ShantanuT01/DACTYL-Pretraining huggingface dataset:
Given $p \in (1, 2)$, we study $L^p$-solutions of a multi-dimensional backward stochastic differential equation with jumps (BSDEJ) whose generator may not be Lipschitz continuous in $(y,z)-$variables. We show that such a BSDEJ with a p-integrable terminal data admits a unique $L^p$ solution by approximating the monotonic generator by a sequence of Lipschitz generators via convolution with mollifiers and using a stability result.
Naive light-front quantization, carried out by a light-front energy integration of covariant amplitudes, is not guaranteed to generate the corresponding Feynman amplitudes. In an explicit example we show that the nonvalence contribution to the minus-component of the EM current of a meson with fermion constituents has a persistent end-point singularity. Only after this term is subtracted, the result is covariant and satisfies current conservation. If the spin-1/2 constituents are replaced by spin zero ones, the singularity does not occur and the result is, without any adjustment, identical to the Feynman amplitude. Numerical estimates of valence and nonvalence contributions are presented for the cases of fermion and boson constituents.
Proton emission from deformed nuclei is described within the non-adiabatic weak coupling model which takes into account the coupling to $\gamma$-vibrations around the axially-symmetric shape. The coupled equations are derived within the Gamow state formalism. A new method, based on the combination of the R-matrix theory and the oscillator expansion technique, is introduced that allows for a substantial increase of the number of coupled channels. As an example, we study the deformed proton emitter $^{141}$Ho.
We report the measured H$\alpha$ fluxes and images of 66 nearby objects observed with the 6-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences. Three of these objects: IC2233, UGC4704, and NGC3432 are late-type spiral galaxies, six objects are distant globular clusters of the M31 galaxy, and the remaining ones are dwarf galaxies. We used the measured H$\alpha$ fluxes to estimate the integrated and specific star-formation rates and analyzed some of the main features of star formation in dwarf galaxies and late-type spirals based on a sample of more than 500 Local volume galaxies.
First we prove a modified version of the famous Lemma on the mean square estimate for exponential sums, by plugging the Cesaro weights in the right hand side of Gallagher's inequality. Then we apply it, in order to establish a mean value estimate for the Dirichlet polynomials.
We present here a detailed X-ray spectral analysis of the AGN belonging to the XMM-Newton bright survey (XBS) that comprises more than 300 AGN up to redshift ~ 2.4. We performed an X-ray analysis following two different approaches: by analyzing individually each AGN X-ray spectrum and by constructing average spectra for different AGN types. From the individual analysis, we find that there seems to be an anti correlation between the spectral index and the sources' hard X-ray luminosity, such that the average photon index for the higher luminosity sources (> 10E44 erg/s) is significantly flatter than the average for the lower luminosity sources. We also find that the intrinsic column density distribution agrees with AGN unified schemes, although a number of exceptions are found (3% of the whole sample), which are much more common among optically classified type 2 AGN. We also find that the so-called "soft-excess", apart from the intrinsic absorption, constitutes the principal deviation from a power-law shape in AGN X-ray spectra and it clearly displays different characteristics, and likely a different origin, for unabsorbed and absorbed AGN. Regarding the shape of the average spectra, we find that it is best reproduced by a combination of an unabsorbed (absorbed) power law, a narrow Fe Kalpha emission line and a small (large) amount of reflection for unabsorbed (absorbed) sources. We do not significantly detect any relativistic contribution to the line emission and we compute an upper limit for its equivalent width (EW) of 230 eV at the 3 sigma confidence level. Finally, by dividing the type 1 AGN sample into high- and low-luminosity sources, we marginally detect a decrease in the narrow Fe Kalpha line EW and in the amount of reflection as the luminosity increases, the "so-called" Iwasawa-Taniguchi effect.
