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1,108,101,564,515
arxiv
\section{INTRODUCTION} \label{sec:INTRO} Quantum and general relativistic field theories have been studied for many years. The metaphysical differences between these have not yet been resolved and a combined theory is not available. A number of enigmas in present day thought suggest that something is wrong. Among th...
1,108,101,564,516
arxiv
\section{Supplementary Information} \subsection{Fisher derivation for the uniform distribution $p(\mu)$} Let us assume the standard Zeno approximations $q(\mu)\approx 1-\Delta^2H_{\Pi} \mu^2$, $\mathcal{P}^{\star}=1$, $(1-\mathcal{P}^{\star})=m\Delta^2H_{\Pi}\chi_2$, and consider the uniform probability distribut...
1,108,101,564,517
arxiv
\section{Introduction} Underwater object detection is a branch of object detection research. Underwater is rich in mineral and biological resources, waiting for human to explore at the same time, there are many unknown dangers. In order to explore more safely and comprehensively, the research of underwater object dete...
1,108,101,564,518
arxiv
\section{INTRODUCTION} \subsection{Motivation and literature overview} Noncooperative generalized games over networks is currently a very active research field, due to the spreading of multi-agent network systems in modern society. Such type of games emerge in several application domains, such as smart grids \cite{dor...
1,108,101,564,519
arxiv
\section{Introduction} MixUp is a data augmentation technique originated from computer vision, where convex interpolations of input images and their corresponding labels are used as additional training source. It has empirically been shown to improve the performance of image classifiers, and leads to decision boundarie...
1,108,101,564,520
arxiv
\section*{References}} \newtheorem{theorem}{Theorem}[section] \theoremstyle{definition} \newtheorem{problem}[theorem]{Problem} \newtheorem{definition}[theorem]{Definition} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{algorithm}[theorem]{Algorithm} \newtheorem{lemma}[theorem]{Lemma} \newtheorem{corollary...
1,108,101,564,521
arxiv
\section{Introduction} \label{intro} Many scientific domains use statistical models with constraints on parameters which often results in difficult estimation and inference problems. For example, in genetics, simplex constraints are used to account for compositional data \citep{wang2019bulk,lu2019generalized}. In risk ...
1,108,101,564,522
arxiv
\section{}\label{s1} \section{Introduction} \label{sec:introduction} \subsection{Background} At its core, Neuro-Symbolic AI (NeSy) is ``the combination of deep learning and symbolic reasoning" \cite{Garcez_Lamb_2020}. The goal of NeSy is to address the weaknesses of each of symbolic and sub-symbolic approa...
1,108,101,564,523
arxiv
\section{Introduction} \label{sec:introduction} Dictionary Learning is an important and widely used tool in Signal Processing and Computer Vision. Its versatility is well acknowledged and it can be applied for denoising or for representation learning prior to classification \cite{aharon2006rm,Mairal:2009-online-dl}...
1,108,101,564,524
arxiv
\section{Introduction} The seminal work of Onsager of 1944 on the exact solution of the planar Ising Model \cite{Ons} has been a source of a considerable part of the subsequent developments in the field of exactly solvable models in Statistical Mechanics and Field Theory. One branch of these developments which origin...
1,108,101,564,525
arxiv
\section{Introduction} Accreting black hole X-ray binaries (BHXBs) typically stay in one of the two distinct spectral states \citep{tanaka95}. In the so-called high/soft state, such a binary has a soft X-ray spectrum and a relatively high X-ray luminosity, which is believed to be dominated by the emission directly ...
1,108,101,564,526
arxiv
\section{Introduction} In group theory, a Zappa-Sz\'{e}p product of two groups $G$ and $H$ generalizes a semi-direct product by encoding a two-way action between $G$ and $H$. In addition to a left action of $G$ on $H$, the Zappa-Sz\'{e}p product encodes an additional right action of $H$ on $G$. An analogue of semi-...
1,108,101,564,527
arxiv
\section{Introduction} The total cross section $\sigma_{tot}(s)$ is a fundamental quantity in collisions of strongly interacting particles. At present one of the main theoretical approaches for the description of $\sigma_{tot}$ is the QCD-inspired formalism \cite{durand,luna001,luna009,giulia001}. In this approach ...
