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TABLE OF CONTENTS
Science Section:
1. Analysis of pH In a Small Lake Over Time
2. How Does Polluted Water Affect Plant Growth?
Math Section:
1. When Is a Fractal a Fractal? A Study of ZnSO4 Aggregates
At Different Molarity.
2. The Fractal Dimension of Populations In the Program
"Anthill"
3. The Effect of Various Anode Shapes on Fractal Growth In an
Electro-deposition Cell
Social Studies Section:
1. The Cheapest Gas In the Nation
2. What Do Students Think About Gun Control?
SCIENCE SECTION
TITLE: Analysis of pH in a Small Lake Over Time
STUDENT RESEARCHER: Sabrina O'Hara
SCHOOL ADDRESS: Fairmont Catholic Grade School
Fairmont, West Virginia
GRADE: 8th
TEACHER: Terry Kerns
I. STATEMENT OF PURPOSE AND HYPOTHESES:
Rock Lake, a man-made lake in Marion County, has had problems
with pH in the past. The purpose of this study was to help
Rock Lake residents have a better understanding of pH in the
lake and its possible causes. I tried to figure out if the pH
varied at the different sites and if the temperature, weather
changes, amount of rain and/or the groundwater springs affected
the pH.
The following null hypotheses were proposed:
1. The location from which the sample was taken will not affect
the pH.
2. The day that the tests are run will not affect the pH.
3. The temperature of the water will not affect the pH.
4. The amount of rain within three days of the test will not
affect the pH.
5. The pH of the underground water supplies will not vary by
location.
6. Differences in pH of the underground water supplies will not
affect pH of nearby lake samples.
II. METHODOLOGY:
1. Selected 17 representative sites on Rock Lake using a 7.5
minute geological survey map and made arrangements to collect
samples from two unused wells at the lake.
2. Collected samples from sites during a three month period.
3. Measured temperature and pH of each sample.
4. Measured amount of rainfall and its pH during study
III. ANALYSIS OF DATA:
In general, the pH increased from August through October for
all sites as well as for the overall average. During any one
test, the pH tended to increase the further the site was
downstream. No apparent pattern between temperature and pH
was found. During the test, the greater the amount of rain
prior to the test, the lower the pH level. The pH of well
water was much lower on the north side of the lake than it was
on the south side. However, no pattern of differences was
noted between the sites on the north and south side of the
lake.
IV. SUMMARY AND CONCLUSION:
1. The data did not support the null hypothesis that the
location from which the sample was taken will not affect the
pH. In general the pH increased the further downstream
2. The data did not support the null hypothesis that the day
that the tests are run will not affect the pH. In general, the
pH increased from August through October.
3. The data did support the null hypothesis that the
temperature of the water will not affect the pH. No apparent
pattern between temperature and pH was found.
4. The data did not support the null hypothesis that the amount
of rain within three days of the test will not affect the pH.
The greater the amount of rain prior to the test the lower the
pH goes.
5. The data did not support the null hypothesis that the pH of
the underground water supplies will not vary by location. The
pH of well water was much lower on the north side of the lake.
6. The data did seem to support the null hypothesis that
differences in pH of the underground water supplies will not
affect pH of nearby lake samples. No pattern of differences
were noted between the north and south side of the lake.
Rock Lake does seem to have a pH problem. Levels rise above
acceptable limits and at times can approach the 8.4 level at
which state regulations prohibit swimming. The cause of this
problem is still to be determined. Considering that the rain
is rather acidic and that the area is one primarily of
sandstone rather than limestone, these basic levels are
surprising.
V. APPLICATION:
Since residents of Rock Lake wish to use the water for
swimming, further studies need to be done to identify specific
causes if they do not want to face closure of the lake during
certain periods.
TITLE: How Much Does Polluted Water Affect Plant Growth?
STUDENT RESEARCHER: Amanda Senules
SCHOOL: Mandeville Middle School
Mandeville, Louisiana
GRADE: 6
TEACHER: John I. Swang, Ph.D.
I. STATEMENT OF PURPOSE AND HYPOTHESIS:
I want to know the effect of polluted water on plant growth.
Water pollution is the pollution of water from the disposal of
trash and wastes into an aquatic body. This may affect plant
growth because the polluted water contains toxic chemicals that
harms plant life. My first hypothesis states that seeds
watered with clean water will germinate faster than seeds
watered with polluted water. My second hypothesis states that
the plant watered with clean water will grow taller than those
watered with polluted water.