We present the stellar surface mass density {\it vs.} gas metallicity ($\Sigma_*-Z$) relation for more than 500,000 spatially-resolved star-forming resolution elements (spaxels) from a sample of 653 disk galaxies included in the SDSS IV MaNGA survey. We find a tight relation between these local properties, with higher metallicities as the surface density increases. This relation extends over three orders of magnitude in the surface mass density and a factor of four in metallicity. We show that this local relationship can simultaneously reproduce two well-known properties of disk galaxies: their global mass-metallicity relationship {\it and} their radial metallicity gradients. We also find that the $\Sigma_* - Z$ relation is largely independent of the galaxy's total stellar mass and specific star-formation rate (sSFR), except at low stellar mass and high sSFR. These results suggest that in the present-day universe local properties play a key role in determining the gas-phase metallicity in typical disk galaxies.
In this note, we use the first order formalism for attractor flows in N=2 SUGRA extremal black hole backgrounds to establish a formal correspondence between the RG flow of moduli in the underlying N=(2,2) SCFT and bulk attractor flows. Starting from a study of moduli flow trajectories in the CFT, we derive a potential which generates the aforesaid flow. This potential is shown to be a symplectic invariant with the same form as the black hole potential which drives the attractor flows in the bulk. We use these results to make comments on the non-renormalization of extremal black hole entropy and indicate a similar correspondence for two-centered forked flows in CFT.
The appearence of long-range correlations near the Dirac point of a Dirac-like spinor model with random vector potential is studied. These correlations originate from a spontaneously broken symmetry and their corresponding Goldstone modes. Using a strong-disorder expansion, correlation functions and matrix elements are analyzed and compared with results from a weak-disorder expansion. The local density of states correlation and the overlap between states above and below the Dirac point are characterized by a long-range behavior. The correlation range decreases with the distance from the Dirac point. Transport is diffusive and the diffusion coefficient is proportional to the one-particle scattering time for any strength of disorder. A consequence of the special properties of particle-hole scattering is a constant microwave conductivity for weak as well as for strong disorder, describing a deviation from conventional Drude-like transport. Some properties of the model can be linked to a kind of Kondo scale, which is generated by disorder. Finally, the properties of the wave functions at the Dirac point are characterized by their participation ratios, indicating a critical state at the Dirac point.
The least $k$ admitting a proper edge colouring $c:E\to\{1,2,\ldots,k\}$ of a graph $G=(V,E)$ without isolated edges such that $\sum_{e\ni u}c(e)\neq \sum_{e\ni v}c(e)$ for every $uv\in E$ is denoted by $\chi'_{\Sigma}(G)$. It has been conjectured that $\chi'_{\Sigma}(G)\leq \Delta + 2$ for every connected graph of order at least three different from the cycle $C_5$, where $\Delta$ is the maximum degree of $G$. It is known that $\chi'_{\Sigma}(G) = \Delta + O(\Delta^\frac{5}{6}\ln^\frac{1}{6}\Delta)$ for a graph $G$ without isolated edges. We improve this upper bound to $\chi'_{\Sigma}(G) = \Delta + O(\Delta^\frac{1}{2})$ using a simpler approach involving a combinatorial algorithm enhanced by the probabilistic method. The same upper bound is provided for the total version of this problem as well.
We develop a systematic method of directly embedding supermembrane wrapped around a circle into matrix string theory. Our purpose is to study connection between matrix string and membrane from an entirely 11 dimensional point of view. The method does neither rely upon the DLCQ limit nor upon string dualities. In principle, this enables us to construct matrix string theory with arbitrary backgrounds from the corresponding supermembrane theory. As a simplest application of the formalism, the matrix-string action with a 7 brane background (Kaluza-Klein Melvin solution) with nontrivial RR vector field is given.
