Mathematics Commons^™

Matching Functions And Graphs At Multiple Levels Of Bloom’S Revised Taxonomy, Kris H. Green

Mathematical and Computing Sciences Faculty/Staff Publications

This paper illustrates the power of Bloom's revised taxonomy for teaching, learning and assessing [3] in aligning our curriculum expectations and our assessment tools in multivariable calculus. The particular assessment tool considered involves a common matching problem to evaluate students' abilities to think about functions from graphical and formulaic representations. Through this analysis we gain additional understanding of why students may have difficulty in performing well on certain activities.

Some New Classes Of Complex Symmetric Operators, Stephan Ramon Garcia, Warren R. Wogen

Pomona Faculty Publications and Research

We say that an operator $T \in B(H)$ is complex symmetric if there exists a conjugate-linear, isometric involution $C:H\to H$ so that $T = CT^*C$. We prove that binormal operators, operators that are algebraic of degree two (including all idempotents), and large classes of rank-one perturbations of normal operators are complex symmetric. From an abstract viewpoint, these results explain why the compressed shift and Volterra integration operator are complex symmetric. Finally, we attempt to describe all complex symmetric partial isometries, obtaining the sharpest possible statement given only the data $(\dim \ker T, \dim \ker T^*)$.

Review: Intertwining Symmetry Algebras Of Quantum Superintegrable Systems, Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.

Review: The Semi-Dynamical Reflection Equation: Solutions And Structure Matrices, Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.

A Vision For Acms, James Bradley

ACMS Journal 2010-2011

This paper presents a vision for the mission of the ACMS. It considers some plausible connections between mathematics and theology as well as some big questions that Christian mathematicians might fruitfully explore. It examines the current cultural norms of the mathematics guild, why these are problematic for Christians, and some possible ways the ACMS might respond.

Traveling Wave Solutions For A Nonlocal Reaction-Diffusion Model Of Influenza A Drift, Joaquin Riviera, Yi Li

Mathematics and Statistics Faculty Publications

In this paper we discuss the existence of traveling wave solutions for a nonlocal reaction-diffusion model of Influenza A proposed in Lin et. al. (2003). The proof for the existence of the traveling wave takes advantage of the different time scales between the evolution of the disease and the progress of the disease in the population. Under this framework we are able to use the techniques from geometric singular perturbation theory to prove the existence of the traveling wave.

Quantum Geons And Noncommutative Spacetimes, A. P. Balachandran, A. Ibort, G. Marmo, M. Martone

Physics - All Scholarship

Physical considerations strongly indicate that spacetime at Planck scales is noncommutative. A popular model for such a spacetime is the Moyal plane. The Poincare group algebra acts on it with a Drinfel'd-twisted coproduct. But the latter is not appropriate for more complicated spacetimes such as those containing the Friedman-Sorkin (topological) geons. They have rich diffeomorphism groups and in particular mapping class groups, so that the statistics groups for N identical geons is strikingly different from the permutation group SN. We generalise the Drinfel'd twist to (essentially) generic groups including to finite and discrete ones and use it to modify the …

Mathematics In Motion: Linear Systems Of Differential Equations On The Differential Analyzer, Devon A. Tivener

Theses, Dissertations and Capstones

In this work, I will provide an introduction to the dierential analyzer, a machine designed to solve dierential equations through a process called mechanical integration. I will give a brief historical account of dierential analyzers of the past, and discuss the Marshall University Dierential Analyzer Project. The goal of this work is to provide an analysis of solutions of systems of dierential equations using a dierential analyzer. In particular, we are interested in the points at which these systems are in equilibrium and the behavior of solutions that start away from equilibrium. After giving a description of linear systems of …

Methods Of Variational Analysis In Pessimistic Bilevel Programming, Samarathunga M. Dassanayaka

Wayne State University Dissertations

Bilevel programming problems are of growing interest both from theoretical and practical points of view. These models are used in various applications, such as economic planning, network design, and so on. The purpose of this dissertation is to study the pessimistic (or strong) version of bilevel programming problems in finite-dimensional spaces. Problems of this type are intrinsically nonsmooth (even for smooth initial data) and can be treated by using appropriate tools of modern variational analysis and generalized differentiation developed by B. Mordukhovich.

This dissertation begins with analyzing pessimistic bilevel programs, formulation of the problems, literature review, practical application, existence of …

Simulating Power For One-Way Anova By Using Non-Normal Error Distributions, Caixia Xu

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Usually we assume that the distribution of the additive errors in a one-way ANOVA linear model is normal. However, exceptions to this assumption about the error distribution may exist. In such cases, we might consider non-normal error distributions, but proceed with the "usual" ANOVA F-test analyses. This study focuses on simulating power for one-way ANOVA when using non-normal error distributions.