1,108,101,564,528
arxiv
\section{Introduction} Stimulated by the applications to the quadratic regulator problem, controllability for distributed parameter systems is usually studied with square integrable controls. Such general controls are hardly realizable in practice and only smooth or piecewise smooth controls, like bang-bang contr...
1,108,101,564,529
arxiv
\section{Introduction} The Large Magellanic Cloud (LMC) has long been recognized as a fundamental benchmark for a wide variety of astrophysical studies. As the closest bulge-less dwarf disk galaxy \citep{b12}, it has turned out to be the ideal local analog for the detailed study of these most common and primeval galax...
1,108,101,564,530
arxiv
\section{Introduction} \label{sec:Introduction} The IR luminescence of bismuth centers discovered in \mbox{\SiOiiAl:Bi} glasses \cite{Fujimoto99, Fujimoto01} has been observed in various glasses and crystals. Despite active studies of the bismuth-related IR luminescence (the present state of the art is reviewed in \cit...
1,108,101,564,531
arxiv
\section*{Supplemental Material} We provide details of the security calculations, the optimization of parameters and all the steps of the covert communication protocol. We also include the complete data obtained for the message transmission. \textit{Calculation of signal and noise states.---} The security of the proto...
1,108,101,564,532
arxiv
\section{Introduction} \label{sec: Introduction} One aspect of the AdS/CFT correspondence that caught significant attention recently is its relation to quantum information (QI). The most prominent discovery in this field is the seminal Ryu-Takayanagi (RT) formula \cite{2006PhRvL..96r1602R}, \begin{equation} \label{eq:...
1,108,101,564,533
arxiv
\section{Introduction} Complex networks is a new emerging branch of random graph theory. For a long time random graphs have been mainly studied by pure mathematics but recently due to the availability of empirical data on real-world networks they have attracted the attention of physics and natural sciences (see for r...
1,108,101,564,534
arxiv
\subsection{Locally Computed Gradient} Consider the link $l\sim (i,j)$, since $w_l=w_{ij}=w_{ji}$ and $w_{ii}=1-\sum_{s\in N_i}w_{is}$, we have: \begin{equation}\label{diff} \frac{\text{d}w_{st}}{\text{d}w_l}= \begin{cases} +1 &\text{if } s=i \text{ and } t=j\\ +1 &\text{if } s=j \text{ and } t=i\\ -1 &\text{if } s=i ...
1,108,101,564,535
arxiv
\section{Introduction} The second part of Hilbert's sixteenth problem asks for a study of the number and relative positions of the limit cycles of a planar polynomial system of ordinary differential equations. The problem was included in Smale's list of problems for the next century \cite{Smale1998}, where he stated t...
1,108,101,564,536
arxiv
\section*{Introduction} We start by explaining how subfactor theory, conformal field theory, and the groups of Richard Thompson got connected. Second, we outline a general program: what do we wish and what are our motivations and aims. Third, we explain our general formalism based on the manipulation of diagrams and ex...
1,108,101,564,537
arxiv
\chapter[Lecture \##1]{}} \newcommand{\mathrm{Enc}}{\mathrm{Enc}} \newcommand{\mathrm{Dec}}{\mathrm{Dec}} \newcommand{\mathrm{Var}}{\mathrm{Var}} \newcommand{\mathbb{Z}}{\mathbb{Z}} \newcommand{\mathbb{F}}{\mathbb{F}} \newcommand{\mathbb{N}}{\mathbb{N}} \newcommand{{\mathbb Z}^{\geq 0}}{{\mathbb Z}^{\geq 0}} \newcomm...
1,108,101,564,538
arxiv
\section*{Introduction} The large deviation principle (LDP) for Brownian motion $\beta$ on $[0,1]$ - contained in Schilder's theorem (\cite{Schilder}) - describes the exponential decay of the probabilities with which $\sqrt{\varepsilon} \beta$ takes values in closed or open subsets of the path space of continuous func...
1,108,101,564,539
arxiv
\section{Introduction} \label{sec:intro} Anomaly detection is the task of identifying anomalous observations~\cite{ivanovska2020,wang2018,prado2016,feng2010,reif2008}. In this paper, we focus on anomaly detection applied to machine health monitoring via audio signal. Detecting anomalies is useful for identifying incip...
