ShantanuT01/DACTYL-Pretraining huggingface dataset:
Building upon the Noether charge formalism of Iyer and Wald, we derive a variational formula for spacetimes admitting a Killing vector field, for a generic energy-momentum distribution with compact support. Applying this general result to the particular case of a binary system of spinning compact objects moving along an exactly circular orbit, modelled using the multipolar gravitational skeleton formalism, we derive a first law of compact binary mechanics at dipolar order. We prove the equivalence of this new result with the canonical Hamiltonian first law previously derived for binary systems of spinning compact objects, for spins colinear with the orbital angular momentum. This paper paves the way to an extension of the first law of binary mechanics to the next quadrupolar order, thereby accounting for the spin-induced and tidally-induced deformability of the compact bodies.
In this paper we study a sequence involving the prime numbers by deriving two asymptotic formulas and finding new upper and lower bounds, which improve the currently known estimates.
The high-mass microquasar Cygnus X-3 has been recently detected in a flaring state by the gamma-ray satellites Fermi and Agile. In the present contribution, we study the high-energy emission from Cygnus X-3 through a model based on the interaction of clumps from the Wolf-Rayet wind with the jet. The clumps inside the jet act as obstacles in which shocks are formed leading to particle acceleration and non-thermal emission. We model the high energy emission produced by the interaction of one clump with the jet and briefly discus the possibility of many clumps interacting with the jet. From the characteristics of the considered scenario, the produced emission could be flare-like due to discontinuous clump penetration, with the GeV long-term activity explained by changes in the wind properties.
In this paper, we consider the following Kirchhoff type equation $$ -\left(a+ b\int_{\R^3}|\nabla u|^2\right)\triangle {u}+V(x)u=f(u),\,\,x\in\R^3, $$ where $a,b>0$ and $f\in C(\R,\R)$, and the potential $V\in C^1(\R^3,\R)$ is positive, bounded and satisfies suitable decay assumptions. By using a new perturbation approach together with a new version of global compactness lemma of Kirchhoff type, we prove the existence and multiplicity of bound state solutions for the above problem with a general nonlinearity. We especially point out that neither the corresponding Ambrosetti-Rabinowitz condition nor any monotonicity assumption is required for $f$. Moreover, the potential $V$ may not be radially symmetry or coercive. As a prototype, the nonlinear term involves the power-type nonlinearity $f(u) = |u|^{p-2}u$ for $p\in (2, 6)$. In particular, our results generalize and improve the results by Li and Ye (J.Differential Equations, 257(2014): 566-600), in the sense that the case $p\in(2,3]$ is left open there.
We examine the formation of dark matter (DM) cores in dwarf galaxies simulated with the EAGLE model of galaxy formation. As in earlier work, we find that the star formation (SF) gas density threshold ($\rho_{\rm th}$) plays a critical role. At low thresholds (LT), gas is unable to reach densities high enough to dominate the gravitational potential before being dispersed by feedback from supernovae. LT runs show little effect on the inner DM profile, even in systems with extended and bursty SF, two ingredients often cited as critical for core formation. For higher thresholds, gas is able to dominate the gravitational potential before being ejected by feedback. This can lead to a substantial reduction in the inner DM content, but only if the gas is gravitationally important over an extended period of time, allowing the halo to contract before gas removal. Rapid assembly and removal of gas in short SF bursts is less effective at altering the inner DM content. Subsequent gas accretion may draw DM back in and reform a cusp, unless SF is bursty enough to prevent it, preserving the core. Thus, for the EAGLE SF+feedback model, there is no simple relation between core formation and SF history, contrary to recent claims. The dependence of the inner DM content of dwarfs on $\rho_{\rm th}$ hinders robust predictions and the interpretation of observations. A simulation of a $(12 \rm \ Mpc)^3$ volume with high $\rho_{\rm th}$ results in dwarfs with sizeable cores over a limited halo mass range, but with insufficient variety in mass profiles to explain the observed diversity of dwarf galaxy rotation curves.
