ShantanuT01/DACTYL-Pretraining huggingface dataset:
Using recent work of the first author~\cite{Bet}, we prove a strong version of the Manin-Peyre's conjectures with a full asymptotic and a power-saving error term for the two varieties respectively in $\mathbb{P}^2 \times \mathbb{P}^2$ with bihomogeneous coordinates $[x_1:x_2:x_3],[y_1:y_2,y_3]$ and in $\mathbb{P}^1\times \mathbb{P}^1 \times \mathbb{P}^1$ with multihomogeneous coordinates $[x_1:y_1],[x_2:y_2],[x_3:y_3]$ defined by the same equation $x_1y_2y_3+x_2y_1y_3+x_3y_1y_2=0$. We thus improve on recent work of Blomer, Br\"udern and Salberger \cite{BBS} and provide a different proof based on a descent on the universal torsor of the conjectures in the case of a del Pezzo surface of degree 6 with singularity type $\mathbf{A}_1$ and three lines (the other existing proof relying on harmonic analysis \cite{CLT}). Together with~\cite{Blomer2014} or with recent work of the second author \cite{Dest2}, this settles the study of the Manin-Peyre's conjectures for this equation.
There has been recent progress in the study of the angular momentum evolution of low mass stars (Krishnamurthi et al 1997a). Theoretical models can now be constructed which reproduce the angular momentum evolution of low mass open cluster stars and the distribution of initial conditions can be inferred from young clusters. In this poster we report on the application of these models to the problem of rotational mixing in halo stars. The distribution of initial conditions inferred from young clusters produces a well-defined halo lithium "plateau" with modest scatter and a small population of outliers. Different choices for the solar calibration produce a range of absolute depletion factors. We show that both the dispersion and the ratio of $^6$Li depletion to $^7$Li depletion increase as the absolute $^7$Li depletion increases. The measured $^6$Li in HD 84937 and the dispersion in the plateau set independent upper bounds on the $^7$Li depletion. Consistency with open clusters and the Sun, along with claims of an intrinsic dispersion in the plateau, set a lower bound. We derive a range of 0.2-0.4 dex $^7$Li depletion in halo field stars. Implications for cosmology are discussed.
We report on the spectral analysis of the peculiar source Cir X-1 observed by the BeppoSAX satellite when the X-ray source was near the periastron. A flare lasting $\sim 6 \times 10^3$ s is present at the beginning of the observation. The luminosity during the persistent emission is $1 \times 10^{38}$ erg s$^{-1}$, while during the flare is $2 \times 10^{38}$ erg s$^{-1}$. We produced broad band (0.1-100 keV) energy spectra during the flare and the persistent emission. At low energies the continuum is well fitted by a model consisting of Comptonization of soft photons, with a temperature of $\sim 0.4$ keV, by electrons at a temperature of $\sim 1$ keV. Out of the flare a power-law component, with photon index $\sim 3$, is dominant at energies higher than 10 keV. This component contributes to $\sim 4%$ of the total luminosity. During the flare its addition is not statistically significant. An absorption edge at $\sim 8.4$ keV, with optical depth $\sim 1$, corresponding to the K-edge of Fe XXIII-XXV, and an iron emission line at 6.7 keV are also present. The iron line energy is in agreement with the ionization level of the absorption edge. The hydrogen column deduced from the absorption edge is $\sim 10^{24}$ cm$^{-2}$, two order of magnitude larger than the absorption measured in this source. We calculated the radius of the region originating the comptonized seed photons, $R_W \sim 150$ km.   We propose a scenario where $R_W$ is the inner disk radius, a highly ionized torus surrounds the accretion disk and a magnetosphere is large up to $R_W$. The absorption edge and the emission line could originate in the photoionized torus, while the comptonized component originates in an inner region of the disk.
We review a surprising correspondence between certain two-dimensional integrable models and the spectral theory of ordinary differential equations. Particular emphasis is given to the relevance of this correspondence to certain problems in PT-symmetric quantum mechanics.
