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2,877,628,089,954 | arxiv | \section{Introduction}
The phenomenon of domino wave - the propagation of toppling in equal-sized and equispaced rectangular blocks, that we will further refer to as dominoes - attracted attention of many researchers. Probably the first call to consider the mechanics behind the domino waves belongs to Daykin (1971) ... |
2,877,628,089,955 | arxiv | \section{Introduction}
\label{intro_sec}
Ultra-luminous infrared galaxies (ULIRGs, defined as having
$L_{IR}>10^{12}L_{\odot}$; \citealt{1987ARA&A..25..187S}) are among the most
luminous objects of the Universe, radiating most of their energy in the
infrared (IR) band.
In the local Universe, ULIRGs are rare objects... |
2,877,628,089,956 | arxiv | \section{Introduction}
One of important problems of gravity physics is to develop a theory of quantum gravity. Till now we do not have a satisfactory and consistent theory of quantum gravity although the classical general relativity is the most successful theory of gravity. General relativity (GR) attract much atte... |
2,877,628,089,957 | arxiv | \partial{\partial}
\def\mathcal{\mathcal}
\def\text{Var\/}{\text{Var\/}}
\newcommand{\boldsymbol}{\boldsymbol}
\newcommand{\begin{equation}}{\begin{equation}}
\newcommand{\end{equation}}{\end{equation}}
\newcommand{\e}[1]{\exp\left( #1\right)}
\newcommand{\mathcal{CAT}}{\mathcal{CAT}}
\newcommand{\mathcal{INV}}{\mathc... |
2,877,628,089,958 | arxiv | \section{Introduction}
Charmonium production off nuclei is one of the most promising probes for studying the properties of matter created in ultrarelativistic heavy-ion collisions.
It was realized long time ago, that only collisions where a large density of particles is produced in the central region give rise to an an... |
2,877,628,089,959 | arxiv | \section{Introduction}
The interplay between superconductivity and magnetism is still
one of the main topics in the field of high-temperature
superconductivity \cite{Mazin10,Lynn2009,pagl10,scal12a,tran14}. While commensurate
antiferromagnetic (AF) order appears to compete with superconductivity,
magnetic excitation... |
2,877,628,089,960 | arxiv | \section{Introduction}
\bigskip\noindent The problem of moment is an interesting topic in Functional Analysis, especially in measure theory. It has important applications in probability theory.\\
\noindent Although there is a significant number of research works in probability theory on this problem (see \cite{g... |
2,877,628,089,961 | arxiv | \section{Introduction}
Consider a weighted hypergraph $H=(V,E,w)$ with $w \in \mathbb R_+^E$ and the corresponding energy:
For $x \in \mathbb R^V$,
\[
Q_H(x) \mathrel{\mathop:}= \sum_{e \in E} w_e \max_{\{u,v\} \in {e \choose 2}} (x_u-x_v)^{2}
\]
The problem of minimizing the energy $Q_H$ over various convex bodies... |
2,877,628,089,962 | arxiv | \section{Introduction}
Since the spin gap was discovered in a typical two-dimensional material
CaV$_4$O$_9$,\cite{STaniguchi-JPSJ64-2758}
the mechanism of the spin gap formation in this system has been intensively
studied by many theoretical methods.
\cite{NKatoh-JPSJ64-4105,KUeda-PRL76-1932,MPGelfand-PRL77-2794,... |
2,877,628,089,963 | arxiv | \section{Introduction}
\label{sec:introduction}
\IEEEPARstart{C}{onvolutional} neural networks (CNNs) are widely used in visual tasks due to their superior performance in extracting features \cite{Krizhevsky2012,Zeiler2014,Sermanet2014,Ren2017,Shelhamer2017}.
The first proposed AlexNet \cite{Krizhevsky2012} leads to... |
2,877,628,089,964 | arxiv | \section{Introduction}
The conversion of gas into stars in galaxies and the role of feedback
mechanisms has been one of the key aspects of extragalactic
astrophysics over the past decades. Several baryonic processes
regulate the star formation efficiency within dark matter
haloes. Simulations of galaxy formation and s... |
2,877,628,089,965 | arxiv | \section{Introduction}
\label{sec:The state of art}
On a first approximation, hodograph transformations are transformations involving
the interchange of dependent and independent variables \cite{clarkson,estevez05-1}. When the
variables are switched, the space of independent variables is called the reciprocal
space. I... |
2,877,628,089,966 | arxiv | \section{Introduction}
\label{intro:sec}
Soft matter systems are characterised by the simultaneous existence
of two intrinsic structural length scales: the omnipresent atomic
or {\it microscopic} scale that is associated with the solvent molecules
and the monomers of the dissolved polymers (if any) and the
{\it mesos... |
2,877,628,089,967 | arxiv | \section{}
\begin{acknowledgments}
We acknowledge support from a Grant-in-Aid from the Japan Society for the Promotion of Science (Grant number 16H02203), and Innovative Science and Technology Initiative for Security, ATLA, Japan.
