Key Ideas So Far. University of California, Berkeley

Size: px
Start display at page:

Download "Key Ideas So Far. University of California, Berkeley"

Transcription

1 EE 105 F 2016 Ky I So Fr Pro. A. M. iknj 1 Univrity o Ciorni, Brky

2 EE 105 F 2016 Sov or tion Lngth Pro. A. M. iknj W hv two qution n two unknown. W r iny in oition to ov or th tion th q 2 n n0 2 q (1 q o q no (2 no 2 q æ è ö ø o 2 q æ è ö ø º n > 0 2

3 EE 105 F 2016 (cont. Pro. A. M. iknj 3 Univrity o Ciorni, Brky

4 EE 105 F 2016 Pro. A. M. iknj P Junction Ccitor Unr thrm quiibrium, th P junction o not rw ny (much currnt But notic tht P junction tor chrg in th c chrg rgion (trnition rgion Sinc th vic i toring chrg, it cting ik ccitor Poitiv chrg i tor in th nrgion, n ngtiv chrg i in th rgion: q q o no 4

5 EE 105 F 2016 Rvr Bi P Junction Pro. A. M. iknj Wht hn i w rvr th P junction? < 0 5 Sinc no currnt i owing, th ntir rvr otnti i ro cro th trnition rgion To ccommot th tr otnti, th chrg in th rgion mut incr I no currnt i owing, th ony wy or th chrg to incr i to grow (hrink th tion rgion

6 EE 105 F 2016 Pro. A. M. iknj 6 otg nnc o tion With Cn ro th mth but in th n w riz tht th qution r th m ct w rc th buitin otnti with th ctiv rvr : ø ö è æ n q X 1 1 ( 2 ( ( ( n n q ø ö è æ 1 ( 2 ( 0 q ø ö è æ 1 ( 2 ( 0 X X 1 ( 0

7 EE 105 F 2016 Chrg ru Bi Pro. A. M. iknj A w incr th rvr, th tion rgion grow to ccommot mor chrg Q J ( q ( q 1 Chrg i not inr unction o votg Thi i noninr ccitor W cn in m ign ccitnc or m ign by brking u th chrg into two trm Q J ( v QJ ( q( v 7

8 EE 105 F 2016 Pro. A. M. iknj 8 rivtion o Sm Sign Ccitnc o Tyor Sri nion: otic tht! J J v Q Q v Q ( ( R j j j q Q C C ú ú û ù ø ö è æ 1 ( 0 j j C q C j q q q q C ø ö è æ ø ö è æ

9 EE 105 F 2016 Pro. A. M. iknj 9 Phyic Intrrttion o tion C otic tht th rion on th righthni i jut th tion with in thrm quiibrium Thi ook ik r t ccitor! j q C j X q C ø ö è æ ( ( j X C

10 EE 105 F 2016 Pro. A. M. iknj A rib Ccitor (rctor Ccitnc vri vru : C C j j 0 Aiction: Rio Tunr 10

11 Currnt in P Junction Pro. Ai M. iknj Pro. Rikky Mur rtmnt o EECS Univrity o Ciorni, Brky

12 EE 105 F 2016 Thrm Gnrtion 12 io unr Thrm Equiibrium Minority Crrir Co to Junction ty J rit, J n, rit E 0 J ni, J i, nty Pro. A. M. iknj Crrir with nrgy Rcomntion bow brrir hight iuion m inc w crrir hv nough nrgy to ntrt brrir rit currnt i m inc minority crrir r w n r btwn: Ony minority crrir gnrt within iuion ngth cn contribut currnt Imortnt Point: Minority rit currnt innnt o brrir! iuion currnt trong (onnti unction o brrir q A

13 EE 105 F 2016 Pro. A. M. iknj Rvr Bi Rvr Bi cu n incr brrir to iuion iuion currnt i ruc onntiy ty nty A q( R rit currnt o not chng 13 t rut: Sm rvr currnt

14 EE 105 F 2016 Pro. A. M. iknj Forwr Bi Forwr cu n onnti incr in th numbr o crrir with uicint nrgy to ntrt brrir iuion currnt incr onntiy ty nty A q( R rit currnt o not chng 14 t rut: Lrg orwr currnt

15 EE 105 F 2016 io I Curv Pro. A. M. iknj I I I ( I S q æ ö I IS 1 è ø 1 q 15 io I rtion i n onnti unction Thi onnti i u to th Botzmnn itribution o crrir vru nrgy For rvr th currnt turtion to th rit currnt u to minority crrir

16 EE 105 F 2016 Minority Crrir t Junction Eg Pro. A. M. iknj Minority crrir concntrtion t bounri o tion rgion incr brrir owr th unction i ( ( n n (minority ho conc. on ni o brrir (mjority ho conc. on i o brrir ( Brrir Enrgy / n( n A q( B / (Botzmnn Lw 16

17 EE 105 F 2016 Pro. A. M. iknj Lw o th Junction Minority crrir concntrtion t th g o th tion rgion r givn by: n ( n A q( B / n ( q( B / 17 ot 1: A n r th mjority crrir concntrtion on th othr i o th junction ot 2: w cn ruc th qution urthr by ubtituting 0 (thrm quiibrium ot 3: umtion tht n << n n << A

18 EE 105 F 2016 Pro. A. M. iknj Minority Crrir Concntrtion n0 q A i n i n 0 q A qa n( n0 æ ö n0 1 è ø L n 0 n0 Minority Crrir iuion Lngth W n W n Th minority crrir concntrtion in th buk rgion or orwr i cying onnti u to rcomntion 18 riv in EE130

19 EE 105 F 2016 Pro. A. M. iknj StyStt Concntrtion Aum tht non o th iuing ho n ctron rcomn à gt tright in n0 q A i n i n 0 q A n 0 n0 W n W n 19 Thi o hn i th minority crrir L iuion ngth r much rgr thn W n, >> W, n, riv in EE 130 n