1,108,101,564,540
arxiv
\section{Introduction} \label{Section: Introduction} \IEEEPARstart{T}{he} evolution of multiple chronic conditions (MCC) follows a complex stochastic process. This path of evolution is often influenced by several factors, including inter-relationship of existing conditions, patient-level modifiable and non-modifiable r...
1,108,101,564,541
arxiv
\section{Abstract} The reconstruction of transmission trees for epidemics from genetic data has been the subject of some recent interest. It has been demonstrated that the transmission tree structure can be investigated by augmenting internal nodes of a phylogenetic tree constructed using pathogen sequences from the e...
1,108,101,564,542
arxiv
\section{Conclusion} \label{sec:con} RecSys-DAN is a novel framework for cross-domain collaborative filtering, particularly, the real-world cold-start recommendation problem. It learns to adapt the user, item and user-item interaction representations from a source domain to a target domain in an unsupervised and adver...
1,108,101,564,543
arxiv
\section{Introduction} The observed thermal states of isolated neutron stars have become the primary source to glean useful and interesting information about the internal structure of neutron stars (NSs). Reconciliation of theoretical cooling curves with observations of nearby isolated cooling NSs is a challenging t...
1,108,101,564,544
arxiv
\section{Introduction} This work aims to solve the following linearly constrained separable convex problem with $n$ blocks of variables \begin{equation} \begin{split} \min\limits_{\mathbf{x}_1,\cdots,\mathbf{x}_n} & \ f(\mathbf{x})=\sum\limits_{i=1}^nf_i(\mathbf{x}_i)=\sum_{i=1}^n\left( g_i(\mathbf{x}_i)+h_i(\mathbf{...
1,108,101,564,545
arxiv
\section{Introduction} \noindent In recent times the study of the spiral structure of the outer Galactic disk has witnessed a renewed interest (see e.g. Levine et al. 2006, V\'azquez et al. 2008, Benjamin 2008), in part due to the claimed discovery of structures in the form of star over-densities which would be produ...
1,108,101,564,546
arxiv
\section{Completely Sidon sets} Let $U_n$ be the unitary generators in $C^*(\bb F_\infty)$.\\ Let $A$ be a $C^*$-algebra. Let $(\psi_n)$ be a bounded sequence in $A$. \begin{dfn} We say that $(\psi_n)$ is completely Sidon if there is $C$ such that for any matricial coefficients $(a_n)$ $$\|\sum a_n \otimes U_n...
1,108,101,564,547
arxiv
\section{Introduction}\label{section_introduction} The valuation and risk management of derivative portfolios form a challenging task in banks, insurance companies, and other financial institutions. The issues are formally explained as follows. Most economic scenario generators can be represented as stochastic models w...
1,108,101,564,548
arxiv
\section{Introduction} In scheduling environments, uncertainty is a common consideration for optimization problems. Commonly, results are either based on worst case considerations or a random distribution over the input. These approaches are known as robust optimization and stochastic optimization, respectively. Howev...
1,108,101,564,549
arxiv
\section{Introduction} Gravitational-wave~(GW) echoes in the post-merger GW signal from a binary coalescence might be a generic feature of quantum corrections at the horizon scale~\cite{Cardoso:2016rao,Cardoso:2016oxy}, and might provide a smoking-gun signature of exotic compact objects~(ECOs) and of exotic states of...
1,108,101,564,550
arxiv
\section{Introduction} One challenge in survey cosmology is to infer the true dark matter density field from observables, i.e. galaxies and galaxy clusters from galaxy surveys in the UV, visible, NIR, or radio, or galaxy clusters detected in X-ray or Sunyaev-Zeldovich (SZ) \citep{Sunyaev72} surveys. All these obser...
1,108,101,564,551
arxiv
\section{Introduction} \label{sec:Intro} Accretion disks in black hole X-ray binaries (BHXRBs) and active galactic nuclei (AGN) are typically described by axisymmetric, time-independent models. A key factor that determines the most suitable model is the accretion rate with respect to the Eddington limit. At the Edding...
