ShantanuT01/DACTYL-Pretraining huggingface dataset:
Here we investigate meaningful families of vector bundles on a very general polarized $K3$ surface $(X,H)$ and on the corresponding Hyper--Kaehler variety given by the Hilbert scheme of points $X^{[k]}:= {\rm Hilb}^k(X)$, for any integer $k \geqslant 2$. In particular, we prove results concerning bigness and stability of such bundles.   First, we give conditions on integers $n$ such that the twist of the tangent bundle of $X$ by the line bundle $nH$ is big and stable on~$X$; we then prove a similar result for a natural twist of the tangent bundle of $X^{[k]}$. Next, we prove global generation, bigness and stability results for tautological bundles on $X^{[k]}$ arising either from line bundles or from Mukai-Lazarsfeld bundles, as well as from Ulrich bundles on $X$, using a careful analysis on Segre classes and numerical computations for $k = 2, 3$.
We present the catalog of 1459 eclipsing binary stars detected in the central 2.4 square degree area of the Small Magellanic Cloud during the OGLE-II microlensing search. The sample includes objects brighter than I=20 mag with periods ranging from about 0.3 to 250 days. The average completeness of the catalog is about 80%. Statistics of the entire sample and well detached systems, suitable for distance determination, are also presented.   The catalog, finding charts and BVI photometry data for all objects are available from the OGLE Internet archive.
The energy-momentum conservation law is used to investigate the interaction of pulses in the framework of nonlinear electrodynamics with Lorentz-invariant constitutive relations. It is shown that for the pulses of the arbitrary shape the interaction results in phase shift only.
Theoretical models of stars constitute a fundamental bedrock upon which much of astrophysics is built, but large swaths of model parameter space remain uncalibrated by observations. The best calibrators are eclipsing binaries in clusters, allowing measurement of masses, radii, luminosities, and temperatures, for stars of known metallicity and age. We present the discovery and detailed characterization of PTFEB132.707+19.810, a P=6.0 day eclipsing binary in the Praesepe cluster ($\tau$~600--800 Myr; [Fe/H]=0.14$\pm$0.04). The system contains two late-type stars (SpT$_P$=M3.5$\pm$0.2; SpT$_S$=M4.3$\pm$0.7) with precise masses ($M_p=0.3953\pm0.0020$~$M_{\odot}$; $M_s=0.2098\pm0.0014$~$M_{\odot}$) and radii ($R_p=0.363\pm0.008$~$R_{\odot}$; $R_s=0.272\pm0.012$~$R_{\odot}$). Neither star meets the predictions of stellar evolutionary models. The primary has the expected radius, but is cooler and less luminous, while the secondary has the expected luminosity, but is cooler and substantially larger (by 20%). The system is not tidally locked or circularized. Exploiting a fortuitous 4:5 commensurability between $P_{orb}$ and $P_{rot,prim}$, we demonstrate that fitting errors from the unknown spot configuration only change the inferred radii by <1--2%. We also analyze subsets of data to test the robustness of radius measurements; the radius sum is more robust to systematic errors and preferable for model comparisons. We also test plausible changes in limb darkening, and find corresponding uncertainties of ~1%. Finally, we validate our pipeline using extant data for GU Boo, finding that our independent results match previous radii to within the mutual uncertainties (2--3%). We therefore suggest that the substantial discrepancies are astrophysical; since they are larger than for old field stars, they may be tied to the intermediate age of PTFEB132.707+19.810.
We extend a previous work on the intrinsic spectral properties and energetics of GRBs with known redshift based on 12 BeppoSAX events by including in the sample a total of 10 more events detected either by BATSE, BeppoSAX or HETE-2. An indication of a trend of the total isotropic equivalent radiated energy, E_rad, with redshift is found and, remarkably, the previously found relationship between the peak energy of the rest-frame nuFnu spectrum, E_p,rest , and E_rad is confirmed and its significance increased. The implications of these results are briefly discussed in the framework of standard models for the prompt emission of GRBs.
