ShantanuT01/DACTYL-Pretraining huggingface dataset:
Using the action of the Galois group of a normal extension of number fields, we generalize and symmetrize various fundamental statements in algebra and algebraic number theory concerning splitting types of prime ideals, factorization types of polynomials modulo primes, and cycle types of the Galois groups of polynomials. One remarkable example is the removal of all artificial constraints from the Kummer-Dedekind Theorem that relates splitting and factorization patterns. Finally, we present an elementary proof that the discriminant of the splitting field of a monic irreducible polynomial with integer coefficients has a computable upper bound in terms of the coefficients. This result, combined with one of Lagarias et al., shows that tests of polynomials for the cycle types of the Galois group are conclusive. In particular, the Galois groups of monic irreducible cubics, quartics, and quintics with integer coefficients can be completely determined in finitely many steps (though not necessarily in one's lifetime).
The one-particle exchange in the double folded model is analyzed. To this aim the Extended Thomas-Fermi approach to the one-body density matrix is used. The nucleon- nucleon force with Yukawa, Gauss and Coulomb-type form factors are considered. The energy dependence of the exchange part of the double folded potential is investigated and a comparison of the present approach with former ones is carried out.
The Milne-Eddington approximation provides an analytic and simple solution to the radiative transfer equation. It can be easily implemented in inversion codes that are used to fit spectro-polarimetric observations to infer average values of the magnetic field vector and the line-of-sight velocity of the solar plasma. However, it is in principle restricted to spectral lines formed under local thermodynamic conditions. We show that a simple modification in the linear source function of the Milne-Eddington approximation is sufficient to infer relevant physical parameters from spectral lines that deviate from local thermodynamic equilibrium. This is not a new modification for the solar community but it has been forgotten for quite some time To check the validity of such approximation we make use of the Mg I b2 and the Ca II lines. We first study the influence of these new terms on the profile shape by means of the response functions. Then, we test the performance of an inversion code including such modification against the presence of noise. The approximation is also tested with realistic spectral lines generated with the RH numerical radiative transfer code. Finally, we confront the code with synthetic profiles generated from magneto-hydrodynamic simulations.
High temperature superconductivity has been found in many kinds of compounds built from planes of Cu and O, separated by spacer layers. Understanding why critical temperatures are so high has been the subject of numerous investigations and extensive controversy. To realize high temperature superconductivity, parent compounds are either hole-doped, such as {La$_{2}$CuO$_4$} (LCO) with Sr (LSCO), or electron doped, such as {Nd$_{2}$CuO$_4$} (NCO) with Ce (NCCO). In the electron doped cuprates, the antiferromagnetic phase is much more robust than the superconducting phase. However, it was recently found that the reduction of residual out-of-plane apical oxygens dramatically affects the phase diagram, driving those compounds to a superconducting phase. Here we use a recently developed first principles method to explore how displacement of the apical oxygen (A-O) in LCO affects the optical gap, spin and charge susceptibilities, and superconducting order parameter. By combining quasiparticle self-consistent GW (QS\emph{GW}) and dynamical mean field theory (DMFT), that LCO is a Mott insulator; but small displacements of the apical oxygens drive the compound to a metallic state through a localization/delocalization transition, with a concomitant maximum $d$-wave order parameter at the transition. We address the question whether NCO can be seen as the limit of LCO with large apical displacements, and elucidate the deep physical reasons why the behaviour of NCO is so different than the hole doped materials. We shed new light on the recent correlation observed between T$_c$ and the charge transfer gap, while also providing a guide towards the design of optimized high-Tc superconductors. Further our results suggest that strong correlation, enough to induce Mott gap, may not be a prerequisite for high-Tc superconductivity.
We show that the changes in the electronic density of states (DOS) in graphene induced by impurity scattering with short-range potentials are completely different from those caused by the long-range Coulomb potential. The spectral weight of the state that eventually disappears into the valence band (as the strength of scattering increases) does not transform into a resonance state. Therefore no unusual screening effects related to a redistribution of the density of states in the valence band are observed. The states induced by the short-range impurities in graphene, therefore, have distinctively different properties compared with the long-range potential case. These properties, in fact, closely resemble the case of a short-range single impurity in other bipartite lattices, such as the square, body centered cubic, and simple cubic lattices.