II. METHODOLOGY:
First, I wrote my statement of purpose and my review of
literature. My review of literature was on water pollution and
plant growth. Then I developed my hypothesis. To test my
hypothesis, I did the following: I soaked 30 radish seeds in
water overnight. I then planted 15 seeds each in 2 pots of the
same size. Each pot contained the same amount of soil and I
planted all of the seeds 1 millimeter deep into the soil. I
placed both pots in a window, so they both received the same
amount of sunlight. I watered the experimental pot with 1
milliliter of polluted water from Lake Ponchartrain every day.
I watered the control pot with 1 milliliter of clean water
every day. I did this for 2 weeks. Every day, I recorded the
average color, height, and number of leaves on all plant for
each pot on my data collection sheet.
My variables held constant were the amount of water given to
each plant, the amount of soil each seed was planted in, the
amount of sunlight given, the amount of seeds planted, the
amount of time each seed was given to grow, the size of the
pots, and the depth each seed was planted in the soil. My
manipulated variables were that the experimental pot was
watered with polluted water from Lake Ponchartrain and the
control pot was watered with clean water. My responding
variables were the average color of the plants, the average
height of the plants, and the average number of leaves on the
plants.
After recording my observations, I analyzed my data using
simple statistics, charts, and graphs. Then I wrote my summary
and conclusion where I accepted or rejected my hypothesis.
Then I applied my findings to every day life. Finally, I
published my abstract in The Student Researcher.
III. ANALYSIS OF DATA:
On the first day, all of my seeds sprouted.
On the last day of my experiment, the plants watered with clean
water grew to an average height of 3 centimeters. They had an
average of 1 leaf per plant and all of the plants were green.
On the last day, the experimental plants watered with polluted
Lake Ponchartrain water grew to an average height of .5
centimeters. There were no leaves on the plants and their
color was green.
IV. SUMMARY AND CONCLUSION:
After analyzing my data, I have come to the conclusion that
plants watered with clean water grow taller, faster, and will
have more leaves than plants watered with polluted water.
Therefore, I accept my first hypothesis which stated that seeds
watered with clean water will germinate faster than seeds
watered with polluted water. I also accept my second
hypothesis which stated that plants watered with clean water
will grow taller than plants watered with polluted water.
V. APPLICATION:
I can apply my findings to every day life by not polluting, and
I can encourage my neighbors not to pollute because it destroys
plant and animal life.
MATH SECTION:
TITLE: When Is A Fractal a Fractal? A Study Of ZnSO4
Aggregates At Different Molarity.
STUDENT RESEARCHERS: Daniel Brecher, Lelia Evans, and Philip
Ording
SCHOOL ADDRESS: Belmont High School
221 Concord Ave.
Belmont, MA 02178
GRADE: 12
TEACHER: Paul Hickman - phickman@copernicus.bbn.com
I. STATEMENT OF PURPOSE AND HYPOTHESIS:
The experiment with copper aggregate was fresh in our minds and
we wanted to find out what other kinds of fractal shapes we
could create by changing the solution or concentration.
Originally, we wanted to compare the copper aggregates to the
zinc aggregates at different molarities, but we realized that
the scope of this investigation was too large. So we settled
on just using ZnSO4. Our hypothesis states that as the
molarity of ZnSO4 solution changes, the fractal dimension of
deposition fractals will change in an inverse relationship.
II. METHODOLOGY:
We mixed solutions of ZnSO4 at different molarities; 0.1 M, 0.2
M, and 0.4 M. Originally we created a 0.05 M solution.
However, after using the 0.2 M and 0.1 M to grow aggregates we
noticed a trend. We knew that the 0.05 M would most likely not
be a fractal [see scan of aggregates; as molarity increased the
branches fill more area--the 0.05M would be a blackened
circle.] So, we decided to go the other direction and make a
0.4 M solution.
We used scotch tape to cover the bottom hole of the cell. This
technique, although excellent for scanning, produced
troublesome bubbles. It took at least three trials, when
making a single cell, to remove the bubbles from the anode.
