ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present the first case of strong gravitational lensing by a QSO : SDSS J0013+1523, at z = 0.120. The discovery is the result of a systematic search for emission lines redshifted behind QSOs, among 22298 spectra of the SDSS data release 7. Apart from the z = 0.120 spectral features of the foreground QSO, the spectrum of SDSS J0013+1523 also displays the OII and Hbeta emission lines and the OIII doublet, all at the same redshift, z = 0.640. Using sharp Keck adaptive optics K-band images obtained using laser guide stars, we unveil two objects within a radius of 2 arcsec from the QSO. Deep Keck optical spectroscopy clearly confirms one of these objects at z = 0.640 and shows traces of the OIII, emission line of the second object, also at z = 0.640. Lens modeling suggests that they represent two images of the same z = 0.640 emission-line galaxy. Our Keck spectra also allow us to measure the redshift of an intervening galaxy at z = 0.394, located 3.2 arcsec away from the line of sight to the QSO. If the z = 0.120 QSO host galaxy is modeled as a singular isothermal sphere, its mass within the Einstein radius is M_E(r < 1 kpc) = 2.16e10 M_Sun and its velocity dispersion is sigma_SIS = 169 km/s. This is about 1 sigma away from the velocity dispersion estimated from the width of the QSO Hbeta emission line, sigma_*(M_BH) = 124 +/- 47 km/s. Deep optical HST imaging will be necessary to constrain the total radial mass profile of the QSO host galaxy using the detailed shape of the lensed source. This first case of a QSO acting as a strong lens on a more distant object opens new directions in the study of QSO host galaxies.
We pursue the investigation of generalizations of the Pascal triangle based on binomial coefficients of finite words. These coefficients count the number of times a finite word appears as a subsequence of another finite word. The finite words occurring in this paper belong to the language of a Parry numeration system satisfying the Bertrand property, i.e., we can add or remove trailing zeroes to valid representations. It is a folklore fact that the Sierpi\'{n}ski gasket is the limit set, for the Hausdorff distance, of a convergent sequence of normalized compact blocks extracted from the classical Pascal triangle modulo $2$. In a similar way, we describe and study the subset of $[0, 1] \times [0, 1]$ associated with the latter generalization of the Pascal triangle modulo a prime number.
We study an inverse first-passage-time problem for Wiener process $X(t)$ subject to hold and jump from a boundary $c.$ Let be given a threshold $S>X(0) \ge c,$ and a distribution function $F$ on $[0, + \infty ).$ The problem consists in finding the distribution of the holding time at $c$ and the distribution of jumps from $c,$ so that the first-passage time of $X(t)$ through $S$ has distribution $F.$
We investigate the statistics of photons emitted by tunneling electrons in a single electronic level plasmonic nanojunction. We compute the waiting-time distribution of successive emitted photons $w(\tau)$. When the cavity damping rate $\kappa$ is larger than the electronic tunneling rate $\Gamma$, we show that in the photon-antibunching regime, $w(\tau)$ indicates that the average delay-time between two successive photon emission events is given by $1/\Gamma$. This is in contrast with the usually considered second-order correlation function of emitted photons, $g^{(2)}(\tau)$, which displays the single time scale $1/\kappa$. Our analysis shows a relevant example for which $w(\tau)$ gives independent information on the photon-emission statistics with respect to $g^{(2)}(\tau)$, leading to a physical insight on the problem. We discuss how this information can be extracted from experiments even in presence of a non-perfect photon detection yield.
The HMW effect in non-commutative quantum mechanics is studied. By solving the Dirac equations on non-commutative (NC) space and non-commutative phase space, we obtain topological HMW phase on NC space and NC phase space respectively, where the additional terms related to the space-space and momentum-momentum non-commutativity are given explicitly.
We discuss the way in which factorisation is partially maintained but nevertheless modified by process-dependent colour factors in hadronic single-spin asymmetries. We also examine QCD evolution of the twist-three gluonic-pole strength defining an effective T-odd Sivers function in the large-x limit, where evolution of the T-even transverse-spin DIS structure function g2 is known to be multiplicative.