\end{acknowledgments}
|
2,877,628,089,968 | arxiv | \section{Introduction}
The scalar field self-coupling and
the Yukawa couplings in the electroweak
theory are believed to vanish in the limit of infinite cut-off, as
suggested by the signs of the perturbative $\beta$-functions.
But the confirmation of this ``triviality'' of these couplings and a
reliable determination ... |
2,877,628,089,969 | arxiv |
\section{Introduction}
\begin{figure*}[t]
\begin{center}
\includegraphics[width=1\linewidth]{Fig/CompareBoundaryDetection.pdf}
\end{center}
\vspace{-1em}
\caption{a) Which visual cues would you draw when sketching out an image? b) Traditional edge detectors \cite{Canny1986ACA} only capture high frequency signals in ... |
2,877,628,089,970 | arxiv | \section{Introduction}
The G-equation is
\begin{equation}\label{e.geqn}
u_t = A|\nabla u| + V(t,x) \cdot \nabla u \ \hbox{ in } \ \mathbb{R}^d \times [t_0,\infty) \ \hbox{ with } \ u(x,t_0) = u_0(x)
\end{equation}
where $V$ is a space-time stationary ergodic random field on $\mathbb{R}_t \times \mathbb{R}^d_x $ tha... |
2,877,628,089,971 | arxiv | \section{Introduction}
The {\em Virasoro algebra} $\mathcal{L}$ is
an infinite-dimensional complex Lie algebra
with the basis $\{L_m,C
\mid m\in \mathbb{Z}\}$ and the Lie bracket defined as follows:
\begin{equation*}
[L_m,L_n]= (n-m)L_{m+n}+\delta_{m+n,0}\frac{m^{3}-m}{12}C\ {\rm and}\ [L_m,C]=0\ {\rm for}\ m... |
2,877,628,089,972 | arxiv | \section{Introduction}
One of the main driving factors for the success of the current deep learning research paradigm is that intelligent systems can obtain open-world perceptions from large amounts of data \cite{brown2020language,he2016deep} through high-capacity function approximators (neural networks, for instance).... |
2,877,628,089,973 | arxiv |
\section{Introduction}
The dualization in Boolean lattices is a central problem in algorithmic enumeration as it is equivalent to the enumeration of the minimal transversals of a hypergraph, the minimal dominating sets of a graph, and to many other generation problems \cite{eiter1995identifying,kante2014enumeration}.... |
2,877,628,089,974 | arxiv | \section{Introduction}
Fix \(0<\beta<1\). Let \(W\) be a wedge in \(\mathbf{R}^3\) of angle \(2\pi\beta\) delimited by two planes. Let \(p\) be a point in the interior of the wedge which is equidistant from the two faces and is located at distance \(1\) from the edge of \(W\). Take \(f\) to be the associated Green's... |
2,877,628,089,975 | arxiv | \section{Introduction}
Within the context of the heterotic superstring and heterotic M-theory \cite{Lukas:1997fg, Lukas:1998yy, Lukas:1998tt, Donagi:1999ez}, there have been a number of vacuum states whose four-dimensional low energy effective field theory \cite{Ovrut:1979pk} has the exact spectrum of the MSSM--with o... |
2,877,628,089,976 | arxiv | \section{INTRODUCTION}
\IEEEPARstart{T}{he} development of small-size, light-weight, low-power and low-cost satellites has witnessed significant growth in the last few years. An important class of small satellites, which is being used by academia, industry and government as a platform for space exploration and resea... |
2,877,628,089,977 | arxiv | \section{Introduction}
Magellanic Cloud PNe (MCPNe) are the nearest large population of extragalactic PNe where the low reddening and favourable viewing angle allows for population-wide studies not possible in the Milky Way. The most important of these is the extragalactic standard candle [O~III] PNLF in which MCPNe s... |
2,877,628,089,978 | arxiv | \section{Introduction}
In the theory of Fuchsian groups, one of the important old problem is the ``\hbox{discreteness} problem": given two elements in ${\rm PSL}(2, \R)$, whether or not the group generated by them is discrete. For an elaborate account of this problem, see Gilman \cite{gilman}. \hbox{Algorithmic} solu... |
2,877,628,089,979 | arxiv | \section{Introduction \label{sec:intro}}
Exoplanet imaging survey instruments reach deep contrast performance by
attenuating the stellar PSF using a
coronagraph~\citep[e.g.][]{oppenheimer2012,macintosh2014,beuzit2008,liu2010}.
