Principles of Physics I Laboratory
Breanna Wilhite

Introduction
In this lab motion will be represented by graphs that plots distance and velocity vs. time. A motion detector will be used to measure the time it takes for a high frequency sound pulse to travel from the detector to an object and back. By using this method sound can determine the distance to the object, or its position. This device will determine in what direction the woman in the video was walking and how fast she was walking. This information will be plotted on a graph and show the motion as the woman moves, whether she speed up or slowed down. Logger Pro will use the change in position to calculate the object’s velocity and acceleration. All of this information is in graph form. A qualitative analysis of the graphs of motion will help you develop an understanding of the concepts of kinematics.

Theory
The motion of an object can be measured using a motion detector. The detector helps in knowing where an object is according to an indication point. How fast and in what direction an object is moving, and how an object is accelerating is necessary in understanding the kinematics graphs. The Motion detector uses pulses of ultrasound that bounces off of an object to determine the position of the person/object. As the person moves, the change in its position is measured many times each second. The change in position is expressed as velocity (meters /second). The change in velocity from moment to moment is expressed as acceleration (meters /second /second). The position of an object at a particular time is then plotted on a graph.

Materials
Logger Pro
3.1.2 Computer

Methods, Procedures, and algorithms
Upon opening Logger Pro, the file labeled “Graph Match” was then opened from the sample movies folder. Once this file was opened, the video analysis panel was then enabled. The “Set Scale” was located on the panel and pressed and a green line was drawn from...

...a connected graph G, a spanning graph of G that is a tree is called a spanning tree. A spanning tree for an undirected graph G = (V,E) is a graph G’ = (V,E’) such that G’ is a tree. In other words, G’ has the same set of vertices, but edges have been removed from E so that the resulting graph is a tree. This amounts to saying that G’ is acyclic. If G is directed, it means that cycles have been removed. Since a tree with |V| vertices has |V|-1 edges, to generate a spanning tree of a connected graph G having |V| vertices and |E| edges we must delete all but (|V|-1) edges from the G. We cannot do that randomly because it has to be a tree which is acyclic and connected. We must delete |E|-(|V|-1) = |E|-|V|+1 edges, none of which is a bridge. A graph G can have several spanning tree.
Removal of any single edge from a spanning tree causes the graph to be unconnected.
For any spanning tree T of graph G, if an edge e that is not in T is added, a cycle is created. And also see one thing if we add any edge from ~G, we will also create a cycle.
Minimum Spanning Trees
A spanning tree is minimum if there is no other spanning tree with smaller cost. If the graph is unweighted, then the cost is just the number of edges. If it has weighted edges, then the cost is the sum of the edge weights of the edges in the spanning tree.
An example of...

...V. Adamchik
1
Graph Theory
Victor Adamchik Fall of 2005
Plan
1. Basic Vocabulary 2. Regular graph 3. Connectivity 4. Representing Graphs
Introduction
A.Aho and J.Ulman acknowledge that “Fundamentally, computer science is a science of abstraction.” Computer scientists must create abstractions of real-world problems that can be represented and manipulated in a computer. Sometimes the process of abstraction is simple. For example, we use a logic to design a computer circuits. Another example - scheduling final exams. For successful scheduling we have to take into account associations between courses, students and rooms. Such set of connections between items is modeled by graphs. Let me reiterate, in our model the set of items (courses, students and rooms) won't be much helpful. We also have to have a set of connections between pairs of items, because we need to study the relationships between connections. The basic idea of graphs were introduced in 18th century by the great Swiss mathematician Leonhard Euler. He used graphs to solve the famous Königsberg bridge problem. Here is a picture (taken from the internet)
V. Adamchik
21-127: Concepts of Mathematics
German city of Königsberg (now it is Russian Kaliningrad) was situated on the river Pregel. It had a park situated on the banks of the river and two islands. Mainland and islands were joined by seven bridges. A problem was whether it...

...Design of filter circuits for impedance matching of wideband transducers
ABSTRACT
Wide band piezo-composite transducer is a next generation transducer for under water application. The impedance matching on the interface between electro-acoustical transducer and electrical transmitter has been the most important subject to confirm the high transmitting efficiency. Because the impedance of a wide band transducer depends on signal frequency, it is difficult to design a matching network between power amplifier and the transducer for maximum power transfer. A novel method is proposed to attain the goal in which, impedance matching is achieved by designing a lumped network. The values of elements in the lumped network are optimized through number of experiments. This approach really develops an effective method for impedance matching design and reduced the time for trial and error. Moreover this method makes the implementation procedure less complex.
Keywords: Wide-band transducer, impedance matching, tuning, equivalent circuit
1. Introduction
Piezoelectric transducers are used for under water applications. As we know higher frequencies are more easily attenuated in water, so low frequency sound waves are used for under water mapping. Basically a transducer converts the electrical signal from power amplifier to acoustic signal, which propagates under water....

