text stringlengths 5.77k 29.6k | extracted_entities sequencelengths 3 70 | refined_entities sequencelengths 0 5 |
|---|---|---|
\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... | [
"Hoffmann-Ostenhof",
"Kostochka",
"Ozeki",
"Ye",
"Bachstein",
"Akbari",
"Jensen",
"Siggers",
"Petersen graph",
"Hamiltonian path",
"Hamiltonian cubic graphs",
"traceable cubic graphs",
"3-connected cubic plane graphs",
"3-connected cubic graph",
"Klein-bottle",
"torus",
"spanning tre... | [
"conjecture",
"graph",
"cycle",
"vertex",
"edge"
] |
\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... | [
"Principle of nano strain-amplifier",
"nanowire strain sensors",
"piezoresistive sensors",
"piezoresistive elements",
"strain sensors",
"nano strain-amplifier structure",
"SiC nanowires",
"dogbone structure",
"tensile strength of materials",
"released micro frame and nanowire",
"classical physic... | [
"nano strain-amplifier",
"SiC nanowires",
"strain sensors",
"piezoresistive sensors",
"nanowire strain sensors"
] |
\section{Introduction}
The concept of synchronistion is based on the adjustment of rhythms of
oscillating systems due to their interaction \cite{pikovsky01}.
Synchronisation phenomenon was recognised by Huygens in the 17th century, time
when he performed experiments to understand this phenomenon \cite{bennett02}... | [
"Huygens",
"Steinmetz et al.",
"Jefferys $\\&$ Haas",
"Brette $\\&$ Gerstner",
"Touboul $\\&$ Brette",
"Erd\\\"os-R\\'enyi network",
"neuronal synchronous rhythms",
"synchronous behaviour of pairs of neurons",
"spiking and bursting synchronisation",
"neuronal network model",
"action potential",
... | [] |
\subsection{Power}
\noindent PMTs that meet the required specifications in terms of pulse rise time, dark current and counting rates, and quantum efficiency require applied high voltages (HV) between $1-2.5$~kV and have maximum current ratings of $0.2-0.5$~mA. For the detector design using 12 read-out channels per modu... | [
"CERN",
"CMS",
"Tiziano Camporesi",
"Joel Butler",
"CMS collaboration",
"Vladimir Ivanchenko",
"Andrea Dotti",
"Mihaly Novak",
"Geant4",
"milliQan project",
"LHC Point 5",
"milli-charged particles"
] | [
"CERN",
"CMS",
"Tiziano Camporesi",
"Joel Butler",
"CMS collaboration"
] |
\section{Introduction}
The black hole information puzzle is the puzzle of whether black hole formation and evaporation is unitary, and debate on this issue has continued for more than 36 years \cite{Page:1993up, Giddings:2006sj, Mathur:2008wi}, since Hawking radiation was discovered \cite{Hawking:1974sw}. Hawking orig... | [
"Black hole",
"Hawking radiation",
"Quantum gravity",
"Maldacena's AdS/CFT conjecture",
"Almheiri",
"Marolf",
"Polchinski",
"Sully",
"Stanford",
"Giddings",
"Donnelly",
"Nomura",
"Bekenstein-Hawking entropy",
"Planck units",
"Gravitational field",
"Bell state",
"Hawking radiation",
... | [
"Black hole",
"Hawking radiation",
"Quantum gravity",
"Gravitational field",
"Unitary transformation"
] |
\section{Introduction}\label{sintro}
\section{Background: CUR and low-rank approximation}\label{sbcgr}
{\em Low-rank approximation} of an $m\times n$ matrix $W$
having a small numerical rank $r$, that is, having
a well-conditioned rank-$r$ matrix nearby,
is one of the most fundamental problems of
numerical lin... | [
"Low-rank approximation",
"Numerical linear algebra",
"Machine learning theory",
"Neural networks",
"Data mining and analysis",
"CUR approximation",
"Floating point arithmetic operation",
"Gaussian (normal) probability distribution",
"Cross-approximation",
"Singular Matrix Database",
"Fast Multi... | [
"CUR approximation",
"Low-rank approximation",
"Numerical linear algebra",
"Gaussian (normal) probability distribution",
"Matrix computations"
] |
\section*{Supplemental Material}
In this Supplemental Material, we provide more numerical data for the ground-state entanglement entropy and entanglement spectrum.