We present seven epochs of spectroscopy on the quadruply imaged quasar SDSS J1004+4112, spanning observed-frame time delays from 1 to 322 days. The spectra reveal differences in the emission lines between the lensed images. Specifically, component A showed a strong enhancement in the blue wings of several high-ionization lines relative to component B, which lasted at least 28 days (observed frame) then faded. Since the predicted time delay between A and B is <30 days, our time coverage suggests that the event was not intrinsic to the quasar. We attribute these variations to microlensing of part of the broad emission line region of the quasar, apparently resolving structure in the source plane on a scale of ~10^{16} cm at z=1.734. In addition, we observed smaller differences in the emission line profiles between components A and B that persisted throughout the time span, which may also be due to microlensing or millilensing. Further spectroscopic monitoring of this system holds considerable promise for resolving the structure of the broad emission line region in quasars.
The tails of the distribution of a mean zero, variance $\sigma^2$ random variable $Y$ satisfy concentration of measure inequalities of the form $\mathbb{P}(Y \ge t) \le \exp(-B(t))$ for $$ B(t)=\frac{t^2}{2( \sigma^2 + ct)} \quad \mbox{for $t \ge 0$, and} \quad B(t)=\frac{t}{c}\left( \log t - \log \log t - \frac{\sigma^2}{c}\right) \quad \mbox{for $t>e$} $$ whenever there exists a zero biased coupling of $Y$ bounded by $c$, under suitable conditions on the existence of the moment generating function of $Y$. These inequalities apply in cases where $Y$ is not a function of independent variables, such as for the Hoeffding statistic $Y=\sum_{i=1}^n a_{i\pi(i)}$ where $A=(a_{ij})_{1 \le i,j \le n} \in \mathbb{R}^{n \times n}$ and the permutation $\pi$ has the uniform distribution over the symmetric group, and when its distribution is constant on cycle type.
The field of single atom catalysis (SAC) has expanded greatly in recent years. While there has been much success developing new synthesis methods, a fundamental disconnect exists between most experiments and the theoretical computations used to model them. The real catalysts are based on powder supports, which inevitably contain a multitude of different facets, different surface sites, defects, hydroxyl groups, and other contaminants due to the environment. This makes it extremely difficult to determine the structure of the active SAC site using current techniques. To be tractable, computations aimed at modelling SAC utilize periodic boundary conditions and low index facets of an idealized support. Thus the reaction barriers and mechanisms determined computationally represent, at best, a plausibility argument, and there is a strong chance that some critical aspect is omitted. One way to better understand what is plausible is by experimental modelling, i.e. comparing the results of computations to experiments based on precisely defined single-crystalline supports prepared in an ultrahigh vacuum (UHV) environment. In this article, we review the status of the surface science literature as it pertains to SAC. We focus on experimental work on supports where the site of the metal atom are unambiguously determined from experiment, in particular the surfaces of rutile and anatase TiO2, the iron oxides Fe2O3 and Fe3O4, as well as CeO2 and MgO. Much of this work is based on scanning probe microscopy in conjunction with spectroscopy, and we highlight the remarkably few studies in which metal atoms are stable on low index surfaces of typical supports. In a perspective, we discuss the possibility for expanding such studies into other relevant supports.
We analyze the longest-range two-pion exchange contributions to the three-nucleon force at leading-loop order in the framework of heavy-baryon chiral effective field theory with explicit $\Delta(1232)$ degrees of freedom. All relevant low-energy constants which appear in the calculation are determined from pion-nucleon scattering. Comparing our results with the ones obtained in the $\Delta$-less theory at N4LO, we find effects of the $\Delta$ isobar for this particular topology to be rather well represented in terms of resonance saturation of various low-energy constants in the $\Delta$-less approach.
