Comparing the Effects of Interactive and Noninteractive Complementary Nutrients on Growth in a Chemostat

We compare the effects of interactive and noninteractive complementary nutrients on the growth of an organism in the chemostat. We also compare these two situations to the case when the nutrients are substitutable. In previous studies, complementary nutrients have been assumed to be noninteractive. However, more recent research indicates that some complementary nutrient relationships are interactive. We show that interactive complementary and substitutable nutrients can lead to higher population densities than do noninteractive complementary nutrients. We numerically illustrate that if the washout rate is high, an organism can persist at higher densities when the complementary nutrients are interactive than when they are noninteractive, which can result in the extinction of the organism. Finally, we present an example by making a small adjustment to the model that leads to a single nutrient model with an intermediate metabolite of the original substrate as the nutrient for the organism

Rock-Paper-Scissors in the Chemostat

Rock-Paper-Scissors is a game played by two players to determine a single winner. Biological relationships of Rock-Paper-Scissors are documented. In this paper, we form a continuous model of Rock-Papers-Scissors in the chemostat that coincides with the biology of such relationships. The basic models that we develop coincide with the observed phenomena. Because the model involves a system of seven nonlinear differential equations, global results are difficult to obtain. We present several numerical studies that are the result of a substantial number of numerical trials to illustrate the various possibilities that might occur in the context of the problem discussed here

A Spitzer Study of Asymptotic Giant Branch Stars. III. Dust Production and Gas Return in Local Group Dwarf Irregular Galaxies

We present the third and final part of a census of Asymptotic Giant Branch (AGB) stars in Local Group dwarf irregular galaxies. Papers I and II presented the results for WLM and IC 1613. Included here are Phoenix, LGS 3, DDO 210, Leo A, Pegasus dIrr, and Sextans A. Spitzer photometry at 3.6, 4.5, 5.8, and 8 are presented, along with a more thorough treatment of background galaxy contamination than was presented in papers I and II. We find that at least a small population of completely optically obscured AGB stars exists in each galaxy, regardless of the galaxy's metallicity, but that higher-metallicity galaxies tend to harbor more stars with slight IR excesses. The optical incompleteness increases for the redder AGB stars, in line with the expectation that some AGB stars are not detected in the optical due to large amounts of extinction associated with in situ dust production. Overall, there is an underrepresentation of 30% - 40% in the optical AGB within the 1 sigma errors for all of the galaxies in our sample. This undetected population is large enough to affect star formation histories derived from optical color-magnitude diagrams. As measured from the [3.6] - [4.5] color excesses, we find average stellar mass-loss rates ranging from 3.1E-7 - 6.6E-6 solar masses per year, and integrated galaxy mass-loss rates ranging from 4.4E-5 - 1.4E-3 solar masses per year. The integrated mass-loss rate is sufficient to sustain the current star formation rate in only LGS 3 and DDO 210, requiring either significant non-dusty mass loss or gas accretion in Phoenix, Leo A, Pegasus dIrr, Sextans A, WLM, and IC 1613 if they are to maintain their status as gas-rich galaxies.Comment: 25 pages, 17 figures, 9 tables, Accepted for publication in ApJ; updated affiliation for Boye

The James Webb Space Telescope Mission

Twenty-six years ago a small committee report, building on earlier studies, expounded a compelling and poetic vision for the future of astronomy, calling for an infrared-optimized space telescope with an aperture of at least $4m$. With the support of their governments in the US, Europe, and Canada, 20,000 people realized that vision as the $6.5m$ James Webb Space Telescope. A generation of astronomers will celebrate their accomplishments for the life of the mission, potentially as long as 20 years, and beyond. This report and the scientific discoveries that follow are extended thank-you notes to the 20,000 team members. The telescope is working perfectly, with much better image quality than expected. In this and accompanying papers, we give a brief history, describe the observatory, outline its objectives and current observing program, and discuss the inventions and people who made it possible. We cite detailed reports on the design and the measured performance on orbit.Comment: Accepted by PASP for the special issue on The James Webb Space Telescope Overview, 29 pages, 4 figure

