ShantanuT01/DACTYL-Pretraining huggingface dataset:
Generalizing older works of Domar and Armitage and Gardiner, we give an inequality for quasinearly subharmonic functions. As an application of this inequality, we improve Domar's, Rippon's and our previous results concerning the existence of the largest subharmonic minorant of a given function. Moreover, and as an another application, we give a sufficient condition for a separately quasinearly subharmonic function to be quasinearly subharmonic. Our result contains the previous results of Lelong, of Avanissian, of Arsove, of Armitage and Gardiner, and of ours.
Using three-dimensional magnetohydrodynamics simulations, we investigate general properties of a blast wave shock interacting with interstellar clouds. The shock-cloud interaction generates a turbulent shell through the vorticity generations. In the turbulent shell, the magnetic field is amplified as a result of turbulent dynamo action. In the case of a young supernova remnant, the corresponding strength of the magnetic field is approximately 1 mG. The propagation speed of the shock wave is significantly stalled in the clouds because of the high density, while the shock maintains a high velocity in the diffuse surrounding. In addition, when the shock wave hits the clouds, reflection shock waves are generated that propagate back into the shocked shell. From these simulation results, many observational characteristics of a young SNR RX J1713.7-3946 that is suggested to be interacting with molecular clouds, can be explained as follows: The reflection shocks can accelerate particles in the turbulent downstream region where the magnetic field strength reaches 1mG, which causes short-time variability of synchrotron X-rays. Since the shock velocity is stalled locally in the clouds, the temperature in the shocked cloud is suppressed below 1 keV. Thus, thermal X-ray line emissions would be faint even if the SNR is interacting with molecular clouds. We also find that the photon index of the $\pi^0$-decay gamma rays generated by cosmic-ray protons can be 1.5, because the penetration depth of high-energy particles into the clumpy clouds depends on their energy, which is consistent with the recent gamma-ray observation by Fermi space telescope.
In this paper we study the three-dimensional analogue of the relation between the irrationality exponent of a real number and the growth of its regular continued fraction partial quotients. As a multidimensional generalisation of continued fractions, we consider Klein polyhedra.
General relativistic corrections to the galaxy power spectrum appearing at the horizon scale, if neglected, may induce biases on the measured values of the cosmological parameters. In this paper, we study the impact of general relativistic effects on non standard cosmologies such as scenarios with a time dependent dark energy equation of state, with a coupling between the dark energy and the dark matter fluids or with non-Gaussianities. We then explore whether general relativistic corrections affect future constraints on cosmological parameters in the case of a constant dark energy equation of state and of non-Gaussianities. We find that relativistic corrections on the power spectrum are not expected to affect the foreseen errors on the cosmological parameters nor to induce large biases on them.
Given a family of $r$-uniform hypergraphs ${\cal F}$ (or $r$-graphs for brevity), the Tur\'an number $ex(n,{\cal F})$ of ${\cal F}$ is the maximum number of edges in an $r$-graph on $n$ vertices that does not contain any member of ${\cal F}$. A pair $\{u,v\}$ is covered in a hypergraph $G$ if some edge of $G$ contains $\{u,v\}$. Given an $r$-graph $F$ and a positive integer $p\geq n(F)$, let $H^F_p$ denote the $r$-graph obtained as follows. Label the vertices of $F$ as $v_1,\ldots, v_{n(F)}$. Add new vertices $v_{n(F)+1},\ldots, v_p$. For each pair of vertices $v_i,v_j$ not covered in $F$, add a set $B_{i,j}$ of $r-2$ new vertices and the edge $\{v_i,v_j\}\cup B_{i,j}$, where the $B_{i,j}$'s are pairwise disjoint over all such pairs $\{i,j\}$. We call $H^F_p$ the expanded $p$-clique with an embedded $F$. For a relatively large family of $F$, we show that for all sufficiently large $n$, $ex(n,H^F_p)=|T_r(n,p-1)|$, where $T_r(n,p-1)$ is the balanced complete $(p-1)$-partite $r$-graph on $n$ vertices. We also establish structural stability of near extremal graphs. Our results generalize or strengthen several earlier results and provide a class of hypergraphs for which the Tur\'an number is exactly determined (for large $n$).