Let G be the (open) set of~$\dot H^{\frac 1 2}$ divergence free vector fields generating a global smooth solution to the three dimensional incompressible Navier-Stokes equations. We prove that any element of G can be perturbed by an arbitrarily large, smooth divergence free vector field which varies slowly in one direction, and the resulting vector field (which remains arbitrarily large) is an element of G if the variation is slow enough. This result implies that through any point in G passes an uncountable number of arbitrarily long segments included in G.
(abridged) We present a study on the effects of the intracluster medium (ICM) on the interstellar medium (ISM) of 10 Virgo cluster spiral galaxies using {\it Spitzer} far-infrared (FIR) and VLA radio continuum imaging. Relying on the FIR-radio correlation within normal galaxies, we use our infrared data to create model radio maps which we compare to the observed radio images. For 6 of our sample galaxies we find regions along their outer edges that are highly deficient in the radio compared with our models. We believe these observations are the signatures of ICM ram pressure. For NGC 4522 we find the radio deficit region to lie just exterior to a region of high radio polarization and flat radio spectral index, although the total 20 cm radio continuum in this region does not appear strongly enhanced. These characteristics seem consistent for other galaxies with radio polarization data in the literature. The strength of the radio deficit is inversely correlated with the time since peak pressure as inferred from stellar population studies and gas stripping simulations, suggesting the strength of the radio deficit is good indicator of the strength of the current ram pressure. We also find that galaxies having {\it local} radio {\it deficits} appear to have {\it enhanced global} radio fluxes. Our preferred physical picture is that the observed radio deficit regions arise from the ICM wind sweeping away cosmic-ray (CR) electrons and the associated magnetic field, thereby creating synchrotron tails as observed for some of our galaxies. We propose that CR particles are also re-accelerated by ICM-driven shocklets behind the observed radio deficit regions which in turn enhances the remaining radio disk brightness.
In this paper we study a free boundary problem modeling the growth of solid tumor spheroid. It consists of two elliptic equations describing nutrient diffusion and pressure distribution within tumor, respectively. The new feature is that nutrient concentration on the boundary is less than external supply due to a Gibbs-Thomson relation and the problem has two radial stationary solutions, which differs from widely studied tumor spheroid model with surface tension effect. We first establish local well-posedness by using a functional approach based on Fourier multiplier method and analytic semigroup theory. Then we investigate stability of each radial stationary solution. By employing a generalized principle of linearized stability, we prove that the radial stationary solution with a smaller radius is always unstable, and there exists a positive threshold value $\gamma_*$ of cell-to-cell adhesiveness $\gamma$, such that the radial stationary solution with a larger radius is asymptotically stable for $\gamma>\gamma_*$, and unstable for $0<\gamma<\gamma_*$.
Broad infrared emission features (e.g., at 3.3, 6.2, 7.7, 8.6, and 11.3 microns) from the gas phase interstellar medium have long been attributed to polycyclic aromatic hydrocarbons (PAHs). A significant portion (10%-20%) of the Milky Way's carbon reservoir is locked in PAH molecules, which makes their characterization integral to our understanding of astrochemistry. In molecular clouds and the dense envelopes and disks of young stellar objects (YSOs), PAHs are expected to be frozen in the icy mantles of dust grains where they should reveal themselves through infrared absorption. To facilitate the search for frozen interstellar PAHs, laboratory experiments were conducted to determine the positions and strengths of the bands of pyrene mixed with H2O and D2O ices. The D2O mixtures are used to measure pyrene bands that are masked by the strong bands of H2O, leading to the first laboratory determination of the band strength for the CH stretching mode of pyrene in water ice near 3.25 microns. Our infrared band strengths were normalized to experimentally determined ultraviolet band strengths, and we find that they are generally ~50% larger than those reported by Bouwman et al. based on theoretical strengths. These improved band strengths were used to reexamine YSO spectra published by Boogert et al. to estimate the contribution of frozen PAHs to absorption in the 5-8 micron spectral region, taking into account the strength of the 3.25 micron CH stretching mode. It is found that frozen neutral PAHs contain 5%-9% of the cosmic carbon budget, and account for 2%-9% of the unidentified absorption in the 5-8 micron region.