20 EE 105 F 2016 io Currnt niti Pro. A. M. iknj i n 0 q A n0 q A n i q A 0 0 n n n (» ( W n0 n 0 W n W n n 0 n 2 i qa n i æ ö n Jn qn» q n0 1 W è ø qa i æ ö n J q»q n0 1 W n n è ø 20 q æ A i 2 öæ ö n J qni 1 W n W è ø è ø riv in EE 130

21 EE 105 F 2016 Fbriction o IC io Pro. A. M. iknj ctho nno n ty nw ty Strt with ty ubtrt Crt nw to hou io n n iuion rgion r th ctho n nno w mut b rvr rom ubtrt Pritic ritnc u to w ritnc 21

22 EE 105 F 2016 io Sm Sign Mo Pro. A. M. iknj Th I rtion o io cn b inriz I i I æ ö I è ø q ( v q qv S 1» S L 2! 3! æ q ( v ö I i» I 1 L è ø i qv» g v 22

23 EE 105 F 2016 io Ccitnc Pro. A. M. iknj 23 W hv ry n tht rvr io ct ik ccitor inc th tion rgion grow n hrink in ron to th i i. Th ccitnc in orwr i givn by S Cj A» 1.4C X But nothr chrg torg mchnim com into y in orwr Minority crrir injct into n n rgion ty in ch rgion or whi On vrg ition chrg i tor in io j0

24 EE 105 F 2016 Chrg Storg Pro. A. M. iknj n0 q ( v i n 0 q ( v n i n 0 n0 W n W n Incring orwr incr minority chrg nity By chrg nutrity, th ourc votg mut uy qu n ooit chrg 1 qi A ti nyi yi: C 2 t Tim to cro junction 24 (or minority crrir itim

25 EE 105 F 2016 Pro. A. M. iknj io Circuit Rctiir (AC to C convrion Avrg vu circuit Pk tctor (AM moutor C rtorr otg oubr / qurur / 25

F O R SOCI AL WORK RESE ARCH

F O R SOCI AL WORK RESE ARCH 7 TH EUROPE AN CONFERENCE F O R SOCI AL WORK RESE ARCH C h a l l e n g e s i n s o c i a l w o r k r e s e a r c h c o n f l i c t s, b a r r i e r s a n d p o s s i b i l i t i e s i n r e l a t i o n

More information

Integration Continued. Integration by Parts Solving Definite Integrals: Area Under a Curve Improper Integrals

Integration Continued. Integration by Parts Solving Definite Integrals: Area Under a Curve Improper Integrals Intgrtion Continud Intgrtion y Prts Solving Dinit Intgrls: Ar Undr Curv Impropr Intgrls Intgrtion y Prts Prticulrly usul whn you r trying to tk th intgrl o som unction tht is th product o n lgric prssion

More information

Week 7: Ch. 11 Semiconductor diodes

Week 7: Ch. 11 Semiconductor diodes Wk 7: Ch. 11 Smiconductor diods Principls o Scintilltion Countrs Smiconductor Diods bsics o smiconductors pur lmnts & dopnts 53 Mtrils ion collction, lkg currnt diod structur, pn, np junctions dpltion

More information

Section 3: Antiderivatives of Formulas

Section 3: Antiderivatives of Formulas Chptr Th Intgrl Appli Clculus 96 Sction : Antirivtivs of Formuls Now w cn put th is of rs n ntirivtivs togthr to gt wy of vluting finit intgrls tht is ct n oftn sy. To vlut finit intgrl f(t) t, w cn fin

More information

CSE 373: AVL trees. Warmup: Warmup. Interlude: Exploring the balance invariant. AVL Trees: Invariants. AVL tree invariants review

CSE 373: AVL trees. Warmup: Warmup. Interlude: Exploring the balance invariant. AVL Trees: Invariants. AVL tree invariants review rmup CSE 7: AVL trs rmup: ht is n invrint? Mihl L Friy, Jn 9, 0 ht r th AVL tr invrints, xtly? Disuss with your nighor. AVL Trs: Invrints Intrlu: Exploring th ln invrint Cor i: xtr invrint to BSTs tht

More information

Fuzzy Reasoning and Optimization Based on a Generalized Bayesian Network

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

More information

UNIT # 08 (PART - I)

UNIT # 08 (PART - I) . r. d[h d[h.5 7.5 mol L S d[o d[so UNIT # 8 (PRT - I CHEMICL INETICS EXERCISE # 6. d[ x [ x [ x. r [X[C ' [X [[B r '[ [B [C. r [NO [Cl. d[so d[h.5 5 mol L S d[nh d[nh. 5. 6. r [ [B r [x [y r' [x [y r'

More information

Elliptical motion, gravity, etc

Elliptical motion, gravity, etc FW Physics 130 G:\130 lctur\ch 13 Elliticl motion.docx g 1 of 7 11/3/010; 6:40 PM; Lst rintd 11/3/010 6:40:00 PM Fig. 1 Elliticl motion, grvity, tc minor xis mjor xis F 1 =A F =B C - D, mjor nd minor xs

More information

Lecture 6 Thermionic Engines

Lecture 6 Thermionic Engines Ltur 6 hrmioni ngins Rviw Rihrdson formul hrmioni ngins Shotty brrir nd diod pn juntion nd diod disussion.997 Copyright Gng Chn, MI For.997 Dirt Solr/hrml to ltril nrgy Convrsion WARR M. ROHSOW HA AD MASS

More information

Lecture 11 Waves in Periodic Potentials Today: Questions you should be able to address after today s lecture:

Lecture 11 Waves in Periodic Potentials Today: Questions you should be able to address after today s lecture: Lctur 11 Wvs in Priodic Potntils Tody: 1. Invrs lttic dfinition in 1D.. rphicl rprsnttion of priodic nd -priodic functions using th -xis nd invrs lttic vctors. 3. Sris solutions to th priodic potntil Hmiltonin

