvl Suln Gry Alortms Sls y Kvn Wyn Copyrt 005 Prson-Ason Wsly All rts rsrv Intrvl Suln Intrvl Suln: Gry Alortms Intrvl suln! Jo strts t s n nss t! Two os omptl ty on't ovrlp! Gol: n mxmum sust

More information

Lecture 20: Minimum Spanning Trees (CLRS 23)

Lecture 20: Minimum Spanning Trees (CLRS 23) Ltur 0: Mnmum Spnnn Trs (CLRS 3) Jun, 00 Grps Lst tm w n (wt) rps (unrt/rt) n ntrou s rp voulry (vrtx,, r, pt, onnt omponnts,... ) W lso suss jny lst n jny mtrx rprsntton W wll us jny lst rprsntton unlss

More information

Paths. Connectivity. Euler and Hamilton Paths. Planar graphs.

Paths. Connectivity. Euler and Hamilton Paths. Planar graphs. Pths.. Eulr n Hmilton Pths.. Pth D. A pth rom s to t is squn o gs {x 0, x 1 }, {x 1, x 2 },... {x n 1, x n }, whr x 0 = s, n x n = t. D. Th lngth o pth is th numr o gs in it. {, } {, } {, } {, } {, } {,

More information

Call for Applications

Call for Applications i Ty Ty v l O 7:H 7 O6 fl x 4 7T q l it y ix k lf t l l H v l lg i li O 7:H7 EDL9 ty i tyi yt Blvi i i g it g vi B l B ll li B i ll iz i ti S B 6 dy li j d ti d l i vi i ik tti w z k ik tti i l w l Hli

More information

Planar convex hulls (I)

Planar convex hulls (I) Covx Hu Covxty Gv st P o ots 2D, tr ovx u s t sst ovx oyo tt ots ots o P A oyo P s ovx or y, P, t st s try P. Pr ovx us (I) Coutto Gotry [s 3250] Lur To Bowo Co ovx o-ovx 1 2 3 Covx Hu Covx Hu Covx Hu

More information

February 12 th December 2018

February 12 th December 2018 208 Fbu 2 th Dcb 208 Whgt Fbu Mch M 2* 3 30 Ju Jul Sptb 4* 5 7 9 Octob Novb Dcb 22* 23 Put ou blu bgs out v d. *Collctios d lt du to Public Holid withi tht wk. Rcclig wk is pik Rcclig wk 2 is blu Th stick

More information

Table of C on t en t s Global Campus 21 in N umbe r s R e g ional Capac it y D e v e lopme nt in E-L e ar ning Structure a n d C o m p o n en ts R ea

Table of C on t en t s Global Campus 21 in N umbe r s R e g ional Capac it y D e v e lopme nt in E-L e ar ning Structure a n d C o m p o n en ts R ea G Blended L ea r ni ng P r o g r a m R eg i o na l C a p a c i t y D ev elo p m ent i n E -L ea r ni ng H R K C r o s s o r d e r u c a t i o n a n d v e l o p m e n t C o p e r a t i o n 3 0 6 0 7 0 5

More information

learning objectives learn what graphs are in mathematical terms learn how to represent graphs in computers learn about typical graph algorithms

learning objectives learn what graphs are in mathematical terms learn how to represent graphs in computers learn about typical graph algorithms rp loritms lrnin ojtivs loritms your sotwr systm sotwr rwr lrn wt rps r in mtmtil trms lrn ow to rprsnt rps in omputrs lrn out typil rp loritms wy rps? intuitivly, rp is orm y vrtis n s twn vrtis rps r

More information

(Minimum) Spanning Trees

(Minimum) Spanning Trees (Mnmum) Spnnn Trs Spnnn trs Kruskl's lortm Novmr 23, 2017 Cn Hrn / Gory Tn 1 Spnnn trs Gvn G = V, E, spnnn tr o G s onnt surp o G wt xtly V 1 s mnml sust o s tt onnts ll t vrts o G G = Spnnn trs Novmr

More information

COMP 250. Lecture 29. graph traversal. Nov. 15/16, 2017

COMP 250. Lecture 29. graph traversal. Nov. 15/16, 2017 COMP 250 Ltur 29 rp trvrsl Nov. 15/16, 2017 1 Toy Rursv rp trvrsl pt rst Non-rursv rp trvrsl pt rst rt rst 2 Hs up! Tr wr w mstks n t sls or S. 001 or toy s ltur. So you r ollown t ltur rorns n usn ts

