ShantanuT01/DACTYL-Pretraining huggingface dataset:
It is well known that if $\mathbb{F}$ is a finite field then $\mathbb{F^{*}}$, the set of non zero elements of $\mathbb{F}$, is a cyclic group. In this paper we will assume $\mathbb{F}=\mathbb{F}_{p}$ (the finite field with p elements, p a prime) and $\mathbb{\mathbb{F}}_{p^{2}}$ is a quadratic extension of $\mathbb{F}_{p}$. In this case, the groups $\mathbb{F}_{p}^{*}$ and $\mathbb{F}_{p^{2}}^{*}$ have orders $p-1$ and $p^{2}-1$ respectively. We will provide necessary and sufficient conditions for an element $u\in\mathbb{F}_{p^{2}}^{*}$ to be a generator. Specifically, we will prove $u$ is a generator of $\mathbb{F}_{p^{2}}^{*}$ if and only if $N(u)$ generates $\mathbb{F}_{p}^{*}$ and $\frac{u^{2}}{N(u)}$ generates Ker$\,N$, where $N:\mathbb{F}_{p^{2}}^{*}\rightarrow\mathbb{F}_{p}^{*}$ denotes the norm map. We will also provide a method for determining if $u$ is not a generator of Ker$\,N$.
We aim to better understand how the spatial structure of molecular clouds is governed by turbulence. For that, we study the large-scale spatial distribution of low density molecular gas and search for characteristic length scales. We employ a 35 square degrees 13CO 1-0 molecular line survey of Cygnus X and visual extinction (A_V) maps of 17 Galactic clouds to analyse the spatial structure using the Delta-variance method. This sample contains a large variety of different molecular cloud types with different star forming activity. The Delta-variance spectra obtained from the A_V maps show differences between low-mass star-forming (SF) clouds and massive giant molecular clouds (GMC) in terms of shape of the spectrum and its power-law exponent beta. Low-mass SF clouds have a double-peak structure with characteristic size scales around 1 pc (though with a large scatter around this value) and 4 pc. GMCs show no characteristic scale in the A_V-maps, which can partly be ascribed to a distance effect due to a larger line-of-sight (LOS) confusion. The Delta-variance for Cygnus, determined from the 13CO survey, shows characteristic scales at 4 pc and 40 pc, either reflecting the filament structure and large-scale turbulence forcing or - for the 4 pc scale - the scale below which the 13CO 1-0 line becomes optically thick. Though there are different processes that can introduce characteristic scales, i.e. geometry, decaying turbulence the transition scale from supersonic to subsonic turbulence (the sonic scale), line-of-sight effects and energy injection due to expanding supernova shells, outflows, HII-regions, and the relative contribution of these effects strongly varies from cloud to cloud, it is remarkable that the resulting turbulent structure of molecular clouds shows similar characteristics.
Photodisintegration of the deuteron above pi-threshold is studied in a coupled channel approach including N-Delta- and pi-d-channels with pion retardation in potentials and exchange currents.
For domains of first kind [7,13] we describe the qualitative behavior of the global bifurcation diagram of the unbounded branch of solutions of the Gel'fand problem crossing the origin. At least to our knowledge this is the first result about the exact monotonicity of the branch of non-minimal solutions which is not just concerned with radial solutions [28] and/or with symmetric domains [23]. Toward our goal we parametrize the branch not by the $L^{\infty}(\Omega)$-norm of the solutions but by the energy of the associated mean field problem. The proof relies on a carefully modified spectral analysis of mean field type equations.
We present a quantum-mechanical study of the exothermic 7LiH reaction with H. Accurate reactive probabilities and rate coefficients are obtained by solving the Schrodinger equation for the motion of the three nuclei on a single Born-Oppenheimer potential energy surface (PES) and using a coupled-channel hyperspherical coordinate method. Our new rates indeed confirm earlier, qualitative predictions and some previous theoretical calculations, as discussed in the main text. In the astrophysical domain we find that the depletion process largely dominates for redshift (z) between 400 and 100, a range significant for early Universe models. This new result from first-principle calculations leads us to definitively surmise that LiH should be already destroyed when the survival processes become important. Because of this very rapid depletion reaction, the fractional abundance of LiH is found to be drastically reduced, so that it should be very difficult to manage to observe it as an imprinted species in the cosmic background radiation (CBR). The present findings appear to settle the question of LiH observability in the early Universe. We further report several state-to-state computed reaction rates in the same range of temperatures of interest for the present problem.