We apply to tensor-multi-scalar gravity the effective fluid analysis based on the representation of the gravitational scalar field as a dissipative effective fluid. This generalization poses new challenges as the effective fluid is now a complicated mixture of individual fluids mutually coupled to each other and many reference frames are possible for its description. They are all legitimate, although not all convenient for specific problems, and they give rise to different physical interpretations. Two of these frames are highlighted.
A promising method for measuring the cosmological parameter combination fsigma_8 is to compare observed peculiar velocities with peculiar velocities predicted from a galaxy density field using perturbation theory. We use N-body simulations and semi-analytic galaxy formation models to quantify the accuracy and precision of this method. Specifically, we examine a number of technical aspects, including the optimal smoothing length applied to the density field, the use of dark matter halos or galaxies as tracers of the density field, the effect of noise in the halo mass estimates or in the stellar-to-halo mass relation, and the effect of finite survey volumes. We find that for a Gaussian smoothing of 4 Mpc/h, the method has only small systematic biases at the level of 5%. Cosmic variance affects current measurements at the 5% level due to the volume of current redshift data sets.
\noindent Let $\mu(f)$ resp. $c(f)$ be the Milnor number resp. the degree of the conductor of an irreducible power series $f\in \bK[[x,y]]$, where $\bK$ is an algebraically closed field of characteristic $p\geq 0$. It is well-known that $\mu(f)\geq c(f)$. We give necessary and sufficient conditions for the equality $\mu(f)=c(f)$ in terms of the semigroup associated with $f$, provided that $p>\ord f$.
The studies of the complex molecular emission lines in millimeter and submillimeter wavelengths towards the hot molecular cores demonstrate valuable details about the chemical complexity in the interstellar medium (ISM). We presented the first detection of the rotational emission lines of the complex organic molecule methyl formate (CH$_{3}$OCHO) towards the hot molecular core region IRAS 18566+0408 using the high-resolution Atacama Large Millimeter/Submillimeter Array (ALMA) band 3 observation. The estimated column density of CH$_{3}$OCHO using the rotational diagram analysis was (4.1$\pm$0.1)$\times$10$^{15}$ cm$^{-2}$ with rotational temperature 102.8$\pm$1.2 K. The estimated fractional abundance of CH$_{3}$OCHO towards the IRAS 18566+0408 relative to hydrogen (H$_{2}$) was 3.90$\times$10$^{-9}$. We noted that the estimated fractional abundance of CH$_{3}$OCHO is fairly consistent with the simulation value predicted by the three-phase warm-up model from Garrod (2013). We also discussed the possible formation mechanism of CH$_{3}$OCHO towards the hot molecular cores.
Recent works on adaptive sparse and on low-rank signal modeling have demonstrated their usefulness in various image / video processing applications. Patch-based methods exploit local patch sparsity, whereas other works apply low-rankness of grouped patches to exploit image non-local structures. However, using either approach alone usually limits performance in image reconstruction or recovery applications. In this work, we propose a simultaneous sparsity and low-rank model, dubbed STROLLR, to better represent natural images. In order to fully utilize both the local and non-local image properties, we develop an image restoration framework using a transform learning scheme with joint low-rank regularization. The approach owes some of its computational efficiency and good performance to the use of transform learning for adaptive sparse representation rather than the popular synthesis dictionary learning algorithms, which involve approximation of NP-hard sparse coding and expensive learning steps. We demonstrate the proposed framework in various applications to image denoising, inpainting, and compressed sensing based magnetic resonance imaging. Results show promising performance compared to state-of-the-art competing methods.
The ring of conditions defined by C. De Concini and C. Procesi is an intersection theory for algebraic cycles in a spherical homogeneous space. In the paper we consider the ring of conditions for the group $(C^*)^n$. Up to a big extend this ring can be reduced to the cohomology rings of smooth projective toric varieties. This ring also can be described using tropical geometry. We recall these known results and provide a new description of this ring in terms of convex integral polyhedra.
Based on density functional perturbation theory, we have studied the vibrational properties of three crystalline phases of tellurium dioxide: paratellurite alpha-TeO2, tellurite beta-TeO2, and the new phase gamma-TeO2, recently identified experimentally. Calculated Raman and IR spectra are in good agreement with available experimental data. The vibrational spectra of alpha- and beta-TeO2 can be interpreted in terms of vibrations of TeO2 molecular units.