In this work we study an anisotropic model of general relativity based on the framework of Finsler geometry. The observed anisotropy of the microwave background radiation is incorporated in the Finslerian structure of space-time. We also examine the electromagnetic (e.m.) field equations in our space. As a result a modified wave equation of e.m. waves yields.
In recent work, we analyzed the dynamics of spherical and nonspherical acoustic perturbations of the Michel flow, describing the steady radial accretion of a relativistic perfect fluid into a nonrotating black hole. We showed that such perturbations undergo quasi-normal oscillations and computed the corresponding complex frequencies as a function of the black hole mass M and the radius r_c of the sonic horizon. It was found that when r_c is much larger than the Schwarzschild radius r_H = 2GM/c^2 of the black hole, these frequencies scale like the surface gravity of the analogue black hole associated with the acoustic metric.   In this work, we analyze the Newtonian limit of the Michel solution and its acoustic perturbations. In this limit, the flow outside the sonic horizon reduces to the transonic Bondi flow, and the acoustic metric reduces to the one introduced by Unruh in the context of experimental black hole evaporation. We show that for the transonic Bondi flow, Unruh's acoustic metric describes an analogue black hole and compute the associated quasi-normal frequencies. We prove that they do indeed scale like the surface gravity of the acoustic black hole, thus providing an explanation for our previous results in the relativistic setting.
Semiconductor quantum dots embedded in optical cavities are promising on-demand sources of single photons. Here, we theoretically study single photon emission from an optically driven two-photon Raman transition between the biexciton and the ground state of a quantum dot. The advantage of this process is that it allows all-optical control of the properties of the emitted single photon with a laser pulse. However, with the presence of other decay channels and excitation-induced quantum interference, on-demand emission of the single Raman photon is generally difficult to achieve. Here we show that laser pulses with non-trivial shapes can be used to maintain excitation conditions for which with increasing pulse intensities the on-demand regime is reached. To provide a realistic picture of the achievable system performance, we include phonon-mediated processes in the theoretical caluclations. While preserving both high photon purity and indistinguishability, we find that although based on a higher-order emission process, for realistic system parameters on-demand Raman photon emission is indeed achievable with suitably tailored laser pulses.
Following is a collection of lecture notes on D-branes, which may be used by the reader as preparation for applications to modern research applications such as: the AdS/CFT and other gauge theory/geometry correspondences, Matrix Theory and stringy non-commutative geometry, etc. In attempting to be reasonably self-contained, the notes start from classical point-particles and develop the subject logically (but selectively) through classical strings, quantisation, D-branes, supergravity, superstrings, string duality, including many detailed applications. Selected focus topics feature D-branes as probes of both spacetime and gauge geometry, highlighting the role of world-volume curvature and gauge couplings, with some non-Abelian cases. Other advanced topics which are discussed are the (presently) novel tools of research such as fractional branes, the enhancon mechanism, D(ielectric)-branes and the emergence of the fuzzy/non-commutative sphere.
We use the 1/N_c method to estimate electromagnetic contributions to vector meson masses and mixings. We identify several new sources of rho-omega mixing coming from short-distance effects. We comment on the extraction of quark masses from the vector meson masses. We also present a simple group theoretical discussion of the electromagnetic mass differences.
Expander graphs are highly connected sparse finite graphs. They play an important role in computer science as basic building blocks for network constructions, error correcting codes, algorithms and more. In recent years they have started to play an increasing role also in pure mathematics: number theory, group theory, geometry and more. This expository article describes their constructions and various applications in pure and applied mathematics.