We have constructed a new formalism for describing a situation with {\color{red} several (dual) strings} present at a time, a {\color{red} string field theory}, by means of a constituent / a strings from objects picture similar to, but importantly different from the "bits" by Charles Thorn\cite{Thorn}. Our "objects" (essentially the bits) represent rather a making a lattice in the {\color{red} light cone variables} on the string. The remarkable feature and simplicity of our formalism is, that the "objects" do {\color{red} NOT interact}, basically just run or sit trivially fixed. {\color{red} Scattering is a fake} in our formalism. This opens also up for hoping for generalizations inspired by hadrons with their partons all having Bjorken variable $x=0$, and thus infinitely many constituents. The p-adic string is an example.
We revise the sunspot observations made by Galileo Galilei and Christoph Scheiner in the context of their controversy on the nature of sunspots. Their sunspot records not included in the current sunspot group database, used as a basis to calculate the sunspot group number, are analyzed. Within the documentary sources consulted in this work, we can highlight the sunspot observations by Scheiner included in the letters sent under the pseudonym Apelles to Marcus Welser and the first sunspot observations made by Galileo, which can be consulted in Le opere di Galileo Galilei. These sunspot observations would extend the temporal coverage for these two observers and filling some gaps in the current group database in the earliest period where the data available is sparse. Moreover, we have detected changes in the quality of the sunspot drawings made by Galileo and Scheiner in their observation series affecting to the number of groups recorded by the two observers. We also compare these records with sunspot observations made by other astronomers of that time. According to this comparison and regarding the same observation days, Scheiner was generally the astronomer who reported more sunspot groups while Harriot, Cigoli, and Galileo recorded a similar number of groups. We conclude these differences are mainly because of the observational method used by the observers.
We use the measured fluxes of polycyclic aromatic hydrocarbon (PAH) emission features at 6.2, 7.7, 8.6, 11.0 and 11.2 $\mu$m in the reflection nebula NGC 2023 to carry out a principal component analysis (PCA) as a means to study previously reported variations in the PAH emission. We find that almost all of the variations (99%) can be explained with just two parameters -- the first two principal components (PCs). We explore the characteristics of these PCs and show that the first PC ($PC_{1}$), which is the primary driver of the variation, represents the amount of emission of a mixture of PAHs with ionized species dominating over neutral species. The second PC ($PC_{2}$) traces variations in the ionization state of the PAHs across the nebula. Correlations of the PCs with various PAH ratios show that the 6.2 and 7.7 $\mu$m bands behave differently than the 8.6 and 11.0 $\mu$m bands, thereby forming two distinct groups of ionized bands. We compare the spatial distribution of the PCs to the physical conditions, in particular to the strength of the radiation field, $G_{0}$, and the $G_{0}/n_{H}$ ratio and find that the variations in $PC_{2}$, i.e. the ionization state of PAHs are strongly affected by $G_{0}$ whereas the amount of PAH emission (as traced by $PC_{1}$) does not depend on $G_0$.
We present an approach to obtain new forms of the nuclear electromagnetic current, which is based on an integral form of the continuity equation. The procedure can be used to restore current conservation in model calculations in which the continuity equation is not verified. Besides, it provides, as a particular result, the so-called Siegert's form of the nuclear current, first obtained by Friar and Fallieros by extending Siegert's theorem to arbitrary values of the momentum transfer. The new currents are explicitly conserved and permit a straightforward analysis of their behavior at both low and high momentum transfers. The results are illustrated with a simple nuclear model which includes a harmonic oscillator mean potential.
We present the first magneto-absorption studies of coupled electron double layers in the quantum Hall regime. Optical absorption spectra in the vicinity of total filling factor nu = 1 reveal intriguing behavior that have no analog in the single electron layer nu = 1 state and demonstrate the interplay between single-particle tunneling and inter-layer Coulomb effects. The spectra provide direct evidence of a ground-state that evolves from a region dominated by single-particle tunneling to a regime in which inter-layer Coulomb interactions determine the nature of the ground-state. Moreover the spectra provide the first direct evidence that the incompressible ground-state at nu = 1 in the many-body regime is not fully pseudospin polarized and is sensitive to the effects of quantum fluctuations in the pseudospin variable.
