Regular languages can be expressed as regular expressions.

Size: px
Start display at page:

Download "Regular languages can be expressed as regular expressions."

Transcription

1 Regulr lnguges cn e expressed s regulr expressions. A generl nondeterministic finite utomton (GNFA) is kind of NFA such tht: There is unique strt stte nd is unique ccept stte. Every pir of nodes re connected y n rrow in ech direction, ech leled with regulr expression. Exceptions re: The strt stte hs no incoming edges. The ccept stte hs no outgoing edges. The lnguge ccepted y the GNFA is the union of ll L(R) such tht R is the regulr expression constructed y conctenting ll the regulr expressions ppering on the pth from the strt stte to the ccept stte in the order they pper. CSC527, Chpter 1, Prt 3 c 2012 Mitsunori Ogihr 12

2 An Exmple of GNFA,, Here the dshed rrows represent rrows with s the lel. CSC527, Chpter 1, Prt 3 c 2012 Mitsunori Ogihr 13

3 Proof Pln 1. Show tht ny NFA cn e converted to n equivlent GNFA. 2. Show tht ny GNFA cn e converted to regulr expression. CSC527, Chpter 1, Prt 3 c 2012 Mitsunori Ogihr 14

4 From n NFA to GNFA Given n NFA N, construct GNFA G s follows: 1. Add specil strt stte q strt nd connect it to the initil stte of N with ɛ s the lel. Connect q strt to ech remining stte with s the lel. CSC527, Chpter 1, Prt 3 c 2012 Mitsunori Ogihr 15

5 From n NFA to GNFA Given n NFA N, construct GNFA G s follows: 1. Add specil strt stte q strt nd connect it to the initil stte of N with ɛ s the lel. Connect q strt to ech remining stte with s the lel. 2. Add specil ccept stte q ccept nd connect to it from ech finl stte of N with ɛ s the lel. Connect from ech of the remining stte of N to q ccept with s the lel. CSC527, Chpter 1, Prt 3 c 2012 Mitsunori Ogihr 16

6 From n NFA to GNFA Given n NFA N, construct GNFA G s follows: 1. Add specil strt stte q strt nd connect it to the initil stte of N with ɛ s the lel. Connect q strt to ech remining stte with s the lel. 2. Add specil ccept stte q ccept nd connect to it from ech finl stte of N with ɛ s the lel. Connect from ech of the remining stte of N to q ccept with s the lel. 3. Add n rrow with s the lel wherever necessry. CSC527, Chpter 1, Prt 3 c 2012 Mitsunori Ogihr 17

7 Before nd After,, CSC527, Chpter 1, Prt 3 c 2012 Mitsunori Ogihr 18

8 Before nd After,,,, CSC527, Chpter 1, Prt 3 c 2012 Mitsunori Ogihr 19

9 Wht Hve We Done? We hve constructed our initil GNFA G so tht: (I) For ech word w in L(N), thereispth[u 0,...,u m ] in G from q strt to q ccept such tht () w is decomposed s w 1 w 2 w m ; () for ll i, 1 i m, w i is memer of the lnguge represented y the regulr expression of the rrow (u i 1,u i ). CSC527, Chpter 1, Prt 3 c 2012 Mitsunori Ogihr 20

10 Wht Hve We Done? We hve constructed our initil GNA G so tht: (I) For ech word w in L(N), thereispth[u 0,...,u m ] in G from q strt to q ccept such tht () w is decomposed s w 1 w 2 w m ; () for ll i, 1 i m, w i is memer of the lnguge represented y the regulr expression of the rrow (u i 1,u i ). (II) For ech word w tht cn e decomposed s in the ove, w is memer of L(N). CSC527, Chpter 1, Prt 3 c 2012 Mitsunori Ogihr 21

11 Convert GNFA to Regulr Expression We will remove intermedite nodes one fter the other while preserving the two properties. Repet the following until there is no stte left other thn the strt stte nd the ccept stte. Select n ritrry stte s. Produce from the current GNFA n equivlent GNFA y: For ech rrow (p, q) such tht p, q s, replce its lel with the lel corresponding to the pths [p, q], [p, s, q], [p, s, s, q], [p, s, s, s, q],... Remove s nd ll edges ttched to it. CSC527, Chpter 1, Prt 3 c 2012 Mitsunori Ogihr 22

12 Stte Elimintion,, ecomes {,}*, CSC527, Chpter 1, Prt 3 c 2012 Mitsunori Ogihr 24

13 Stte Elimintion {,}*, ecomes {,}* {,}* CSC527, Chpter 1, Prt 3 c 2012 Mitsunori Ogihr 25

14 Stte Elimintion {,}* {,}* ecomes {,}* {,}* CSC527, Chpter 1, Prt 3 c 2012 Mitsunori Ogihr 26

15 Stte Elimintion {,}* {,}* ecomes {,}* {,}* CSC527, Chpter 1, Prt 3 c 2012 Mitsunori Ogihr 27

16 Stte Elimintion {,}* {,}* ecomes {,}* {,}* CSC527, Chpter 1, Prt 3 c 2012 Mitsunori Ogihr 28

17 Stte Elimintion {,}* {,}* ecomes {,}* {,}* CSC527, Chpter 1, Prt 3 c 2012 Mitsunori Ogihr 29

18 Stte Elimintion {,}* {,}* ecomes {,}* {,}* CSC527, Chpter 1, Prt 3 c 2012 Mitsunori Ogihr 30

19 Stte Elimintion {,}* {,}* ecomes {,}* {,}* The conversion hs een completed. CSC527, Chpter 1, Prt 3 c 2012 Mitsunori Ogihr 31

Math Circles Finite Automata Question Sheet 3 (Solutions)