Transfinite graphs have been defined and examined in a variety of prior works, but transfinite digraphs had not as yet been investigated. The present work embarks upon such a task. As with the ordinals, transfinite digraphs appear in a hierarchy of ranks indexed by the countable ordinals. The digraphs of rank 0 are the conventional digraphs. Those of rank 1 are constructed by defining certain extremities of 0-ranked digraphs, and then partitioning those extremities to obtain vertices of rank 1. Then, digraphs of rank 0 are connected together at those vertices of rank 1 to obtain a digraph of rank 1. This process can be continued through the natural-number ranks. However, to achieve a digraph whose rank is the first infinite ordinal $\omega$ (i.e., the first limit ordinal), a special kind of transfinite digraph, which we call a digraph with an "arrow rank" must first be constructed in a way different from those of natural-number rank. Then, digraphs of still higher ranks can be constructed in a way similar to that for the natural-number ranked digraphs. However, just before each limit-ordinal rank, a digraph of arrow rank must be set up.
Ion trap quantum hardware promises to provide a computational advantage over classical computing for specific problem spaces while also providing an alternative hardware implementation path to cryogenic quantum systems as typified by IBM's quantum hardware. However, programming ion trap systems currently requires both strategies to mitigate high levels of noise and also tools to ease the challenge of programming these systems with pulse- or gate-level operations.   This work focuses on improving the state-of-the-art for quantum programming of ion trap testbeds through the use of a quantum language specification, QCOR, and by demonstrating multi-level optimizations at the language, intermediate representation, and hardware backend levels. We implement a new QCOR/XACC backend to target a general ion trap testbed and then demonstrate the usage of multi-level optimizations to improve circuit fidelity and to reduce gate count. These techniques include the usage of a backend-specific numerical optimizer and physical gate optimizations to minimize the number of native instructions sent to the hardware. We evaluate our compiler backend using several QCOR benchmark programs, finding that on present testbed hardware, our compiler backend maintains the number of two-qubit native operations but decreases the number of single-qubit native operations by 1.54 times compared to the previous compiler regime. For projected testbed hardware upgrades, our compiler sees a reduction in two-qubit native operations by 2.40 times and one-qubit native operations by 6.13 times.
We propose a class of linear elastic three-dimensional metamaterials for which the effective parameters bulk modulus and mass density can be adjusted independently over a large range|which is not possible for ordinary materials. First, we systematically evaluate the static mechanical properties and the phonon dispersion relations. We show that the two are quantitatively consistent in the long-wavelength limit. To demonstrate the feasibility, corresponding fabricated polymer microstructures are presented. Finally, we discuss calculations for laminates composed of alternating layers of two different metamaterials with equal bulk modulus yet different mass density. This leads to metamaterials with effectively anisotropic uniaxial dynamic mass density tensors.
In this paper, we study the Carlitz's degenerate Bernoulli numbers and polynomials and give some formulae and identities related to those numbers and polynomials.
HR 8799 is an hF0 mA5 gamma Doradus, lambda Bootis, Vega-type star best known for hosting four directly imaged candidate planetary companions. Using the CHARA Array interferometer, we measure HR 8799's limb-darkened angular diameter to be 0.342 +/- 0.008 mas; this is the smallest interferometrically measured stellar diameter to date, with an error of only 2%. By combining our measurement with the star's parallax and photometry from the literature, we greatly improve upon previous estimates of its fundamental parameters, including stellar radius (1.44 +/- 0.06 R_Sun), effective temperature (7193 +/- 87 K, consistent with F0), luminosity (5.05 +/- 0.29 L_Sun), and the extent of the habitable zone (1.62 AU to 3.32 AU). These improved stellar properties permit much more precise comparisons with stellar evolutionary models, from which a mass and age can be determined, once the metallicity of the star is known. Considering the observational properties of other lambda Bootis stars and the indirect evidence for youth of HR 8799, we argue that the internal abundance, and what we refer to as the effective abundance, is most likely near-solar. Finally, using the Yonsei-Yale evolutionary models with uniformly scaled solar-like abundances, we estimate HR 8799's mass and age considering two possibilities: 1.516 +0.038/-0.024 M_Sun and 33 +7/-13 Myr if the star is contracting toward the zero age main-sequence or 1.513 +0.023/-0.024 M_Sun and 90 +381/-50 Myr if it is expanding from it. This improved estimate of HR 8799's age with realistic uncertainties provides the best constraints to date on the masses of its orbiting companions, and strongly suggests they are indeed planets. They nevertheless all appear to orbit well outside the habitable zone of this young star.
