arxiv_id stringlengths 0 16 | text stringlengths 10 1.65M |
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gr-qc/0508040 | \section{\label{sec:Int}Introduction}
General relativity has many successful predictions, some of them
are passing experimental tests with high precision, for example
mercury's perihelion and gravitational redshift. On the other
hand, the most spectacular and promising prediction is the
existence of black holes. In th... |
astro-ph/0508515 | \section{Introduction}
On February 7, 2004, during a routine Galactic plane scan, the
\textit{INTEGRAL} observatory detected a source which was not in the
\textit {INTEGRAL}\ reference catalog. Search in the archive led to the
identification of several \textit {ROSAT}\ sources in the \textit {INTEGRAL}\ error box.
Am... |
gr-qc/0508086 | \section{Introduction}
One of the motivations for the quantization of cosmological models was
that of avoiding the initial {\it Big Bang} singularity.
Since the pioneering work in quantum cosmology due to DeWitt \cite{dewitt},
workers in this field have been attempting to prove
that quantum cosmological models entai... |
2010.15530 | \section{Introduction} \label{section1}
Consider a discrete nonlinear system
\begin{equation}
y_{k} = f_0(x_k,w_k),\label{sistema}
\end{equation}
where $f_0(\cdot,\cdot)$ is not known, $k$ is the discrete time instant, $y_k\in {\mathcal{Y}} \subseteq \R$ is the output of the
system, $w_k$ accounts for parametric uncer... |
2010.15630 | \section{Half-quantized Hall conductance of the 3D TI with antiparallel magnetization alignment surfaces in Fig.~1}
\begin{figure}[htbp]
\includegraphics[scale=0.3]{half_hall_cond.eps}
\caption{It shows numerical simulations of the Hall conductance of the top surface. The red curve is obtained from a 2D massive ... |
2012.04609 | \section{Introduction}
In dynamics we are interested in the orbits under some law of motion, but it is usually a better way to have a global view of the dynamics to understand it from a probabilistic point of view. That is, instead of being concerned with the orbit of any point we want to say important information abou... |
2006.08578 | \section{Introduction}
Quantum knot invariants arise in theoretical quantum physics, where a knot can be regarded as the spacetime orbit of a charged particle. A typical example of such an invariant is the $n$-colored Jones polynomial of the knot $K=4_1$ (the figure-eight knot), which is given by\footnote{Throughout t... |
1008.2560 | \section{Introduction}
\label{sec: intro}
Measurements of the distance--redshift relation of type Ia supernovae (SNeIa)
firmly established contemporary accelerated cosmological expansion \citep{riess98, perlmutter98}
and SNIa distances remain one of the most promising probes of dark energy.
To determine wh... |
1008.1892 | \section{Introduction}
Due to the incomplete Fourier plane sampling of radio synthesis observations, deconvolution is essential for making high fidelity images. The traditional CLEAN \cite{Hogbom} algorithm and its variants are widely used for this deconvolution. There are several limitations of clean being applied to ... |
2005.12119 | \section*{Introduction}
The radiative transfer of the cosmic microwave background (CMB) is
based on the numerical resolution of a hierarchy of equations coupling
CMB multipoles, together with Einstein equations for the
dynamics of linear metric perturbations. As the CMB is polarized, we have in general a triple hierar... |
1610.01984 | \section{Introduction}
The $\sigma$ Orionis cluster contains several hundred young stars surrounding the multiple star system $\sigma$ Orionis \citep[see review by][]{walter08}. The clustering of 15 B-type stars in the region was first noted by \citet{garrison67}, and it was included in the catalog of open clusters b... |
1610.02174 | \section{Introduction}
\label{introduction}
As a simple four-atomic molecule, formaldehyde, H$_2$CO, also known as methanal, is
of great fundamental interest. Its rotational spectrum is of great importance for radio
astronomy. It was only the seventh molecule to be detected in the interstellar medium
in 1969 \cite{... |
2110.10803 | \section{Introduction}
\label{introduction}
Extreme multi-label classification (XMLC) is a supervised learning problem, where only a few labels from an enormous label space, reaching orders of millions, are relevant per data point. Notable examples of problems where XMLC framework can be effectively leveraged are tagg... |
