arXiv subjects

Benjamin L. Jeffers

Publications and source records attributed to Benjamin L. Jeffers.

3 recordsLinked to original sources

arXiv2022

Solutions of the Variational Equation for an nth Order Boundary Value Problem with an Integral Boundary Condition

In this paper, we discuss differentiation of solutions to the boundary value problem $y^{(n)} = f(x, y, y^{'}, y^{''}, \ldots, y^{(n-1)}), \; a<x<b,\; y^{(i)}(x_j) = y_{ij},\; 0\leq i \leq m_j, \; 1 \leq j \leq k-1$, and $y^{(i)}(x_k) + \int_c^d p y(x)\;dx = y_{ik}, \;0 \leq i \leq m_k,\;\sum_{i=1}^km_i=n$ with respect to the boundary data. We show that under certain conditions, partial derivatives of the solution $y(x)$ of the boundary value problem with respect to the various boundary data exist and solve the associated variational equation along $y(x)$.

math.CA↗

arXiv2022

Linearly Mismatched Free-by-Cyclic Groups are Asynchronously Automatic

We call the family of free-by-cyclic groups defined by $G = \left< a, t, b_1, b_2, \ldots b_k \mid at = ta, b_1^{-1}tb_1 = a^{n_1}t, \ldots b_k^{-1}tb_k = a^{n_k}t \right>$ for $n_1, n_2, \ldots n_k \in \mathbb Z$ linearly mismatched since the automorphisms used to define the HNN extensions grow linearly at different rates. Using techniques from Elder's thesis, namely words with a parallel stable letter structure, we prove that linearly mismatched free-by-cyclic groups are asynchronously automatic, and thus they have a solvable word problem.

math.GR↗

arXiv2022

Structure of Cross-wired Lamplighter Groups

We answer a question posed by Cornulier, Fisher, and Kashyap, proving that for a closed cocompact subgroup $Γ$ of $\text{Isom}(\text{DL}(n, n))$ not contained in $\text{Isom}^+(\text{DL}(n, n))$, the sequence $1 \to H \to Γ\to D_\infty \to 1$ splits, where $H$ is the unique open normal subgroup such that $Γ/H \cong D_\infty$.

math.GR↗