ShantanuT01/DACTYL-Pretraining huggingface dataset:
This paper studies the Sobolev regularity estimates for weak solutions of a class of degenerate, and singular quasi-linear elliptic problems of the form $\text{div}[\mathbf{A}(x,u, \nabla u)]= \text{div}[\mathbf{F}]$ with non-homogeneous Dirichlet boundary conditions over bounded non-smooth domains. The coefficients $\mathbf{A}$ could be be singular, and degenerate or both in $x$ in the sense that they behave like some weight function $\mu$, which is in the $A_2$ class of Muckenhoupt weights. Global and interior weighted $W^{1,p}(\Omega, \omega)$-regularity estimates are established for weak solutions of these equations with some other weight function $\omega$. The results obtained are even new for the case $\mu =1$ because of the dependence on the solution $u$ of $\mathbf{A}$. In case of linear equations, our $W^{1,p}$-regularity estimates can be viewed as the Sobolev's counterpart of the H\"{o}lder's regularity estimates established by B. Fabes, C. E. Kenig, and R. P. Serapioni.
We consider optimal state discrimination in a general convex operational framework, so-called generalized probabilistic theories (GPTs), and present a general method of optimal discrimination by applying the complementarity problem from convex optimization. The method exploits the convex geometry of states but not other detailed conditions or relations of states and effects. We also show that properties in optimal quantum state discrimination are shared in GPTs in general: i) no measurement sometimes gives optimal discrimination, and ii) optimal measurement is not unique.
In loop quantum gravity, matter fields can have support only on the `polymer-like' excitations of quantum geometry, and their algebras of observables and Hilbert spaces of states can not refer to a classical, background geometry. Therefore, to adequately handle the matter sector, one has to address two issues already at the kinematic level. First, one has to construct the appropriate background independent operator algebras and Hilbert spaces. Second, to make contact with low energy physics, one has to relate this `polymer description' of matter fields to the standard Fock description in Minkowski space. While this task has been completed for gauge fields, important gaps remained in the treatment of scalar fields. The purpose of this letter is to fill these gaps.
We give a complete (global) characterization of complex perverse sheaves on semi-abelian varieties in terms of their cohomology jump loci. Our results generalize Schnell's work on perverse sheaves on complex abelian varieties, as well as Gabber-Loeser's results on perverse sheaves on complex affine tori. We apply our results to the study of cohomology jump loci of smooth quasi-projective varieties, to the topology of the Albanese map, and in the context of homological duality properties of complex algebraic varieties.
Basing on the Bohr collective quadrupole Hamiltonian the $A$-dependence of the Grodzins product is derived and the proportionality coefficient for the Grodzins relation is evaluated. The result obtained is in a correspondence with the experimental data.
We report results of the first global three-dimensional magnetohydrodynamic simulations of the waves excited in an accretion disc by a rotating star with a dipole magnetic field misaligned from the star's rotation axis (which is aligned with the disc axis). The main results are the following: (1) If the magnetosphere of the star corotates approximately with the inner disc, then we observe a strong one-armed bending wave (a warp). This warp corotates with the star and has a maximum amplitude between corotation radius and the radius of the vertical resonance. The disc's center of mass can deviate from the equatorial plane up to the distance of z_w\approx 0.1 r. However, the effective height of the warp can be larger, h_w \approx 0.3 r due to the finite thickness of the disc. Stars with a range of misalignment angles excite warps. However, the amplitude of the warps is larger for misalignment angles between 15 and 60 degrees. (2) If the magnetosphere rotates slower, than the inner disc, then a bending wave is excited at the disc-magnetosphere boundary, but does not form a large-scale warp. Instead, high-frequency oscillations become strong at the inner region of the disc. These are (a) trapped density waves which form inside the radius where the disc angular velocity has a maximum, and (b) inner bending waves which appear in the case of accretion through magnetic Raleigh-Taylor instability. These two types of waves are connected with the inner disc and their frequencies will vary with accretion rate. Bending oscillations at lower frequencies are also excited including global oscillations of the disc. In cases where the simulation region is small, slowly-precessing warp forms. Simulations are applicable to young stars, cataclysmic variables, and accreting millisecond pulsars.