1107.1054 | \section{Introduction}
CTB 37A (also called G348.5+0.1, $\rmn{RA}(2000)=17^{\rmn{h}} 14^{\rmn{m}} 06^{\rmn{s}}$,
$\rmn{Dec.}~(2000)=-38\degr 32\arcmin$) was discovered by
\citet{b5} in the radio band and has a shell-type morphology with
an angular size of 15 arcmin. From Very Large Array observations
at wavelengt... |
2211.14609 | \section{Introduction}
Given dramatic changes in lifestyles in modern society, millions of people nowadays are affected by anxiety, depression, exhaustion, and other emotional problems. The demand for proper emotional care is accumulating and accelerating at an increasingly rapid rate. Music, as being extensively studi... |
astro-ph/9901252 | \section{Introduction}
The study of resolved stellar populations provides a powerful tool to follow
galaxy evolution directly in terms of physical parameters such as age (star
formation history, SFH), chemical composition and enrichment history, initial
mass function, environment, and dynamical history of the syste... |
astro-ph/9901001 | \section{Introduction}
The dipole anisotropy of the Cosmic Microwave Background (CMB)
radiation is generally interpreted as a Doppler effect due to the
motion of the Sun with respect to the CMB rest-frame. The velocity of
the Local Group (LG), 627$\pm$22\,\unit{km~s\mone}\ towards \lb{276\pm3}{30\pm3},
is now well det... |
1804.09275 | \section{Introduction}\label{sec:1}
\begin{figure*}[!hbt]
\centering
\includegraphics[width = 1.5\columnwidth]{g_over_omega}
\caption{\label{fig:g-w_r} (Color online) Evolution in cavity QED of the highest value of $g/\omega$, with $\omega$ the cavity frequency, as function of time for different physical platforms. Th... |
0811.0362 | \section{Introduction}\label{sec:Introduction}
A particular exact solution to a classical field equation is often regarded as to an extended particle under certain special conditions,
a so-called soliton (for a review, \cite{Rajaraman}),
which is important in study of nonperturbative properties
of field theories.
T... |
1503.03677 | \section{Introduction}
What is the Cosmological Constant? How can be computed? These are some of the
many puzzling questions which are still unsolved. Basically the Cosmological
Constant can be connected to the energy of the vacuum. However, the absence of
a complete Quantum Gravitational theory increases the num... |
1503.03522 | \section{Introduction}
When atomic spectral lines coalesce into broad unresolved patterns due to physical broadening mechanisms (Stark effect, auto-ionization, etc.), they can be handled by so-called statistical methods (Bauche et al., 1988). Global characteristics - average energy, variance, asymmetry and sharpness... |
1503.03907 | \section{Introduction}
The treatment of linear perturbations has become a prolific field in modern cosmology. The advent of inflationary universe models \cite{inflationmodels} generated great interest in cosmological perturbations and gave rise to a lot of activity in this area. Beyond its early success, the stu... |
2208.09335 | \section{Introduction}\label{sec:intro}
Comparing model predictions to observations drawn from an astronomical catalogue requires knowledge of the selection effects and incompleteness affecting the observed list of objects. Knowing what we could not observe could be as essential as what we observed, even for simple end... |
2006.11707 | \section{Introduction}
Coronal mass ejections (CMEs) are clouds of magnetized plasma that erupt from the Sun's atmosphere and propagate into the interplanetary space. They are often accompanied by a large amount of magnetic energy release and can cause extreme space weather events when arriving at the Earth. Studies h... |
1803.09242 | \section{Introduction}
In the last two decades we have witnessed an impressive surge in experimental advances pushing the frontier of realising and controlling (effectively) closed non-equilibrium quantum many-body systems.\cite{Bloch-08,ReichelVuletic11,Polkovnikov-11} This is of fundamental importance as the conseque... |
1310.5350 | \section{Introduction\label{intro} }
Gravitational lensing is a powerful astrophysical as well as cosmological
probe to study the lens object, and the source as well as the background geometry
and it indirectly serves as a probe of gravitational physics. Gravitational