Gravity generated by large masses has been observed using a variety of probes from atomic interferometers to torsional balances. However, gravitational coupling between small masses has never been observed so far. Here, we demonstrate sensitive displacement sensing of the Brownian motion of an optically trapped 7-mg pendulum motion whose natural quality factor is increased to $10^8$ through dissipation dilution. The sensitivity for an integration time of one second corresponds to the displacement generated by the gravitational coupling between the probe and a mm separated 100 mg mass, whose position is modulated at the pendulum mechanical resonant frequency. Development of such a sensitive displacement sensor using a mg-scale device will pave the way for a new class of experiments where gravitational coupling between small masses in quantum regimes can be achieved.
New multi-color light curves of the very short period K-type eclipsing binary V1799 Ori were obtained and analyzed with the W-D code. The photometric solutions reveal that the system is a W-type shallow-contact binary with a mass ratio of $q=1.335(\pm0.005)$ and a degree of contact about $f = 3.5(\pm1.1)\%$. In general, the results are in good agreement with which is reported by Samec. The remarkable O'Connell effects in the light curves are well explained by employing star spots on the binary surface, which confirms that the system is active at present. Several new times of light minimum were obtained. All the available times of light minimum were collected, along with the recalculated and new obtained. Applying a least-squares method to the constructed O-C diagram, a new ephemeris was derived for V1799 Ori. The orbital period is found to show a continuous weak increase at a rate of $1.8(\pm0.6)\times10^{-8}$ days$\cdot$yr$^{-1}$. The extreme-shallow contact, together with the period increase, suggests that the binary may be at a critical stage predicted by the TRO theory. \keywords{binaries : close -- binaries : eclipsing -- stars: individual (V1799 Ori)
Recently, Blanco-Chac\'on proved the equivalence between the Ring Learning With Errors and Polynomial Learning With Errors problems for some families of cyclotomic number fields by giving some upper bounds for the condition number $\operatorname{Cond}(V_n)$ of the Vandermonde matrix $V_n$ associated to the $n$th cyclotomic polynomial. We prove some results on the singular values of $V_n$ and, in particular, we determine $\operatorname{Cond}(V_n)$ for $n = 2^k p^\ell$, where $k, \ell \geq 0$ are integers and $p$ is an odd prime number.
We consider a 2-dimensional thin domain with order of thickness {\epsilon} which presents oscillations of amplitude also {\epsilon} on both boundaries, top and bottom, but the period of the oscillations are of different order at the top and at the bottom. We study the behavior of the Laplace operator with Neumann boundary condition and obtain its asymptotic homogenized limit as the parameter {\epsilon} goes to 0. We are interested in understanding how this different oscillatory behavior at the boundary, influences the limit problem.
We study the relativistic dynamics of brane probes in singular warped spacetimes and establish limits for such analysis. The behavior of the semiclassical brane probe wave functions implies that unitarity boundary conditions can be imposed at the singularity.
The Atacama Large Millimeter/submillimeter Array (ALMA) is a new powerful tool for observing the Sun at high spatial, temporal, and spectral resolution. These capabilities can address a broad range of fundamental scientific questions in solar physics. The radiation observed by ALMA originates mostly from the chromosphere - a complex and dynamic region between the photosphere and corona, which plays a crucial role in the transport of energy and matter and, ultimately, the heating of the outer layers of the solar atmosphere. Based on first solar test observations, strategies for regular solar campaigns are currently being developed. State-of-the-art numerical simulations of the solar atmosphere and modeling of instrumental effects can help constrain and optimize future observing modes for ALMA. Here we present a short technical description of ALMA and an overview of past efforts and future possibilities for solar observations at submillimeter and millimeter wavelengths. In addition, selected numerical simulations and observations at other wavelengths demonstrate ALMA's scientific potential for studying the Sun for a large range of science cases.
