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2205.15082 | \section{Introduction}
Consider a scalar, autonomous ordinary differential equation (ODE) of the form
\begin{equation}\label{eq:ode}
\begin{split}
\frac{dX}{dt}(t) &= a(X(t)) \qquad \text{for } t > 0, \\
X(0) &= 0
\end{split}
\end{equation}
where \( a\from{\mathbb R} \rightarrow {\mathbb R} \) is Borel measurab... |
2205.15013 | \section{Definitions and Basic Identities}
Let the coefficient of a power series be defined as:
\begin{equation}
[q^n] \sum_{k=0}^{\infty} a_k q^k = a_n
\end{equation}
Let $P(n)$ be the number of integer partitions of $n$, and let $P(n,m)$ be the
number of integer partitions of $n$ into exactly $m$ parts.
Let $P(n,m,... |
2205.15024 | \section{Counterexample}\label{sec:counterexample}
\begin{thm} \label{thm:mainTheorem}
Let $\textup{R}_8$ be the dihedral quandle of order $8$. Then
\begin{displaymath}
\left|\Delta^2\left(\textup{R}_8\right)/\Delta^3\left(\textup{R}_8\right)\right|= 16.
\end{displaymath}
\end{thm}
\noindent From... |
2205.15032 | "\\section{Introduction}\r\nBy a finite partially ordered set (poset) \\(I\\) of size \\(n\\) we mea(...TRUNCATED) |
2302.11221 | "\\section{\\protect\\bigskip \\textbf{Introduction}}\n\nWe know that the Mac Donald polynomials and(...TRUNCATED) |
2205.14924 | "\\section{Introduction}\r\n\t\\subsection{Background}\r\n\tDenote by $ \\|\\cdot\\| $ the distance (...TRUNCATED) |
2302.12183 | "\\section{Introduction} \n\nFractional calculus is nowadays a well consolidated field of research \(...TRUNCATED) |
2302.12079 | "\\section{Introduction}\n\nLet $C$ be a germ of complex plane curve singularity with \\(r\\geq 1\\)(...TRUNCATED) |
2302.12082 | "\\section{Introduction}\nA random matrix is a matrix whose entries are random variables. As\neigen(...TRUNCATED) |
2302.12062 | "\\section{Introduction}\r\n\r\nThe quantum dilogarithm is a $q$-series with many remarkable propert(...TRUNCATED) |
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