ShantanuT01/DACTYL-Pretraining huggingface dataset:
By a random process with immigration at random times we mean a shot noise process with a random response function (response process) in which shots occur at arbitrary random times. The so defined random processes generalize random processes with immigration at the epochs of a renewal process which were introduced in [Iksanov et al. (2017). Bernoulli, 23, 1233--1278] and bear a strong resemblance to a random characteristic in general branching processes and the counting process in a fixed generation of a branching random walk generated by a general point process. We provide sufficient conditions which ensure weak convergence of finite-dimensional distributions of these processes to certain Gaussian processes. Our main result is specialised to several particular instances of random times and response processes.
We present and discuss the Halpha (6563 A) observations of the contact (W UMa type) binaries AE Phoenicis and YY Eridani, obtaineded in 1989, 1990 and 1995 with the CAT/CES telescope of the Southern European Observatory (ESO). In particular, we compare the intrinsic equivalent widths of both components with the NextGen theoretical models and the saturation limit. We find that the average Halpha equivalent widths are close to the saturation border and that the primary components have excess Halpha-emission, indicating enhanced chromospheric activity. This is compatible with both theoretical and observational suggestions that the primary is the more magnetically active component and is filled with (mostly unresolvable) dark spots and associated chromospheric plages.
The mass (volume and areal densities) versus velocity as well as the size versus velocity distributions of a shock-induced cloud of particles are investigated using large scale molecular dynamics (MD) simulations. A generic 3D tin crystal with a sinusoidal free surface roughness (single wavelength) is set in contact with vacuum and shock-loaded so that it melts directly on shock. At the reflection of the shock wave onto the perturbations of the free surface, 2D sheets/jets of liquid metal are ejected. The simulations show that the distributions may be described by an analytical model based on the propagation of a fragmentation zone, from the tip of the sheets to the free surface, within which the kinetic energy of the atoms decreases as this zone comes closer to the free surface on late times. As this kinetic energy drives (i) the (self-similar) expansion of the zone once it has broken away from the sheet and (ii) the average size of the particles which result from fragmentation in the zone, the ejected mass and the average size of the particles progressively increase in the cloud as fragmentation occurs closer to the free surface. Though relative to nanometric scales, our model reproduces quantitatively experimental profiles and may help in their analysis.
By making use of the weak gravitational field approximation, we obtain a linearized solution of the gravitational vacuum field equation in an anisotropic spacetime. The plane-wave solution and dispersion relation of gravitational wave is presented explicitly. There is possibility that the speed of gravitational wave is larger than the speed of light and the casuality still holds. We show that the energy-momentum of gravitational wave in the ansiotropic spacetime is still well defined and conserved.
We exploit the recent observations of extremely metal-poor (EMP) stars in the Galactic halo and investigate the constraints on the IMF of the stellar population that left these low-mass survivors of [Fe/H]<-2.5 and the chemical evolution that they took part in. A high-mass IMF with the typical mass~10Msun and the overwhelming contribution of low-mass members of binaries to the EMP survivors are derived from the statistics of carbon-enriched EMP stars with and without the enhancement of s-process elements (Komiya et al. 2007). We first examine the analysis to confirm their results for various assumptions on the mass-ratio distribution function. As compared with the uniform distribution, the increase or decrease function of the mass ratio gives a higher- or lower-mass IMF, and a lower-mass IMF results for the independent distribution with the both members in the same IMF, but the derived ranges of typical mass differ less than by a factor of two and overlap for the extreme cases. Furthermore, we prove that the same constraints are placed on the IMF from the surface density of EMP stars estimated from the surveys and the chemical evolution consistent with the metal yields of theoretical supernova models. We then apply the derived high-mass IMF with the binary contribution to show that the observed MDF of EMP stars can be reproduced not only for the shape but also for the number of EMP stars. In particular, the scarcity of stars below [Fe/H]<-4 is naturally explained in terms of the hierarchical structure formation, and there is no indication of significant changes in the IMF for the EMP Population. The present study indicates that 3 HMP stars of [Fe/H]<-4 are the primordial stars that were born as the low-mass members of binaries before the host clouds were polluted by their own supernovae.