The metallicity gradient and the stellar distribution within the Local Group dwarf galaxy NGC 6822 has been studied photometrically using asymptotic branch stars (AGB). In order to study the stellar and metallicity distribution, the carbon- and oxygen-rich AGB stars have been isolated using deep high-quality near-infrared UKIRT photometry. The ratio between them, the C/M ratio, has been used to derive the [Fe/H] abundance within the galaxy. The [Fe/H] abundance and stellar distribution were analysed as a function of galactic radius. A mean C/M ratio of 0.288 +/- 0.014 has been found which corresponds to an iron abundance of [Fe/H] =-1.14 +/-0.08 dex, with variations in the north and south, as well as at larger galactocentric distances. Variations in the magnitude of the tip of the red giant branch has also been detected.
We study the spin-$\frac32$ Hubbard-Kondo lattice model by means of the Composite Operator Method, after applying a Holstein-Primakov transformation. The spin and particle dynamics in the ferromagnetic state are calculated by taking into account strong on-site correlations between electrons and antiferromagnetic exchange among $\frac32$ spins, together with usual Hund coupling between electrons and spins.
The Benjamin-Ono equation describes the propagation of internal waves in a stratified fluid. In the present work, we study large time dynamics of its regular solutions via some probabilistic point of view. We prove the existence of an invariant measure concentrated on $C^\infty(\T)$ and establish some qualitative properties of this measure. We then deduce a recurrence property of regular solutions and other corollaries using ergodic theorems. The approach used in this paper applies to other equations with infinitely many conservation laws, such as the KdV and cubic Schr\"odinger equations in 1D. It uses the fluctuation-dissipation-limit approach and relies on a \textit{uniform} smoothing lemma for stationary solutions to the damped-driven Benjamin-Ono equation.
We prove a quantitative regularity theorem and blowup criterion for classical solutions of the three-dimensional Navier-Stokes equations satisfying certain critical conditions. The solutions we consider have $\|r^{1-\frac3q}u\|_{L_t^\infty L_x^q}<\infty$ where $r=\sqrt{x_1^2+x_2^2}$ and either $q\in(3,\infty)$, or $u$ is axisymmetric and $q\in(2,3]$. Using the strategy of Tao (2019), we obtain improved subcritical estimates for such solutions depending only on the double exponential of the critical norm. One consequence is a double logarithmic lower bound on the blowup rate. We make use of some tools such as a decomposition of the solution that allows us to use energy methods in these spaces, as well as a Carleman inequality for the heat equation suited for proving quantitative backward uniqueness in cylindrical regions.
It was proven in 1915 by Leopold Theisinger that the $H_n$ harmonic numbers are never integers. In 1996 Conway and Guy have defined the concept of hyperharmonic numbers. The question naturally arises: are there any integer hyperharmonic numbers? The author gives a partial answer to this question and conjectures that the answer is "no".
We examine whether the spectral energy distribution of UV continuum emission of active galactic nuclei changes during flux variation. We used multi-epoch photometric data of QSOs in the Stripe 82 observed by the SDSS Legacy Survey and selected 10 bright QSOs observed with high photometric accuracies, in the redshift range of z = 1.0-2.4 where strong broad emission lines such as Ly\alpha and CIV do not contaminate SDSS filters, to examine spectral variation of the UV continuum emission with broadband photometries. All target QSOs showed clear flux variations during the monitoring period 1998-2007, and the multi-epoch flux data in two different bands obtained on the same night showed a linear flux-to-flux relationship for all target QSOs. Assigning the flux in the longer wavelength to the x-axis in the flux-to-flux diagram, the x-intercept of the best-fit linear regression line was positive for most targets, which means that their colors in the observing bands become bluer as they become brighter. Then, the host-galaxy flux was estimated on the basis of the correlation between the stellar mass of the bulge of the host galaxy and the central black hole mass. We found that the longer-wavelength flux of the host galaxy was systematically smaller than that of the fainter extension of the best-fit regression line at the same shorter-wavelength flux for most targets. This result strongly indicates that the spectral shape of the continuum emission of QSOs in the UV region usually becomes bluer as it becomes brighter. We found that the multi-epoch flux-to-flux plots could be fitted well with the standard accretion disk model changing the mass accretion rate with a constant black hole mass for most targets. This finding strongly supports the standard accretion disk model for UV continuum emission of QSOs.