1,108,101,564,552
arxiv
\section{INTRODUCTION}\label{sec:intro} Mixed-morphology supernova remnants (SNRs) are characterized a center-filled thermal X-ray morphology with a synchrotron radio shell, accounting for more than 25\% of Galactic SNRs \citep{1998ApJ...503L.167R}. Most of the mixed-morphology SNRs are interacting with the dense inter...
1,108,101,564,553
arxiv
\section{Introduction} Clusters of galaxies are attracting considerable attention for their cosmological applications. A conceptually simple observation, such as the number of clusters per unit volume, is able to put strong constraints on the cosmological parameters (or their combinations), for example on the equation...
1,108,101,564,554
arxiv
\section{Introduction} \label{sec:intro} Chaotic dynamical systems are characterized by the existence of a \textit{predictability horizon} in time, beyond which the information on the state available from the initial conditions is not enough for meaningful predictions. Thus it appears a difficult task to perform an o...
1,108,101,564,555
arxiv
\section{Introduction}\label{Section1} In Bayesian statistics, it is a common problem to collect and compute random samples from a probability distribution. Markov Chain Monte Carlo (MCMC) is an intensive technique commonly used to address this problem when direct sampling is often arduous or impossible. MCMC using Ba...
1,108,101,564,556
arxiv
\section{Introduction} The Calogero model and its various generalizations is one of the most studied integrable systems in physics and mathematics \cite{Calogero-1969,Sutherland-1971,Moser}. In its most basic form it describes $N$ identical non-relativistic particles in one dimension interacting through two-body inver...
1,108,101,564,557
arxiv
\section{Introduction} Quantum discrimination of two optical quantum states plays a crucial rule in quantum information processing tasks, e.g., continuous-variable quantum key distributions and optical quantum communications \cite{silberhorn2002continuous,grosshans2003quantum,ghorai2019asymptotic,yuan2020free}. Due ...
1,108,101,564,558
arxiv
\section{Conclusion} \label{sec:conclude} We believe that the quantum computing field can learn from classical computing design techniques. The PRK are a powerful design tool, and we posit that there is a need for a similar approach for hardware/software co-design for quantum computing. We have introduced the concep...
1,108,101,564,559
arxiv
\section{Introduction} The inflationary paradigm \cite{inflation} provides a simple framework to generate primordial nearly scale-invariant perturbations with a slightly red tilt, as well as small non-gaussianties which are in good agreement with observations \cite{Planck1,Planck3,Planck4}. Despite its successes, the ...
1,108,101,564,560
arxiv
\section{Introduction} Relation extraction (RE) is a task of identifying typed relations between known entity mentions in a sentence. Most existing RE models treat each relation in a sentence individually~\cite{miwa2016end,nguyen2015perspective}. However, a sentence typically contains multiple relations ...
1,108,101,564,561
arxiv
\section{Introduction} In this paper we investigate further the deformed T-dual (DTD) supercoset sigma models introduced in \cite{Borsato:2016pas}, and we find results that are of interest also when considering the undeformed case, i.e. when applying just non-abelian T-duality (NATD). The construction of DTD models i...
1,108,101,564,562
arxiv
\section{Introduction} A classical-quantum channel $W:\,{\mathcal X}\to{\mathcal S}({\mathcal H})$ models a device with a set of possible inputs ${\mathcal X}$, which, on an input $x\in{\mathcal X}$, outputs a quantum system with finite-dimensional Hilbert space ${\mathcal H}$ in state $W(x)$. For every such channel...
1,108,101,564,563
arxiv
\section*{Introduction} The beautiful theory of cluster tilting in triangulated categories has been developed by Iyama and Yoshino; as an important outcome of this the authors gave in \cite[Theorem 1.2 and Theorem 1.3]{iyama-yoshino} the classification of rigid indecomposable MCM modules over two Veronese embeddings i...
1,108,101,564,564
arxiv
\section{INTRODUCTION} Clusters of galaxies are the most massive gravitationally bound objects in the Universe. They include hundreds of galaxies within a radius of 1--2 Mpc (e.g., Abell 1958). Dispersions of the member galaxy redshifts indicate that the gravitational potential of the cluster is much deeper than can ...