Math Circles Finite Automata Question Sheet 3 (Solutions) Mth Circles Finite Automt Question Sheet 3 (Solutions) Nickols Rollick nrollick@uwterloo.c Novemer 2, 28 Note: These solutions my give you the nswers to ll the prolems, ut they usully won t tell you how

More information

Kirchhoff s Rules. Kirchhoff s Laws. Kirchhoff s Rules. Kirchhoff s Laws. Practice. Understanding SPH4UW. Kirchhoff s Voltage Rule (KVR):

Kirchhoff s Rules. Kirchhoff s Laws. Kirchhoff s Rules. Kirchhoff s Laws. Practice. Understanding SPH4UW. Kirchhoff s Voltage Rule (KVR): SPH4UW Kirchhoff s ules Kirchhoff s oltge ule (K): Sum of voltge drops round loop is zero. Kirchhoff s Lws Kirchhoff s Current ule (KC): Current going in equls current coming out. Kirchhoff s ules etween

More information

Student Book SERIES. Fractions. Name

Student Book SERIES. Fractions. Name D Student Book Nme Series D Contents Topic Introducing frctions (pp. ) modelling frctions frctions of collection compring nd ordering frctions frction ingo pply Dte completed / / / / / / / / Topic Types

More information

1 tray of toffee 1 bar of toffee. 10 In the decimal number, 0 7, the 7 refers to 7 tenths or

1 tray of toffee 1 bar of toffee. 10 In the decimal number, 0 7, the 7 refers to 7 tenths or Chpter 3 Deciml Numers Do you know wht DECIMAL is? In chpter, we delt with units, s, 0 s nd 00 s. When you tke single unit nd divide it into (or 0 or 00) its, wht we then hve re deciml frctions of whole

More information

Mesh and Node Equations: More Circuits Containing Dependent Sources

Mesh and Node Equations: More Circuits Containing Dependent Sources Mesh nd Node Equtions: More Circuits Contining Dependent Sources Introduction The circuits in this set of problems ech contin single dependent source. These circuits cn be nlyzed using mesh eqution or

More information

Student Book SERIES. Patterns and Algebra. Name

Student Book SERIES. Patterns and Algebra. Name E Student Book 3 + 7 5 + 5 Nme Contents Series E Topic Ptterns nd functions (pp. ) identifying nd creting ptterns skip counting completing nd descriing ptterns predicting repeting ptterns predicting growing

More information

Geometric quantities for polar curves

Geometric quantities for polar curves Roerto s Notes on Integrl Clculus Chpter 5: Bsic pplictions of integrtion Section 10 Geometric quntities for polr curves Wht you need to know lredy: How to use integrls to compute res nd lengths of regions

More information

Sequential Logic (2) Synchronous vs Asynchronous Sequential Circuit. Clock Signal. Synchronous Sequential Circuits. FSM Overview 9/10/12

Sequential Logic (2) Synchronous vs Asynchronous Sequential Circuit. Clock Signal. Synchronous Sequential Circuits. FSM Overview 9/10/12 9//2 Sequentil (2) ENGG5 st Semester, 22 Dr. Hden So Deprtment of Electricl nd Electronic Engineering http://www.eee.hku.hk/~engg5 Snchronous vs Asnchronous Sequentil Circuit This Course snchronous Sequentil

More information

Spiral Tilings with C-curves

Spiral Tilings with C-curves Spirl Tilings with -curves Using ombintorics to Augment Trdition hris K. Plmer 19 North Albny Avenue hicgo, Illinois, 0 chris@shdowfolds.com www.shdowfolds.com Abstrct Spirl tilings used by rtisns through

More information

Aquauno Select MINUTES. (duration) FREQUENCY LED. OFF 8h AQUAUNO SELECT 5 MIN FREQUENCY. the timer is being programmed;

Aquauno Select MINUTES. (duration) FREQUENCY LED. OFF 8h AQUAUNO SELECT 5 MIN FREQUENCY. the timer is being programmed; Aquuno Select Pg. INSTALLATION. Attch the timer to cold wter tp, following these simple instructions. Do not instll the timer in pit or vlve ox, elow ground level or indoors. Do not use the timer with

More information

Dataflow Language Model. DataFlow Models. Applications of Dataflow. Dataflow Languages. Kahn process networks. A Kahn Process (1)

Dataflow Language Model. DataFlow Models. Applications of Dataflow. Dataflow Languages. Kahn process networks. A Kahn Process (1) The slides contin revisited mterils from: Peter Mrwedel, TU Dortmund Lothr Thiele, ETH Zurich Frnk Vhid, University of liforni, Riverside Dtflow Lnguge Model Drsticlly different wy of looking t computtion:

More information

(CATALYST GROUP) B"sic Electric"l Engineering

(CATALYST GROUP) Bsic Electricl Engineering (CATALYST GROUP) B"sic Electric"l Engineering 1. Kirchhoff s current l"w st"tes th"t (") net current flow "t the junction is positive (b) Hebr"ic sum of the currents meeting "t the junction is zero (c)

More information

CHAPTER 2 LITERATURE STUDY

CHAPTER 2 LITERATURE STUDY CHAPTER LITERATURE STUDY. Introduction Multipliction involves two bsic opertions: the genertion of the prtil products nd their ccumultion. Therefore, there re two possible wys to speed up the multipliction:

More information

Mixed CMOS PTL Adders

Mixed CMOS PTL Adders Anis do XXVI Congresso d SBC WCOMPA l I Workshop de Computção e Aplicções 14 20 de julho de 2006 Cmpo Grnde, MS Mixed CMOS PTL Adders Déor Mott, Reginldo d N. Tvres Engenhri em Sistems Digitis Universidde

More information

ITEC2620 Introduction to Data Structures

ITEC2620 Introduction to Data Structures /5/20 ITEC220 Introdution to Dt Strutures Leture 0 Gme Trees Two-Plyer Gmes Rules for gme define the sttespe Nodes re gme sttes Links re possile moves Build serh tree y rute fore Exmple I Exmple II A Our

