AMC AMS AMR ACS ACR ASR MSR MCR MCS CRS
|
|
- Joella Newman
- 6 years ago
- Views:
Transcription
1 Sectio 6.5: Combiatios Example Recall our five frieds, Ala, Cassie, Maggie, Seth ad Roger from the example at the begiig of the previous sectio. The have wo tickets for a cocert i Chicago ad everybody would like to go. However, they caot afford two more tickets ad must choose a group of three people from the five to go to the cocert. Ala decides to make a fair decisio o who gets the tickets, by writig the iitials of each possible group of idividuals from the 5 frieds o a separate piece of paper ad puttig all of the pieces of paper i a hat. He will the draw oe piece of paper from the hat at radom to select the lucky group. The order i which the ames of the idividuals is writte is irrelevat. The complete list of the 0 possible groups of size three from the five frieds is show below: AMC AMS AMR ACS ACR ASR MSR MCR MCS CRS Note that for every group o this list, it appears 6! times o the list of possible photographs of three of the five frieds that we saw i the last lecture: AMC AMS AMR ACS ACR ACM ASM ARM ASC ARC CAM MAS MAR CAS CAR CMA MSA MRA CSA CRA M AC SAM RAM SAC RCA MCA SMA RMA SCA RAC ASR MSR MCR MCS CRS ARS MRS MRC MSC CSR SAR SM R RM C CSM RCS SRA SRM RCM CM S RSC RSA M RS CRM SM C SCR RAS M SR CM R SCM SRC Its easy to see that the reaso for this is because every group of three idividuals ca be permuted i! 6 ways to create! differet photographs. Whe selectig a group from the hat to receive the tickets, the order i which the ames of the idividuals appear o the slip of paper is irrelevat. The group AMC is the same as the group CAM, so oly oe of the! permutatios of this group should be i the hat for selectio. Thus the umber of ways to select a subset of three idividuals from the five frieds to receive the three tickets is 60! P (5, )! 5!!!. Ala has listed all Combiatios of the five frieds, take at a time to put i the hat. The umber of such combiatios, which is 0, is deoted by C(5, ). I terms of set theory he has listed all subsets of objects i the set of 5 objects {A, B, C, D, E}. Defiitio A Combiatio of objects take R at a time is a selectio (Sample, Team) of R objects take from amog the. The order i which the objects are chose does ot matter. The key characteristics of a combiatio are. A combiatio selects elemets from a sigle set.. Repetitios are ot allowed.
2 . The order i which the selected elemets are arraged is ot sigificat. The umber of such combiatios is deoted by the symbol C(, R) or ( R). We have C(, R) R Example Evaluate C(0, ). ( ) ( R ) R (R ) (R ) P (, R) R!! R!( R)! Example(Choosig a team) How may ways are there to choose a team of 7 people from a class of 40 studets i order to make a team for Bookstore Basketball? Example(Roud Robis) I a soccer touramet with 5 teams, each team must play each other team exactly oce. How may matches must be played? Example(Poker Hads) A poker had cosists of five cards dealt at radom from a stadard deck of 5. How may differet poker hads are possible? Example A stadard deck of cards cosists of hearts, diamods, spades ad clubs. How may poker hads cosist etirely of clubs? Example How may poker hads cosist of red cards oly? Example How may poker hads cosist of kigs ad quees? Example (Quality Cotrol) A factory produces lightbulbs ad ships them i boxes of 50 to their customers. A quality cotrol ispector checks a box by takig out a sample of size 5 ad checkig if ay of those 5 bulbs are defective. If at least oe defective bulb is foud the box is ot shipped, otherwise the box is shipped. How may differet samples of size five ca be take from a box of 50 bulbs? Example If a box of 50 lightbulbs cotais 0 defective lightbulbs ad 0 o-defective lightbulbs, how may samples of size 5 ca be draw from the box so that all of the lightbulbs i the sample are good?
3 Problems usig a mixture of coutig priciples Example How may poker hads have at least two kigs? Example I the Notre Dame Jugglig club, there are 5 graduate studets ad 7 udergraduate studets. All would like to atted a jugglig performace i Chicago. However, they oly have fudig from Studet Activities for 5 people to atted. The fudig will oly apply if at least three of those attedig are udergraduates. I how may ways ca 5 people be chose to go to the performace so that the fudig will be grated? Example Gio s Pizza Parlor offers three types of crust, types of cheese, 4 vegetable toppigs ad meat toppigs. Pat always chooses oe type of crust, oe type of cheese, vegetable toppigs ad two meat toppigs. how may differet pizzas ca Pat create? Example How may subsets of a set of size 5 have at least 4 elemets? Special Cases ad Formulas It is immediate from our formula C(, R)! R!( R)! that C(, R) C(, R). Thus C(0, ) C(0, 7) ad C(00, 98) C(00, ) etc... By defiitio (for coveiece) 0! ad C(, 0), which makes sese sice there is exactly oe subset with zero elemets i every set. C(, )! ( )!, which makes sese sice there are exactly subsets with oe elemet i a set with elemets. C(, ) C(, 0) which makes sese because... (fiish the setece).
