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Recent Articles in Mathematics
Free Resolutions Of Orbit Closures For Representations With Finitely Many Orbits, Federico Galetto 
Northeastern University
Free Resolutions Of Orbit Closures For Representations With Finitely Many Orbits, Federico Galetto
Mathematics Dissertations
The irreducible representations of reductive groups with finitely many orbits are parametrized by graded simple Lie algebras. For the exceptional Lie algebras, Kraśkiewicz and Weyman exhibit the Hilbert polynomials and the expected minimal free resolutions of the normalization of the orbit closures. We present an interactive method to construct explicitly these and related resolutions in Macaulay2. The method is then used in the cases of the Lie algebras of type E6, F4, G2, and select cases of type E7 to confirm the shape of the expected resolutions as well as some geometric properties of the orbit ...
Computer Programming To Advance Gravitational Lensing, Alex Roche 
Bridgewater State University
Computer Programming To Advance Gravitational Lensing, Alex Roche
Undergraduate Review
The purpose of this research was to create a computer code that would numerically test a Poisson equation relating the mass distribution of a lens galaxy cluster to weak gravitational shear. Einstein’s theory of general relativity predicts that space-time is bent by massive objects, and in weak gravitational lensing, galaxy clusters act as lenses. The observable result is that galaxies far behind the gravitational lens will appear slightly more elliptical than they actually are. The ellipticity of the background galaxies is quantifiable and is directly related to the weak gravitational shear, and the shear is used to determine the ...
Exploring Diagonals In The Calkin-Wilf Tree, Matthew Gagne Bridgewater State University
Exploring Diagonals In The Calkin-Wilf Tree, Matthew Gagne
Undergraduate Review
For centuries, people have been interested in patterns. Even in that which appears random, humans have been trying to understand the underlying order of things. Mathematicians throughout time have studied many phenomena, including infinite sequences of numbers and have been able, at times, to see structure. Many have found the satisfaction, even joy, of discovering patterns in sequences. A typical way to describe this is by a recursive formula. A recursive definition defines a term in the sequence using the previous terms in the sequence. Even more satisfying than a recursive formula is a closed formula. With this, one can ...
Constructions Of K-Orbit Abstract Polytopes, Ilanit Shtull-Leber Helfand Northeastern University
Constructions Of K-Orbit Abstract Polytopes, Ilanit Shtull-Leber Helfand
Mathematics Dissertations
The desire to derive new polytopes from old polytopes dates back to the classical study of polytopes, as many of the Archimedian solids can be obtained from Platonic solids through the act of truncation. In this dissertation, we apply these ideas to the setting of abstract polytopes. We present a number of constructions of abstract polytopes, which will generally share some properties with the polytopes from which they were derived. Most notably, we are interested in the circumstances under which the automorphism group of the derived polytope is isomorphic to the automorphism group of the original polytope. We construct polytopes ...
Decreasing Math Anxiety Through A Quadratics Unit, Lee C. Hooker 
The College at Brockport: State University of New York
Decreasing Math Anxiety Through A Quadratics Unit, Lee C. Hooker
Education and Human Development Master's Theses
Anxiety related to the learning of mathematics is referred to as math anxiety and has been shown to have a negative influence on student performance. Research reveals that math anxiety is something that can be unlearned and informs about the potential causes and treatments of math anxiety in the mathematics classroom. A majority of math anxiety experienced by students has been caused by teachers’ repetitious teaching styles. Research presents various teaching strategies that have helped teachers when working with students who have math anxiety. These strategies include writing, class discussions, cooperative groups, kinesthetic activities, use of manipulatives, and various, frequent ...
Speleothem Laminae Counting And Growth Rate, Corey Wilson 
University of South Florida
Speleothem Laminae Counting And Growth Rate, Corey Wilson
Undergraduate Journal of Mathematical Modeling: One + Two
The goal of this project is to determine if there is a correlation between annual laminae in speleothems and Uranium dating. To do this, we counted laminae using high-resolution images and calculated a line of the best fit for the resulting data. We found that our data could supplement Uranium dating, but unless more data is obtained, laminae counting gives relatively imprecise age and growth rate estimates.
