ShantanuT01/DACTYL-Pretraining huggingface dataset:
Let R be a complete discrete valuation ring of mixed characteristics, with algebraically closed residue field k. We study the existence problem of equivariant liftings to R of Galois covers of nodal curves over k. Using formal geometry, we show that this problem is actually a local one. We apply this local-to-global principle to obtain new results concerning the existence of such liftings.
The Lasserre's reconstruction algorithm is extended to the D-polytopes with the construction of their shape space. Thus, the areas of d-skeletons $(1\leq d\leq D)$ can be expressed as functions of the areas and normal bi-vectors of the (D-1)-faces of D-polytopes. As weak solutions of the simplicity constraints in all dimensional loop quantum gravity, the simple coherent intertwiners are employed to describe semiclassical D-polytopes. New general geometric operators based on D-polytopes are proposed by using the Lasserre's reconstruction algorithm and the coherent intertwiners. Such kind of geometric operators have expected semiclassical property by the definition. The consistent semiclassical limit with respect to the semiclassical D-polytopes can be obtained for the usual D-volume operator in all dimensional loop quantum gravity by fixing its undetermined regularization factor case by case.
We present a wide field survey of satellite galaxies in M106 (NGC 4258) covering a $1.7\degr \times 2\degr$ field around M106 using Canada-France-Hawaii Telescope/MegaCam. We find 16 satellite galaxy candidates of M106.   Eight of these galaxies are found to be dwarf galaxies that are much smaller and fainter than the remaining galaxies. Four of these galaxies are new findings. Surface brightness profiles of 15 out of 16 satellite galaxies can be represented well by an exponential disk profile with varying scale length. We derive the surface number density distribution of these satellite galaxies. The central number density profile (d $<100$ kpc) is well fitted by a power-law with a power index of $-2.1\pm0.5$, similar to the expected power index of isothermal distribution. The luminosity function of these satellites is represented well by the Schechter function with a faint end slope of $-1.19^{+0.03}_{-0.06}$. Integrated photometric properties (total luminosity, total colour, and disk scale length) and the spatial distribution of these satellite galaxies are found to be roughly similar to those of the Milky Way and M31.
We investigate a relation between surface densities of star formation rate (SFR) and stellar mass ($M_{*}$) at a $\sim 1$ kpc scale namely spatially resolved star formation main sequence (SFMS) in massive ($\log(M_{*}/M_{\odot})>10.5$) face-on disc galaxies at $0.01<z<0.02$ and $0.8<z<1.8$ and examine evolution of the relation. The spatially resolved SFMS of $z\sim 0$ galaxies is discussed in a companion paper. For $z\sim 1$ sample, we use 8 bands imaging dataset from CANDELS and 3D-HST and perform a pixel-to-pixel SED fitting to derive the spatially resolved SFR and $M_{*}$. We find a linear spatially resolved SFMS in the $z\sim 1$ galaxies that lie on the global SFMS, while a 'flattening' at high $\Sigma_{*}$ end is found in that relation for the galaxies that lie below the global SFMS. Comparison with the spatially resolved SFMS of the $z\sim 0$ galaxies shows smaller difference in the specific SFR (sSFR) at low $\Sigma_{*}$ than that at high $\Sigma_{*}$. This trend is consistent with the evolution of the sSFR$(r)$ radial profile, which shows a faster decrease in the central region than in the outskirt, agrees with the inside-out quenching scenario. We then derive an empirical model for the evolution of the $\Sigma_{*}(r)$, $\Sigma_{\rm SFR}(r)$ and sSFR$(r)$ radial profiles. Based on the empirical model, we estimate the radial profile of the quenching timescale and reproduce the observed spatially resolved SFMS at $z\sim 1$ and $z\sim 0$.