lensing can help us to detect or infer the ex... |
1506.03332 | \section{Introduction}
This paper studies, as a reflection group, the full general linear group $\mathrm{GL}(V)\cong \mathrm{GL}_n(\F)$, where
$V$ is an $n$-dimensional
vector space over a field $\F$. An element $g$ in $\mathrm{GL}(V)$
is called a \defn{reflection} if its \defn{fixed subspace}
$V^g:=\{v\in V:\ gv=v... |
1506.03395 | \section{Introduction}
The importance of low surface brightness (LSB) galaxies to galaxy studies is not that
they dominate the total galaxy population of the Universe (they do not, Hayward,
Irwin \& Bregman 2005; Rosenbaum \& Bomans 2004; Schombert, Pildis \& Eder 1997) nor
that they represent a special form of star f... |
2101.10176 | \section{Introduction}
In this article, the fundamental gap of a domain is the difference between the first two eigenvalues of the Laplacian with zero Dirichlet boundary conditions. For convex domains in $\mathbb R^n$ or $\mathbb S^n$, $n\geq 2$, it is known from \cite{fundamental, seto2019sharp,dai2018fundamental,h... |
2102.02512 | \section{Introduction}
Clouds play a major role in regulating weather and climate on Earth, by modulating the incoming solar radiation. Despite substantial scientific advances in the last decades, clouds still represent the primary source of uncertainty in climate projections \citep{pincus2018shallow,IPCC}.
A key chal... |
1602.04771 | \section{Introduction}
Over the last decades, the so-called {\it cosmological constant problem} has been one of the major challenges in theoretical physics. The issue refers to the absence of gravitational effects, particularly at the cosmological level, of the vacuum energy density predicted by quantum field theories... |
2012.04863 | \section{Introduction}
Given a group of human students, assuming they work equally hard, there are three major factors determining which students learn better than others, including intelligence, learning skills, and learning materials. People with higher intelligence quotient (IQ) are stronger learners. Learning mater... |
1105.2506 | \section{Introduction}
How the outer atmosphere of the Sun, the solar corona, is heated to
several million degrees Kelvin is one of the most compelling
questions in space science \citep{Klimchuk_2006}. Simple thermal
conduction from below is clearly not the answer, since the corona is
more than two orders of magnitud... |
2004.06452 | \section{Introduction}
It is not easy to find an astrophysical phenomenon with as little
clue to the physical nature of the cause of the phenomenon as
the (quasi)periodic modulation of the light curves RR~Lyrae stars
(or, as commonly known, the Blazhko effect -- \citealt{1907AN....175..325B}).
Although several... |
2004.02846 | \section{Introduction}
The concept of Hausdorff dimension has led to interesting results in
the theory of profinite groups; for instance, see~\cite{KlThZR19} and
the references therein. Let $G$ be an infinite countably based
profinite group and let $\mathcal{S}$ be a \emph{filtration series} of
$G$, that is, a chain ... |
1810.08937 | \section{Introduction} \label{sec0}
Let $p$ be a prime and $k=\overline{{\mathbb{F}}}_p$ be an algebraic closure of the
field with $p$ elements. Let $G$ be a connected reductive algebraic
group over $k$ and assume that $G$ is defined over the finite subfield
${\mathbb{F}}_q\subseteq k$, where $q$ is a power of~$p$.... |
1810.08999 | \section{\label{sec:intro}Introduction}
Optically pumped magnetometers, (OPMs), have increasingly been in the spotlight for their broad span of applications ranging from fundamental physics experiments to medical physics. Examples include measurements of the electric dipole moment (EDM)~\cite{edm1,edm2} and searches f... |
1208.1734 | \section{Introduction}
\label{sec:intro}
Renormalization group (RG) methods play an important role in {\it ab initio} nuclear theory by extending the range of many computational methods and improving their convergence patterns \cite{Bogner:2003wn, Bogner:2009bt, Furnstahl:2012fn}. There are numerous RG methods that h... |
1208.1443 | \section{Introduction}
\label{sec:intro}
Expressing convex optimization problems in conic form, as the minimization
of a linear functional over an affine slice of a convex cone, has been an
important method in the development of modern convex optimization theory.