1,108,101,564,565
arxiv
\section{Introduction}\label{sec:intro} The white-light continuum of a solar flare (WLF) was the first manifestation of a flare ever detected \citep{1859MNRAs..20...13C,1859MNRAs..20...16H}. Nevertheless its origin has remained enigmatic over the intervening centuries. This continuum contains a large fraction of the to...
1,108,101,564,566
arxiv
\section{Introduction} Supersymmetry~(SUSY)~\cite{haberkane,Nilles:1983ge} is one of the best motivated candidates for physics beyond the Standard Model~(SM). Besides providing a unification of the strong and electroweak gauge couplings and a suitable cold dark matter candidate, the lightest stable SUSY part...
1,108,101,564,567
arxiv
\section{Introduction}\label{introduction} Recently, the interest in studying new alternative theories of gravity has been increasing see, for instance, \cite{alternative}. In spite of its efficiency, the unmodified general theory of relativity is not able to answer some fundamental questions. Some of the most impor...
1,108,101,564,568
arxiv
\section{\@startsection {section}{1}{\z@}% {-3.5ex \@plus -1ex \@minus -.2ex}% {1.3ex \@plus.2ex}% {\center\small\sc\mathversion{bold}\MakeUppercase}} \def\subsection#1{\@startsection {subsection}{2}{0pt}% {-3.5ex \@plus -1ex \@minus -.2ex}% {1ex \@plus.2ex}% {\bf\mathversion{bold}}{#1}} \def\subsubsection#1{\@starts...
1,108,101,564,569
arxiv
\section{Motivations} Without doubts the construction of a quantum theory of gravity is the single most pressing challenge the contemporary high energy physics community is facing. We still do not know exactly what this theory is; however we can investigate some particular limits of it and build toy models, whose pre...
1,108,101,564,570
arxiv
\section{Introduction} \label{sec:intro} Let $\Omega = \{\omega_J : \, J \subseteq [n]\}$ be the sample space freely generated by $n$ random events $A_1, \dots, A_n$, so that $\{\omega_J\} = \bigcap_{j \in J} A_j \cap \bigcap_{j \notin J} \overline{A}_j =: \A^J$ for all subsets $J \subseteq [n]$. Here, as usual, fo...
1,108,101,564,571
arxiv
\section{Introduction} \label{sec:intro} \begin{figure*} \begin{center} \begin{tabular}{cc} \includegraphics[clip,width=0.4\textwidth]{fig01a.pdf} \hspace{1.0cm} & \includegraphics[clip,width=0.4\textwidth]{fig01b.pdf}\tabularnewline \end{tabular} \end{center} \caption{Examples of the magnetos...
1,108,101,564,572
arxiv
\section{Introduction} Prototype learning is a type of supervised learning, where class labels are represented by `prototypes', that is, by points in a suitably chosen output space. Instead of minimizing a general loss function, the learning model is trained by minimizing the distance of its output to the prototype of...
1,108,101,564,573
arxiv
\section{\textcolor{black}{Introduction\medskip{} }} \end{singlespace} \begin{singlespace} \textcolor{black}{} \begin{figure} \begin{centering} \textcolor{black}{\includegraphics[scale=0.85]{NI_Figure1}} \par\end{centering} \textcolor{black}{\medskip{} } \begin{spacing}{0.5} \raggedright{}\textbf{\textcolor{black}{\...
1,108,101,564,574
arxiv
\section{Introduction} In the $\Lambda$CDM paradigm, structure in the Universe arises from the initial density perturbations of an (almost) homogeneous dark matter distribution. Due to gravitational evolution, this leads to the appearance of collapsed structures, i.e. dark matter haloes. Some of the baryonic matter, ...
1,108,101,564,575
arxiv
\section{Introduction} Plate tectonic theory provides a kinematic framework for describing crustal motion at the Earth's surface. Rates of motion for the largest tectonic plates have been inferred independently over million-year time-scales from geologic observations \citep{demets1990current} and decadal time-scales fr...
1,108,101,564,576
arxiv
\section{Introduction} Three-dimensional General Relativity is one of the simplest gravitational systems \cite{Deser:1983tn,Deser:1983nh} and, in particular, solutions with negative cosmological constant (AdS${}_3$) have received special attention, due to their holographic nature \cite{Brown:1986nw, Witten:1998qj}. Th...
