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\section{Introduction}
Even with advances in modern computational capabilities, high-fidelity, full-scale simulations of chemically reacting flows in realistic applications remain computationally expensive \cite{HUANGMPLSVT,doi:10.1080/10618562.2014.911848,doi:10.2514/6.2018-4675,doi:10.25... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
Three dimensional (3D) gravity provided us
with many important clues about higher dimensional physics.
It help that this theory with a negative cosmological constant $\Lambda$
has non-trivial solutions, such as the Ba\~nados-Teitelboim-Zanelli
black-hole spacetime \cite{Banados:wn}, which pro... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
An orbit following calculation of charged particles is one of the
classic problems.
It is straightforward, but remains to be an important tool for studying
particle confinement in laboratory plasmas.
In high beta magnetic
confinement devices, Larmor radius
of energetic particles can be comparab... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
For an equilibrium system, adding more transitions to its state space increases the activity. Naively, one would think that this intuitive result holds also for systems that are out of equilibrium. However, unlike in equilibrium systems, the added transitions between states do not have to obey d... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
Traditional model checking techniques focus on a systematic check of the validity of
a temporal logic formula on a precise mathematical model. The answer to the
model checking question is either
true or false. Although this classic approach is
... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
Let $(Y,\lambda)$ be a contact three manifold and $X_{\lambda}$ be the Reeb vector field of it. That is, $X_{\lambda}$ is the unique vector field satisfying $i_{X_{\lambda}}\lambda=1$ and $d\lambda(X_{\lambda},\,\,)=0$. A smooth map $\gamma : \mathbb{R}/T\mathbb{Z} \to Y$ is called a Reeb orbit... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
Counting processes constitute a mathematical framework for modeling specific random events within a time series. The nature of the application and the structural features of a given time series may call for sophisticated models whose complexity goes beyond the standard Poisson process. For insta... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{ Introduction and main results}
In [9], Hawkins showed that a deformation of the differential
graded algebra of differential forms $\Omega^*(P)$ on a manifold $P$
gives arise to a Poisson tensor on $P$ (which characterizes the
deformation) and a torsion-free and flat contravariant connection
whose metacurvatu... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
\label{sec:intro}
Extended ``halos'' of diffuse {Lyman-alpha (Ly$\alpha$)} emission, extending to many times larger radii than starlight, are nearly ubiquitous around rapidly-star-forming galaxies at redshift $z > 2$ \citep[e.g.][]{steidel11, wisotzki16, leclercq17, wisotzki18}.
While there is no... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
\label{SecIntro}
\begin{figure}[t]
\centering \includegraphics[width=0.85\linewidth]{figures/intro.pdf}
\caption{ Comparative results of four popular point cloud classifiers, \ie PointNet \cite{qi2016pointnet}, PointNet++ \cite{qi2017pointnetplusplus}, DGCNN \cite{Wang2019DynamicGC} and Spherica... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Playing Field}
Let $M$ be a connected 4-manifold without boundary.
We will work with 2-columns $v:M\to\mathbb{C}^2$ of complex-valued
half-densities (a half-density is a quantity which transforms as the square root
of a density under changes of local coordinates).
The inner product on such 2-columns is define... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{ Introduction}
Let $q$ be a prime power and $\mathbb{F}_q$ be a finite field of $q$ elements. The problem of
estimating the number of irreducible polynomials
of degree $d$ over the finite field ${\mathbb F}_{q}$
with some prescribed coefficients has been largely
studied; see surveys by S. D. Cohen such as ... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
The exploration of the phase diagram of strongly interacting matter and
search for the signals of the phase transition from hadronic to quark-gluon
phase are very important in both
theory and experiment. As a fundamental tool, lattice QCD provides us the best
framework for investigation of non-p... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
The atmospheric mixing angle has experimentally turn out to be quite large \cite{exper} and,
according to recent analysis \cite{Fogli}, its $1\sigma$ range is $\theta_{23}=38^\circ -47^\circ$.
