# Mathematics Commons™

## All Articles in Mathematics

16,453 full-text articles. Page 459 of 468.

Radiographic Imagery Of A Variable Density 3d Object, 2010 University of South Florida

#### Radiographic Imagery Of A Variable Density 3d Object, Justin Stottlemyer

##### Undergraduate Journal of Mathematical Modeling: One + Two

The purpose of this project is to develop a mathematical model to study 4D (three spatial dimensions plus density) shapes using 3D projections. In the model, the projection is represented as a function that can be applied to data produced by a radiation detector. The projection is visualized as a three-dimensional graph where x and y coordinates represent position and the z coordinate corresponds to the object's density and thickness. Contour plots of such 3D graphs can be used to construct traditional 2D radiographic images.

Pasteurization Of Milk, 2010 University of South Florida

#### Pasteurization Of Milk, Alejandro Barbosa Alzate

##### Undergraduate Journal of Mathematical Modeling: One + Two

We determined the time it takes milk, which is heated from 60°F to 150°F, to achieve pasteurization and compared this result with the standard pasteurization process of heating milk at a constant temperature of 150°F for 30 minutes. Instead of directly quantifying the bacterium population, we considered the bacteria to milk concentration ratio. To solve for the unknown time, we equated the final bacterium concentration ratio achieved through both varied temperature and constant temperature. After equating the final pasteurization concentrations we were unable to find an analytical solution, so we used numerical techniques to find the unknown ...

Brazilian Pepper's Impact On Barrier Island Biodiversity, 2010 University of South Florida

#### Brazilian Pepper's Impact On Barrier Island Biodiversity, Grayson Mccormick

##### Undergraduate Journal of Mathematical Modeling: One + Two

The Brazilian pepper is an invasive plant responsible for destruction of habitats of species native to Florida. We attempted to measure the impact of the Brazilian pepper on native plants by studying how it affects the biodiversity of Honeymoon Island, one of Florida's barrier islands. For this purpose we determined the population sizes of the Brazilian pepper along with five other species of plants on two quadrats of land laid out in Honeymoon Island State Park. Both Simpson's Index of Diversity and Shannon-Wiener Index were used to estimate the biodiversity and assess the impact of the Brazilian pepper ...

Inverse Kinematics, 2010 University of South Florida

#### Inverse Kinematics, Joel Sereno

##### Undergraduate Journal of Mathematical Modeling: One + Two

Inverse kinematics is the process of converting a Cartesian point in space into a set of joint angles to more efficiently move the end effector of a robot to a desired orientation. This project investigates the inverse kinematics of a robotic hand with fingers under various scenarios. Assuming the parameters of a provided robot, a general equation for the end effector point was calculated and used to plot the region of space that it can reach. Further, the benefits obtained from the addition of a prismatic joint versus an extra variable angle joint were considered. The results confirmed that having ...

Escape Velocity, 2010 University of South Florida

#### Escape Velocity, Nikola Vlacic

##### Undergraduate Journal of Mathematical Modeling: One + Two

In this project, we investigated if it is feasible for a single staged rocket with constant thrust to attain escape velocity. We derived an equation for the velocity and position of a single staged rocket that launches vertically. From this equation, we determined if an ideal model of a rocket is able to reach escape velocity.

2010 University of South Florida

#### Nerve Cell Deterioration Associated With Alzheimer's Disease, Yaping Tu

##### Undergraduate Journal of Mathematical Modeling: One + Two

Alzheimer's disease is an extremely serious condition that is challenging to diagnose. We have used experimental data to compare the rate of decay of entorhinal cortex (EC) neurons in various stages of Alzheimer's. We observed that the rate of EC neuron decay in the patients without Alzheimer's is close to zero, linear in mild cases, and quadratic in severe cases. We believe that described estimates may help to diagnose the disease as well as its stage.

Embedded Systems - Missile Detection/Interception, 2010 University of South Florida

#### Embedded Systems - Missile Detection/Interception, Luis Cintron

##### Undergraduate Journal of Mathematical Modeling: One + Two

Missile defense systems are often related to major military resources aimed at shielding a specific region from incoming attacks. They are intended to detect, track, intercept, and destruct incoming enemy missiles. These systems vary in cost, efficiency, dependability, and technology. In present times, the possession of these types of systems is associated with large capacity military countries. Demonstrated here are the mathematical techniques behind missile systems which calculate trajectories of incoming missiles and potential intercept positions after initial missile detection. This procedure involved the use of vector-valued functions, systems of equations, and knowledge of projectile motion concepts.

