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Articles 1 - 4 of 4
Full-Text Articles in Physical Sciences and Mathematics
When A Mechanical Model Goes Nonlinear, Lisa D. Humphreys, P. J. Mckenna
When A Mechanical Model Goes Nonlinear, Lisa D. Humphreys, P. J. Mckenna
Faculty Publications
This paper had its origin in a curious discovery by the first author in research performed with an undergraduate student. The following odd fact was noticed: when a mechanical model of a suspension bridge (linear near equilibrium but allowed to slacken at large distance in one direction) is shaken with a low-frequency periodic force, several different periodic responses can result, many with high-frequency components.
Particular Solutions For Axisymmetric Helmholtz-Type Operators, A.S. Muleshkov, M.A. Golberg, C.S. Chen
Particular Solutions For Axisymmetric Helmholtz-Type Operators, A.S. Muleshkov, M.A. Golberg, C.S. Chen
Faculty Publications
In this paper, we consider the solution of the axisymmetric heat equation with axisymmetric data in an axisymmetric domain in R-3. To solve this problem, we remove the time-dependence by various transform or time-stepping methods. This converts the problem to one of a sequence of modified inhomogeneous Helmholtz equations. Generalizing previous work, we consider solving these equations by boundary-type methods. In order to do this, one needs to subtract off a particular solution, so that one obtains a sequence of modified homogeneous Helmholtz equations. We do this by modifying the usual Dual Reciprocity Method (DRM) and approximating the right-hand sides …
Conjugacy Classes And Finite P-Groups, Edith Adan-Bante
Conjugacy Classes And Finite P-Groups, Edith Adan-Bante
Faculty Publications
Let G be a finite p-group, where p is a prime number, and a ∈ G. Denote by Cl(a) = {gag−1| g ∈ G} the conjugacy class of a in G. Assume that |Cl(a)| = p n . Then Cl(a) Cl(a−1) = {xy | x ∈ Cl(a), y ∈ Cl(a−1)} is the union of at least n(p − 1) + 1 distinct conjugacy classes of G.
Graphs Whose Minimal Rank Is Two: The Finite Fields Case, Wayne Barrett, Hein Van Der Holst, Raphael Loewy
Graphs Whose Minimal Rank Is Two: The Finite Fields Case, Wayne Barrett, Hein Van Der Holst, Raphael Loewy
Faculty Publications
Let F be a finite field, G = (V,E) be an undirected graph on n vertices, and let S(F,G) be the set of all symmetric n × n matrices over F whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. Let mr(F,G) be the minimum rank of all matrices in S(F,G). If F is a finite field with p^t elements, p does not = 2, it is shown that mr(F,G) ≤ 2 if and only if the complement of G is the join of a complete graph with either the union of at most …