We introduce the notion of a rigid quasilocal frame (RQF) as a geometrically natural way to define a "system" in general relativity. An RQF is defined as a two-parameter family of timelike worldlines comprising the worldtube boundary of the history of a finite spatial volume, with the rigidity conditions that the congruence of worldlines is expansion-free (constant size) and shear-free (constant shape). This definition of a system is anticipated to yield simple, exact geometrical insights into the problem of motion in general relativity. It begins by answering the questions what is in motion (a rigid two-dimensional system boundary), and what motions of this rigid boundary are possible. Nearly a century ago Herglotz and Noether showed that a three-parameter family of timelike worldlines in Minkowski space satisfying Born's 1909 rigidity conditions has only three degrees of freedom instead of the six we are familiar with from Newtonian mechanics. We argue that in fact we can implement Born's notion of rigid motion in both flat spacetime (this paper) and arbitrary curved spacetimes containing sources (subsequent papers) - with precisely the expected three translational and three rotational degrees of freedom - provided the system is defined quasilocally as the two-dimensional set of points comprising the boundary of a finite spatial volume, rather than the three-dimensional set of points within the volume.
Most of the existing tracking methods link the detected boxes to the tracklets using a linear combination of feature cosine distances and box overlap. But the problem of inconsistent features of an object in two different frames still exists. In addition, when extracting features, only appearance information is utilized, neither the location relationship nor the information of the tracklets is considered. We present an accurate and end-to-end learning framework for multi-object tracking, namely \textbf{TPAGT}. It re-extracts the features of the tracklets in the current frame based on motion predicting, which is the key to solve the problem of features inconsistent. The adaptive graph neural network in TPAGT is adopted to fuse locations, appearance, and historical information, and plays an important role in distinguishing different objects. In the training phase, we propose the balanced MSE LOSS to successfully overcome the unbalanced samples. Experiments show that our method reaches state-of-the-art performance. It achieves 76.5\% MOTA on the MOT16 challenge and 76.2\% MOTA on the MOT17 challenge.
Convective motions in the solar atmosphere cause spectral lines to become asymmetric and shifted in wavelength. For photospheric lines, this differential Doppler shift varies from the solar disk center to the limb. Precise and comprehensive observations of the convective blueshift and its center-to-limb variation improve our understanding of the atmospheric hydrodynamics and ensuing line formation, and provide the basis to refine 3D models of the solar atmosphere. We performed systematical spectroscopic measurements of the convective blueshift of the quiet Sun with the Laser Absolute Reference Spectrograph (LARS) at the German Vacuum Tower Telescope. The spatial scanning of the solar disk covered four radial (meridional and equatorial) axes. The high-resolution spectra of 26 photospheric to chromospheric lines in the visible range were calibrated with a laser frequency comb to absolute wavelengths at the 1m/s accuracy. Applying ephemeris and reference corrections, the bisector analysis provided line asymmetries and Doppler shifts with an uncertainty of only few m/s. To allow for a comparison with other observations, we convolved the results to lower spectral resolutions. Typically, a blueshifted "C"-shaped curve at disk center transforms into a less blueshifted "\"-shape toward the solar limb. The comparison of all lines reveals the systematic dependence of the convective blueshift on the line depth. Synthetic models yield considerable deviations from the observed center-to-limb variation. The obtained Doppler shifts of the quiet Sun can serve as an absolute reference for other observations, the relative calibration of Dopplergrams, and the necessary refinement of atmospheric models. Based on this, the development of high-precision models of stellar surface convection will advance the detection of (potentially habitable) exoplanets by radial velocity measurements.
