ShantanuT01/DACTYL-Pretraining huggingface dataset:
We prove two bounds for discrete moments of Weyl sums. The first one can be obtained using a standard approach. The second one involves an observation how this method can be improved, which leads to a sharper bound in certain ranges. The proofs both build on the recently proved main conjecture for Vinogradov's mean value theorem.   We present two selected applications: First, we prove a new $k$- th derivative test for the number of integer points close to a curve by an exponential sum approach. This yields a stronger bound than existing results obtained via geometric methods, but it is only applicable for specific functions. As second application we prove a new improvement of the polynomial large sieve inequality for one-variable polynomials of degree $k \geq 4$.
Carbon is one of the most abundant metals in the universe because of its synthesis in the fundamental triple alpha reaction. The knowledge of carbon abundances in different environments is one key ingredient to our understanding of stellar and galactochemical evolution. Studies of luminous OB-type stars allow us to address both topics even in galaxies beyond our own. Unfortunately the history of carbon abundance determinations from these objects in the last three decades is one of limited success. Analyses of the strong and weak line spectra of C II as well as C III tend to be largely discrepant. We present results of quantitative spectral analyses based on a sophisticated model atom for non-LTE line-formation calculations of C II-IV. As a first application, carbon abundances in a sample of B-type dwarfs and giants in nearby associations and in the field are determined. Consistency is finally achieved for all measurable lines (up to 40) from the three ionization stages. This includes in particular the notorious C II 4267 and 6578/6582 A features which are highly important for abundance determinations of fast-rotating and extragalactic objects. The long-standing problem of carbon line-formation can now be regarded as solved, with the previous difficulties related to the use of inaccurate atomic data and stellar parameters. A highly homogeneous and slightly sub-solar present-day carbon abundance from young stars in the solar vicinity of log C/H+12= 8.32+/-0.04 is derived
The inner radius of the accretion disc around a black hole in the low/hard state can be measured in one of two ways. Firstly, via the extent of broadening of the iron emission line, and secondly, from the luminosity and temperature of the weak soft component seen in this state, assuming it is the disc. We use both of these methods on all the low/hard state spectra taken in timing mode of XMM-Newton's EPIC-pn. We find that the two methods are not consistent with each other, and the difference is not always in a single direction. The two methods are neither model independent, nor are they independent of current calibration issues. We find that the remaining small residuals in the EPIC-pn timing mode response at the <3% level can have a dramatic effect on the fit parameters for the reflected spectrum. There is also a mismatch in cross-calibration with RXTE, which makes it difficult to use simultaneous data to extend the bandpass of the spectral fits. Nonetheless, it is clear from the data that the iron line is noticeably broader and stronger at higher L/LEdd, which is consistent with the truncated disc models. We also show that it is likely that the soft component changes character, from a stable component consistent with a truncated disc at high L/LEdd, to a variable one with much smaller radius at low L/LEdd. This adds to growing evidence for a complex soft component in the low/hard state, possibly resulting from clumps torn from the edge of the truncated disc.
The electronic states of a mesoscopic ring are assessed in the presence of Rashba Spin Orbit coupling and a $U(1)$ gauge field. Spin symmetric coupling to an ideal lead is implemented following B\"uttiker's voltage probe. The exact density of states is derived using the reservoir uncoupled eigenstates as basis functions mixed by the reservoir coupling. The decay time of uncoupled electron eigenstates is derived by fitting the broadening profiles. The spin and charge persistent currents are computed in the presence of the SO interaction and the reservoir coupling for two distinct scenarios of the electron filling fraction. The degradation of the persistent currents depends uniformly on the reservoir coupling but nonuniformly in temperature, the latter due to the fact that currents emerge from different depths of the Fermi sea, and thus for some regimes of flux, they are provided with a protective gap. Such flux regimes can be tailored by the SO coupling for both charge and spin currents.