1,108,101,564,577
arxiv
\section{Introduction} \label{introduction} Observation of the microwave sky reveals that the temperature of the cosmic microwave background (CMB) radiation is not exactly the same in all directions. These small fluctuations in the temperature are imprinted on the entire sky, implying that the CMB is anisotropic. These...
1,108,101,564,578
arxiv
\section{Introduction} Central to the theory of quantum integrable systems is quantum $R$-matrix satisfying the celebrated Yang-Baxter equation. General $R$-matrices with additive spectral parameter are parametrized via elliptic functions. The simplest elliptic $R$-matrix is \begin{equation} \label{02} R(\lambda )=\su...
1,108,101,564,579
arxiv
\section{Introduction} Redundant robots---which have more \gls{DoF} than required for a task---have been widely studied and deployed due to their intrinsic flexibility. The higher dimensionality of the joint configuration space \gls{wrt} the task space makes these systems more adaptable as multiple solutions...
1,108,101,564,580
arxiv
\section{\bf Statement of the problem with motivation} Extreme value laws are limit laws of linearly normalized partial maxima $M_n=$ \\ $\max\{X_1, \ldots, X_n\}$ of independent and identically distributed (iid) random variables (rvs) $X_1,X_2,\ldots,$ with common distribution function (df) $F,$ namely, \begin{equatio...
1,108,101,564,581
arxiv
\section{Introduction} In general, the performance of a device is intimately connected through fundamental physical laws to the properties of the materials or the sub-elements employed in its realization, and these connections may have far reaching implications to whole branches of engineering. For instance, the energy...
1,108,101,564,582
arxiv
\section{Introduction} \begin{comment} Recommender systems help users mitigate the information overload problem by suggesting relevant items. To generate personalized recommendations they apply machine learning algorithms, regretfully making them vulnerable to attacks that can be carried out by injecting malicious inpu...
1,108,101,564,583
arxiv
\section{Introduction} Our goal in this paper is to prove the following two main results. For a graph $G$, we write $\Delta(G)$, $\omega(G)$, and $\chi(G)$ to denote the maximum degree, clique number, and chromatic number of $G$. When the context is clear, we simply write $\Delta$, $\omega$, and $\chi$. \begin{thm} \...
1,108,101,564,584
arxiv
\section{Transfer functions in {\fontfamily{pcr}\fontshape{tt}\selectfont KBHtablesNN.fits}} \label{appendix3a} The transfer functions are stored in the file {\tt KBHtablesNN.fits} as binary extensions and parametrized by the value of the observer inclination angle $\theta_{\rm o}$ and the horizon of the black hole ...
1,108,101,564,585
arxiv
\section{Introduction} Inspired by Michael Berry and Jonathan Robbins's approach in \cite{BR1997} to understand the spin-statistics theorem quantum mechanically (and, essentially, geometrically!), Michael Atiyah proposed in a series of related papers in 2000-2001 (\cite{Ati-2000}, \cite{Ati-2001}) a geometric construc...
1,108,101,564,586
arxiv
\section{Introduction}\label{sec:introduction} A Disc Jockey (DJ) is a musician who plays a sequence of existing music tracks or sound sources seamlessly by manipulating the audio content based on musical elements. The outcomes can be medleys (mix), mash-ups, remixes, or even new tracks, depending on how much DJs edit ...
1,108,101,564,587
arxiv
\section*{#1}} \usepackage{graphicx \usepackage{dcolumn \usepackage{bm \usepackage{amstext} \usepackage{amssymb} \usepackage{amsmath} \usepackage{graphicx} \usepackage{color} \usepackage{bbold} \usepackage{delimset} \usepackage[caption=false,justification=justified]{subfig} \usepackage[colorlinks=true]{hyperr...
1,108,101,564,588
arxiv
\section{Introduction} The starting point of this paper is a recent solution of the IKKT-type matrix models with mass term \cite{Sperling:2019xar}, which is naturally interpreted as 3+1-dimensional cosmological FLRW quantum space-time. It was shown that the fluctuation modes around this background include spin-2 ...