The Davey-Stewartson 1(DS1) system[9] is an integrable model in two dimensions. A quantum DS1 system with 2 colour-components in two dimensions has been formulated. This two-dimensional problem has been reduced to two one-dimensional many-body problems with 2 colour-components. The solutions of the two-dimensional problem under consideration has been constructed from the resulting problems in one dimensions. For latters with the $\delta $-function interactions and being solved by the Bethe ansatz, we introduce symmetrical and antisymmetrical Young operators of the permutation group and obtain the exact solutions for the quantum DS1 system. The application of the solusions is discussed.
In Aristotelian Electrodynamics (AE), due to radiation over-damping, the velocity rather than the acceleration of a charge is determined by the local electromagnetic field. Treating electrons and positrons separately, AE seems to give a faithful description of the flow of charges in a pulsar magnetosphere. AE might allow to calculate the pulsar emission in full detail, at all energies except the radio.   But AE is not a full theory -- the plasma production processes must be added. Here we show that the pulsar magnetosphere and the resulting emission are sensitive to the plasma production rate near the light cylinder. In strong pulsars (high production rate, due to photon-photon collisions), the number of field lines closing beyond the light cylinder decreases. This reduces both the pulsar efficiency (the ratio of the pulsed bolometric luminosity to the spin-down power) and the characteristic photon energy, in overall agreement with the Fermi data.   For weak pulsars (low production rate), our numerical implementation of AE works stably and seems to be ready to calculate the lightcurves and spectra. But for strong pulsars, the code (included) needs improvement or better understanding.
We report the detection of giant pulse emission from PSR B0950+08 in 24 hours of observations made at 39.4 MHz, with a bandwidth of 16 MHz, using the first station of the Long Wavelength Array, LWA1. We detected 119 giant pulses from PSR B0950+08 (at its dispersion measure), which we define as having SNRs at least 10 times larger than for the mean pulse in our data set. These 119 pulses are 0.035% of the total number of pulse periods in the 24 hours of observations. The rate of giant pulses is about 5.0 per hour. The cumulative distribution of pulse strength $S$ is a steep power law, $N(>S)\propto S^{-4.7}$, but much less steep than would be expected if we were observing the tail of a Gaussian distribution of normal pulses. We detected no other transient pulses in a dispersion measure range from 1 to 90 pc cm$^{-3}$, in the beam tracking PSR B0950+08. The giant pulses have a narrower temporal width than the mean pulse (17.8 ms, on average, vs. 30.5 ms). The pulse widths are consistent with a previously observed weak dependence on observing frequency, which may be indicative of a deviation from a Kolmogorov spectrum of electron density irregularities along the line of sight. The rate and strength of these giant pulses is less than has been observed at $\sim$100 MHz. Additionally, the mean (normal) pulse flux density we observed is less than at $\sim$100 MHz. These results suggest this pulsar is weaker and produces less frequent giant pulses at 39 MHz than at 100 MHz.
In the present work a consistent kinematic-based framework for glueball states is proposed. It relates the glueball, the Pomeron, QCD lattice calculations, the $0^{++}$ scalar states $f_0(1710)$ and $\chi_{c0}(1P)$, the $2^{++}$ states $f_J(2220)$ and $\chi_{c2}(2P)$, the baryonic charmed state $\Xi_c^+(2645)$.
We show that substantially more than a quarter of the odd integers of the form $pq$ up to $x$, with $p,q$ both prime, satisfy $p\equiv q\equiv 3 \pmod 4$.
Inside the moduli space of curves of genus 2 with 2 marked points we consider the loci of curves admitting a map to P^1 of degree d totally ramified over the two marked points, for d>= 2. Such loci have codimension two. We compute the class of their compactifications in the moduli space of stable curves. Several results will be deduced from this computation.