We measure the high magnetic field ($B$) microwave conductivity, Re$\sigma_{xx}$, of a high mobility 2D electron system containing an antidot array. Re$\sigma_{xx}$ vs frequency ($f$) increases strongly in the regime of the fractional quantum Hall effect series, with Landau filling $1/3<\nu<2/3$. At microwave $f$, Re$\sigma_{xx}$ vs $B$ exhibits a broad peak centered around $\nu=1/2$. On the peak, the 10 GHz Re$\sigma_{xx}$ can exceed its dc-limit value by a factor of 5. This enhanced microwave conductivity is unobservable for temperature $T \gtrsim 0.5$ K, and grows more pronounced as $T$ is decreased. The effect may be due to excitations supported by the antidot edges, but different from the well-known edge magnetoplasmons.
Magnetic fields are believed to play an important role in controlling the stability and contraction of dense condensations of gas and dust leading to the formation of stars and planetary systems. In the present study, the magnetic field of FeSt 1-457, a cold starless molecular cloud core, was mapped on the basis of the polarized near-infrared light from 185 background stars after being dichroically absorbed by dust aligned with the magnetic field in the core. A distinct "hourglass-shaped" magnetic field was identified in the region of the core, which was interpreted as the first evidence of a magnetic field structure distorted by mass condensation in a starless core. The steep curvature of the magnetic field lines obtained in the present study indicates that the distortion was mainly created during the formation phase of the dense core. The derived mass-to-magnetic flux ratio indicates that the core is in a magnetically supercritical state. However, the stability of the core can be considered to be in a nearly critical state if the additional contributions from the thermal and turbulent support are included. Further diffusion of the magnetic field and/or turbulent dissipation would cause the onset of dynamical collapse of the core. The geometrical relationship between the direction of the magnetic field lines and the elongation of the core was found to be in good agreement with the theoretical predictions for the formation of Sun-like stars under the influence of a magnetic field.
We review the recent result of Sato, Sekimoto, Hondou, and Takagi (cond-mat/0008393) on the irreversibility inevitably observed in systems consisting of many non-interacting ``small'' pieces. We focus on quantum models, and supply an explicit lower bound for the work required to complete a cyclic process.
We study the relativistic orbit of binary black holes in systems with small mass ratio. The trajectory of the smaller object (another black hole or a neutron star), represented as a particle, is determined by the geodesic equation on the perturbed massive black hole spacetime. The particle itself generates the gravitational perturbations leading to a problem that needs regularization. Here we study perturbations around a Schwarzschild black hole using Moncrief's gauge invariant formalism. We decompose the perturbations into $\ell-$multipoles to show that all $\ell-$metric coefficients are $C^0$ at the location of the particle. Summing over $\ell$, to reconstruct the full metric, gives a formally divergent result. We succeed in bringing this sum to a generalized Riemann's $\zeta-$function regularization scheme and show that this is tantamount to subtract the $\ell\to\infty$ piece to each multipole. We explicitly carry out this regularization and numerically compute the first order geodesics. Application of this method to general orbits around rotating black holes would generate accurate templates for gravitational wave laser interferometric detectors.
Bulk and spectroscopic properties of 4He are studied within an equation of motion phonon method. Such a method generates a basis of n-phonon (n = 0, 1, 2, 3...) states composed of tensor products of particle-hole Tamm-Dancoff phonons and then solves the full eigenvalue problem in such a basis. The method does not rely on any approximation and is free of any contamination induced by the center of mass, in virtue of a procedure exploiting the singular value decomposition of rectangular matrices. Two potentials, both derived from the chiral effective field theory, are adopted in a self-consistent calculation performed within a space including up to three phonons. The latter basis states are treated under a simplifying assumption. A comparative analysis with the experimental data points out the different performances of the two potentials. It shows also that the calculation succeeds only partially in the description of the spectroscopic properties and suggests a recipe for further improvements.