The charged particles produced in heavy ion collisions consist of two parts: One is from the freeze-out of hot and dense matter formed in collisions. The other is from the leading particles. In this paper, the hot and dense matter is assumed to expand according to the hydrodynamic model including phase transition and decouples into particles via the prescription of Cooper-Frye. The leading particles are as usual supposed to have Gaussian rapidity distributions with the number equaling that of participants. The investigations of this paper show that, unlike low energy situations, the leading particles are essential in describing the pseudorapidity distributions of charged particles produced in high energy heavy ion collisions. This might be due to the different transparencies of nuclei at different energies.
In the first two papers of this series, Larsen et al (2010a,b) describe our faint CCD survey in the inner Galaxy and map the over-density of Thick Disk stars in Quadrant I (Q1) to 5 kpc or more along the line of sight. The regions showing the strongest excess are above the density contours of the bar in the Galactic disk. In this third paper on the asymmetric Thick Disk, we report on radial velocities and derived metallicity parameters for over 4000 stars in Q1, above and below the plane and in Q4 above the plane. We confirm the corresponding kinematic asymmetry first reported by Parker et al. (2004), extended to greater distances and with more spatial coverage. The Thick Disk stars in Q1 have a rotational lag of 60 -- 70 km/s relative to circular rotation, and the Metal-Weak Thick Disk stars have an even greater lag of 100 km/s. Both lag their corresponding populations in Q4 by approximately 30 km/s. Interestingly, the Disk stars in Q1 also appear to participate in the rotational lag by about 30 km/s. The enhanced rotational lag for the Thick Disk in Q1 extends to 4 kpc or more from the Sun. At 3 to 4 kpc, our sight lines extend above the density contours on the near side of the bar, and as our lines of sight pass directly over the bar the rotational lag appears to decrease. This is consistent with a "gravitational wake" induced by the rotating bar in the Disk which would trap and pile up stars behind it. We conclude that a dynamical interaction with the stellar bar is the most probable explanation for the observed kinematic and spatial asymmetries.
In existing linear response theories for adiabatically driven cyclic heat engines, Onsager symmetry is identified only phenomenologically, and a relation between global and local Onsager coefficients, defined over one cycle and at any instant of a cycle, respectively, is not derived. To address this limitation, we develop a linear response theory for the speed of adiabatically changing parameters and temperature differences in generic Gaussian heat engines obeying Fokker--Planck dynamics. We establish a hierarchical relationship between the global linear response relations, defined over one cycle of the heat engines, and the local ones, defined at any instant of the cycle. This yields a detailed expression for the global Onsager coefficients in terms of the local Onsager coefficients. Moreover, we derive an efficiency bound, which is tighter than the Carnot bound, for adiabatically driven linear irreversible heat engines based on the detailed global Onsager coefficients. Finally, we demonstrate the application of the theory using the simplest stochastic Brownian heat engine model.
The Sommerfeld enhancement plays an important role in dark matter (DM) physics, and can significantly enhance the annihilation cross section of non-relativistic DM particles. In this paper, we study the effect of neutrino forces, which are generated by the exchange of a pair of light neutrinos, on the Sommerfeld enhancement. We demonstrate that in certain cases, a neutrino force can cause a significant correction to the Sommerfeld enhancement. Models that can realise DM-neutrino interactions and sizeable Sommerfeld enhancement are also briefly discussed, together with the impacts on DM phenomenology of neutrino forces.
We study the number of non-isomorphic functional graphs of affine-linear transformations from (\F_q)^n to itself, and we prove upper and lower bounds on this quantity for n large. As a corollary to our result, we prove bounds on the number of conjugacy classes in the symmetric group S_{q^n} that intersect AGL_n(q).