4 The Biomial Theorem The Biomial theorem says that for ay positive iteger ad two umbers x ad y, we have (x y) x 0 x y For example if 4, the the theorem says that ( ) ( ) 4 4 (x y) 4 x 4 x y 0 ( ) ( ) x y xy x y xy y 4. 4 y. Example (a) Check that the above equatio is true for 4, x, y. (b) Check that the above equatio is true for 4, x, y. Thigs to Note 4 4 (X Y) 4 ( 4 0)x 4 ( 4 )x y ( 4 )x y ( 4 )x y ( 4 4)y 4 Symmetry C(4, ) C(4, ) Powers of x ad y are switched Note how the powers relate to the lower umbers i the coefficiets. Note how the powers decrease o the x s ad icrease o the y s as we move from left to right. Note how the powers i each term of the expressio add to. Note the symmetry i the expasio. ( 4 ) x y is a Term of the expressio ad ( 4 ) is the coefficiet of that term. 4
5 Note that the sum of the coefficiets of the terms of the expasio of (x y) 4 is equal to the total umber of subsets oe ca make usig a set of size 4. Settig x ad y i the above equatio, we get the formula: 4 0 Applyig the same proof to the geeral case, we get the formula: 0 4 C(, 0) C(, ) C(, ) C(, )... C(, ) for ay coutig umber. Thus the umber of subsets of a set with elemets is. Example A set has te elemets. How may of its subsets have at least two elemets? Example How may tips could you leave at a restaurat, if you have a half-dollar, a oe dollar coi, a two dollar ote ad a five dollar ote? 5
6 Extra: Taxi Cab Geometry revisited. Recall that the umber of taxi cab routes (always travelig south or east) from A to B is the umber of differet rearragemets of the sequece SSSSEEEEE which is 9! 4!5! C(9, 4) C(9, 5). The sequece SSSSEEEEE is show i red ad the sequece ESSEEESES i blue. A Ca you thik of ay reaso why the umber of routes should equal the umber of ways to choose 4 objects from a set of 9 objects? B 6
AMC AMS AMR ACS ACR ASR MSR MCR MCS CRS
Sectio 6.5: Combiatios Example Recall our five frieds, Ala, Cassie, Maggie, Seth ad Roger from the example at the begiig of the previous sectio. The have wo tickets for a cocert i Chicago ad everybody
More informationCombinations AMC AMS AMR ACS ACR ASR MSR MCR MCS CRS
Example Recall our five friends, Alan, Cassie, Maggie, Seth and Roger from the example at the beginning of the previous section. They have won 3 tickets for a concert in Chicago and everybody would like
More informationAMC AMS AMR ACS ACR ASR MSR MCR MCS CRS
Combinations Example Five friends, Alan, Cassie, Maggie, Seth and Roger, have won 3 tickets for a concert. They can t afford two more tickets. In how many ways can they choose three people from among the
More informationCombinations Example Five friends, Alan, Cassie, Maggie, Seth and Roger, have won 3 tickets for a concert. They can t afford two more tickets.
Combinations Example Five friends, Alan, Cassie, Maggie, Seth and Roger, have won 3 tickets for a concert. They can t afford two more tickets. In how many ways can they choose three people from among the
More informationP (5, 3) and as we have seen P (5, 3) = 60.
Section 6.4: Permutations In this section we study a useful formula for the number of permutations of n objects taken k at a time. It is really just a special application of the multiplication principle,
More informationCombinatorics. Chapter Permutations. Reading questions. Counting Problems. Counting Technique: The Product Rule
Chapter 3 Combiatorics 3.1 Permutatios Readig questios 1. Defie what a permutatio is i your ow words. 2. What is a fixed poit i a permutatio? 3. What do we assume about mutual disjoitedess whe creatig
More informationPERMUTATION AND COMBINATION
MPC 1 PERMUTATION AND COMBINATION Syllabus : Fudametal priciples of coutig; Permutatio as a arragemet ad combiatio as selectio, Meaig of P(, r) ad C(, r). Simple applicatios. Permutatios are arragemets
More information8. Combinatorial Structures
Virtual Laboratories > 0. Foudatios > 1 2 3 4 5 6 7 8 9 8. Combiatorial Structures The purpose of this sectio is to study several combiatorial structures that are of basic importace i probability. Permutatios
More informationPERMUTATIONS AND COMBINATIONS
www.sakshieducatio.com PERMUTATIONS AND COMBINATIONS OBJECTIVE PROBLEMS. There are parcels ad 5 post-offices. I how may differet ways the registratio of parcel ca be made 5 (a) 0 (b) 5 (c) 5 (d) 5. I how
More informationWe often find the probability of an event by counting the number of elements in a simple sample space.
outig Methods We ofte fid the probability of a evet by coutig the umber of elemets i a simple sample space. Basic methods of coutig are: Permutatios ombiatios Permutatio A arragemet of objects i a defiite
More information}, how many different strings of length n 1 exist? }, how many different strings of length n 2 exist that contain at least one a 1
1. [5] Give sets A ad B, each of cardiality 1, how may fuctios map A i a oe-tooe fashio oto B? 2. [5] a. Give the set of r symbols { a 1, a 2,..., a r }, how may differet strigs of legth 1 exist? [5]b.