Many designs have significantly reduced sensitivity within a $5 ~\lambda/D $
angular region ... |
2,877,628,089,980 | arxiv | \subsection{#1}\setcounter{theorem}{0} \setcounter{equation}{0}
\par\noindent}
\renewcommand{\theequation}{\arabic{subsection}.\arabic{equation}}
\renewcommand{\thesubsection}{\arabic{subsection}}
\newtheorem{theorem}{Theorem}
\renewcommand{\thetheorem}{\arabic{subsection}.\arabic{theorem}}
\newtheorem{lemma}[theorem]{... |
2,877,628,089,981 | arxiv | \section{Introduction\label{sec:intro}}
Quasars are one of the most powerful astrophysical sources in the universe with a bolometric luminosity, $L_{\rm Bol} \gtrsim 10^{45}$ erg s$^{-1}$ (e.g., \citealp{Hickox+2018}). Owing to their high luminosities, we can find them even in the distant universe ($z>7$; \citealp{Mort... |
2,877,628,089,982 | arxiv | \section{Introduction}
Extragalactic high energy gamma-ray astronomy has developed from an emerging discipline
into a fully fledged research field over the past several decades.
Following its initial success in the 1990s with the first AGN discoveries of Mrk~421 and Mrk~501
\cite{Punch:1992xw,Quinn:1996dj}, the fiel... |
2,877,628,089,983 | arxiv | \section{INTRODUCTION}
\label{sect:Introduction}
\ Two-dimensional magnetic systems have been a subject of intensive
investigation for almost half a century now. Both ferro- and
anti-ferromagnetic systems have been studied extensively,
experimentally as well as theoretically, revealing a myriad of
interesting propertie... |
2,877,628,089,984 | arxiv | \section{Introduction}
The Heisenberg commutation relations are
\begin{equation}
\left[ {\widehat{P}}_{i},{\widehat{Q}}_{j}\right] =i \hbar \delta _{i,j}\text{\boldmath
$1$}
\label{MG: Heisenberg commutation relations}
\end{equation}
\noindent where $i,j,...=1,...,n$.\ \ The hermitian operators ${\widehat{P}... |
2,877,628,089,985 | arxiv | \section*{\large\contentsname
\@mkboth{%
\MakeUppercase\contentsname}{\MakeUppercase\contentsname}}%
{\baselineskip=15pt plus 2pt minus 1pt
\@starttoc{toc}}%
}
\renewenvironment{thebibliography}[1]
{\section*{\centering{\refname}
\@mkboth{\MakeUppercase\refname}{\MakeUppercase... |
2,877,628,089,986 | arxiv | \subsubsection{%
\@startsection{subsubsection}{3}{\z@}%
{-3.25ex\@plus -1ex \@minus -.2ex}%
{-1.5ex \@plus .2ex}%
{\normalfont\normalsize\bfseries}%
}
\makeatother
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{corollary}[theorem]{Corollary}
\allowdisplaybreaks
\title{Collabora... |
2,877,628,089,987 | arxiv | \section{Introduction}
Measurements of the diffuse ultraviolet (UV) radiation field have to contend with a number of contaminating sources including atmospheric emission lines and the zodiacal light \citep{murthy2009}. These foreground sources are particularly important at high galactic latitudes where the Galactic co... |
2,877,628,089,988 | arxiv | \section{Introduction}
In this paper we examine in detail the notion of `equi-homogeneity', which is a regularity property of sets introduced by Olson, Robinson \& Sharples \cite{ORS} to study the Assouad dimension of products of `generalised Cantor sets' i.e. Cantor sets in which we allow the portion removed to vary a... |
2,877,628,089,989 | arxiv | \section{Introduction}\label{intro}
This fairly detailed introduction aims at providing a comprehensive and
nontechnical overview of the paper, including its asymptotic theory
aspects, and a rough description of some of the rank-based test
statistics to be derived. It is expected to be accessible
to a broad read... |
2,877,628,089,990 | arxiv | \section{ Introduction}
\label{sec:introduction}
The refined de Sitter (dS) conjecture, the latest version of the Swampland conjecture, was recently proposed by Ooguri, Palti, Shiu and Vafa~\cite{Ooguri:2018wrx} after an earlier version proposed by Obied, Ooguri, Spondyneikeo and Vafa~\cite{Obied:2018sgi}. The conje... |
2,877,628,089,991 | arxiv | \section{Introduction}
\setcounter{equation}{0}
In this paper, we study the properties of the parabolic Besov
spaces ${\mathcal B}^{\al, \frac12 \al}_p ({\bf R}^{n+1})$ and the
parabolic Sobolev spaces ${\mathcal L}^p_\al({\bf R}^{n+1})$ for $1
\leq p \leq \infty, \,\, \al \in {\bf R}$. We also, study the... |
2,877,628,089,992 | arxiv | \section{Introduction}
It is an important problem to estimate the size of a maximum independent set
in a graph, and Hoffman's bound\footnote{
See \cite{Haemers} for the history of the bound, and some related results
including Delsarte's LP bound and Lov\'asz' theta bound.