...Paul Erdos and Alfred Renyi. Their work suggested that systems such as communications could be effectively modelled by connecting nodes with randomly placed links. Their simple approach revitalised graph theory and led to the emergence of the field of random networks.
An important prediction of random network theory is regardless of the random placement of links most nodes will still have approximately the same number of links. In fact, in a random network the nodes follow a Poisson distribution with a bell shape (see Fig.1). Random networks are also called exponential, because the probability that a node is connected to k other sites decreases exponentially for large k. This is better described by the famous small world networks. It was Watts and Strogatz in 1998 that recognised that a class of random graphs could be categorised as small world networks. They noted that graphs could be classified according to their clustering coefficient and their diameter. Many random graphs show a small diameter and also have a small clustering coefficient. What Strogatz and Watts found was that in real world networks the diameter is still small but has a clustering coefficient significantly higher than expected by random chance. Watts and Strogatz thus proposed a simple model of random graphs with (a) a small diameter and (b) a large clustering coefficient.
I wasn't until 1998 when Albert-Lászlǒ Barabási...

...Double stub impedance matching
Impedance matching can be achieved by inserting two stubs at specified
locations along transmission line as shown below
There are two design parameters for double stub matching:
The length of the first stub line Lstub1
The length of the second stub line Lstub2
In the double stub configuration, the stubs are inserted at predetermined
locations. In this way, if the load impedance is changed, one simply has to
replace the stubs with another set of different length.
The drawback of double stub tuning is that a certain range of load admittances
cannot be matched once the stub locations are fixed.
Three stubs are necessary to guarantee that match is always possible.
The length of the first stub is selected so that the admittance at the location of
the second stub (before the second stub is inserted) has real part equal to the
characteristic admittance of the line
If one moves from the location of the second stub back to the load, the circle of
the allowed normalized admittances is mapped into another circle, obtained by
pivoting the original circle about the center of the chart.
At the location of the first stub, the allowed normalized admittances are found
on an auxiliary circle which is obtained by rotating the unitary conductance
circle counterclockwise, by an angle
Given the load impedance, we need to follow these steps to complete the double
stub design:
(a) Find...

...Application of Accounting Concepts
Matching Principle & Accrual Concept
Accrued / Prepaid Expense & Accrued or Advance Revenue
To ensure an accurate matching of expenses and revenue under the accrual basis, it is necessary
to include all revenue earned but not received and expenses incurred but not paid. Such
adjustments comprise adjustments for :
Accrued Revenue
Accrued Expenses
On the other hand, many recorded costs and revenues benefit more than one accounting
period. Therefore, adjusting entries are required to apportion them between the periods
affected. These include:
Revenue Received in Advance
Prepaid Expenses
Supplies
Application of Accounting Concepts
Matching Principle
Provision for bad / doubtful debt ( Inc / Dec ) in P & L
Bad debt losses be matched against the period’s credit
sales that gives rise to such losses. However, a bad
debt loss may not materialise until a later period after
the sale. To overcome this problem, the doubtful /
bad debt losses are estimated and a provision made in
anticipation of such losses.
Application of Accounting Concepts
Matching Principle
Depreciation of fixed assets
As a fixed asset benefits the business over
several years, its cost must be allocated as an
expense to the years it benefits to ensure
accurate matching of expenses against revenue
earned from using the asset for each year.
Application of Accounting Concepts
Prudence Concept
Provision...

...Graphs
Data Structures and Algorithms
Prepared by: Engr. Martinez
Graph Concepts
Graph Concepts
Graphs are of 2 types
Undirected Graph
Undirected Graph examples
Directed Graph
Directed Graph example
Directed Graph
Directed GraphGraph Relationships
Graph RelationshipsGraph Relationships
Basic terms involved in graphs:
Basic terms involved in graphs:
Basic terms involved in graphs:
Degree of vertex
The number of edges incident onto the vertex For an undirected graph The degree of a vertex u is the number of edges connected to u. For a directed graph The out-degree of a vertex u is the number edges leaving u, and its in-degree is the number of edges ending at u
Degree of vertex
Edges are of 2 types
Directed edge: A directed edge between the vertices vi and vj is an ordered pair. It is denoted by . Undirected edge: An undirected edge between the vertices vi and vj is an unordered pair. It is denoted by (vi,vj).
Different Types of Graphs
Subgraph Connected graph Completely connected graph
1. Subgraphs
A subgraph of a graph G = (V,E) is a...

...Graphs and Function
What is the relation between the graphs and function and how was it applied in the real world?
Graphs are frequently used in national magazines and newspaper to present information about things such as the world’s busiest airports (O’Hare in China is first, Heathrow in London is sixth), about the advertising-dollar receivers in the United States (newspaper are first, radio is fourth) and about NCAA men’s golf team title winner (Yael is first, Houston is second). The function concept is very closely connected to graphs, and functions are the heart of mathematics.
I gathered my information from books especially algebra books and some are from the internet. I went to the library to look for some books and I borrowed some so I have many resources of information.
Many real-life relations between two quantities expressed in the form of equation are functions. To visualize these relationships, geometric figures called graphs are used. Modern technology provides us with graphing utilities needed to draw these graphs as well as enhance man’s knowledge of graphing techniques. Scientist and astronomers identify, visualize, and explore graphical patterns useful in analyzing data about the universe. Economist and businessmen draw mathematical models to find curves of best fit. Generally, the use of function and graphs is found in every...