Context. Emission and absorption line profiles which are formed in the interaction of pre-main sequence (PMS) stars and their circumstellar environment are found to be variable at various timescales. Aims. We investigate the patterns and timescales of temporal line profile variability in order to explore the dynamical circumstellar environment of the PMS Herbig Ae star V351 Ori. Methods.We obtained 45 high-resolution (R~28,000) spectra of V351 Ori at timescales of hours, days, and months.We analysed the H\alpha line profiles and also examined the H\beta, NaD1 and NaD2 line profiles to explore the nature of the spectroscopic variability. Results. The H\alpha line profiles showed strong variations over all timescales. The shape of the profiles changed over timescales of a day. Single as well as simultaneous event(s) of blue-shifted and red-shifted transient absorption components (TACs), i.e. signatures of outflow and infall, were also observed in the H\alpha line profiles. The shortest period of variation in the TACs was < 1 hour. All transient absorption events were found to decelerate with a rate of a few to fractions of m s-2. The depth and width of the TACs were also changing with time. The presence of elongated red-shifted components at some epochs supports the episodic nature of accretion. Conclusions. Variable emission and absorption components detected in H\alpha line profiles show the dynamic nature of interaction between V351 Ori and its circumstellar environment. The H\alpha non-photospheric profiles of the star most probably originate in the disk wind. Episodic accretion of gaseous material at a slow rate and outflow of clumpy gaseous material are still occurring in V351 Ori at an age of ~6.5 Myr. Dynamic magnetospheric accretion and disk wind emerge as the most satisfactory model for interpreting the observed line profile variations of V351 Ori.
Various Monte Carlo techniques are used to determine the complete phase diagrams of the square well model for the attractive ranges $\lambda = 1.15$ and $\lambda = 1.25$. The results for the latter case are in agreement with earlier Monte Carlo simulations for the fluid-fluid coexistence curve and yield new results for the liquidus-solidus lines. Our results for $\lambda = 1.15$ are new. We find that the fluid-fluid critical point is metastable for both cases, with the case $\lambda = 1.25$ being just below the threshold value for metastability. We compare our results with prior studies and with experimental results for the gamma-II crystallin.
Low-mass helium-core white-dwarfs (WDs) with masses below 0.5 Msun are known to be formed in binary star systems but unexpectedly a significant fraction of them seem to be single. On the other hand, in Cataclysmic Variables (CVs) a large number of low-mass WD primary stars is predicted but not observed. We recently showed that the latter problem can be solved if consequential angular momentum loss causes especially CVs with low-mass WDs to merge and form single stars. Here we simulate the population of single WDs resulting from single star evolution and from binary star mergers taking into account these new merging CVs. We show that according to the revised model of CV evolution, merging CVs might be the dominant channel leading to the formation of low-mass single WDs and that the predicted relative numbers are consistent with observations. This can be interpreted as further evidence for the revised model of CV evolution we recently suggested. This model includes consequential angular momentum loss that increases with decreasing WD mass and might not only explain the absence of low-mass WD primaries in CVs but also the existence of single low-mass WDs.
We report complete near-infrared (0.9-2.4 $\mu$m) spectral observations of the largest know trans-neptunian objects (TNO) 28976 = 2001 KX$_{76}$ taken in two different nights using the new Near Infrared Camera Spectrometer (NICS) attached to the 3.56m Telescopio Nazionale Galileo (TNG). The spectra are featureless and correspond to a neutral colored object. Our observations indicate that the surface of 2001 KX$_{76}$ is probably highly evolved due to long term irradiation, and that collisional resurfacing processes have not played an important role in its evolution.
We consider the Schroedinger operator in R^3 with N point interactions placed at Y=(y_1, ... ,y_N), y_j in R^3, of strength a=(a_1, ... ,a_N). Exploiting the spectral theorem and the rather explicit expression for the resolvent we prove a (weighted) dispersive estimate for the corresponding Schroedinger flow.   In the special case N=1 the proof is directly obtained from the unitary group which is known in closed form.