Using a general Ginzburg-Landau effective Lagrangian, we study the topological structure and low-lying collective modes of dense QCD having both chiral and diquark condensates, for two and three massless flavors. As we found earlier, the QCD axial anomaly acts as an external field applied to the chiral condensate in a color superconductor and, as a new critical point emerges, leads to a crossover between the broken chiral symmetry and color superconducting phases. At intermediate densities where both chiral and diquark condensates are present, we derive a generalized Gell-Mann- Oakes-Renner relation between the masses of pseudoscalar bosons and the magnitude of the chiral and diquark-condensates. We show explicitly the continuity of the ordinary pion at low densities to a generalized pion at high densities.
Recently there were many quantum protocols devoted to solve the millionaire problem and private comparison problem by adding a semi-honest third party. They all require complicated quantum methods, while still leak a non-trivial amount of information to at least one of the parties. But it will be shown here that once the third party is introduced, there are very simple protocols which require quantum key distribution as the only quantum resource, and the amount of information leaked can be made arbitrarily small. Furthermore, even a dishonest third party cannot spoil the protocols. Thus our solutions surpass all existing protocols on both feasibility and security.
We present a complete solution of the WZW model on the supergroup GL(1|1). Our analysis begins with a careful study of its minisuperspace limit (``harmonic analysis on the supergroup''). Its spectrum is shown to contain indecomposable representations. This is interpreted as a geometric signal for the appearance of logarithms in the correlators of the full field theory. We then discuss the representation theory of the gl(1|1) current algebra and propose an Ansatz for the state space of the WZW model. The latter is established through an explicit computation of the correlation function. We show in particular, that the 4-point functions of the theory factorize on the proposed set of states and that the model possesses an interesting spectral flow symmetry. The note concludes with some remarks on generalizations to other supergroups.
We calculate the finite temperature and non-equilibrium electric current through systems described generically at low energy by a singlet and \emph{two} spin doublets for $N$ and $N \pm 1$ electrons respectively, coupled asymmetrically to two conducting leads, which allows for destructive interference in the conductance.   The model is suitable for studying transport in a great variety of systems such us aromatic molecules, different geometries of quantum dots and rings with applied magnetic flux. As a consequence of the interplay between interference and Kondo effect, we find changes by several orders of magnitude in the values of the conductance and its temperature dependence as the doublet level splitting is changed by some external parameter. The differential conductance at finite bias is negative for some parameters.
Galaxies grow primarily via accretion-driven star formation in discs and merger-driven growth of bulges. These processes are implicit in semi-analytical models of galaxy formation, with bulge growth in particular relating directly to the hierarchical build-up of halos and their galaxies. In this paper, we consider several implementations of two semi-analytical models. Focusing on implementations in which bulges are formed during mergers only, we examine the fractions of elliptical galaxies and both passive and star-forming disk galaxies as functions of stellar and halo mass, for central and satellite systems. This is compared to an observational cross-matched SDSS+RC3 z ~ 0 sample of galaxies with accurate visual morphological classifications and M_{stellar} > 10^10.5 M_{sol}. The models qualitatively reproduce the observed increase of elliptical fraction with stellar mass, and with halo mass for central galaxies, supporting the idea that observed ellipticals form during major mergers. However, the overall elliptical fraction produced by the models is much too high compared with the z ~ 0 data. Since the "passive" -- i.e. non-star-forming -- fractions are approximately reproduced, and since the fraction which are star-forming disc galaxies is also reproduced, the problem is that the models overproduce ellipticals at the expense of passive S0 and spiral galaxies. Bulge-growth implementations (tuned to reproduce simulations) which allow the survival of residual discs in major mergers still destroy too much of the disc. Increasing the lifetime of satellites, or allowing significant disc regrowth around merger remnants, merely increases the fraction of star-forming disc galaxies. Instead, it seems necessary to reduce the mass ratios of merging galaxies, so that most mergers produce modest bulge growth in disc-galaxy remnants instead of ellipticals. [Abridged]
Suggested a non-linear, non-gauge invariant model of Maxwell equations, based on the Kaluza-Klein theory. The spectrum of elementary charges and masses is obtained.