More information7. Counting Measure. Definitions and Basic Properties
Virtual Laboratories > 0. Foudatios > 1 2 3 4 5 6 7 8 9 7. Coutig Measure Defiitios ad Basic Properties Suppose that S is a fiite set. If A S the the cardiality of A is the umber of elemets i A, ad is
More informationPermutation Enumeration
RMT 2012 Power Roud Rubric February 18, 2012 Permutatio Eumeratio 1 (a List all permutatios of {1, 2, 3} (b Give a expressio for the umber of permutatios of {1, 2, 3,, } i terms of Compute the umber for
More informationCh 9 Sequences, Series, and Probability
Ch 9 Sequeces, Series, ad Probability Have you ever bee to a casio ad played blackjack? It is the oly game i the casio that you ca wi based o the Law of large umbers. I the early 1990s a group of math
More informationCS3203 #5. 6/9/04 Janak J Parekh
CS3203 #5 6/9/04 Jaak J Parekh Admiistrivia Exam o Moday All slides should be up We ll try ad have solutios for HWs #1 ad #2 out by Friday I kow the HW is due o the same day; ot much I ca do, uless you
More informationCounting and Probability CMSC 250
Coutig ad Probabilit CMSC 50 1 Coutig Coutig elemets i a list: how ma itegers i the list from 1 to 10? how ma itegers i the list from m to? assumig m CMSC 50 How Ma i a List? How ma positive three-digit
More informationPERMUTATIONS AND COMBINATIONS
Chapter 7 PERMUTATIONS AND COMBINATIONS Every body of discovery is mathematical i form because there is o other guidace we ca have DARWIN 7.1 Itroductio Suppose you have a suitcase with a umber lock. The
More informationCOLLEGE ALGEBRA LECTURES Copyrights and Author: Kevin Pinegar
OLLEGE ALGEBRA LETURES opyrights ad Author: Kevi iegar 8.3 Advaced outig Techiques: ermutatios Ad ombiatios Factorial Notatio Before we ca discuss permutatio ad combiatio formulas we must itroduce factorial
More informationCOMBINATORICS 2. Recall, in the previous lesson, we looked at Taxicabs machines, which always took the shortest path home
COMBINATORICS BEGINNER CIRCLE 1/0/013 1. ADVANCE TAXICABS Recall, i the previous lesso, we looked at Taxicabs machies, which always took the shortest path home taxipath We couted the umber of ways that
More information1. How many possible ways are there to form five-letter words using only the letters A H? How many such words consist of five distinct letters?
COMBINATORICS EXERCISES Stepha Wager 1. How may possible ways are there to form five-letter words usig oly the letters A H? How may such words cosist of five distict letters? 2. How may differet umber
More informationCounting on r-fibonacci Numbers
Claremot Colleges Scholarship @ Claremot All HMC Faculty Publicatios ad Research HMC Faculty Scholarship 5-1-2015 Coutig o r-fiboacci Numbers Arthur Bejami Harvey Mudd College Curtis Heberle Harvey Mudd
More informationExtra Practice 1. Name Date. Lesson 1.1: Patterns in Division
Master 1.22 Extra Practice 1 Lesso 1.1: Patters i Divisio 1. Which umbers are divisible by 4? By 5? How do you kow? a) 90 b) 134 c) 395 d) 1724 e) 30 f) 560 g) 3015 h) 74 i) 748 2. Write a 5-digit umber
More informationChapter (6) Discrete Probability Distributions Examples
hapter () Discrete robability Distributios Eamples Eample () Two balaced dice are rolled. Let X be the sum of the two dice. Obtai the probability distributio of X. Solutio Whe the two balaced dice are
More informationCounting III. Today we ll briefly review some facts you dervied in recitation on Friday and then turn to some applications of counting.
6.04/18.06J Mathematics for Computer Sciece April 5, 005 Srii Devadas ad Eric Lehma Lecture Notes Coutig III Today we ll briefly review some facts you dervied i recitatio o Friday ad the tur to some applicatios
More informationTHE LUCAS TRIANGLE RECOUNTED. Arthur T. Benjamin Dept. of Mathematics, Harvey Mudd College, Claremont, CA Introduction
THE LUCAS TRIANLE RECOUNTED Arthur T Bejami Dept of Mathematics, Harvey Mudd College, Claremot, CA 91711 bejami@hmcedu 1 Itroductio I 2], Neville Robbis explores may properties of the Lucas triagle, a
More informationLogarithms APPENDIX IV. 265 Appendix
APPENDIX IV Logarithms Sometimes, a umerical expressio may ivolve multiplicatio, divisio or ratioal powers of large umbers. For such calculatios, logarithms are very useful. They help us i makig difficult
More informationx y z HD(x, y) + HD(y, z) HD(x, z)
Massachusetts Istitute of Techology Departmet of Electrical Egieerig ad Computer Sciece 6.02 Solutios to Chapter 5 Updated: February 16, 2012 Please sed iformatio about errors or omissios to hari; questios
More informationAS Exercise A: The multiplication principle. Probability using permutations and combinations. Multiplication principle. Example.