Building a large sample of kiloparsec (kpc)-scale dual active galactic nuclei (AGNs) amongst merging galaxies is of vital importance to understand the co-evolution between host galaxies and their central super massive black holes (SMBHs). Doing so, with just such a sample, we have developed an innovative method of systematically searching and identifying dual AGNs of amongst kpc scale merging galaxies and selected 222 candidates at redshifts $\leqslant$ 0.25. All the selected candidates have FIRST radio detection and at least one of two cores previously revealed as AGN spectroscopically. We report the first results from A SysTematic seaRch fOr Dual Agns in meRgINg Galaxies (ASTRO-DARING), which consist of spatially resolved long-slit spectroscopic observations of 41 targets selected from our merging galaxies sample carried out between November 2014 and February 2017, using the Yunnan Faint Object Spectrograph and Camera (YFOSC) mounted on the 2.4 meter telescope in Lijiang of Yunnan Observatories. Of these 16 are likely dual AGNs and 15 are newly identified. The efficiency of ASTRO-DARING is thus nearly 40 per cent. With this method, we plan to build the first even sample of more than 50 dual AGNs constructed using a consistent approach. Further analysis of the dual AGN sample shall provide vital clues for understanding the co-evolution of galaxies and SMBHs.
Computational difficulties aside, nonequilibrium Green's functions appear ideally suited for investigating the dynamics of central nuclear reactions. Many particles actively participate in those reactions. At the two energy extremes for the collisions, the limiting cases of the Green's function approach have been successful: the time-dependent Hartree-Fock theory at low energy and Boltzmann equation at high. The strategy for computational adaptation of the Green's function to central reactions is discussed. The strategy involves, in particular, incremental progression from one to three dimensions to develop and assess approximations, discarding of far-away function elements, use of effective interactions and preparation of initial states for the reactions through adiabatic switching. At this stage we concentrate on inclusion of correlations in one dimension, where relatively few approximations are needed, and we carry out reference calculations that can benchmark approximations needed for more dimensions. We switch on short-range interactions generating the correlations adiabatically in the Kadanoff-Baym equations to arrive at correlated ground states for uniform matter. As the energy of the correlated matter does not quite match the expectations for nuclear matter we add mean field to arrive at the match in energy. From there on, we move to finite systems. In switching on the correlations we observe emergence of extended tails in momentum distributions and evolution of single particle occupations away from 1 and 0.
In this paper, we consider the Cauchy's problem of global existence and scattering behavior of small, smooth, and localized solutions of cubic fractional Schr\"odinger equations in one dimension, \begin{equation*}   \mathrm{i} \partial_t u- (-\Delta)^{\frac{\alpha}{2}} u=c_*|u|^2u, \end{equation*} where $\alpha \in (\frac{1}{3},1), c_* \in \mathbb{R}$. Our work is a generalization of the result due to Ionescu and Pusateri \cite{IP}, where the case $\alpha=\frac{1}{2}$ was considered. The highlight in this paper is to give a modified dispersive estimate in weighted Sobolev spaces for cubic fractional Schr\"odinger equations, which could be used for $ \alpha \in (\frac{1}{3},1)$. Based on this modified dispersive estimate, we prove the global existence and modified scattering behavior of solutions combining space-time resonance and bootstrap arguments.
We report the observation of a field-induced transformation from the easy-plane antiferromagnetic structure to the easy-axis ferrimagnetic structure in a single crystal of TbFe_4.4Al_7.6 (tetragonal ThMn_12 structure) at 5 K. Such a field-induced, irreversible transition has been identified for the first time. This transition is accompanied by a giant orthorhombic distortion: epsilon_aa = - epsilon_bb ~ 3.5x10^-4 that is associated with a magnetic hardness (mu_0H_C ~ 3 T) that is unprecedented in this category of materials.
We determine the exact time-resolved photoemission spectroscopy for a nesting driven charge-density-wave (described by the spinless Falicov-Kimball model within dynamical mean-field theory). The pump-probe experiment involves two light pulses: the first is an ultrashort intense pump pulse that excites the system into nonequilibrium, and the second is a lower amplitude higher frequency probe pulse that photoexcites electrons. We examine three different cases: the strongly correlated metal, the quantum-critical charge density wave and the critical Mott insulator. Our results show that the quantum critical charge density wave has an ultra efficient relaxation channel that allows electrons to be de-excited during the pump pulse, resulting in little net excitation. In contrast, the metal and the Mott insulator show excitations that are closer to what one expects from these systems. In addition, the pump field produces spectral band narrowing, peak sharpening, and a spectral gap reduction, all of which rapidly return to their field free values after the pump is over.