We grew two aggregates of each molarity simultaneously by
connecting them in parallel. To eliminate any variables, we
made the anodes the same size and position and applied the same
voltage to the cell. We grew each aggregate for 15 minutes and
then disconnected the power source to stop the growth.
Next, we removed the scotch tape from the bottom of the cell
and scanned the aggregates into the computer. So as not to
scan the anode wire, we placed a piece of white paper, with a
slit for the anode, over the cell. Then we saved the scanned
images as MacPaint files. Using MacPaint, we made some
corrections on the aggregates: we touched-up stray points which
appeared only after scanning and we removed the blobs at the
end of the 0.4 M aggregates (these blobs were composed of
copper which plated from the copper cathode ring as the
branches of the zinc got too close to the ring).
We measured the fractal dimensions of the aggregates using the
box and circle methods and compared these results.
We analyzed our results by putting the values we found for both
the box and circle methods on a single graph, showing an
inverse relationship.
III. ANALYSIS OF DATA:
.1a M .1b M .2a M .2b M .4a M .4b m
Box 1.934 1.938 1.771 1.750 1.386 1.422
Circle 1.993 * 1.974 * 1.806 1.839 1.566 1.636
* When we measured the aggregate by the fast circle method, the
lowest radius was pulling the log graph to a too-steep
position, making the fractal dimension greater than two, which
is not possible. (.1a = 2.183, .1b = 2.069). To solve this
problem, we eliminated the first data point which was a hole in
the fractal, where the cathode was located.
IV. SUMMARY AND CONCLUSION:
As we discussed above, our data shows that there is an inverse
relationship between the solution molarity and the fractal
dimension of the aggregates formed by these solutions. This
conclusion contradicts our prediction that a higher molarity
would produce a denser, higher-fractal-dimension aggregate.
One observation of the aggregate growth helped us understand
the inverse relationship between fractal dimension and
molarity: the higher molarity aggregates grew faster than the
lower molarity aggregates. Aggregate growth is a process by
which positively charged zinc ions in solution migrate towards
the negative electrode and plate out. Since the voltage was
constant, the ions, whether in high or low concentration, in
every cell move at the same rate towards the cathode. The
higher molarity solution contains more zinc ions in solution.
In this case, the aggregate will grow faster because there are
more ions present. Aggregates which are formed at faster rate
are more likely to form a node, a bump resulting from
inconsistencies in plating ions.
A node which protrudes from an aggregate has more edges than
the rest of the aggregate, and therefore the node will collect
more plating ions and grow at a faster rate. High molarity
solutions grow more nodes, and these nodes grow into branches.
In the lowest molarity solution, 0.1 M, there are fewer ions.
The aggregate will grow slowly and therefore fewer nodes will
form. The plating occurs equally around the cathode causing a
nearly perfect, dense circle. This accounts for the increasing
fractal character as the molarity increases.
V. APPLICATION:
Many patterns of growth existing in nature have useful
functions. Crystals of silicon are sliced for microchip and
other electronic devices. Plating is used in the production of
jewelry and electronic parts. We hope that our findings will
contribute to a better understanding of the factors which alter
and shape patterns of growth.
TITLE: The Fractal Dimension of Populations in the Program
ÒAnthillÓ
STUDENT RESEARCHERS: Chris Baird, Julia Stoyanovich
SCHOOL ADDRESS: Belmont High School
221 Concord Ave.
Belmont, MA 02178
GRADE: 11/12
TEACHER: Paul Hickman - phickman@copernicus.bbn.com
I. STATEMENT OF PURPOSE AND HYPOTHESIS:
We want to find out whether there is a connection between the
initial parameters of population growth, such as time and size
of population, and the fractal dimension or jaggedness of the
pattern of sites visited by the population. Our hypothesis is
that there is a certain connection, but we do not know what
kind of correlation there will be.
II. METHODOLOGY:
We carried out a research project using the Beta version of
"Anthill," a two-dimensional random walk program by Paul
Trunfio from Boston University.
1. To acquire data, we ran Anthill many times, changing the
corresponding variable(s). After a certain amount of time we
paused the growth and copied the image, using the program
Capture 4.0 by Yves Lempereur, and saved them as a Macpaint
files. From there we used the program Fractal Dimension 5.1 by
Brandon Volbright to measure the fractal dimension of the
pictures. We used both options of the program: box and circle
method, and averaged them. Than we compared the dimensions of
these growths for one variable and plotted the values in the
program Graphical Analysis 1.3.1.1 by Dave Vernier and Todd
Bates.
