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    Potential Scenario
    139

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    2018-Yu-Craciun-Mathematical_Analysis_of_Chemical_Reaction_Systems
    These models of chemical reactions are systems of coupled nonlinear differential equations on the positive orthant.
    biochemicalkineticsreactionreaction networkmass action
    Modeling Scenario
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    126

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    6-030-SaltAndTorricelli-ModelingScenario
    We build on a model for the height of a falling column of water with a small hole in the container at the bottom of the column of water. We use data from one video of a falling column of water.
    whole picturetankmixingflowcolumn of watersalt mixinggraduated cylinderapertureTorricelli's Law
    Potential Scenario
    155

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    58

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    2003-Richard-Carson-Tracer kinetic modeling in PET
    The use of radiopharmaceuticals and the imaging of their biodistribution and kinetics with modern instrumentation are key components to successful developments in PET.
    Metabolismtomographyradiopharmaceuticalspositron emission
    Potential Scenario
    184

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    83

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    2014-Enderling-Chaplain-Mathematical Modeling of Tumor Growth and Treatment
    Herein we describe fundamentals of mathematical modeling of tumor growth and tumor-host interactions, and summarize some of the seminal and most prominent approaches.
    cancertumor modelingangiogenesistumor growthpatient care
    Potential Scenario
    127

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    64

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    2013-Michael-Evans-Growth and Decay
    Sometimes, we can describe processes of growth and decay—whether physical, chemical, biological or sociological—by mathematical models.
    exponential growthexponential decayisotopespopulationsresource depletion
    Potential Scenario
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    64

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    2002-Nelson-Perelson-Mathematical analysis of delay differential equations models of HIV-1 infection
    We develop and analyze a set of models that include intracellular delays, combination antiretroviral therapy, and the dynamics of both infected and uninfected T cells.
    infectionHIVT cells
    Potential Scenario
    169

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    35

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    1991-Thoddi_Kotiah-Difference and differential equations in the mathematics of finance
    Many problems arising in the mathematics of finance involve identical money flows at regular time intervals and are typically solved by appropriate valuation at a focal date or by setting up an equation of value.
    financesavingsgrowth fundinterestmortgageannuitydepreciation
    Modeling Scenario
    394

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    297

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    1-061-PotatoCooling-ModelingScenario
    We model the cooling of a baked potato and compare it to student-collected data.
    least sum of square errorsNewton's Law of Coolingcoolingpotato
    Modeling Scenario
    212

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    431

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    5-002-RelationshipDynamics-ModelingScenario
    The different possible dynamics of a two-person romantic relationship are modeled -- as a linear two dimensional system of equations -- and analyzed.
    love affairRomeo and Juliet
    Potential Scenario
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    53

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    2017-Agmour-EtAl-Optimization of the Two Fishermen's Profits Exploiting Three Competing Species Where Prices Depend on Harvest
    The main purpose of this work is to define the fishing effort that maximizes the profit of each fisherman, but all of them have to respect two constraints: the first one is the sustainable management of the resources and the second one is...
    FishingharvestNash equilibriumoptimizeprofits
    Potential Scenario
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    53

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    2012-Augustus-Wali-Mathematical Modeling of Uganda Population Growth
    The purpose of this paper focuses on the application of logistic equation to model the population growth of Uganda using data from 1980 to 2010 (inclusive).
    population growthlogistic growthDrug and Alcohol detoxificationcarrying capacityvital coefficients
    Potential Scenario
    251

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    61

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    1968-Wagner-Aghajanian-Bing-Correlation of performance test scores with tissue concentration of lysergic acid diethylamide
    This paper offers a two compartment model of lysergic acid diethylamide (LSD) in volunteer students and through parameter estimation models the amount of LSD in the tissue after its initial administration through the plasma.
    LSDcorrelation coefficientcompartment modellysergic acid diethylamideperformancetest scoretissue concentration
    Potential Scenario
    267

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    35

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    2008-Claire_Vailance-Reaction_Kinetics-Course_Notes
    This is but one of several set of notes which may interest the reader on chemical kinetics.
    kineticsparametersrate constantchemical kineticsreactions
    Potential Scenario
    391

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    45

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    2011-Yuan-EtAl-Real life applications of ODEs for Undergraduates
    This study introduces real-life mathematical theories and models of international relationships suitable for undergraduate ordinary differential equations, by investigating contradicts between different nations or alliances.
    arms raceRichardson modelBattle of Curupaytíinternational relationships
    Potential Scenario
    99

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    46

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    2003-Givens-Bonfima-Direct observation of normal modes in coupled oscillators
    We propose a simple and inexpensive method to directly observe each normal mode of a system of coupled oscillators, as well as to measure its corresponding frequency, without performing Fourier analysis or using expensive apparatus.
    frequencyresonancecoupled oscillator
    Article or Presentation
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    29

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    2013-Brian_Winkel-An_Optimal_Control_Model_in_Insect_Colonies
    we find and develop background material on an application of optimal control theory to model the evolutionary strategy of an insect colony to produce the maximum number of queen or reproducer insects in the colony at the end of a season.
    insect colonyoptimal controlparameter
    Technique Narrative
    465

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    228

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    1-002-IntegratingFactor-TechniqueNarrative
    We develop a strategy to solve first order differential equations by transforming one side of the equation to the derivative of a product of two functions, thereby making it easy to antidifferentiate that side.
    Integrating Factor
    Potential Scenario
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    2011-Carl_Leinbach-Beyond Newton's law of cooling - estimation of time since death
    The paper offers an excellent history of temperature-based methods and then proceeds to demonstrate these with some data. Here the history is rich and will support student investigation as well as faculty development.
    time of deathNewton's aw of cooling
    Potential Scenario
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    2020-Cline_Fasteen_Francis_Sullivan_Wendt-Vision_for_Projects_Across_Mathematics_Curriculum
    We consider the use of projects in math courses as a mechanism for promoting coding, communication, and interdisciplinary application of math skills. Final projects play an important role, but we also discuss several alternate types of projects.
    modelinginterdisciplinarywritingcodingprojecttechnical writing
    Potential Scenario
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    2017-Biswasa-EtAl-Mathematical Modeling Applied to Sustainable Management of Marine Resources
    We study a nonlinear mathematical model of fishery management to understand dynamics of a fishery resource system in an aquatic environment that consists of two zones; one free fishing zone and another reserve zone where fishing is strictly...
    natural resourcesmarine resourcesfishery model