In this paper we construct a modular form f of weight one attached to an imaginary quadratic field K. This form, which is non-holomorphic and not a cusp form, has several curious properties. Its negative Fourier coefficients are non-zero precisely for neqative integers -n such that n >0 is a norm from K, and these coefficients involve the exponential integral. The Mellin transform of f has a simple expression in terms of the Dedekind zeta function of K and the difference of the logarithmic derivatives of Riemann zeta function and of the Dirichlet L-series of K. Finally, the positive Fourier coefficients of f are connected with the theory of complex multiplication and arise in the work of Gross and Zagier on singular moduli.
The general theory of N = 1 supergravity with supermatter is studied using a canonical approach. The supersymmetry and gauge constraint generators are found. The framework is applied to the study of a Friedmann minisuperspace model. We consider a Friedmann k = + 1 geometry and a family of spin-0 as well as spin-1 gauge fields together with their odd (anti-commuting) spin-1/2 partners. The quantum supersymmetry constraints give rise to a set of first-order coupled partial differential equations for the components of the wave function. As an intermediate stage in this project, we put both the spin-1 field and its fermionic partner equal to zero. The physical states of our simplified model correspond effectively to those of a mini-superspace quantum cosmological model possessing N=4 local supersymmetry coupled to complex scalars with spin-1/2 partners. The different supermatter models are given by specifying a K\"ahler metric for the scalars; the allowed quantum states then depend on the K\"ahler geometries. For the cases of spherically symmetric and flat K\"ahler geometries we find the general solution for the quantum state with a very simple form. However, although they allow a Hartle-Hawking state, they do not allow a wormhole state.
In this work, we show that uniform integrability is not a necessary condition for central limit theorems (CLT) to hold for normalized multilevel Monte Carlo (MLMC) estimators and we provide near optimal weaker conditions under which the CLT is achieved. In particular, if the variance decay rate dominates the computational cost rate (i.e., $\beta > \gamma$), we prove that the CLT applies to the standard (variance minimizing) MLMC estimator.   For other settings where the CLT may not apply to the standard MLMC estimator, we propose an alternative estimator, called the mass-shifted MLMC estimator, to which the CLT always applies.   This comes at a small efficiency loss: the computational cost of achieving mean square approximation error $\mathcal{O}(\epsilon^2)$ is at worst a factor $\mathcal{O}(\log(1/\epsilon))$ higher with the mass-shifted estimator than with the standard one.
Long-term records of sunspot number and concentrations of cosmogenic radionuclides (10Be and 14C) on the Earth reveal the variation of the Sun's magnetic activity over hundreds and thousands of years. We identify several clear periods in sunspot, 10Be, and 14C data as 1000, 500, 350, 200 and 100 years. We found that the periods of the first five spherical harmonics of the slow magnetic Rossby mode in the presence of a steady toroidal magnetic field of 1200-1300 G in the lower tachocline are in perfect agreement with the time scales of observed variations. The steady toroidal magnetic field can be generated in the lower tachocline either due to the steady dynamo magnetic field for low magnetic diffusivity or due to the action of the latitudinal differential rotation on the weak poloidal primordial magnetic field, which penetrates from the radiative interior. The slow magnetic Rossby waves lead to variations of the steady toroidal magnetic field in the lower tachocline, which modulate the dynamo magnetic field and consequently the solar cycle strength. This result constitutes a key point for long-term prediction of the cycle strength. According to our model, the next deep minimum in solar activity is expected during the first half of this century.
We present stellar population age and metallicity trends for a sample of 59 S0 galaxies based on optical SDSS and NIR J & H photometry. When combined with optical g and r passband imaging data from the SDSS archive and stellar population models, we obtain radial age and metallicity trends out to at least 5 effective radii for most of the galaxies in our sample. The sample covers a range in stellar mass and light concentration. We find an average central light-weighted age of ~ 4 Gyr and central metallicity [Z/H] ~ 0.2 dex. Almost all galaxies show a negative metallicity gradient from the center out, with an average value of Delta[Z/H]/Delta(log(r/Re)) = -0.6. An age increase, decrease, and minimal change with radius is observed for 58%, 19%, and 23%, respectively, for a mean age gradient of Delta(age)/Delta(log(r/Re)) = 2.3 Gyr dex^{-1}. For 14 out of 59 galaxies, the light-weighted age of the outer region is greater than 10 Gyr. We find that galaxies with both lower mass and lower concentration have younger light-weighted ages and lower light-weighted metallicities. This mass-metallicity relation extends into the outer regions of our S0 galaxies. Our results are consistent with the formation of S0 galaxies through the transformation of spiral galaxy disks. Determining the structural component that makes up the outer region of galaxies with old outksirts is a necessary step to understand the formation history of S0 galaxies.