From the theoretical point of view this invites to speculate on the possibility
of maximal flavour vio... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
\label{sec:introduction}
Protoplanetary discs evolve over million year time scales during which the accretion rate $\dot{M}$ onto the central star drops, from typically $5\times 10^{-6}M_\odot$/yr around the youngest stars to $10^{-9}M_\odot$/yr after $3-10$ Myr \citep{1998ApJ...495..385H}. Thi... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
The colored degree matrix problem, \cite{hmcd2016} also known as finding edge packing \cite{bushetal2012}, edge disjoint realizations \cite{guinezetal2011} or degree constrained edge partitioning \cite{bentzetal2009}, asks if a series of degree sequences have edge disjoint realizations. The gener... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction and Results}
Let $X$ be a smooth projective curve of genus 2 over an algebraically
closed field $k$ of characteristic $p > 0$.
Let $\Omega$ be its canonical bundle.
Define the (absolute)
Frobenius morphism \cite{Ka1, Ka2}
\begin{equation*}
F : X \longrightarrow X
\end{equation*}
which maps local... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}\label{intro}
Evidences for the acceleration of cosmic expansion now prevail \cite{SNIA,newSN,data}, however we do not yet possess a compelling explanation for what causes the acceleration. Two major efforts for the acceleration mechanism have been
adding a new substance (termed as dark energy) ... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
Observer design for linear systems is generally acknowledged to be
understood well enough. For discrete-time linear system $x^{+}=Ax$
with output $y=Cx$, Luenberger observer \cite{luenberger64}
dynamics read
\begin{eqnarray}\label{eqn:luenberger}
\xhat^{+}=A\xhat+L(y-C\xhat)
\end{eqnarray}
and ... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
Let $u(t) \in C^0([0,T]; X)$ satisfy a first order evolution equation $\partial_t u(t) = A_1(t) u(t)$ in a Banach space $X$.
In this situation, the associated evolution operator $U(t,s)$ satisfying
\[
u(t) = U(t,s) u_s, \quad u(s) = u_s \in X
\]
is assumed to exist as a two-parameter $C^0$-semi... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
\setcounter{equation}{0}
Coulomb gauge Yang-Mills theory (and by extension Quantum Chromodynamics)
is a fascinating, yet frustrating endeavor. On the one hand, Coulomb
gauge offers great potential for understanding such issues as confinement
\cite{Zwanziger:1998ez,Gribov:1977wm}; on the othe... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
\label{introduction}
Fraud is encountered in a variety of domains. It comes in all different shapes and sizes, from traditional fraud, e.g. (simple) tax cheating, to more sophisticated, where entire \textit{groups} of individuals are collaborating in order to commit fraud. Such groups can be foun... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
\label{intro}
A drop placed on a partially wetting substrate will make a finite angle with the
surface, given by Young's equation~\cite{Young},
\begin{equation}
\cos\ensuremath{\theta_{\mathrm{Y}}}=\frac{\gamma_{\mathrm{SV}}-\gamma_{\mathrm{SL}}}{\gamma}\;,
\label{eqn:young}
\end{equation}
where... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
In this paper we consider the problem of maintaining a dynamic set of
$N$ two-dimensional points from $\mathbb{R}^2$ in external memory,
where the set of points can be updated by the insertion and deletion
of points, and where two types of queries are supported: 3-sided range
reporting queires... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
\label{intro}
Among the various approximations existing in the literature
to describe a diluted Bose
condensed gas at finite temperature, the generalized
random phase approximation (GRPA) has been the subject of several
studies \cite{Reidl,Zhang,condenson,Levitov,gap}.
