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 A_{1} and A_{2 ...}

Quantum Mechanical Example Of Anti-Tunneling, 2010 University of South Florida

#### Quantum Mechanical Example Of Anti-Tunneling, Tim Mitchell

*Undergraduate Journal of Mathematical Modeling: One + Two*

The probability of a particle being reflected by a semi-infinite energy barrier was solved using Schrödinger's equations that describe the quantum mechanical behavior of the particle. The continuity of the functions at the origin allowed the wave functions and their respective derivatives to be equated. Solution of the resulting system yielded values A_{1} and B_{1} which were used to calculate the reflection coefficient, (B_{1}/A_{1})^{2}. The conclusions obtained from these results stated that the particle would be reflected by the barrier when E

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.

Power Consumption Of A Mosfet, 2010 University of South Florida

#### Power Consumption Of A Mosfet, Frederick Selkey

*Undergraduate Journal of Mathematical Modeling: One + Two*

A MOSFET is defined as metal oxide semiconductor field effect transistor. These electrical components are combined or integrated to form control and logic functions for laptop and desktop computers, power controls in printing devices, motor controls and are used in many other electrical circuits. All electrical devices consume electrical power based on current and voltage. For this paper we calculated the power consumption of a Toshiba 2SK3563 MOSFET during its triode mode by finding the area under the current-voltage characteristic curve.

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 ...

Dosimetry Calculations Of Radiopharmaceuticals, 2010 University of South Florida

#### Dosimetry Calculations Of Radiopharmaceuticals, Kelbe Jahnke

*Undergraduate Journal of Mathematical Modeling: One + Two*

The goal of this project is to determine the absorbed dose of radiation to a patient using ^{99m}Tc-MAA as a tracer for a lung scan using the MIRD formula accounting only for the radiation dose contributed by the target organ. The radiation dose for other organs to the target organ is considered negligible as the uptake of ^{99m}Tc-MAA from other organs is less than 1%. In addition to calculating the absorbed dose of radiation, the initial dose rate was also calculated by back solving to determine the total mass of the lungs. The radiation dose to the patient ...

Light Attenuation At Molasses Reef, 2010 University of South Florida

#### Light Attenuation At Molasses Reef, Ashley Earls

*Undergraduate Journal of Mathematical Modeling: One + Two*

Estimating the amount of light available at different depths of the ocean is important for gaining a better understanding of coral reefs. It is especially useful to be able to get such estimates without having to perform direct measurements. Although accurate, the direct measurements are costly, time consuming, and usually limited to relatively small areas of interest.

One statistic that could be useful for estimating the amount of available light is the rate at which it declines with depth (the rate of light attenuation). In this project, this rate is calculated for four different wavelengths using data for 30m water ...

Motion Of A Pendulum, 2010 University of South Florida

#### Motion Of A Pendulum, Jared Wynn

*Undergraduate Journal of Mathematical Modeling: One + Two*

The objective of this project is to derive and solve the equation of motion for a pendulum swinging at small angles in one dimension. The pendulum may be either a simple pendulum like a ball hanging from a string or a physical pendulum like a pendulum on a clock. For simplicity, we only considered small rotational angles so that the equation of motion becomes a harmonic oscillator.

Maximum Power From A Solar Panel, 2010 University of South Florida

#### Maximum Power From A Solar Panel, Michael Miller

*Undergraduate Journal of Mathematical Modeling: One + Two*

Solar energy has become a promising alternative to conventional fossil fuel sources. Solar panels are used to collect solar radiation and convert it into electricity. One of the techniques used to maximize the effectiveness of this energy alternative is to maximize the power output of the solar collector. In this project the maximum power is calculated by determining the voltage and the current of maximum power. These quantities are determined by finding the maximum value for the equation for power using differentiation. After the maximum values are found for each time of day, each individual quantity, voltage of maximum power ...

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.

Calculating Optimal Inventory Size, 2010 University of South Florida

#### Calculating Optimal Inventory Size, Ruby Perez

*Undergraduate Journal of Mathematical Modeling: One + Two*

The purpose of the project is to find the optimal value for the Economic Order Quantity Model and then use a lean manufacturing Kanban equation to find a numeric value that will minimize the total cost and the inventory size.

Hyperbolic Geometry: A Guide To Models And Motion, 2010 University of Redlands

#### Hyperbolic Geometry: A Guide To Models And Motion, Danielle J. Strieby

*Undergraduate Honors Theses*

Twentieth century mathematics can be characterized by the study of functions. The most interesting functions are those that preserve the structure at hand. In many branches of mathematics transformations are looked at and classified. In geometry, transformations of a plane are very important. A transformation that distance is called an isometry. The classification of isometries is known in Euclidean geometry, and one will learn about each of them in any geometry course. Classification of isometries for the hyperbolic plane are not as well known, but they have been classified. In this paper we will discover hyperbolic geometry, investigate some of ...

