Physical Sciences and Mathematics Commons^™

Linear Codes And Error-Correction, Karen Brown

Presidential Scholars Theses (1990 – 2006)

The process of encoding information for transmission from one source to another is a vital process in many areas of science and technology. Whenever coded information is sent, there arises a certain possibility that an error will occur, either during transmission or in decoding. Therefore, it is imperative to develop methods to detect and correct errors in a code. The study of coding theory is a "new" area of mathematics which is relatively undeveloped.

This paper focuses on the properties of linear codes -and their corresponding methods of error-correction. To simplify the issue, only binary block codes are studied; hence …

The Modeling Of Phosphorus Dynamics In A Lake System, Todd N. Swift

Presidential Scholars Theses (1990 – 2006)

We have constructed a basic closed stock and flow model of lake phosphorus cycling that includes three stock concentrations: inorganic phosphorus, phosphorus in living organic material, and phosphorus in dead organic material. Stocks are connected by flows that are made stock dependent in a plausible manner. The model exhibits two equilibrium points, one stable and the other unstable, with an interesting crossover between them. Below a certain total phosphorus threshold, stable equilibrium is characterized by all of the phosphorus stock residing in the inorganic form, suggesting the collapse of the biological system. Above the threshold, this is not true. We …