1,108,101,564,589
arxiv
\section{Higgs Gluon Fusion \texorpdfstring{$\mu = m_{H}$}{Higgs mass scale} Results} \begin{table}[H] \centerline{ \begin{tabular}{c|ccc} \hline $\sigma$ order & PDF order & $\sigma + \Delta \sigma_{+} - \Delta \sigma_{-}$ (pb) & $\sigma$ (pb) $+\ \Delta \sigma_{+} - \Delta \sigma_{-}$ (\%) \\ \hline \multicolumn{4}{...
1,108,101,564,590
arxiv
\section{Introduction} The Gross-Pitaevskii equation for a Bose-Einstein condensate (BEC) with symmetric harmonic trap is given by \begin{equation} -iu_{t}-\Delta u+(x^{2}+y^{2})u+\left\vert u\right\vert ^{2}u=0. \label{Ec \end{equation} Periodic solutions of \eqref{Ec} play an important role in the understa...
1,108,101,564,591
arxiv
\section{Introduction and main results} This paper concerns the asymptotic behavior of analytic functions $f$ whose order of growth $\sigma_M(f)$ and the lower order $\lambda_M(f)$, defined via the maximum modulus function $M(r,f)=\max\{ |f(z)|:|z|=r \}$, are distinct. In particular, we search for asymptotic lower e...
1,108,101,564,592
arxiv
\section{The Argument So Far} In Parts I[1] and II[2], the basic facts concerning zero-divisors (ZDs) as they arise in the hypercomplex context were presented and proved. ``Basic,'' in the context of this monograph, means seven things. First, they emerged as a side-effect of applying CDP a minimum of 4 times to the Rea...
1,108,101,564,593
arxiv
\section{introduction For $m \ge 3$, the {\it $m$-gonal number} is described as the total number of dots to constitute a regular $m$-gon. One may easily induce a formula \begin{equation} \label{m number} P_m(x)=\frac{m-2}{2}x^2-\frac{m-4}{2}x \end{equation} for the total number of dots to constitute a regular $m$-...
1,108,101,564,594
arxiv
\section{Introduction} \IEEEPARstart{B}{iometrics} offers a secure and convenient way for access control. Face biometrics is one of the most convenient modalities for biometric authentication due to its non-intrusive nature. Even though face recognition systems are reaching human performance in identifying persons in...
1,108,101,564,595
arxiv
\section{Introduction} The weak mixing angle is defined as a ratio of the gauge couplings \begin{equation} \hat{s}^2(Q) = \frac{\hat{g}^{\prime 2}(Q)}{\hat{g}^2(Q)+\hat{g}^{\prime 2}(Q)} \;, \label{eq:1} \end{equation} where $\hat{g}$ and $\hat{g}^\prime$ are the $SU(2)$ and $U(1)_Y$ gauge couplings respectively. Th...
1,108,101,564,596
arxiv
\section{Introduction} Poor eating habits have been linked to an increased risk of cardiovascular disease, cancer, obesity, diabetes, cataracts, and possibly dementia \cite{Rosenberg09}. As such, there is growing interest in recording the food intake of at-risk individuals and exploring diet interventions to prevent l...
1,108,101,564,597
arxiv
\section{Introduction} A morphism $\varphi : H \rightarrow G$ between two groups $H$ and $G$ is said to be \emph{elementary} if the following condition holds: for every first-order formula $\theta(x_1,\ldots,x_k)$ with $k$ free variables in the language of groups, and for every $k$-tuple $(h_1,\ldots,h_k)\in H^k$, t...
1,108,101,564,598
arxiv
\section{Introduction} \IEEEPARstart{I}{n} cities, parking lots are costly in terms of space, construction and maintenance costs. Parking lots take up 6.57\% of urban land use \cite{davis2010environmental} and collectively make up nearly 7000 $\text{km}^2$ of land use in the United States \cite{jakle200...
