Rose–Hulman Institute of Technology
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Entropy Generation Analysis for Heat Exchanger Operation Subject to Step Changes in Inlet Conditions
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Modeling an infection outbreak with quarantine: The SIBKR Model
Full text linkInfluenza is a respiratory infection that places a substantial burden in the world population each year. In this project, we study and interpret a data set from a flu outbreak in a British boarding school in 1978 with mathematical modeling. First, we propose a generalization of the SIR model based on the quarantine measure in place and establish the long-time behavior of the model. By analyzing the model mathematically, we determine the analytic formulas of the basic reproduction number, the long-time limit of solutions, and the maximum number of infection population. Moreover, we estimate the parameters of the model based on the data set. Finally, we evaluate the effect of the quarantine measure by numerical computations with various alternative sets of parameters in the model
Approximating Equilibria in Restricted Games
Full text linkWe consider optimal play in restricted games with linear constraints, and use ϵ-equilibria to find near-equilibrium states in these games. We present three mathematical optimization formulations -- a mixed-integer linear program (MILP), a quadratic program with linear constraints (QP), and a quadratically constrained program (QCP) -- to both approximate and identify these states. The MILP has a short runtime relative to the QP and QCP for large games (a factor 100 faster for |S|=9) and exhibits linear growth in run time, but provides only relatively weak upper bound. The QP and QCP provide a tight bound and the precise value respectively, and outperform the LP for small games (|S| ≤ 5), but they exhibit an exponential growth of the required runtime
Concept Maps Afford Connections from Mathematics and Physics to Electrical Engineering Courses
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Counting Hamming-Graceful Labelings of Paths
Full text linkLet Γ be a graph of m edges and n vertices. A Hamming-graceful labeling of Γ labels vertices with binary strings of length m and the edge labels are induced by the Hamming distance between vertex labels. It is known that all paths have Hamming-graceful labelings, thus the question arises, how many possible labelings exist for a path of a given size. We develop an algebraic way to generate labelings, conjecture a method for counting, prove this for small examples, and verify larger examples using a Python program
