DISCRETE MATHEMATICS
W W L CHEN
c
W W L Chen, 1991, 2008.
This chapter is available free to all individuals, on the understanding that it is not to be used for financial gain,
and may be downloaded an
Chapter 6
Eigenvalues and Eigenvectors
6.1 Introduction to Eigenvalues
Linear equations Ax D b come from steady state problems. Eigenvalues have their greatest
importance in dynamic problems. The solu
21-228 Homework 3
Due September 25, 2001
1. Remember that we have defined a relation to be a special kind
of set. For (a) or (b) either give a proof for a yes answer, or a
counterexample for a no answ
Math 341
Homework #5
(1.7) #3. With T defined by T (~x) = A~x, find an ~x whose image under T is ~b, and
determine if ~x is unique.
1 0 1
0
A = 3 1 5 , ~b = 5
6
4 2 1
Solution: We are to solve the eq
Homework I
1. Five jobs are waiting to be run. Their expected run times are 9, 6, 3, 5 and X. In
what order should they be run in order to minimize average waiting time? (Hint:
Though the answer is si
Depth first search
CS122 Algorithms and Data Structures
n
n
n
n
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MW 11:00 am - 12:15 pm, MSEC 101
Instructor: Xiao Qin
Lecture 15: Graphs (2)
n
n
Starting from vertex v
Mark v as marked
Select u as a
Edward Bingham
June 19, 2011
CS 4410 Homework 4
File-System Interface
Design the Directory Hierarchy of a system that needs to satisfy the requirements below:
There must be a root directory.
Each us
Numerical Integration: The Trapezoidal and Simpson Rules - Konat
e
a function f is dened on an interval ]a, b[, and is assumed to be enough
regular.
1. The Trapezoidal Rule: We divide [a, b] in n subi
Polynomial-Time Verifiable
Now, imagine that we have a super-smart
computer, such that for each decision
problem given to it, it has the ability to
guess a short proof (if there is one)
With the hel
Propositional vs. Predicate Logic
In propositional logic, each possible atomic fact requires a
separate unique propositional symbol.
If there are n people and m locations, representing the fact
that s
PSU Eligibility 2013
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29 years
29 yearsGeneral
32 years-OB
Aptitude test for testers
Version 1.1
Introduction
The testers aptitude test has been compiled to assist the test manager/team leader
in the recruiting of good quality testers. This test should be use
10.3.1
Section 3: Equivalence Relations
Definition: Let R be a binary relation on A. R is
an equivalence relation on A if R is reflexive,
symmetric, and transitive.
From the last section, we demonst
Exercise 19.1 Briefly answer the following questions:
1. Define the term functional dependency.
2. Why are some functional dependencies called trivial?
3. Give a set of FDs for the relation schema R(A
Graph Theory
Planar Graphs
Aim
To introduce what a planar graph is.
Learning Outcomes
At the end of this section you will:
Know what a planar graph is,
Know how to use Eulers Formula to check if a g
55. The older of an internal node in a B+-tree index is the maximum number of children it
can have. Suppose that a child pointer takes 6 bytes, the search field value takes 14 bytes,
and the block siz
Example Problems
Thursday, 3 April 2003
1) Given memory partitions of 100K, 500K, 200K, 300K, and 600K (in order), how
would each of the First-fit, Best-fit, and Worst-fit algorithms place processes o
CSE522S- Advanced Operating Systems
Spring 2008
Quiz 4: Virtual Memory
Fred Kuhns
4/28/2008
1) Multiprogramming enables programs to complete faster than when they are run
sequentially. We can develop
Free Sample Test
CSTest ID: 2260
www.gateforum.com
Answer Keys
1
D
2
A
3
D
4
D
5
C
6
C
7
B
8
C
9
C
10
B
11
C
12
D
13
D
14
A
15
B
16
D
17
D
18
50
19
6
20
16
21
31
22
15
23
A
24
B
25
B
26
A
27
B
28
D
29
Operating Systems/Process and Process Management
Test Problems
Test Problems
3.1 Suppose the following jobs arrive for processing at the times indicated, each job
will run the listed amount of time.
J
Operating Systems, 122
Practical Session 8
Deadlocks
1
Deadlocks
The ultimate form of starvation.
A set of processes is deadlocked if each process
in the set is waiting for an event that only
another
Lecture 7: Minimum Spanning Trees and
Prims Algorithm
CLRS Chapter 23
Outline of this Lecture
Spanning trees and minimum spanning trees.
The minimum spanning tree (MST) problem.
The generic algorithm
Operating Systems/Interprocess Communication
Worked out Examples
Worked out Examples
7.1
What is disadvantage of pipes?
Ans:
The disadvantage of this type of IPC is that
a. they operate in one dimensi
Tirgul 12
File System + Assignment 3
I-Nodes
Question 1
What is number of disk accesses when a user executes the command
more /usr/tmp/a.txt
?
Assumptions:
Size of 'a.txt' is 1 block.
The i-node of th
Test
Operating Systems
1. A critical section is a program segment
a) which would run in a certain specified amount of time.
b) which avoids deadlocks
c) where shared resources are accessed
d) which mu
Lecture 8: Kruskals MST Algorithm
CLRS Chapter 23
Main Topics of This Lecture
Kruskals algorithm
Another, but different, greedy MST algorithm
Introduction to UNION-FIND data structure.
Used in Kruskal
Operating Systems/Introduction to OS
Multiple Choice Questions
Multiple Choice Questions
1.1
Suppose you were assigned a certain terminal and you used to log in from that
terminal. One fine morning yo
Microprogramming Concepts
O p e r a tio n c o d e
A d d re s s
O p -c o d e
B ra n c h a d d re s s
In s tr u c t io n r e g is te r
The microprogrammed control unit takes a
macro-instruction (machine
Operating Systems/File Systems and Management
Multiple Choice Questions
Multiple Choice Questions
1. UNIX uses ls to list files in a directory. The corresponding command in MS
environment is:
a. lf
b.
Operating Systems/File Systems and Management
Test Problems
Test Problems
2.1 Suppose we have files F1 to F4 in sizes of 7178, 572, 499 and 1195 bytes. Our
disks have fixed physical block size of 512