ShantanuT01/DACTYL-Pretraining huggingface dataset:
We consider the Cauchy problem for plate equations with rotational inertia and frictional damping terms. We will derive asymptotic profiles of the solution in L^2-sense as time goes to infinity in the case when the initial data have high and low regularity, respectively. Especially, in the low regularity case of the initial data one encounters the regularity-loss structure of the solutions, and the analysis is more delicate. We employ the so-called Fourier splitting method combined with the explicit expression of the solutions (high frequency estimates) and the method due to Ikehata (low frequency estimates).
X-ray polarimetry promises to give new information about high-energy astrophysical sources, such as binary black hole systems, micro-quasars, active galactic nuclei, and gamma-ray bursts. We designed, built and tested a hard X-ray polarimeter X-Calibur to be used in the focal plane of the InFOCuS grazing incidence hard X-ray telescope. X-Calibur combines a low-Z Compton scatterer with a CZT detector assembly to measure the polarization of 10-80 keV X-rays making use of the fact that polarized photons Compton scatter preferentially perpendicular to the electric field orientation. X-Calibur achieves a high detection efficiency of order unity.
This paper is a written version of a talk on rare (FCNC) D meson decays as presented at the Electroweak Moriond 2002. The presentation proceeds in two parts. We first consider Standard Model predictions, taking into account both short-distance and long distance effects. Then several New Physics options (e.g. supersymmatry, strong dynamics, extra large dimenions, etc) are considered.
We study an antiferromagnetic order in the ground state of the half-filled Hubbard model on the Penrose lattice and investigate the effects of quasiperiodic lattice structure. In the limit of infinitesimal Coulomb repulsion $U \rightarrow +0$, the staggered magnetizations persist to be finite, and their values are determined by confined states, which are strictly localized with thermodynamics degeneracy. The magnetizations exhibit an exotic spatial pattern, and have the same sign in each of cluster regions, the size of which ranges from 31 sites to infinity. With increasing $U$, they continuously evolve to those of the corresponding spin model in the $U=\infty$ limit. In both limits of $U$, local magnetizations exhibit a fairly intricate spatial pattern that reflects the quasiperiodic structure, but the pattern differs between the two limits. We have analyzed this pattern change by a mode analysis by the singular value decomposition method for the fractal-like magnetization pattern projected into the perpendicular space.
This article is a survey of P. Katsylo's proof that the moduli space of smooth projective complex curves of genus 3 is rational. We hope to make the argument more comprehensible and transparent by emphasizing the underlying geometry in the proof and its key structural features.
The main objective of this work is to present a process to compute the Markov renewal matrix for Markov renewal processes with countable infinite spaces, which semi-Markov matrixes are immigration and death type and assume a tridiagonal form. These processes occur often in practical applications. And the difficulty in obtaining friendly results for that matrix is a great obstacle to its application in practical cases modelling. It is considered the application to the MMinf queue particular case.
We present a calculation of interference effects in Hjj production via gluon fusion and via vector boson fusion, respectively, beyond tree level. We reproduce results recently discussed in the literature, but go beyond this calculation by including a class of diagrams not considered previously. Special care is taken in developing a numerically stable and flexible parton level Monte-Carlo program which allows us to study cross sections and kinematic distributions within experimentally relevant selection cuts. Loop-induced interference contributions are found to exhibit kinematical distributions different in shape from vector boson fusion. Due to the small interference cross section and cancelation among different quark flavor contributions their impact on the signal process is found to be negligible in all regions of phase space, however.
Galactic winds are a key physical mechanism for understanding galaxy formation and evolution, yet empirical and theoretical constraints for the character of winds are limited and discrepant. Recent empirical models find that local star-forming galaxies have a deficit of oxygen that scales with galaxy stellar mass. The oxygen deficit provides unique empirical constraints on the magnitude of mass loss, composition of outflowing material and metal reaccretion onto galaxies. We formulate the oxygen deficit constraints so they may be easily implemented into theoretical models of galaxy evolution. We parameterize an effective metal loading factor which combines the uncertainties of metal outflows and metal reaccretion into a single function of galaxy virial velocity. We determine the effective metal loading factor by forward-fitting the oxygen deficit. The effective metal loading factor we derive has important implications for the implementation of mass loss in models of galaxy evolution.
