Chapter 3 Test 3.1 and 3.3 Completion Complete each sentence or statement. 1. The state of matter that exists only at extremely low temperatures is called a Bose-Einstein ____________________. 2. When water boils‚ some of its molecules have enough _________________________ to overcome the attraction of neighboring molecules. 3. The ____________________ theory of matter states that all particles of matter are in constant motion. 4. During vaporization‚ a substance changes from
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The diagrams illustrate some changes to a small island which has been developed for tourism. It is clear that the island has changed considerably with the introduction of tourism‚ and six new features can be seen in the second diagram. The main developments are that the island is accessible and visitors have somewhere to stay. Looking at the maps in more detail‚ we can see that small huts have been built to accommodate visitors to the island. The other physical structures that have been added are
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The bar chart illustrates the unemployment rate in Germany compared to the unemployment rate in Ireland. The y-axis shows the rate of unemployment which is defined by the number of unemployed persons as a percentage of the labor force. On the x-axis you can read the year. In 2000‚ 8 per cent of the German workforce was unemployed‚ which was twice as high as Ireland. Unemployment in Germany declined slightly in 2001. However‚ after this the unemployment rate rose steadily over the next four years
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tructureResearch on Graphs in Data Structure Source: http://www.algolist.net/Algorithms/Graph/Undirected/Depth-first_search Introduction to graphs Graphs are widely-used structure in computer science and different computer applications. We don’t say data structurehere and see the difference. Graphs mean to store and analyze metadata‚ the connections‚ which present in data. For instance‚ consider cities in your country. Road network‚ which connects them‚ can be represented as a graph and then analyzed
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Introduction in Graph Theory (BASIC CONCEPTS) BASIC CONCEPTS We used decision trees in Unit DT and used them to study decision making. However‚ we did not look at their structure as trees. In fact‚ we didn’t even define a tree precisely. What is a tree? It is a particular type of graph‚ which brings us to the subject of this unit. What is a Graph? There are various types of graphs‚ each with its own definition. Unfortunately‚ some people apply the term “graph” rather loosely‚ so
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DESCRIBING GRAPHS AND CHARTS The function of a line graph is to describe a TREND pictorially. You therefore should try and describe the trend in it. If there are many lines in the graph(s)‚ then just generally describe the trend. If there is only one or two‚ then use more detail. So‚ describe the movement of the line(s) of the graph giving numerical detail at the important points of the line. To describe the movement‚ there is some language which will always be useful. Below is a list of language
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Graphs - Introduction Terminology Graph ADT Data Structures Reading: 12.1-12.2 COSC 2011‚ Summer 2004 Definition • A graph is a pair (V‚ E)‚ where – V is a set of nodes‚ called vertices – E is a collection of pairs of vertices‚ called edges • Both are objects (i.e. store data) G E B F A Vertex city computer web page airport C D COSC 2011‚ Summer 2004 H Edge road cable hyperlink flight Example Applications • • • • • Electronic circuits – Printed circuit board – Integrated circuit Transportation
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1.2 Basics of Functions and Their Graphs Introduction to Relations Domain and Range of a Relation Any set of ordered pairs (x‚y) is called a relation in x and y. Furthermore‚ The set of first components in the ordered pairs is called the domain of the relation. The set of second components in the ordered pairs is called the range of the relation. Definition of Function and Vertical Line Test Definition of a Function Given a relation in x and y‚ we say “y is a function of x” if for every
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Graphs‚ Groups and Surfaces 1 Introduction In this paper‚ we will discuss the interactions among graphs‚ groups and surfaces. For any given graph‚ we know that there is an automorphism group associated with it. On the other hand‚ for any group‚ we could associate with it a graph representation‚ namely a Cayley graph of presentations of the group. We will first describe such a correspondence. Also‚ a graph is always embeddable in some surface. So we will then focus on properties of graphs
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How many optimal solutions are there for a given problem ? - 4- Combinatorial Optimization (C.O.) problems Different fields in Optimization: Linear Programming Non-Linear Optimization Integer – Mixed Linear Programming Graph / network optimization Routing‚ Scheduling‚ Supply Chain‚… Combinatorial optimization studies optimization on finite and discrete domains. Find the minimum s* of f on a finite set S. f ( s ) Min f ( s) sS - 5- Characteristics
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