meta stringlengths 139 139 | red_pajama_subset stringclasses 1
value | prompt stringlengths 1 200 | answer stringlengths 0 518k |
|---|---|---|---|
{'timestamp': '2016-07-19T02:04:55', 'yymm': '1607', 'arxiv_id': '1607.04768', 'language': 'en', 'url': 'https://arxiv.org/abs/1607.04768'} | arxiv | \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 dist | ance between the vertices $u$ and $v$ in graph $G$ is denoted by $d_G(u,v)$. A cycle $C$ is called \textit{chordless} if $C$ has no \textit{cycle chord} (that is an edge not in the edge set of $C$ whose endpoints lie on the vertices of $C$).
The \textit{Induced subgraph} on vertex set $S$ is denoted by $\langle S\rangl... |
{'timestamp': '2016-07-18T02:07:38', 'yymm': '1607', 'arxiv_id': '1607.04531', 'language': 'en', 'url': 'https://arxiv.org/abs/1607.04531'} | arxiv | \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 physical model.}
\label{fig:fig1}
\vspace{-1em}
\end{figure*}
Figure \ref{fig:fig1}(a) and 1(b) show the concept of the conventional structures of piezoresistive sensors. The piezoresistive el... |
{'timestamp': '2016-08-09T02:04:29', 'yymm': '1607', 'arxiv_id': '1607.04828', 'language': 'en', 'url': 'https://arxiv.org/abs/1607.04828'} | arxiv | \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 in galaxies changes as a function of redshift is
therefore crucial to understanding how these processes evolve over
cosmological time. The standard model of the gaseous interstellar
medium (ISM) in ga... |
{'timestamp': '2016-07-18T02:07:27', 'yymm': '1607', 'arxiv_id': '1607.04520', 'language': 'en', 'url': 'https://arxiv.org/abs/1607.04520'} | arxiv | \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 Lipschitz, bounded domain, $1<p<2^*-1$, $\rho>0$ is a fixed
parameter, and both $U\in H^1_0(\Omega)$ and $\lambda\in{\mathbb{R}}$ are unknown. More precisely,
we investigate conditions on $p$ and $\rh... |
"{'timestamp': '2016-07-20T02:04:30', 'yymm': '1607', 'arxiv_id': '1607.04648', 'language': 'en', 'u(...TRUNCATED) | arxiv | "\\section{Introduction}\n\\label{sec:intro}\nDespite the immense popularity and availability of onl(...TRUNCATED) | "atic images.\nGiven the breakthroughs of deep convolutional neural networks \nfor detecting objects(...TRUNCATED) |
"{'timestamp': '2017-01-26T02:07:48', 'yymm': '1607', 'arxiv_id': '1607.04617', 'language': 'en', 'u(...TRUNCATED) | arxiv | "\\section{Introduction}\n\nThe wave-particle duality is an alternative statement of the complementa(...TRUNCATED) | "r and the ondulatory} nature of quantum entities \\cite{Bohr1928}. It can be illustrated in a two-w(...TRUNCATED) |
"{'timestamp': '2016-07-19T02:06:15', 'yymm': '1607', 'arxiv_id': '1607.04824', 'language': 'en', 'u(...TRUNCATED) | arxiv | "\\section{#1}\\setcounter{equation}{0}}\n\\newcommand{\\subsect}[1]{\\subsection{#1}}\n\\renewcomma(...TRUNCATED) | " \\magstep1\n\\font\\mbss=msbm5 scaled \\magstep1\n\\newfam\\mbff\n\\textfont\\mbff=\\mbn\n\\script(...TRUNCATED) |
"{'timestamp': '2016-12-01T02:04:39', 'yymm': '1607', 'arxiv_id': '1607.04724', 'language': 'en', 'u(...TRUNCATED) | arxiv | "\\section{Introduction}\n\\label{sec:introduction} \nIn recent years there has been a resurgen(...TRUNCATED) | "states of hard sphere systems; see for reviews \nRefs. \\onlinecite{charbonneau16, b(...TRUNCATED) |
"{'timestamp': '2016-10-28T02:00:49', 'yymm': '1607', 'arxiv_id': '1607.04921', 'language': 'en', 'u(...TRUNCATED) | arxiv | "\\section{Introduction} \\label{sec:intro}\n\nThe production of hadrons and jets at a future Electr(...TRUNCATED) | "hich comprise the visible matter in the universe. Measurements of inclusive jet and hadron product(...TRUNCATED) |
"{'timestamp': '2016-07-19T02:02:47', 'yymm': '1607', 'arxiv_id': '1607.04707', 'language': 'en', 'u(...TRUNCATED) | arxiv | "\\section{Introduction}\n\\label{sec:intro}\n\n\nCompact stars have a large number of pulsation mod(...TRUNCATED) | "APJ140:417:1964,PRL12:114:1964}. In general, these modes are very difficult to observe in the elect(...TRUNCATED) |
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