LPL dominance over Steward is demonstrated through several lines of evidence including observations and modelling of previous April Fools day behavior. The decrease in Steward coolness is attributed to the departure of interesting graduate students from Steward that enrolled at LPL.
The \lq\lq effective geometry" formalism is used to study the perturbations of a perfect barotropic Newtonian self-gravitating rotating and compressible fluid coupled with gravitational backreaction. The case of a uniformly rotating polytrope with index $n=1$ is investigated, due to its analytical tractability. Special attention is devoted to the geometrical properties of the underlying background acoustic metric, focusing in particular on null geodesics as well as on the analog light cone structure.
We use a transformation due to Bekenstein to relate the ADM and Bondi masses of asymptotically-flat solutions of the Einstein equations with, respectively, scalar sources and conformal-scalar sources. Although the conformal-scalar energy-momentum tensor does not satisfy the Dominant Energy Condition one may, by this means, still conclude that the ADM mass is positive.
We present an analysis of mid-and far-infrared (IR) spectrum and spectral energy distribution (SED) of the LBV R71 in the LMC.This work aims to understand the overall contribution of high-mass LBVs to the total dust-mass budget of the interstellar medium (ISM) of the LMC and compare this with the contribution from low-mass asymptotic giant branch (AGB) stars. As a case study, we analyze the SED of R71. We compiled all the available photometric and spectroscopic observational fluxes from various telescopes for a wide wavelength range (0.36 -- 250\,$\mu$m). We determined the dust composition from the spectroscopic data, and derived the ejected dust mass, dust mass-loss rate, and other dust shell properties by modeling the SED of R71. We noted nine spectral features in the dust shell of R71 by analyzing Spitzer spectroscopic data. Among these, we identified three new crystalline silicate features. We computed our model spectrum by using 3D radiative transfer code MCMax. Our model calculation shows that dust is dominated by amorphous silicates, with some crystalline silicates, metallic iron, and a very tiny amount of polycyclic aromatic hydrocarbon (PAH) molecules. The presence of both silicates and PAHs indicates that the dust has a mixed chemistry. We derived a dust mass of 0.01 M$_\odot$, from which we arrive at a total ejected mass of $\approx$ 5 M$_\odot$. This implies a time-averaged dust mass-loss rate of 2.5$\times$10$^{-6}$ M$_\odot$\,yr$^{-1}$ with an explosion about 4000 years ago. We assume that the other five confirmed dusty LBVs in the LMC loose mass at a similar rate, and estimate the total contribution to the mass budget of the LMC to be $\approx$ 10$^{-5}$ M$_\odot$\,yr$^{-1}$, which is comparable to the contribution by all the AGB stars in the LMC. Based on our analysis on R71, we speculate that LBVs as a class may be an important dust source in the ISM of the LMC.
Blue and Visual photoelectric light curves have been achieved for the eclipsing binary SW Lac in 1995. Nine moments of minimum light were derived. Period of 0.320854 days have been determined as the mean of those derived from blue and visual observations. B and V light curves have been analyzed using W-D code where the system has been viewed through the ellipsoidal model. The system geometrical and physical parameters were determined and compared with those published recently.
An asymptotic formula is established for the number of rational points of bounded anticanonical height which lie on a certain Zariski dense subset of the biprojective hypersurface $x_1y_1^2+\dots+x_4y_4^2=0$ in $\mathbb{P}^3\times\mathbb{P}^3$. This confirms the modified Manin conjecture for this variety, in which the removal of a thin set of rational points is allowed.
We consider the non-local operator of variable order as follows   $$Lf(x)= \int_{\R^d\setminus\{0\}}\big(f(x+z)-f(x)-\<\nabla f(x),z\>   \I_{\{|z|\le 1\}}\big)\frac{n(x,z)}{|z|^{d+\alpha(x)}}\,dz.$$ Under mild conditions on $\alpha(x)$ and $n(x,z)$, we establish the H\"{o}lder regularity for the associated semigroups. The proof is based on the probabilistic coupling method, and it successfully applies to both stable-like processes in the sense of Bass and time-change of symmetric stable processes.