Contrary to a broadly accepted assumption we show that random (Ga,In)P is not an exception with respect to the crude classification of the phonon mode behavior of random mixed crystals in terms of 1-bond->1-mode systems or 2-bond->1-mode systems, as established from the simple criterion derived by Elliott et al. [Rev.Mod.Phys. 46, 465 (1974)]. Consistent understanding of the puzzling Raman/infrared behavior of (Ga,In)P, that has been a subject of controversy, is achieved via a basic version of our 1-bond->2-mode model. The Raman/infrared features from (Ga,In)P are accordingly re-assigned, with considerable change with respect to the previous approaches. Besides, we show that the idea of two bond lengths per species in alloys, supported by our 1-bond->2-phonon picture, opens an attractive area for the discussion of spontaneous ordering in GaInP_2, and in mixed crystals in general. The whole discussion is supported by detailed re-examination of the (Ga,In)P Raman/infrared data in the literature, full contour modeling of the transverse and longitudinal optical Raman lineshapes via our phenomenological 1-bond->2-mode model, and first-principles bond length calculations.
We present a concise review of the recent important experimental developments on neutrino mixing (hints for sterile neutrinos, large $\theta_{13}$, possible non maximal $\theta_{23}$, approaching sensitivity on $\delta_{CP}$) and their implications on models of neutrino mixing. The new data disfavour many models but the surviving ones still span a wide range going from Anarchy (no structure, no symmetry in the lepton sector) to a maximum of symmetry, as for the models based on discrete non-abelian flavour groups.
We study a random walk in random environment on the non-negative integers. The random environment is not homogeneous in law, but is a mixture of two kinds of site, one in asymptotically vanishing proportion. The two kinds of site are (i) points endowed with probabilities drawn from a symmetric distribution with heavy tails at 0 and 1, and (ii) `fast points' with a fixed systematic drift. Without these fast points, the model is related to the diffusion in heavy-tailed (`stable') random potential studied by Schumacher and Singh; the fast points perturb that model. The two components compete to determine the behaviour of the random walk; we identify phase transitions in terms of the model parameters. We give conditions for recurrence and transience, and prove almost-sure bounds for the trajectories of the walk.
Toric codes are evaluation codes obtained from an integral convex polytope $P \subset \R^n$ and finite field $\F_q$. They are, in a sense, a natural extension of Reed-Solomon codes, and have been studied recently by J. Hansen and D. Joyner. In this paper, we obtain upper and lower bounds on the minimum distance of a toric code constructed from a polygon $P \subset \R^2$ by examining Minkowski sum decompositions of subpolygons of $P$. Our results give a simple and unifying explanation of bounds of Hansen and empirical results of Joyner; they also apply to previously unknown cases.
We investigate temperature errors of Coulomb blockade thermometer (CBT) arising from inevitable non-uniformities in tunnel junction arrays. The errors are proportional to the junction resistance variance in the universal operation regime and this result holds approximately also beyond this originally studied high temperature range. We present both analytical and numerical results, and discuss briefly their implications on achievable uniformity based on state-of-the-art fabrication of sensors.
The abundance of alpha elements and iron in stars of globular clusters shows the composition of the gaseous medium, in which they have been formed. In the present paper, we discuss a possibility to consider dense clouds of circumgalactic gas (partial Lyman limit systems and Lyman limit systems) observed in the 100 - 130 kpc neighbourhood of galaxies at redshifts of 0.1<z<1.1 as being the residual parts of clouds, in which globular clusters have been formed. Conclusions have been drawn based on statistical analysis of the abundance of magnesium and iron in globular clusters and in circumgalactic clouds and on the spatial location of objects of both types.
In this paper we compare the mass function slopes of Galactic globular clusters recently determined by Sollima & Baumgardt (2017) with a set of dedicated N-body simulations of star clusters containing between 65,000 to 200,000 stars. We study clusters starting with a range of initial mass functions (IMFs), black hole retention fractions and orbital parameters in the parent galaxy. We find that the present-day mass functions of globular clusters agree well with those expected for star clusters starting with Kroupa or Chabrier IMFs, and are incompatible with clusters starting with single power-law mass functions for the low-mass stars. The amount of mass segregation seen in the globular clusters studied by Sollima & Baumgardt (2017) can be fully explained by two-body relaxation driven mass segregation from initially unsegregated star clusters. Based on the present-day global mass functions, we expect that a typical globular cluster in our sample has lost about 75% of its mass since formation, while the most evolved clusters have already lost more than 90% of their initial mass and should dissolve within the next 1 to 2 Gyr. Most clusters studied by Sollima & Baumgardt also show a large difference between their central and global MF slopes, implying that the majority of Galactic globular clusters is either near or already past core collapse. The strong mass segregation seen in most clusters also implies that only a small fraction of all black holes formed in globular clusters still reside in them.