More information

(1) Non-linear system

(1) Non-linear system Liner vs. non-liner systems in impednce mesurements I INTRODUCTION Electrochemicl Impednce Spectroscopy (EIS) is n interesting tool devoted to the study of liner systems. However, electrochemicl systems

More information

MAXIMUM FLOWS IN FUZZY NETWORKS WITH FUNNEL-SHAPED NODES

MAXIMUM FLOWS IN FUZZY NETWORKS WITH FUNNEL-SHAPED NODES MAXIMUM FLOWS IN FUZZY NETWORKS WITH FUNNEL-SHAPED NODES Romn V. Tyshchuk Informtion Systems Deprtment, AMI corportion, Donetsk, Ukrine E-mil: rt_science@hotmil.com 1 INTRODUCTION During the considertion

More information

Direct Current Circuits. Chapter Outline Electromotive Force 28.2 Resistors in Series and in Parallel 28.3 Kirchhoff s Rules 28.

Direct Current Circuits. Chapter Outline Electromotive Force 28.2 Resistors in Series and in Parallel 28.3 Kirchhoff s Rules 28. P U Z Z L E R If ll these pplinces were operting t one time, circuit reker would proly e tripped, preventing potentilly dngerous sitution. Wht cuses circuit reker to trip when too mny electricl devices

More information

510 Series Color Jetprinter

510 Series Color Jetprinter 510 Series Color Jetprinter User s Guide for Windows Setup trouleshooting A checklist to find solutions to common setup prolems. Printer overview Lern out the printer prts nd the printer softwre. Printing

More information

Example. Check that the Jacobian of the transformation to spherical coordinates is

Example. Check that the Jacobian of the transformation to spherical coordinates is lss, given on Feb 3, 2, for Mth 3, Winter 2 Recll tht the fctor which ppers in chnge of vrible formul when integrting is the Jcobin, which is the determinnt of mtrix of first order prtil derivtives. Exmple.

More information

EE Controls Lab #2: Implementing State-Transition Logic on a PLC

EE Controls Lab #2: Implementing State-Transition Logic on a PLC Objective: EE 44 - Controls Lb #2: Implementing Stte-rnsition Logic on PLC ssuming tht speed is not of essence, PLC's cn be used to implement stte trnsition logic. he dvntge of using PLC over using hrdwre

More information

Multi-beam antennas in a broadband wireless access system

Multi-beam antennas in a broadband wireless access system Multi-em ntenns in rodnd wireless ccess system Ulrik Engström, Mrtin Johnsson, nders Derneryd nd jörn Johnnisson ntenn Reserch Center Ericsson Reserch Ericsson SE-4 84 Mölndl Sweden E-mil: ulrik.engstrom@ericsson.com,

More information

Unit 1: Chapter 4 Roots & Powers

Unit 1: Chapter 4 Roots & Powers Unit 1: Chpter 4 Roots & Powers Big Ides Any number tht cn be written s the frction mm, nn 0, where m nd n re integers, is nn rtionl. Eponents cn be used to represent roots nd reciprocls of rtionl numbers.

More information

Digital Design. Sequential Logic Design -- Controllers. Copyright 2007 Frank Vahid

Digital Design. Sequential Logic Design -- Controllers. Copyright 2007 Frank Vahid Digitl Design Sequentil Logic Design -- Controllers Slides to ccompny the tetook Digitl Design, First Edition, y, John Wiley nd Sons Pulishers, 27. http://www.ddvhid.com Copyright 27 Instructors of courses

More information

Using Compass 3 to Program the Senso Diva Page 1

Using Compass 3 to Program the Senso Diva Page 1 Pge 1 Selection of Senso Div Instrument Style SD-CIC Custom CIC Up to 50-60dB HL Hering Loss SD-XM Custom ITE or ITC with Loctor Up to 60-70dB HL Hering Loss SD-9M BTE with Loctor Up to 70-80dB HL Hering

More information

Lecture 20. Intro to line integrals. Dan Nichols MATH 233, Spring 2018 University of Massachusetts.

Lecture 20. Intro to line integrals. Dan Nichols MATH 233, Spring 2018 University of Massachusetts. Lecture 2 Intro to line integrls Dn Nichols nichols@mth.umss.edu MATH 233, Spring 218 University of Msschusetts April 12, 218 (2) onservtive vector fields We wnt to determine if F P (x, y), Q(x, y) is

More information

Birka B22: threaded in variation

Birka B22: threaded in variation Tblet Weving: 4-Hole Ptterns Stringcrfter The chrt, fining your wy roun the pttern, n suggestions for viking style bris for rnks in the Drchenwl Acemy of Defence You will nee: 22 crs 1 repet 88 Thres:

More information

MEASURE THE CHARACTERISTIC CURVES RELEVANT TO AN NPN TRANSISTOR

MEASURE THE CHARACTERISTIC CURVES RELEVANT TO AN NPN TRANSISTOR Electricity Electronics Bipolr Trnsistors MEASURE THE HARATERISTI URVES RELEVANT TO AN NPN TRANSISTOR Mesure the input chrcteristic, i.e. the bse current IB s function of the bse emitter voltge UBE. Mesure

More information

Network Theorems. Objectives 9.1 INTRODUCTION 9.2 SUPERPOSITION THEOREM

Network Theorems. Objectives 9.1 INTRODUCTION 9.2 SUPERPOSITION THEOREM M09_BOYL3605_13_S_C09.indd Pge 359 24/11/14 1:59 PM f403 /204/PH01893/9780133923605_BOYLSTAD/BOYLSTAD_NTRO_CRCUT_ANALYSS13_S_978013... Network Theorems Ojectives Become fmilir with the superposition theorem