In this paper, we propose a novel method, X-Distill, to improve the self-supervised training of monocular depth via cross-task knowledge distillation from semantic segmentation to depth estimation. More specifically, during training, we utilize a pretrained semantic segmentation teacher network and transfer its semantic knowledge to the depth network. In order to enable such knowledge distillation across two different visual tasks, we introduce a small, trainable network that translates the predicted depth map to a semantic segmentation map, which can then be supervised by the teacher network. In this way, this small network enables the backpropagation from the semantic segmentation teacher's supervision to the depth network during training. In addition, since the commonly used object classes in semantic segmentation are not directly transferable to depth, we study the visual and geometric characteristics of the objects and design a new way of grouping them that can be shared by both tasks. It is noteworthy that our approach only modifies the training process and does not incur additional computation during inference. We extensively evaluate the efficacy of our proposed approach on the standard KITTI benchmark and compare it with the latest state of the art. We further test the generalizability of our approach on Make3D. Overall, the results show that our approach significantly improves the depth estimation accuracy and outperforms the state of the art.
In an age of large astronomical dateset and severe cosmological tensions, the case for model independent analyses is compelling. We present a set of 14 baryon acoustic oscillations measurements in thin redshift shells with 3% precision that were obtained by analyzing BOSS DR12 and eBOSS DR16 galaxies in the redshift range $0.32<z<0.66$. Thanks to the use of thin shells, the analysis is carried out using just redshifts and angles so that the fiducial model is only introduced when considering the mock catalogs, necessary for the covariance matrix estimation and the pipeline validation. We compare our measurements, with and without supernova data, to the corresponding constraints from Planck 2018, finding good compatibility. A Monte Python module for this likelihood is available at https://github.com/ranier137/angularBAO .
When the singlet-doublet fermion dark matter model is extended with additional $Z_2$--odd real singlet scalars, neutrino masses and mixings can be generated at one-loop level. In this work, we discuss the salient features arising from the combination of the two resulting simplified dark matter models. When the $Z_2$-lightest odd particle is a scalar singlet, $\operatorname{Br}(\mu\to e \gamma)$ could be measurable provided that the singlet-doublet fermion mixing is small enough. In this scenario, also the new decay channels of vector-like fermions into scalars can generate interesting leptonic plus missing transverse energy signals at the LHC. On the other hand, in the case of doublet-like fermion dark matter, scalar coannihilations lead to an increase in the relic density which allow to lower the bound of doublet-like fermion dark matter.
We consider lepton mixing in an extension of the Standard Model with three right-handed neutrino singlets. We require that the three lepton numbers L_e, L_\mu, and L_\tau be separately conserved in the Yukawa couplings, and we assume that they are softly broken only by the Majorana mass matrix M_R of the neutrino singlets. In this framework, where lepton-number breaking occurs at a scale much higher than the electroweak scale, deviations from family-lepton-number conservation are calculable and finite, and lepton mixing stems exclusively from M_R. We then show that a discrete symmetry exists such that, in the lepton mixing matrix U, maximal atmospheric neutrino mixing together with U_{e3}=0 can be obtained naturally. Alternatively, if one assumes that there are two different scales in M_R and that the lepton number \bar L = L_e - L_\mu - L_\tau is conserved in between them, then maximal solar neutrino mixing follows naturally. If both the discrete symmetry and intermediate \bar L conservation are introduced, bimaximal mixing is achieved.
We propose a new approach to characterizing the depths of optical lattices, in which an atomic gas is given a finite initial momentum, which leads to high amplitude oscillations in the zeroth diffraction order which are robust to finite-temperature effects. We present a simplified model yielding an analytic formula describing such oscillations for a gas assumed to be at zero temperature. This model is extended to include atoms with initial momenta detuned from our chosen initial value, before analyzing the full finite-temperature response of the system. Finally we present a steady-state solution to the finite-temperature system, which in principle makes possible the measurement of both the lattice depth, and initial temperature of the atomic gas simultaneously.