More information

Rectangular Waveguides

Rectangular Waveguides Rtgulr Wvguids Wvguids tt://www.tllguid.o/wvguidlirit.tl Uss To rdu ttutio loss ig rquis ig owr C ort ol ov rti rquis Ats s ig-ss iltr Norll irulr or rtgulr W will ssu losslss rtgulr tt://www..surr..u/prsol/d.jris/wguid.tl

More information

Beechwood Music Department Staff

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

More information

CMPS 2200 Fall Graphs. Carola Wenk. Slides courtesy of Charles Leiserson with changes and additions by Carola Wenk

CMPS 2200 Fall Graphs. Carola Wenk. Slides courtesy of Charles Leiserson with changes and additions by Carola Wenk CMPS 2200 Fll 2017 Grps Crol Wnk Sls ourtsy o Crls Lsrson wt ns n tons y Crol Wnk 10/23/17 CMPS 2200 Intro. to Alortms 1 Grps Dnton. A rt rp (rp) G = (V, E) s n orr pr onsstn o st V o vrts (snulr: vrtx),

More information

F102 1/4 AMP +240 VDC SEE FIGURE 5-14 FILAMENT AND OVEN CKTS BLU J811 BREAK-IN TB103 TO S103 TRANSMITTER ASSOCIATED CAL OFF FUNCTION NOTE 2 STANDBY

F102 1/4 AMP +240 VDC SEE FIGURE 5-14 FILAMENT AND OVEN CKTS BLU J811 BREAK-IN TB103 TO S103 TRANSMITTER ASSOCIATED CAL OFF FUNCTION NOTE 2 STANDBY OWR OR F0 M NOT S0 RT OF FUNTI FL0 T0 OWR SULY SUSSIS T0 T0 WIR FOR 0 V OWR SULY SUSSIS T0 WIR FOR V 0 0 RT V0 RT V0. V RT V0 RT V0 NOT. V. V NOT +0 V 0 +0 V. V 0 FUNTI NOT L +0 V S FIUR - FILMNT N OVN

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

OpenMx Matrices and Operators

OpenMx Matrices and Operators OpnMx Mtris n Oprtors Sr Mln Mtris: t uilin loks Mny typs? Dnots r lmnt mxmtrix( typ= Zro", nrow=, nol=, nm="" ) mxmtrix( typ= Unit", nrow=, nol=, nm="" ) mxmtrix( typ= Int", nrow=, nol=, nm="" ) mxmtrix(

More information

Gavilan JCCD Trustee Areas Plan Adopted November 10, 2015

Gavilan JCCD Trustee Areas Plan Adopted November 10, 2015 Gvil JCCD Tust A Pl Aopt Novmb, S Jos US p Ls Pl Aopt // Cit/Csus Dsigt Plc ighw Cit Aom ollist igm S Jos Ts Pios c Ps 4 ut S Bito ut ils Aom ollist igm Ts Pios S Bito ut Lpoff & Goblt Dmogphic sch, Ic.

More information

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

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

More information

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

NUCON NRNON CONRNC ON CURRN RN N CHNOOGY, 011 oo uul o w ul x ol volv y y oll. y ov,., - o lo ll vy ul o Mo l u v ul (G) v Gl vlu oll. u 3- [11]. 000

NUCON NRNON CONRNC ON CURRN RN N CHNOOGY, 011 oo uul o w ul x ol volv y y oll. y ov,., - o lo ll vy ul o Mo l u v ul (G) v Gl vlu oll. u 3- [11]. 000 NU O HMB NRM UNVRY, HNOOGY, C 8 0 81, 8 3-1 01 CMBR, 0 1 1 l oll oll ov ll lvly lu ul uu oll ul. w o lo u uol u z. ul l u oll ul. quk, oll, vl l, lk lo, - ul o u v (G) v Gl o oll. ul l u vlu oll ul uj

More information

Multicast routing algorithm based on Extended Simulated Annealing Algorithm

Multicast routing algorithm based on Extended Simulated Annealing Algorithm 7t WSEAS Int. Con. on MATHEMATICAL METHODS n COMPUTATIONAL TECHNIQUES IN ELECTRICAL ENGINEERING, Soi, 27-29/10/05 (pp129-133) Multist outing lgoitm s on Extn Simult Annling Algoitm Jin-Ku Jong*, Sung-Ok