We investigate the problem of finding the optimal convex decomposition of a bipartite quantum state into a separable part and a positive remainder, in which the weight of the separable part is maximal. This weight is naturally identified with the degree of separability of the state. In a recent work, the problem was solved for two-qubit states using semidefinite programming. In this paper, we describe a procedure to obtain the optimal decomposition of a bipartite state of any finite dimension via a sequence of semidefinite relaxations. The sequence of decompositions thus obtained is shown to converge to the optimal one. This provides, for the first time, a systematic method to determine the so-called optimal Lewenstein-Sanpera decomposition of any bipartite state. Numerical results are provided to illustrate this procedure, and the special case of rank-2 states is also discussed.
We investigate an intermittent stochastic process, in which the diffusive motion with time-dependent diffusion coefficient $D(t)\sim t^{\alpha-1}$, $\alpha>0$ (scaled Brownian motion), is stochastically reset to its initial position and starts anew. The resetting follows a renewal process with either exponential or power-law distribution of the waiting times between successive renewals. The resetting events, however, do not affect the time dependence of the diffusion coefficient, so that the whole process appears to be a non-renewal one. We discuss the mean squared displacement of a particle and probability density function of its positions in such a process. We show that scaled Brownian motion with resetting demonstrates a rich behavior whose properties essentially depend on the interplay of the parameters of the resetting process and the particle's displacement in a free motion. The motion of particles can remain either almost unaffected by resetting, but can also get slowed down or even be completely suppressed. Especially interesting are the nonstationary situations in which the mean squared displacement stagnates but the distribution of positions does not tend to any steady state. \color{black} This behavior is compared to the situation (discussed in the other paper of this series) in which the memory on the value of the diffusion coefficient at a resetting time is erased, so that the whole process is a fully renewal one. We show that the properties of the probability densities in such processes (erazing or retaining the memory on the diffusion coefficient) are vastly different. \color{black}
The gravitational action is not always additive in the usual sense. We provide a general prescription for the change in action that results when different portions of the boundary of a spacetime are topologically identified. We discuss possible implications for the superposition law of quantum gravity. We present a definition of `generalized additivity' which does hold for arbitrary spacetime composition.
Bondi's approach to the construction of a coordinate system is used with a different choice of gauge, in accordance with which the radial coordinate r is an affine parameter, to cast the metric tensor into a form suitable for use with the Newman-Penrose null tetrad formalism. The choice of tetrad has the result that the equations and all the functions that appear in them are real-valued. A group classification of the Sachs equations in this gauge leads to a unique expression for the first of the five independent elements $\Psi_0$ of the Weyl spinor, and to the corresponding exact solutions for two of the metric functions on an initial null hypersurface. A proof is presented that the result for $\Psi_0$ constitutes the appropriate characteristic initial value function for all physically realistic axisymmetric, non-rotating vacuum spacetimes. Integration of the field equations on the axis of symmetry when an equatorial symmetry plane is also present, and on the equatorial plane itself when time rates of change can be neglected, shows that these data produce results consistent with Newton's laws and with the Schwarzschild solution in the appropriate limits. The solution on the axis of symmetry indicates that the Weyl curvature increases without limit between black holes as their separation decreases.
In this paper the revised Kajantie-Byckling approach and improved phase space sampling techniques for the massive multi-particle final states are presented. The application of the developed procedures to the processes representative for LHC physics indicates the possibility of a substantial simplification of multi-particle phase space sampling while retaining a respectable weight variance reduction and unweighing efficiencies in the event generation process.
We define cohomological complexes of locally compact abelian groups associated with varieties over $p$-adic fields and prove a duality theorem under some assumption. Our duality takes the form of Pontryagin duality between locally compact motivic cohomology groups.
We prove an equivalence between the derived category of a variety and the equivariant/graded singularity category of a corresponding singular variety. The equivalence also holds at the dg level.