It is generally agreed that there is matter in the universe and, in this paper, we show that the existence of matter is extremely problematic for the proposed Rh = ct universe. Considering a dark energy component with an equation of state of w=-1/3, it is shown that the presence of matter destroys the strict expansion properties that define the evolution of Rh = ct cosmologies, distorting the observational properties that are touted as its success. We further examine whether an evolving dark energy component can save this form of cosmological expansion in the presence of matter by resulting in an expansion consistent with a mean value of <w> = -1/3, finding that the presence of mass requires unphysical forms of the dark energy component in the early universe. We conclude that matter in the universe significantly limits the fundamental properties of the Rh = ct cosmology, and that novel, and unphysical, evolution of the matter component would be required to save it. Given this, Rh = ct cosmology is not simpler or more accurate description of the universe than prevailing cosmological models, and its presentation to date possesses significant flaws.
Observing gamma ray bursts (GRBs) in the TeV energy range can be extremely valuable in providing insight to GRB radiation mechanisms and in constraining source distances. The Milagrito detector was an air shower array which used the water Cherenkov technique to search for TeV sources. Data from this detector was analyzed to look for a TeV component of GRBs coincident with low energy -rays detected by the BATSE instrument on the Compton Gamma Ray Observatory. A sample of 54 BATSE GRBs which were in the field of view of the Milagrito detector during its lifetime (February 1997 to May 1998) was used.
We consider fully nonlinear uniformly elliptic equations with quadratic growth in the gradient, such as $$ -F(x,u,Du,D^2u) =\lambda c(x)u+\langle M(x)D u, D u \rangle +h(x) $$ in a bounded domain with a Dirichlet boundary condition, here $\lambda \in\mathbb{R}$, $c,\, h \in L^p(\Omega)$, $p>n\geq 1$, $c\gneqq 0$ and the matrix $M$ satisfies $0<\mu_1 I\leq M\leq \mu_2 I$. Recently this problem was studied in the "coercive" case $\lambda c\le0$, where uniqueness of solutions can be expected, and it was conjectured that the solution set is more complex for noncoercive equations. This conjecture was verified in 2015 by Arcoya, de Coster, Jeanjean and Tanaka for equations in divergence form, by exploiting the integral formulation of the problem. Here we show that similar phenomena occur for general, even fully nonlinear, equations in nondivergence form. We use different techniques based on the maximum principle.   We develop a new method to obtain the crucial uniform a priori bounds, which permit to us to use degree theory. This method is based on basic regularity estimates such as half-Harnack inequalities, and on a V\'azquez type strong maximum principle for our kind of equations.
We find conditions which guarantee moment (in)determinacy of powers and products of nonnegative random variables. We establish new and general results which are based either on the rate of growth of the moments of a random variable or on conditions about the distribution itself. For the class of generalized gamma random variables we show that the power and the product of such variables share the same moment determinacy property. A similar statement holds for half-logistic random variables. Besides answering new questions in this area, we either extend some previously known results or provide new and transparent proofs of existing results.
The BL Lac object 3C66A is one of the most luminous extragalactic sources at TeV $\gamma$-rays (VHE, i.e. $E >100$ GeV). Since TeV $\gamma$-ray radiation is absorbed by the extragalactic background light (EBL), it is crucial to know the redshift of the source in order to reconstruct its original spectral energy distribution, as well as to constrain EBL models. However, the optical spectrum of this BL\,Lac is almost featureless, so a direct measurement of $z$ is very difficult; in fact, the published redshift value for this source ($z=0.444$) has been strongly questioned. Based on EBL absorption arguments, several constraints to its redshift, in the range $0.096 < z < 0.5$, were proposed.   Since these AGNs are hosted, typically, in early type galaxies that are members of groups or clusters, we have analysed spectro-photometrically the environment of 3C66A, with the goal of finding the galaxy group hosting this blazar. This study was made using optical images of a $5.5 \times 5.5$\,arcmin$^{2}$ field centred on the blazar, and spectra of 24 sources obtained with Gemini/GMOS-N multi-object spectroscopy.   We found spectroscopic evidence of two galaxy groups along the blazar's line of sight: one at $z \simeq 0.020$ and a second one at $z \simeq 0.340$. The first one is consistent with a known foreground structure, while the second group here presented has six spectroscopically confirmed members. Their location along a red sequence in the colour-magnitude diagram allows us to identify 34 additional candidate members of the more distant group. The blazar's spectrum shows broad absorption features that we identify as arising in the intergalactic medium, thus allowing us to tentatively set a redshift lower limit at $z_{3C66A} \ge 0.33$. As a consequence, we propose that 3C66A is hosted in a galaxy that belongs to a cluster at $z=0.340$.