More information

Homework #1 due Monday at 6pm. White drop box in Student Lounge on the second floor of Cory. Tuesday labs cancelled next week

Homework #1 due Monday at 6pm. White drop box in Student Lounge on the second floor of Cory. Tuesday labs cancelled next week Announcements Homework #1 due Mondy t 6pm White drop ox in Student Lounge on the second floor of Cory Tuesdy ls cncelled next week Attend your other l slot Books on reserve in Bechtel Hmley, 2 nd nd 3

More information

Solutions to exercise 1 in ETS052 Computer Communication

Solutions to exercise 1 in ETS052 Computer Communication Solutions to exercise in TS52 Computer Communiction 23 Septemer, 23 If it occupies millisecond = 3 seconds, then second is occupied y 3 = 3 its = kps. kps If it occupies 2 microseconds = 2 6 seconds, then

More information

On the Description of Communications Between Software Components with UML

On the Description of Communications Between Software Components with UML On the Description of Communictions Between Softwre Components with UML Zhiwei An Dennis Peters Fculty of Engineering nd Applied Science Memoril University of Newfoundlnd St. John s NL A1B 3X5 zhiwei@engr.mun.c

More information

mac profile Configuration Guide Adobe Photoshop CS/CC Sawgrass Virtuoso SG400/SG800 Macintosh v

mac profile Configuration Guide Adobe Photoshop CS/CC Sawgrass Virtuoso SG400/SG800 Macintosh v mc profile Mcintosh 10.5-10.10 Configurtion Guide Adoe Photoshop CS/CC Swgrss Virtuoso SG400/SG800 v20150427 Configurtion Guide - Photoshop CS/CC Swgrss SG400/800 Before proceeding, ensure the correct

More information

Subword Permutation Instructions for Two-Dimensional Multimedia Processing in MicroSIMD Architectures

Subword Permutation Instructions for Two-Dimensional Multimedia Processing in MicroSIMD Architectures Suword Permuttion Instructions for Two-Dimensionl Multimedi Processing in MicroSIMD rchitectures Ruy. Lee Princeton University rlee@ee.princeton.edu strct MicroSIMD rchitectures incorporting suword prllelism

More information

First Round Solutions Grades 4, 5, and 6

First Round Solutions Grades 4, 5, and 6 First Round Solutions Grdes 4, 5, nd 1) There re four bsic rectngles not mde up of smller ones There re three more rectngles mde up of two smller ones ech, two rectngles mde up of three smller ones ech,

More information

Section 17.2: Line Integrals. 1 Objectives. 2 Assignments. 3 Maple Commands. 1. Compute line integrals in IR 2 and IR Read Section 17.

Section 17.2: Line Integrals. 1 Objectives. 2 Assignments. 3 Maple Commands. 1. Compute line integrals in IR 2 and IR Read Section 17. Section 7.: Line Integrls Objectives. ompute line integrls in IR nd IR 3. Assignments. Red Section 7.. Problems:,5,9,,3,7,,4 3. hllenge: 6,3,37 4. Red Section 7.3 3 Mple ommnds Mple cn ctully evlute line

More information

ET 51 EXTERIOR ROOF DRIP SIDE FINISH MOULDING INSTALLATION

ET 51 EXTERIOR ROOF DRIP SIDE FINISH MOULDING INSTALLATION EXTERIOR ROOF DRIP SIDE FINISH MOULDING 51 INSTALLATION The procedure descried elow is for the LH side. Use the sme procedure for oth the RH nd LH sides, unless otherwise specified. 1. INSTALL ROOF SIDE

More information

The Discussion of this exercise covers the following points:

The Discussion of this exercise covers the following points: Exercise 4 Bttery Chrging Methods EXERCISE OBJECTIVE When you hve completed this exercise, you will be fmilir with the different chrging methods nd chrge-control techniques commonly used when chrging Ni-MI

More information

Re: PCT Minimum Documentation: Updating of the Inventory of Patent Documents According to PCT Rule 34.1

Re: PCT Minimum Documentation: Updating of the Inventory of Patent Documents According to PCT Rule 34.1 C. SCIT 2508 00 August 10, 2000 Re: PCT Minimum Documenttion: Updting of the Inventory of Ptent Documents According to PCT Rule 34.1 Sir, Mdm, The current version of the Inventory of Ptent Documents for

More information

Translate and Classify Conic Sections

Translate and Classify Conic Sections TEKS 9.6 A.5.A, A.5.B, A.5.D, A.5.E Trnslte nd Clssif Conic Sections Before You grphed nd wrote equtions of conic sections. Now You will trnslte conic sections. Wh? So ou cn model motion, s in E. 49. Ke

More information

CS 135: Computer Architecture I. Boolean Algebra. Basic Logic Gates

CS 135: Computer Architecture I. Boolean Algebra. Basic Logic Gates Bsic Logic Gtes : Computer Architecture I Boolen Algebr Instructor: Prof. Bhgi Nrhri Dept. of Computer Science Course URL: www.ses.gwu.edu/~bhgiweb/cs35/ Digitl Logic Circuits We sw how we cn build the

More information

The Math Learning Center PO Box 12929, Salem, Oregon Math Learning Center

The Math Learning Center PO Box 12929, Salem, Oregon Math Learning Center Resource Overview Quntile Mesure: Skill or Concept: 300Q Model the concept of ddition for sums to 10. (QT N 36) Model the concept of sutrction using numers less thn or equl to 10. (QT N 37) Write ddition

More information

Sinusoidal Steady State Analysis

Sinusoidal Steady State Analysis CHAPTER 8 Snusodl Stedy Stte Anlyss 8.1. Generl Approch In the prevous chpter, we hve lerned tht the stedy-stte response of crcut to snusodl nputs cn e otned y usng phsors. In ths chpter, we present mny