This abstraction is useful (at least ... |
2301.03433 | \section*{SUPPLEMENTAL MATERIAL}
\subsection{Constraints on a linear temporal variation of the fine-structure constant and its coupling to gravity}\label{sec:lpi}
Previous optical frequency comparisons of $\nu_\textrm{E3}$ and $\nu_\textrm{E2}$ in our group found the strictest limits on a linear temporal variation of t... |
1109.3092 | \section{Introduction}
Given two graphs $G$ and $H$, the \emph{strong product} of $G$ and $H$, denoted by $G\boxtimes H$, is the graph obtained by substituting each vertex in $G$ with a copy of $H$. The graph $C_5 \boxtimes K_3$ (see Figure \ref{fig:borodin}) has appeared as an exemplary graph in several situations... |
1109.2860 | \section*{1. Introduction.}
As shown in \cite{Aksenov}, the study of the Newman phenomenon in the multiplicative sequences leads naturally to the study of the norms (over $\mathbb Q$ or over a subfield of small degree) of numbers of the form $r(\zeta)$ where $\zeta$ is a primitive $p$-th root of unity ($p$ being prime)... |
1109.2911 | \section{Introduction}
Hawking's calculation of black hole evaporation~\cite{Hawking:1974sw}
leads to a direct conflict between general relativity and the unitary
evolution of quantum mechanics~\cite{Hawking:1976ra}. This prompted
the suggestion that the requirement of unitary evolution should be
relaxed~\cite{Hawking... |
0902.3885 | \section{Introduction}
\setlength{\baselineskip}{7mm}
Hawking radiation from black holes is one of the most important effects in black hole thermodynamics and the quantum effect of gravity \cite{Hawking:1974rv, Hawking:1974sw}.
There are several derivations of Hawking radiation and recently one interesting method was p... |
0902.3834 | \section{Introduction}
\label{sec:intro}
The main goal of experiments which perform ultrarelativistic heavy-ion collisions is to produce and
study the properties of a deconfined plasma of quarks and gluons. This new state of matter,
the quark-gluon plasma (QGP), is expected to be formed once the temperature of nucle... |
0902.3252 | \section{Introduction}
Recently quantum field theory on noncommutative spaces has been studied
extensively, see e.g. \cite{NCreviews} and references therein. General quantum
mechanical arguments indicate that it is not possible to measure a classical
background space-time at the Planck scale, due to the effects of the... |
2001.09387 | \section{Introduction}\label{intro}
\setlength{\epigraphwidth}{2.3in}
\epigraph{A little learning is a dangerous thing.}{Alexander Pope\\ \textit{An Essay on Criticism}}
This is a paper on the value of information. The setting is a two player sender-receiver, signaling, or communication, game. There is an unknown stat... |
1612.04176 | \section{Introduction}
Intentionally transferring energy along with information, using radio frequency (RF) signals, is an attractive alternative to perpetually and remotely power energy harvesting sensors that have limited physical accessibility. It is foreseeable that in next generation wireless systems, a picocell ... |
1606.06287 | \subsection*{Acknowledgements}
The author thanks Matthew Daws for various helpful exchanges on operator-space tensor products, and Adam Skalski for comments and corrections on an earlier draft of this note.
He also wishes to thank John Rainwater for supplying the key ideas in the proof of Theorem~\ref{t:mainthm}. Rain... |
2107.01136 | \subsection{Benchmark Families}\label{sec:benchmarkfamilies}
The upper part of \Cref{tab:benchmarks} shows the results for live updates from specification patterns introduced by Menghi et. al.~\cite{RobotSpecifications}, where \textbf{Reactivity} implements additional interaction with the environment.
The specification... |
2205.03545 | \section{Introduction}
\label{Intro}
A mathematical function `$f$' in the `$x$' domain can be transformed to a function `$F$' in the `$u$' domain
using the integral
\begin{equation}
F(u) = \int_{a}^{b} f(x) \, K(u,x) dx.
