Finite Field Numerical Ranges

Supervisor: Dr. Rebekah Yates | Houghton University

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We investigate the numerical ranges of square matrices with entries from finite fields. We devote particular attention to the numerical ranges of matrices with norm-0 eigenvectors.

The Polynomial Shift Operator on Time Scales

Supervisor: Dr. Tom Cuchta | Fairmont State University

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​We attempt to derive a functional representation for the polynomial shift operator on the quantum time scale. The main approach we utilize involves taking the Laplace transform of a polynomial function, differentiating in the complex numbers, and then taking the inverse Laplace.

The Discrete Anger Function

Supervisor: Dr. Tom Cuchta | Fairmont State University

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We derive a discrete analogue to the continuous Anger function by solving the discrete Anger differential equation. We then investigate various properties of the discrete Anger function, including its hypergeometric representation, recurrence relations, and derivative relations.

Diversity and Similarity of Models Using SELFIES

Supervisor: Dr. Wei Hu | Houghton University

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We explore four different approaches to generating molecules as SELFIES strings, evaluating the diversity scores and Tanimoto similarity for each method.

Bayesian Parameter Estimation & Model Comparison

Supervisor: Dr. Gautam Rupak | Mississippi State University​

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We use the Bayesian nested sampling algorithm implemented in Python to determine unknown parameters and compare models for neutron capture on carbon-14.

Patterns in the Coefficients of Chebyshev Polynomials

Supervisor: Dr. Brandon Bate | Houghton University​

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We sum the coefficients of Chebyshev polynomials and arrange them in a triangular array, observing fractal-like characteristics in their prime factorizations that appear similar to those in Pascal’s triangle.