We examine the spectrum of a massive scalar particle interacting with the strong gravitational field of a static, spherically symmetric object which is not quite massive enough to be a black hole. As was found in the case of massless particles, there exists a dense spectrum of long lived resonances (meta-stable states), which leads to an energy-averaged cross section for particle capture which approaches the absorption cross-section for a Schwarzschild black hole. However, the generalisation to non-zero mass introduces new phenomena, along with important qualitative changes to the scattering properties. In contrast to the massless case, there exists a spectrum of bound states with almost identical structure to that of the resonances, allowing for the possibility of radiative transitions and particle capture. The resonance lifetimes for elastic processes are parametrically larger than for massless particles, meaning the absorption cross-section approaches the black hole case faster than for massless scalars.
In this paper we extend our previously discovered exact solution for an SU(2) gauge theory coupled to a massless, non-interacting scalar field, to the general group SU(N+1). Using the first-order formalism of Bogomolny, an exact, spherically symmetric solution for the gauge and scalar fields is found. This solution is similiar to the Schwarzschild solution of general relativity, in that the gauge and scalar fields become infinite at a radius, $r_0 = K$, from the origin. It is speculated that this may be the confinement mechanism that has long been sought for in non-Abelian gauge theories, since any particle which carries the SU(N+1) charge would become permanently trapped once it entered the region $r < r_0$. The energy of the field configuration of this solution is calculated.
We report the discovery of a correlation among three prompt emission properties of GRBs. These are the isotropic peak luminosity L_iso, the peak energy of the time-integrated prompt emission spectrum E_pk, and the ``high signal" timescale T_0.45, previously used to characterize the variability behavior of bursts. In the rest frame of the source the found correlation reads L_iso\propto E_pk^1.62 T_0.45^-0.49. We find other strong correlations, but at the cost of increasing the number of variables, involving the variability and the isotropic energy of the prompt emission. With respect to the previous tight correlations found in GRBs the newly found correlation does not require any information from the afterglow phase of the bursts, nor any model-dependent assumption. In the popular scenario in which we are receiving beamed radiation originating in a fireball pointing at us, the found correlation preserves its form in the comoving frame. This helps to explain the small scatter of the correlation, and underlines the role of the local brightness (i.e. the brightness of the visible fraction of the fireball surface). This correlation has been found for 19 objects, and it is hard to establish if any selection bias affects it. Its connection with the prompt local brightness is promising, but a solid physical understanding is still to be found. Despite all that, we find that some properties of the correlation, which we discuss, support its true existence, and this has important implications for the GRB physics. Furthermore, it is possible to use such correlation as an accurate redshift estimator, and its tightness will allow us to use it as a tool to constrain the cosmological parameters (abridged)
We compare a star and a ring network of interacting spins in terms of the entanglement they can provide between the nearest and the next to nearest neighbor spins in the ground state. We then investigate whether this entanglement can be optimized by allowing the system to interact through a weighted combination of the star and the ring geometries. We find that such a weighted combination is indeed optimal in certain circumstances for providing the highest entanglement between two chosen spins. The entanglement shows jumps and counterintuitive behavior as the relative weighting of the star and the ring interactions is varied. We give an exact mathematical explanation of the behavior for a five qubit system (four spins in a ring and a central spin) and an intuitive explanation for larger systems. For the case of four spins in a ring plus a central spin, we demonstrate how a four qubit GHZ state can be generated as a simple derivative of the ground state. Our calculations also demonstrate that some of the multi-particle entangled states derivable from the ground state of a star network are sufficiently robust to the presence of nearest neighbor ring interactions.