Probability usig permutatios ad combiatios Multiplicatio priciple If A ca be doe i ways, ad B ca be doe i m ways, the A followed by B ca be doe i m ways. 1. A die ad a coi are throw together. How may results
More informationRoberto s Notes on Infinite Series Chapter 1: Series Section 2. Infinite series
Roberto s Notes o Ifiite Series Chapter : Series Sectio Ifiite series What you eed to ow already: What sequeces are. Basic termiology ad otatio for sequeces. What you ca lear here: What a ifiite series
More informationMath 7 Flipped Mastery Self Tester Worksheet Name: Class:. Chapter 1 (Unit 1) Patterns and Relationships - Accommodated 1.1 Patterns In Division /36
Chapter 1 (Uit 1) Patters ad Relatioships - Accommodated 1.1 Patters I Divisio /36 Divisibility Rule Cheats; A whole umber is divisible by 2 if it is a eve umber A whole umber is divisible by 4 if the
More information2. There are n letter and n addressed envelopes. The probability that all the letters are not kept in the right envelope, is. (c)
PAGE # CHAPTER EXERCISE I. A sigle letter is selected at radom from the word PROBABILITY. The probability that the selected letter is a vowel is / / / 0. There are letter ad addressed evelopes. The probability
More informationlecture notes September 2, Sequential Choice
18.310 lecture otes September 2, 2013 Sequetial Choice Lecturer: Michel Goemas 1 A game Cosider the followig game. I have 100 blak cards. I write dow 100 differet umbers o the cards; I ca choose ay umbers
More informationDiscrete Mathematics and Probability Theory Spring 2014 Anant Sahai Note 12
EECS 70 Discrete Mathematics ad Probability Theory Sprig 204 Aat Sahai Note 2 Probability Examples Based o Coutig We will ow look at examples of radom experimets ad their correspodig sample spaces, alog
More informationSummary of Random Variable Concepts April 19, 2000
Summary of Radom Variable Cocepts April 9, 2000 his is a list of importat cocepts we have covered, rather tha a review that derives or explais them. he first ad primary viewpoit: A radom process is a idexed
More informationarxiv: v2 [math.co] 15 Oct 2018
THE 21 CARD TRICK AND IT GENERALIZATION DIBYAJYOTI DEB arxiv:1809.04072v2 [math.co] 15 Oct 2018 Abstract. The 21 card trick is well kow. It was recetly show i a episode of the popular YouTube chael Numberphile.
More informationx 1 + x x n n = x 1 x 2 + x x n n = x 2 x 3 + x x n n = x 3 x 5 + x x n = x n
Sectio 6 7A Samplig Distributio of the Sample Meas To Create a Samplig Distributio of the Sample Meas take every possible sample of size from the distributio of x values ad the fid the mea of each sample
More informationUnit 5: Estimating with Confidence
Uit 5: Estimatig with Cofidece Sectio 8.2 The Practice of Statistics, 4 th editio For AP* STARNES, YATES, MOORE Uit 5 Estimatig with Cofidece 8.1 8.2 8.3 Cofidece Itervals: The Basics Estimatig a Populatio
More informationCHAPTER 5 A NEAR-LOSSLESS RUN-LENGTH CODER
95 CHAPTER 5 A NEAR-LOSSLESS RUN-LENGTH CODER 5.1 GENERAL Ru-legth codig is a lossless image compressio techique, which produces modest compressio ratios. Oe way of icreasig the compressio ratio of a ru-legth
More informationHIGHER SECONDARY FIRST YEAR MATHEMATICS. ALGEBRA Creative Questions Time : 1.15 Hrs Marks : 45 Part - I Choose the correct answer 10 1 = 10.
