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concrete mathematics a foundation for computer science phần 8 doc

Applied Mathematics for Database Professionals phần 8 doc

Applied Mathematics for Database Professionals phần 8 doc

... count(*)from DEPT dwhere d.MGR = r.MGR); CHAPTER 11 ■ IMPLEMENTING DATABASE DESIGNS IN ORACLE 288 7451CH11.qxd 5/15/07 2:26 PM Page 288 where not exists(select 'This employee is assigned as a ... Here is the formal specification of this table constraint:CHAPTER 11 ■ IMPLEMENTING DATABASE DESIGNS IN ORACLE2 68 7451CH11.qxd 5/15/07 2:26 PM Page 2 68 Listing 11-25. Tuple Constraints for GRD ... beimplemented procedurally for PSSR8. It is worth mentioning that you could actually formally prove that thepreceding conjunction is logically equivalent with the PSSR8 predicate. It requires...
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Schaum’s Outline Series OF Principles of Computer Science phần 1 doc

Schaum’s Outline Series OF Principles of Computer Science phần 1 doc

... Horses 17 5Hackers 17 6Can Computers Kill? 17 7Summary 17 8Review Questions 17 9APPENDIX Answers to Review Questions 18 0Index 217 CONTENTS vii SCHAUM’S OUTLINE OF Principles of COMPUTER SCIENCE ... most modern computers.4 INTRODUCTION TO COMPUTER SCIENCE [CHAP. 1 SCHAUM’S OUTLINE OF Principles of COMPUTER SCIENCE CARL REYNOLDSDepartment of Computer Science Rochester Institute of TechnologyPAUL ... Systems 99Management of Input and Output 99Processes and Scheduling 10 1Threads 10 2Synchronization 10 3Semaphores 10 6Monitors 10 8Deadlock 11 1Scheduling 11 4Memory Management 11 6Memory Management...
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concrete mathematics a foundation for computer science phần 1 pdf

concrete mathematics a foundation for computer science phần 1 pdf

... recurrence makes it possible to build a table of small values veryquickly. Perhaps we’ll be able to spot a pattern and guess the answer.n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 J(n) 1 1 3 1 3 5 7 1 3 ... index.ISBN o-2 01- 14236-8 1. Mathematics 19 61- 2. Electronic data processing Mathematics. I. Knuth, Donald Ervin, 19 38-.II. Patashnik, Oren, 19 54-.III. Title.QA39.2.C733 19 88 510 dc1988-3779CIPSixth ... J. Hammersley [14 5]THIS BOOK IS BASED on a course of the same name that has been taughtannually at Stanford University since 19 70. About fifty students have taken iteach year-juniors and...
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concrete mathematics a foundation for computer science phần 2 pptx

concrete mathematics a foundation for computer science phần 2 pptx

... as a binary operation, just as addition and subtraction arebinary operations. Mathematicians have used mod this way informally for a long time, taking various quantities mod 10, mod 27 7, and ... name andconquer. a = ~ap’J , a- ’ = a+ a’;The change of vari-able from k to j isb = [va-‘l ,va-’ = b -v’.Thus a = {a ‘} is the fractional part of a- ‘, and v’ is the mumble-fractionalpart ... notations for rising powers as well as falling powers.Mathematicians have long had both sine and cosine, tangent and cotangent,secant and cosecant, max and min; now we also have both floor and ceiling.To...
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concrete mathematics a foundation for computer science phần 3 ppsx

concrete mathematics a foundation for computer science phần 3 ppsx

... 87 106 1 93 299 492 685 878 1071 12641'1'1'2&apos ;3& apos; 4' 7'11'18'25&apos ;32 ' 39 ' 71'110'181'252&apos ;32 3' 39 4' 465""are ... lo1'10'9'8'7'b'5'4&apos ;3& apos;5'2&apos ;3& apos;1'2'1'2'1'2'1'1'~'1'1'1'1' 1Is it true that m’n - mn’ = 1 whenever m/n immediately ... BBBBBBBBEach of the nm possible patterns appears at least once in this array ofmN(m,n) strings, and some patterns appear more than once. How manytimes does a pattern a~ . . . a, ,-, appear? That’s...
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concrete mathematics a foundation for computer science phần 4 ppsx

concrete mathematics a foundation for computer science phần 4 ppsx

... n fans. How manyways h(n, k) are there for exactly k fans to get their own hats back? For example, if n = 4 and if the hats and fans are named A, B, C, D,the 4! = 24 possible ways for hats ... land generate the following numbers ofrightful owners:ABCD 4 BACD 2 CABD1DABC0ABDC 2 BADC0CADB0DACB1ACBD 2 BCAD1CBAD 2 DBAC1ACDB1BCDA0CBDA1DBCA 2ADBC1BDAC0CDAB0DCAB0ADCB ... an auxiliary variable z, A( z) = ac +a, z +a2 z2+ = to@“.k>O(5.52)It’s appropriate to use the letter z as the name of the auxiliary variable, be-cause we’ll often be thinking of z as a...
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concrete mathematics a foundation for computer science phần 5 pps