More information

REVIEW, pages

REVIEW, pages REVIEW, pges 510 515 6.1 1. Point P(10, 4) is on the terminl rm of n ngle u in stndrd position. ) Determine the distnce of P from the origin. The distnce of P from the origin is r. r x 2 y 2 Substitute:

More information

9.4. ; 65. A family of curves has polar equations. ; 66. The astronomer Giovanni Cassini ( ) studied the family of curves with polar equations

9.4. ; 65. A family of curves has polar equations. ; 66. The astronomer Giovanni Cassini ( ) studied the family of curves with polar equations 54 CHAPTER 9 PARAMETRIC EQUATINS AND PLAR CRDINATES 49. r, 5. r sin 3, 5 54 Find the points on the given curve where the tngent line is horizontl or verticl. 5. r 3 cos 5. r e 53. r cos 54. r sin 55. Show

More information

Make Your Math Super Powered

Make Your Math Super Powered Mke Your Mth Super Powered: Use Gmes, Chllenges, nd Puzzles Where s the fun? Lern Mth Workshop model by prticipting in one nd explore fun nocost/low-cost gmes nd puzzles tht you cn esily bring into your

More information

Series. Teacher. Numbers

Series. Teacher. Numbers Series B Techer Copyright 2009 3P Lerning. All rights reserved. First edition printed 2009 in Austrli. A ctlogue record for this book is vilble from 3P Lerning Ltd. ISBN 978-1-921860-17-1 Ownership of

More information

Energy Harvesting Two-Way Channels With Decoding and Processing Costs

Energy Harvesting Two-Way Channels With Decoding and Processing Costs IEEE TRANSACTIONS ON GREEN COMMUNICATIONS AND NETWORKING, VOL., NO., MARCH 07 3 Energy Hrvesting Two-Wy Chnnels With Decoding nd Processing Costs Ahmed Arf, Student Member, IEEE, Abdulrhmn Bknin, Student

More information

Abacaba-Dabacaba! by Michael Naylor Western Washington University

Abacaba-Dabacaba! by Michael Naylor Western Washington University Abcb-Dbcb! by Michel Nylor Western Wshington University The Abcb structure shows up in n mzing vriety of plces. This rticle explores 10 surprising ides which ll shre this pttern, pth tht will tke us through

More information

SOLVING TRIANGLES USING THE SINE AND COSINE RULES

SOLVING TRIANGLES USING THE SINE AND COSINE RULES Mthemtics Revision Guides - Solving Generl Tringles - Sine nd Cosine Rules Pge 1 of 17 M.K. HOME TUITION Mthemtics Revision Guides Level: GCSE Higher Tier SOLVING TRIANGLES USING THE SINE AND COSINE RULES

More information

ASSEMBLY INSTRUCTIONS

ASSEMBLY INSTRUCTIONS ASSEMBLY INSTRUCTIONS Multi Line 6 x8 255x193x203cm / 100 1 /2 x76 x80 Poly-Tex, Inc. PO Box 458 27725 Dnville Avenue Cstle Rock, MN 55010 We Site: www.poly-tex.com English - 69717 Hoy Greenhouse Service

More information

Discontinued AN6262N, AN6263N. (planed maintenance type, maintenance type, planed discontinued typed, discontinued type)

Discontinued AN6262N, AN6263N. (planed maintenance type, maintenance type, planed discontinued typed, discontinued type) ICs for Cssette, Cssette Deck ANN, ANN Puse Detection s of Rdio Cssette, Cssette Deck Overview The ANN nd the ANN re the puse detection integrted circuits which select the progrm on the cssette tpe. In

More information

Algorithms for Memory Hierarchies Lecture 14

Algorithms for Memory Hierarchies Lecture 14 Algorithms for emory Hierrchies Lecture 4 Lecturer: Nodri Sitchinv Scribe: ichel Hmnn Prllelism nd Cche Obliviousness The combintion of prllelism nd cche obliviousness is n ongoing topic of reserch, in

More information

REVIEW QUESTIONS. Figure For Review Question Figure For Review Question Figure For Review Question 10.2.

REVIEW QUESTIONS. Figure For Review Question Figure For Review Question Figure For Review Question 10.2. HAPTE 0 Sinusoidl Stedy-Stte Anlysis 42 EVIEW QUESTIONS 0. The voltge cross the cpcitor in Fig. 0.43 is: () 5 0 V () 7.07 45 V (c) 7.07 45 V (d) 5 45 V Ω 0.5 efer to the circuit in Fig. 0.47 nd oserve

More information

A Development of Earthing-Resistance-Estimation Instrument

A Development of Earthing-Resistance-Estimation Instrument A Development of Erthing-Resistnce-Estimtion Instrument HITOSHI KIJIMA Abstrct: - Whenever erth construction work is done, the implnted number nd depth of electrodes hve to be estimted in order to obtin

More information

Annabelle Dollhouse. Assembly Instructions. 37 x2

Annabelle Dollhouse. Assembly Instructions. 37 x2 HRWRE. Cross owel olt x 13 pcs 1 11/16 in / 43 mm. Cross owel Nut x 13 pcs nnabelle ollhouse PRTS LIST: 1 ssembly Instructions 2 3 please visit 4 C. Hex olt x 4 pcs 1 9/16 in / 40 mm. Screw x 52 pcs 13/16

More information

PROGRAMMING MANUAL MTMA/01 MTMV/01 FB00329-EN

PROGRAMMING MANUAL MTMA/01 MTMV/01 FB00329-EN RMMING MNUL MTM/01 MTMV/01 FB00329-EN Generl precutions Red the instructions crefully efore eginning the instlltion nd crry out the ctions s specified y the mnufcturer. The instlltion, progrmming, commissioning