} is one the most useful algebraic tools for th... |
2,877,628,089,993 | arxiv | \section{Introduction}
Various cosmological observations, including the type Ia Supernova
[1], the cosmic microwave background radiation [2] and the large
scale structure [3,4], have shown that the universe is undergoing
an accelerating expansion and it entered this accelerating phase
only in the near past. The ... |
2,877,628,089,994 | arxiv | \section{Acknowledgements}
This work acknowledges the support from the National Science Foundation, Grant No.2110279, and the Fulbright-University of Bordeaux Doctoral Research Award.
|
2,877,628,089,995 | arxiv | \section{Introduction}
\label{sec:introduction}
Percolation is the study of connectivity in random systems, particularly of the transition that occurs when the connectivity first becomes long-ranged \cite{stauffer:aharony}. Examples are the formation of gels in polymer systems \cite{flory:41}, conductivity in random ... |
2,877,628,089,996 | arxiv |
\subsection{Assessing the Diversity of a Music List}\label{sec:qual1}
Interviewees mentioned several aspects related to what diversity means to them, and how it has been interpreted while comparing lists of tracks and artists.
When asked about their strategy in choosing the most diverse lists, they often started th... |
2,877,628,089,997 | arxiv | \section{Introduction}
\label{secIntro}
\IEEEPARstart{S}{parse} linear arrays sample a spatial aperture with fewer sensors than required by a standard half-wavelength sampled array. Many sparse array designs prune or thin a uniform linear array (ULA), so the sparse array sensor locations fall on an underlying half... |
2,877,628,089,998 | arxiv | \section{Introduction}\label{s:introduction}
Ultraluminous infrared galaxies (ULIRGs) exhibit some of the most
extreme star formation rates in the Universe. The volume density of
higher redshift ULIRGs peaks at z$\sim$2-3 \citep{chapman05a}$-$this
is also the peak epoch in the cosmic star formation rate density and
v... |
2,877,628,089,999 | arxiv | \section{Introduction}
The 4D light field camera can simultaneously record spatial and angular information of light rays incident at pixels of the tensor by inserting a microlens array between the main lens and image sensor. Due to its abundant information captured through one imaging, compared to traditional 2D image... |
2,877,628,090,000 | arxiv | \section{Introduction}
The last few decades have been characterized by an exponential growth in the amount of news sources available, with the task of following news stories in real-time becoming very difficult to perform manually. As such, a demand has risen for systems that are capable of monitoring and organizing a... |
2,877,628,090,001 | arxiv | \section{Introduction}
The prediction of landslides, in particular the discovering of the triggering mechanism, is one of the challenging problems in earth science. The term landslide has been defined in the literature as a movement of a mass of rock, debris or earth down a slope under the force of gravity \cite{Varn... |
2,877,628,090,002 | arxiv | \section{Introduction}
The notion of dichotomy spectrum of linear time-varying systems initiated from the work of Sacker and Sell in 1970s (see \cite{SackerSell1978}). Since then this notion has played an important role in the qualitative theory of time-varying systems including the stability theory (see \cite{Barreir... |
2,877,628,090,003 | arxiv | \section{Introduction}\label{sec:I}
The possibility of measuring parity non-conservation (PNC) in atoms was first considered by Zeldovich in 1959\,\cite{Zeldovich}. However, atomic PNC experiments begun only after Bouchiat and Bouchiat showed that parity mixing of atomic states scales as $\sim\rm{Z}^3$ and measurable s... |
2,877,628,090,004 | arxiv | \subsection{Application to $q$-Gaussian}
Let us start with a preliminary result and consider the integral, for $q>1$, $a$ and $b$ in general complex and $\Re(b)>0$,
\begin{multline}
\int\exp_q(ia z-bz^2)\ddz\\
=\int\exp_q\left[-\left(\sqrt{b}z-\frac{ia}{2\sqrt b}\right)^2-\frac{a^2}{4b}\right]\dd z\\
=\frac{1}{\sqrt b}... |
2,877,628,090,005 | arxiv | \section{\label{sec:level1}Introduction}
One of the main goals of thermodynamics has been to study heat engines and thermodynamic processes, dating back to the now famous work of Sardi Carnot in 1824 \cite{Carnot}. With the advent of nano physics and the control of quantum systems down to single atoms a better underst... |
2,877,628,090,006 | arxiv | \section{ Introduction and preliminaries}
The notion of selectors comes from {\it Topology}.
