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Full-Text Articles in Physical Sciences and Mathematics
Clique-Relaxed Graph Coloring, Charles Dunn, Jennifer Firkins Nordstrom, Cassandra Naymie, Erin Pitney, William Sehorn, Charlie Suer
Clique-Relaxed Graph Coloring, Charles Dunn, Jennifer Firkins Nordstrom, Cassandra Naymie, Erin Pitney, William Sehorn, Charlie Suer
Faculty Publications
We define a generalization of the chromatic number of a graph G called the k-clique-relaxed chromatic number, denoted χ(k)(G). We prove bounds on χ(k)(G) for all graphs G, including corollaries for outerplanar and planar graphs. We also define the k-clique-relaxed game chromatic number, χg(k)(G), of a graph G. We prove χg(2)(G)≤ 4 for all outerplanar graphs G, and give an example of an outerplanar graph H with χg(2)(H) ≥ 3. Finally, we prove that if H is a member …
Higher Dimensional Lattice Chains And Delannoy Numbers, John S. Caughman, Charles L. Dunn, Nancy Ann Neudauer, Colin L. Starr
Higher Dimensional Lattice Chains And Delannoy Numbers, John S. Caughman, Charles L. Dunn, Nancy Ann Neudauer, Colin L. Starr
Faculty Publications
Fix nonnegative integers n1 , . . ., nd, and let L denote the lattice of points (a1 , . . ., ad) ∈ ℤd that satisfy 0 ≤ ai ≤ ni for 1 ≤ i ≤ d. Let L be partially ordered by the usual dominance ordering. In this paper we use elementary combinatorial arguments to derive new expressions for the number of chains and the number of Delannoy paths in L. Setting ni = n (for all i) in these expressions yields a new …
Scanning Capacitance Spectroscopy On N+-P Asymmetrical Junctions In Multicrystalline Si Solar Cells, Chun-Sheng Jiang, Jennifer T. Heath, Helio R. Moutinho, Mowafak M. Al-Jassim
Scanning Capacitance Spectroscopy On N+-P Asymmetrical Junctions In Multicrystalline Si Solar Cells, Chun-Sheng Jiang, Jennifer T. Heath, Helio R. Moutinho, Mowafak M. Al-Jassim
Faculty Publications
We report on a scanning capacitance spectroscopy (SCS) study on the n+-p junction of multicrystalline silicon solar cells. We found that the spectra taken at space intervals of ∼10 nm exhibit characteristic features that depend strongly on the location relative to the junction. The capacitance-voltage spectra exhibit a local minimum capacitance value at the electrical junction, which allows the junction to be identified with ∼10-nm resolution. The spectra also show complicated transitions from the junction to the n-region with two local capacitance minima on the capacitance-voltage curves; similar spectra to that have not been previously reported in …
Perspectives On Deepening Teachers’ Mathematics Content Knowledge: The Case Of The Oregon Mathematics Leadership Institute, Libby Knott, Martha Vancleave
Perspectives On Deepening Teachers’ Mathematics Content Knowledge: The Case Of The Oregon Mathematics Leadership Institute, Libby Knott, Martha Vancleave
Faculty Publications
The Oregon Mathematics Leadership Institute (OMLI) project served 180 Oregon teachers, and 90 administrators, across the K-12 grades from ten partner districts. OMLI offered a residential, three-week summer institute. Over the course of three consecutive summers, teachers were immersed in a total of six mathematics content classes– Algebra, Data & Chance, Discrete Mathematics, Geometry, Measurement & Change, and Number & Operations—along with an annual collegial leadership course. Each content class was designed and taught by a team of expert faculty from universities, community colleges, and K-12 districts. Each team chose a few “big ideas” on which to focus the course. …