This approximation ha... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
Macromolecular crystals represent at the same time a particular case of a solid
state system as well as that of a polymer system. The simplest and paradigmatic
case in this field is crystalline polyethylene. As is well known, it is very
difficult to obtain reliable experimental data for these ... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}\label{Introduction}
Consider the Laplace-Beltrami operator
\begin{eqnarray}\label{renxing_eqn}
\Delta_{\alpha}=\frac{\alpha}{2}\sum_{i=1}^my_i^2\frac{\partial^2}{\partial y_i^2} + \sum_{1\leq i\ne j\leq m}\frac{1}{y_i-y_j}\cdot y_i^2\frac{\partial}{\partial y_i}
\end{eqnarray}
defined on the set... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
Musculoskeletal Disorders (MSDs) makes up the vast proposition of the occupational diseases \cite{Eurogip}. Inappropriate physical load is viewed as a risk factor of MSD \cite{Chaffin1999}. Biomechanical analysis of joint moments and muscle loads will provide insight into MSDs.
Over the past ... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
One of the most important outcomes expected of a successful theory of
quantum gravity is a clear and unambiguous solution to the problems
associated with the curvature singularities that are predicted by
classical general relativity. This expectation is natural since
quantum mechanics is known t... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
\IEEEPARstart{U}{ltrasound} elastography (USE), a non-invasive clinical diagnostic technique, measures the mechanical property, the stiffness, that has a significant correlation with the tissue pathology. Adjunct to conventional B-mode ultrasound, USE improves the diagnostic quality and can prov... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
This work considers the adaptation of particle
filtering~\cite{Gordon1993,Doucet2001} to modern graphics processing units
(GPUs). Such devices are typical of a trend away from faster clock speeds
toward expanding parallelism to maximise throughput at the processor
level. Capitalising on this wid... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Batched Triangle Listing}\label{sec:batched-triangle}
In this section, we extend our algorithms in the previous sections to handle
batches of more than one update. Our results are in the batched model (formally defined in~\cref{sec:prelims}) where in
each batch of updates, $O(1)$ updates occur \emph{adjacent ... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
The problem of inhomogeneous charge and magnetic ordering in strongly correlated electron systems (SCES) is one of the most intensively studied problems of the contemporary condensed matter physics. The motivation behind these studies is the inhomogeneous charge ordering (e.g., striped phases) w... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
Delta Scuti stars are very complex pulsators. They are located on and above the main sequence,
they pulsate mainly in p-type and g-type non-radial modes, beside the radial ones. The modes
are excited by the $\kappa$-mechanism in the He ionization zone (\citealt{Unno81, Aerts10}).
The amplitud... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
Progress in 3d human pose and shape estimation has been sustained over the past years as several statistical 3d human body models\cite{ghum2020,pavlakoscvpr2019,SMPL2015}, as well as learning and inference techniques have been developed\cite{sminchisescu_ijrr03,bogo2016,SMPL2015,ghum2020,dmhs_cv... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
The Milky Way is an excellent testing ground of our understanding of Galaxy evolution, due to the ability to resolve individual stars and study stellar populations in greater detail than in other galaxies. However, understanding the composition, structure, and origin of the Milky Way disk is st... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{}
\tiny
\fontsize{8}{11}\helveticabold { \section{Keywords:} neutron star, gravitational waves, gamma-ray burst, nucleosynthesis, r-process, kilonova}
\end{abstract}
\section{Introduction}\label{sec:intro}
Although the birth of "multi-messenger" astronomy dates back to the detection of the first solar ne... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{\label{Introduction}Introduction}
To understand what controls $T_{\rm c}$~in high temperature superconductors remains a major challenge.
Several studies suggest that in contrast to cuprates where chemical substitution controls electron concentration,
the dominant effect of chemical substitution in iron-base... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
The last decade has seen two major breakthroughs in the field of experimental astronomy.