More information

22.615, MHD Theory of Fusion Systems Prof. Freidberg Lecture 8: Effect of a Vertical Field on Tokamak Equilibrium

22.615, MHD Theory of Fusion Systems Prof. Freidberg Lecture 8: Effect of a Vertical Field on Tokamak Equilibrium .65, MHD Thory of usion Systms Prof. ridrg Lctur 8: Effct of Vrticl ild on Tokmk Equilirium Toroidl orc lnc y Mns of Vrticl ild. Lt us riw why th rticl fild is imortnt. 3. or ry short tims, th cuum chmr

More information

12/3/12. Outline. Part 10. Graphs. Circuits. Euler paths/circuits. Euler s bridge problem (Bridges of Konigsberg Problem)

12/3/12. Outline. Part 10. Graphs. Circuits. Euler paths/circuits. Euler s bridge problem (Bridges of Konigsberg Problem) 12/3/12 Outlin Prt 10. Grphs CS 200 Algorithms n Dt Struturs Introution Trminology Implmnting Grphs Grph Trvrsls Topologil Sorting Shortst Pths Spnning Trs Minimum Spnning Trs Ciruits 1 Ciruits Cyl 2 Eulr

More information

5/9/13. Part 10. Graphs. Outline. Circuits. Introduction Terminology Implementing Graphs

5/9/13. Part 10. Graphs. Outline. Circuits. Introduction Terminology Implementing Graphs Prt 10. Grphs CS 200 Algorithms n Dt Struturs 1 Introution Trminology Implmnting Grphs Outlin Grph Trvrsls Topologil Sorting Shortst Pths Spnning Trs Minimum Spnning Trs Ciruits 2 Ciruits Cyl A spil yl

More information

Page 1. Question 19.1b Electric Charge II Question 19.2a Conductors I. ConcepTest Clicker Questions Chapter 19. Physics, 4 th Edition James S.

Page 1. Question 19.1b Electric Charge II Question 19.2a Conductors I. ConcepTest Clicker Questions Chapter 19. Physics, 4 th Edition James S. ConTst Clikr ustions Chtr 19 Physis, 4 th Eition Jms S. Wlkr ustion 19.1 Two hrg blls r rlling h othr s thy hng from th iling. Wht n you sy bout thir hrgs? Eltri Chrg I on is ositiv, th othr is ngtiv both

More information

T i t l e o f t h e w o r k : L a M a r e a Y o k o h a m a. A r t i s t : M a r i a n o P e n s o t t i ( P l a y w r i g h t, D i r e c t o r )

T i t l e o f t h e w o r k : L a M a r e a Y o k o h a m a. A r t i s t : M a r i a n o P e n s o t t i ( P l a y w r i g h t, D i r e c t o r ) v e r. E N G O u t l i n e T i t l e o f t h e w o r k : L a M a r e a Y o k o h a m a A r t i s t : M a r i a n o P e n s o t t i ( P l a y w r i g h t, D i r e c t o r ) C o n t e n t s : T h i s w o

More information

Minimum Spanning Trees

Minimum Spanning Trees Minimum Spnning Trs Minimum Spnning Trs Problm A town hs st of houss nd st of rods A rod conncts nd only houss A rod conncting houss u nd v hs rpir cost w(u, v) Gol: Rpir nough (nd no mor) rods such tht:

More information

Walk Like a Mathematician Learning Task:

Walk Like a Mathematician Learning Task: Gori Dprtmnt of Euction Wlk Lik Mthmticin Lrnin Tsk: Mtrics llow us to prform mny usful mthmticl tsks which orinrily rquir lr numbr of computtions. Som typs of problms which cn b on fficintly with mtrics

More information

Lecture contents. Bloch theorem k-vector Brillouin zone Almost free-electron model Bands Effective mass Holes. NNSE 508 EM Lecture #9

Lecture contents. Bloch theorem k-vector Brillouin zone Almost free-electron model Bands Effective mass Holes. NNSE 508 EM Lecture #9 Lctur contnts Bloch thorm -vctor Brillouin zon Almost fr-lctron modl Bnds ffctiv mss Hols Trnsltionl symmtry: Bloch thorm On-lctron Schrödingr qution ch stt cn ccommo up to lctrons: If Vr is priodic function:

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

. ffflffluary 7, 1855.

. ffflffluary 7, 1855. x B B - Y 8 B > ) - ( vv B ( v v v (B/ x< / Y 8 8 > [ x v 6 ) > ( - ) - x ( < v x { > v v q < 8 - - - 4 B ( v - / v x [ - - B v B --------- v v ( v < v v v q B v B B v?8 Y X $ v x B ( B B B B ) ( - v -

More information

Outline. Circuits. Euler paths/circuits 4/25/12. Part 10. Graphs. Euler s bridge problem (Bridges of Konigsberg Problem)

Outline. Circuits. Euler paths/circuits 4/25/12. Part 10. Graphs. Euler s bridge problem (Bridges of Konigsberg Problem) 4/25/12 Outlin Prt 10. Grphs CS 200 Algorithms n Dt Struturs Introution Trminology Implmnting Grphs Grph Trvrsls Topologil Sorting Shortst Pths Spnning Trs Minimum Spnning Trs Ciruits 1 2 Eulr s rig prolm

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

Overview. Splay trees. Balanced binary search trees. Inge Li Gørtz. Self-adjusting BST (Sleator-Tarjan 1983).