Social Network Gaming Trends, 2010 University of South Florida

#### Social Network Gaming Trends, Michael Gathwright

##### Undergraduate Journal of Mathematical Modeling: One + Two

The purpose of this project was to determine how long the social network game Scratch-Offs, created by game development company Spice Rack Media, will remain financially viable. The game Scratch-Offs is a freeware game (users pay nothing for the actual software) and is funded through micro transactions (users must pay small amounts of money to play actual games). This implies a relationship between total games played and revenue earned. Using data provided by Spice Rack, we were able to develop an exponential equation that accurately depicts usage trends over time. This equation was used to determine the date Scratch-Offs will ...

The Progression Of Sequential Reactions, 2010 University of South Florida

#### The Progression Of Sequential Reactions, Jack Mcgeachy

##### Undergraduate Journal of Mathematical Modeling: One + Two

Sequential reactions consist of linked reactions in which the product of the first reaction becomes the substrate of a second reaction. Sequential reactions occur in industrially important processes, such as the chlorination of methane. A generalized series of three sequential reactions was analyzed in order to determine the times at which each chemical species reaches its maximum. To determine the concentration of each species as a function of time, the differential rate laws for each species were solved. The solution of each gave the concentration curve of the chemical species. The concentration curves of species A1 and A2 ...

Locomotion Of A Running Quadruped Robotic System, 2010 University of South Florida

##### Undergraduate Journal of Mathematical Modeling: One + Two

Very little is known about the locomotion of quadruped robotic systems. In Latin, the term quadruped means 'having four feet'. The robotic system analyzed in this project was a software simulation program modeled after a horse. Simulation data was recorded to resolve the relationship between foot position and impulses required to accelerate or to decelerate the system while trotting. These sets of data were then analyzed in MATLAB to produce graphical representations which allowed for a better understanding of the robot's motion in the simulation environment. A function was fit to the graph of discrete data values measured in ...

Finding The Area Of An Irregularly Shaped Room, 2010 University of South Florida

#### Finding The Area Of An Irregularly Shaped Room, Justin Walls

##### Undergraduate Journal of Mathematical Modeling: One + Two

This experiment utilized integration in a practical sense by determining the floor area of an irregularly shaped room. By taking the integral summation of three sections formed from semi-circles, the desired areas as well as positive results were found. The final data determined that the floor area of the irregularly shaped room was around 580 square feet.

An Examination Of The Association Of Selected Toxic Metals With Total And Central Obesity Indices: Nhanes 99-02, 2010 Old Dominion University

#### An Examination Of The Association Of Selected Toxic Metals With Total And Central Obesity Indices: Nhanes 99-02, Miguel A. Padilla, Mai Elobeid, Douglas M. Ruden, David B. Allison

##### Psychology Faculty Publications

It is conceivable that toxic metals contribute to obesity by influencing various aspects of metabolism, such as by substituting for essential micronutrients and vital metals, or by inducing oxidative stress. Deficiency of the essential metal zinc decreases adiposity in humans and rodent models, whereas deficiencies of chromium, copper, iron, and magnesium increases adiposity. This study utilized the NHANES 99-02 data to explore the association between waist circumference and body mass index with the body burdens of selected toxic metals (barium, cadmium, cobalt, cesium, molybdenum, lead, antimony, thallium, and tungsten). Some of the associations were significant direct relationships (barium and thallium ...

EΠi + 1=0: The History & Development, 2010 Bridgewater State University

#### EΠi + 1=0: The History & Development, Dawne Charters-Nelson

I have on occasion run across the equation in books, articles and in conversation with other mathematicians. In each of these encounters the person alluded to a fascination with this equation which links the five most important constants in the whole of analysis:

• 0 = The additive identity
• 1 = The multiplicative identity
• π = The circular constant
• e = The base of the natural logarithms
• i = The imaginary unit

Being a novice mathematician, I wondered how all these fundamental constants could end up in one equation and what it meant. Along with this thought came the realization that there was some fun investigating ...

