id stringlengths 40 40 | text stringlengths 1 2.96M |
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b7c40b41b7eedaa408f87d154284a1aba126589c | \section{Introduction}
Let $G$ be a simple undirected graph with the \textit{vertex set} $V(G)$ and the \textit{edge set} $E(G)$. A vertex with degree one is called a \textit{pendant vertex}. The distance between the vertices $u$ and $v$ in graph $G$ is denoted by $d_G(u,v)$. A cycle $C$ is called \textit{chordless} if... |
1b77ae9f541b19668cc96624c7ec0f83945284e2 | \section{Principle of nano strain-amplifier}
\begin{figure*}[t!]
\centering
\includegraphics[width=5.4in]{Fig1}
\vspace{-0.5em}
\caption{Schematic sketches of nanowire strain sensors. (a)(b) Conventional non-released and released NW structure;
(c)(d) The proposed nano strain-amplifier and its simplified... |
467d37196f1b4f439bbd55a25dd550222fb466db | \section{Introduction}\label{intro}
Gas has a fundamental role in shaping the evolution of galaxies,
through its accretion on to massive haloes, cooling and subsequent
fuelling of star formation, to the triggering of extreme luminous
activity around super massive black holes. Determining how the
physical state of gas ... |
bdfca2090653522b89d9415dc698595c4bfce1ec | \section{Introduction}
Given $\rho>0$, we consider the problem
\begin{equation}\label{eq:main_prob_U}
\begin{cases}
-\Delta U + \lambda U = |U|^{p-1}U & \text{in }\Omega,\smallskip\\
\int_\Omega U^2\,dx = \rho, \quad U=0 & \text{on }\partial\Omega,
\end{cases}
\end{equation}
where $\Omega\subset{\mathbb{R}}^N$ is a ... |
0139d272d2b2af4606ec78c8e956da717b63bad8 | "\\section{Introduction}\n\\label{sec:intro}\nDespite the immense popularity and availability of onl(...TRUNCATED) |
ef6fecbf91bf23ce97668d9e0f68279d16e146af | "\\section{Introduction}\n\nThe wave-particle duality is an alternative statement of the complementa(...TRUNCATED) |
12790d44df56e9367af1706e5d4b7a67a1df785f | "\\section{#1}\\setcounter{equation}{0}}\n\\newcommand{\\subsect}[1]{\\subsection{#1}}\n\\renewcomma(...TRUNCATED) |
3935b10ebd2ab44f820e6d8233731be14a55d558 | "\\section{Introduction}\n\\label{sec:introduction} \nIn recent years there has been a resurgen(...TRUNCATED) |
417ff865a9cbac3a94a3b3975ec2721852d90a63 | "\\section{Introduction} \\label{sec:intro}\n\nThe production of hadrons and jets at a future Electr(...TRUNCATED) |
1c5ca046551cfa4aa819c11109c3debac9a8e52b | "\\section{Introduction}\n\\label{sec:intro}\n\n\nCompact stars have a large number of pulsation mod(...TRUNCATED) |
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