More information

ECE 274 Digital Logic

ECE 274 Digital Logic ECE - Digitl Logic (Textbook - Required) ECE Digitl Logic Instructor: Romn Lysecky, rlysecky@ece.rizon.edu Office Hours: TBA, ECE F Lecture: MWF :-: PM, ILC Course Website: http://www.ece.rizon.edu/~ece/

More information

A COMPARISON OF CIRCUIT IMPLEMENTATIONS FROM A SECURITY PERSPECTIVE

A COMPARISON OF CIRCUIT IMPLEMENTATIONS FROM A SECURITY PERSPECTIVE A COMPARISON OF CIRCUIT IMPLEMENTATIONS FROM A SECURITY PERSPECTIVE Mster Thesis Division of Electronic Devices Deprtment of Electricl Engineering Linköping University y Timmy Sundström LITH-ISY-EX--05/3698--SE

More information

arxiv: v1 [cs.cc] 29 Mar 2012

arxiv: v1 [cs.cc] 29 Mar 2012 Solving Mhjong Solitire ords with peeking Michiel de Bondt rxiv:1203.6559v1 [cs.cc] 29 Mr 2012 Decemer 22, 2013 Astrct We first prove tht solving Mhjong Solitire ords with peeking is NPcomplete, even if

More information

On Decidability of LTL Model Checking for Process Rewrite Systems

On Decidability of LTL Model Checking for Process Rewrite Systems On Decidbility of LTL Model Checking for Process Rewrite Systems Lur Bozzelli 1, Mojmír Křetínský 2, Vojtěch Řehák 2, nd Jn Strejček 2 1 Diprtimento di Mtemtic e Aplliczioni, Università degli Studi di

More information

Experiment 3: The research of Thevenin theorem

Experiment 3: The research of Thevenin theorem Experiment 3: The reserch of Thevenin theorem 1. Purpose ) Vlidte Thevenin theorem; ) Mster the methods to mesure the equivlent prmeters of liner twoterminl ctive. c) Study the conditions of the mximum

More information

Patterns and Relationships

Patterns and Relationships Series Techer Ptterns nd Reltionships opyright 009 3P Lerning. All rights reserved. First edition printed 009 in Austrli. A ctlogue record for this ook is ville from 3P Lerning Ltd. ISBN 978-1-91860-3-4

More information

CAL. NX15 DUO-DISPLAY QUARTZ

CAL. NX15 DUO-DISPLAY QUARTZ L. NX15 UO-ISPLY QURTZ l nlogue time disply l igitl time nd clendr l hronogrph l Tchymeter l t recll function l lrm l Illuminting light (Electroluminescent pnel) ENGLISH Illuminting light (TIME/LENR mode

More information

Math 116 Calculus II

Math 116 Calculus II Mth 6 Clculus II Contents 7 Additionl topics in Integrtion 7. Integrtion by prts..................................... 7.4 Numericl Integrtion.................................... 7 7.5 Improper Integrl......................................

More information

General Instructions 03HEL1010DDFW-V3. Please retain product label and instructions for future reference. 10x10 Helios Summer House

General Instructions 03HEL1010DDFW-V3. Please retain product label and instructions for future reference. 10x10 Helios Summer House Generl Instructions Plese retin product lel nd instructions for future reference 03HEL1010DDFW-V3 x2 All uilding s should e erected y two dults Winter = High Moisture = Expnsion Summer = Low Moisture =

More information

GEI E INSTRUCTIONS M ULTI-CONTACT AUXILIARY RELAYS TYPE HFA53. GE Protection and Control 205 Great Valley Parkway Malvern, PA

GEI E INSTRUCTIONS M ULTI-CONTACT AUXILIARY RELAYS TYPE HFA53. GE Protection and Control 205 Great Valley Parkway Malvern, PA GEI-6871 9E INSTRUCTIONS M ULTI-CONTACT AUXILIARY RELAYS TYPE HFA53 GE Protection nd Control 205 Gret Vlley Prkwy Mlvern, PA 19355-1337 2 for Semi-flush Mounting (Front View) Connected Rely with Flnge

More information

TUR DOORS SHOWER DOORS

TUR DOORS SHOWER DOORS TUR DOORS SHOWER DOORS INSTALLATION INSTRUCTIONS TUB DOORS: LBTDB6062 SHOWER DOORS: LBSDB4876 LBSDB6076 VERSION: 3.2 PREPARATION FOR INSTALLATION TUB DOORS SHOWER DOORS PREPARATION FOR INSTALLATION READ

More information

CS2204 DIGITAL LOGIC & STATE MACHINE DESIGN SPRING 2005

CS2204 DIGITAL LOGIC & STATE MACHINE DESIGN SPRING 2005 CS2204 DIGITAL LOGIC & STATE MACHINE DESIGN SPRING 2005 EXPERIMENT 1 FUNDAMENTALS 1. GOALS : Lern how to develop cr lrm digitl circuit during which the following re introduced : CS2204 l fundmentls, nd

More information

Exercise 1-1. The Sine Wave EXERCISE OBJECTIVE DISCUSSION OUTLINE. Relationship between a rotating phasor and a sine wave DISCUSSION

Exercise 1-1. The Sine Wave EXERCISE OBJECTIVE DISCUSSION OUTLINE. Relationship between a rotating phasor and a sine wave DISCUSSION Exercise 1-1 The Sine Wve EXERCISE OBJECTIVE When you hve completed this exercise, you will be fmilir with the notion of sine wve nd how it cn be expressed s phsor rotting round the center of circle. You

More information

Patterns and Algebra

Patterns and Algebra Student Book Series D Mthletis Instnt Workooks Copyright Series D Contents Topi Ptterns nd funtions identifying nd reting ptterns skip ounting ompleting nd desriing ptterns numer ptterns in tles growing