The submillimeter CO lines are formed in warm and dense molecular gas and are therefore sensitive to the physical conditions whereas the CO (J=1-0) line is a tracer of the total molecular gas mass. In order to be able to compare the properties of molecular gas in nearby and distant galaxies, we have observed C and CO submillimeter lines (including the 12CO(6-5) and 12CO(7-6) lines) in a sample of nearby galaxies using the CSO. We have obtained a complete view of the CO cooling curve (also called CO spectral energy distribution) by combining the submillimeter CSO data with previous observations found in the literature. We made use of Large Velocity Gradient (LVG) models to analyse the observed CO cooling curve, predict CO line intensities from J=1-0 to J=15-14 in the studied galaxies, and derive the physical properties of the warm and dense molecular gas : the kinetic temperature (TK); the gas density (n(H2)); the N(12CO)/$\Delta v$. The predictions for the line intensities and for the total CO cooling power, obtained from LVG modelling have been compared with predictions from Photo Dissociation Regions (PDR) models. We show how the CO SED varies according to the galaxy star forming activity. For active nuclei, the peak is located near the 12CO(6-5) or 12CO(7-6) rotational lines, while, for normal nuclei, most of the energy is carried by the 12CO(4-3) and 12CO(5-4) lines. Whatever the spectral type of the nucleus, the observed C cooling rate is lower than the observed CO cooling rate (by a factor of around 4). The CO cooling curve of nearby starburst galaxies (e.g. NGC 253) has a quite similar shape to the CO cooling curve of distant galaxies. Therefore, the CO cooling curves are useful diagnostics for the star forming activity in distant objects.
We determine, to within O(1), the expected minimal position at level n in certain branching random walks. The walks under consideration have displacement vector (v_1,v_2,...), where each v_j is the sum of j independent Exponential(1) random variables and the different v_i need not be independent. In particular, our analysis applies to the Poisson-Dirichlet branching random walk and to the Poisson-weighted infinite tree. As a corollary, we also determine the expected height of a random recursive tree to within O(1).
We use the extensive $Gaia$ Data Release 2 set of Long Period Variables to select a sample of Oxygen-rich Miras throughout the Milky Way disk and bulge for study. Exploiting the relation between Mira pulsation period and stellar age/chemistry, we slice the stellar density of the Galactic disk and bulge as a function of period. We find the morphology of both components evolves as a function of stellar age/chemistry with the stellar disk being stubby at old ages, becoming progressively thinner and more radially extended at younger stellar ages, consistent with the picture of inside-out and upside-down formation of the Milky Way's disk. We see evidence of a perturbed disk, with large-scale stellar over-densities visible both in and away from the stellar plane. We find the bulge is well modelled by a triaxial boxy distribution with an axis ratio of $\sim [1:0.4:0.3]$. The oldest of the Miras ($\sim$ 9-10 Gyr) show little bar-like morphology, whilst the younger stars appear inclined at a viewing angle of $\sim 21^{\circ}$ to the Sun-Galactic Centre line. This suggests that bar formation and buckling took place 8-9 Gyr ago, with the older Miras being hot enough to avoid being trapped by the growing bar. We find the youngest Miras to exhibit a strong peanut morphology, bearing the characteristic X-shape of an inclined bar structure.
Let $\Omega$ be a bounded smooth domain in $\mathbb{R}^N$. We study positive solutions of equation (E) $-L_\mu u+ u^q = 0$ in $\Omega$ where $L_\mu=\Delta + \frac{\mu}{\delta^2}$,   $0<\mu$, $q>1$ and $\delta(x)=\mathrm{dist}\,(x,\partial\Omega)$. A positive solution of (E) is moderate if it is dominated by an $L_\mu$-harmonic function. If $\mu<C_H(\Omega)$ (the Hardy constant for $\Omega$) every positive $L_\mu$- harmonic functions can be represented in terms of a finite measure on $\partial\Omega$ via the Martin representation theorem. However the classical measure boundary trace of any such solution is zero. We introduce a notion of normalized boundary trace by which we obtain a complete classification of the positive moderate solutions of (E) in the subcritical case, $1<q<q_{\mu,c}$. (The critical value depends only on $N$ and $\mu$.) For $q\geq q_{\mu,c}$ there exists no moderate solution with an isolated singularity on the boundary. The normalized boundary trace and associated boundary value problems are also discussed in detail for the linear operator $L_\mu$. These results form the basis for the study of the nonlinear problem.