First, we verify that the physical parameters estimated for the four directly detected gravitational wave (GW) events involving coalescence of binary black holes (BHs) indeed uphold the second law of BH thermodynamics, strengthening further the case for BH physics. Non-spherical gravitational collapse leading to BH formation may entail very high GW luminosities during the final phase of implosion, reaching non-negligible fraction of Dyson luminosity $\sim c^5/G $.   Most galaxies harbor supermassive black holes (SMBHs) in their nuclear regions. Several bright quasars detected at redshifts $\gtrsim$ 6 are powered by accreting SMBHs of mass $\gtrsim 10^9 M_\odot$ when the universe was only $\sim 10^9$ yrs old. We posit that creation of SMBHs occurs due to collapse (on dynamical time scales $\sim 10^8$ yrs) of ultra-light bosonic dark matter (DM) particles that have undergone Bose-Einstein condensation. Furthermore, oscillations in DM Bose-Einstein condensates (BECs) triggered by tidal forces in interacting galaxies can lead to bursts of star formation in the galactic nuclei because of frequent collisions of gas clouds due to changing gravitational field.   We buttress our proposal by first employing simple but tangible physical arguments, and then by making use of Gross-Pitaevskii equation to study the formation of rotating SMBHs having mass $\gtrsim 10^9 M_\odot$. We also make simple estimates of GW amplitude as well as luminosity ensuing from the time varying configuration of BECs, constituted by the ultra-light dark bosons, and remark on the possibility of detecting such GWs using Pulsar Timing Arrays.
In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian distribution. We also derive useful results regarding the expected value of certain quadratic forms based solely on covariances between matrices. Previous definitions of matrix normal distributions are severely under-parameterized, assuming unrealistic structure on the covariance (see Section 2). We believe that our generalization is better equipped for use in practice.
We propose mechanisms for the spin Hall effect in metallic systems arising from the coupling between conduction electrons and local magnetic moments that are dynamically fluctuating. Both a side-jump-type mechanism and a skew-scattering-type mechanism are considered. In either case, dynamical spin fluctuation gives rise to a nontrivial temperature dependence in the spin Hall conductivity. This leads to the enhancement in the spin Hall conductivity at nonzero temperatures near the ferromagnetic instability. The proposed mechanisms could be observed in $4d$ or $5d$ metallic compounds.
Magnetic semiconductors have aroused interest due to their various functionalities related to spintronic devices. Manganese (Mn) as a substitutional impurity in A3B5 semiconductors supplies not only holes, but also localized spins. The ejection of Mn atoms with an uncompensated magnetic moment leads to the appearance of ferromagnetic properties. The most suitable material characterized by long-term spin dynamics is n-type GaAs. In p-type GaAs, the spin relaxation time of electrons is generally much shorter. For purposes of this research, electron-spin relaxation times in 3D and 2D p-type GaAs were studied. Calculation of impurity densities and charge state of magnetic acceptors demonstrate the essential composition of the material. Comparison of theoretical and experimental data in optical-spin orientation of electrons reveal the longest spin relaxation time of 77 ns in 2D GaAs:Mn, less than twice the best time in the p-type 3D GaAs material.
We investigate the time evolution of the entropy for a paradigmatic conservative dynamical system, the standard map, for different values of its controlling parameter $a$. When the phase space is sufficiently ``chaotic'' (i.e., for large $|a|$), we reproduce previous results. For small values of $|a|$, when the phase space becomes an intricate structure with the coexistence of chaotic and regular regions, an anomalous regime emerges. We characterize this anomalous regime with the generalized nonextensive entropy, and we observe that for values of $a$ approaching zero, it lasts for an increasingly large time. This scenario displays a striking analogy with recent observations made in isolated classical long-range $N$-body Hamiltonians, where, for a large class of initial conditions, a metastable state (whose duration diverges with $1/N\to 0$) is observed before it crosses over to the usual, Boltzmann-Gibbs regime.