More information

MATH 118 PROBLEM SET 6

MATH 118 PROBLEM SET 6 MATH 118 PROBLEM SET 6 WASEEM LUTFI, GABRIEL MATSON, AND AMY PIRCHER Section 1 #16: Show tht if is qudrtic residue modulo m, nd b 1 (mod m, then b is lso qudrtic residue Then rove tht the roduct of the

More information

INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad

INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad Hll Ticket No Question Pper Code: AEC009 INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigl, Hyderd - 500 043 MODEL QUESTION PAPER Four Yer B.Tech V Semester End Exmintions, Novemer - 2018 Regultions:

More information

Analysis of circuits containing active elements by using modified T - graphs

Analysis of circuits containing active elements by using modified T - graphs Anlsis of circuits contining ctive elements using modified T - grphs DALBO BOLEK *) nd EA BOLKOA**) Deprtment of Telecommunictions *) dioelectronics **) Brno Universit of Technolog Purknov 8, 6 Brno CECH

More information

ECE 274 Digital Logic. Digital Design. Datapath Components Shifters, Comparators, Counters, Multipliers Digital Design

ECE 274 Digital Logic. Digital Design. Datapath Components Shifters, Comparators, Counters, Multipliers Digital Design ECE 27 Digitl Logic Shifters, Comprtors, Counters, Multipliers Digitl Design..7 Digitl Design Chpter : Slides to ccompny the textbook Digitl Design, First Edition, by Frnk Vhid, John Wiley nd Sons Publishers,

More information

Elettra Evolution OK! OK! b. User manual

Elettra Evolution OK! OK! b. User manual Elettr Evolution User mnul Pg. 1 INSTALLING THE SOLENOID VALVE. The progrmmle solenoi vlve is fully wtertight n will funtion even if instlle permnently uner wter t epth of up to one metre (IP68 ingress

More information

METHOD OF LOCATION USING SIGNALS OF UNKNOWN ORIGIN. Inventor: Brian L. Baskin

METHOD OF LOCATION USING SIGNALS OF UNKNOWN ORIGIN. Inventor: Brian L. Baskin METHOD OF LOCATION USING SIGNALS OF UNKNOWN ORIGIN Inventor: Brin L. Bskin 1 ABSTRACT The present invention encompsses method of loction comprising: using plurlity of signl trnsceivers to receive one or

More information

Question 1 TELE4353. Question 1, cnt d. What is CDMA? Direct Sequence Spread Spectrum System Model. What is direct sequence CDMA?

Question 1 TELE4353. Question 1, cnt d. What is CDMA? Direct Sequence Spread Spectrum System Model. What is direct sequence CDMA? TELE45 Mobie nd Steite Couniction Systes Tutori 5 week - S 4 Question A ceur obie couniction syste is using direct sequence code diision utipe ccess CDMA technique with coherent binry phse shift keying

More information

Joanna Towler, Roading Engineer, Professional Services, NZTA National Office Dave Bates, Operations Manager, NZTA National Office

Joanna Towler, Roading Engineer, Professional Services, NZTA National Office Dave Bates, Operations Manager, NZTA National Office . TECHNICA MEMOANDM To Cc repred By Endorsed By NZTA Network Mngement Consultnts nd Contrctors NZTA egionl Opertions Mngers nd Are Mngers Dve Btes, Opertions Mnger, NZTA Ntionl Office Jonn Towler, oding

More information

Domination and Independence on Square Chessboard

Domination and Independence on Square Chessboard Engineering nd Technology Journl Vol. 5, Prt, No. 1, 017 A.A. Omrn Deprtment of Mthemtics, College of Eduction for Pure Science, University of bylon, bylon, Irq pure.hmed.omrn@uobby lon.edu.iq Domintion

More information

How to remove BRNS/BRFS series from a PWB

How to remove BRNS/BRFS series from a PWB Applictions mnul for BRNS/BRFS series How to remove BRNS/BRFS series from PWB VER1.0 Applictions Mnul BRNS/BRFS series Pge 1. Overview 1-1 1.1 Overview 1-1 2. Preprtion 2-1 2.1 2.2 2.3 Removl tool Adhesive

More information

Topic 20: Huffman Coding

Topic 20: Huffman Coding Topic 0: Huffmn Coding The uthor should gze t Noh, nd... lern, s they did in the Ark, to crowd gret del of mtter into very smll compss. Sydney Smith, dinburgh Review Agend ncoding Compression Huffmn Coding

More information

Fubini for continuous functions over intervals

Fubini for continuous functions over intervals Fuini for ontinuous funtions over intervls We first prove the following theorem for ontinuous funtions. Theorem. Let f(x) e ontinuous on ompt intervl =[, [,. Then [, [, [ [ f(x, y)(x, y) = f(x, y)y x =

More information

SPECIAL EDITION. Spring 2012 Ezine. where crafty is contagious

SPECIAL EDITION. Spring 2012 Ezine.   where crafty is contagious Spring 2012 Ezine SPECIAL EDITION www.clubchiccircle.com where crfty is contgious shmrock sttionery It is so esy to mke these festive homemde crds! Mke homemde stmp from the end of n pencil erser. With

More information

Algebra Practice. Dr. Barbara Sandall, Ed.D., and Travis Olson, M.S.