The recently published experimental data for specific heat C_p of liquid helium in zero gravity conditions very close to the lambda-transition have been discussed. We have shown that these data allow different interpretations. They can be well interpreted within the perturbative RG approach and within our recently developed theory, as well. Allowing the logarithmic correction, the corresponding fits lie almost on top of each other over the whole range of the reduced temperatures t (for bin averaged data) 6.3 x 10^{-10} < t < 8.8 x 10^{-3}. However, the plot of the effective exponent alpha_eff(t) suggests that the behaviour of C_p, probably, changes very close to the lambda-transition temperature. To clarify this question, we need more accurate data for t<10^{-7}. In addition, we show that the experimental data for superfluid fraction of liquid helium close to the critical point within 3 x 10^{-7} < t < 10^{-4} can be better fit by our exponents nu=9/13, Delta=5/13 than by the RG exponents (nu approximately 0.6705 and Delta about 0.5). The latter ones are preferable to fit the whole measured range 3 x 10^{-7} < t < 10^{-2} where, however, remarkable systematic deviations appear. Our estimated value 0.694 +/- 0.017 of the asymptotic exponent nu well agrees with the theoretical prediction nu=9/13.
It is shown that a fermion mass matrix changing in orientation (rotating) with changing scales can give a simple yet near-quantitative explanation for quark mixing, neutrino oscillations and the fermion mass hierarchy.
We introduce 3+1 timelike foliation of the four dimensional Lorentz manifold to derive the 3+1 Sen-Ashtekar-Barbero-Immirzi formalism in case of $SO(2,1)$ rotation gauge group, which is possible due to the existence of the $so(2,1)$ algebra isomorphism to $R^3_{2,1}$ algebra with respect to the vector product. We prove that the newly introduced flux and extrinsic curvature variables preserve the symplectic structure of the original variables. We then introduce the modified rotational constraint and succeed to write it as a Gauss constraint of a newly obtained connection. The newly obtained connection is slightly different from the classical 3+1 spacelike Sen-Ashtekar-Barbero-Immirzi connection as it contains in addition the Minkowski metric $\eta_{ij}$ as a coefficient. Our result has a very simple form and clearly shows how $so(2,1)$ connection is different from $so(3)$ one. Also it is the first time that the key-stone fact that makes the whole formalism work in timelike 3+1 case, i.e. $so(2,1) \simeq R^3_{2,1}$ isomorphism and its relation to the $so(2,1)$ connection has been researched.
Given $n$ pairwise disjoint sets $X_1,\ldots, X_n$, we call the elements of $S=X_1\times\ldots\times X_n$ strings. A nonempty set of strings $W\subseteq S$ is said to be well-connected if for every $v\in W$ and for every $i\, (1\le i\le n)$, there is another element $v'\in W$ which differs from $v$ only in its $i$th coordinate. We prove a conjecture of Yaokun Wu and Yanzhen Xiong by showing that every set of more than $\prod_{i=1}^n|X_i|-\prod_{i=1}^n(|X_i|-1)$ strings has a well-connected subset. This bound is tight.