www.tbtpsc.com HIGHER SEONDARY FIRST YEAR MATHEMATIS ALGEBRA eative Questios Time :. Hs Maks : Pat - I hoose the coect aswe =. The co-efficiet of middle tem i the epasio of is a) b)...( )! c).6,...( )
More informationX-Bar and S-Squared Charts
STATGRAPHICS Rev. 7/4/009 X-Bar ad S-Squared Charts Summary The X-Bar ad S-Squared Charts procedure creates cotrol charts for a sigle umeric variable where the data have bee collected i subgroups. It creates
More informationAPPLICATION NOTE UNDERSTANDING EFFECTIVE BITS
APPLICATION NOTE AN95091 INTRODUCTION UNDERSTANDING EFFECTIVE BITS Toy Girard, Sigatec, Desig ad Applicatios Egieer Oe criteria ofte used to evaluate a Aalog to Digital Coverter (ADC) or data acquisitio
More informationCombinatorics. ChaPTer a The addition and multiplication principles introduction. The addition principle
ChaPTer Combiatorics ChaPTer CoTeTS a The additio ad multiplicatio priciples b Permutatios C Factorials D Permutatios usig P r e Permutatios ivolvig restrictios F Arragemets i a circle G Combiatios usig
More informationOn the Number of Permutations on n Objects with. greatest cycle length
Ž. ADVANCES IN APPLIED MATHEMATICS 0, 9807 998 ARTICLE NO. AM970567 O the Number of Permutatios o Obects with Greatest Cycle Legth k Solomo W. Golomb ad Peter Gaal Commuicatio Scieces Istitute, Uiersity
More informationYou Think You ve Got Problems? Marc Brodie Associate Professor of Mathematics, WJU
You Thik You ve Got Problems? Marc Brodie Associate Professor of Mathematics, WJU Itroductio. My life, like that of ay other s, has its share of problems. I cosider myself fortuate, however, to have more
More informationMath 140 Introductory Statistics
6. Probability Distributio from Data Math Itroductory Statistics Professor Silvia Ferádez Chapter 6 Based o the book Statistics i Actio by A. Watkis, R. Scheaffer, ad G. Cobb. We have three ways of specifyig
More informationCS 201: Adversary arguments. This handout presents two lower bounds for selection problems using adversary arguments ëknu73,
CS 01 Schlag Jauary 6, 1999 Witer `99 CS 01: Adversary argumets This hadout presets two lower bouds for selectio problems usig adversary argumets ëku73, HS78, FG76ë. I these proofs a imagiary adversary
More informationPOWERS OF 3RD ORDER MAGIC SQUARES
Fuzzy Sets, Rough Sets ad Multivalued Operatios ad Applicatios, Vol. 4, No. 1, (Jauary-Jue 01): 37 43 Iteratioal Sciece Press POWERS OF 3RD ORDER MAGIC SQUARES Sreerajii K.S. 1 ad V. Madhukar Mallayya
More informationPermutations: The number of arrangements of n objects taken r at a time is. P (n, r) = n (n 1) (n r + 1) =
Section 6.6: Mixed Counting Problems We have studied a number of counting principles and techniques since the beginning of the course and when we tackle a counting problem, we may have to use one or a
More informationH2 Mathematics Pure Mathematics Section A Comprehensive Checklist of Concepts and Skills by Mr Wee Wen Shih. Visit: wenshih.wordpress.
H2 Mathematics Pure Mathematics Sectio A Comprehesive Checklist of Cocepts ad Skills by Mr Wee We Shih Visit: weshih.wordpress.com Updated: Ja 2010 Syllabus topic 1: Fuctios ad graphs 1.1 Checklist o Fuctios
More informationLecture 4: Frequency Reuse Concepts
EE 499: Wireless & Mobile Commuicatios (8) Lecture 4: Frequecy euse Cocepts Distace betwee Co-Chael Cell Ceters Kowig the relatio betwee,, ad, we ca easily fid distace betwee the ceter poits of two co
More informationTechnical Explanation for Counters
Techical Explaatio for ers CSM_er_TG_E Itroductio What Is a er? A er is a device that couts the umber of objects or the umber of operatios. It is called a er because it couts the umber of ON/OFF sigals
More informationMixed Counting Problems
We have studied a number of counting principles and techniques since the beginning of the course and when we tackle a counting problem, we may have to use one or a combination of these principles. The
More informationCross-Layer Performance of a Distributed Real-Time MAC Protocol Supporting Variable Bit Rate Multiclass Services in WPANs
Cross-Layer Performace of a Distributed Real-Time MAC Protocol Supportig Variable Bit Rate Multiclass Services i WPANs David Tug Chog Wog, Jo W. Ma, ad ee Chaig Chua 3 Istitute for Ifocomm Research, Heg
More informationOptimal Arrangement of Buoys Observable by Means of Radar
Optimal Arragemet of Buoys Observable by Meas of Radar TOMASZ PRACZYK Istitute of Naval Weapo ad Computer Sciece Polish Naval Academy Śmidowicza 69, 8-03 Gdyia POLAND t.praczy@amw.gdyia.pl Abstract: -
More informationGeneral Model :Algorithms in the Real World. Applications. Block Codes
Geeral Model 5-853:Algorithms i the Real World Error Correctig Codes I Overview Hammig Codes Liear Codes 5-853 Page message (m) coder codeword (c) oisy chael decoder codeword (c ) message or error Errors
More informationShuffling Cards. D.J.W. Telkamp. Utrecht University Mathematics Bachelor s Thesis. Supervised by Dr. K. Dajani
Shufflig Cards Utrecht Uiversity Mathematics Bachelor s Thesis D.J.W. Telkamp Supervised by Dr. K. Dajai Jue 3, 207 Cotets Itroductio 2 2 Prerequisites 2 2. Problems with the variatio distace................