We study the effect of free boundaries in finite magnetic systems of cubic shape on the field and temperature dependence of the magnetization within the isotropic model of D-component spin vectors in the limit D \to \infty. This model is described by a closed system of equations and captures the Goldstone-mode effects such as global rotation of the magnetic moment and spin-wave fluctuations. We have obtained an exact relation between the intrinsic (short-range) magnetization M = M(H,T) of the system and the supermagnetization m = m(H,T) which is induced by the field. We have shown, analytically at low temperatures and fields and numerically in a wide range of these parameters, that boundary effects leading to the decrease of M with respect to the bulk value are stronger than the finite-size effects making a positive contribution to M. The inhomogeneities of the magnetization caused by the boundaries are long ranged and extend far into the depth of the system.
In this paper we discuss a priori estimates derived from the energy method to the initial value problem for the cubic nonlinear Schr\"odinger on the sphere $S^2$. Exploring suitable a priori estimates, we prove the existence of solution for data whose regularity is $s=1/4$.
We present the results from ASCA observations of NGC 3783 carried out during 1993 and 1996. Variability is observed both between the two epochs and within the individual observations, the latter due to a non-stationary process.   We find the spectra at both epochs to contain features due to absorption by ionized material, predominantly due to Ovii and Oviii. We find the opacity for such material to decrease by a factor approx 2 in the approx 0.7--1.0 keV band between the epochs while the photoionizing flux increases by approx25%. By comparison with detailed photoionization models we show this behaviour is inconsistent with that expected from a single-zone of photoionized gas. A deficit in the data compared to such models, consistent with excess absorption by Oviii, supports the suggestion that the material consists of two or more zones.   Significant Fe K-shell emission is also observed during both epochs. We show this emission is dominated by the asymmetric line profile expected from the innermost regions of the accretion flow. We find no evidence that the Fe emission varied in either shape or equivalent width between the two epochs.
Cubic yttria-stabilized zirconia is widely used in industrial electrochemical devices. While its fast oxygen ion diffusion is well understood, why cation diffusion is much slower-its activation energy (~5 eV) is 10 times that of anion diffusion-remains a mystery. Indeed, all previous computational studies predicted more than 5 eV is needed for forming a cation defect, and another 5 eV for moving one. In contrast, our ab initio calculations have correctly predicted the experimentally observed cation diffusivity. We found Schottky pairs are the dominant defects that provide cation vacancies, and their local environments and migrating path are dictated by packing preferences. As a cation exchanges position with a neighboring vacancy, it passes by an empty interstitial site and severely displaces two oxygen neighbors with shortened Zr-O distances. This causes a short-range repulsion against the migrating cation and a long-range disturbance of the surrounding, which explains why cation diffusion is relatively difficult. In comparison, cubic zirconia's migrating oxygen only minimally disturbs neighboring Zr, which explains why it is a fast oxygen conductor.
We discuss various aspects of the geometry of theta characteristics including the birational geometry of the spin moduli space of curves, parametrization of moduli via special K3 surfaces, as well as the relation with classical theta function theory and string theory in the form of the superstring measure. A historical view of the development of the subject is also presented.
Fix a rectangular Young diagram R, and consider all the products of Schur functions s(mu) s(mu^c), where mu and mu^c run over all (unordered) pairs of partitions which are complementary with respect to R.   Theorem: The self-complementary products, s(mu)^2 where mu=mu^c, are linearly independent of all other s(mu) s(mu^c).   Conjecture: The products s(mu) s(mu^c) are all linearly independent.
We consider the anisotropic mean curvature flow of entire Lipschitz graphs. We prove existence and uniqueness of expanding self-similar solutions which are asymptotic to a prescribed cone, and we characterize the long time behavior of solutions, after suitable rescaling, when the initial datum is a sublinear perturbation of a cone. In the case of regular anisotropies, we prove the stability of self-similar solutions asymptotic to strictly mean convex cones, with respect to perturbations vanishing at infinity. We also show the stability of hyperplanes, with a proof which is novel also for the isotropic mean curvature flow.