\subsection*{Ground-state entanglement entropy}
In the main text, we have discussed the ground-state entanglement entropy $S(\overline{\rho})$ obtained b... | [
"Gaussian unitary ensemble",
"Poisson distribution",
"Lanczos iterations"
] | [
"Gaussian unitary ensemble",
"Poisson distribution",
"Lanczos iterations"
] |
\section{Gibbs' Canonical Ensemble}
From Gibbs' 1902 text {\it Elementary Principles in Statistical Mechanics}, page 183 :
\begin{quotation}
``If a system of a great number of degrees of freedom is microcanonically distributed
in phase, any very small part of it may be regarded as canonically distributed.''
\end{quotat... | [
"Gibbs' Canonical Ensemble",
"Elementary Principles in Statistical Mechanics",
"J. Willard Gibbs",
"Hamiltonian",
"Canonical",
"Boltzmann's equation",
"H Theorem",
"Maxwell-Boltzmann velocity distribution",
"Steve Brush",
"Vorlesungen \\\"uber Gastheorie",
"Tolman's 1938 tome",
"The Principles... | [] |
\section{Introduction}
In recent decades acoustic techniques in solid state physics demonstrate serious progress, especially by moving to previously unattainable high-frequency band, up to a terahertz frequencies \cite{ps-ultrasonics}.
Considerable efforts in this direction, called often picosecond ultrasonics, are... | [
"Acoustic techniques",
"Solid state physics",
"Picosecond ultrasonics",
"Femtosecond lasers",
"Terahertz sasers",
"Superconductor based detectors",
"Bolometers",
"Superconductor contacts",
"Semiconductor-based approaches",
"Photo-electric acoustic wave detection",
"Schottky diodes",
"Piezoelec... | [
"metal",
"semiconductor",
"Schottky diodes",
"deformation potential",
"Piezoelectric"
] |
\section{Introduction}
In his book ``Proximal Flows''~\cite[Section~\RNum{2}.3, p.\ 19]{glasner1976proximal} Glasner
defines the notion of a {\em strongly amenable group}: A group is
strongly amenable if each of its proximal actions on a compact
space has a fixed point. A continuous action $G \curvearrowright X$ of a
... | [
"Proximal Flows",
"Glasner",
"Weiss",
"Richard Thompson's group",
"Eli Glasner",
"Benjamin Weiss",
"Thompson's group",
"Schreier graph",
"Gromov-Hausdorff limit",
"proximal action",
"product topology",
"compact space",
"F-action",
"F-space",
"Thompson's group",
"Bernoulli",
"Borel"
] | [
"Glasner",
"proximal action",
"Proximal Flows",
"Thompson's group",
"Schreier graph"
] |
\section*{Abstract}{\small
Here is considered the full evolution of a spherical supernova remnant.
We start by calculating the early time ejecta-dominated stage and
continue through the different phases of interaction with the circumstellar
medium, and end with the dissipation and merger phase.
The physical connect... | [
"Supernova remnant",
"Astrophysics",
"Interstellar medium",
"X-rays",
"Infrared",
"Radio continuum",
"Synchrotron emission",
"Chevalier",
"Ejecta dominated phase",
"Sedov-Taylor phase",
"Truelove and McKee",
"Pressure-driven snowplow phase",
"Momentum conserving shell phase",
"Interstellar... | [
"Supernova remnant",
"Interstellar medium",
"circumstellar medium",
"Ejecta dominated phase",
"Sedov-Taylor phase"
] |
\section{Introduction}
The motivation for this note was the observation that the basic recursion relation for the modified Bessel function $K$[1],
$$K_0(z)+\left(\frac{2}{z}\right)K_1(z)=K_2(z)$$
can be expressed as the symmetry with respect to $m=0$ and $n=1$ of the sum
$$\sum_{k=0}^n K_{k-m-1}(z)\left(\frac{z}{2}\... | [
"Gauss hypergeometric function",
"G.E. Andrews",
"R. Askey",
"R. Roy",
"Cambridge University Press",
"A.P. Prudnikov",
"Yu. A.Brychkov",
"O.I. Marichev",
"Gordon and Breach"
] | [
"Gauss hypergeometric function",
"G.E. Andrews",
"R. Askey",
"R. Roy",
"Cambridge University Press"
] |
End of preview. Expand in Data Studio
README.md exists but content is empty.
- Downloads last month
- 3