More informationApplication of Improved Genetic Algorithm to Two-side Assembly Line Balancing
206 3 rd Iteratioal Coferece o Mechaical, Idustrial, ad Maufacturig Egieerig (MIME 206) ISBN: 978--60595-33-7 Applicatio of Improved Geetic Algorithm to Two-side Assembly Lie Balacig Ximi Zhag, Qia Wag,
More informationThe Multiplication Principle
The Multiplication Principle Two step multiplication principle: Assume that a task can be broken up into two consecutive steps. If step 1 can be performed in m ways and for each of these, step 2 can be
More informationProcedia - Social and Behavioral Sciences 128 ( 2014 ) EPC-TKS 2013
Available olie at www.sciecedirect.com ScieceDirect Procedia - Social ad Behavioral Scieces 18 ( 014 ) 399 405 EPC-TKS 013 Iductive derivatio of formulae by a computer Sava Grozdev a *, Veseli Nekov b
More information4.3 COLLEGE ALGEBRA. Logarithms. Logarithms. Logarithms 11/5/2015. Logarithmic Functions
0 TH EDITION COLLEGE ALGEBRA 4. Logarithic Fuctios Logarithic Equatios Logarithic Fuctios Properties of LIAL HORNSBY SCHNEIDER 4. - 4. - The previous sectio dealt with epoetial fuctios of the for y = a
More informationCoat 1. Coat 2. Coat 1. Coat 2
Section 6.3 : The Multiplication Principle Two step multiplication principle: Assume that a task can be broken up into two consecutive steps. If step 1 can be performed in m ways and for each of these,
More informationCHAPTER 8 JOINT PAPR REDUCTION AND ICI CANCELLATION IN OFDM SYSTEMS
CHAPTER 8 JOIT PAPR REDUCTIO AD ICI CACELLATIO I OFDM SYSTEMS Itercarrier Iterferece (ICI) is aother major issue i implemetig a OFDM system. As discussed i chapter 3, the OFDM subcarriers are arrowbad
More information3. Error Correcting Codes
3. Error Correctig Codes Refereces V. Bhargava, Forward Error Correctio Schemes for Digital Commuicatios, IEEE Commuicatios Magazie, Vol 21 No1 11 19, Jauary 1983 Mischa Schwartz, Iformatio Trasmissio
More informationData Mining the Online Encyclopedia of Integer Sequences for New Identities Hieu Nguyen
Slide 1 of 18 Data Miig the Olie Ecyclopedia of Iteger Sequeces for New Idetities Hieu Nguye Rowa Uiversity MAA-NJ Sectio Sprig Meetig March 31, 2012 2 MAA-NJ Sprig Meetig Data Miig OEIS.b ü Ackowledgemets
More informationA SELECTIVE POINTER FORWARDING STRATEGY FOR LOCATION TRACKING IN PERSONAL COMMUNICATION SYSTEMS
A SELETIVE POINTE FOWADING STATEGY FO LOATION TAKING IN PESONAL OUNIATION SYSTES Seo G. hag ad hae Y. Lee Departmet of Idustrial Egieerig, KAIST 373-, Kusug-Dog, Taejo, Korea, 305-70 cylee@heuristic.kaist.ac.kr
More informationA study on the efficient compression algorithm of the voice/data integrated multiplexer
A study o the efficiet compressio algorithm of the voice/data itegrated multiplexer Gyou-Yo CHO' ad Dog-Ho CHO' * Dept. of Computer Egieerig. KyiigHee Uiv. Kiheugup Yogiku Kyuggido, KOREA 449-71 PHONE
More informationCoat 1. Hat A Coat 2. Coat 1. 0 Hat B Another solution. Coat 2. Hat C Coat 1
Section 5.4 : The Multiplication Principle Two step multiplication principle: Assume that a task can be broken up into two consecutive steps. If step 1 can be performed in m ways and for each of these,
More informationCrafting Well-Built Sentences. Varying Sentence Patterns. Breaking the Rules to Create Fluency. Capturing a Smooth and Rhythmic Flow
SENTENCE FLUENCY k e y q u a l i t i e s Craftig Well-Built Seteces Varyig Setece Patters Breakig the Rules to Create Fluecy Capturig a Smooth ad Rhythmic Flow crafting WELL-BUILT SENTENCES Do my seteces
More informationA generalization of Eulerian numbers via rook placements
A geeralizatio of Euleria umbers via rook placemets Esther Baaia Steve Butler Christopher Cox Jeffrey Davis Jacob Ladgraf Scarlitte Poce Abstract We cosider a geeralizatio of Euleria umbers which cout
More informationA SIMPLE METHOD OF GOAL DIRECTED LOSSY SYNTHESIS AND NETWORK OPTIMIZATION
A SIMPL MOD OF GOAL DIRCD LOSSY SYNSIS AND NWORK OPIMIZAION Karel ájek a), ratislav Michal, Jiří Sedláček a) Uiversity of Defece, Kouicova 65,63 00 Bro,Czech Republic, Bro Uiversity of echology, Kolejí
More informationHybrid BIST Optimization for Core-based Systems with Test Pattern Broadcasting