We define the class of admissible linear embeddings of flag varieties. The definition is given in the general language of algebraic geometry. We then prove that an admissible linear embedding of flag varieties has a certain explicit form in terms of linear algebra. This result enables us to show that any direct limit of admissible embeddings of flag varieties is isomorphic to an ind-variety of generalized flags as defined in [DP]. These latter ind-varieties have been introduced in terms of the ind-group SL(\infty) (respectively, O(\infty) or Sp(\infty) for isotropic generalized flags), and the current paper constructs them in purely algebraic-geometric terms
We present a pion photoproduction model on the free nucleon based on an Effective Lagrangian Approach (ELA) which includes the nucleon resonances ($\Delta(1232)$, N(1440), N(1520), N(1535), $\Delta (1620)$, N(1650), and $\Delta (1700)$), in addition to Born and vector meson exchange terms. The model incorporates a new theoretical treatment of spin-3/2 resonances, first introduced by Pascalutsa, avoiding pathologies present in previous models. Other main features of the model are chiral symmetry, gauge invariance, and crossing symmetry. We use the model combined with modern optimization techniques to assess the parameters of the nucleon resonances on the basis of world data on electromagnetic multipoles. We present results for electromagnetic multipoles, differential cross sections, asymmetries, and total cross sections for all one pion photoproduction processes on free nucleons. We find overall agreement with data from threshold up to 1 GeV in laboratory frame.
In this article, we study the asymptotic behavior of the spatial integral of the solution to the hyperbolic Anderson model in dimension $d\leq 2$, as the domain of the integral gets large (for fixed time $t$). This equation is driven by a spatially homogeneous Gaussian noise, whose covariance function is either integrable, or is given by the Riesz kernel. The novelty is that the noise does not depend on time, which means that It\^o's martingale theory for stochastic integration cannot be used. Using a combination of Malliavin calculus with Stein's method, we show that with proper normalization and centering, the spatial integral of the solution converges to a standard normal distribution, by estimating the speed of this convergence in the total variation distance. We also prove the corresponding functional limit theorem for the spatial integral process.
Arrival directions of ultra-high energy cosmic rays from the direction of ten brightest radio sources lying within 50 Mpc from our Galaxy were studied by using recent models of the largescale Galactic magnetic field. A detailed study, where also small-scale turbulent magnetic field component was implemented, is presented for the radiogalaxy Virgo A. This radiogalaxy is located far from the Galactic plane which leads to a unique image of this UHECR source candidate, if the flux is composed from a mixture of intermediate mass nuclei. We present a method suitable for identifying cosmic rays arriving from this close-by radiogalaxy.
Let K be a finite unramified extension of Q_p. We parametrize the (phi, Gamma)-modules corresponding to reducible two-dimensional mod p representations of G_K and characterize those which have reducible crystalline lifts with certain Hodge-Tate weights.
In this paper we introduce the concepts of the distinguishing number and the distinguishing chromatic number of a poset. For a distributive lattice $L$ and its set $Q_L$ of join-irreducibles, we use classic lattice theory to show that any linear extension of $Q_L$ generates a distinguishing 2-coloring of $L$. We prove general upper bounds for the distinguishing chromatic number and particular upper bounds for the Boolean lattice and for divisibility lattices. In addition, we show that the distinguishing number of any twin-free Cohen-Macaulay planar lattice is at most 2.
In this contribution we present a construction of large networks of diameter two and of order $\frac{1}{2}d^2$ for every degree $d\geq 8$, based on Cayley graphs with surprisingly simple underlying groups. For several small degrees we construct Cayley graphs of diameter two and of order greater than $\frac23$ of Moore bound and we show that Cayley graphs of degrees $d\in\{16,17,18,23,24,31,\dots,35\}$ constructed in this paper are the largest currently known vertex-transitive graphs of diameter two.
In order to find out whether empty singular boundaries can arise in higher dimensional Gravity, we study the solution of Einstein's equations consisting in a ($N+2$)-dimensional static and hyperplane symmetric perfect fluid satisfying the equation of state $\rho=\eta\, p$, being $\rho$ an arbitrary constant and $N\geq2$. We show that this spacetime has some weird properties. In particular, in the case $\eta>-1$, it has an empty (without matter) repulsive singular boundary.   We also study the behavior of geodesics and the Cauchy problem for the propagation of massless scalar field in this spacetime. For $\eta>1$, we find that only vertical null geodesics touch the boundary and bounce, and all of them start and finish at $z=\infty$; whereas non-vertical null as well as all time-like ones are bounded between two planes determined by initial conditions. We obtain that the Cauchy problem for the propagation of a massless scalar field is well-posed and waves are completely reflected at the singularity, if we only demand the waves to have finite energy, although no boundary condition is required.