Overview. Splay trees. Balanced binary search trees. Inge Li Gørtz. Self-adjusting BST (Sleator-Tarjan 1983). Ovrvw B r rh r: R-k r -3-4 r 00 Ig L Gør Amor Dm rogrmmg Nwork fow Srg mhg Srg g Comuo gomr Irouo o NP-om Rom gorhm B r rh r -3-4 r Aow,, or 3 k r o Prf Evr h from roo o f h m gh mr h E w E R E R rgr h

More information

The pn junction: 2 Current vs Voltage (IV) characteristics

The pn junction: 2 Current vs Voltage (IV) characteristics Th pn junction: Currnt vs Voltag (V) charactristics Considr a pn junction in quilibrium with no applid xtrnal voltag: o th V E F E F V p-typ Dpltion rgion n-typ Elctron movmnt across th junction: 1. n

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

Lecture 10: PN Junction & MOS Capacitors

Lecture 10: PN Junction & MOS Capacitors Lecture 10: P Junction & MOS Cpcitors Prof. iknej eprtment of EECS Lecture Outline Review: P Junctions Therml Equilibrium P Junctions with Reverse Bis (3.3-3.6 MOS Cpcitors (3.7-3.9: Accumultion, epletion,

More information

TOPIC 5: INTEGRATION

TOPIC 5: INTEGRATION TOPIC 5: INTEGRATION. Th indfinit intgrl In mny rspcts, th oprtion of intgrtion tht w r studying hr is th invrs oprtion of drivtion. Dfinition.. Th function F is n ntidrivtiv (or primitiv) of th function

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

ECE-305: Fall 2017 Metal Oxide Semiconductor Devices

ECE-305: Fall 2017 Metal Oxide Semiconductor Devices C-305: Fall 2017 Metal Oxide Semiconductor Devices Pierret, Semiconductor Device Fundamentals (SDF) Chapters 15+16 (pp. 525-530, 563-599) Professor Peter Bermel lectrical and Computer ngineering Purdue

More information

ESCI 341 Atmospheric Thermodynamics Lesson 14 Curved Droplets and Solutions Dr. DeCaria

ESCI 341 Atmospheric Thermodynamics Lesson 14 Curved Droplets and Solutions Dr. DeCaria ESCI 41 Atmophric hrmodynamic Lon 14 Curd Dropt and Soution Dr. DCaria Rfrnc: hrmodynamic and an Introduction to hrmotatitic, Can Phyica Chmitry, Lin A hort Cour in Coud Phyic, Rogr and Yau hrmodynamic

More information

APPH 4200 Physics of Fluids

APPH 4200 Physics of Fluids APPH 42 Physics of Fluids Problem Solving and Vorticity (Ch. 5) 1.!! Quick Review 2.! Vorticity 3.! Kelvin s Theorem 4.! Examples 1 How to solve fluid problems? (Like those in textbook) Ç"Tt=l I $T1P#(

More information

CS September 2018

CS September 2018 Loil los Distriut Systms 06. Loil los Assin squn numrs to msss All ooprtin prosss n r on orr o vnts vs. physil los: rport tim o y Assum no ntrl tim sour Eh systm mintins its own lol lo No totl orrin o

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

EE1000 Project 4 Digital Volt Meter

EE1000 Project 4 Digital Volt Meter Ovrviw EE1000 Projt 4 Diitl Volt Mtr In this projt, w mk vi tht n msur volts in th rn o 0 to 4 Volts with on iit o ury. Th input is n nlo volt n th output is sinl 7-smnt iit tht tlls us wht tht input s

More information

# 1 ' 10 ' 100. Decimal point = 4 hundred. = 6 tens (or sixty) = 5 ones (or five) = 2 tenths. = 7 hundredths.

# 1 ' 10 ' 100. Decimal point = 4 hundred. = 6 tens (or sixty) = 5 ones (or five) = 2 tenths. = 7 hundredths. How os it work? Pl vlu o imls rprsnt prts o whol numr or ojt # 0 000 Tns o thousns # 000 # 00 Thousns Hunrs Tns Ons # 0 Diml point st iml pl: ' 0 # 0 on tnth n iml pl: ' 0 # 00 on hunrth r iml pl: ' 0

More information

BENEFITS OF COMPLETING COLLEGE Lesson Plan #1

BENEFITS OF COMPLETING COLLEGE Lesson Plan #1 BNFITS OF COMPLTING COLLG L P #1 Ti: Bi Ci C: Ovvi & B J Hi Py P: ( y, i i i /i) S i i v i i i ii i ii i. Li O(): ( i /k y ) I ii i i i i, i ii i y i ii ii i. Ti i iii i y i y i iky i j y jy i ki y v.

More information

2 tel

2   tel Us. Timeless, sophisticated wall decor that is classic yet modern. Our style has no limitations; from traditional to contemporar y, with global design inspiration. The attention to detail and hand- craf

More information

Lecture 27: PN Junctions

Lecture 27: PN Junctions EECS 15 Srig 5, Lecture 7 Lecture 7: P Juctio Prof. ikej ertmet of EECS EECS 15 Fll 3, Lecture 7 Prof. A. ikej iffuio iffuio occur whe there exit cocetrtio griet I the figure below, imgie tht we fill the

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

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

, between the vertical lines x a and x b. Given a demand curve, having price as a function of quantity, p f (x) at height k is the curve f ( x,

, between the vertical lines x a and x b. Given a demand curve, having price as a function of quantity, p f (x) at height k is the curve f ( x, Clculus for Businss nd Socil Scincs - Prof D Yun Finl Em Rviw vrsion 5/9/7 Chck wbsit for ny postd typos nd updts Pls rport ny typos This rviw sht contins summris of nw topics only (This rviw sht dos hv

More information

Zero Point Energy: Thermodynamic Equilibrium and Planck Radiation Law

Zero Point Energy: Thermodynamic Equilibrium and Planck Radiation Law Gaug Institut Journa Vo. No 4, Novmbr 005, Zro Point Enrgy: Thrmodynamic Equiibrium and Panck Radiation Law Novmbr, 005 vick@adnc.com Abstract: In a rcnt papr, w provd that Panck s radiation aw with zro

