Rose–Hulman Institute of Technology
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Characterization of collimation quality of Gaussian beams obtained from engineered diffusers
No full textIncorporation of a Multi-disciplinary Manufacturing Project Experience in Biomedical Engineering
No full textk-Distinct Lattice Paths
Full text linkLattice paths can be used to model scheduling and routing problems, and, therefore, identifying maximum sets of k-distinct paths is of general interest. We extend the work previously done by Gillman et. al. to determine the order of a maximum set of k-distinct lattice paths. In particular, we disprove a conjecture by Gillman that a greedy algorithm gives this maximum order and also refine an upper bound given by Brewer et. al. We illustrate that brute force is an inefficient method to determine the maximum order, as it has time complexity O(nk)
The Chromatic Index of Ring Graphs
Full text linkThe goal of graph edge coloring is to color a graph G with as few colors as possible such that each edge receives a color and that adjacent edges, that is, different edges incident to a common vertex, receive different colors. The chromatic index, denoted χ′(G), is the minimum number of colors required for such a coloring to be possible. There are two important lower bounds for χ′(G) on every graph: maximum degree, denoted ∆(G), and density, denoted ω(G). Combining these two lower bounds, we know that every graph’s chromatic index must be at least ∆(G) or ω(G), whichever is greater. In this paper, we prove that the chromatic index of every ring graph is exactly equal to this lower bound
Using an Art-Inspired, Entrepreneurial Mindset to Encourage Self-Directed Learning and Enhance Proficiency with Computer Aided Analysis
No full textIncorporating an entrepreneur mindset, bio-Inspired design, and STEAM approach to enhancing learning in a CAD modeling class
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