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Natural products are those chemical agents made by plants and microorganisms that are not directly involved in the growth, development, or reproduction of the organism. These natural products, or secondary metabolites, are used by the organism as defenses against predators, parasites and diseases, or to facilitate the reproductive process. Many of these compounds are isolated in very minute amounts, and some of them display significant biological activity. They have been used as excellent leads for the development of new drugs. Some of these natural products have a complex structure and development of new chemical methodology is required for their synthesis. Our group is interested in developing new strategies for the synthesis of natural products that possess large rings and possess heteroatoms. Members of our research group acquire necessary laboratory expertise to carry out complex chemical transformations, learn the skills to purify and characterize chemical intermediates, and develop the skills to accomplish a multi-step synthesis. Extensive use of nuclear magnetic resonance spectroscopy is necessary to elucidate or confirm the structure of the molecules prepared in the lab.
Mentor: Dr. Horacio F. Olivio, Associate Professor, Division of Medicinal and Natural Products Chemistry
Curves in space can twist and tangle and knot. This project studies knots, in particular those that have some kind of rotational or reflection symmetry. To visualize a smooth curve on a computer, we usually draw a polygon with many small edges. However, we can also represent a smooth closed curve by finite trigonometric polynomials in each of the three coordinates. In this project, we will discover how symmetries of the knots correspond to symmetries of the polynomials. We also will explore the problem of adjusting an almost-symmetric knot to get one that is really symmetric.
Background: The Workshop in Orthogonal Polynomials, along with the linear algebra that the workshop assumes, will be good preparation for this project. We will use Maple (or similar computer system) for calculations and visualization, so it will be helpful if at least some of the students working on this project have prior experience with Maple, Mathematica, or Matlab.
If you select this project you will be enrolled in a five week workshop, Orthogonal Polynomials. This workshop will meet daily for five weeks and will provide you with the mathematical background for your project.
Mentor: Dr. Jonathan Simon, Professor of Mathematics, The University of Iowa
Ethanol plants consume energy for cooking the mash, drying the whole stillage and evaporating the thin stillage to produce Soluble to blend with DDG. This project will examine the energy consumption in each of these unit processes and will evaluate the possibility of generating renewable energy from ethanol plant waste stream, e, g., thin stillage to substitute the natural gas or coal.
Mentor: Dr. Samir Kumar Khanal, Applied Statistics, Iowa State University
Studies in human and animal health and nutrition often involve monitoring change over some period of time. For example, subjects may be taken measured weekly to examine the effects of different diets on growth. Progression of a disease, or the effects of different interventions on reducing risk of disease, are monitored by having subjects report for annual or semi-annual examinations. These are called repeated measures studies. In other studies, time to some event such as detection of a tumor or death from a disease is recorded. The analysis of such data is called survival analysis. This project will provide an introduction to some basic statistical methods for such studies and analyze data from a current study of a human or animal health issue.
Mentor: Dr. Kenneth Koehler, Mathematics, University of Northern Iowa
A square matrix A is said to be a compartment matrix if: 1. all diagonal entries are negative or zero; 2. all off-diagonal entries are positive or zero; and 3. all column sums are negative or zero. Such matrices can be shown to have eigenvalues with negative or zero real parts. Some biological models lead to differential equations X' = AX + f, where X is a column-vector whose entries represent quantities in the various compartments, the derivative is with respect to time, f is a column vector and A is a compartment matrix. Such a compartmental model is used in Chapter 7 of the textbook, An Introduction to the Mathematics of Biology, by E.K. Yeargers, R.W. Shonkwiler and J.V. Herod, to model lead in the bodies of mammals.
The properties of compartmental models will be studied and the possibility of using compartmental models to study the presence of other chemical toxins in humans will be investigated. Background for the study will be provided in a five-week course on differential equations to be taught by Professor Douglas Mupasiri. Work on the project itself will begin in the fifth week of the session.
Mentor: Dr. Jerry Ridenhour
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