We present the average metallicity and star-formation rate of Lya emitters (LAEs) measured from our large-area survey with three narrow-band (NB) filters covering the Lya, [OII]3727, and Ha+[NII] lines of LAEs at z=2.2. We select 919 z=2.2 LAEs from Subaru/Suprime-Cam NB data in conjunction with Magellan/IMACS spectroscopy. Of these LAEs, 561 and 105 are observed with KPNO/NEWFIRM near-infrared NB filters whose central wavelengths are matched to redshifted [OII] and Ha nebular lines, respectively. By stacking the near-infrared images of the LAEs, we successfully obtain average nebular-line fluxes of LAEs, the majority of which are too faint to be identified individually by narrow-band imaging or deep spectroscopy. The stacked object has an Ha luminosity of 1.7x10^{42} erg s^{-1} corresponding to a star formation rate (SFR) of 14 M_{sun} yr^{-1}. We place, for the first time, a firm lower limit to the average metallicity of LAEs of Z>~0.09 Z_{sun} (2sigma) based on the [OII]/(Ha+[NII]) index together with photo-ionization models and empirical relations. This lower limit of metallicity rules out the hypothesis that LAEs, so far observed at z~2, are extremely metal poor (Z<2x10^{-2} Z_{sun}) young galaxies at the 4sigma level. This limit is higher than a simple extrapolation of the observed mass-metallicity relation of z~2 UV-selected galaxies toward lower masses (5x10^{8} M_{sun}), but roughly consistent with a recently proposed fundamental mass-metallicity relation when the LAEs' relatively low SFR is taken into account. The Ha and Lya luminosities of our NB-selected LAEs indicate that the escape fraction of Lya photons is ~12-30 %, much higher than the values derived for other galaxy populations at z~2.
We study the temporal approach to equilibrium of the Gibbs' and conditional entropies for both invertible deterministic dynamics as well as non-invertible stochastic systems in the presence of white noise. The conditional entropy will either remain constant or monotonically increase to its maximum of zero. However, the Gibbs' entropy may have a variety of patterns of approach to its final value ranging from a monotone increase or decrease to an oscillatory approach. We have illustrated all of these behaviors using examples in which both entropy dynamics can be determined analytically.
We describe a method for understanding averages over newforms on $\Gamma_0(q)$ in terms of averages over all forms of some level. The method is simplest when $q$ is divisible by the cubes of its prime divisors.
The three dimensional carrier confinement in GaN nanodiscs embedded in GaN/AlGaN nanowires and its effect on their photoluminescence properties is analyzed for Al concentrations between x = 0.08 and 1. Structural analysis by high resolution transmission electron microscopy reveals the presence of a lateral AlGaN shell due to a composition dependent lateral growth rate of the barrier material. The structural properties are used as input parameters for three dimensional numerical simulations of the confinement which show that the presence of the AlGaN shell has to be considered to explain the observed dependence of the emission energy on the Al concentration in the barrier. The simulations reveal that the maximum in the emission energy for x ~ 30% is assigned to the smallest lateral strain gradient and consequently the lowest radial internal electric fields in the nanodiscs. Higher Al-concentrations in the barrier cause high radial electric fields that can overcome the exciton binding energy and result in substantially reduced emission intensities. Effects of polarization-induced axial internal electric fields on the photoluminescence characteristics have been investigated using nanowire samples with nanodisc heights ranging between 1.2 nm and 3.5 nm at different Al concentrations. The influence of the quantum confined Stark effect is significantly reduced compared to GaN/AlGaN quantum well structures which is attributed to the formation of misfit dislocations at the heterointerfaces which weakens the internal electric polarization fields.
Two inequalities involving the Euler totient function and the sum of the $k$-th powers of the divisors of balancing numbers are explored.