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, Z_R, and the initial ratio of the rotational and translational temperatures, T_R0 / T_L0, 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′ …

Global Caccioppoli-Type And Poincar ´E Inequalities With Orlicz Norms, Ravi P. Agarwal, Shusen Ding

Mathematics and System Engineering Faculty Publications

We obtain global weighted Caccioppoli-type and Poincaré inequalities in terms of Orlicz norms for solutions to the nonhomogeneous A -harmonic equation d A(x,d)=B(x,d).

The Fibonacci Sequence, Arik Avagyan

A with Honors Projects

A review was made of the Fibonacci sequence, its characteristics and applications.

Variational Analysis In Parametric Optimization, Yen Nhi Nguyen Thi

Wayne State University Dissertations

The dissertation is devoted to the development of variational analysis and generalized differentiation in infinite dimensions. We derive new calculus rules for both first-order partial subdifferentials and second-order partial subdifferentials in the framework of general Banach spaces as well as more developed rules in the framework of Asplund spaces. This calculus is applied in the study of sensitivity analysis for solution maps to the parameterized generalized equations in Asplund spaces, where both bases and fields are parameter-dependent multifunctions. We analyze the parametric sensitivity of either stationary points or stationary point multiplier multifunctions associated with parameterized optimization problems under consideration. The …

On The Convergence Of Greedy Algorithms For Initial Segments Of The Haar Basis, S J. Dilworth, E Odell, Th Schlumprecht, Andras Zsak

Faculty Publications

We consider the X-Greedy Algorithm and the Dual Greedy Algorithm in a finite-dimensional Banach space with a strictly monotone basis as the dictionary. We show that when the dictionary is an initial segment of the Haar basis in Lp[0, 1] (1< p < 1) then the algorithms terminate after finitely many iterations and that the number of iterations is bounded by a function of the length of the initial segment. We also prove a more general result for a class of strictly monotone bases.

Local Versus Global Search In Channel Graphs, A.H. Hunter, Nicholas Pippenger

All HMC Faculty Publications and Research

Previous studies of search in channel graphs has assumed that the search is global; that is, that the status of any link can be probed by the search algorithm at any time. We consider for the first time local search, for which only links to which an idle path from the source has already been established may be probed. We show that some well known channel graphs may require exponentially more probes, on the average, when search must be local than when it may be global.

Voting In Agreeable Societies, Deborah E. Berg '06, Serguei Norine, Francis E. Su, Robin Thomas, Paul Wollan

All HMC Faculty Publications and Research

No abstract provided in this article.

Early Intervention In College Mathematics Courses: A Component Of The Stem Rrg Program Funded By The Us Department Of Education, Rohitha Goonatilake, Eduardo Chappa

The Mathematics Enthusiast

Student preparedness in entry level college mathematics courses has decreased in the past. In order for students to be successful in these courses, early intervention is required. Texas A&M International University (TAMIU) has implemented an early intervention program, the Mathematics Enrichment Program (MEP), which will target freshman students entering College Algebra courses in Spring 2009. This project is part of the STEM Recruitment, Retention, and Graduation program, recently funded by the US Department of Education. This paper will highlight the components of the project, most importantly the extent of the intervention, how the project is planned, and preliminary results.

New Year Tidings, Bharath Sriraman

The Mathematics Enthusiast

No abstract provided.

Leading Learning Within A Plc: Implementing New Mathematics Content, Ann Heirdsfield, Janeen Lamb, Gayle Spry

The Mathematics Enthusiast

This paper does two things. Firstly, it examines the literature that coalesces around theoretical models of teacher professional development (PD) within a professional learning community (PLC). Secondly, these models are used to analyse support provided to two year 3 teachers, while implementing the draft Queensland mathematics syllabus. The findings from this study suggest that the development of this small PLC extended the teachers’ Zone of Enactment which in turn led to teacher action and reflection. This was demonstrated by the teachers leading their own learning as well as that of their students.

Tme Volume 7, Number 1

The Mathematics Enthusiast

No abstract provided.

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.

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, 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 A_{2 …}

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 A₁ and B₁ which were used to calculate the reflection coefficient, (B₁/A₁)². The conclusions obtained from these results stated that the particle would be reflected by the barrier when E

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.

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.

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.

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 heating time.

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.