We study matrix models related to $SO/Sp$ gauge theories with flavors. We give the effective superpotentials for gauge theories with arbitrary tree level superpotential up to first instanton level. For quartic tree level superpotential we obtained exact one-cut solution. We also derive Seiberg-Witten curve for these gauge theories from matrix model argument.
We try to understand and justify Schubert Calculus the way Schubert did it.
The Broad Line Radio Galaxy 3C 111, characterized by a Fanaroff-Riley II (FRII) radio morphology, is one of the sources of the Misaligned Active Galactic Nuclei sample, consisting of Radio Galaxies and Steep Spectrum Radio Quasars, recently detected by the Fermi-Large Area Telescope. Our analysis of the 24-month gamma-ray light curve shows that 3C 111 was only occasionally detected at high energies. It was bright at the end of 2008 and faint, below the Fermi-Large Area Telescope sensitivity threshold, for the rest of the time. A multifrequency campaign of 3C~111, ongoing in the same period, revealed an increase of the mm, optical and X-ray fluxes in 2008 September-November, interpreted by Chatterjee et al. (2011) as due to the passage of a superluminal knot through the jet core. The temporal coincidence of the mm-optical-X-ray outburst with the GeV activity suggests a co-spatiality of the events, allowing, for the first time, the localization of the gamma-ray dissipative zone in a FRII jet. We argue that the GeV photons of 3C 111 are produced in a compact region confined within 0.1 pc and at a distance of about 0.3 pc from the black hole.
We present the X-ray source catalog for the 479 ks Chandra exposure of the SDSS J1030+0524 field, that is centered on a region that shows the best evidence to date of an overdensity around a z > 6 quasar, and also includes a galaxy overdensity around a Compton-thick Fanaroff-Riley type II radio galaxy at z = 1.7. Using wavdetect for initial source detection and ACIS Extract for source photometry and significance assessment, we create preliminary catalogs of sources that are detected in the full, soft, and hard bands, respectively. We produce X-ray simulations that mirror our Chandra observation to filter our preliminary catalogs and get a completeness level of > 91% and a reliability level of 95% in each band. The catalogs in the three bands are then matched into a final main catalog of 256 unique sources. Among them, 244, 193, and 208 are detected in the full, soft, and hard bands, respectively. This makes J1030 field the fifth deepest extragalactic X-ray survey to date. The field is part of the Multiwavelength Survey by Yale-Chile (MUSYC), and is also covered by optical imaging data from the Large Binocular Camera (LBC) at the Large Binocular Telescope, near-IR imaging data from the Canada France Hawaii Telescope WIRCam, and Spitzer IRAC. Thanks to its dense multi-wavelength coverage, J1030 represents a legacy field for the study of large-scale structures around distant accreting supermassive black holes. Using a likelihood ratio analysis, we associate multi-band counterparts for 252 (98.4%) of the 256 Chandra sources, with an estimated reliability of 95%. Finally, we compute the cumulative number of sources in each X-ray band, finding that they are in general agreement with the results from the Chandra Deep Fields.
We obtain a bijection between some set of multidimensional sequences and this of $d$-type plane forests which is based on the breadth first search algorithm. This coding sequence is related to the sequence of population sizes indexed by the generations, through a Lamperti type transformation. The same transformation in then obtained in continuous time for multitype branching processes with discrete values. We show that any such process can be obtained from a $d^2$ dimensional compound Poisson process time changed by some integral functional. Our proof bears on the discretisation of branching forests with edge lengths.
We present FDTD calculations for transmission of light and other electromagnetic waves through periodic arrays of slits in a metallic slab. The results show resonant, frequency dependent, transmittance peaks for subwavelength widths of the slits which can be up to a factor of ten with respect to those out of resonance. Although our conclusions agree with previous work by Lezec and Thio as regards both the magnitude of the enhancement and the lack of contribution of surface plasmon polaritons of the metal surface to this effect, we derive an interpretation from a theory that deals with emerging beam- Rayleigh anomalies of the grating, and with Fabry-Perot resonances of the perforated slab considered as an effective medium.