concrete mathematics a foundation for computer science phần 5 pps

... same pattern holds for continued fractions of any depth. It is easilyproved by induction; we have, for example,K(ao,al,az ,a3 +l /a4 ) := K(ao,al ,a2 ,a3 ,a4 )K(al, az, a3 + l /a4 1K(al,az,as,ad) ... arisenaturally. Let’s consider the pedigree of a male bee. Each male (also knownas a drone) is produced asexually from a female (also known as a queen); eachfemale, however, has two parents, a male ... continued fraction can also be obtained directly: Let CQ = a and for k 3 0 letak = Lakj ;1ak = ak+ Kkfl(6.142)The a s are called the “partial quotients” of a. If a is rational, say m/n,this...
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concrete mathematics a foundation for computer science phần 6 doc

concrete mathematics a foundation for computer science phần 6 doc

... because 2 - & z0. 268 . This needs to be taken into account if wetry to use formula (7.38) in numerical calculations. For example, a fairlyexpensive name-brand hand Icalculator comes ... 0;) as n -+ 00, un:less z = 0. This shows that formal power seriescan be manipulated algebraically without worrying about convergence.Example 6: A recurrence that goes ail the way back.Let’s ... many spanning trees f, are in such a graph? A spanning tree is a subgraph containing all the vertices, and containingenough edges to make the subgraph connected yet not so many that it hasa...
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concrete mathematics a foundation for computer science phần 7 pot

concrete mathematics a foundation for computer science phần 7 pot

... month each person is reassignedto an adjacent state, each adjacent state being equally likely. (Here’s a diagram of the adjacencies:The initial states are circled.) For example, Alice is restationed ... (8.82) that A would probably beat B, that B would probably beat C, and that C wouldprobably beat A; but all three patterns are simultaneously in the game.)What are each player’s chances of ... we can interpret these formulas in a particularlysimple way. Given a pattern A of m heads and tails, let A: A = fIkpl [Ack’ =A( kj] .k=l(8 .76 )We can easily find the binary representation...
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concrete mathematics a foundation for computer science phần 8 doc

concrete mathematics a foundation for computer science phần 8 doc

... “Eulerian” (eighteenth-century) mathematics. 9.3 0 MANIPULATION 447This may look worse than the sum we began with, but it’s actually a step for- ward, because we have very good approximations for ... actually 15 485 863. Exercise 21 shows that a still moreaccurate approximation to P, results if we begin with a still more accurateapproximation to n(n) in place of (9.46). 9.6 FINAL SUMMATIONS ... result formally. 9.6 FINAL SUMMATIONS 473Actually I’m notinto dominance.We have to make D, small enough that we can make a good estimate; for example, we had better not let k get near n, or...
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concrete mathematics a foundation for computer science phần 9 pps

concrete mathematics a foundation for computer science phần 9 pps

... resultsabout Fermat’sLast Theorem; seeRibenboim j249j.j A ANSWERS TO EXERCISES 527If the harmonicaa and a bb. Thus each bb behaves like a drone in the bee tree and each aabehaves like a ... therebyeliminating an upper parameter and a lower parameter. Thus, for example,we get closed forms for F( a, b; a - 1; z), F( a, b; a - 2; z), etc.Gauss [116, $71 derived analogous relations ... x.(The values of a, b, c must, in fact, be even higher than this resultindicates! Inkeri [160] has proved that A sketch of his proof appears in [2 49, pages 228-2 291 , a book that containsan extensive...
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concrete mathematics a foundation for computer science phần 10 docx

concrete mathematics a foundation for computer science phần 10 docx

... V. Waugh and Margaret W. Maxfield, “Side-and-diagonal num-bers,” Mathematics Magazine 40 (1967), 74-83.298 Warren Weaver, “Lewis Carroll and a geometrical paradox,” AmericanMathematical Monthly ... Mark HaimanAndrei Broder, Jim McGrathOren PatashnikJoan Feigenbaum, Dave HelmboldAnna KarlinOren Patashnik, Alex SchafferPang Chen, Stefan SharkanskyArif Merchant, Stefan SharkanskyIn addition, ... sum602. for 1x1,” American Mathematical Monthly 96 (1989), 525-526.131 Ronald L. Graham, Donald E. Knuth, and Oren Patashnik, Concrete 102 . Mathematics: A Foundation for Computer Science. Addison-Wesley,1989....
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