Hybrid BIST Optimizatio for Core-based Systems with Test Patter Broadcastig Raimud Ubar, Masim Jeihhi Departmet of Computer Egieerig Talli Techical Uiversity, Estoia {raiub, masim}@pld.ttu.ee Gert Jerva,
More informationShuffling. Shahrzad Haddadan. March 7, 2013
Shufflig Shahrzad Haddada March 7, 2013 Abstract I this paper we will talk about two well-kow shufflig methods, the Top to Radom ad the Riffle Shuffle. We are iterested i the umber of shuffles that will
More informationSampling Distribution Theory
Poulatio ad amle: amlig Distributio Theory. A oulatio is a well-defied grou of idividuals whose characteristics are to be studied. Poulatios may be fiite or ifiite. (a) Fiite Poulatio: A oulatio is said
More informationA New Design of Log-Periodic Dipole Array (LPDA) Antenna
Joural of Commuicatio Egieerig, Vol., No., Ja.-Jue 0 67 A New Desig of Log-Periodic Dipole Array (LPDA) Atea Javad Ghalibafa, Seyed Mohammad Hashemi, ad Seyed Hassa Sedighy Departmet of Electrical Egieerig,
More informationNovel pseudo random number generation using variant logic framework
Edith Cowa Uiversity Research Olie Iteratioal Cyber Resiliece coferece Cofereces, Symposia ad Campus Evets 011 Novel pseudo radom umber geeratio usig variat logic framework Jeffrey Zheg Yua Uiversity,
More informationA SIMPLE METHOD OF GOAL DIRECTED LOSSY SYNTHESIS AND NETWORK OPTIMIZATION
49 A SIMPL MOD OF GOAL DIRCD LOSSY SYNSIS AND NWORK OPIMIZAION K. ájek a),. Michal b), J. Sedláek b), M. Steibauer b) a) Uiversity of Defece, Kouicova 65,63 00 ro,czech Republic, b) ro Uiversity of echology,
More informationMultiple Contrast Test (MCT) for Dose-response Microarray studies: A Resampling-based Approach
Multiple Cotrast Test (MCT) for Dose-respose Microarray studies: A Resamplig-based Approach Setia Pramaa Iteruiversity Istitute for Biostatistics ad Statistical Bioiformatics, Uiversiteit Hasselt, Diepebeek,
More informationA RULE OF THUMB FOR RIFFLE SHUFFLING
A RULE OF THUMB FOR RIFFLE SHUFFLING SAMI ASSAF, PERSI DIACONIS, AND K. SOUNDARARAJAN Abstract. We study how may riffle shuffles are required to mix cards if oly certai features of the deck are of iterest,
More informationWavelet Transform. CSEP 590 Data Compression Autumn Wavelet Transformed Barbara (Enhanced) Wavelet Transformed Barbara (Actual)
Wavelet Trasform CSEP 59 Data Compressio Autum 7 Wavelet Trasform Codig PACW Wavelet Trasform A family of atios that filters the data ito low resolutio data plus detail data high pass filter low pass filter
More information13 Legislative Bargaining
1 Legislative Bargaiig Oe of the most popular legislative models is a model due to Baro & Ferejoh (1989). The model has bee used i applicatios where the role of committees have bee studies, how the legislative
More informationFault Diagnosis in Rolling Element Bearing Using Filtered Vibration and Acoustic Signal
Volume 8 o. 8 208, 95-02 ISS: 3-8080 (prited versio); ISS: 34-3395 (o-lie versio) url: http://www.ijpam.eu ijpam.eu Fault Diagosis i Rollig Elemet Usig Filtered Vibratio ad Acoustic Sigal Sudarsa Sahoo,
More informationA New Space-Repetition Code Based on One Bit Feedback Compared to Alamouti Space-Time Code
Proceedigs of the 4th WSEAS It. Coferece o Electromagetics, Wireless ad Optical Commuicatios, Veice, Italy, November 0-, 006 107 A New Space-Repetitio Code Based o Oe Bit Feedback Compared to Alamouti
More informationMathematical Explorations of Card Tricks
Joh Carroll Uiversity Carroll Collected Seior Hoors Projects Theses, Essays, ad Seior Hoors Projects Sprig 2015 Mathematical Exploratios of Card Tricks Timothy R. Weeks Joh Carroll Uiversity, tweeks15@jcu.edu
More informationCompound Controller for DC Motor Servo System Based on Inner-Loop Extended State Observer
BULGARIAN ACADEMY OF SCIENCES CYBERNETICS AND INFORMATION TECHNOLOGIES Volume 6, No 5 Special Issue o Applicatio of Advaced Computig ad Simulatio i Iformatio Systems Sofia 06 Prit ISSN: 3-970; Olie ISSN:
More informationCombinatorics and probability
Departmet of Mathematics Ma 3/03 KC Border Itroductio to Probability ad Statistics Witer 208 Lecture 3: Combiatorics ad probability Relevat textboo passages: Pitma [2]: Sectios.5.6, pp. 7 77; Appedix,