\end{equation}
This process is known as an integral transform and the function $K(u,x)$ is the k... |
1609.07834 | \section{Introduction}
\label{sec:intro}
In epidemiology, observational studies are often used to investigate the relation between an exposure and a health outcome of interest. However, several potential biases might jeopardize our inference and conclusions \cite{greenland2005multiple}. Selection bias arises when the ... |
1609.07468 | \section{Introduction}
For every group $G$ there is a functor $\mathbb{A} \colon \mathrm{Or}G \to \mathrm{Spectra}$ from the orbit category of $G$ to the category of spectra sending $G/H$ to (a spectrum weakly equivalent to) the non-connective $A$-theory spectrum $\mathbb{A}(BH)$. For any such functor $\mathbb{F} \col... |
2209.12877 | \section{Introduction}
\label{sec:intro}
The central problem in Boolean function complexity is to understand
exactly how hard it is to compute explicit functions. The hardness
naturally depends on the computation model to be used, and depending
on the model, several complexity measures for functions have been
studied e... |
2010.00615 | \section{\@startsection {section}{1}{\z@}{-3.5ex plus -1ex minus
\makeatother
\newcommand{\bbm}[1]{\left[\begin{matrix} #1 \end{matrix}\right]}
\newcommand{\sbm}[1]{\left[\begin{smallmatrix} #1
\end{smallmatrix}\right]}
\section{Introduction} \label{sec1}
\setcounter{equation}{0}
\vspace{-1mm}
\ \ \ Consid... |
1508.03827 | \subsubsection{\@startsection{subsubsection}{3}{10pt}{-1.25ex plus -1ex minus -.1ex}{0ex plus 0ex}{\normalsize\bf}}
\def\paragraph{\@startsection{paragraph}{4}{10pt}{-1.25ex plus -1ex minus -.1ex}{0ex plus 0ex}{\normalsize\textit}}
\renewcommand\@biblabel[1]{#1}
\renewcommand\@makefntext[1
{\noindent\make... |
1508.03510 | \section{Calculation of the theoretical PQPD}
To describe the reconstructed PQPD $W(S_1,S_2,S_3)$ we calculate the theoretical distribution for our case. Thus we consider a horizontally polarized weak coherent state and only single-photon and no-photon detection events. In this case the density operator looks like
... |
0905.4408 | \section{Introduction}\label{se:introduction}
Nonlinear hyperbolic conservation laws on networks have recently attracted
a lot of interest in various fields: car traffic
\cite{C-G-P,garavello-piccoli_ARModel_2006,gp-book,Holden-Risebro_siam_1995},
gas dynamics~\cite{MR2418671,MR2223073,MR2219276,MR2247787,MR2311526,
... |
2009.09892 | \section{Introduction}
Let $\mathcal{B}\left( \mathcal{H} \right)$ denote the ${{C}^{*}}$ -algebra of all bounded linear operators on a complex Hilbert space $\mathcal{H}$ with inner product $\left\langle \cdot,\cdot \right\rangle $. For $A\in \mathcal{B}\left( \mathcal{H} \right)$, let $\omega \left( A \right)$ and $\... |
2109.11083 | \section{Introduction}
Molecular dynamics (MD) describes the motion of a molecular system based on classical Newtonian mechanics.
In the classical mechanics, particles or coarse grained beads feature in masses and charges and their dynamics is driven by empirical force fields\cite{MM-Leach2001,CHARMMFF}.
The empirical ... |
1304.7204 | \section{Proof of Lemma \ref{l:procedure}}
\begin{proof}
Assume that $\phi$ is satisfiable. By Lemma \ref{l:shortpaths} and Lemma \ref{l:narrowtrees} there exists a small model $\str{T}\models \phi$.