In the first main result of this paper we prove that one can approximate discontinious solutions of the 1d Navier Stokes system with solutions of the 1d Navier-Stokes-Korteweg system as the capilarity parameter tends to 0. Moreover, we allow the viscosity coefficients $\mu$ = $\mu$ ($\rho$) to degenerate near vaccum. In order to obtain this result, we propose two main technical novelties. First of all, we provide an upper bound for the density verifing NSK that does not degenerate when the capillarity coefficient tends to 0. Second of all, we are able to show that the positive part of the effective velocity is bounded uniformly w.r.t. the capillary coefficient. This turns out to be crucial in providing a lower bound for the density. The second main result states the existene of unique finite-energy global strong solutions for the 1d Navier-Stokes system assuming only that $\rho$0, 1/$\rho$0 $\in$ L $\infty$. This last result finds itself a natural application in the context of the mathematical modeling of multiphase flows.
Let $Q$ be a Riemannian $G$-manifold. This paper is concerned with the symmetry reduction of Brownian motion in $Q$ and ramifications thereof in a Hamiltonian context. Specializing to the case of polar actions we discuss various versions of the stochastic Hamilton-Jacobi equation associated to the symmetry reduction of Brownian motion and observe some similarities to the Schr\"odinger equation of the quantum free particle reduction as described by Feher and Pusztai. As an application we use this reduction scheme to derive examples of quantum Calogero-Moser systems from a stochastic setting.
This note introduces some bijections relating core partitions and tuples of integers. We apply these bijections to count the number of cores with various types of restriction, including fixed number of parts, limited size of parts, parts divisible by some integer, and distinct parts. For example, we prove that the number of $2t$-core partitions into $l$ even parts equals the number of $t$-core partitions into $l$ parts. We also generalize one expression for simultaneous cores, which was given by Baek, Nam and Yu, recently. Subsequently, we use this expression to obtain recurrence satisfied by numbers of $(s,s+1,\cdots,s+r)-$core partitions for $s\geq1$.
One essential problem in skeleton-based action recognition is how to extract discriminative features over all skeleton joints. However, the complexity of the State-Of-The-Art (SOTA) models of this task tends to be exceedingly sophisticated and over-parameterized, where the low efficiency in model training and inference has obstructed the development in the field, especially for large-scale action datasets. In this work, we propose an efficient but strong baseline based on Graph Convolutional Network (GCN), where three main improvements are aggregated, i.e., early fused Multiple Input Branches (MIB), Residual GCN (ResGCN) with bottleneck structure and Part-wise Attention (PartAtt) block. Firstly, an MIB is designed to enrich informative skeleton features and remain compact representations at an early fusion stage. Then, inspired by the success of the ResNet architecture in Convolutional Neural Network (CNN), a ResGCN module is introduced in GCN to alleviate computational costs and reduce learning difficulties in model training while maintain the model accuracy. Finally, a PartAtt block is proposed to discover the most essential body parts over a whole action sequence and obtain more explainable representations for different skeleton action sequences. Extensive experiments on two large-scale datasets, i.e., NTU RGB+D 60 and 120, validate that the proposed baseline slightly outperforms other SOTA models and meanwhile requires much fewer parameters during training and inference procedures, e.g., at most 34 times less than DGNN, which is one of the best SOTA methods.
Predictions of the existence of well-defined deeply bound pionic atom states for heavy nuclei and the eventual observation of such states by the (d,3He) reaction have revived interest in the pion-nucleus interaction at threshold and in its relation to the corresponding pion-nucleon interaction. Explanation of the 'anomalous' s-wave repulsion in terms of partial restoration of chiral symmetry and/or in terms of energy-dependence effects have been tested in global fits to pionic atom data and in a recent dedicated elastic scattering experiment. The role of neutron density distributions in this context is discussed in detail for the first time.
Unitarity randomized benchmarking (URB) is an experimental procedure for estimating the coherence of implemented quantum gates independently of state preparation and measurement errors. These estimates of the coherence are measured by the unitarity. A central problem in this experiment is relating the number of data points to rigorous confidence intervals. In this work we provide a bound on the required number of data points for Clifford URB as a function of confidence and experimental parameters. This bound has favorable scaling in the regime of near-unitary noise and is asymptotically independent of the length of the gate sequences used. We also show that, in contrast to standard randomized benchmarking, a nontrivial number of data points is always required to overcome the randomness introduced by state preparation and measurement errors even in the limit of perfect gates. Our bound is sufficiently sharp to benchmark small-dimensional systems in realistic parameter regimes using a modest number of data points. For example, we show that the unitarity of single-qubit Clifford gates can be rigorously estimated using few hundred data points under the assumption of gate-independent noise. This is a reduction of orders of magnitude compared to previously known bounds.