We start with a 2-charge D1-D5 BPS geometry that has the shape of a ring; this geometry is regular everywhere. In the dual CFT there exists a perturbation that creates one unit of excitation for left movers, and thus adds one unit of momentum P. This implies that there exists a corresponding normalizable perturbation on the near-ring D1-D5 geometry. We find this perturbation, and observe that it is smooth everywhere. We thus find an example of `hair' for the black ring carrying three charges -- D1, D5 and one unit of P. The near-ring geometry of the D1-D5 supertube can be dualized to a D6 brane carrying fluxes corresponding to the `true' charges, while the quantum of P dualizes to a D0 brane. We observe that the fluxes on the D6 brane are at the threshold between bound and unbound states of D0-D6, and our wavefunction helps us learn something about binding at this threshold.
A microscopic angular momentum projection after variation is used to describe quadrupole collectivity in (^{30,32,34}Mg) and (^{32,34,36,38}Si). The Hartree-Fock-Bogoliubov states obtained in the quadrupole constrained mean field approach are taken as intrinsic states for the projection. Excitation energies of the first (2^{+}) states and the (B(E2,0^{+}\to 2^{+})) transition probabilities are given. A reasonable agreement with available experimental data is obtained. It is also shown that the mean field picture of those nuclei is strongly modified by the projection.
Given an elliptic curve with supersingular reduction at an odd prime p, Iovita and Pollack have generalised results of Kobayashi to define even and odd Coleman maps at p over Lubin-Tate extensions given by a formal group of height 1. We generalise this construction to modular forms of higher weights.
We present a detailed study of how the Star Formation Rate (SFR) relates to the interstellar medium (ISM) of M31 at ~140pc scales. The SFR is calculated using the far-ultraviolet and 24um emission, corrected for the old stellar population in M31. We find a global value for the SFR of 0.25+/-0.05Msun/yr and compare this with the SFR found using the total far-infrared (FIR) luminosity. There is general agreement in regions where young stars dominate the dust heating. Atomic hydrogen (HI) and molecular gas (traced by carbon monoxide, CO) or the dust mass is used to trace the total gas in the ISM. We show that the global surface densities of SFR and gas mass place M31 amongst a set of low-SFR galaxies in the plot of Kennicutt (1998b). The relationship between SFR and gas surface density is tested in six radial annuli across M31, assuming a power law relationship with index, N. The star formation law using total gas traced by HI and CO gives a global index of N=2.03+/-0.04, with a significant variation with radius; the highest values are observed in the 10kpc ring. We suggest that this slope is due to HI turning molecular at ~10Msun/pc2. When looking at H2 regions, we measure a higher mean SFR suggesting a better spatial correlation between H2 and SF. We find N~0.6 with consistent results throughout the disk - this is at the low end of values found in previous work and argues against a superlinear SF law on small scales.
We study the finite-size effects, like the surface and Coulomb energies, on the hadron-quark mixed phase in neutron stars. The equilibrium conditions for coexisting hadronic and quark phases are derived by minimizing the total energy including the surface and Coulomb contributions, which are different from the Gibbs conditions without finite-size effects. We employ the relativistic mean-field model to describe the hadronic phase, while the Nambu-Jona-Lasinio model with vector interactions is used for the quark phase. It is found that finite-size effects can significantly reduce the region of the mixed phase, and the results lie between those of the Gibbs and Maxwell constructions. We show that a massive star may contain a mixed-phase core and its size depends on the surface tension of the hadron-quark interface and the vector coupling between quarks. The repulsive vector interaction in the Nambu-Jona-Lasinio model can stiffen the equation of state of quark matter, and therefore, delay the phase transition and increase the maximum mass of neutron stars.
