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    Potential Scenario
    149

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    45

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    1999-Leonid_Hanin-Which tank empties first
    Suppose that water towers like those shown in the opening are initially filled with water and have the same volume, height, and cross-sectional outlet area. Which one empties first?
    tankTorricelli's Lawspherical tankemptyfrustrum of conecylinder
    Modeling Scenario
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    277

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    1-029-ConeToCubeFlow-ModelingScenario
    An inverted right circular cone with a hole at the bottom is suspended above an open-topped cube which also has a hole in the center of the bottom. The cone is filled with water and we model water flow from cone to cube and out the bottom of the...
    waterflowTorricelli's Lawconecube
    Modeling Scenario
    255

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    283

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    1-055-WaterFallingInCone-ModelingScenario
    We offer an opportunity to model the height of a falling body of water in a right circular cone (funnel) and to estimate an appropriate parameter based on data collected from a video of the experiment found on YouTube.
    Torricelli's Lawdischarge coefficientconecontraction coefficient
    Modeling Scenario
    376

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    301

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    1-026-Evaporation-ModelingScenario
    We provide data on evaporation of 91% isopropyl alcohol in six different Petri dishes and one conical funnel and on evaporation of water in one Petri dish. We ask students to develop a mathematical model for the rate of change in the respective...
    evaporationconealcoholPetri dish
    Potential Scenario
    143

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    44

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    2008-Chernyshov-EtAl-The Problem of Modelling of Economic Dynamics in Differential Form
    The authors have tried to analyze procedures of the construction of differential equations that are employed for modeling of macroeconomic processes. The results prove to be rather unexpected.
    Fredholm integral equation ofLeontief’s modelmacroeconomic processes
    Potential Scenario
    154

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    62

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    2007-Mogen_Steffensen-Differential Equations in Finance and Life Insurance
    The mathematics of finance and the mathematics of life insurance were always intersecting. Life insurance contracts specify an exchange of streams of payments between the insurance company and the contract holder.
    financedisabilitylife insurancemortalityinsuraneThiele’s equationBlack-Scholes equation
    Potential Scenario
    144

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    79

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    2008-William_Revelle-Cues Tendencies and Actions-The Dynamics of Action Revisited
    This article describes a reparameterization of the original theory of dynamics of action and applies the power of simple modeling to the study of action, emotions, and social behavior.
    psychologytask referenceachievement motivationdynamics of action
    Potential Scenario
    212

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    26

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    2014-John_Cain-Chemical Reaction Kinetics Mathematical Underpinnings
    The usual way of deriving kinetic equations involves application of the principle of conservation of mass in conjunction with the law of mass action. Here, examples of kinetic models for several basic processes are discussed.
    kineticsbiochemical reactionreactantsproducts
    Potential Scenario
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    2016-Erno_Keszei-Chemical Kinetics for Beginners
    The most important goal of kinetic research is the identification and characterisation of elementary molecular events which make possible the transformation of reactants into products.
    kineticszeroth order reactionfirst order reactionsecond order reactionreaction ratesthird order reaction
    Article or Presentation
    130

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    54

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    2011-Carl_Leinbach-Beyond_Newton_law_of_cooling_estimation_of_time_since_death
    The estimate of the time since death. Thus, the time of death is strictly that, an estimate. However, the time of death can be an important piece of information in some coroner’s cases, especially those that involve criminal or insurance...
    Newton's Law of Coolingtime of deathdouble exponentialcoroner
    Potential Scenario
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    43

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    2000-Dwayne-Anderson-Estimates of the future membership of the Church of Jesus Christ of Latter-Day Saints
    Thus, the purpose of this paper is to model the membership of the Church of the Latter Day Saints from the available data on membership from 1844 to 2000.
    population dynamicslogisticLatter-Day Saints
    Article or Presentation
    174

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    40

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    2008-Keith_Landry-Brian_Winkel-Peak_Frequency_Responses_and_Tuned_Mass_Dampers
    We present two applications of systems of ordinary differential equations concerning excitation of a structure through resonance and (1) peak frequency responses with stabilization of the structure by means of a (2) Tuned Mass Damper (TMD).
    vibrationresonancetuned mass damperpeak frequency responseexcitation
    Article or Presentation
    158

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    66

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    1981-Nielsen_Francois-Rachel_Rosenfeld-Substantive_Interpretations_of_Differential_Equation_Models
    The interpretation of parameters of dynamic models is illustrated with reference to research on two substantive topics: political mobilization and intragenerational mobility.
    differential equationsdynamical systemsFirst order linearintragenerational mobilitypolitical mobilizationmobility
    Potential Scenario
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    40

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    2012-José_Sérgio_Domingues-Gompertz Model - Resolution and Analysis for Tumors
    The main objective of this paper is to use the Gompertz equation in order to study the development of blood irrigated solid tumors, using parameters defined in some important bibliographic references about the mathematical modelling of tumors.
    tumorGompertz equationgrowth tumor
    Potential Scenario
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    61

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    2011-Mandal-EtAl-Mathematical models of malaria
    The first aim of this article is to develop, starting from the basic models, a hierarchical structure of a range of deterministic models of different levels of complexity. The second is to elaborate, using some of the representative mathematical...
    epidemiologytransmissionhost-parasitemalariaRoss model
    Potential Scenario
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    2000-Erdman-Morelock-A Study of Kinetics The Estimation and Simulation of Systems of First-Order Differential Equations
    This paper introduces new and old features of the SAS System for the estimation and simulation of systems of first-order differential equations with emphasis on examples in kinetics.
    kineticsSAScompartmentpharmacokinetics
    Potential Scenario
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    96

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    2001-Smith-Moore-The SIR Model for Spread of Disease
    A multiple part tour of SIR Models freely available with Maple, Mathematics, and MatLab support files at MAA site.
    epidemicSIR modelEuler's methodherd immunityHong Kong flu
    Potential Scenario
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    1988-Michael Intriligator-Dagobert Brito-A Predator-Prey Model of Guerrilla Warfare
    The authors present a three variable: numbers of guerrillas, numbers of regular (government) soldiers, and size of population controlled by the guerrillas, at time t), nonlinear system of three differential equations.
    combat modelguerrilla warfaregovernment
    Potential Scenario
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    1957-Axelrod_ Brady_Witkop_Evarts-The Distribution and Metabolism of Lysergic Acid Diethylamide
    The development of a specific and sensitive method for the estimation of LSD in biological materials has enabled us to study the tissue distribution, excretion, rate of biotransformation, and metabolism of the drug, as well as the subcellular...
    mathematical modeldataLSDMetabolismbloodstreamlysergic acid diethylamidedistribution
    Potential Scenario
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    56

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    2018-Adeniji-EtAl-InverseProblemHolling-TannerModel
    We consider the inverse problem of parameter identification of nonlinear system of ODEs for a specific case of complete information about solution of the Holling-Tanner model for finite number of points for the finite time interval.
    goal functionabsolute error curvesinvers methodholling-Tanner model