More information

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

( ) ( ) ( ) 0. Conservation of Energy & Poynting Theorem. From Maxwell s equations we have. M t. From above it can be shown (HW) 8 Conson o n & Ponn To Fo wll s quons w D B σ σ Fo bo n b sown (W) o s W w bo on o s l us n su su ul ow ns [W/ ] [W] su P su B W W 4 444 s W A A s V A A : W W R o n o so n n: [/s W] W W 4 44 9 W : W F

More information

PLAYGROUND SALE Take up to 40% off. Plus FREE equipment * with select purchase DETAILS INSIDE

PLAYGROUND SALE Take up to 40% off. Plus FREE equipment * with select purchase DETAILS INSIDE PLYROUND SL Tk up t 40% ff Plu FR quipnt * with lct puch DTILS INSID T BONUS QUIPMNT FR! T BONUS QUIPMNT FR * Mk qulifing $10K, $0K $30K puch f thi ORDR $10K ORDR $0K ORDR $30K T ON FR* T TO FR* T THR

More information

-Z ONGRE::IONAL ACTION ON FY 1987 SUPPLEMENTAL 1/1

-Z ONGRE::IONAL ACTION ON FY 1987 SUPPLEMENTAL 1/1 -Z-433 6 --OGRE::OA ATO O FY 987 SUPPEMETA / APPR)PRATO RfQUEST PAY AD PROGRAM(U) DE ARTMET OF DEES AS O' D 9J8,:A:SF ED DEFS! WA-H ODM U 7 / A 25 MRGOPf RESOUTO TEST HART / / AD-A 83 96 (~Go w - %A uj

More information

(2) If we multiplied a row of B by λ, then the value is also multiplied by λ(here lambda could be 0). namely

(2) If we multiplied a row of B by λ, then the value is also multiplied by λ(here lambda could be 0). namely . DETERMINANT.. Dtrminnt. Introution:I you think row vtor o mtrix s oorint o vtors in sp, thn th gomtri mning o th rnk o th mtrix is th imnsion o th prlllppi spnn y thm. But w r not only r out th imnsion,

More information

Available online Journal of Scientific and Engineering Research, 2016, 3(6): Research Article

Available online  Journal of Scientific and Engineering Research, 2016, 3(6): Research Article Av www.. Ju St E R, 2016, 3(6):131-138 R At ISSN: 2394-2630 CODEN(USA): JSERBR Cutvt R Au Su H Lv I y t Mt Btt M Zu H Ut, Su, W Hy Dtt Ay Futy Autu, Uvt Tw, J. Tw N. 9 P, 25136,Wt Sut, I, E-: 65@y. Att

More information

INFLUENCE OF ANTICLIMBING DEVICE ON THE VARIATION OF LOADS ON WHEELS IN DIESEL ELECTRIC 4000 HP

INFLUENCE OF ANTICLIMBING DEVICE ON THE VARIATION OF LOADS ON WHEELS IN DIESEL ELECTRIC 4000 HP U..B. Si. Bull., Si D, Vol.,., SS 454-5 UEE O AMBG DEVE O HE VARAO O OADS O WHEES DESE EER 4 H onl ătălin OESU Dipozitiul nt intodu ini uplimnt p oţil oiilo loomotilo. n lu pzint iti to ini, unţi d dtl

More information

7 ACM FOR FRAME 2SET 6 FRAME 2SET 5 ACM FOR MAIN FRAME 2SET 4 MAIN FRAME 2SET 3 POLE ASSLY 1 2 CROWN STRUCTURE ASSLY 1 1 CROWN ASSLY 1

7 ACM FOR FRAME 2SET 6 FRAME 2SET 5 ACM FOR MAIN FRAME 2SET 4 MAIN FRAME 2SET 3 POLE ASSLY 1 2 CROWN STRUCTURE ASSLY 1 1 CROWN ASSLY 1 7 M OR RM 2ST 6 RM 2ST 5 M OR MIN RM 2ST 4 MIN RM 2ST 3 POL SSLY 1 2 ROWN STRUTUR SSLY 1 1 ROWN SSLY 1 SR.NO. SRIPTION QTY. a LL IMNSIONS R IN mm I N MT Pi IOLMI 1'NTION LT. Tm: XPLO VIW OR POL MOUNT MLM