First, the detection in 2015 of gravitational waves from a binary black hole merger
\cite{LIGOScientific:2016aoc} heralded the arrival of gravitational wave astronomy
as an experimental science. Second, the ... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\chapter{Introduction}
\epigraph{$\mlq$\textit{Qui est-ce ? Ah, tr\`{e}s bien, faites entrer l'infini.}$\mrq$}{Aragon}
\section{Motivation}
\subsection{Periods}
A \textbf{\textit{period}} \footnote{For an enlightening survey, see the reference article $\cite{KZ}$.} denotes a complex number that can be expressed a... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction and definitions}
An embedding of the complete graph on $v$ vertices with each edge on both a $m$-cycle and an $n$-cycle is termed a {\em biembedding}. A biembedding is necessarily 2-colorable with the faces that are $m$-cycles receiving one color while those faces that are $n$-cycles receiving the... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
The magneto-electric (ME) effect, i.e. the production of an electric polarization (magnetic moment) by
application of a magnetic (electric) field, has been known for a long time. Multiferroics, e.g. materials that
show ferromagnetism and ferroelectricity coexisting, have also been known where spi... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
While fashion is a multi-billion dollar global industry it comes with severe \textbf{environmental and social costs} worldwide. The fashion industry is considered to be the world's second largest polluter, after oil and gas. Fashion accounts for 20 to 35 percent of microplastic flows into the oce... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{\label{sec:Intro}Introduction}
\textit{Introduction.} \textcolor{black}{Epidemic models are useful for understanding the general dynamics of infectious diseases, rumors, election outcomes, fads, and computer viruses\cite{keeling:infectious_diseases,AnderssonBook,RevModPhys.87.925,rodrigues2016application,billi... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
The evolution of the clustering of galaxies as a function of redshift
provides a sensitive probe of the underlying cosmology and theories of
structure formation. In an ideal world we would measure the spatial
correlation function of galaxies as a function of redshift and type
and use this to com... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction} \label{sec:intro}
We explore the implications of two simple insights: First, a change in one asset's price relative to all other assets' prices must cause the distribution of relative asset prices to change. Second, an increase in the price of a relatively high-priced asset increases the dispers... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
\indent
The Minimal Supersymmetric Standard model (MSSM) is an attractive
extension \cite{Haber:1984rc,Nilles:1983ge} of the very successful Standard Model.
One property of this theory is its rich spectrum of new heavy particles
which might be discovered at the LHC if they are lighter than $\app... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
The AdS/CFT correspondence \cite{MGW} has been deeply revealed by
comparing the anomalous dimensions of certain single trace operators in
the planar limit of the $\mathcal{N}=4$ super Yang-Mills (SYM) theory
and the energies of certain string states in the type IIB string theory on
$AdS_5 \time... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
The evolution of a signal $E(x,t)\in\mathbb{C}$ in optical fiber,
where $x\ge0$ denotes the position in the fiber and $t\in\mathbb{R}$
the time, is well-described through the \emph{nonlinear Schr\"odinger
equation (NSE)}. Through proper scaling and coordinate transforms,
the NSE can be brought i... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
\label{sec:introduction}
For over a decade dopants in Si have constituted the key elements in
proposals for the implementation of a solid state quantum
computer.~\cite{kane98,vrijen00,skinner03,barrett03,hollenberg041} Spin or charge qubits operate through controlled
manipulation (by applied elec... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction} \label{sec:1}
Suppose we observe $p$-dimensional Gaussian vectors
$x_1, \ldots, x_n \stackrel{i.i.d.}{\sim} \mathcal{N}(0, \Sigma)$, with
$\Sigma = \Sigma_{p}$ the underlying $p$-by-$p$ population covariance matrix.
Traditionally, to estimate $\Sigma$, we form the empirical (sample)
covari... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
Optimizing the exploitation of patchy resources is a long-standing dilemma in
a variety of search problems, including robotic
exploration~\cite{Wawerla:2009}, human decision
processes~\cite{Gittins:1973}, and especially in animal
foraging~\cite{MP66,Pyke:1977,VLRS11,Charnov:1976}. In foraging, ... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
Gamma-ray lines from solar flares were first observed in 1972 with the
gamma-ray spectrometer (GRS) aboard the {\it OSO-7} satellite \citep{chu73}.