We present the results from the 1.2 mm continuum image obtained as part of the ALMA Spectroscopic Survey in the Hubble Ultra Deep Field (ASPECS). The 1.2 mm continuum image has a size of 2.9 (4.2) arcmin$^2$ within a primary beam response of 50% (10%) and a rms value of $9.3\thinspace{\rm\mu Jy\thinspace beam^{-1}}$. We detect 35 sources at high significance (Fidelity $\geq0.5$), 32 of these have well characterized near-infrared HST counterparts.   We estimate the 1.2 mm number counts to flux levels of $<30\thinspace{\rm\mu Jy}$ in two different ways: we first use the detected sources to constrain the number counts and find a significant flattening of the counts below $S_\nu \sim 0.1$ mJy. In a second approach, we constrain the number counts by using a probability of deflection statistics (P(D)) analysis. For this latter approach, we describe new methods to accurately measure the noise in interferometric imaging (employing jack-knifing in the cube and in the visibility plane). This independent measurement confirms the flattening of the number counts. Our analysis of the differential number counts shows that we are detecting $\sim$93% ($\sim$100% if we include the lower fidelity detections) of the total continuum dust emission associated to galaxies in the HUDF.   The ancillary data allows us to study the dependence of the 1.2 mm number counts on redshift ($z=0-4$), galaxy dust mass (${\rm M}_{\rm dust}=10^{7}-10^{9}{\rm M}_{\odot}$), stellar mass (${\rm M}_{*}=10^{9}-10^{12}{\rm M}_{\odot}$), and star-formation rate (${\rm SFR}=1-1000\thinspace{\rm M}_{\odot}\thinspace{\rm yr^{-1}}$). In an accompanying paper we show that the number counts are crucial to constrain galaxy evolution models and the understanding of star-forming galaxies at high redshift.
This paper analyzes stochastic networks consisting of a set of finite capacity sites where different classes of individuals move according to some routing policy. The associated Markov jump processes are analyzed under a thermodynamic limit regime, that is, when the networks have some symmetry properties and when the number of nodes goes to infinity. An intriguing stability property is proved: under some conditions on the parameters, it is shown that, in the limit, several stable equilibrium points coexist for the empirical distribution. The key ingredient of the proof of this property is a dimension reduction achieved by the introduction of two energy functions and a convenient mapping of their local minima and saddle points. Networks with a unique equilibrium point are also presented.
We study dispersive mixed-order systems of pseudodifferential operators in the setting of $L^p$-Sobolev spaces. Under the weak condition of quasi-hyperbolicity, these operators generate a semigroup in the space of tempered distributions. However, if the basic space is a tuple of $L^p$-Sobolev spaces, a strongly continuous semigroup is in many cases only generated if $p=2$ or $n=1$. The results are applied to the linear thermoelastic plate equation inertial term and with Fourier's or Maxwell-Cattaneo's law of heat conduction.
The explosive BN/KL outflow emerging from OMC1 behind the Orion Nebula may have been powered by the dynamical decay of a non-hierarchical multiple system $\sim$500 years ago that ejected the massive stars I, BN, and source n, with velocities of about 10 to 30 km s$^{-1}$. New proper motion measurements of H$_2$ features show that within the errors of measurement, the outflow originated from the site of stellar ejection. Combined with published data, these measurements indicate an outflow age of $\sim$500 years, similar to the time since stellar ejection. The total kinetic energy of the ejected stars and the outflow is about 2 to $6 \times 10^{47}$ ergs. It is proposed that the gravitational potential energy released by the formation of a short-period binary, most likely source I, resulted in stellar ejection and powered the outflow. A scenario is presented for the formation of a compact, non-hierarchical multiple star system, its decay into an ejected binary and two high-velocity stars, and launch of the outflow. Three mechanisms may have contributed to the explosion in the gas: (i) Unbinding of the circum-cluster envelope following stellar ejection, (ii) disruption of circumstellar disks and high-speed expulsion of the resulting debris during the final stellar encounter, and (iii) the release of stored magnetic energy. Plausible proto-stellar disk end envelope properties can produce the observed outflow mass, velocity, and kinetic energy distributions. The ejected stars may have acquired new disks by fall-back or Bondi-Hoyle accretion with axes roughly orthogonal to their velocities. The expulsion of gas and stars from OMC1 may have been driven by stellar interactions.
We build on the formalism developed in [arXiv:1906.08372v1] to propose new representations of solutions to Stein equations. We provide new uniform and non uniform bounds on these solutions (a.k.a.\ Stein factors). We use these representations to obtain representations for differences between expectations in terms of solutions to the Stein equations. We apply these to compute abstract Stein-type bounds on Kolmogorov, Total Variation and Wasserstein distances between arbitrary distributions. We apply our results to several illustrative examples, and compare our results with current literature on the same topic, whenever possible. In all occurrences our results are competitive.
