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Full-Text Articles in Mathematics
Hamilton Cycles In Bidirected Complete Graphs, Arthur Busch, Mohammed A. Mutar, Daniel Slilaty
Hamilton Cycles In Bidirected Complete Graphs, Arthur Busch, Mohammed A. Mutar, Daniel Slilaty
Mathematics and Statistics Faculty Publications
Zaslavsky observed that the topics of directed cycles in directed graphs and alternating cycles in edge 2-colored graphs have a common generalization in the study of coherent cycles in bidirected graphs. There are classical theorems by Camion, Harary and Moser, Häggkvist and Manoussakis, and Saad which relate strong connectivity and Hamiltonicity in directed "complete" graphs and edge 2-colored "complete" graphs. We prove two analogues to these theorems for bidirected "complete" signed graphs.
Fluid-Structure Interaction Modelling Of Neighboring Tubes With Primary Cilium Analysis, Nerion Zekaj, Shawn D. Ryan, Andrew Resnick
Fluid-Structure Interaction Modelling Of Neighboring Tubes With Primary Cilium Analysis, Nerion Zekaj, Shawn D. Ryan, Andrew Resnick
Mathematics and Statistics Faculty Publications
We have developed a numerical model of two osculating cylindrical elastic renal tubules to investigate the impact of neighboring tubules on the stress applied to a primary cilium. We hypothesize that the stress at the base of the primary cilium will depend on the mechanical coupling of the tubules due to local constrained motion of the tubule wall. The objective of this work was to determine the in-plane stresses of a primary cilium attached to the inner wall of one renal tubule subject to the applied pulsatile flow, with a neighboring renal tube filled with stagnant fluid in close proximity …
Symplectic Reduction Along A Submanifold, Peter Crooks, Maxence Mayrand
Symplectic Reduction Along A Submanifold, Peter Crooks, Maxence Mayrand
Mathematics and Statistics Faculty Publications
We introduce the process of symplectic reduction along a submanifold as a uniform approach to taking quotients in symplectic geometry. This construction holds in the categories of smooth manifolds, complex analytic spaces, and complex algebraic varieties, and has an interpretation in terms of derived stacks in shifted symplectic geometry. It also encompasses Marsden-Weinstein-Meyer reduction, Mikami-Weinstein reduction, the pre-images of Poisson transversals under moment maps, symplectic cutting, symplectic implosion, and the Ginzburg-Kazhdan construction of Moore-Tachikawa varieties in topological quantum field theory. A key feature of our construction is a concrete and systematic association of a Hamiltonian G-space 𝔐𝐺,𝑆 to …
Leveraging The "Large" In Large Lecture Statistics Classes, Kady Schneiter, Kimberleigh Felix Hadfield, Jenny Lee Clements
Leveraging The "Large" In Large Lecture Statistics Classes, Kady Schneiter, Kimberleigh Felix Hadfield, Jenny Lee Clements
Mathematics and Statistics Faculty Publications
Being a teacher or a student in a class with a large enrollment can be intimidating. Often, teachers view comforts that are common to small classes as unattainable in a larger class, including knowing students’ names, using active learning, employing group work, and creating group discussion. Students in large classes may find that the class size leads to isolation. At Utah State University, we offer introductory statistics classes for various audiences using a large lecture format. The authors have collectively led these large lectures dozens of times and found that, despite its shortcomings, the large lecture format can be an …
Characterization Of A Family Of Rotationally Symmetric Spherical Quadrangulations, Lowell Abrams, Daniel Slilaty
Characterization Of A Family Of Rotationally Symmetric Spherical Quadrangulations, Lowell Abrams, Daniel Slilaty
Mathematics and Statistics Faculty Publications
A spherical quadrangulation is an embedding of a graph G in the sphere in which each facial boundary walk has length four. Vertices that are not of degree four in G are called curvature vertices. In this paper we classify all spherical quadrangulations with n-fold rotational symmetry (n ≥ 3) that have minimum degree 3 and the least possible number of curvature vertices, and describe all such spherical quadrangulations in terms of nets of quadrilaterals. The description reveals that such rotationally symmetric quadrangulations necessarily also have a pole-exchanging symmetry.