Since then, repeated observations with various space missions, including the
{\it Solar Maximum Mission}/GRS (e.g. Share \& Murphy 1995), all four ... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{\label{intro} Introduction}
In a QCD-like theory with Dirac fermions, the measure of
the euclidean functional integral is positive when all fermions
have a positive mass, and, as a consequence, there is no topological term
induced by the fermionic part of the theory.
This generalizes to all types of fermion {\... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
Human matting is an important image editing task which enables accurate separation of humans from their backgrounds. It aims to estimate the per-pixel opacity of the foreground regions, making it valuable to use the extracted human image in some recomposition scenarios, including digital image a... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{\label{sec:level1}Introduction}
There has been a lot of progress on the development algorithms for quantum computing in recent years. Phase estimation is an important step in many quantum computing algorithms\cite{kitaev1995quantum, berry2000optimal, kitaev2002classical, o2009iterative, svore2013faster, paes... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
\subsection{Background and Preliminaries}
Circle packing builds a connection between combinatoric and geometry. It was used by Thurston \cite{T1} to construct hyperbolic 3-manifolds or 3-orbifolds. Inspired by Thurston's work, Cooper and Rivin \cite{CR} studied the deformation of ball packings, w... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}\label{Sec:Intro}
Introducing new and surprising concepts to students is a good way to get them excited about mathematics. One of these concepts is non-Euclidean geometry. Since we live on a globe, spherical geometry is quite intuitive to many but it also offers a couple of surprises because most... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Transverse momentum spectra of open charm mesons at LHC}
Recently ALICE, LHCb and ATLAS collaborations have measured inclusive transverse momentum spectra
of open charm mesons in proton-proton collisions
at $\sqrt{s}=7$ TeV \cite{ALICE,LHCb,ATLAS}. These measurements are very
interesting from the theoretica... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
One of Franco Tricerri's interests was in Hermitian manifolds.
In \cite{T-V} various types of Hermitian structures are
discussed and conditions on the Lee form are of paramount importance.
That Hermitian structures are closely connected with harmonic
morphisms is shown in \cite{B-W} and \cite{W... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{INTRODUCTION}\label{intro}
The analysis of the spectra of \ion{H}{ii} regions provides information about the
chemical composition of the present-day interstellar medium in different kinds of
star-forming galaxies and in different regions across these galaxies. The results
supply fundamental input for our mode... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
Let $(R, \mathfrak m, k)$ be a local ring (a commutative Noetherian ring with unique maximal ideal $\mathfrak m$) and let $M$ and $N$ be finitely generated nonzero $R$-modules. We say the pair $(M,N)$ satisfies the {\it depth formula} provided:
$$\depth(M)+\depth(N)=\depth(R)+\depth(M\otimes_{R}... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
Theoretical attempts to unify gauge forces necessarily lead to new
particles with masses way above the electroweak scale $v=174\ensuremath{\;\mbox{GeV}}$
defined by the vacuum expectation value (vev) of the Standard-Model (SM)
Higgs boson. Such heavy particles generally lead to unduly large
radia... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
\label{sec1}
One can argue that thin matter shells in general relativity provide
the simplest class of spacetimes after vacuum spacetimes. Indeed, thin
shells, besides giving instances of static and dynamic spacetimes,
allow themselves to be scrutinized in relation to their entropic and
therm... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
Secret sharing schemes are modifications of cooperative games to the situation when not money but information is shared. Instead of dividing a certain sum of money between participants a secret sharing scheme divides a secret into shares---which is then distributed among participants---so that s... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
Though inflation is commonly invoked as the mechanism in the early universe that solves the horizon and flatness problems by exponentially diluting away any inhomogeneities, it has been argued that if it runs for long enough it actually does not produce such a flat, smooth spacetime. This is bec... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Anisotropic shuriken model}
\label{sec:Model}
The shuriken lattice is made of corner-sharing triangles with 6 sites per unit cell [see Fig.~\ref{fig:UnitCell}]. As opposed to its kagome parent where all spins belong to hexagonal loops, the shuriken lattice forms two kinds of loops made of either 4 or 8 sites.... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
One of major contributions by Stone to Measure Theory is a representation
pre-intergrals $I\left( f\right) $ as intergrals $\int fd\mu$ for some
measure $\mu$ (see \cite{S48}). He found in particular that the natural
framework to get such a representation is the function Riesz spaces $E$ close... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
Discrete time quantum walks, or quantum walks (QWs) in short, are space-time discrete unitary dynamical systems first appeared as the space-time discretization of $1+1$ dimensional Dirac equation related to Feynman path integral \cite{FH10Book}.