2. We ran the program several times with constant parameters
to make sure that the pictures are different each time, with
their fractal dimension the same, showing the program is based
on randomness.
3. We ran the program, changing only the number of ants. We
used 1, 2, 3, 4, 10, 25, 50, 75, 100, 150 for the number of
ants. We organized sample images of population growth and their
values into groups with 1, 2, 3, 4 in one group, and 1, 50,
100, 150 in another. Since the fractal dimension for the low
values of number of ants showed little change, we found it
necessary to also investigate high values.
4. The final step of our research was to observe the
correlation between the time the program is run and the fractal
dimension of the resulting pattern. We ran Anthill with the
same set of parameters (1 ant, no deaths or births, equal
probabilities of direction) for 20, 30, 40, 60, 90, and 120
seconds. We organized a sampling of these images with 30, 60,
90, and 120 seconds.
5. To check the accuracy of our results, we picked a value for
the variable we were testing and applied it to the relationship
we had found. The fractal dimension value from this function
was a prediction which we then compared to actual results to
check the validity of the relationship.
III. ANALYSIS OF DATA:
1. For the constant variables we did find different images
that have similar fractal dimensions, showing the program's
true randomness.
2. When we first investigated the variable of number of ants
we used 1, 2, 3, and 4 ants. We found that the fractal
dimension did not change significantly.
3. We thought that even though we had acquired almost constant
results for fractal dimension of changing number of ants, there
still might be an increasing relationship. Therefore we tried
much higher values of the number of ants: 10, 25, 50, 75, 100,
and 150. We found that the fractal dimension did change, it
proved to be an increasing non-linear function. Our prediction
made by applying this function was close to the measured value,
showing the accuracy of our result.
4. When we ran the program, changing only the time, and
leaving all the other parameters constant, we discovered a
correlation between the time and the fractal dimension of the
resulting pattern. The relation was a linear increasing
function. Predicting a value for fractal dimension through
this linear function, we came up with accurate results, showing
the validity of this relationship.
IV. SUMMARY AND CONCLUSION:
1. The Fractal Dimension does depend on both number of ants
and time as we thought.
2. The Fractal Dimension is an increasing function of the
number of ants. The function is not linear. The more the
ants, the greater the jaggedness.
3. The Fractal Dimension is an increasing function of time.
The function is linear. The longer the ants do their job, the
greater the jaggedness.
V. APPLICATION:
The results of our research can be used in predicting the
behavior of some natural systems, such as forest fires, insect
or animal population growth, the spread of disease, etc. The
research can be continued by discovering the connection between
the rest of parameters, and the final image.
TITLE: The Effect of Various Anode Shapes on Fractal Growth in
an Electrodeposition Cell
STUDENT RESEARCHERS: Paris Gartaganis, Tom Glennon, Laureen
Laglagaron
SCHOOL ADDRESS: Belmont High School
221 Concord Ave.
Belmont, MA 02178
GRADE: 12
TEACHER: Paul Hickman - phickman@copernicus.bbn.com
I. STATEMENT OF PURPOSE AND HYPOTHESIS:
Electrodeposition produces fractal shapes. In our investigation
we wanted to find out more about different anode shapes and the
fractals they produced. This investigation dealt with
symmetrical and asymmetrical shapes, the growth patterns
produced and the ability to predict fractal shapes. We also
examined the difference in fractal dimension of each aggregate
grown and its correlation with the anode shape. We used five
different anode shapes (A circle, a square, a triangle, a D-
shape, and a shamrock) with varying area but consistent
perimeter. The purpose of this investigation was to see if we
are able to predict the aggregate growth, dependent on the
anode shape, and to see what factors influence fractal growth.
We were interested in the effects of different shaped anodes on
fractal growth. The fractals in an electrodeposition cell are
produced due to ions coming towards the center cathode. Our
hypothesis states that the aggregate would assume a pattern
that was influenced by the shape of the anode, although not an
exact replica of the shape.