We describe properties of Hadamard products of algebraic varieties. We show any Hadamard power of a line is a linear space, and we construct star configurations from products of collinear points. Tropical geometry is used to find the degree of Hadamard products of other linear spaces.
Assume that $A\subseteq \Fp, B\subseteq \Fp^{*}$, $\1/4\leqslant\frac{|B|}{|A|},$ $|A|=p^{\alpha}, |B|=p^{\beta}$. We will prove that for $p\geqslant p_0(\beta)$ one has $$\sum_{b\in B}E_{+}(A, bA)\leqslant 15 p^{-\frac{\min\{\beta, 1-\alpha\}}{308}}|A|^3|B|.$$ Here $E_{+}(A, bA)$ is an additive energy between subset $A$ and it's multiplicative shift $bA$. This improves previously known estimates of this type.
Robin's theorem is one of the ingenious reformulation of the Riemann hypothesis (RH). It states that the RH is true if and only if $\sigma(n)<e^\gamma n\log\log n$ for all $n>5040$ where $\sigma(n)$ is the sum of divisors of $n$ and $\gamma$ is Euler's constant. In this paper we show that how the RH is delicate in terms of certain subsets of superabundant numbers, namely extremely abundant numbers and some of its specific supersets.
In this paper we develop a white noise framework for the study of stochastic partial differential equations driven by a d-parameter (pure jump) Levy white noise. As an example we use this theory to solve the stochastic Poisson equation with respect to Levy white noise for any dimension d. The solution is a stochastic distribution process given explicitly. We also show that if d\leq 3, then this solution can be represented as a classical random field in L2(\mu ), where \mu is the probability law of the Levy process.   The starting point of our theory is a chaos expansion in terms of generalized   Charlier polynomials. Based on this expansion we define Kondratiev spaces and the Levy Hermite transform.
Background: Extensions of single-reference (SR) energy-density-functionals (EDFs) to multi-reference (MR) applications involve using the generalized Wick theorem (GWT), which leads to singular energy kernels that cannot be properly integrated to restore symmetries, unless the EDFs are generated by true interactions.   Purpose: We propose a new method to regularize the MR EDFs, which is based on using auxiliary quantities obtained by multiplying the kernels with appropriate powers of overlaps.   Methods: Regularized matrix elements of two-body interactions are obtained by integrating the auxiliary quantities and then solving simple linear equations.   Results: We implement the new regularization method within the self-consistent Skyrme-Hartree-Fock approach and we perform a proof-of-principle angular-momentum projection (AMP) of states in odd-odd nucleus 26Al. We show that for EDFs generated by true interactions, our regularization method gives results identical to those obtained within the standard AMP procedure. We also show that for EDFs that do not correspond to true interactions, it gives stable and converging results that are different than unstable and non-converging standard AMP values.   Conclusions: The new regularization method proposed in this work may provide us with a relatively inexpensive and efficient tool to generalize SR EDFs to MR applications, thus allowing for symmetry restoration and configuration mixing performed for typical nuclear EDFs, which most often do not correspond to true interactions.
Using newly obtained high-resolution data ($R\sim{1\times{10}^{5}}$) from the \textit{Hubble Space Telescope}, and archival UV data from the \textit{Far Ultraviolet Spectroscopic Explorer} we have conducted a detailed UV survey of the three hot, metal-polluted white dwarfs WD0455-282, WD0621-376, and WD2211-495. Using bespoke model atmospheres we measured $T_{\mathrm{eff}}$, log $g$, and photospheric abundances for these stars. In conjunction with data from Gaia we measured masses, radii, and gravitational redshift velocities for our sample of objects. We compared the measured photospheric abundances with those predicted by radiative levitation theory, and found that the observed Si abundances in all three white dwarfs, and the observed Fe abundances in WD0621-376 and WD2211-495, were larger than those predicted by an order of magnitude. These findings imply not only an external origin for the metals, but also ongoing accretion, as the metals not supported by radiative levitation would sink on extremely short timescales. We measured the radial velocities of several absorption features along the line of sight to the three objects in our sample, allowing us to determine the velocities of the photospheric and interstellar components along the line of sight for each star. Interestingly, we made detections of circumstellar absorption along the line of sight to WD0455-282 with three velocity components. To our knowledge, this is the first such detection of multi-component circumstellar absorption along the line of sight to a white dwarf.