Modern Differential Equations: Theory, Applications, Technology

Georgia Southern faculty members Martha L. Abell, James P. Braselton, and John A. Rafter co-authored Modern Differential Equations: Theory, Applications, Technology, Second Edition. 1. Introduction to Differential Equations. Introduction. A Graphical Approach to Solutions: Slope Fields and Direction Fields. Summary. Review Exercises. 2. First Order Equations. Separable Equations. First-Order Linear Equations. Substitution Methods and Special Equations. Exact Equations. Theory of First-Order-Equations. Numerical Methods for First-Order Equations. Summary. Review Exercises. Differential Equations at Work. Modeling the Spread of a Disease. Linear Population Model with Harvesting. Logistic Model with Harvesting. Logistic Model with Predation. 3. Applications of First Order Equations. Population Growth and Decay. Newton\u27s Law of Cooling and Related Problems. Free-Falling Bodies. Summary. Review Exercises. Chapter 3 Differential Equations at Work. Mathematics of Finance. Algae Growth. Dialysis. Antibiotic Production. 4. Higher Order Equations. Second-Order Equations: An Introduction. Solutions of Second-Order Linear Homogeneous Equations with Constant Coefficients. Higher Order Equations: An Introduction. Solutions to Higher Order Linear Homogeneous Equations with Constant Coefficients. Introduction to Solving Nonhomogeneous Equations with Constant Coefficients: Method of Undetermined Coefficients. Nonhomogeneous Equations with Constant Coefficients: Variation of Parameters. Cauchy-Euler Equations. Series Solutions of Ordinary Differential Equations. Summary. Review Exercises. Differential Equations at Work. Testing for Diabetes. Modeling the Motion of a Skier. The Schröinger Equation. 5. Applications of Higher Order Equations. Simple Harmonic Motion. Damped Motion. Forced Motion. Other Applications. The Pendulum Problem. Summary. Review Exercises. Differential Equations at Work. Rack-and-Gear Systems. Soft Springs. Hard Springs. Aging Springs. Bodé Plots. 6. Systems of First Order Equations. Introduction. Review of Matrix Algebra and Calculus. Preliminary Definitions and Notation. First-Order Linear Homogeneous Systems with Constant Coefficients. First-Order Linear Nonhomogeneous Systems: Undetermined Coefficients and Variation of Parameters. Phase Portraits. Nonlinear Systems. Numerical Methods. Summary. Review Exercises. Differential Equations at Work. Modeling a Fox Population in Which Rabies is Present. Controlling the Spread of Disease. FitzHugh-Nagumo Model. 7. Applications of First-Order Systems. Mechanical and Electrical Problems with First-Order Linear Systems. Diffusion and Population Problems with First-Order Linear Systems. Nonlinear Systems of Equations. Summary. Review Exercises. Differential Equations at Work. Competing Species. Food Chains. Chemical Reactor. 8. Laplace Transforms. The Laplace Transform: Preliminary Definitions and Notation. Solving Initial-Value Problems with the Laplace Transform. Laplace Transforms of Several Important Functions. The Convolution Theorem. Laplace Transform Methods for Solving Systems. Applications Using Laplace Transforms. Summary. Review Exercises. Differential Equations at Work. The Tautochrone. Vibration Absorbers. Airplane Wing. Free Vibration of a Three-Story Building. Control Systems. 9. Fourier Series. Boundary-Value Problems, Eigenvalue Problems, Sturm-Liouville Problems. Fourier Sine Series and Cosine Series. Fourier Series. Generalized Fourier Series. Summary. Review Exercises. Differential Equations at Work. Free Vibration of a Three-Story Building. Forced Damped Spring-Mass System. Approximations with Fourier Series. 10. Partial Differential Equations. Introduction to Partial Differential Equations and Separation of Variables. The One-Dimensional Heat Equation. The One-Dimensional Wave Equation. Problems in Two Dimensions: Laplace\u27s Equation. Two-Dimensional Problems in a Circular Region. Summary. Review Exercises. Differential Equations at Work. Laplace Transforms. Waves in a Steel Rod. Media Sterilization. Numerical Methods for Solving Partial Differential Equations. Answers to Selected Questions. Index.https://digitalcommons.georgiasouthern.edu/math-sci-facbookshelf/1054/thumbnail.jp

The Maple V Handbook

Georgia Southern faculty members Martha L. Abell and James P. Braselton co-authored The Maple V Handbook. Covers built-in functions, miscellaneous library functions, and numerous packages. Each listing includes an explanation of functionality, annotated examples, and numerous cross-references, in a format useful to both beginning and advanced users. Many examples are used from the areas of calculus, linear algebra, ordinary and partial differential equations, and graphics.https://digitalcommons.georgiasouthern.edu/math-sci-facbookshelf/1058/thumbnail.jp

Mathematica By Example

This third edition of Mathematica by Example is completely compatible with recent Mathematica versions. Highly readable and informative, this volume is geared toward the beginning Mathematica user, and focuses on the most often used features of this powerful tool. The book covers popular applications of mathematics within different areas including calculus, linear algebra, ordinary differential equations, and partial differential equations. Key Features: * Fully compatible with recent releases of Mathematica * Includes CD-ROM containing all input used in text * Focuses on the beginning Mathematica user * Covers all the basics needed to get up and running with Mathematica, especially for use in mathematics*Written by authors of several successful AP books on Mathematicahttps://digitalcommons.georgiasouthern.edu/math-sci-facbookshelf/1071/thumbnail.jp