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2023

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Articles 1171 - 1174 of 1174

Full-Text Articles in Mathematics

Strong Homotopy Lie Algebras And Hypergraphs, Samuel J. Bevins, Marco Aldi Jan 2023

Strong Homotopy Lie Algebras And Hypergraphs, Samuel J. Bevins, Marco Aldi

Undergraduate Research Posters

We study hypergraphs by attaching a nilpotent strong homotopy Lie algebra. We especially focus on hypergraph theoretic information that is encoded in the cohomology of the resulting strong homotopy Lie algebra.

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Machine-Assisted Discovery Of Integrable Symplectic Mappings, T. Zolkin, Y. Kharkov, S. Nagaitsev Jan 2023

Machine-Assisted Discovery Of Integrable Symplectic Mappings, T. Zolkin, Y. Kharkov, S. Nagaitsev

Physics Faculty Publications

We present a new automated method for finding integrable symplectic maps of the plane. These dynamical systems possess a hidden symmetry associated with an existence of conserved quantities, i.e., integrals of motion. The core idea of the algorithm is based on the knowledge that the evolution of an integrable system in the phase space is restricted to a lower-dimensional submanifold. Limiting ourselves to polygon invariants of motion, we analyze the shape of individual trajectories thus successfully distinguishing integrable motion from chaotic cases. For example, our method rediscovers some of the famous McMillan-Suris integrable mappings and ultradiscrete Painlevé equations. In total, …

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Some 2-Color Rado Numbers For A Linear Equation With A Negative Constant, Rachel Bergjord Jan 2023

Some 2-Color Rado Numbers For A Linear Equation With A Negative Constant, Rachel Bergjord

Electronic Theses and Dissertations

An r-coloring is a function Δ that assigns a color to each natural number from 1 to some number n using colors 0, 1, . . . , r − 1. A monochromatic solution (in Δ) to an equation L with m variables is an ordered m-tuple (x1, x2, . . . , xm) where Δ(x1) = Δ(x2) = · · · = Δ(xm) and (x1, x2, . . . , xm−1, xm) solves L. Given a linear equation L and t ∈ N, the t-color Rado number for L is the least integer n (if it exists) such that …

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Classification On Boundary-Equilibria And Singular Continuums Of Continuous Piecewise Linear Systems, Hebai Chen, Zhaosheng Feng, Hao Yang, Linfeng Zhou Jan 2023

Classification On Boundary-Equilibria And Singular Continuums Of Continuous Piecewise Linear Systems, Hebai Chen, Zhaosheng Feng, Hao Yang, Linfeng Zhou

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we show that any switching hypersurface of n -dimensional continuous piecewise linear systems is an (n−1) -dimensional hyperplane. For two-dimensional continuous piecewise linear systems, we present local phase portraits and indices near the boundary equilibria (i.e. equilibria at the switching line) and singular continuum (i.e. continuum of nonisolated equilibria) between two parallel switching lines. The index of singular continuum is defined. Then we show that boundary-equilibria and singular continuums can appear with many parallel switching lines.

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