More information

a b c cat CAT A B C Aa Bb Cc cat cat Lesson 1 (Part 1) Verbal lesson: Capital Letters Make The Same Sound Lesson 1 (Part 1) continued...

a b c cat CAT A B C Aa Bb Cc cat cat Lesson 1 (Part 1) Verbal lesson: Capital Letters Make The Same Sound Lesson 1 (Part 1) continued... Progrssiv Printing T.M. CPITLS g 4½+ Th sy, fun (n FR!) wy to tch cpitl lttrs. ook : C o - For Kinrgrtn or First Gr (not for pr-school). - Tchs tht cpitl lttrs mk th sm souns s th littl lttrs. - Tchs th

More information

Chem 104A, Fall 2016, Midterm 1 Key

Chem 104A, Fall 2016, Midterm 1 Key hm 104A, ll 2016, Mitrm 1 Ky 1) onstruct microstt tl for p 4 configurtion. Pls numrt th ms n ml for ch lctron in ch microstt in th tl. (Us th formt ml m s. Tht is spin -½ lctron in n s oritl woul writtn

More information

Oppgavesett kap. 6 (1 av..)

Oppgavesett kap. 6 (1 av..) Oppgvstt kp. 6 (1 v..) hns.brnn@go.uio.no Problm 1 () Wht is homognous nucltion? Why dos Figur 6.2 in th book show tht w won't gt homognous nucltion in th tmosphr? ˆ Homognous nucltion crts cloud droplts

More information

PHYS ,Fall 05, Term Exam #1, Oct., 12, 2005

PHYS ,Fall 05, Term Exam #1, Oct., 12, 2005 PHYS1444-,Fall 5, Trm Exam #1, Oct., 1, 5 Nam: Kys 1. circular ring of charg of raius an a total charg Q lis in th x-y plan with its cntr at th origin. small positiv tst charg q is plac at th origin. What

More information

shhgs@wgqqh.com chinapub 2002 7 Bruc Eckl 1000 7 Bruc Eckl 1000 Th gnsis of th computr rvolution was in a machin. Th gnsis of our programming languags thus tnds to look lik that Bruc machin. 10 7 www.wgqqh.com/shhgs/tij.html

More information

Last time: introduced our first computational model the DFA.

Last time: introduced our first computational model the DFA. Lctur 7 Homwork #7: 2.2.1, 2.2.2, 2.2.3 (hnd in c nd d), Misc: Givn: M, NFA Prov: (q,xy) * (p,y) iff (q,x) * (p,) (follow proof don in clss tody) Lst tim: introducd our first computtionl modl th DFA. Tody

More information

Ayuntamiento de Madrid

Ayuntamiento de Madrid 9 v vx-xvv \ ü - v q v ó - ) q ó v Ó ü " v" > - v x -- ü ) Ü v " ñ v é - - v j? j 7 Á v ü - - v - ü

More information

ECE COMBINATIONAL BUILDING BLOCKS - INVEST 13 DECODERS AND ENCODERS

ECE COMBINATIONAL BUILDING BLOCKS - INVEST 13 DECODERS AND ENCODERS C 24 - COMBINATIONAL BUILDING BLOCKS - INVST 3 DCODS AND NCODS FALL 23 AP FLZ To o "wll" on this invstition you must not only t th riht nswrs ut must lso o nt, omplt n onis writups tht mk ovious wht h

More information

Problems (Show your work!)

Problems (Show your work!) Prctice Midter Multiple Choice 1. A. C 3. D 4. D 5. D 6. E 7. D 8. A 9. C 9. In word, 3.5*10 11 i E. 350 billion (I nubered 9 twice by itke!) 10. D 11. B 1. D 13. E 14. A 15. C 16. B 17. A 18. A 19. E

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

( ) Geometric Operations and Morphing. Geometric Transformation. Forward v.s. Inverse Mapping. I (x,y ) Image Processing - Lesson 4 IDC-CG 1

( ) Geometric Operations and Morphing. Geometric Transformation. Forward v.s. Inverse Mapping. I (x,y ) Image Processing - Lesson 4 IDC-CG 1 Img Procssing - Lsson 4 Gomtric Oprtions nd Morphing Gomtric Trnsformtion Oprtions dpnd on Pil s Coordints. Contt fr. Indpndnt of pil vlus. f f (, ) (, ) ( f (, ), f ( ) ) I(, ) I', (,) (, ) I(,) I (,

More information

The Reign of Grace and Life. Romans 5:12-21 (5:12-14, 17 focus)

The Reign of Grace and Life. Romans 5:12-21 (5:12-14, 17 focus) Th Rig of Gc d Lif Rom 5:12-21 (5:12-14, 17 focu) Th Ifluc of O h d ud Adolph H J o ph Smith B i t l m t Fid Idi Gdhi Ci Lu Gu ich N itz y l M d i M ch Nlo h Vig T L M uhmmd B m i o t T Ju Chit w I N h

More information

The Transfer Function. The Transfer Function. The Transfer Function. The Transfer Function. The Transfer Function. The Transfer Function

The Transfer Function. The Transfer Function. The Transfer Function. The Transfer Function. The Transfer Function. The Transfer Function A gnraliation of th frquncy rsons function Th convolution sum scrition of an LTI iscrt-tim systm with an imuls rsons h[n] is givn by h y [ n] [ ] x[ n ] Taing th -transforms of both sis w gt n n h n n

More information

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

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

More information

ETIKA V PROFESII PSYCHOLÓGA

ETIKA V PROFESII PSYCHOLÓGA P r a ž s k á v y s o k á š k o l a p s y c h o s o c i á l n í c h s t u d i í ETIKA V PROFESII PSYCHOLÓGA N a t á l i a S l o b o d n í k o v á v e d ú c i p r á c e : P h D r. M a r t i n S t r o u