Mazur's Theorem states that there are precisely 15 possibilities for the torsion subgroup of an elliptic curve defined over the rational numbers. It was previously shown by Harron and Snowden that the number of isomorphism classes of elliptic curves of height up to $X$ that have a specific torsion subgroup $G$ is on the order of $X^{1/{d(G)}}$, for some positive $d(G)$ depending on $G$. We compute $d(G)$ for these groups over $\mathbb{Q}[i]$. Furthermore, in a collection of recent papers it was proven that there are 9 more possibilities for the torsion subgroup in the base field $\mathbb{Q}[i]$. We compute the value of $d(G)$ for these new groups.
We speculate that the dark halos of dwarf galaxies and low surface brightness galaxies soften their central cusps by the decay of a fraction of cold dark matter (CDM) particles to a stable particle with a recoiling velocity of a few tens km s$^{-1}$, after they have driven the formation of galactic halos. This process, however, does not necessarily produce a significant reduction of the central dark matter density of satellite dwarf spheroidals like Draco or Fornax. It is shown that the recovered distribution of concentration parameters $c$ for the initial (before decay) Navarro-Frenk-White halos, is in good agreement with CDM predictions. Other interesting potentials of unstable CDM are highlighted.
Consider steady-state weak solutions to the incompressible Navier-Stokes equations in six spatial dimensions. We prove that the 2D Hausdorff measure of the set of singular points is equal to zero. This problem was mentioned in 1988 by Struwe [24], during his study of the five dimensional case.
We study gravitational perturbations of Schwarzschild spacetime by solving a hyperboloidal initial value problem for the Bardeen-Press equation. Compactification along hyperboloidal surfaces in a scri-fixing gauge allows us to have access to the gravitational waveform at null infinity in a general setup. We argue that this hyperboloidal approach leads to a more accurate and efficient calculation of the radiation signal than the common approach where a timelike outer boundary is introduced. The method can be generalized to study perturbations of Kerr spacetime using the Teukolsky equation.
We give a bound on the number of points of order two on the theta divisor of a principally polarized abelian variety A. When A is the Jacobian of a curve C the result can be applied in estimating the number of effective square roots of a fixed line bundle on C.
In addition to coherent pulsation, many accreting neutron stars exhibit flaring activity and strong aperiodic variability on time scales similar to or shorter than their pulsation period. Such a behavior shows that the accretion flow in the vicinity of the accretor must be highly non-stationary. Although from the theoretical point of view the problem of non-stationary accretion has been addressed by many authors, observational study of this phenomenon is often problematic as it requires very high statistics of X-ray data and a specific analysis technique. In our research we used high-resolution data taken with RXTE and INTEGRAL on a sample of bright transient and persistent pulsars, to perform an in-depth study of their variability on time scales comparable to the pulsation period - "pulse-to-pulse variability". The high-quality data allowed us to collect individual pulses of different amplitude and reveal differences in their spectra (such an analysis we refer to as "pulse-to-pulse spectroscopy"). The described approach allowed us for the first time to study luminosity-dependence of pulsars' X-ray spectra in observations where the averaged (over many pulse cycles) luminosity of the source remained constant and discuss them in the frame of the current physical models of the accretion flow close to the neutron star surface.
The bilateral filter is a versatile non-linear filter that has found diverse applications in image processing, computer vision, computer graphics, and computational photography. A widely-used form of the filter is the Gaussian bilateral filter in which both the spatial and range kernels are Gaussian. A direct implementation of this filter requires $O(\sigma^2)$ operations per pixel, where $\sigma$ is the standard deviation of the spatial Gaussian. In this paper, we propose an accurate approximation algorithm that can cut down the computational complexity to $O(1)$ per pixel for any arbitrary $\sigma$ (constant-time implementation). This is based on the observation that the range kernel operates via the translations of a fixed Gaussian over the range space, and that these translated Gaussians can be accurately approximated using the so-called Gauss-polynomials. The overall algorithm emerging from this approximation involves a series of spatial Gaussian filtering, which can be implemented in constant-time using separability and recursion. We present some preliminary results to demonstrate that the proposed algorithm compares favorably with some of the existing fast algorithms in terms of speed and accuracy.