Let $X$ be a topological space, $exp \ X$ denotes the set of all non-empty closed subsets of $X$ endowed with some (initially, the Vietoris) topology, $\mathcal{F}$ be a non-empty closed subset of $exp \ X$. A continuous map... |
2,877,628,090,007 | arxiv | \section{Introduction}
An important achievement of the research community in logic is the invention of proof assistants. Such tools allow for interactively writing proofs, which are then checked automatically and can then be reused in other developments. Unfortunately, a proof written in a proof assistant cannot be r... |
2,877,628,090,008 | arxiv | \section{Introduction}
Throughout this work, we consider $q\in(0,1)$. The $q$-number is
defined to be the number of the form
\begin{align*}
\left[ \alpha \right]_q = \frac{{q^\alpha - 1}}{{q - 1}},
\qquad \text{for any } \alpha \in \mathbb{C}.
\end{align*}
In particular, if $\alpha =n\in \mathbb{N}$, then th... |
2,877,628,090,009 | arxiv |
\section{Introduction}
How do we infer what people believe and desire from their observable behavior? One way to address this problem is to invoke some version of the \emph{principle of charity}: We attribute beliefs and desires to an agent that \emph{rationalize} the behavior we observe \cite{Davidson1973, Lewis1974... |
2,877,628,090,010 | arxiv | \section{Introduction}\label{sec:introduction}
Recent years show an advancing interest in the field of autonomous
vessels. This is due to the variety of challenging applications where
autonomous systems can be advantageous to humanly-operated vessels but also because
of the task to solve the arising complex problems th... |
2,877,628,090,011 | arxiv | \section{Introduction}
\label{sec_intro}
The solar dynamo consists of poloidal magnetic field being wound up to generate
toroidal magnetic field, while a process involving the Coriolis force
creates poloidal field from the toroidal field \citep[see reviews by,
e.g.][]{Ossendrijver:2003, Charbonneau:2010, Charb... |
2,877,628,090,012 | arxiv | \section{Introduction}
In relativistic heavy-ion collisions carried out at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC), one aims at searching for a new form of matter --- the Quark-Gluon Plasma (QGP)~\cite{PBM_QGP} and studying its properties in laboratory. The production of J/$\psi$ ... |
2,877,628,090,013 | arxiv | \section{Introduction to Fracking}
Fracking, the common term for hydraulic fracturing, dates back to the late 1940's with the first commercial applications in 1949. The original process was a secondary recovery method designed to enhance production in reservoirs where primary recovery had decreased to the point where p... |
2,877,628,090,014 | arxiv | \section{Introduction}
There is an extensive literature on two-stage and multistage voting.
Although some of this study exists within economics, multistage elections and
runoffs have been greatly influential in computational social choice
during the past decade, due to such work as that
of Elkind and Lipmaa~\shortcite... |
2,877,628,090,015 | arxiv | \section{Introduction}
Colloidal particles, trapped at fluid interfaces by adsorption energies much larger than the
thermal energy, can form effectively two-dimensional colloidal monolayers \cite{Pie80}. During the last two decades these systems
have received significant attention both in basic research as well as in... |
2,877,628,090,016 | arxiv | \section{Introduction.}
\subsection{}
Let $B$ be a definite quaternion algebra over $\Q$ with the discriminant $d_B$~(cf.~Section 1.1) and $D$ be a divisor of $d_B$.