Modeling Flow Rate To Estimate Hydraulic Conductivity In A Parabolic Ceramic Water Filter, Ileana Wald University of South Florida
Modeling Flow Rate To Estimate Hydraulic Conductivity In A Parabolic Ceramic Water Filter, Ileana Wald
Undergraduate Journal of Mathematical Modeling: One + Two
In this project we model volumetric flow rate through a parabolic ceramic water filter (CWF) to determine how quickly it can process water while still improving its quality. The volumetric flow rate is dependent upon the pore size of the filter, the surface area, and the height of water in the filter (hydraulic head). We derive differential equations governing this flow from the conservation of mass principle and Darcy's Law and find the flow rate with respect to time. We then use methods of calculus to find optimal specifications for the filter. This work is related to the research ...
The Elevation To Area Relationship Of Lake Behnke, Kaitlin Deutsch University of South Florida
The Elevation To Area Relationship Of Lake Behnke, Kaitlin Deutsch
Undergraduate Journal of Mathematical Modeling: One + Two
The objective of this project was to determine the area-to-depth relationship in Lake Behnke, which acts as the principal stormwater drainage basin for the University of South Florida campus in Tampa, Florida. Data previously collected in a stormwater management study by Jeffery Earhart illustrated a linear correlation between the lake's area and depth; however, that study was conducted in 1998, and this present work serves to double check that correlation. We analyzed a bathymetric map of Lake Behnke that displayed several contour lines indicating depth and approximated the area inside each closed curve with a contour integral. The resulting ...
Overfishing Of The Common Snook, Allison Ashcroft University of South Florida
Overfishing Of The Common Snook, Allison Ashcroft
Undergraduate Journal of Mathematical Modeling: One + Two
The chief aim of this project is to determine if the populations of the common snook, Centropomus Undecimalis, in the Atlantic and Gulf coast are being affected by overfishing. This is established by evaluating the intrinsic rate of change for these populations and their carrying capacities. It turns out that the carrying capacity for the population of the Atlantic coast is approximately one million snook and its intrinsic rate is 0.00621, while the carrying capacity of the Gulf coast's population is 2.9 million snook and its intrinsic rate is 0.00165. The decline of both populations is ...
Complexity Of Mitochondrial Genome Sequences, Brandon Toun University of South Florida
Complexity Of Mitochondrial Genome Sequences, Brandon Toun
Undergraduate Journal of Mathematical Modeling: One + Two
The purpose of this project is to compare the complexities of different species' mitochondrial genome sequences. Using an implementation of Deflate compression algorithm from Java standard library, we were able to compress mitochondrial genomes of nine different species. The complexity of each sequence is estimated as a ratio of the original sequence length to the length of the compressed sequence. In addition, we show how a notion of topological entropy from symbolic dynamics can be used as another complexity measure of nucleotide sequences.
The Subset Sum Problem: Reducing Time Complexity Of Np-Completeness With Quantum Search, Bo Moon University of South Florida
The Subset Sum Problem: Reducing Time Complexity Of Np-Completeness With Quantum Search, Bo Moon
Undergraduate Journal of Mathematical Modeling: One + Two
The Subset Sum Problem is a member of the NP-complete class, so no known polynomial time algorithm exists for it. Although there are polynomial time approximations and heuristics, these are not always acceptable, yet exact-solution algorithms are unfeasible for large input. Quantum computation offers new insights for not only the Subset Sum Problem but also the entire NP-complete class; most notably, Grover's quantum algorithm for an unstructured database search can be tailored to identify solutions to problems within mathematics and computer science. This paper discusses the physical and conceptual feasibility of quantum computation and demonstrates the utility of quantum ...
U.S. Oil Reserves And Peak Oil, Trang Luong University of South Florida
U.S. Oil Reserves And Peak Oil, Trang Luong
Undergraduate Journal of Mathematical Modeling: One + Two
We use calculus methods to estimate the quantity of U.S. oil reserves. We consider a model that consists of an exponential function with four unknown constants. We fit real oil production data to determine the unknown constants. With the constants determined we use the function to find the year in which the U.S. oil production reached its peak. We also estimate the amount of petroleum produced until the end of 2006, and the undiscovered oil reserves to be produced in the future.
Average Light Intensity Inside A Photobioreactor, Herby Jean University of South Florida
Average Light Intensity Inside A Photobioreactor, Herby Jean
Undergraduate Journal of Mathematical Modeling: One + Two
For energy production, microalgae are one of the few alternatives with high potential. Similar to plants, algae require energy acquired from light sources to grow. This project uses calculus to determine the light intensity inside of a photobioreactor filled with algae. Under preset conditions along with estimated values, we applied Lambert-Beer's law to formulate an equation to calculate how much light intensity escapes a photobioreactor and determine the average light intensity that was present inside the reactor.