We assemble a statistical set of global mass models for ~2,000 nearly spherical SDSS galaxies at a mean redshift of 0.12 based on their aperture velocity dispersions and newly derived luminosity profiles in conjunction with published velocity dispersion profiles and empirical properties and relations of galaxy and halo parameters. When two-component (i.e. stellar plus dark) mass models are fitted to the SDSS aperture velocity dispersions, the predicted velocity dispersion profile (VP) slopes within the effective radius R_eff match well the distribution in observed elliptical galaxies. In contrast, the single-component models cannot reproduce the VP slope distribution. From a number of input variations the models exhibit for the radial range 0.1 R_eff < r < R_eff a tight correlation <gamma_e>=(1.865+/-0.008)+(-4.93+/-0.15)<eta> where <gamma_e> is the mean slope absolute value of the total mass density and <eta> is the mean slope of the velocity dispersion profile, which leads to a super-isothermal <gamma_e> = 2.15+/-0.04 for <eta>=-0.058+/-0.008 in observed elliptical galaxies. Furthermore, the successful two-component models appear to imply a typical slope curvature pattern in the total mass profile because for the observed steep luminosity (stellar mass) profile and the weak lensing inferred halo profile at large radii a total mass profile with monotonically varying slope would require too high DM density in the optical region giving rise to too large aperture velocity dispersion and too shallow VP.
Magnetic reconnection is invoked as an efficient particle accelerator in a variety of astrophysical sources of non-thermal high-energy radiation. With large-scale two-dimensional particle-in-cell simulations of relativistic reconnection (i.e., with magnetization $\sigma\gg1$) in pair plasmas, we study the long-term evolution of the power-law slope and high-energy cutoff of the spectrum of accelerated particles. We find that the high-energy spectral cutoff does not saturate at $\gamma_{\rm cut}\sim 4\sigma$, as claimed by earlier studies, but it steadily grows with time as long as the reconnection process stays active. At late times, the cutoff scales approximately as $\gamma_{\rm cut}\propto \sqrt{t}$, regardless of the flow magnetization and initial temperature. We show that the particles dominating the high-energy spectral cutoff reside in plasmoids, and in particular in a strongly magnetised ring around the plasmoid core. The growth of their energy is driven by the increase in the local field strength, coupled with the conservation of the first adiabatic invariant. We also find that the power-law slope of the spectrum ($p=-{\rm d}\log N/{\rm d}\log \gamma$) evolves with time. For $\sigma\gtrsim10$, the spectrum is hard at early times ($p\lesssim 2$), but it tends to asymptote to $p\sim 2$; the steepening of the power-law slope allows the spectral cutoff to extend to higher and higher energies, without violating the fixed energy budget of the system. Our results demonstrate that relativistic reconnection is a viable candidate for accelerating the high-energy particles emitting in relativistic astrophysical sources.
The fact that not all measurements can be carried out simultaneously is a peculiar feature of quantum mechanics and responsible for many key phenomena in the theory, such as complementarity or uncertainty relations. For the special case of projective measurements quantum behavior can be characterized by the commutator but for generalized measurements it is not easy to decide whether two measurements can still be understood in classical terms or whether they show already quantum features. We prove that generalized measurements which do not fulfill the notion of joint measurability are nonclassical, as they can be used for the task of quantum steering. This shows that the notion of joint measurability is, among several definitions, the proper one to characterize quantum behavior. Moreover, the equivalence allows to derive novel steering inequalities from known results on joint measurability and new criteria for joint measurability from known results on the steerability of states.
It is well known that phantom energy, which is characterized by the equation of state $p=\omega\rho$, $\omega <-1$, can support Morris-Thorne wormholes since it leads to a violation of the null energy condition. The purpose of this note is to show that the converse is also true in the following sense: for a typical shape function, the equation of state of exotic matter in the vicinity of the throat is given by $p_r=\omega\rho$, $\omega <-1$, where $p_r$ is the radial pressure. Some implications thereof are also considered.