II. METHODOLOGY:
We constructed five anode shapes made out of copper wire which
all had the same perimeter of 24 cm. These five shapes were
square, triangle, circle, shamrock, and a D-shape. We used an
electrodeposition cell which is two glass plates held together
with metal clamps, with a center hole for the wire, to conduct
our investigation. We then grew aggregates with a 0.2 M CuSO4
solution with the same current of 10 volts for each. After the
aggregate finished growing we scanned it into the computer
using the AppleScan program and touched up the aggregates using
MacPaint. Once we had our aggregates on MacPaint, we were able
to measure the fractal dimension using the computer program
called Fractal Dimension 5.1.
III. ANALYSIS OF DATA:
The shapes of the aggregates were not in correlation with the
shape of the anodes. Since each anode perimeter was 24 cm, the
area of each anode was different. The area of the circle was
38.4845 cm2, the area of the triangle was 27.71 cm2, the area
of the D-shape was 25.13 cm2, the area of the square was 36
cm2, and the area of the shamrock was 25.92 cm2. The speed of
the aggregate growth and the density of the aggregate were both
affected by the area.
Fractal Dimension: Using the program Fractal Dimension 5.1 we
measured the Fractal Dimension of each aggregate using the box
method and the circle method. The FD of each aggregate are as
follows:
Circle: Shamrock:
box= 1.587 box= 1.616
circle= 1.650 circle= 1.647
Triangle: D-shape:
box= 1.649 box= 1.616
circle= 1.650 circle= 1.656
Square:
box= 1.650
circle= 1.659
IV. SUMMARY AND CONCLUSION:
From the results that we obtained in our experiment, we found
that it was nearly impossible to predict aggregate growth based
on the shape of the anode. It is difficult to establish a
concrete result that would provide an explanation for varying
anodes because we did not notice a substantial difference
between aggregates formed with different anode shapes. We
rejected our hypothesis that different anode shapes would
affect fractal growth because we did not notice a significant
difference between fractal growth shapes.
Once we analyzed our aggregates, it was easy to come up with
reasons for our result, but they were not based on concrete
evidence and could be influenced by our want to notice a
difference between aggregate shapes. To firmly establish any
theory, we would have to repeat this experiment to ensure that
the results were consistent and not limited to our first
findings.
One hypothesis that we considered was in the difference of
'branching' between the aggregates and the density of this
branching. Our theory was that aggregates formed with an anode
which had a small area were less branched, possibly because the
aggregate could not grow to its full potential without hitting
the anode. However, this theory was limited only to our
findings and must be validated through numerous experiments.
We also confirmed our assumption that the strength of the field
did have an effect on aggregate growth. As the strength of the
field increased, the rate of growth of the aggregate also
increased. We were surprised that the difference in anode
shape did not produce a significant, visual change in
aggregates, but we realized that because aggregates are formed
so randomly, it was difficult to constrict this randomness to
particular shapes.
V. APPLICATION:
Since our hypothesis was not validated in our findings, we have
developed procedures which might help other researchers
investigate the topic of fractal growth. Other researchers who
investigate the topic of fractal growth might try to limit
their research by using a consistent area as opposed to a
consistent perimeter, varying the solution used, or using
larger anodes. In order to apply our results, other
investigators might want to verify our results by repeating our
experiment numerous times.
SOCIAL STUDIES SECTION
Title: Cheapest Gas In The Land
Student Researchers: Mr. Carbone's Math Class
School: North Stratfield School
Fairfield, Connecticut
Grade: 4
Teacher: Mr. V. Carbone
I. STATEMENT OF PURPOSE AND HYPOTHESIS:
We want to find out which state sells the cheapest gas. Our
hypothesis states that Georgia sells the cheapest gas.
II. METHODOLOGY:
We will ask other schools to join us in this project. They
will provide information from their state on gas prices. We
will get the following information: regular, unleaded, and
super. If we are provided with more than one set of prices
from one town, we will use the cheapest set for our data.