From the end of 20th century, QWs started to attrac... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
Elastic hadron scattering in the Regge regime (high center-of-mass energy and small scattering angle) has long been understood to have particularly interesting features. Written in terms of the Mandelstam variables $s$ and $t$, the scattering amplitude scales as $s^{\alpha(t)}$, where $\alpha(t... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
The heterotic $E_8 \times E_8$ and the heterotic $SO(32)$ hold a special place when it comes to relating string vacua to experimental phenomena. In this note, we speculate about the fundamental role being played by the $SO(8)$ group representations, displaying the triality structure which is th... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
In order to study qualitative effects of magnetism in plasma
dynamics a very simple model is introduced. Two overlapping
homogeneous spheres of equal radii, and of equal but oppositely
signed charge densities, are assumed to move, relative to each
other, with negligible dissipation (resistivity) ... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
Within the framework of grand unified theories, as a result of
vacuum symmetry breaking phase transitions, different types of
topological defects could be produced in the early universe
\cite{Kibb80,Vile94}. In particular, cosmic strings have attracted
considerable attention. Although the recent... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
\subsection{Background and Motivation}
The optimal control of distributed parameter systems has important applications in various scientific areas, such as physics, chemistry, engineering, medicine, and finance. We refer to, e.g. \cite{glowinski1994exact, glowinski1995exact, glowinski2008exact, l... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Terminology and Introduction}
Let $G$ be a finite undirected graph with multiple edges but without loops.
We denote $V(G)$ as the vertex set and $E(G)$ as the edge set of $G$.
By $n=n(G)=|V(G)|$ and $m=m(G)=|E(G)|$ we refer to the {\it order} and the {\it size} of $G$, respectively.
For an edge $e\in E(G)$... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
The problem of realizing and manipulating Majorana fermions in condensed matter systems is currently a topic of great theoretical and experimental interest. Roughly, Majorana fermions constitute `half' of a usual fermion. That is, creating an ordinary fermion $f$ requires superposing two Major... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
In this paper, we prove an inverse Strichartz theorem for
certain
Schr\"{o}dinger
evolutions on the real line with $L^2$ initial data.
Recall that solutions to the linear Schr\"{o}dinger equation
\begin{align}
\label{e:intro_free_particle}
i\partial_t u = -\tfrac{1}{2} \Delta u \quad\text{wi... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{\@startsection {section}{1}{\z@}{-3.5ex plus -1ex minus
-.2ex}{2.3ex plus .2ex}{\large\bf}}
\def\subsection{\@startsection{subsection}{2}{\z@}{-3.25ex plus -1ex
minus -.2ex}{1.5ex plus .2ex}{\normalsize\bf}}
\makeatother
\makeatletter
\def\arabic{section}.\arabic{equation}{\arabic{section}.\arabic{equation}}
... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
To understand the origin of cosmic rays (CRs), it is important
to distinguish
between the lower energy CRs which can be contained within
the magnetic field of our Galaxy and thus have energies of
up to about $3 \times 10^{18}$ eV for heavy
nuclei, and those that are even more energetic.