The procedure accepts $\phi$ by making all its guesses in accordance to $\str{T}$, i.e.~in the first step it sets $\bar... |
1304.7086 | \section{Introduction}
In \cite{HL1999}, Connor Lazarov and the second author gave general conditions which guarantee that the Bismut superconnection formalism extends in full generality to families of non-compact manifolds. This allowed us to prove a families index theorem for generalized Dirac operators defined a... |
2010.02496 | \section*{References} |
2104.02089 | \section{Introduction} \label{sec:intro}
Galaxies can be found in environments of very different nature, ranging from very low (isolated galaxies) to high density (massive cluster cores), with filaments and groups laying in between these extreme conditions. Both the properties of galaxies and the relative fractions of ... |
1004.0341 | \section{Introduction}\label{sec:int}
Let $\Omega$ be an open bounded subset of $\RR^N$, $1\le N\le 3$, with smooth boundary $\Gamma$. We are interested in the following evolution problem
\begin{eqnarray}
\partial_t v & - & \Delta \mu + (j+\sigma)''(v)\ \mu - \overline{(j+\sigma)''(v)\ \mu} = 0 \,, \quad (t,x)\i... |
1004.0387 | \section{Introduction}
The study of strongly interacting matter under extreme conditions of temperature and/or density is one of the most fascinating areas of contemporary subatomic physics. This program aims to explore the many facets of the {\it bulk} behavior of Quantum ChromoDynamics (QCD): The theory of the str... |
hep-th/9312137 | \section*{Contents}
\contentsline {section}{\numberline {1}Introduction}{\pageref{AS}}
\contentsline {section}{\numberline {2}An Equation for the Complete
Effective Action}{\pageref{BS}}
\contentsline {subsection}{\numberline {2.1}Do We Need an Equation?
--- Methodological Considerations}{\pageref{BS1}}
\contentsline ... |
2101.00656 | \section*{Results and Discussion}
\subsection*{Modelling flows on hypergraphs}.
We model flows on hypergraphs with random walks, using
hypergraphs with nodes $V$, hyperedges $E$ with weights $\omega$, and hyperedge-dependent node weights $\gamma$.
Each hyperedge $e$ has a weight $\omega(e)$.
Each node $u$ with incident... |
1403.2037 | \section{Introduction and Preliminary}
Long-Guang and Xian in \cite{Xian} generalized the concept of a metric space, replacing the set of real numbers by an ordered Banach space and obtained some fixed point theorems for mapping satisfy different contractive conditions.\\
Recently Wei-Shih Du in \cite{Du1} has prove... |
2004.07494 | \section{Introduction}\label{intro}
Let $\mathcal{H}$ be a complex Hilbert space with inner product $\langle \cdot,\cdot\rangle$ and $\mathcal{B}(\mathcal{H})$ be the $\mathbb{C}^*$- algebra of all bounded linear operators on $\mathcal{H}$.
For $T\in
\mathcal{L(H)}$, the {\it numerical range} of $T$ is defined as
... |
1801.06178 | \section{Introduction}
A number of strongly correlated materials with a metallic parent state exhibit a variety of non-Fermi liquid (NFL) properties. Some of the best known examples of such behavior occur in the ruthenates \cite{hussey,gegenwart,kapitulnik,allen}, cobaltates~\cite{Taillefer1,Ong1}, iron-based supercon... |
0909.5687 | \section{{\bf 1. INTRODUCTION\/}
Li$_2$CuO$_2$ is the first \cite{Hoppe1970} and the most frequently studied compound of the
growing class of edge-shared spin-chain cuprates
\cite{Matsuda1996,Matsuda2001,MasudaPRB2005,Enderle2005,Drechsler2007PRL,Drechsler2007JP}. Owing to its structural
simplicity with ideally planar ... |
0909.4897 | \section{Formalism}
The width difference between mass eigenstates is then given
by~\cite{Beneke:1996gn}
\begin{equation}
\label{dgdef} \Delta \Gamma_{B_s}\equiv\Gamma_L-\Gamma_H =
-2\Gamma_{12}=-2\Gamma_{21},
\end{equation}
where $\Gamma_{ij}$ are the elements of the decay-width matrix,
$i,j=1,2$ ($|1\rangle=|B_s\rangl... |
1202.3583 | \section{Introduction}
Maxwell's equations for electromagnetic waves in Kerr nonlinear
dielectric materials read
\begin{subequations}\label{E:Maxwell}
\begin{align}
\label{E:Ampere}
\pa_t \CD &= \nabla \times \CH,\\
\label{E:Faraday}
\mu_0\pa_t \CH &= -\nabla \times \CE,\\
\label{E:Gauss}
\nabl... |