III. ANALYSIS OF DATA:
Town, State Regular Unleaded Super
Prescott, Arizona $1.10 $1.12 $1.19
N. Hampton, Mass. $1.13 $1.29 $1.39
Georgetown, Kentucky $ .99 $1.01 $1.05
Huntsville, Texas $1.19 $1.23 $1.32
West Palm Beach, FL. $1.19 $1.29 $1.37
Mandeville, LA. $1.09 $1.19 $1.30
Mansville, Mass. $---- $1.29 $1.41
Georgia $1.09 $---- $----
Salisbury, MD $1.15 $---- $----
Waco, Texas $1.02 $1.12 $1.19
Luling, LA $ .99 $1.08 $1.18
Fairfield, CT $1.29 $1.39 $1.49
Salt Lake City Utah $1.03 $1.11 $1.13
Miami, FL $1.19 $---- $1.28
Ludlow, Vermont $---- $1.12 $1.29
Ocean City, Maryland $1.07 $1.17 $1.29
West Dover, Vermont $1.09 $1.15 $1.23
Yonkers, New York $1.29 $---- $1.47
Greensfield, Mass. $1.23 $1.33 $1.42
Willington, Vermont $1.06 $1.10 $1.17
Atlanta, Georgia $ .95 $1.09 $1.19
IV. SUMMARY AND CONCLUSION:
We accept our hypothesis for regular gas. Georgia had the
least expensive gas for regular unleaded at $ .95. We reject
our hypothesis for midgrade unleaded and super unleaded.
Kentucky had the cheapest gas prices in these areas at $1.01
midgrade unleaded and $1.05 for super.
V. APPLICATION TO LIFE:
1. If you were going on a trip, you might want this information
for your expenses.
2. Other gas stations might want to know these prices so they
are not too expensive.
3. If you were driving from one state to another on a trip, you
might want to wait and fill up in the other state if the gas
prices there are less expensive.
4. If you were moving to another state, you might want to know
the price of gas in that state.
TITLE: What Do Students Think About Gun Control?
STUDENT RESEARCHER: Austin Feldbaum
SCHOOL: Mandeville Middle School
Mandeville, Louisiana
GRADE: 6
TEACHER: John I. Swang, Ph.D.
I. STATEMENT OF PURPOSE AND HYPOTHESIS:
I wanted to know more about what students think of gun control.
Gun control is a big issue in America today. Seven out of
eight U.S. citizens are for stronger gun control laws. Yet
over the years the public's opinion has had little effect on
Congress. My hypothesis states that the majority of students I
survey will be for stricter gun control laws.
II. METHODOLOGY:
First, I wrote my statement of purpose. Then I did my review
of literature and developed my hypothesis. Next, I developed
my questionnaire, drew a random sample of twelve sixth grade
students at M.M.S. and administered my survey to them. I also
sent my questionnaire out over the N.S.R.C.'s electronic school
district to a non-random sample of students from all over the
world. Then I scored my questionnaires when returned, recorded
my data on a data collection sheet, and analyzed my data with
simple charts and graphs. Then I wrote my summary and
conclusion. Next, I applied what I found to the world outside
my classroom. Finally, I wrote an abstract of my research and
published it in a journal of student research.
III. ANALYSIS OF DATA:
I received a total of 898 responses to my survey from students
in grades 4 through 12 from schools in Wisconsin, Louisiana,
South Carolina, Illinois, Texas, California, Washington,
Alabama, Arizona, Utah, New York, Israel, and Canada.
A majority of 72% thought that citizens should be allowed to
own guns in their homes. A majority of 64% agreed with
Congress' decision to ban assault rifles. A majority of 80%
agreed with a seven day wait before the sale of a handgun. A
majority of 58% did not think that Congress should ban rifle
clips with over five bullets. A majority of 73% thought that
gun control is one of the country's biggest problems. A
majority of 87% did not think that Congress should ban all
firearms. A majority of 78% thought that there should be
mandatory jail sentences for all crimes involving the use of
handguns. A majority of 85% thought that there should be
longer jail sentences for second-time gun offenders. A
majority of 58% did not keep a hand gun in their home. A
majority of 74% thought that the national government and the
state governments should write and passed gun control laws.
IV. SUMMARY AND CONCLUSION:
The majority of the students surveyed believe that citizens
should be allowed to have guns in their homes, but they
themselves did not have guns in their homes. The majority of
students think that gun control is one of our country's main
problems. In general, they think that there should be stricter
gun control laws written by the federal or state governments.
Therefore, I accept my hypothesis which stated that the
majority of the students would be for stricter gun control
laws.
V. APPLICATION:
I will send what I found to the U.S. Congress and state
governments to tell legislators there what sixth grade students
at M.M.S. and around the country think about gun control. It
could be of help to them as they debate this problem and try to
solve it.
© 1995 John I. Swang, Ph.D.