From 903055812fa35e0533b940ddb2d8db8c2a20af2b Mon Sep 17 00:00:00 2001
From: Douglas Rumbaugh <dbr4@psu.edu>
Date: Mon, 16 Jun 2025 13:03:49 -0400
Subject: updates

---
 paper.tex | 28 ----------------------------
 1 file changed, 28 deletions(-)

(limited to 'paper.tex')

diff --git a/paper.tex b/paper.tex
index 76d07fd..1eac710 100644
--- a/paper.tex
+++ b/paper.tex
@@ -437,34 +437,6 @@ of Engineering Science and Mechanics
 %\end{singlespace}
 
 \backmatter
-
-\newpage
-\begin{align*}
-	B(n) &\in \Theta(n \log n) \\
-	\mathscr{Q}_S(n) &\in \Theta(\log n + k)
-\end{align*}
-
-\begin{align}
-I(n) \in \Theta\left(B\left(\frac{n}{2}\right)\right) \\
-I(n) \in \Theta(n \log n)
-\end{align}
-
-\begin{equation}
-\mathscr{Q}(n) = \mathscr{Q}_S\left(\frac{n}{2}\right) + \mathscr{Q}_S\left(\frac{n}{2}\right)
-\end{equation}
-
-\begin{equation}
-\mathscr{Q}(n) \in \Theta\left(\log^2n + k\log n\right)
-\end{equation}
-
-
-
-
-
-\begin{align*}
-I_A(n) \in \Theta \left(\frac{B(n)}{n}\cdot \log n\right) \\
-\mathscr{Q}(n) \in O \left(\mathscr{Q}_S(n) \cdot \log n\right)
-\end{align*}
 %Vita
 \vita{chapters/vita}
 
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