We recall that Arakawa lifting is a theta lifting to a cusp form on the quaternion unitary group $GSp(1,1)_{\A_{\Q}}$ from a pair consisting of an ell... |
2,877,628,090,017 | arxiv | \section{Introduction}
The unique interacting binary system AR Scorpii (AR~Sco hereafter) has been called a white dwarf ``pulsar'' because its bright electromagnetic flashes appear to be generated by the spin-down energy of its degenerate primary stellar component \citep{marsh16, stiller18, gaibor20}. The binary consi... |
2,877,628,090,018 | arxiv | \section{Introduction and motivation}
The dynamics of QCD generates dynamically a mass for its fundamental quanta. For the quarks the running mass exceeds largely the contribution due to the Higgs mechanism for
small momenta. Indeed, recent lattice simulations at zero temperature of the Landau gauge quark propagator~\... |
2,877,628,090,019 | arxiv | \section{Introduction}\label{A}
Jan Paseka [1999, 2002, 2003] introduced the notion of {\em Hilbert module} on an involutive quantale: it is a module equipped with an {\em inner product}. This provides for an order-theoretic notion of ``inner product space'', originally intended as a generalisation of complete lattice... |
2,877,628,090,020 | arxiv | \section{Introduction}\label{sec:introduction}
Music generation is an important component of computational and AI creativity, leading to many potential applications including automatic background music generation for video,
music improvisation in human-computer music performance
and customizing stylistic music for ind... |
2,877,628,090,021 | arxiv | \section{Introduction\label{sec:Introduction}}
Active matter is an important field of research that considers
particle systems whose microscopic components are characterized by systematic
persistent dynamic rules and by various types of mutual interactions.
On a microscopic scale, the persistent dynamics
breaks the... |
2,877,628,090,022 | arxiv | \section{Introduction}
The generation and the growth of water waves by wind is an old problem in geophysical fluid dynamics, with a wide range of applications, and challenges that have occupied the community for at least 150 years \citep{helmholtz1868, kelvin1871}. \citet{jeffreys25} suggested that wind waves grow beca... |
2,877,628,090,023 | arxiv | \section{Acknowledgment}
\section{Introduction}
\label{sec:Introduction}
Understanding maintenance activities is critical for practitioners to effectively support the evolution of their projects in terms of enhancing cost-effectiveness, managing technical debt, and better allocation of maintenance related resources. T... |
2,877,628,090,024 | arxiv | \section{Introduction} \label{sec:intorduction}
Wireless data traffic is growing at an unprecedented rate, exacerbating the demand for improved design strategies for the next generation wireless infrastructure \cite{Furuskar2015}. Deployment of small base stations (sBSs) to offload wireless data from a macro base stati... |
2,877,628,090,025 | arxiv | \section{Introduction}\label{sec0}
\par
In the paper we characterize Pilipovi{\'c} spaces of the form
$\mathcal H _{\flat _\sigma}(\rr d)$ and $\mathcal H _{0,\flat _\sigma}
(\rr d)$, considered in \cite{FeGaTo1,Toft14},
in terms of estimates of powers of the harmonic oscillator,
on the involved functions.
\par
Th... |
2,877,628,090,026 | arxiv | \section{Introduction}\label{introduction}
When studying number theory problems, one often runs into nonlinear exponential sums of the form
\begin{eqnarray*}
\sum_{n=1}^{\infty}a_n
e\left(t \varphi\left(\frac{n}{X}\right)\right)V\left(\frac{n}{X}\right),
\end{eqnarray*}
where $a_n$ is some arithmetic function, here an... |
2,877,628,090,027 | arxiv | \section{Introduction}
Historically, star clusters have been used as natural laboratories in which to test the theory of stellar evolution. This is particularly true for massive stars, where the short lifetimes and non-monotonic mass-luminosity relation make it very difficult to infer the evolutionary state of isolated... |
2,877,628,090,028 | arxiv | \section{Overview}
This supplementary material includes behavior analysis, ablation studies, limitations, visualizations, and future direction of our PU-Transformer for point cloud upsampling.