We give a full list of known $\mathcal{N}=1$ supersymmetric quantum field theories related by the Seiberg electric-magnetic duality conjectures for $SU(N), SP(2N)$ and $G_2$ gauge groups. Many of the presented dualities are new, not considered earlier in the literature. For all these theories we construct superconformal indices and express them in terms of elliptic hypergeometric integrals. This gives a systematic extension of the related Romelsberger and Dolan-Osborn results. Equality of indices in dual theories leads to various identities for elliptic hypergeometric integrals. About half of them were proven earlier, and another half represents new challenging conjectures. In particular, we conjecture a dozen new elliptic beta integrals on root systems extending the univariate elliptic beta integral discovered by the first author.
We report on X-ray observations of the radio-intermediate, X-ray bright Seyfert 1 galaxy, III Zw 2, obtained with XMM-Newton, Suzaku, and Swift over the past 17-years. The source brightness varies significantly over yearly time scales, but more modestly over periods of days. Pointed observations with XMM-Newton in 2000 and Suzaku in 2011 show spectral differences despite comparable X-ray fluxes. The Suzaku spectra are consistent with a power law continuum and a narrow Gaussian emission feature at ~6.4 keV, whereas the earlier XMM-Newton spectrum requires a broader Gaussian profile and soft-excess below ~2 keV. A potential interpretation is that the primary power law emission, perhaps from a jet base, preferentially illuminates the inner accretion disc in 2000, but the distant torus in 2011. The interpretation could be consistent with the hypothesised precessing radio jet in III Zw 2 that may have originated from disc instabilities due to an ongoing merging event.
We present multi-wavelength imaging and near-IR spectroscopy for ten gravitationally lensed galaxies at 0.9<z<2.5 selected from a new, large sample of strong lens systems in the Sloan Digital Sky Survey (SDSS) DR7. We derive stellar masses from the rest-frame UV to near-IR spectral energy distributions, star formation rates (SFR) from the dust-corrected Ha flux, and metallicities from the [N II]/Ha flux ratio. We combine the lensed galaxies with a sample of sixty star-forming galaxies from the literature in the same redshift range for which measurements of [N II]/Ha have been published. Due to the lensing magnification, the lensed galaxies probe intrinsic stellar masses that are on average a factor of 11 lower than have been studied so far at these redshifts. They have specific star formation rates that are an order of magnitude higher than seen for main-sequence star-forming galaxies at z~2. We measure an evolution of 0.16+/-0.06 dex in the mass-metallicity relation between z~1.4 and z~2.2. In contrast to previous claims, the redshift evolution is smaller at low stellar masses. We do not see a correlation between metallicity and SFR at fixed stellar mass. The combined sample is in general agreement with the local fundamental relation between metallicity, stellar mass and SFR from Mannucci et al. (2010, 2011). Using the Kennicutt-Schmidt law to infer gas fractions, we investigate the importance of gas inflows and outflows on the shape of the mass-metallicity relation using simple analytical models. This suggests that the Maiolino et al.(2008) calibration of the [N II]/Ha flux ratio is biased high. We conclude that both an absolute metallicity calibration and direct measurements of the gas mass are needed to use the observed mass-metallicity relation to gain insight into the impact of gas flows on the chemical evolution of galaxies.
The magnetic properties in manganite have been found to be highly sensitive to the doping and structural manipulations. Here, we report the effect of B-site bismuth doping on the magnetic and transport properties in La0.5Ca0.5Mn1-xBixO3 (LCMBO) thin films (for x = 0, 0.02 and 0.05) for high-efficiency spintronics devices. For thin film of LCMBO (with x = 0.02), a significant increase in the magnetization and ferromagnetic ordering temperature (TC) are observed. Also, about 98% magnetoresistance (MR) and unusually large (~ 42%) anisotropic magnetoresistance (AMR) is observed at 50 K in the same LCMBO (for x = 0.02) thin film. This observed improvement in TC, MR and AMR in LCMBO (with x = 0.02) thin film may be attributed to the modulation of the trapped electrons through JT-distortions due to the replacement of Mn+3 ions by larger Bi+3 ions. With further increase in bismuth doping (for x = 0.05) at the B-site, a significant decrease in magnetization and TC have been observed.