1,108,101,564,599
arxiv
1,108,101,564,600
arxiv
\section{#1}\setcounter{equation}{0}} \def\thesection.\arabic{equation}{\thesection.\arabic{equation}} \newcommand{\OL}[1]{ \hspace{.5pt}\overline{\hspace{-.5pt}#1 \hspace{-.5pt}}\hspace{.5pt} } \textwidth = 6.5 in \textheight = 9 in \oddsidemargin = 0.0 in \evensidemargin = 0.0 in \headheight = 0.0 in \headsep ...
1,108,101,564,601
arxiv
\section{Introduction} In the standard model of particle physics \cite{SM} there are open questions which have not yet found an answer. Chief among these is the fermion family or generation puzzle as to why the first generation of quarks and leptons (up quark, down quark, electron and electron neutrino) are replicate...
1,108,101,564,602
arxiv
\section{Introduction} With an exponential population growth rate, it has become critical to produce sufficient food to meet global needs. However, food production is a complex process involving many issues such as climate change, soil pollution, plant diseases, etc. Plant diseases are not only a significant threat to...
1,108,101,564,603
arxiv
\section{Introduction} \allowdisplaybreaks Dynamic autocatalysis mechanisms are inherent to several real-world dynamical networks including most of the planet's cells from bacteria to human, engineered networks as well as economic systems \cite{chandra11, Autocatalytic, buzi11, buzi2010control}. In an interconnected c...
1,108,101,564,604
arxiv
\section{Introduction} There are two significances in General Relativity (GR) which cause it not to be a fundamental theory of gravity and needs to be modified or extended. The idea of short range or Ultra Violet (UV) modification of GR, which arises from the non-renormalizability of the theory \cite{Stelle:1976gc}, an...
1,108,101,564,605
arxiv
\section{An example on $\mathbb P^4$} \section*{Acknowledgments} We thank Robert Lazarsfeld for raising the question and for useful discussions.
1,108,101,564,606
arxiv
\section{Introduction} The discovery of cosmic acceleration \citep{Riess1998,Perlmutter1999} is a phenomenon in search of a theoretical explanation. On one hand, the acceleration can be explained by introducing dark energy which provides negative pressure \citep{Peebles2002}. On the other hand, on cosmological scales,...
1,108,101,564,607
arxiv
\section{Introduction} The spectral theory of self-adjoint and unitary operators is a well established topic in mathematics with a rich structure revealed by numerous important results, and which has found many applications, particularly in mathematical physics. See for example the textbooks \cite{Ka, RS, DS, D4, Ku} ...
1,108,101,564,608
arxiv
\section{Introduction} In recent years, the advent of new millimeter (mm) and submillimeter (submm) facilities, such as the Atacama Large Millimeter/submillimeter Array (ALMA), with unprecedented sensitivity and frequency coverage, has improved the detectability of cool gas in high-redshift star-forming galaxies \cite...
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arxiv
\section{Introduction}
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arxiv
\section{Introduction} \setcounter{equation}{0} We have seen how string/M theory can be exploited to study non-perturbative dynamics of low energy supersymmetric gauge theories in various dimensions. One of the main motivations is to understand the D brane dynamics where the gauge theory is realized on the worldvo...
1,108,101,564,611
arxiv
\section{Introduction} Class IV-VI narrow-gap compound semiconductors have been of great interest for many decades not only for their scientific interest but also for their use in novel technological instrumentation such as infrared optoelectronics and thermoelectric devices.\cite{Nimtz} Crystalizing in the rock salt ...
1,108,101,564,612
arxiv
\section{Introduction}\label{intro} The variational quantum circuit (VQC, also known as parameterised quantum circuit, PQC) approach, first proposed for solving the ground state energy of molecules \cite{peruzzo2014variational}, have been extended to many open research problems including in the field of quantum machin...
1,108,101,564,613
arxiv
\section{Introduction} \label{intro} For massive, hot stars of spectral types OBA, scattering and absorption in spectral lines transfer momentum from the star's intense radiation field to the plasma, and so provide the force necessary to overcome gravity and drive a strong stellar wind outflow \citep[see][for an exte...
1,108,101,564,614
arxiv
\section{Introduction} \label{intro} Semi-inclusive hadron-production processes are important for investigating properties of quark-hadron matters in heavy-ion collisions and for finding the origin of the nucleon spin in lepton-nucleon scattering and polarized proton-proton collisions. Fragmentation functions (FFs) ...