\section{Behavior Analysis}
\noindent \textbf{Positional Fusion Block:}
Although our Positional Fusion block utilizes similar ... |
2,877,628,090,029 | arxiv | \section{INTRODUCTION}
Microlensing is sensitive to planets orbiting low-mass stars and brown dwarfs (BDs) that are difficult to detect by other methods, such as the radial velocity and transit method.
Although faint low-mass stars such as M dwarfs comprise $\sim 70 \%$ of stars in the solar neighborhood and the Galax... |
2,877,628,090,030 | arxiv | \section{Introduction}
Monte Carlo simulation of diffusion processes is of great interest, as it underlies methods of statistical inference from discrete observations in a variety of applications \citep[e.g.][]{gol:wil:2006, gol:wil:2008, chi:etal:ip, bla:sor:2014, bla:etal:2016}. Our interest in this paper is in the \... |
2,877,628,090,031 | arxiv |
\chapter{Israel matching conditions}
\label{Isapp}
In this appendix we derive the Israel matching conditions \cite{Israel} from scratch, based on the treatment presented in \cite{Poisson}.
We begin with a timelike (or spacelike) hypersurface $\Sigma$, pierced by a congruence of geodesics which intersect it orthogon... |
2,877,628,090,032 | arxiv | \section{Introduction}
In recent years, the use of wavefunction-based post-Kohn--Sham or post-Hartree--Fock methods to solve problems in materials science has proliferated. \cite{muller_wavefunction-based_2012}
This is in part driven by an interest in obtaining precise energies (accurate to within 1mHa) for complex s... |
2,877,628,090,033 | arxiv | \section{Introducción}
Esta comunicación está dirigida a personas que no tienen conocimientos previos sobre el cruce interdisciplinario entre la lingüística y la estadística. Tiene el doble propósito de ser una aportación desde el punto de vista de la lingüística teórica y, a la vez, ser útil para la documentación y p... |
2,877,628,090,034 | arxiv | \section{}
\label{}
\section{Introduction}
Magnetic resonance imaging (MRI) is an important non-invasive imaging technique, which enables excellent assessments of structural and functional conditions with no radiation in a reproducible manner. Basically, MRI is aimed to reconstruct the images from the observed s... |
2,877,628,090,035 | arxiv | \section{Introduction}
\label{sec:intro}
Over the past decade, as smartphone cameras started to rival and even beat DSLR cameras in resolution, a large number of
ultra high resolution (UHR) images, each of more than ten million pixels, are produced, stored and transmitted everyday. However, these images are almost alwa... |
2,877,628,090,036 | arxiv | \section{Introduction}
The great majority of phase transitions are characterized by spontaneous symmetry
breaking and can be described by the qualitative changes in the order parameter
behavior associated with long-range order \cite{Landau_1,Bogolubov_2}. This
concerns both first-order as well as second-order ph... |
2,877,628,090,037 | arxiv | \section{Introduction}\label{sec:intro}
General Relativity (GR) has undergone brilliant successes since its inception 100
years ago (see, e.g., the review \cite{2015Univ....1...38I} and references therein).
Einstein's theory is the standard paradigm for describing the gravitational interaction,
verified by m... |
2,877,628,090,038 | arxiv | \subsection{}
Given smooth proper schemes $X_1, X_2$ over a field $k$ and an object $E\in D^b(X_1\times X_2)$ of the bounded derived category of coherent sheaves on $X_1\times X_2$
define a triangulated functor
\begin{equation}
\Phi_E: D^b(X_1) \tilde{o} D^b(X_2)
\end{equation}
sending a bounded complex $M$ of co... |
2,877,628,090,039 | arxiv |
\subsection{Fibre Assignment}\label{sec:tiling_code}
In eBOSS the selection of targets for spectroscopic observation was performed through the survey `tiling' process with the goal of maximising the number of targets that receive a fibre with a given number of tiles \citep{blanton03}.
The fraction of targets of a g... |
2,877,628,090,040 | arxiv | \section{Introduction}
Electron bunches of femtosecond-to-attosecond-scale duration are useful tools for studying ultrafast atomic-scale processes, including structural phase transitions in condensed matter~\cite{Siwick2003An-Atomic-Level,Baum20074D-Visualizatio,Morrison2014A-photoinduced-,Gedik2007Nonequilibrium-,Musu... |
2,877,628,090,041 | arxiv | \section{Introduction}
Free boundary problems (FBP) are of great importance, both physically and mathematically. FBP are boundary value problems for partial differential equations where an unknown moving boundary must be determined \cite{AlSo,Ca,Ru,Ta}.