We investigate the shallow increase in globular cluster half-light radii with projected galactocentric distance $R_{gc}$ observed in the giant galaxies M87, NGC 1399, and NGC 5128. To model the trend in each galaxy, we explore the effects of orbital anisotropy and tidally under-filling clusters. While a strong degeneracy exists between the two parameters, we use kinematic studies to help constrain the distance $R_\beta$ beyond which cluster orbits become anisotropic, as well as the distance $R_{f\alpha}$ beyond which clusters are tidally under-filling. For M87 we find $R_\beta > 27$ kpc and $20 < R_{f\alpha} < 40$ kpc and for NGC 1399 $R_\beta > 13$ kpc and $10 < R_{f\alpha} < 30$ kpc. The connection of $R_{f\alpha}$ with each galaxy's mass profile indicates the relationship between size and $R_{gc}$ may be imposed at formation, with only inner clusters being tidally affected. The best fitted models suggest the dynamical histories of brightest cluster galaxies yield similar present-day distributions of cluster properties. For NGC 5128, the central giant in a small galaxy group, we find $R_\beta > 5$ kpc and $R_{f\alpha} > 30$ kpc. While we cannot rule out a dependence on $R_{gc}$, NGC 5128 is well fitted by a tidally filling cluster population with an isotropic distribution of orbits, suggesting it may have formed via an initial fast accretion phase. Perturbations from the surrounding environment may also affect a galaxy's orbital anisotropy profile, as outer clusters in M87 and NGC 1399 have primarily radial orbits while outer NGC 5128 clusters remain isotropic.
We investigate the electronic density redistribution of rotated bilayer graphene under a perpendicular electric field, showing that the layers are actually coupled even for large angles. This layer-layer coupling is evidenced by the charge transfer on these structures as a function of the external voltage. We find an inhomogeneous excess charge distribution that is related to the moir\'e patterns for small angles, but that persists for larger angles where the carriers' velocity is equal to that of single layer graphene. Our results show that rotated bilayer systems are coupled for all rotation angles.
We present the results of a systematic search for old isolated neutron stars (ONSs) in the direction of two giant molecular clouds in Cygnus (Rift and OB7). From theoretical calculations, we expect the detection of a large number of ONSs with the PSPC on board ROSAT. By analyzing the PSPC pointings in the direction of the clouds, we find four sources characterized by count rates ($\sim 10^{-3}$ c s$^{-1}$) and spectral properties consistent with the hypothesis that the X--ray radiation is produced by ONSs and also characterized by the absence of any measurable optical counterpart within their error circle in the digitized red plates of the Palomar All Sky Survey. The importance of follow--up deep observations in the direction of these ONS candidates is discussed. The observational and theoretical approach presented here could be fruitfully applied also to the systematic search for ONSs in other regions of the Galaxy.
We prove two finiteness results for reductions of Hecke orbits of abelian varieties over local fields: one in the case of supersingular reduction and one in the case of reductive monodromy. As an application, we show that only finitely many abelian varieties on a fixed isogeny leaf admit CM lifts, which in particular implies that in each fixed dimension $g$ only finitely many supersingular abelian varieties admit CM lifts. Combining this with the Kuga-Satake construction, we also show that only finitely many supersingular $K3$-surfaces admit CM lifts. Our tools include $p$-adic Hodge theory and group theoretic techniques.
It is shown that minimally coupled scalar field in Brans-Dicke theory with varying speed of light can solve the quintessence problem and it is possible to have a non-decelerated expansion of the present universe with BD-theory for anisotropic models without any matter.
A new operator formalism for the reduction of degrees of freedom in the evolution of discrete partial differential equations (PDE) via real space Renormalization Group is introduced, in which cell-overlapping is the key concept. Applications to 1+1-dimensional PDEs are presented for linear and quadratic equations which are first order in time.