The bul... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
Let $k\geq 2$ be fixed. Erd\H{o}s, Faudree, Rousseau and Schelp \cite{erdos2} observed the following fact.
\begin{fact}\label{fact1} Every graph on $n\geq k-1$ vertices with at least
$$(k-1)(n-k+2)+{k-2\choose 2}$$
edges contains a subgraph of minimum degree at least $k$.
\end{fact}
This fact ... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
Mixed univariate distributions have been introduced and studied in the last years by compounding continuous and discrete distributions. Marshall and Olkin (1997) introduced a class of distributions which can be obtained by minimum and maximum of independent and identically distributed (iid) cont... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Problem statement}
Given alphabets $ {\cal X} $ and $ {\cal Z} $,
an $n$-\emph{block denoiser} is a mapping $\re:{\cal Z}^n \rightarrow
{\cal X}^n$.
For any $z^n \in {\cal Z}^n$, let $\re(z^n)[i]$ denote the $i$-th term of
the sequence $\re(z^n)$.
Fixing a per symbol loss function $ \Lambda(\cdot,\cdot) $, for... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
Wireless ad hoc networks have received significant attention
due to their many applications in, for instance, environmental monitoring or emergency disaster relief, where wiring
is difficult. Unlike wired networks, wireless ad hoc networks lack a backbone infrastructure. Communication takes plac... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
One of the most basic questions in cosmology is whether the universe
had a beginning or has simply existed forever. It was addressed in
the singularity theorems of Penrose and Hawking \cite{HawkingEllis}, with the
conclusion that the initial singularity is not avoidable. These
theorems rely o... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
Let $\cH$ be a real Hilbert space endowed with weak topology defined by the inner product
$\langle \cdot , \cdot \rangle$ and its induced norm $\| \cdot \|$. Let $C \subseteq \cH$ be a
nonempty closed convex subset and $f: \cH \times \cH \to \R \cup \{+\infty\}$ a bifunction
such that $f(x, y) <... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
\footnote{This is the peer reviewed version of the article which has been published in final form at \textit{Progress in Photovoltaics: Research and Applications} (\href{http://dx.doi.org/10.1002/pip.2787}{DOI: 10.1002/pip.2787}). This article may be used for non-commercial purposes in accordance... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
In this work, we study deterministic distributed algorithms under three different assumptions; see Figure~\ref{fig:models}.
\begin{itemize}[leftmargin=4em]
\item[($\mathsf{ID}$)] \emph{Networks with unique identifiers}. Each node is given a unique $O(\log n)$-bit label.
\item[($\mathsf{O... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
The Hubbard model has played the role as a prototype of the strongly
correlated electron system and the one-dimensional case has been well
understood since the exact Bethe Ansatz solution by Lieb and Wu
\cite{Liebwu,Lieb,Ovch,Shiba,Coll,Woyn,Ogata,Weng}.
Our main understanding of the one-dimensi... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
The transport of excitations, energy, charge or correlations is a topic of current interest both in the classical as well as in the quantum regimes. For example, efficient and coherent transport of excitations has been shown to play a crucial role in biological processes such as photosynthesis~\c... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\subsection{One-dimensional Burgers' equation}\label{subsec:Burgers}
\ifx
Here we propose two alternative approaches to select the reduced basis size that accounts for specified accuracy levels in the reduced-order model solutions.
Assume we have a probability space $(\Omega, \mathcal{F},\mathcal{P})$. These techniques... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction} \label{sec1}
Classification is one of the most critical issues in data mining, pattern recognition, and machine learning. Numerous classification methods have been successful in various applications
but, when these methods are performed on the imbalanced datasets, the performance of minority clas... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
\section{Introduction}
Since the thermodynamics of black holes has been established, the entropy of horizon is a fascinated research
interest. The recent popular topic is the additional equalities in thermodynamics, which are expected to be useful of understanding the origin of black hole entropy at the microscopic lev... | {
"redpajama_set_name": "RedPajamaArXiv"
} |
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