Gauged N=8 supergravity in four dimensions is now known to admit a deformation characterized by a real parameter $\omega$ lying in the interval $0\le\omega\le \pi/8$. We analyse the fluctuations about its anti-de Sitter vacuum, and show that the full N=8 supersymmetry can be maintained by the boundary conditions only for $\omega=0$. For non-vanishing $\omega$, and requiring that there be no propagating spin s>1 fields on the boundary, we show that N=3 is the maximum degree of supersymmetry that can be preserved by the boundary conditions. We then construct in detail the consistent truncation of the N=8 theory to give $\omega$-deformed SO(6) gauged N=6 supergravity, again with $\omega$ in the range $0\le\omega\le \pi/8$. We show that this theory admits fully N=6 supersymmetry-preserving boundary conditions not only for $\omega=0$, but also for $\omega=\pi/8$. These two theories are related by a U(1) electric-magnetic duality. We observe that the only three-point functions that depend on $\omega$ involve the coupling of an SO(6) gauge field with the U(1) gauge field and a scalar or pseudo-scalar field. We compute these correlation functions and compare them with those of the undeformed N=6 theory. We find that the correlation functions in the $\omega=\pi/8$ theory holographically correspond to amplitudes in the U(N)_k x U(N)_{-k} ABJM model in which the U(1) Noether current is replaced by a dynamical U(1) gauge field. We also show that the $\omega$-deformed N=6 gauged supergravities can be obtained via consistent reductions from the eleven-dimensional or ten-dimensional type IIA supergravities.
Vacation queueing systems are widely used as an extension of the classical queueing theory. We consider both working vacations and regular vacations in this paper, and compare systems with vacations to the regular $M/M/1$ system via mean service rates and expected numbers of customers, using matrix-analytic methods.
Reconstruction of the linear power spectrum from observational data provides a way to compare cosmological models to a large amount of data, as Peacock & Dodds (1994, 1996) have shown. By applying the appropriate corrections to the observational power spectrum it is possible to recover the underlying linear power spectrum for any cosmological model. Using extensive N-body simulations we demonstrate that the method is applicable to a wide range of cosmological models. However, we find that the recovery of the linear power spectrum from observations following PD94 is misleading because the corrections are model- dependent. When we apply the proper corrections for a given model to the observational power spectrum, we find that no model in our test group recovers the linear power spectrum well for the bias suggested by PD94 between Abell, Radio, Optical, and IRAS catalogs 4.5:1.9:1.3:1, with b_IRAS=1. When we allow b_IRAS to vary we find that: (i)CHDM models give very good fits to observations if optically-selected galaxies are slightly biased b_Opt=1.1 (ii) Most LCDM models give worse but acceptable fits if blue galaxies are considerably antibiased: 0.6<b_Opt<0.9 and fail if optical galaxies are biased. (iii)There is a universal shape of the recovered linear power spectrum of all LCDM models over their entire range of explored wavenumbers,0.01<k<0.6h\Mpc. Recovered spectra of CDM and CHDM models are nearly the same as that of LCDM in the region 0.01<k<0.2h/Mpc but diverge from this spectrum at higher k.
We have investigated the Mn-site substitution effect in Nd$_{0.45}$Sr$_{0.55}$MnO$_3$ single crystal, which has an $A$-type layered antiferromagnetic ($A$-AFM) phase with the 3$d_{x^2-y^2}$-type orbital-order. Substitution of Fe or Ga for Mn-site suppresses both the $A$-AFM order and competing ferromagnetic (FM) correlation whereas Cr substitution suppresses only the $A$-AFM order but reactivates the underlying FM correlation via double-exchange mechanism along the AFM coupled $c$-direction. In Nd$_{0.45}$Sr$_{0.55}$Mn$_{0.95}$Cr$_{0.05}$O$_3$, the $A$-AFM state with the orbital-order is changed into the orbital-disordered three-dimensional FM metallic state by applying magnetic field of $\mu_0 H = 12$ T, which is much smaller than that of the parent compound Nd$_{0.45}$Sr$_{0.55}$MnO$_3$.
Correlation functions of Toda field vertices are investigated by applying the method of integrating zero-mode developed for Liouville theory. We generalize the relations among the zero-, two- and three-point couplings known in Liouville case to arbitrary Toda theories. Two- and three-point functions of Toda vertices associated with the simple roots are obtained.