The destruction of quantum coherence can pump energy into a system. For our examples this is paradoxical since the destroyed correlations are ordinarily considered negligible. Mathematically the explanation is straightforward and physically one can identify the degrees of freedom supplying this energy. Nevertheless, the energy input can be calculated without specific reference to those degrees of freedom.
Electromagnetic field is considered in the framework of Clifford algebra $\C_2$ over a field of complex numbers. It is shown here that a modulo 2 periodicity of complex Clifford algebras may be connected with electromagnetic field.
The Chandra X-ray Observatory (CXO) imaged the high-mass gamma-ray binary (HMGB) HESS J0632+057 with the Advanced CCD Imaging Spectrometer (ACIS). We analyzed the CXO data together with 967 ks of archival Swift-XRT observations. On arcsecond scales we find a hint of asymmetric extended emission. On arcminute scales, a region of extended emission ("the blob"), located $\sim$5.5' east of the binary, is seen in both the CXO-ACIS and the Swift-XRT images. The blob does not have a counterpart in the radio, NIR, IR, or optical images. The ACIS spectrum of the blob fits either an absorbed power-law model with photon index $\Gamma\simeq2.6$, or a thermal plasma model with $kT\simeq3$ keV. Since the blob's absorbing column, $N_{\rm H}$, is significantly larger than that of the binary we conclude that the blob and binary are not directly related. The somewhat larger very deep XRT image suggests that the binary may be located within a shell (or cavity). The four ACIS spectra taken within the $\sim$20 day interval near the light curve minimum suggests that the $N_{\rm H}$ is varying on timescales of days, possibly due to the inhomogeneous circumbinary environment. The XRT spectra extracted from the wider orbital phase intervals support significant changes in $N_{\rm H}$ near the light curve maximum/minimum, which may be responsible for the substantial systematic residuals seen near 1 keV, and provide tentative evidence for a Fe line at 6.4 keV. We find no significant periodic signal in the ACIS data up to 0.156 Hz.
We use analytic estimates and numerical simulations of test particles interacting with magnetohydrodynamic (MHD) turbulence to show that subsonic MHD turbulence produces efficient second-order Fermi acceleration of relativistic particles. This acceleration is not well-described by standard quasi-linear theory but is a consequence of resonance broadening of wave-particle interactions in MHD turbulence. We provide momentum diffusion coefficients that can be used for astrophysical and heliospheric applications and discuss the implications of our results for accretion flows onto black holes. In particular, we show that particle acceleration by subsonic turbulence in radiatively inefficient accretion flows can produce a non-thermal tail in the electron distribution function that is likely important for modeling and interpreting the emission from low luminosity systems such as Sgr A* and M87.
Cosmic ray antiprotons provide an important probe for the study of cosmic-ray propagation in the interstellar space and to investigate the existence of Galactic dark matter. Cosmic rays are hampered by the Moon, therefore a deficit of cosmic rays in its direction is expected (the so-called "Moon shadow"). The Earth-Moon system acts as a magnetic spectrometer. In fact, due to the geomagnetic field the center of the Moon shifts westward by an amount depending on the primary cosmic ray energy. Paths of primary antiprotons are therefore deflected in an opposite sense in their way to the Earth. This effect allows, in principle, the search of antiparticles in the opposite direction of the observed Moon shadow.   The ARGO-YBJ experiment, in stable data taking since November 2007 with an energy threshold of a few hundreds of GeV, is observing the Moon shadow with high statistical significance. Using about 1 year data, an upper limit of the antip/p flux ratio in the few-TeV energy region is set to a few percent with a confidence level of 90%.