More information

Exhibit 2-9/30/15 Invoice Filing Page 1841 of Page 3660 Docket No

Exhibit 2-9/30/15 Invoice Filing Page 1841 of Page 3660 Docket No xhibit 2-9/3/15 Invie Filing Pge 1841 f Pge 366 Dket. 44498 F u v 7? u ' 1 L ffi s xs L. s 91 S'.e q ; t w W yn S. s t = p '1 F? 5! 4 ` p V -', {} f6 3 j v > ; gl. li -. " F LL tfi = g us J 3 y 4 @" V)

More information

1 Introduction to Modulo 7 Arithmetic

1 Introduction to Modulo 7 Arithmetic 1 Introution to Moulo 7 Arithmti Bor w try our hn t solvin som hr Moulr KnKns, lt s tk los look t on moulr rithmti, mo 7 rithmti. You ll s in this sminr tht rithmti moulo prim is quit irnt rom th ons w

More information

Who is this Great Team? Nickname. Strangest Gift/Friend. Hometown. Best Teacher. Hobby. Travel Destination. 8 G People, Places & Possibilities

Who is this Great Team? Nickname. Strangest Gift/Friend. Hometown. Best Teacher. Hobby. Travel Destination. 8 G People, Places & Possibilities Who i thi Gt Tm? Exi Sh th foowing i of infomtion bot of with o tb o tm mt. Yo o not hv to wit n of it own. Yo wi b givn on 5 mint to omih thi tk. Stngt Gift/Fin Niknm Homtown Bt Th Hobb Tv Dtintion Robt

More information

DATA Search I 魏忠钰. 复旦大学大数据学院 School of Data Science, Fudan University. March 7 th, 2018

DATA Search I 魏忠钰. 复旦大学大数据学院 School of Data Science, Fudan University. March 7 th, 2018 DATA620006 魏忠钰 Serch I Mrch 7 th, 2018 Outline Serch Problems Uninformed Serch Depth-First Serch Bredth-First Serch Uniform-Cost Serch Rel world tsk - Pc-mn Serch problems A serch problem consists of:

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

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

Helping Kids Prepare For Life (253)

Helping Kids Prepare For Life   (253) Hlpi Ki Pp F Lif.l.i. (253)-589-7489 Tilli it it L Livit iv f fiv CIS U H. Vip pt fll t Tilli Elt l tpi tff tt f vi t t CIS T Hll f i Cltt N Cli. - L ivi i CIS f Bill Milli CIS pit Dil Cili Ti l iz it

More information

G-001 SACO SACO BAY BIDDEFORD INDEX OF NAVIGATION AIDS GENERAL NOTES: GENERAL PLAN A6 SCALE: 1" = 1000' CANADA MAINE STATE PLANE GEOGRAPHIC NO.

G-001 SACO SACO BAY BIDDEFORD INDEX OF NAVIGATION AIDS GENERAL NOTES: GENERAL PLAN A6 SCALE: 1 = 1000' CANADA MAINE STATE PLANE GEOGRAPHIC NO. 2 3 6 7 8 9 0 2 3 20000 230000 220000 ST TORY M 8-OOT W ST 2880000 2880000 L ROOK RL OTS: UKI OR TUR RKWTR (TYP) U O ROOK. SOUIS R I T TTS. T RR PL IS M LOWR LOW WTR (MLLW) IS S O T 983-200 TIL PO. SOUIS

More information

Distributed Set Reachability

Distributed Set Reachability Dstt St Rty S Gj Mt T Mx-P Isttt Its, Usty U Gy SIGMOD 2016, S Fs, USA Dstt St Rty Dstt St Rty (DSR) s zt ty xt t sts stt stt Dstt St Rty 2 Dstt St Rty Dstt St Rty (DSR) s zt ty xt t sts stt stt Dstt St

More information

CS 241 Analysis of Algorithms

CS 241 Analysis of Algorithms CS 241 Anlysis o Algorithms Prossor Eri Aron Ltur T Th 9:00m Ltur Mting Lotion: OLB 205 Businss HW6 u lry HW7 out tr Thnksgiving Ring: Ch. 22.1-22.3 1 Grphs (S S. B.4) Grphs ommonly rprsnt onntions mong

More information

Daily Skill Practice

Daily Skill Practice G CD-0 Dily Skill Pti 00 Wkk ## W i t it Eh. gh y w m y il A ll? + = 8 Dy 8= 0. =. Nm. C h l lit tl k ty i g. I h hi ty w ig h, m y hw hi g w ig h?. W Wkk ##00 A A = t, >, = W it < t t m t m k t. Dy Dy