We consider a Brownian particle in a ``meandering'' periodic potential when the ambient temperature is a periodically or stochastically varying function of time. Though far from equilibrium, the linear response of the particle to an external static force is exactly the same as in the equilibrium case, i.e. for constant temperature. Even more surprising is the non-linear response: the particle slows down and then even starts to move in the direction opposite to the applied force.
In anticipation of the Gaia astrometric mission, a large sample of spectroscopic binaries has been observed since 2010 with the SOPHIE spectrograph at the Haute--Provence Observatory. Our aim is to derive the orbital elements of double-lined spectroscopic binaries (SB2s) with an accuracy sufficient to finally obtain the masses of the components with relative errors as small as 1 % when the astrometric measurements of Gaia are taken into account. In this paper we present the results from five years of observations of 10 SB2 systems with periods ranging from 37 to 881 days. Using the TODMOR algorithm we computed radial velocities from the spectra, and then derived the orbital elements of these binary systems. The minimum masses of the components are then obtained with an accuracy better than 1.2 % for the ten binaries. Combining the radial velocities with existing interferometric measurements, we derived the masses of the primary and secondary components of HIP 87895 with an accuracy of 0.98 % and 1.2 % respectively.
We compare the luminosity function and rate inferred from the GBM long bursts peak flux distribution with those inferred from the Swift and BATSE peak flux distribution. We find that the GBM, BATSE and the Swift peak fluxes can be fitted by the same luminosity function implying the consistency of these three samples. Using the trigger algorithm of the LAT instrument we derive important information on the flux at 100 MeV compared to lower energy detected by the GBM. We find that the simple extension of the synchrotron emission to high energy cannot justify the low rate of GRBs detected by LAT and for several GRBs detected by the GBM, the flux at >100 MeV should be suppressed. Two bursts, GRB090217 and GRB 090202B, detected by LAT have very soft spectra in the GBM and therefore their high energy emission cannot be due to an extension of the synchrotron.
I defend my arguments in quant-ph/9806002, which have recently been criticized by L. Vaidman (quant-ph/9811092). I emphasize that the correct usage of the ABL rule applies not to a genuine counterfactual statement but rather to a conjunction of material conditionals. I argue that the only kind of valid counterfactual statement one can make using the ABL rule is a ``might'' counterfactual, which is not adequate for the attribution of `elements of reality' to a quantum system.
We exhaustively analyze the toric symmetries of CP^3 and its toric blowups. Our motivation is to study toric symmetry as a computational technique in Gromov-Witten theory and Donaldson-Thomas theory. We identify all nontrivial toric symmetries. The induced nontrivial isomorphisms lift and provide new symmetries at the level of Gromov-Witten Theory and Donaldson-Thomas Theory. The polytopes of the toric varieties in question include the permutohedron, the cyclohedron, the associahedron, and in fact all graph associahedra, among others.
Using the density-matrix renormalization group, we determine the phase diagram of the spin 1/2 Heisenberg antiferromagnet on a honeycomb lattice with a nearest neighbor interaction J1 and a frustrating, next-neighbor exchange J2. As frustration increases, the ground state exhibits Neel, plaquette and dimer orders, with critical points at J2/J1 = 0.22 and 0.35. We observe that both the spin gap and the corresponding order parameters vanish continuously at both the critical points, indicating the presence of deconfined quantum criticality.
The physics of radioactive ion beams implies the description of weakly-bound nuclear systems. One key aspect concerns the coupling to low-lying collective-type excited states, which for these systems might not be stable levels, but particle emitting resonances. In this work we describe how the scattering cross section and compound spectra change when the colliding fragments have such collective excitations featuring particle emission. We explore this question in the framework of a multi-channel algebraic scattering method of determining nucleon-nucleus cross sections at low energies. For a range of light-mass, particle-unstable nuclear targets, scattering cross sections as well as the spectra of the compound nuclei formed have been determined from calculations that do and do not consider particle emission widths for nuclear states. Assuming a resonance character for target states markedly varies evaluated cross sections from those obtained assuming the target spectrum to have entirely discrete states.