The magnetocrystalline anisotropy exhibited in PrPd$_2$Ge$_2$ single crystal has been investigated by measuring the magnetization, magnetic susceptibility, electrical resistivity and heat capacity. PrPd$_2$Ge$_2$ crystallizes in the well known ThCr$_2$Si$_2$\--type tetragonal structure. The antiferromagnetic ordering is confirmed as 5.1~K with the [001]-axis as the easy axis of magnetization. A superzone gap formation is observed from the electrical resistivity measurement when the current is passed along the [001] direction. The crystal electric field (CEF) analysis on the magnetic susceptibility, magnetization and the heat capacity measurements confirms a doublet ground state with a relatively low over all CEF level splitting. The CEF level spacings and the Zeeman splitting at high fields become comparable and lead to metamagnetic transition at 34~T due to the CEF level crossing.
Using the Chandra X-ray Observatory, we have pinpointed the location of a faint X-ray point source (CXOUJ182913.1-125113) and an associated diffuse nebula in the composite supernova remnant G18.95-1.1. These objects appear to be the long-sought pulsar and its wind nebula. The X-ray spectrum of the point source is best described by an absorbed powerlaw model with Gamma=1.6 and an N_H of ~1x10^(22) cm^(-2). This model predicts a relatively low unabsorbed X-ray luminosity of about L_X (0.5-8.0keV) = 4.1x10^(31)D_2^2 erg s^(-1), where D_2 is the distance in units of 2kpc. The best-fitted model of the diffuse nebula is a combination of thermal (kT = 0.48keV) and non-thermal (1.4 < Gamma < 1.9) emission. The unabsorbed X-ray luminosity of L_X = 5.4x10^(33)D_2^2 erg s^(-1) in the 0.5-8keV energy band seems to be largely dominated by the thermal component from the SNR, providing 87% of L_X in this band. No radio or X-ray pulsations have been reported for CXOUJ182913.1-125113. If we assume an age of ~5300yr for G18.95-1.1 and use the X-ray luminosity for the pulsar and the wind nebula together with the relationship between spin-down luminosity (via magnetic dipole radiation) and period, we estimate the pulsar's period to be P = 0.4s. Compared to other rotation-powered pulsars, a magnetic field of 2.2x10^(13)G is implied by its location in the P-Pdot diagram, a value which is close to that of the quantum critical field.
In this note we describe the image of $\PP^2$ in $ Gr(2, \CC^{4})$ under a morphism given by a rank two vector bundle on $\PP^2$ with Chern classes $(2,2).$
A degenerate optical parametric oscillator network is proposed to solve the NP-hard problem of finding a ground state of the Ising model. The underlying operating mechanism originates from the bistable output phase of each oscillator and the inherent preference of the network in selecting oscillation modes with the minimum photon decay rate. Computational experiments are performed on all instances reducible to the NP-hard MAX-CUT problems on cubic graphs of order up to 20. The numerical results reasonably suggest the effectiveness of the proposed network.
The aim of this work is to study the imprints that different models for black hole (BH) and neutron star (NS) formation have on the Galactic distribution of X-ray binaries (XRBs) which contain these objects. We find that the root mean square of the height above the Galactic plane of BH- and NS-XRBs is a powerful proxy to discriminate among different formation scenarios, and that binary evolution following the BH/NS formation does not significantly affect the Galactic distributions of the binaries. We find that a population model in which at least some BHs receive a (relatively) high natal kick fits the observed BH-XRBs best. For the NS case, we find that a high NK distribution, consistent with the one derived from the measurement of pulsar proper motion, is the most preferable. We also analyse the simple method we previously used to estimate the minimal peculiar velocity of an individual BH-XRB at birth. We find that this method may be less reliable in the bulge of the Galaxy for certain models of the Galactic potential, but that our estimate is excellent for most of the BH-XRBs.