More information

Improving Union. Implementation. Union-by-size Code. Union-by-Size Find Analysis. Path Compression! Improving Find find(e)

Improving Union. Implementation. Union-by-size Code. Union-by-Size Find Analysis. Path Compression! Improving Find find(e) POW CSE 36: Dt Struturs Top #10 T Dynm (Equvln) Duo: Unon-y-Sz & Pt Comprsson Wk!! Luk MDowll Summr Qurtr 003 M! ZING Wt s Goo Mz? Mz Construton lortm Gvn: ollton o rooms V Conntons twn t rooms (ntlly

More information

G-001 CHATHAM HARBOR AUNT LYDIA'S COVE CHATHAM ATLANTIC OCEAN INDEX OF NAVIGATION AIDS GENERAL NOTES: GENERAL PLAN A6 SCALE: 1" = 500' CANADA

G-001 CHATHAM HARBOR AUNT LYDIA'S COVE CHATHAM ATLANTIC OCEAN INDEX OF NAVIGATION AIDS GENERAL NOTES: GENERAL PLAN A6 SCALE: 1 = 500' CANADA TR ISL ROR UST 8 O. R-2,4-3 R-4 IX O VITIO IS STT PL ORPI OORITS POSITIO 27698 4-39'-" 88 69-6'-4."W 278248 4-4'-" 8968 69-6'-4"W 27973 4-4'-2" 88 69-6'-"W W MPSIR OOR UUST PORTL MI OR 27 8-OOT OR L -

More information

Grade 7/8 Math Circles March 4/5, Graph Theory I- Solutions

Grade 7/8 Math Circles March 4/5, Graph Theory I- Solutions ulty o Mtmtis Wtrloo, Ontrio N ntr or ution in Mtmtis n omputin r / Mt irls Mr /, 0 rp Tory - Solutions * inits lln qustion. Tr t ollowin wlks on t rp low. or on, stt wtr it is pt? ow o you know? () n

More information

Theory of Spatial Problems

Theory of Spatial Problems Chpt 7 ho of Sptil Polms 7. Diffntil tions of iliim (-D) Z Y X Inol si nknon stss componnts:. 7- 7. Stt of Stss t Point t n sfc ith otd noml N th sfc componnts ltd to (dtmind ) th 6 stss componnts X N

More information

Divided. diamonds. Mimic the look of facets in a bracelet that s deceptively deep RIGHT-ANGLE WEAVE. designed by Peggy Brinkman Matteliano

Divided. diamonds. Mimic the look of facets in a bracelet that s deceptively deep RIGHT-ANGLE WEAVE. designed by Peggy Brinkman Matteliano RIGHT-ANGLE WEAVE Dv mons Mm t look o ts n rlt tt s ptvly p sn y Py Brnkmn Mttlno Dv your mons nto trnls o two or our olors. FCT-SCON0216_BNB66 2012 Klm Pulsn Co. Ts mtrl my not rprou n ny orm wtout prmsson

More information

CEDAR ISLAND / KEATON BEACH TAYLOR COUNTY, FLORIDA POST-HURRICANE HERMINE EXAMINATION SURVEY FY16 4-FOOT PROJECT

CEDAR ISLAND / KEATON BEACH TAYLOR COUNTY, FLORIDA POST-HURRICANE HERMINE EXAMINATION SURVEY FY16 4-FOOT PROJECT 10 9 8 7 6 5 JUG ISLN R KL H R H R ROSMR LN W W HITTIL R JO MORGN R LRW TR RK R L M PNSOL GUL G O R G I TLLHSS JKSONVILL ORLNO OO TMP TLNTI ON N US rmy orps of ngineers Jacksonville istrict ST ON THIS

More information

Ash Wednesday. First Introit thing. * Dómi- nos. di- di- nos, tú- ré- spi- Ps. ne. Dó- mi- Sál- vum. intra-vé-runt. Gló- ri-

Ash Wednesday. First Introit thing. * Dómi- nos. di- di- nos, tú- ré- spi- Ps. ne. Dó- mi- Sál- vum. intra-vé-runt. Gló- ri- sh Wdsdy 7 gn mult- tú- st Frst Intrt thng X-áud m. ns ní- m-sr-cór- Ps. -qu Ptr - m- Sál- vum m * usqu 1 d fc á-rum sp- m-sr-t- ó- num Gló- r- Fí- l- Sp-rí- : quó-n- m ntr-vé-runt á- n-mm c * m- quó-n-

More information

Grain Reserves, Volatility and the WTO

Grain Reserves, Volatility and the WTO Grain Reserves, Volatility and the WTO Sophia Murphy Institute for Agriculture and Trade Policy www.iatp.org Is v o la tility a b a d th in g? De pe n d s o n w h e re yo u s it (pro d uc e r, tra d e

More information

In which direction do compass needles always align? Why?