We present a dynamical study of the narrow-line regions in two nearby QSO2s. We construct dynamical models based on detailed photoionization models of the emission-line gas, including the effects of internal dust, to apply to observations of large-scale outflows from these AGNs. We use Mrk 477 and Mrk 34 in order to test our models against recent HST STIS observations of [O III] emission-line kinematics since these AGNs possess more energetic outflows than found in Seyfert galaxies. We find that the outflows within 500 pc are consistent with radiative acceleration of dusty gas, however, the outflows in Mrk 34 are significantly more extended and may not be directly accelerated by radiation. We characterize the properties of X-ray winds found from the expansion of [O III]-emitting gas close to the black hole. We show that such winds possess the kinetic energy density to disturb [O III] gas at 1.8 kpc, and have sufficient energy to entrain the [O III] clouds at 1.2 kpc. Assuming that the X-ray wind possesses the same radial mass distribution as the [O III] gas, we find that the peak kinetic luminosity for this wind is 2% of Mrk 34's bolometric luminosity, which is in the 0.5% - 5% range required by some models for efficient feedback. Our work shows that, although the kinetic luminosity as measured from [O III]-emitting gas is frequently low, X-ray winds may provide more than one order of magnitude higher kinetic power.
We experimentally demonstrate magnetostatic coupling between a nanopillar pseudo spin valve structure and a linear array of dipole coupled Permalloy nanomagnets. Using magnetic force microscopy, we study the interaction between the spin valve and the first element of the array, and present evidence that the nanomagnet couples with the hard layer of the spin valve for two spin valves with distinctly different composition. Our study includes a statistical analysis of antiferromagnetic order within the linear array, and provides insight into the range of behavior that these arrays can display. These results bear directly on the design of magnetic quantum cellular automata (MQCA) logic devices, showing that multilayer devices can couple to simple nanomagnets. Redesigning the hard layer of the magnetoresistive devices would make them operational as an electronic input that will allow integration of MQCA networks in complex electronic circuitry.
Evolutionary models taking into account radiative accelerations, thermal diffusion, and gravitational settling for 28 elements, including all those contributing to OPAL stellar opacities, have been calculated for solar metallicity stars of 0.5 to 1.4 solar masses. The Sun has been used to calibrate the models. Isochrones are fitted to the observed color-magnitude diagrams (CMDs) of M67 and NGC188, and ages of 3.7 and 6.4 Gyr are respectively determined. Convective core overshooting is not required to match the turnoff morphology of either cluster, including the luminosity of the gap in M67, because central convective cores are larger when diffusive processes are treated. This is due mainly to the enhanced helium and metal abundances in the central regions of such models. The observation of solar metallicity open clusters with ages in the range 4.8--5.7Gyr would further test the calculations of atomic diffusion in central stellar regions: according to non-diffusive isochrones, clusters should not have gaps near their main-sequence turnoffs if they are older than ~4.8Gyr, whereas diffusive isochrones predict that gaps should persist up to ages of ~5.7Gyr. Surface abundance isochrones are also calculated. In the case of M67 and NGC188, surface abundance variations are expected to be small. Abundance differences between stars of very similar Teff are expected close to the turnoff, especially for elements between P and Ca. Moreover, in comparison with the results obtained for giants, small generalized underabundances are expected in main-sequence stars. The lithium to beryllium ratio is discussed briefly and compared to observations.