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

MASSACHUSETTS INSTITUTE OF TECHNOLOGY HAYSTACK OBSERVATORY WESTFORD, MASSACHUSETTS

MASSACHUSETTS INSTITUTE OF TECHNOLOGY HAYSTACK OBSERVATORY WESTFORD, MASSACHUSETTS VSRT MEMO #05 MASSACHUSETTS INSTITUTE OF TECHNOLOGY HAYSTACK OBSERVATORY WESTFORD, MASSACHUSETTS 01886 Fbrury 3, 009 Tlphon: 781-981-507 Fx: 781-981-0590 To: VSRT Group From: Aln E.E. Rogrs Subjct: Simplifid

More information

Bayesian belief networks: Inference

Bayesian belief networks: Inference C 740 Knowd rprntton ctur 0 n f ntwork: nfrnc o ukrcht o@c.ptt.du 539 nnott qur C 750 chn rnn n f ntwork. 1. Drctd ccc rph Nod rndo vr nk n nk ncod ndpndnc. urr rthquk r ohnc rc C 750 chn rnn n f ntwork.

More information

Seven-Segment Display Driver

Seven-Segment Display Driver 7-Smnt Disply Drivr, Ron s in 7-Smnt Disply Drivr, Ron s in Prolm 62. 00 0 0 00 0000 000 00 000 0 000 00 0 00 00 0 0 0 000 00 0 00 BCD Diits in inry Dsin Drivr Loi 4 inputs, 7 outputs 7 mps, h with 6 on

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

sin sin 1 d r d Ae r 2

sin sin 1 d r d Ae r 2 Diffction k f c f Th Huygn-Fnl Pincil tt: Evy unobtuct oint of vfont, t givn intnt, v ouc of hicl cony vlt (ith th m funcy tht of th imy v. Th mlitu of th oticl fil t ny oint byon i th uoition of ll th

More information

1. (25pts) Answer the following questions. Justify your answers. (Use the space provided below and the next page)

1. (25pts) Answer the following questions. Justify your answers. (Use the space provided below and the next page) Phyi 6 xam#3 1. (pt) Anwr th foowing qution. Jutify your anwr. (U th pa providd bow and th nxt pag) a). Two inrtia obrvr ar in rativ motion. Whih of th foowing quantiti wi thy agr or diagr on? i) thir

More information

2014 CANADIAN SURF LIFESAVING CHAMPIONSHIPS PROGRAM

2014 CANADIAN SURF LIFESAVING CHAMPIONSHIPS PROGRAM 2014 CANAIAN URF LIFEAVING CHAMPIONHIP PROGRAM Lv Lv vy b v, w,, w Lv y w k Lv z by I Oy C (IOC) Cw G F T IOC z I L v F (IL) w v v IL N Mb Oz v b v T Lv y v by v C I Lv W C z I L v F Cw Lv C z Ry L v y

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

ELEG 413 Lecture #6. Mark Mirotznik, Ph.D. Professor The University of Delaware

ELEG 413 Lecture #6. Mark Mirotznik, Ph.D. Professor The University of Delaware LG 43 Lctur #6 Mrk Mirtnik, Ph.D. Prfssr Th Univrsity f Dlwr mil: mirtni@c.udl.du Wv Prpgtin nd Plritin TM: Trnsvrs lctrmgntic Wvs A md is prticulr fild cnfigurtin. Fr givn lctrmgntic bundry vlu prblm,

More information

Instructions for Section 1

Instructions for Section 1 Instructions for Sction 1 Choos th rspons tht is corrct for th qustion. A corrct nswr scors 1, n incorrct nswr scors 0. Mrks will not b dductd for incorrct nswrs. You should ttmpt vry qustion. No mrks

More information

A Simple Code Generator. Code generation Algorithm. Register and Address Descriptors. Example 3/31/2008. Code Generation

A Simple Code Generator. Code generation Algorithm. Register and Address Descriptors. Example 3/31/2008. Code Generation A Simpl Co Gnrtor Co Gnrtion Chptr 8 II Gnrt o for singl si lok How to us rgistrs? In most mhin rhitturs, som or ll of th oprnsmust in rgistrs Rgistrs mk goo tmporris Hol vlus tht r omput in on si lok

More information

Least Favorable Distributions to Facilitate the Design of Detection Systems with Sensors at Deterministic Locations

Least Favorable Distributions to Facilitate the Design of Detection Systems with Sensors at Deterministic Locations Last Favorabl Distributions to Facilitat th Dsign o Dtction Systms with Snsors at Dtrministic Locations Bndito J. B. Fonsca Jr. Sptmbr 204 2 Motivation Rgion o intrst (city, park, stadium 3 Motivation

More information

CSC Design and Analysis of Algorithms. Example: Change-Making Problem

CSC Design and Analysis of Algorithms. Example: Change-Making Problem CSC 801- Dsign n Anlysis of Algorithms Ltur 11 Gry Thniqu Exmpl: Chng-Mking Prolm Givn unlimit mounts of oins of nomintions 1 > > m, giv hng for mount n with th lst numr of oins Exmpl: 1 = 25, 2 =10, =

More information

LEADER TEST SERIES / JOINT PACKAGE COURSE TARGET : PRE-MEDICAL 2017

LEADER TEST SERIES / JOINT PACKAGE COURSE TARGET : PRE-MEDICAL 2017 Tst Typ : MJR émù é. n n L ù ét ù ê m ú ê ú ê ú ë û ëlû ëtû DISTC LRIG PRGRMM (cadmic Sssion : 6 7) LDR TST SRIS / JIT PCKG CURS TRGT : PRMDICL 7 TST DT : 9 4 7 SWR KY HIT SHT Tst Pattrn : IIMS Qu. 4 5

More information

Ch 1.2: Solutions of Some Differential Equations

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

More information

/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

Minimum Spanning Trees

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

More information

Framework for functional tree simulation applied to 'golden delicious' apple trees