1202.3375 | \section{Introduction}
Interaction effects are expected to be
important for the physics of bilayer graphene and may cause
a formation of correlated many-body phases.\cite{Castro,Kotov}
This needs to be contrasted to intrinsic monolayer graphene in which a vanishing
density of states at the Dirac points suppresses the... |
1202.3247 | \section{Introduction}
This paper is a companion technical report to the article ``Continuation-Passing
C: from threads to events through continuations'' \cite{cpc2012}. It contains
the complete version of the proofs presented in the article. It does not,
however, give any background or motivation for our work: plea... |
2109.11738 | \section{Introduction} \label{sec:intro}
Modeling galaxy formation in the cosmological context is one of the greatest challenges in astrophysics and cosmology today. In past few decades, the broad contours of galaxy formation physics are investigated and built \citep{2010gfe..book.....M,2012RAA....12..917S,2015ARA&A..5... |
2109.11744 | \section{Introduction}
Let $\zeta(s)$ be the Riemann zeta-function and $s=\sigma+\ie t$, where $\sigma$ and $t$ are real numbers. One of the great problems in zeta-function theory is to determine the true order of $|\zeta(s)|$ in the critical strip. Due to the functional equation we can assume $1/2 \leq\sigma\leq 1$... |
quant-ph/0511025 | \section{Introduction}
\subsection{Quantum nondeterminism}
Classical nondeterminism, although being an unrealistic model
of computation, is a fundamental concept
in computational complexity with practical applications,
as shown, for example, by the importance of the theory of $NP$-completeness.
There are two differ... |
physics/0511237 | \section{Introduction}
In 1812, Massachusetts governor Elbridge Gerry, got help from his political party
by crafting a district and won his own election. At the time, someone produced an illustration
of the districting and emphasized its similarities with a salamander. The term
{\it {Gerrymander}} was then coined f... |
2011.05465 | \section{Introduction}
Every topological space in this article is assumed to be metrizable and separable.
Erd\H{o}s space is defined to be the space
$$ \mathfrak{E} = \{(x_n)_{n\in \omega} \in \ell^2 : x_i \in \mathbb{Q} , \textit{for all } i\in \omega \},$$
where $\ell^2$ is the Hilbert space of square-summable sequ... |
1305.7364 | \section{Introduction}
Bursting is an important signaling component of neurons, characterized by a periodic {alternation} of bursts and quiescent periods. Bursts are {transient}, but high-frequency trains of spikes, contrasting with the absence of spikes during the quiescent periods. Bursting activity has been record... |
1305.6907 | \section*{Acknowledgements}
VB thanks KITP-UCSB for hospitality during the course of this work and
F. Halzen, A. Karle, J. Learned, D. Marfatia, S. Pakvasa and
{W.P. Pan}
for email communications.
This research was supported in part by the National Science Foundation
under Grant No. NSF PHY11-25915 and in part by the... |
2206.12895 | \section{Introduction}
Clustering is an important problem in unsupervised learning that has been widely studied in statistics, data mining, network analysis, etc.~\citep{punj1983cluster,Article:Dhillon_01,Article:Banerjee_05,berkhin2006survey,Article:Abbasi07}. The goal of clustering is to partition a set of data poi... |
2010.13676 | \section{Introduction}
\label{sec:introduction}
\input{introduction}
\section{Related Work}
\label{sec:related-work}
\input{related-work}
\section{Robust Face Frontalization}
\label{sec:frontalization-landmarks}
\subsection{Outline of the Proposed Method}
\label{sec:outline}
\input{outline}
\subsection{Frontalizatio... |
2010.13638 | \section{Introduction}
\setcounter{lemma}{0} \setcounter{theorem}{0}
\setcounter{equation}{0}\setcounter{proposition}{0}
\setcounter{Rem}{0}\setcounter{conjecture}{0}
For $m,n\in\N=\{0,1,2\ldots\}$, the truncated hypergeometric series ${}_{m+1}F_m$ is defined by
$$
{}_{m+1}F_m\bigg[\begin{matrix}x_0&x_1&\ldots&... |
2010.13701 | \section{Introduction}
This document is a model and instructions for \LaTeX.
Please observe the conference page limits.
