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\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... | b7c40b41b7eedaa408f87d154284a1aba126589c |
\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.... | 1b77ae9f541b19668cc96624c7ec0f83945284e2 |
\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 i... | 467d37196f1b4f439bbd55a25dd550222fb466db |
\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 Lip... | bdfca2090653522b89d9415dc698595c4bfce1ec |
\section{Introduction} \label{sec:intro} Despite the immense popularity and availability of online video content via outlets such as Youtube and Facebook, most work on object detection focuses on static images. Given the breakthroughs of deep convolutional neural networks for detecting objects in static images, the app... | 0139d272d2b2af4606ec78c8e956da717b63bad8 |
\section{Introduction} The wave-particle duality is an alternative statement of the complementarity principle, and it establishes the relation between \ankb{corpuscular and undulatory}{the corpuscular and the ondulatory} nature of quantum entities \cite{Bohr1928}. It can be illustrated in a two-way interferometer, wher... | ef6fecbf91bf23ce97668d9e0f68279d16e146af |
\section{#1}\setcounter{equation}{0}} \newcommand{\subsect}[1]{\subsection{#1}} \renewcommand{\theequation}{\arabic{section}.\arabic{equation}} \font\mbn=msbm10 scaled \magstep1 \font\mbs=msbm7 scaled \magstep1 \font\mbss=msbm5 scaled \magstep1 \newfam\mbff \textfont\mbff=\mbn \scriptfont\mbff=\mbs \scriptscriptfont\mb... | 12790d44df56e9367af1706e5d4b7a67a1df785f |
\section{Introduction} \label{sec:introduction} In recent years there has been a resurgence of interest in the properties of metastable states, due mostly to the studies of the jammed states of hard sphere systems; see for reviews Refs. \onlinecite{charbonneau16, baule16}. There are many topics to study, including for ... | 3935b10ebd2ab44f820e6d8233731be14a55d558 |
\section{Introduction} \label{sec:intro} The production of hadrons and jets at a future Electron Ion Collider (EIC) will play a central role in understanding the structure of the protons and nuclei which comprise the visible matter in the universe. Measurements of inclusive jet and hadron production with transversely p... | 417ff865a9cbac3a94a3b3975ec2721852d90a63 |
\section{Introduction} \label{sec:intro} Compact stars have a large number of pulsation modes that have been extensively studied since the seminal work of Chandrasekhar on radial oscillations \cite{APJ140:417:1964,PRL12:114:1964}. In general, these modes are very difficult to observe in the electromagnetic spectrum; th... | 1c5ca046551cfa4aa819c11109c3debac9a8e52b |
\section{Introduction} Ultra-cold molecules can play important roles in studies of many-body quantum physics~\cite{pupillo2008cold}, quantum logic operations~\cite{demille2002quantum}, and ultra-cold chemistry~\cite{ni2010dipolar}. In our recent studies of LiRb, motivated largely by its large permanent dipole moment~\c... | d95635bc08fd14ade0a89cf08420e98ffd0f6b8b |
\section{Introduction}\label{sec:introduction} The use of GPS for localizing sensor nodes in a sensor network is considered to be excessively expensive and wasteful, also in some cases intractable, \cite{bul:00,bis:06}. Instead many solutions for the localization problem tend to use inter-sensor distance or range measu... | d8a5e808b3b90b0513cf0c72dcfd2e3df48814d2 |
\section{Introduction} Quantum theory of gravity is one of the most sought-after goals in physics. Despite continuous efforts to tackle this important problem, resulting in interesting proposals such as superstring theory and loop quantum gravity, there is still no clear sign of the theory of quantum gravity \cite{Giul... | 3a890d61b35aff2fdcf6bc715cfb6957a8a2cb8c |
\part{Background} \bigskip \addcontentsline{toc}{section}{1. Preliminaries} \textbf{\S 1. Preliminaries} \stepcounter{section} \bigskip The prerequisites for reading this paper are a background of one year of graduate level study in set theory, a working knowledge of forcing, and some basic familiarity with proper forc... | 6e964ae3be26a56c939b5985e33af46f1e30cd66 |
\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}. To da... | 1ba0a8c597a5b6ee0830ca23c5b9ab8ce3b62efd |
\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... | a5fd2f310d6714cde82b7c04bb3e6f796c5aae70 |
\section{Introduction Throughout this paper, let $R$ denote a commutative Noetherian ring with identity and ${\mathfrak a}$ a proper ideal of $R$. For any non-zero $R$-module $M$, the ith local cohomology module of $M$ is defined as $$H^{i}_{{\mathfrak a}}(M):=\lim_{\underset{n\geq 1}{\longrightarrow}} \operatorname{Ex... | 2f59f7879be9c80f1df4909ebccace08db257c28 |
\section{Introduction} To write high-quality program code for a Multi-Processor System-on-Chip (MPSoC), software developers must fully understand how their code will be executed on-chip. Debugging and tracing tools can help developers to gain this understanding. They are a keyhole through which developers can peek and ... | c06ec0f30465dd21ff3ea5027d2bbfa652a2e3e5 |