Algebra Practice. Dr. Barbara Sandall, Ed.D., and Travis Olson, M.S. By Dr. Brr Sndll, Ed.D., Dr. Melfried Olson, Ed.D., nd Trvis Olson, M.S. COPYRIGHT 2006 Mrk Twin Medi, Inc. ISBN 978-1-58037-754-6 Printing No. 404042-EB Mrk Twin Medi, Inc., Pulishers Distriuted y Crson-Dellos

More information

Module 9. DC Machines. Version 2 EE IIT, Kharagpur

Module 9. DC Machines. Version 2 EE IIT, Kharagpur Module 9 DC Mchines Version EE IIT, Khrgpur esson 40 osses, Efficiency nd Testing of D.C. Mchines Version EE IIT, Khrgpur Contents 40 osses, efficiency nd testing of D.C. mchines (esson-40) 4 40.1 Gols

More information

001CK CK0012 FR-001CK0013 FR EN English

001CK CK0012 FR-001CK0013 FR EN English AUDIO ENTRY KIT FA00959EN 001DC00AC 001DC0EARY 7 10 001CS1PLCO INSTALLATION MANUAL 001CK0009 001CK001 FR001CK0013 FR EN English Generl Notes A Red the instructions crefully before beginning the instlltion

More information

Fitting & User Instructions

Fitting & User Instructions Issue 03 Alexnder Universl Furniture Risers Note: These frmes require the ddition of n ttchment. (See pges 4 - ) Bse Frme Mrk Bse Frme Mrk Fitting & User Instructions These instructions pply to the rising

More information

Operation Manual. Product Code 885-V55. Computerized Embroidery Machine GETTING READY EMBROIDERY APPENDIX

Operation Manual. Product Code 885-V55. Computerized Embroidery Machine GETTING READY EMBROIDERY APPENDIX Computerized Emroidery Mchine Opertion Mnul Product Code 885-V55 GETTING READY EMBROIDERY APPENDIX Be sure to red this document efore using the mchine. We recommend tht you keep this document nery for

More information

(1) Primary Trigonometric Ratios (SOH CAH TOA): Given a right triangle OPQ with acute angle, we have the following trig ratios: ADJ

(1) Primary Trigonometric Ratios (SOH CAH TOA): Given a right triangle OPQ with acute angle, we have the following trig ratios: ADJ Tringles nd Trigonometry Prepred y: S diyy Hendrikson Nme: Dte: Suppose we were sked to solve the following tringles: Notie tht eh tringle hs missing informtion, whih inludes side lengths nd ngles. When

More information

ECE 274 Digital Logic Fall 2009 Digital Design

ECE 274 Digital Logic Fall 2009 Digital Design igitl Logic ll igitl esign MW -:PM, IL Romn Lysecky, rlysecky@ece.rizon.edu http://www.ece.rizon.edu/~ece hpter : Introduction Slides to ccompny the textbook igitl esign, irst dition, by rnk Vhid, John

More information

Proposed Cable Tables for SAS2

Proposed Cable Tables for SAS2 Tle 50 Requirements for internl le ssemlies using SASDrive onnetors n kplnes. Requirement, Units 1,5 Gps 3Gps 6 Gps Bulk le or kplne:, Differentil impene ohm 100 ± 10 100 g Common-moe impene ohm 32,5 ±

More information

SAMPLING S Y S T E M S. w w w. s a m p l i n g. c o m. Label Solutions. Labels for Production and Quality Control use

SAMPLING S Y S T E M S. w w w. s a m p l i n g. c o m. Label Solutions. Labels for Production and Quality Control use w w w. s m p l i n g. c o m Lbel Solutions 2017 Lbels for Production nd use SYSTEMS Which type lbel is right for me? Smpling Systems fer two types stndrd lbel bcking: Ultr Ahesive Lbels PhrmLbels 1. Ultr

More information

Misty. Sudnow Dot Songs

Misty. Sudnow Dot Songs Sudnow Dot Songs isty T The Dot Song is nottionl system tht depicts voiced chords in wy where the non-music reder cn find these firly redily. But the Dot Song is not intended be red, not s sight reder

More information

Skills Practice Skills Practice for Lesson 4.1

Skills Practice Skills Practice for Lesson 4.1 Skills Prctice Skills Prctice for Lesson.1 Nme Dte Tiling Bthroom Wll Simplifying Squre Root Expressions Vocbulry Mtch ech definition to its corresponding term. 1. n expression tht involves root. rdicnd

More information

ABOUT THIS MANUAL ABOUT THIS MANUAL

ABOUT THIS MANUAL ABOUT THIS MANUAL ABOUT THIS MANUAL ABOUT THIS MANUAL This mnul provides detils on IQ Designer, which is ville with the upgrde. Mke sure tht the mchine hs een upgrded to the most recent version. When you find this icon

More information

Passive and Active DC Breakers in the Three Gorges-Changzhou HVDC Project

Passive and Active DC Breakers in the Three Gorges-Changzhou HVDC Project Pssive nd Active DC Brekers in the Three Gorges-Chngzhou HVDC Project Dg Andersson, Dr, nd Anders Henriksson, B.Sc.E.E, ABB, Sweden explined below) re Abstrct--A new type of DC breker, bsed on stndrd SF

More information

Operation Manual. Addendum. Embroidery Machine. Product Code: 884-T13

Operation Manual. Addendum. Embroidery Machine. Product Code: 884-T13 Emroidery Mchine Opertion Mnul Addendum Product Code: 884-T13 Be sure to red this document efore using the mchine. We recommend tht you keep this document nery for future reference. ABOUT THIS MANUAL ABOUT

More information

& Y Connected resistors, Light emitting diode.

& Y Connected resistors, Light emitting diode. & Y Connected resistors, Light emitting diode. Experiment # 02 Ojectives: To get some hndson experience with the physicl instruments. To investigte the equivlent resistors, nd Y connected resistors, nd

More information

Interference Cancellation Method without Feedback Amount for Three Users Interference Channel

Interference Cancellation Method without Feedback Amount for Three Users Interference Channel Open Access Librry Journl 07, Volume, e57 ISSN Online: -97 ISSN Print: -9705 Interference Cncelltion Method without Feedbc Amount for Three Users Interference Chnnel Xini Tin, otin Zhng, Wenie Ji School

More information