\section{Ease of Use}
\subsection{Maintaining the Integrity of the Specifications}
The IEEEtran class file is used to format your paper and style the text. All margins,
column widths, line spaces... |
hep-ph/9606434 | \section{Introduction}
The traditional way to reduce the independent parameters of a theory
is the introduction of a symmetry. Grand Unified Theories (GUTs)
\cite {pati1,gut1,GUTS} are
representative examples of such attempts. For instance, the minimal
$SU(5)$ reduces the gauge couplings of the
Standard Model (SM) ... |
cond-mat/9606105 | \section*{Acknowledgements}
\acknowledgments
This work was supported in part by grants DMR-9122645 and DMR-8819885.
We are grateful to Phil Nelson for a careful reading of the manuscript.
TCL and FCM are also grateful to Exxon Research and Engineering where a
portion of this work was carried out. |
1509.06582 | \section{Introduction}
This work is concerned with optimization problems of the form
\begin{equation}
\label{eq:prob_convex}
\min_{u\in X} G(u) + F(K(u))
\end{equation}
for proper, convex and lower semicontinuous functionals $G: X\to \overline{\mathbb{R}}:=\mathbb{R}\cup \{\infty\}$ and $F: Y\to\overline{\math... |
2112.06817 | \subsection*{Non-expected utility decision criteria}
A careful inspection of the proof of manipulation-proofness (Theorem 3) reveals two important facts. First, notice that we never used any properties of the underlying probability space beside that (i) the random variable representing the risk faced by the insured had... |
cond-mat/9204009 | \section{Identify the Broken Symmetry}
What is it which distinguishes the hundreds of different states of matter?
Why do we say that water and olive oil are in the same state (the liquid
phase), while we say aluminum and (magnetized) iron are in different states?
Through long experience, we've discovered that most pha... |
2108.01674 | \section*{Supplemental Material}
In this \emph{Letter}, we presented the results for the NLO evolution of the first three moments of the track functions under the simplified assumption that $T_q=T_{\bar q}$, and that the track functions are equal for all quark flavors. This simplified case was sufficient to illustrate... |
2005.10284 | \section{Introduction} \label{sec:intro}
Explaining the outcomes of complex machine learning models is a prerequisite for establishing trust between the machines and users. As humans increasingly rely on DNNs to process large amounts of data and make decisions, it is crucial to develop solutions that can interpret the... |
2005.11849 | \section{Introduction}
Grammatical error correction (GEC) is the automatic correction of grammatical and other language-related errors in text.
Most works regard this task as a translation task and use encoder--decoder (Enc--Dec) architectures to convert ungrammatical sentences to grammatical ones.
This Enc--Dec approa... |
2203.01686 | \section{Introduction}
Kernel smoothers form an essential suite of statistical techniques for data analysis in the 21st century due to their ability to convey complex statistical information in a concise and intuitive visual format. This ability arises from their shared characteristic of transforming data samples into... |
1810.05493 | \section{Introduction\label{ch:intro}}
The present work is devoted to conceptual and computational problems
in pre-Born--Oppenheimer (pre-BO) molecular structure theory.
Without the Born--Oppenheimer (BO) approximation,\cite{BoOp27,Born51,BoHu54}
in a ``pre-BO world'',
we can gain in accuracy for the numerical results ... |
2112.01646 | \section{Introduction}
`Quantum Blur' is a method for manipulating images using quantum circuits~\cite{wootton-fdg,capdeville-21}, devised as first step towards showing that aspects of quantum computing could be used for procedural generation~\cite{wootton-fdg,wootton-cog,hamido-21}. Images are first translated into c... |
0902.4472 | \section{Introduction}
After the primordially ubiquitous H and He, oxygen is the third most
abundant chemical element in the Universe, and the first among those
produced via stellar nucleosynthesis. It is a catalyst in the CNO
process, which is the main conversion channel of H into He in the
interiors of stars more ma... |
0902.4715 | \section{Introduction}
If the dark matter in the Universe
is comprised of stable, weakly-interacting massive particles (WIMPs), in many instances
this leads to the prediction that WIMPs will self-annihilate into Standard Model (SM) particles
that may be visible with the upcoming generation of high-energy particle dete... |
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