Pendulums are simple mechanical systems that have been studied for centuries and exhibit many aspects of modern dynamical systems theory.

Dynamical Systems 37J46, 65P99

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Motivated by recent work on optimal approximation by polynomials in the unit disk, we consider the following noncommutative approximation problem: for a polynomial $f$ in $d$ freely noncommuting arguments, find a free polynomial $p_n$, of degree at most $n$, to minimize $c_n := \|p_nf-1\|^2$.

Functional Analysis

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A cap set is a subset of $\mathbb{F}_3^n$ with no solutions to $x+y+z=0$ other than when $x=y=z$.

Combinatorics Discrete Mathematics Number Theory 05D10, 11B25, 11B30, 11B50, 11B75 (Primary) 0504, 0508, 05B05, 1104, 11P99, 11Y99 (Secondary)

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We give a new proof of local convergence of a multigrid method called iterative aggregation/disaggregation (IAD) for computing steady-states of Markov chains.

Numerical Analysis Statistical Mechanics Numerical Analysis Chemical Physics 60J22, 82C80, 65C05

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In 1965, Erd\H{o}s and P\'{o}sa proved that there is a duality between the maximum size of a packing of cycles and the minimum size of a vertex set hitting all cycles.

Combinatorics 05C38, 05C70, 05C78, 05C25

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We also give an explicit description of cup-products in the cohomology of locally constant constructible sheaves over smooth projective curves.

Algebraic Geometry Number Theory 14F20 (Primary), 11G20, 11Y16, 03D99 (Secondary)

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In this paper, we consider stationary symmetric helix pairs under the M\"obius energy.

Differential Geometry Analysis of PDEs Complex Variables

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A corner is a triple of points in $\Bbb{Z}^2$ of the form $(x, y),(x+d, y),(x, y+d)$ where $d\neq 0$.

Combinatorics Number Theory

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This paper revisits Buridan's Bridge paradox (Sophismata, chapter 8, Sophism 17), itself close kin to the Liar paradox, a version of which also appears in Bradwardine's Insolubilia.

History and Overview Logic 03-03, 03B47, 03B44

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In particular, we discuss results for certain dyadic models in the context of existence, uniqueness and regularity of solutions.

Analysis of PDEs 35Q35, 76D03, 76W05

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