We complete the description of semistable models for modular curves associated with maximal subgroups of $\mathrm{GL}_2 ({\mathbb F}_p )$ (for $p$ any prime, $p>5$). That is, in the new cases of non-split Cartan modular curves and exceptional subgroups, we identify the irreducible components and singularities of the reduction mod $p$, and the complete local rings at the singularities. We review the case of split Cartan modular curves. This description suffices for computing the group of connected components of the fibre at $p$ of the N\'eron model of the Jacobian.
We examine the dynamical evolution and statistical properties of the supernova ejecta of massive primordial stars in a cosmological framework to determine whether this first population of stars could have enriched the universe to the levels and dispersions seen by the most recent observations of the Lyman-Alpha forest. We evolve a lambda CDM model in a 1 Mpc^3 volume to a redshift of z = 15 and add ``bubbles'' of metal corresponding to the supernova ejecta of the first generation of massive stars in all dark matter halos with masses greater than 5 times 10^5 solar masses. These initial conditions are then evolved to z = 3 and the distribution and levels of metals are compared to observations. In the absence of further star formation the primordial metal is initially contained in halos and filaments. Photoevaporation of metal-enriched gas due to the metagalactic ultraviolet background radiation at the epoch of reionization (z ~ 6) causes a sharp increase of the metal volume filling factor. At z = 3, ~ 2.5% of the simulation volume (approx. 20% of the total gas mass) is filled with gas enriched above a metallicity of 10^-4 Z_solar, and less than 0.6% of the volume is enriched above a metallicity of 10^-3 Z_solar. This suggests that, even with the most optimistic prescription for placement of primordial supernova and the amount of metals produced by each supernova, this population of stars cannot entirely be responsible for the enrichment of the Lyman-$\alpha$ forest to the levels and dispersions seen by current observations unless we have severely underestimated the duration of the Pop III epoch. However, comparison to observations show that Pop III supernovae can be significant contributors to the very low overdensity Lyman-Alpha forest.
We prove that certain quotients of entire functions are characteristic functions. Under some conditions, the probability measure corresponding to a characteristic function of that type has a density which can be expressed as a generalized Dirichlet series, which in turn is an infinite linear combination of exponential or Laplace densities. These results are applied to several examples.
We build a sample of 298 spectroscopically-confirmed galaxies at redshift z~2, selected in the z-band from the GOODS-MUSIC catalog. By exploiting the rest frame 8 um luminosity as a proxy of the star formation rate (SFR) we check the accuracy of the standard SED-fitting technique, finding it is not accurate enough to provide reliable estimates of the galaxy physical parameters. We then develop a new SED-fitting method that includes the IR luminosity as a prior and a generalized Calzetti law with a variable RV . Then we exploit such a new method to re-analyze our galaxy sample, and to robustly determine SFRs, stellar masses and ages. We find that there is a general trend of increasing attenuation with the SFR. Moreover, we find that the SFRs range between a few to 1000 solar mass per year, the masses from one billion to 400 billion solar masses, while the ages from a few tens of Myr to more than 1 Gyr. We discuss how individual age easurements of highly attenuated objects indicate that dust must form within a few tens of Myr and be copious already at ~100 Myr. In addition, we find that low luminous galaxies harbor, on average, significantly older stellar populations and are also less massive than brighter ones; we discuss how these findings and the well known 'downsizing' scenario are consistent in a framework where less massive galaxies form first, but their star formation lasts longer. Finally, we find that the near-IR attenuation is not scarce for luminous objects, contrary to what is customarily assumed; we discuss how this affects the interpretation of the observed mass-to-light ratios.
A multiple (loc. Cohen Macaulay) structure, X, on a space curve C in P3 is said to be primitive if X is locally contained in a smooth surface. We give numerical conditions for C to be a "primitive" set theoretic complete intersection (i.e. to have a primitive multiple structure which is a complete intersection).