We present optical-line gas metallicity diagnostics established by the combination of local SDSS galaxies and the largest compilation of extremely metal-poor galaxies (EMPGs) including new EMPGs identified by the Subaru EMPRESS survey. A total of 103 EMPGs are included that cover a large parameter space of magnitude (Mi=-19 to -7) and H-beta equivalent width (10-600 Ang), i.e., wide ranges of stellar mass and star-formation rate. Using reliable metallicity measurements of the direct method for these galaxies, we derive the relationships between strong optical-line ratios and gas-phase metallicity over the range of 12+log(O/H)=~6.9-8.9 corresponding to 0.02-2 solar metallicity Zsun. We confirm that R23-index, ([OIII]+[OII])/H-beta, is the most accurate metallicity indicator with the metallicity uncertainty of 0.14 dex over the range among various popular metallicity indicators. The other metallicity indicators show large scatters in the metal-poor range (<0.1 Zsun). It is explained by our CLOUDY photoionization modeling that, unlike R23-index, the other metallicity indicators do not use a sum of singly and doubly ionized lines and cannot trace both low and high ionization gas. We find that the accuracy of the metallicity indicators is significantly improved, if one uses H-beta equivalent width measurements that tightly correlate with ionization states. In this work, we also present the relation of physical properties with UV-continuum slope beta and ionization production rate xi_ion derived with GALEX data for the EMPGs, and provide local anchors of galaxy properties together with the optical-line metallicity indicators that are available in the form of ASCII table and useful for forthcoming JWST spectroscopic studies.
Galactic extinction is tested using galaxy number counts at low Galactic latitude obtained from five band photometry of the Sloan Digital Sky Survey. The spatial variation of galaxy number counts for low extinction regions of $E(B-V) < 0.15$ is consistent with the all-sky reddening map of Schlegel, Finkbeiner, & Davis (1998) and the standard extinction law. For higher extinction regions of $E(B-V) > 0.15$, however, the map of Schlegel et al.(1998) overestimates the reddening by a factor up to 1.4, which is likely ascribed to the departure from proportionality of reddening to infrared emissivity of dust. This result is consistent with the analysis of Arce & Goodman (1999) for the Taurus dark cloud complex.
Let $\{\xi_1,\xi_2,\ldots\}$ be a sequence of independent random variables, and $\eta$ be a counting random variable independent of this sequence. We consider conditions for $\{\xi_1,\xi_2,\ldots\}$ and $\eta$ under which the distribution function of the random sum $S_{\eta}=\xi_1+\xi_2+\cdots+\xi_{\eta}$ belongs to the class of consistently varying distributions. In our consideration, the random variables $\{\xi_1,\xi_2,\ldots\}$ are not necessarily identically distributed.
We study the size estimate problem for the two-phase shallow shell equations in this paper. Our aim is to derive bounds on the volume fraction of each phase assuming that the material properties of the two phases are given. The approach in this paper is based on the translation method. One of the key steps is to connect the shallow shell equations to the thin plate equation.
Several ways are demonstrated of how periodic potentials can be exploited for sorting molecules or other small objects which only differ by their chirality. With the help of a static bias force, the two chiral partners can be made to move along orthogonal directions. Time-periodic external forces even lead to motion into exactly opposite directions.
For the prescribed scalar curvature equation on $S^n$ ($n \ge 6$), we consider the situation where the number of bubbles tends to infinity in the Lyapunov-Schmidt (finite dimension) reduction method. In an outstanding paper by Wei and Yan, the special case where the bubbles are arranged "evenly" (close to a great circle) is considered. Here we are concerned with the generic scenario, where the bubbles are "planted" (arranged) in general position, in adjacent to the critical points of the prescribed function. The main interest of this article is to extract key information in the finite dimensional reduced functional, as well as in its first partial derivatives. Overall, there are two main contributions in the "expansions", namely, interaction between bubbles and curvature involvement. As each bubble becomes infinitesimally close to other bubbles in the neighborhood, the errors in the expansions are carefully estimated in terms of the geometric parameters. This lays the foundation for our next step on constructing blow-up sequences of solutions with dense blow-up points (clustered blow-up), where the (non-radial symmetric) prescribed scalar curvature function has non-isolated critical points.