Effects Of Multitemperature Nonequilibrium On Compressible Homogeneous Turbulence, 2010 Old Dominion University

#### Effects Of Multitemperature Nonequilibrium On Compressible Homogeneous Turbulence, Wei Liao, Yan Peng, Li-Shi Luo

##### Mathematics & Statistics Faculty Publications

We study the effects of the rotational-translational energy exchange on the compressible decaying homogeneous isotropic turbulence (DHIT) in three dimensions through direct numerical simulations. We use the gas-kinetic scheme coupled with multitemperature nonequilibrium based on the Jeans-Landau-Teller model. We investigate the effects of the relaxation time of rotational temperature, ZR, and the initial ratio of the rotational and translational temperatures, TR0 / TL0, on the dynamics of various turbulence statistics including the kinetic energy K (t), the dissipation rate ε (t), the energy spectrum E (k,t), the root mean square of the velocity divergence θ′ (t), the ...

If Mowat And Davis Are Correct, Then Teaching Is Hard: A Response To Elizabeth Mowat & Brent Davis, 2010 St. John Fisher College

#### If Mowat And Davis Are Correct, Then Teaching Is Hard: A Response To Elizabeth Mowat & Brent Davis, Kris H. Green, Bernard P. Ricca

##### Mathematical and Computing Sciences Faculty/Staff Publications

In lieu of an abstract, below is the article's first paragraph.

Mowat & Davis (this issue) present a model of learning mathematics that relies heavily on ideas from network (or graph) theory. The important questions (to us, at least) concern the dynamics of the nodes and links. Answers – even tentative ones such as we present here – to these questions lead to a second set of questions concerning the implications of these answers to teachers and researchers.

2010 University of Southern Mississippi

#### An F4-Style Involutive Basis Algorithm, Miao Yu

##### Mathematics Student Presentations

This paper introduces a new algorithm for computing Gröbner bases. To avoid as much ambiguity as possible, this algorithm combines the F4 algorithm and basic algorithm of involutive bases and it replaces the symbolic precomputation of S-polynomials and ordinary division in F4 by a new symbolic precomputation of non-multiplicative prolongations and involutive division. This innovation makes the sparse matrix of F4 in a deterministic way. As an example the Cyclic-4 problem is presented.

Calculating The Time Constant Of An Rc Circuit, 2010 University of South Florida

#### Calculating The Time Constant Of An Rc Circuit, Sean Dunford

##### Undergraduate Journal of Mathematical Modeling: One + Two

In this experiment, a capacitor was charged to its full capacitance then discharged through a resistor. By timing how long it took the capacitor to fully discharge through the resistor, we can determine the RC time constant using calculus.

Effect Of Tire Pressure On Efficiency, 2010 University of South Florida

#### Effect Of Tire Pressure On Efficiency, Miles Mullins

##### Undergraduate Journal of Mathematical Modeling: One + Two

Many people ignore tire pressure in their day-to-day lives. In a country striving for maximum efficiency, neglecting to maintain correct tire pressure can noticeably affect the amount of horsepower required to overcome the drag forces due to tire/roadway friction. In order to quantify these horsepower changes, 21 test trials were conducted by allowing a test vehicle to coast from 50 mph down to 20 mph at pressures ranging from 50 psi to 20 psi. After compiling the results, it was shown that lower tire pressures increased the horsepower necessary to propel the automobile.

2010 University of South Florida

#### The Sir Epidemiology Model In Predicting Herd Immunity, Joanna Nicho

##### Undergraduate Journal of Mathematical Modeling: One + Two

The Simple Epidemic Model uses three states to describe the spread of an infection: the susceptible (S), the infected (I), and the recovered (R). This model follows the trend of an infection over time and can predict whether an infection will spread. Using this model, epidemiologists may calculate the percentage of the population that needs to be vaccinated in order to provide a population immunity from a disease. This study will compare the vaccination percentage required for herd immunity to measles, mumps, and rubella against the current percentage of vaccinated individuals.

Optimization Of A Chemical Reaction Train, 2010 University of South Florida

#### Optimization Of A Chemical Reaction Train, Bahar Sansar

##### Undergraduate Journal of Mathematical Modeling: One + Two

This project consists of the optimization of a chemical reactor train. The reactor considered here is the continuous stirred tank reactor (CSTR), one of the reactor models used in engineering. Given the design equation for the CSTR and the cost function for a reactor, the following values are determined; the optimum number of reactors in the reaction train, the volume of each reactor and the total cost.