More informationMath 166: Topics in Contemporary Mathematics II
Math 166: Topics in Contemporary Mathematics II Xin Ma Texas A&M University September 30, 2017 Xin Ma (TAMU) Math 166 September 30, 2017 1 / 11 Last Time Factorials For any natural number n, we define
More informationGrade 6 Math Review Unit 3(Chapter 1) Answer Key
Grade 6 Math Review Uit (Chapter 1) Aswer Key 1. A) A pottery makig class charges a registratio fee of $25.00. For each item of pottery you make you pay a additioal $5.00. Write a expressio to represet
More informationSapana P. Dubey. (Department of applied mathematics,piet, Nagpur,India) I. INTRODUCTION
IOSR Joural of Mathematics (IOSR-JM) www.iosrjourals.org COMPETITION IN COMMUNICATION NETWORK: A GAME WITH PENALTY Sapaa P. Dubey (Departmet of applied mathematics,piet, Nagpur,Idia) ABSTRACT : We are
More informationSingle Bit DACs in a Nutshell. Part I DAC Basics
Sigle Bit DACs i a Nutshell Part I DAC Basics By Dave Va Ess, Pricipal Applicatio Egieer, Cypress Semicoductor May embedded applicatios require geeratig aalog outputs uder digital cotrol. It may be a DC
More informationSIDELOBE SUPPRESSION IN OFDM SYSTEMS
SIDELOBE SUPPRESSION IN OFDM SYSTEMS Iva Cosovic Germa Aerospace Ceter (DLR), Ist. of Commuicatios ad Navigatio Oberpfaffehofe, 82234 Wesslig, Germay iva.cosovic@dlr.de Vijayasarathi Jaardhaam Muich Uiversity
More informationDESIGN OF A COFFEE VENDING MACHINE USING SINGLE ELECTRON DEVICES
1 Iteratioal Symposium o Electroic System Desig DESIGN OF A COFFEE VENDING MACHINE USING SINGLE ELECTRON DEVICES (A example of sequetial circuit desig) Biplab Roy (1), ad Biswarup Mukherjee () Dept. Of
More informationH(X,Y) = H(X) + H(Y X)
Today s Topics Iformatio Theory Mohamed Hamada oftware gieerig ab The Uiversity of Aizu mail: hamada@u-aizu.ac.jp UR: http://www.u-aizu.ac.jp/~hamada tropy review tropy ad Data Compressio Uiquely decodable
More informationCHAPTER 8 Additional Probability Topics
CHAPTER 8 Additional Probability Topics 8.1. Conditional Probability Conditional probability arises in probability experiments when the person performing the experiment is given some extra information
More informationADSP ADSP ADSP ADSP. Advanced Digital Signal Processing (18-792) Spring Fall Semester, Department of Electrical and Computer Engineering
ADSP ADSP ADSP ADSP Advaced Digital Sigal Processig (8-79) Sprig Fall Semester, 7 Departmet of Electrical ad Computer Egieerig OTES O RADOM PROCESSES I. Itroductio Radom processes are at the heart of most
More informationBOUNDS FOR OUT DEGREE EQUITABLE DOMINATION NUMBERS IN GRAPHS
BULLETIN OF THE INTERNATIONAL MATHEMATICAL VIRTUAL INSTITUTE ISSN 2303-4874 (p), ISSN (o) 2303-4955 www.imvibl.org/bulletin Vol. 3(2013), 149-154 Former BULLETIN OF THE SOCIETY OF MATHEMATICIANS BANJA
More informationSurvey of Low Power Techniques for ROMs
Survey of Low Power Techiques for ROMs Edwi de Agel Crystal Semicoductor Corporatio P.O Box 17847 Austi, TX 78744 Earl E. Swartzlader, Jr. Departmet of Electrical ad Computer Egieerig Uiversity of Texas
More informationChapter 1. Probability
Chapter 1. Probability 1.1 Basic Concepts Scientific method a. For a given problem, we define measures that explains the problem well. b. Data is collected with observation and the measures are calculated.
More informationTest Time Minimization for Hybrid BIST with Test Pattern Broadcasting
Test Time Miimizatio for Hybrid BIST with Test Patter Broadcastig Raimud Ubar, Maksim Jeihhi Departmet of Computer Egieerig Talli Techical Uiversity EE-126 18 Talli, Estoia {raiub, maksim}@pld.ttu.ee Gert
More informationThroughput/Delay Analysis of Spectrally Phase- Encoded Optical CDMA over WDM Networks
Throughput/Delay Aalysis of pectrally Phase- Ecoded Optical over etwors K. Putsri *,. ittichivapa * ad H.M.H.halaby ** * Kig Mogut s Istitute of Techology Ladrabag Departmet of Telecommuicatios Egieerig,
More informationSimulation of Laser Manipulation of Bloch. Vector in Adiabatic Regime
Advaces i Applied Physics, Vol. 2, 214, o. 2, 53-63 HIKAI Ltd, www.m-hikari.com http://dx.doi.org/1.12988/aap.214.4113 Simulatio of Laser Maipulatio of Bloch Vector i Adiabatic egime yuzi Yao Murora Istitute
More information