In which direction do compass needles always align? Why? AQA Trloy Unt 6.7 Mntsm n Eltromntsm - Hr 1 Complt t p ll: Mnt or s typ o or n t s stronst t t o t mnt. Tr r two typs o mnt pol: n. Wrt wt woul ppn twn t pols n o t mnt ntrtons low: Drw t mnt l lns on

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

Tangram Fractions Overview: Students will analyze standard and nonstandard

Tangram Fractions Overview: Students will analyze standard and nonstandard ACTIVITY 1 Mtrils: Stunt opis o tnrm mstrs trnsprnis o tnrm mstrs sissors PROCEDURE Skills: Dsriin n nmin polyons Stuyin onrun Comprin rtions Tnrm Frtions Ovrviw: Stunts will nlyz stnr n nonstnr tnrms

More information

Uninformed Search Lecture 4

Uninformed Search Lecture 4 Lecture 4 Wht re common serch strtegies tht operte given only serch problem? How do they compre? 1 Agend A quick refresher DFS, BFS, ID-DFS, UCS Unifiction! 2 Serch Problem Formlism Defined vi the following

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

What are S M U s? SMU = Software Maintenance Upgrade Software patch del iv ery u nit wh ich once ins tal l ed and activ ated prov ides a point-fix for

What are S M U s? SMU = Software Maintenance Upgrade Software patch del iv ery u nit wh ich once ins tal l ed and activ ated prov ides a point-fix for SMU 101 2 0 0 7 C i s c o S y s t e m s, I n c. A l l r i g h t s r e s e r v e d. 1 What are S M U s? SMU = Software Maintenance Upgrade Software patch del iv ery u nit wh ich once ins tal l ed and activ

More information

An undirected graph G = (V, E) V a set of vertices E a set of unordered edges (v,w) where v, w in V

An undirected graph G = (V, E) V a set of vertices E a set of unordered edges (v,w) where v, w in V Unirt Grphs An unirt grph G = (V, E) V st o vrtis E st o unorr gs (v,w) whr v, w in V USE: to mol symmtri rltionships twn ntitis vrtis v n w r jnt i thr is n g (v,w) [or (w,v)] th g (v,w) is inint upon

More information

Class Diagrams. CSC 440/540: Software Engineering Slide #1

Class Diagrams. CSC 440/540: Software Engineering Slide #1 Class Diagrams CSC 440/540: Software Engineering Slide # Topics. Design class diagrams (DCDs) 2. DCD development process 3. Associations and Attributes 4. Dependencies 5. Composition and Constraints 6.

More information

Form and content. Iowa Research Online. University of Iowa. Ann A Rahim Khan University of Iowa. Theses and Dissertations

Form and content. Iowa Research Online. University of Iowa. Ann A Rahim Khan University of Iowa. Theses and Dissertations University of Iowa Iowa Research Online Theses and Dissertations 1979 Form and content Ann A Rahim Khan University of Iowa Posted with permission of the author. This thesis is available at Iowa Research

More information

SOUTH. Bus Map. From 25 October travelsouthyorkshire.com/sbp

SOUTH. Bus Map. From 25 October travelsouthyorkshire.com/sbp SOUT SFFIL u Mp F Ocb 1 N Sff p vb f Tv Su Y If Sff vuc/sp Sff u Pp - v Sff Sff u Pp cu w pv u w: u p bu w b vu c f u-p v Fqu vc ub f u Fw u c bu w w f cc v w cv f? 3 f-p p Sff bu Ipv cu fc b up % 0,000

More information

WEB CONNECTION SCHEDULE

WEB CONNECTION SCHEDULE W ONNTION M IZ W T () ING T ONNTION W IZ OT () & () Wx0 W0x Wx Wx Wx Wx0 Wx Wx Wx Wx Wx Wx Wx Wx Wx0 Wx Wx0 Wx Wx0 Wx Wx Wx Wx Wx Wx W0x0 W0x W0X0 /" /" - /"Ø /" /" - /"Ø /" /" - /"Ø /" /" - /"Ø / /" -

More information