Multiresolution Inverse Wavelet Reconstruction From A Fourier Partial Sum, 2010 CUNY Kingsborough Community College

#### Multiresolution Inverse Wavelet Reconstruction From A Fourier Partial Sum, Nataniel Greene

*Publications and Research*

The Gibbs phenomenon refers to the lack of uniform convergence which occurs in many orthogonal basis approximations to piecewise smooth functions. This lack of uniform convergence manifests itself in spurious oscillations near the points of discontinuity and a low order of convergence away from the discontinuities.In previous work [11,12] we described a numerical procedure for overcoming the Gibbs phenomenon called the Inverse Wavelet Reconstruction method (IWR). The method takes the Fourier coefficients of an oscillatory partial sum and uses them to construct the wavelet coefficients of a non-oscillatory wavelet series. However, we only described the method standard wavelet ...

The Linus Sequence, 2010 University of Memphis

#### The Linus Sequence, Paul Balister, Steven Kalikow, Amites Sarkar

*Mathematics*

Define the Linus sequence *L _{n}* for

*n*≥ 1 as a 0–1 sequence with

*L*

_{1}= 0, and

*L*chosen so as to minimize the length of the longest immediately repeated block

_{n}*L*

_{n−2r+1}

*L*=

_{n−r}*L*

_{n−r+1}

*L*. Define the Sally sequence

_{n}*S*as the length

_{n}*r*of the longest repeated block that was avoided by the choice of

*L*. We prove several results about these sequences, such as exponential decay of the frequency of highly periodic subwords of the Linus sequence, zero entropy of any stationary process ...

_{n}Curvature Measures For Nonlinear Regression Models Using Continuous Designs With Applications To Optimal Design, 2010 Loyola University Chicago

#### Curvature Measures For Nonlinear Regression Models Using Continuous Designs With Applications To Optimal Design, Timothy O'Brien, Somsri Jamroenpinyo, Chinnaphong Bumrungsup

*Mathematics and Statistics: Faculty Publications and Other Works*

We present and illustrate the methodology to calculate curvature measures for continuous designs, and extend design criteria to incorporate continuous designs. These design algorithms include quadratic design procedures, a subset design criterion, a second-order mean-square error design criterion, and a marginal curvature design methodology. A discussion of confidence intervals is also provided for continuous designs.

Conventions, Definitions, Identities, And Other Useful Formulae, 2010 Loyola University Chicago

#### Conventions, Definitions, Identities, And Other Useful Formulae, Robert A. Mcnees Iv

*Physics: Faculty Publications and Other Works*

As the name suggests, these notes contain a summary of important conventions, definitions, identities, and various formulas that I often refer to. They may prove useful for researchers working in General Relativity, Supergravity, String Theory, Cosmology, and related areas.

Towards An Automation Of The Circle Method, 2010 Georgia Southern University

#### Towards An Automation Of The Circle Method, Andrew Sills

*Andrew V. Sills*

The derivation of the Hardy-Ramanujan-Rademacher formula for the number of partitions of *n* is reviewed. Next, the steps for ﬁnding analogous formulas for certain restricted classes of partitions or overpartitions is examined, bearing in mind how these calculations can be automated in a CAS. Finally, a number of new formulas of this type which were conjectured with the aid of *Mathematica* are presented along with results of a test for their numerical accuracy.

Chvátal-Erdös Type Theorems, 2010 University of Memphis

#### Chvátal-Erdös Type Theorems, Ralph J. Faudree, Jill R. Faudree, Ronald J. Gould, Michael S. Jacobson, Colton Magnant

*Colton Magnant*

The Chvátal-Erdös theorems imply that if G is a graph of order n ≥ 3 with κ(G) ≥ α(G), then G is hamiltonian, and if κ(G) > α(G), then G is hamiltonian-connected. We generalize these results by replacing the connectivity and independence number conditions with a weaker minimum degree and independence number condition in the presence of sufficient connectivity. More specifically, it is noted that if G is a graph of order n and k ≥ 2 is a positive integer such that κ(G) ≥ k, δ(G) > (n+k2-k)/(k+1), and δ(G) ≥ α(G)+k-2, then G ...

Some Implications Of Chu's 10Ψ10 Generalization Of Bailey's 6Ψ6 Summation Formula, 2010 West Chester University of Pennsylvania

#### Some Implications Of Chu's 10Ψ10 Generalization Of Bailey's 6Ψ6 Summation Formula, James Mclaughlin, Andrew Sills, Peter Zimmer

*Mathematical Sciences Faculty Publications*

Lucy Slater used Bailey's 6**ψ**6 summation formula to derive the Bailey pairs she used to construct her famous list of 130 identities of the Rogers-Ramanujan type.

In the present paper we apply the same techniques to Chu's 10**ψ**10 generalization of Bailey's formula to produce quite general Bailey pairs. Slater's Bailey pairs are then recovered as special limiting cases of these more general pairs.

In re-examining Slater's work, we find that her Bailey pairs are, for the most part, special cases of more general Bailey pairs containing one or more free parameters ...