NASA's Interface Region Imaging Spectrograph (IRIS) small explorer mission will study how the solar atmosphere is energized. IRIS contains an imaging spectrograph that covers the Mg II h&k lines as well as a slit-jaw imager centered at Mg II k. Understanding the observations requires forward modeling of Mg II h&k line formation from 3D radiation-MHD models.   We compute the vertically emergent h&k intensity from a snapshot of a dynamic 3D radiation-MHD model of the solar atmosphere, and investigate which diagnostic information about the atmosphere is contained in the synthetic line profiles. We find that the Doppler shift of the central line depression correlates strongly with the vertical velocity at optical depth unity, which is typically located less than 200 km below the transition region (TR). By combining the Doppler shifts of the h and the k line we can retrieve the sign of the velocity gradient just below the TR. The intensity in the central line depression is anticorrelated with the formation height, especially in subfields of a few square Mm. This intensity could thus be used to measure the spatial variation of the height of the transition region. The intensity in the line-core emission peaks correlates with the temperature at its formation height, especially for strong emission peaks. The peaks can thus be exploited as a temperature diagnostic. The wavelength difference between the blue and red peaks provides a diagnostic of the velocity gradients in the upper chromosphere. The intensity ratio of the blue and red peaks correlates strongly with the average velocity in the upper chromosphere. We conclude that the Mg II h&k lines are excellent probes of the very upper chromosphere just below the transition region, a height regime that is impossible to probe with other spectral lines.
We consider a model for the low-luminosity gamma-ray burst GRB 060218 that plausibly accounts for multiwavelength observations to day 20. The model components are: (1) a long-lived ($t_j \sim 3000$ s) central engine and accompanying low-luminosity ($L_j \sim 10^{47}$ erg s$^{-1}$), semirelativistic ($\gamma \sim 10$) jet; (2) a low-mass ($ \sim 10^{-2} M_\odot$) envelope surrounding the progenitor star; and (3) a modest amount of dust ($A_V \sim 0.1$ mag) in the interstellar environment. Blackbody emission from the transparency radius in a low-power jet outflow can fit the prompt thermal X-ray emission, and the nonthermal X-rays and gamma-rays may be produced via Compton scattering of thermal photons from hot leptons in the jet interior or the external shocks. The later mildly relativistic phase of this outflow can produce the radio emission via synchrotron radiation from the forward shock. Meanwhile, interaction of the associated SN 2006aj with a circumstellar envelope extending to $\sim10^{13}$ cm can explain the early optical emission. The X-ray afterglow can be interpreted as a light echo of the prompt emission from dust at $\sim 30$ pc. Our model is a plausible alternative to that of Nakar, who recently proposed shock breakout of a jet smothered by an extended envelope as the source of prompt emission. Both our results and Nakar's suggest that bursts such as GRB 060218 may originate from unusual progenitors with extended circumstellar envelopes, and that a jet is necessary to decouple the prompt emission from the supernova.
Irreducible characters in the symmetric group are of special interest in combinatorics. They can be expressed either combinatorially with ribbon tableaux, or algebraically with contents. In this paper, these two expressions are related in a combinatorial way. We first introduce a fine structure in the famous jeu de taquin called "trace forest", with which we are able to count certain types of ribbon tableaux, leading to a simple bijective proof of a character evaluation formula in terms of contents that dates back to Frobenius (1901). Inspired by this proof, we give an inductive scheme that gives combinatorial proofs to more complicated formulae for characters in terms of contents.
In this paper, we find a bound for the number of the positive solutions to the titled equation, improving a result of Togb\'e. As a consequence, we prove a conjecture of Togb\'e in a few cases.
The damping of the axionic string motion due to the surrounding plasma is estimated by a detailed calculation of the fermion scatter from a global string and it is shown that the friction force on the string can be neglected before the axionic domain wall formation in most cases, which is one of the important necessary conditions for the scaling distribution of the strings. The energy density of the axion produced by the collapse of the axionic domain walls is also evaluated using the axionic string distribution, and it is found to be larger or at least comparable to the axion density which originates from the axionic strings.