Model For Facial Cooling, Jacalyn Sampson University of South Florida
Model For Facial Cooling, Jacalyn Sampson
Undergraduate Journal of Mathematical Modeling: One + Two
The goal of this project is to estimate the ambient temperature and the wind speed that cause painful sensation in a cheek. Our findings confirm that the higher the wind speed, the less cold air is required to cause cheek pain.
Design Of A Rainwater Catchment System, Neil Cammardella University of South Florida
Design Of A Rainwater Catchment System, Neil Cammardella
Undergraduate Journal of Mathematical Modeling: One + Two
Certain dimensions of a rainwater catchment and storage system were optimized using climatological and sociological data. Using only daily demand and average daily rain fall data, the following dimensions were optimized: 1) The horizontal roof area needed to collect the daily demand of water, 2) The tank size needed to store all the water collected during a heavy rain event, 3) When full, how long the tank will be able to provide water without rain, and 4) The diameter of the outlet flow orifice. With these calculations, we can design a rainwater catchment system that can capture the daily demand ...
Optimal Operation Of A Concentrator, Katrina Stine University of South Florida
Optimal Operation Of A Concentrator, Katrina Stine
Undergraduate Journal of Mathematical Modeling: One + Two
Concentrators are used in the industrial world to remove water from a chemical or substance by heating the liquid until the water evaporates thereby concentrating the remaining substance. The goal of this project is to find the optimum cycle time, number of cycles per year, and the heating element area that would minimize the total annual cost and hours of operation of an industrial concentrator. It was found that the specified concentrator would achieve a minimum total cost of $48,720.50 per year and take 993.8 hours to meet the production goal of evaporating one million kilograms of ...
Going Ballistic: Bullet Trajectories, Amanda Wade University of South Florida
Going Ballistic: Bullet Trajectories, Amanda Wade
Undergraduate Journal of Mathematical Modeling: One + Two
This project seeks to answer at what angle does a gun marksman have to aim in order to hit the center of a target one meter off the ground and 1000 meters away? We begin by modeling the bullet's trajectory using Euler's method with the help of a Microsoft Excel spreadsheet solver, and then systematically search for the angle corresponding to the center of the target. It was found that a marksman shooting a target 1000 meters away and 1 meter off the ground has to aim the rifle 0.436° above horizontal to hit the center.
Length Of A Hanging Cable, Eric Costello University of South Florida
Length Of A Hanging Cable, Eric Costello
Undergraduate Journal of Mathematical Modeling: One + Two
The shape of a cable hanging under its own weight and uniform horizontal tension between two power poles is a catenary. The catenary is a curve which has an equation defined by a hyperbolic cosine function and a scaling factor. The scaling factor for power cables hanging under their own weight is equal to the horizontal tension on the cable divided by the weight of the cable. Both of these values are unknown for this problem. Newton's method was used to approximate the scaling factor and the arc length function to determine the length of the cable. A script ...
Optimization Of A Pressure-Treating Process, Josean Velez University of South Florida
Optimization Of A Pressure-Treating Process, Josean Velez
Undergraduate Journal of Mathematical Modeling: One + Two
A company that pressure-treats wood wants to minimize its annual cost without using more than 250 days of operation per year. In addition, they want to find the corresponding value of time, batches and cost for each category. We develop an expression in terms of boards per batch to model the total cost of the treatment process. We then take the derivative and use Newton's Method to find the number of boards per batch that minimizes total cost.
The Effects Of Age On Short-Term Memory Loss Due To Proactive Interference, Alisha Berkauzer University of South Florida
The Effects Of Age On Short-Term Memory Loss Due To Proactive Interference, Alisha Berkauzer
Undergraduate Journal of Mathematical Modeling: One + Two
This project focused on how proactive interference affects the short-term memory of people based on their age. The goal was to find the prime age for learning information and storing it in one's memory. Seven people from ages fifteen to forty were tested individually, using a set color pattern, in order to see how well each individual could remember the different color patterns as difficulty of the pattern increased. The obtained data was fitted by the polynomial regression. The “fitted” curve shows that as age increases, the individual's performance in memorizing the more difficult patterns decreases. Also, the ...
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