In this paper, we extend to a non-consecutive case, the study of the pattern matching condition on the wreath product of the cyclic group and the symmetric group initiated by the authors in a previous paper. The main focus of our paper is (colored) patterns of length 2, although a number of enumerative results for longer patterns are also presented. A new non-trivial bijective interpretation for the Catalan numbers is found, in terms of simultaneously bi-avoiding two patterns in a wreath product.
Extragalactic astronomy with photons ends at ~0.1 PeV, but we know there are astrophysical sources for seven more decades of energy beyond this. To probe the highest energy sources and particles in the universe, new messengers, such as neutrinos, and detectors with planet-sized areas are required. This note provides a glimpse of the possibilities.
We investigate the associated production of heavy quarkonia, with angular-momentum quantum numbers ^{2S+1}L_J = ^1S_0, ^3S_1, ^1P_1, ^3P_J (J = 0, 1, 2), and photons, Z bosons, and W bosons in photon-photon, photon-hadron, and hadron-hadron collisions within the factorization formalism of nonrelativistic quantum chromodynamics providing all contributing partonic cross sections in analytic form. In the case of photoproduction, we also include the resolved-photon contributions. We present numerical results for the processes involving J/psi and chi_{cJ} mesons appropriate for the Fermilab Tevatron, CERN LHC, DESY TESLA, operated in the e^+ e^- and gamma gamma modes, and DESY THERA.
We construct an extension of the standard Kogut-Susskind lattice model for classical 3+1 dimensional Yang-Mills theory, in which ``classical particle'' degrees of freedom are added. We argue that this will correctly reproduce the ``hard thermal loop'' effects of hard degrees of freedom, while giving a local implementation which is numerically tractable. We prove that the extended system is Hamiltonian and has the same thermodynamics as dimensionally reduced hot Yang-Mills theory put on a lattice. We present a numerical update algorithm and study the abelian theory to verify that the classical gauge theory self-energy is correctly modified. Then we use the extended system to study the diffusion constant for Chern-Simons number. We verify the Arnold-Son-Yaffe picture that the diffusion constant is inversely proportional to hard thermal loop strength. Our numbers correspond to a diffusion constant of Gamma = 29 +- 6 alpha_w^5 T^4 for m_D^2 = 11 g^2 T^2/6.
In this article we investigate the hitting time of some given boundaries for Bessel processes. The main motivation comes from mathematical finance when dealing with volatility models, but the results can also be used in optimal control problems. The aim here is to construct a new and efficient algorithm in order to approach this hitting time. As an application we will consider the hitting time of a given level for the Cox-Ingersoll-Ross process. The main tools we use are on one side, an adaptation of the method of images to this particular situation and on the other side, the connection that exists between Cox-Ingersoll-Ross processes and Bessel processes.
To alleviate the discrepancy between the prediction of the primordial lithium abundance in the universe and the abundances observed in Pop II dwarfs and subgiant stars, it has been suggested that the stars observable today have undergone photospheric depletion of Li. To constrain the nature of such depletion, we conduct a homogeneous analysis of a very large sample of stars in the metal-poor globular cluster NGC6397, covering well all evolutionary phases from below the main sequence turn-off to high up the red giant branch. Non-LTE Li abundances or abundance upper limits are obtained for all stars, and for a size-able sub-set of the targets also Na abundances are obtained. The sodium abundances are used to distinguish stars formed out of pristine material from stars formed out of material affected by pollution from a previous generation of more massive stars. The dwarfs, turn-off, and early subgiant stars form a thin abundance plateau, disrupted in the middle of the subgiant branch by the lithium dilution caused by the first dredge-up. A second steep abundance drop is seen at the red giant branch bump. The turn-off stars are more lithium-poor, by up to 0.1 dex, than subgiants that have not yet undergone dredge-up. In addition, hotter dwarfs are slightly more lithium-poor than cooler dwarfs, which may be a signature of the so-called Li dip in the cluster, commonly seen among PopI stars. A considerably large spread in Na abundance confirms that NGC6397 has suffered from intra-cluster pollution in its infancy and a limited number of Na-enhanced and Li-deficient stars strongly contribute to form a significant anti-correlation between the abundances of Na and Li. The inferred Li abundances are compared to predictions from stellar structure models including atomic diffusion and ad-hoc turbulence below the convection zone.