\section{Introduction} \label{sec:intro} The Type~Ia supernova (SN~Ia) SN~2011fe was discovered on 2011 August 24, just 11~hr after explosion \citep{nugent11}. It is among the nearest ($\sim 6.9$~Mpc) and youngest ($\sim 11$~hr) SNe~Ia ever discovered. Extensive spectroscopic and photometric studies of SN~2011fe indica... | d18a74adc6f563a5494f9cf0ee38af9746eada63 |
\section{High-field instability from spin-wave theory} In the asymptotic high-field limit all spins are aligned along the field axis. Magnon excitations are suppressed by a large energy gap. By lowering the field strength the magnon gap decreases and eventually vanishes at some critical field strength $h_{\mathrm{c}0}$... | 185e9f90d93d078196d46d0c79174714237f3669 |
\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 origi... | c7dfc98266d9a9c36e71efeb0e655803ef3a7190 |
\section{Results} The actuation concept consists of two elements. First, the conversion of rotation into time-reversible translation is achieved by each particle separately, hence, a single-particle problem. Second, the breaking of the time reversibility arises from the interaction between the particles in a cluster. I... | 5410a4b3a1b09f1912adf6ec69edc991a5231d5d |
\section{Introduction} Currents of spin angular momentum play a central role in the field of spintronics. Significant contributions have been made by spin currents, such as control of magnetizations by spin transfer torque,\citep{PhysRevLett.84.3149,demidov2011control,berger1996emission,ralph2008spin} transmission of e... | 842d24bc33ac769220affce1ce229e3d0c36375b |
\section{Introduction}\label{introduction} \setcounter{equation}{0} \numberwithin{equation}{section} In the present paper, we consider the equation \begin{equation}\label{1.1} -y''(x)+q(x)y(x )=f(x),\quad x\in \mathbb R \end{equation} where $f\in L_p^{\loc}(\mathbb R)$, $p\in[1,\infty)$ and \begin{equation}\label{1.2} ... | 7c6ec6b07f6e9cc57c84968ebb95269aa2395b34 |
\section{Introduction} Spectral embedding methods are based on analyzing Markov chains on a high-dimensional data set $\left\{x_i\right\}_{i=1}^{n} \subset \mathbb{R}^d$. There are a variety of different methods, see e.g. Belkin \& Niyogi \cite{belk}, Coifman \& Lafon \cite{coif1}, Coifman \& Maggioni \cite{coif2}, Don... | 48196a99e6c64a2673a380447e415ed30b20c95a |
\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 linear algeb... | ff44ea6d25a77da54b74b5060a441c09c58b4dfa |
\section{Introduction} NGC 4660 is an E5 elliptical galaxy with a strong incrusted disk component, and has frequently been used as a `classic' example of this type of galaxy. As such it has appeared frequently in the literature. It is located in the Virgo cluster, and has been identified as a member of the nearest comp... | daee9918f4f93de04946c46745d1c314288d3d3e |
\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 by a... | 5fab997cf8b27e973a64a061be0aa50cb3e2044f |
\section{Introduction} The shallow water equations (Saint-Venant \cite{Saint-Venant1871}) are a common $(d - 1)$ approximation to the $d$--dimensional Navier-Stokes equations to model incompressible, free surface flows. Due to the ability of high-order Galerkin methods to keep dissipation and dispersion errors low (Ain... | d53bbf469ca04bb5fbd7062a450cba2c00479b10 |
\section{Introduction and Summary of Results} The problem of admissible functional-classes has been of recent interest in the context of higher-spin (HS) theories \cite{Vasiliev:1990en}. In particular, in \cite{Kessel:2015kna,Boulanger:2015ova} the quadratic interaction term sourcing Fronsdal's equations was extracted ... | 9b897dee32341df521b91e8a88f9d2b9a04e562f |
\section{Introduction} \blfootnote{ % % % % \hspace{-0.65cm} This work is licensed under a Creative Commons Attribution 4.0 International License. License details: \url{http://creativecommons.org/licenses/by/4.0/} } Argumentation mining is a relatively new challenge in corpus-based discourse analysis that involves auto... | 03df1d25322bbd4914a5768042c64fe6efc97101 |
\section{Menger co-analytic groups} We shall assume all spaces are completely regular. \begin{defn} A topological space is \textbf{analytic} if it is a continuous image of $\mathbb{P}$, the space of irrationals. A space is \textbf{Lusin} if it is an injective continuous image of $\mathbb{P}$. (This is the terminology o... | ff4a6df1a52f4891034852c14c652312e4fea285 |
\section{Introduction} There are many open questions regarding the strength and geometry of the magnetic field in radio galaxies and their relation to other properties of the radio source. The observed degree of polarization depends on the intrinsic properties, such as the regularity and orientation of the source magne... | 31ec072526eada9187ae9e5d9bca9e7b1fe6f89c |