Let $E$ be an optimal elliptic curve defined over $\mathbb{Q}$. The critical subgroup of $E$ is defined by Mazur and Swinnerton-Dyer as the subgroup of $E(\mathbb{Q})$ generated by traces of branch points under a modular parametrization of $E$. We prove that for all rank two elliptic curves with conductor smaller than 1000, the critical subgroup is torsion. First, we define a family of critical polynomials attached to $E$ and describe two algorithms to compute such polynomials. We then give a sufficient condition for the critical subgroup to be torsion in terms of the factorization of critical polynomials. Finally, a table of critical polynomials is obtained for all elliptic curves of rank two and conductor smaller than 1000, from which we deduce our result.
We make quantitative predictions for the rapidity and centrality dependencies of hadron multiplicities in $AA$, $pA$ and $pp$ collisions at the LHC energies basing on the ideas of parton saturation in the Color Glass Condensate.
In the present paper we study the convergence of the solution of the two dimensional (2-D) stochastic Leray-$\alpha$ model to the solution of the 2-D stochastic Navier-Stokes equations. We are mainly interested in the rate of convergence, as $\alpha$ tends to 0, of the error function which is the difference between the two solutions in an appropriate topology. We show that when properly localized the error function converges in mean square as $\alpha\to 0$ and the convergence is of order $O(\alpha)$. We also prove that the error converges in probability to zero with order at most $O(\alpha)$.
We use state-of-the-art, three-dimensional non-local thermodynamic equilibrium (non-LTE) radiative magnetohydrodynamic simulations of the quiet solar atmosphere to carry out detailed tests of chromospheric magnetic field diagnostics from free-free radiation at millimeter and submillimeter wavelengths (mm/submm). The vertical component of the magnetic field was deduced from the mm/submm brightness spectra and the degree of circular polarization synthesized at millimeter frequencies. We used the frequency bands observed by the Atacama Large Millimeter/Submillimeter Array (ALMA) as a convenient reference. The magnetic field maps obtained describe the longitudinal magnetic field at the effective formation heights of the relevant wavelengths in the solar chromosphere. The comparison of the deduced and model chromospheric magnetic fields at the spatial resolution of both the model and current observations demonstrates a good correlation, but has a tendency to underestimate the model field. The systematic discrepancy of about 10 percent is probably due to averaging of the restored field over the heights contributing to the radiation, weighted by the strength of the contribution. On the whole, the method of probing the longitudinal component of the magnetic field with free-free emission at mm/submm wavelengths is found to be applicable to measurements of the weak quiet-Sun magnetic fields. However, successful exploitation of this technique requires very accurate measurements of the polarization properties (primary beam and receiver polarization response) of the antennas, which will be the principal factor that determines the level to which chromospheric magnetic fields can be measured. Consequently, high-resolution and high-precision observations of circularly polarized radiation at millimeter wavelengths can be a powerful tool for producing chromospheric longitudinal magnetograms.
The effect of quantizing magnetic field on the electron transport is investigated in a two dimensional topological insulator (2D TI) based on a 8 nm (013) HgTe quantum well (QW). The local resistance behavior is indicative of a metal-insulator transition at $B\approx 6$ T. On the whole the experimental data agrees with the theory according to which the helical edge states transport in a 2D TI persists from zero up to a critical magnetic field $B_c$ after which a gap opens up in the 2D TI spectrum.
We prove that with high probability, every eigenvector of a random matrix is delocalized in the sense that any subset of its coordinates carries a non-negligible portion of its $\ell_2$ norm. Our results pertain to a wide class of random matrices, including matrices with independent entries, symmetric and skew-symmetric matrices, as well as some other naturally arising ensembles. The matrices can be real and complex; in the latter case we assume that the real and imaginary parts of the entries are independent.