We perform a detailed physical analysis for a class of exact solutions for the Einstein-Maxwell equations. The linear equation of state consistent with quark stars has been incorporated in the model. The physical analysis of the exact solutions is performed by considering the charged anisotropic stars for the particular nonsingular exact model obtained by Maharaj, Sunzu and Ray. In performing such an analysis we regain masses obtained by previous researchers for isotropic and anisotropic matter. It is also indicated that other masses and radii may be generated which are in acceptable ranges consistent with observed values of stellar objects. A study of the mass-radius relation indicates the effect of the electromagnetic field and anisotropy on the mass of the relativistic star.
We present observations in the optical, near-infrared and millimetre bands of the Ultraluminous Infrared galaxy IRAS 19254-7245, also known as "The Superantennae". This galaxy is an interacting system with a double nucleus and long tails extending for about 350 kpc. We studied in detail the southern component of the system which is optically classified as a Sy2 galaxy. We have developed a method to determine the parameters of the emission lines in a spectrum in the case of multiple components and severe blending. Our data allow us to build a picture of the environment around the nucleus of the galaxy with unprecedented detail. The optical lines show a complex dynamical structure that is not observable in the near-infrared. In addition we find typical features of AGN such as the coronal lines of [FeVII]5721 and [SiVI]1.96. We also detect strong emission from [FeII]1.64 and $H_2$.
The three generation superstring models in the free fermionic models have had remarkable success in describing the real--world. The most explored models use the NAHE set to obtain three generations and to separate the hidden and observable sectors. It is of course well known that the full NAHE set is not required in order to construct three generation free fermionic models. I argue that all the semi--realistic free fermionic models that have been constructed to date correspond to $Z_2\times Z_2$ orbifolds. Thus, the successes of the semi--realistic free fermionic models, if taken seriously, suggest that the true string vacuum is a $Z_2\times Z_2$ orbifold with nontrivial background fields and quantized Wilson lines.
Gravitational radiation in plane-symmetric space-times can be encoded in a complex potential, satisfying a non-linear wave equation. An effective energy tensor for the radiation is given, taking a scalar-field form in terms of the potential, entering the field equations in the same way as the matter energy tensor. It reduces to the Isaacson energy tensor in the linearized, high-frequency approximation. An energy conservation equation is derived for a quasi-local energy, essentially the Hawking energy. A transverse pressure exerted by interacting low-frequency gravitational radiation is predicted.
When Lenz proposed a simple model for phase transitions in magnetism, he couldn't have imagined that the "Ising model" was to become a jewel in field of equilibrium statistical mechanics. Its role spans the spectrum, from a good pedagogical example to a universality class in critical phenomena. A quarter century ago, Katz, Lebowitz and Spohn found a similar treasure. By introducing a seemingly trivial modification to the Ising lattice gas, they took it into the vast realms of non-equilibrium statistical mechanics. An abundant variety of unexpected behavior emerged and caught many of us by surprise. We present a brief review of some of the new insights garnered and some of the outstanding puzzles, as well as speculate on the model's role in the future of non-equilibrium statistical physics.
Given an ambient variety $X$ and a fixed subvariety $Z$ we give sufficient conditions for the existence of a boundary $\Delta$ such that $Z$ is a log canonical center for the pair $(X, \Delta)$. We also show that under some additional hypotheses $\Delta$ can be chosen such that $(X, \Delta)$ has log canonical singularities.