We investigate intermediate inflation in the framework of a Galileon scalar field. To this aim, we first obtain the inflationary observables, including the scalar spectral index, the tensor-to-scalar ratio, the running of the scalar spectral index, as well as the non-Gaussianity parameters. Then, we examine the observational viability of the intermediate inflation within the framework of a Galileon scenario. Our results show that although the prediction of intermediate inflation in the standard framework is completely ruled out by the Planck 2015 observations, it can be put inside the allowed regions of the Planck 2015 TT,TE,EE+lowP data in the Galileon setting. Moreover, we determine the parameter space of the Galileon intermediate inflation for which the model is consistent with the Planck 2015 data. Besides, we derive the consistency relation in the Galileon scenario, and find that it differs from the standard inflation. We also estimate the running of the scalar spectral index and find that it is in well agreement with the 95\% CL constraint of the Planck 2015 results. Finally, we evaluate the local, equilateral, orthogonal, and enfolded non-Gaussianity parameters, and conclude that not only is the shape of non-Gaussianity approximately close to the equilateral one, but that it also satisfies the 68\% CL bound from the Planck 2015 data.
We study the degenerations of intermediate Jacobians by means of log geometry. We extend the family of intermediate Jacobians over a punctured disc to a "log intermediate Jacobian" over a disc.
Let $\Delta(x)$ be the error term of the Dirichlet divisor problem. An asymptotic formula with the error term $O(T^{53/28+\epsilon})$ is established for the integral $\int_1^T\Delta^4(x)dx.$   Similar results are also established for some other well-known error terms in the analytic number theory .
Recent Halpha surveys such as SHS and IPHAS have improved the completeness of the Galactic planetary nebula (PN) census. We now know of ~3,000 PNe in the Galaxy, but this is far short of most estimates, typically ~25,000 or more for the total population. The size of the Galactic PN population is required to derive an accurate estimate of the chemical enrichment rates of nitrogen, carbon, and helium. In addition, a high PN count (~20,000) is strong evidence that most 1-8 Msun main sequence stars will go through a PN phase, while a low count (<10,000) argues that special conditions (e.g., a close binary interaction) are required to form a PN. We describe a technique for finding hundreds more PNe using the existing data collections of the digital sky surveys, thereby improving the census of Galactic PNe.
In this paper, we prove existence and regularity results for solutions of some nonlinear Dirichlet problems for an elliptic equation defined by a degenerate coercive operator and a singular right hand side. \begin{equation}\label{01} \left\{ \begin{array}{lll} -\displaystyle\mbox{div}( a(x,u,\nabla u))&=\displaystyle\frac{f}{u^{\gamma}} & \mbox{ in } \Omega \\ u&>0 &\mbox{ in }\Omega \\ u&=0 &\mbox{ on } \delta\Omega \end{array} \right. \end{equation} where $\Omega $ is bounded open subset of $I\!\!R^{N}(N\geq2),$ $\gamma>0$ and $ f$ is a nonnegative function that belongs to some Lebesgue space.
In this study, a complete study of the effect of hydrothermal reaction temperatures on the synthesis and physical properties of V2O5 using the green facile mild hydrothermal method has been performed with six different temperatures 100 {\deg}C to 200 {\deg}C, in the step of 20 {\deg}C. . The XRD pattern confirm the stable orthorhombic crystal structure of the synthesized samples at all reaction temperatures. The SEM and TEM images demonstrate the particle-like morphology, and these characterizations affirmed that the particles size became larger with the increase of reaction temperatures. The FTIR analysis is employed to study the functional groups, and the obtained results are consistent with the XRD analysis. The bandgap has been estimated at various reaction temperatures using UV-vis diffuse reflectance spectra (UV-DRS) and was found to be varied 2.09 eV to 2.15 eV that are suitable range to absorb a significant amount of visible light. The photocatalysis of methylene blue (MB) with synthesized samples has been accomplished to investigate photocatalytic efficiency. The pure V2O5 synthesized at lower reaction temperature (100 {\deg}C) possess a lower bandgap and, accordingly, higher photocatalytic efficiency.