Framework for functional tree simulation applied to 'golden delicious' apple trees Purdue University Purdue e-pubs Open Access Theses Theses and Dissertations Spring 2015 Framework for functional tree simulation applied to 'golden delicious' apple trees Marek Fiser Purdue University

More information

CSE 373: More on graphs; DFS and BFS. Michael Lee Wednesday, Feb 14, 2018

CSE 373: More on graphs; DFS and BFS. Michael Lee Wednesday, Feb 14, 2018 CSE 373: Mor on grphs; DFS n BFS Mihl L Wnsy, F 14, 2018 1 Wrmup Wrmup: Disuss with your nighor: Rmin your nighor: wht is simpl grph? Suppos w hv simpl, irt grph with x nos. Wht is th mximum numr of gs

More information

Case Study VI Answers PHA 5127 Fall 2006

Case Study VI Answers PHA 5127 Fall 2006 Qustion. A ptint is givn 250 mg immit-rls thophyllin tblt (Tblt A). A wk ltr, th sm ptint is givn 250 mg sustin-rls thophyllin tblt (Tblt B). Th tblts follow on-comprtmntl mol n hv first-orr bsorption

More information

General Neoclassical Closure Theory: Diagonalizing the Drift Kinetic Operator

General Neoclassical Closure Theory: Diagonalizing the Drift Kinetic Operator General Neoclassical Closure Theory: Diagonalizing the Drift Kinetic Operator E. D. Held eheld@cc.usu.edu Utah State University General Neoclassical Closure Theory:Diagonalizing the Drift Kinetic Operator

More information

" W I T H M C A L I C E T O " W ^ V H, 3 D N O N E ^ N D O H A - R I T Y F O R A. L L. NOBODY'S 6LAIM, deaths off Wm. itafftkon and Mrs. Kennodyb..

 W I T H M C A L I C E T O  W ^ V H, 3 D N O N E ^ N D O H A - R I T Y F O R A. L L. NOBODY'S 6LAIM, deaths off Wm. itafftkon and Mrs. Kennodyb.. ~ M M U M M «««M URZZ F)R U V Q Y \ $ R YJ UMUM!!!!!! MD M C C V 3 D D R Y F R V CUY MC MRC 2 89 39 C F C D J M R Y F! < «F C V C F :: $6 FC MC VR D UCQ C x M M R q R Y Y J C [ CM F FURUR D UDRR JD J YDR

More information

this is called an indeterninateformof-oior.fi?afleleitns derivatives can now differentiable and give 0 on on open interval containing I agree to.

this is called an indeterninateformof-oior.fi?afleleitns derivatives can now differentiable and give 0 on on open interval containing I agree to. hl sidd r L Hospitl s Rul 11/7/18 Pronouncd Loh mtims splld Non p t mtims w wnt vlut limit ii m itn ) but irst indtrnintmori?lltns indtrmint t inn gl in which cs th clld n i 9kt ti not ncssrily snsign

More information

Graphs Depth First Search

Graphs Depth First Search Grp Dpt Frt Sr SFO 337 LAX 1843 1743 1233 802 DFW ORD - 1 - Grp Sr Aort - 2 - Outo Ø By unrtnn t tur, you ou to: q L rp orn to t orr n w vrt r ovr, xpor ro n n n pt-rt r. q Cy o t pt-rt r tr,, orwr n ro

More information

V={A,B,C,D,E} E={ (A,D),(A,E),(B,D), (B,E),(C,D),(C,E)}

V={A,B,C,D,E} E={ (A,D),(A,E),(B,D), (B,E),(C,D),(C,E)} Introution Computr Sin & Enginring 423/823 Dsign n Anlysis of Algorithms Ltur 03 Elmntry Grph Algorithms (Chptr 22) Stphn Sott (Apt from Vinohnrn N. Vriym) I Grphs r strt t typs tht r pplil to numrous

More information

! " # $! % & '! , ) ( + - (. ) ( ) * + / 0 1 2 3 0 / 4 5 / 6 0 ; 8 7 < = 7 > 8 7 8 9 : Œ Š ž P P h ˆ Š ˆ Œ ˆ Š ˆ Ž Ž Ý Ü Ý Ü Ý Ž Ý ê ç è ± ¹ ¼ ¹ ä ± ¹ w ç ¹ è ¼ è Œ ¹ ± ¹ è ¹ è ä ç w ¹ ã ¼ ¹ ä ¹ ¼ ¹ ±

More information

Econometric modelling and forecasting of intraday electricity prices

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

More information

ECE 407 Computer Aided Design for Electronic Systems. Instructor: Maria K. Michael. Overview. CAD tools for multi-level logic synthesis:

ECE 407 Computer Aided Design for Electronic Systems. Instructor: Maria K. Michael. Overview. CAD tools for multi-level logic synthesis: 407 Computr Aidd Dsign for Elctronic Systms Multi-lvl Logic Synthsis Instructor: Maria K. Michal 1 Ovrviw Major Synthsis Phass Logic Synthsis: 2-lvl Multi-lvl FSM CAD tools for multi-lvl logic synthsis:

More information

1. M. (As Lovely as the Dawn) a thím níi thıíng qua as like peas is of. { p ngøn t a hên thïi. the. a ant your each. VÀng M i MıÏi TÀng

1. M. (As Lovely as the Dawn) a thím níi thıíng qua as like peas is of. { p ngøn t a hên thïi. the. a ant your each. VÀng M i MıÏi TÀng MẸ MRI (s Love s Dwn) VERSES ( = c. 76) Melody Keybd minh by binh d ng cung beu ll jes wves VıÔt s Your Un The chi u ch n ti n sflng ty cre tic s r ng tàng vøo d t l y s ginst full M oi love fr hum fil