Given Prym-Tyurin varieties of exponent $q$ with respect to a finite group $G$, a subgroup $H$ and a set of rational irreducible representations of $G$ satisfying some additional properties, we construct a Prym-Tyurin variety of exponent $[G:H]q$ in a natural way. We study an example of this result, starting from the dihedral group $\mathbf{D}_p$ for any odd prime $p$. This generalizes the construction of arXiv:math/0412103v2[math.AG] for $p=3$. Finally, we compute the isogeny decomposition of the Jacobian of the curve underlying the above mentioned example.
We consider a hypersurface in $\mathbb{C}^n$ with an isolated singular point at the origin, and study the mixed Hodge structure of the stalk of its intersection cohomology complex at the origin. In particular we express the dimension of each graded piece of the weight filtration of this mixed Hodge structure in terms of the numbers of the Jordan blocks in the Milnor monodromy.
We report new detections and limits from a NOEMA and ALMA CO(1-0) search for molecular outflows in 13 local galaxies with high FIR surface brightness, and combine with results from the literature. CO line ratios and outflow structure provide some constraints on the conversion from observables to quantities such as molecular mass outflow rates. Ratios between outflow emission in higher J CO transitions and in CO(1-0) typically are consistent with excitation Ri1<~1. For IRAS 13120-5453, however, R31=2.10 indicates optically thin CO in the outflow. Like much of the outflow literature, we use alpha(CO) = 0.8, and we present arguments for using C=1 in deriving molecular mass outflow rates Mdot = C*M*v/R. We compare the two main methods for molecular outflow detection: CO mm interferometry and Herschel OH spectroscopy. For 26 sources studied with both methods, we find 80% agreement in detecting vout>~150km/s outflows, and non-matches can be plausibly ascribed to outflow geometry and SNR. For 12 bright ULIRGs with detailed OH-based outflow modeling, CO outflows are detected in all but one. Outflow masses, velocities, and sizes for these 11 sources agree well between the two methods, and modest remaining differences may relate to the different but overlapping regions sampled by CO emission and OH absorption. Outflow properties correlate better with AGN luminosity and with bolometric luminosity than with FIR surface brightness. The most massive outflows are found for systems with current AGN activity, but significant outflows in non-AGN systems must relate to star formation or to AGN activity in the recent past. We report scaling relations for the increase of outflow mass, rate, momentum rate, and kinetic power with bolometric luminosity. Short ~10^6yr flow times and some sources with resolved multiple outflow episodes support a role of intermittent driving, likely by AGN. (abridged)
Context: Their high intrinsic brightness and small dispersion in absolute magnitude make red clump (RC) stars a prime tracer of Galactic structure and kinematics. Aims: We aim to derive accurate, multi-epoch radial velocities and atmospheric parameters (Teff, log g, [M/H], Vrot sin i) of a large sample of carefully selected RC stars, fainter than those present in other spectroscopic surveys and located over a great circle at high Galactic latitudes. Methods: We acquired data of the program stars of high signal-to-noise ratio (S/N) and high resolution with the Asiago Echelle spectrograph. Radial velocities were obtained by applying cross-correlation and atmospheric parameters via chi2 fit to a synthetic spectral library. Extensive tests were carried out by re-observing with the same instrument a large number of standard stars taken from a variety of sources in the literature. During these tests, we found that the absolute Tycho VT magnitude of local red clump stars is not dependent on metallicity. Results: A total of 277 red clump stars (101 of them with a second epoch observation) of the extended solar neighborhood and 55 calibration stars were observed and included in an output catalog that contains (in addition to relevant support astrometric and photometric data taken from literature) the main output of our survey: accurate multi-epoch radial velocities (sigma(RV)=< 0.4 km/s), accurate atmospheric parameters (sigma(Teff)=68 K, sigma(log g)=0.11 dex, sigma([M/H])=0.10 dex, sigma(Vrot sin i)=1.1 km/sec), distances, and space velocities (U,V,W).