The hydrodynamic expansion of quark-gluon plasmas with spherical and longitudinally boost-invariant geometries is studied as a function of the initial energy density. The sensitivity of the collective flow pattern to uncertainties in the nuclear matter equation of state is explored. We concentrate on the effect of a possible finite width, $\Delta T \sim 0.1 T_c$, of the transition region between quark-gluon plasma and hadronic phase. Although slow deflagration solutions that act to stall the expansion do not exist for $\Delta T > 0.08 T_c$, we find, nevertheless, that the equation of state remains sufficiently soft in the transition region to delay the propagation of ordinary rarefaction waves for a considerable time. We compute the dependence of the pion-interferometry correlation function on $\Delta T$, since this is the most promising observable for time-delayed expansion. The signature of time delay, proposed by Pratt and Bertsch, is an enhancement of the ratio of the inverse width of the pion correlation function in out-direction to that in side-direction. One of our main results is that this generic signature of quark-gluon plasma formation is rather robust to the uncertainties in the width of the transition region. Furthermore, for longitudinal boost-invariant geometries, the signal is likely to be maximized around RHIC energies, $\sqrt{s} \sim 200$ AGeV.
We analyze existence, multiplicity and oscillatory behavior of positive radial solutions to a class of quasilinear equations governed by the Lorentz-Minkowski mean curvature operator. The equation is set in a ball or an annulus of $\mathbb R^N$, is subject to homogeneous Neumann boundary conditions, and involves a nonlinear term on which we do not impose any growth condition at infinity. The main tool that we use is the shooting method for ODEs.
Controlled plastic forming of nanoscale metallic objects by applying mechanical load is a challenge, since defect-free nanocrystals usually yield at near theoretical shear strength, followed by an uncontrolled catastrophic failure. Herein, instead of mechanical load, we utilize chemical stress from imbalanced interdiffusion to manipulate the shape of nanowhiskers. Bimetallic Au-Fe nanowhiskers with an ultra-high bending strength were synthesized employing the molecular beam epitaxy technique. The one-sided Fe coating on the defect-free, single-crystalline Au nanowhisker exhibited both single- and poly-crystalline regions. Annealing the bimetallic nanowhiskers at elevated temperatures led to gradual change of curvature and irreversible bending, which is attributed to the grain boundary Kirkendall effect during the diffusion of Au along the grain boundaries in the Fe layer. The results of this study demonstrate a high potential of chemical interdiffusion in the controlled plastic forming of ultra-strong metal nanostructures.
We offer an improved method for using a nuclear-magnetic-resonance quantum computer (NMRQC) to solve the Deutsch-Jozsa problem. Two known obstacles to the application of the NMRQC are exponential diminishment of density-matrix elements with the number of bits, threatening weak signal levels, and the high cost of preparing a suitable starting state. A third obstacle is a heretofore unnoticed restriction on measurement operators available for use by an NMRQC. Variations on the function classes of the Deutsch-Jozsa problem are introduced, both to extend the range of problems advantageous for quantum computation and to escape all three obstacles to use of an NMRQC. By adapting it to one such function class, the Deutsch-Jozsa problem is made solvable without exponential loss of signal. The method involves an extra work bit and a polynomially more involved Oracle; it uses the thermal-equilibrium density matrix systematically for an arbitrary number of spins, thereby avoiding both the preparation of a pseudopure state and temporal averaging.
Peculiar property of electronic order is clarified for the two-channel Kondo lattice. With two conduction electrons per site, the order parameter is a composite quantity involving both local and itinerant degrees of freedom. In contrast to the ordinary Kondo lattice, a heavy electron band is absent above the transition temperature, but is rapidly formed below it. The change of entropy associated with the ordering is found to be close to $\ln \sqrt 2$ per site. This entropy corresponds to the residual entropy in a two-channel Kondo impurity, which has been regarded as due to localized free Majorana particles. The present composite order is interpreted as instability of Majorana particles toward non-Kramers conduction electrons plus heavy fermions that involve localized electrons.
Since 2013 we are performing with the Nancay Radio Telescope (NRT) a monitoring program of >100 Galactic disk OH/IR stars, having bright 1612-MHz OH maser emission. The variations of the maser emission are used to probe the underlying stellar variability. We wish to understand how the large-amplitude variations are lost during the AGB - post-AGB transition. The fading out of pulsations with steadily declining amplitudes seems to be a viable process.