More information

Graphs. Graphs. Graphs: Basic Terminology. Directed Graphs. Dr Papalaskari 1

Graphs. Graphs. Graphs: Basic Terminology. Directed Graphs. Dr Papalaskari 1 CSC 00 Disrt Struturs : Introuon to Grph Thory Grphs Grphs CSC 00 Disrt Struturs Villnov Univrsity Grphs r isrt struturs onsisng o vrs n gs tht onnt ths vrs. Grphs n us to mol: omputr systms/ntworks mthml

More information

Jonathan Turner Exam 2-10/28/03

Jonathan Turner Exam 2-10/28/03 CS Algorihm n Progrm Prolm Exm Soluion S Soluion Jonhn Turnr Exm //. ( poin) In h Fioni hp ruur, u wn vrx u n i prn v u ing u v i v h lry lo hil in i l m hil o om ohr vrx. Suppo w hng hi, o h ing u i prorm

More information

An Example file... log.txt

An Example file... log.txt # ' ' Start of fie & %$ " 1 - : 5? ;., B - ( * * B - ( * * F I / 0. )- +, * ( ) 8 8 7 /. 6 )- +, 5 5 3 2( 7 7 +, 6 6 9( 3 5( ) 7-0 +, => - +< ( ) )- +, 7 / +, 5 9 (. 6 )- 0 * D>. C )- +, (A :, C 0 )- +,

More information

² Ý ² ª ² Þ ² Þ Ң Þ ² Þ. ² à INTROIT. huc. per. xi, sti. su- sur. sum, cum. ia : ia, ia : am, num. VR Mi. est. lis. sci. ia, cta. ia.

² Ý ² ª ² Þ ² Þ Ң Þ ² Þ. ² à INTROIT. huc. per. xi, sti. su- sur. sum, cum. ia : ia, ia : am, num. VR Mi. est. lis. sci. ia, cta. ia. str Dy Ps. 138 R 7 r r x, t huc t m m, l : p - í pr m m num m, l l : VR M rá s f ct st sc n -, l l -. Rpt nphn s fr s VR ftr ch vrs Ps. 1. D n, pr bá m, t c g ví m : c g ví ss s nm m m, t r r r c nm m

More information

2. The Laplace Transform

2. The Laplace Transform Th aac Tranorm Inroucion Th aac ranorm i a unamna an vry uu oo or uying many nginring robm To in h aac ranorm w conir a comx variab σ, whr σ i h ra ar an i h imaginary ar or ix vau o σ an w viw a a oin

More information

Scandinavia SUMMER / GROUPS. & Beyond 2014

Scandinavia SUMMER / GROUPS. & Beyond 2014 / & 2014 25 f f Fx f 211 9 Öæ Höf æ å f 807 ø 19 øø ä 2111 1 Z F ø 1328 H f fö F H å fö ö 149 H 1 ö f Hø ø Hf 1191 2089 ä ø å F ä 1907 ä 1599 H 1796 F ø ä Jä J ( ) ø F ø 19 ö ø 15 á Å f 2286 æ f ó ä H

More information

CSE 373. Graphs 1: Concepts, Depth/Breadth-First Search reading: Weiss Ch. 9. slides created by Marty Stepp

CSE 373. Graphs 1: Concepts, Depth/Breadth-First Search reading: Weiss Ch. 9. slides created by Marty Stepp CSE 373 Grphs 1: Conpts, Dpth/Brth-First Srh ring: Wiss Ch. 9 slis rt y Mrty Stpp http://www.s.wshington.u/373/ Univrsity o Wshington, ll rights rsrv. 1 Wht is grph? 56 Tokyo Sttl Soul 128 16 30 181 140

More information

Agent-based Proof Search with Indexed Formulas

Agent-based Proof Search with Indexed Formulas 5 I7. - $ '! " gent-based Proof earch with Indexed ormulas Malte Hübner, erge utexier, and Christoph Benzmüller with thans to Voler orge aarland University, aarbrücen, Germany Calculemus 2002, Marseille,

More information

11 6'-0" 9'-8 1 2" SLOPE DN. FLOOR DRAIN W/ OIL SEPARATOR TO SEWER (TYP.) C.J. 101A SLOPE PER GRADING PLAN

11 6'-0 9'-8 1 2 SLOPE DN. FLOOR DRAIN W/ OIL SEPARATOR TO SEWER (TYP.) C.J. 101A SLOPE PER GRADING PLAN '- " '- ". '- " '-" '- " N X OO TU @ " O.. IU.. PRIMINRY RIN.. I T.. UIIN PRMIT T '-" '-" '- " '- " X OO TU @ " O.. / () YR ". I (-R: T.) X OO TU @ " O.. ONRIP OF OUMNT: This document, and the ideas and

More information

Multi-Section Coupled Line Couplers

Multi-Section Coupled Line Couplers /0/009 MultiSction Coupld Lin Couplrs /8 Multi-Sction Coupld Lin Couplrs W cn dd multipl coupld lins in sris to incrs couplr ndwidth. Figur 7.5 (p. 6) An N-sction coupld lin l W typiclly dsign th couplr

More information

GUC (Dr. Hany Hammad) 9/28/2016

GUC (Dr. Hany Hammad) 9/28/2016 U (r. Hny Hd) 9/8/06 ctur # 3 ignl flow grphs (cont.): ignl-flow grph rprsnttion of : ssiv sgl-port dvic. owr g qutions rnsducr powr g. Oprtg powr g. vill powr g. ppliction to Ntwork nlyzr lirtion. Nois

More information

4/16/2014. PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107

4/16/2014. PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107 PHY 71 Elctroynmics 1-1:5 AM MWF Olin 17 Pln for ctur 3: Spcil Topics in Elctroynmics: Elctromgntic spcts of suprconuctivity -- continu 4/14/14 PHY 71 Spring 14 -- ctur 3 1 4/14/14 PHY 71 Spring 14 --

More information