\section{Introduction}\label{sec:intro} The constraint satisfaction problem (CSP) provides a framework in which it is possible to express, in a natural way, many combinatorial problems encountered in computer science and AI~\cite{Cohen06:handbook,Creignou01:book,Feder98:monotone}. An instance of the CSP consists of a s... | 3831f5d43651b93443f7b97153ed8ff9384f90a1 |
\section{Introduction} \label{sec:Introduction} Topological insulators (TIs) form a class of materials with unique properties, associated with a non-trivial topology of their quasiparticle band structure (for a review, see Refs.~\cite{Zhang:rev, Hasan-Kane:rev, Hasan-Moore:rev, Ando:rev}). The key feature of two-dimens... | bcd73857a29c93a81082cd2b5634975a37343c29 |
\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... | 4df0043dbd096d6c69998163b90855e98340756c |
\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 sti... | fe9f0cbedace3b1bc230475543afbb1bc2881730 |
\section{Introduction} \label{sec:intro} Atmospheric metals are not expected to be present in isolated white dwarfs (WDs) with effective temperatures below $\sim25,000$ K. At these temperatures, radiative forces become too weak \citep{chayer95} to significantly counteract the quick gravitational settling that sinks mat... | f059ade8ca1b6c7457fa8310cb89acd964da485d |
\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 t... | 307a7516e620bdb53ec72d9db06c57a1b2448573 |
\section{Introduction} \label{sec:1} The influence of social groups in pedestrian dynamics, especially in evacuation scenarios, is an area of recent interest, see e.g. \cite{mueller2,mueller} and other contributions in these proceedings. The situations that are considered are widespread and well-known in everyday life.... | e446ef41a60af69ad04b265c37552ed3922672e1 |
\section{Introduction} \label{sec:intro} Policy search algorithms based on supervised learning from a computational or human ``teacher'' have gained prominence in recent years due to their ability to optimize complex policies for autonomous flight \cite{rmswd-lmruc-13}, video game playing \cite{rgb-rilsp-11,gsllw-amcts... | b2626f3873b25d41c2de31c91c507e7e8082993f |
\section{Introduction} Spatio--temporal models are widely used by practitioners. Explaining economic, environmental, social, or biological phenomena, such as peer influence, neighbourhood effects, contagion, epidemics, interdependent preferences, climate change, and so on, are only some of the interesting applications ... | c2084d91152fccc47f8e0c5b3c965e679a0d55ea |
\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 connection ... | ea26d50ef9855d66aef5d2296d47fb43cf42e00c |
\section{Introduction} The purpose of this paper is to provide a convenient operadic framework for the cumulants of free probability theory. In~\cite{DrummondColeParkTerilla:HPTI,DrummondColeParkTerilla:HPTII}, the author and his collaborators described an operadic framework for so-called Boolean and classical cumulant... | ba21779ca4df037124955b1d43a715e5c701dcfa |
\section{Introduction} The Navier-Stokes equations (NSEs) represent a formulation of the Newton's laws of motion for a continuous distribution of matter in a fluid state, characterized by an inability to support shear stresses, see \cite{Doering-Gibbon}. The NSEs allow to determine the velocity field and the pressure o... | c119738c8140213d35cc0c262585ef2842765f45 |
\section{Introduction} Germanium is widely used as a detector material in experiments searching for a rare process like the interaction of weakly interacting massive particles (WIMPs)~\cite{dmreview}. It is possible to build detectors with very good energy resolution based on the measurement of the ionization produced ... | d1c27e8f8bf8c3fc658b94c78ecb9ad84b736d71 |
\section{Introduction.} Katz \cite[5.3.1]{Katz90ESDE} discovered that the hypergeometric $\sD$-modules on $\bA^1_{\bC}\setminus\{0\}$ can be described as the multiplicative convolution of hypergeometric $\sD$-modules of rank one. Precisely speaking, Katz proved the statement (ii) in the following theorem (the statement... | 8b38a56a8d3dfec99cda595719feed3583d351f9 |
\section{Introduction} Many problems, particularly in combinatorics, reduce to asking whether some graph with a given property exists, or alternatively, asking how many such non-isomorphic graphs exist. Such graph search and graph enumeration problems are notoriously difficult, in no small part due to the extremely lar... | 461c005ff63aee7aa7a74b332faadbc07ca57726 |
\section{\label{intro}Introduction} The ``instanton calculus'' is a common approach for studying the non-perturbative semiclassical effects in gauge theories and sigma models. One of the first and perhaps the best known illustration of this approach is the $O(3)$ Non-Linear Sigma Model (NLSM) in two dimensions, where m... | 50d97946ad5e25c8d148a3d665dd68f161cea3ba |
\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}\rig... | 702ece0f7a9b408770cf6d81d20d81b11c11d0e5 |
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