In this paper, we formulate a FBP for a nonlinear diffusion-co... |
2,877,628,090,042 | arxiv | \section{Hopf algebras}
\label{sec:hopf}
Let us start with a brief history of Hopf algebras:
Hopf algebras were originally introduced to mathematics in 1941 to enable
similar aspects of groups and algebras to be described in a unified manner \cite{Hopf}.
An article by Woronowicz in 1987 \cite{Woronowicz},
which pro... |
2,877,628,090,043 | arxiv | \section{Introduction} \label{intro}
The C-metric is one of the earliest known exact solutions to Einstein gravity, and still many of its features remain relevant for various reasons today. Its compact and elegant form appears almost oblivious to reality as the years unfold as new features and applications have been f... |
2,877,628,090,044 | arxiv | \section{Introduction}
\subsection{Motivation}\label{Motivation}
It is no exaggeration to say that type decomposition and Murray-von Neumann equivalence of projections are absolutely fundamental to the theory of von Neumann algebras. These concepts have been extended to other operators in a couple of different ways ... |
2,877,628,090,045 | arxiv | \section{From operational risk to cyber risk}\label{sec:ORcyber}
\vspace{-2ex}
For a very long time, IT risks were classified in operational risk. Many databases recording operational failure events also contain cyber incidents, which have been modelled using traditional operational research methods. Recently, as cyber... |
2,877,628,090,046 | arxiv | \section{Introduction}
Let $X$ be a (real or complex) Banach space and let $x(t) \in X$ describe the state of a physical system at time $t \geq 0$.
With $a(t) = \ddot{x}(t)$ denoting the acceleration of system, the Newton's second law of motion states that
\begin{equation}
F(t) = Ma(t) \text{ for } t \geq 0, \label{E... |
2,877,628,090,047 | arxiv | \section{Introduction}
The conventional picture of the atom is simple: a central nucleus clouded by orbiting electrons. Arranging the atoms in various ways and at specific distances from each other leads to the ``structure'' of molecules, solids, and liquids: the tetrahedral structure of methane; the rock-salt structur... |
2,877,628,090,048 | arxiv | \section{Introduction}
The subject of this talk has become of considerable current
interest, as evidenced by the other presentations at this meeting
\cite{wagner,mueller,lipatov} on both experimental and theoretical
developments. The main thrust of this one is to argue that, despite
a growing tendency for experimental... |
2,877,628,090,049 | arxiv | \section*{Introduction}\label {0}
In this article, we continue the work of \cite{AZ,AF} on the
classification of finite-dimensional complex pointed Hopf algebras
$H$ with $G=G(H)$ non-abelian. We follow the Lifting Method -- see
\cite{AS-cambr} for a general reference; in particular, we focus
on the problem of determi... |
2,877,628,090,050 | arxiv | \section{Introduction}
Given a hypergraph $\mathcal{H}$, let $v(\mathcal{H})$ denote the number of vertices of $\mathcal{H}$ and $e(\mathcal{H})$ denote the number of hyperedges. We denote the sets of vertices and hyperedges of $\mathcal{H}$ by $V(\mathcal{H})$ and $E(\mathcal{H})$, respectively. We say that a hypergr... |
2,877,628,090,051 | arxiv | \subsection{Fuzzification}
Mass-to-charge peaks that affect the expert classification are
converted to a fuzzy logic level based on their relative
abundance. The truth level for a particular ion in a specific
classification can be Boolean by setting a threshold: when the
abundance is above the appropriate side of the ... |
2,877,628,090,052 | arxiv | \section{Introduction}
In light unstable nuclei,
various exotic structures such as the magic number breaking,
new cluster structures, and the neutron halo structure, have been discovered.
In a series of Be isotopes, it has been revealed that
the structure changes rapidly with the increase of the neutron number ... |
2,877,628,090,053 | arxiv | \section{#1}}
\setcounter{footnote}{1}
\def\textmatrix#1\\#3\\{\bigl({#1 \atop #3}\ {#2 \atop #4}\bigr)}
\newcommand{\bydef}{\stackrel{\rm def}{=}}
\newcommand{\cle}{{\mathcal{E}}}
\newcommand{\clh}{\mathcal{H}}
\newcommand{\clk}{{\mathcal{K}}}
\newcommand{\cll}{{\mathcal{L}}}
\newcommand{\clm}{{\mathca... |
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