ShantanuT01/DACTYL-Pretraining huggingface dataset:
Let $\xi$ be a real irrational number. We are interested in sequences of linear forms in 1 and $\xi$, with integer coefficients, which tend to 0. Does such a sequence exist such that the linear forms are small (with given rate of decrease) and the coefficients have some given rate of growth? If these rates are essentially geometric, a necessary condition for such a sequence to exist is that the linear forms are not too small, a condition which can be expressed precisely using the irrationality exponent of $\xi$. We prove that this condition is actually sufficient, even for arbitrary rates of growth and decrease. We also make some remarks and ask some questions about multivariate generalizations connected to Fischler-Zudilin's new proof of Nesterenko's linear independence criterion.
We recall the path breaking contributions of the nuclear theory group of the Variable Energy Cyclotron Centre, Kolkata. From a beginning of just one person in 1970s, the group has steadily developed into a leading group in the country today, with seminal contributions to almost the entire range of nuclear physics, viz., low energy nuclear reactions, nuclear structure, deep inelastic collisions, fission, liquid to gas phase transitions, nuclear matter, equation of state, mass formulae, neutron stars, relativistic heavy ion collisions, medium modification of hadron properties, quark gluon plasma, and cosmology of early universe.
This paper describes a method for searching for common sets of descriptors between collections of images. The presented method operates on local interest keypoints, which are generated using the SURF algorithm. The use of a dictionary of descriptors allowed achieving good performance of the content-based image retrieval. The method can be used to initially determine a set of similar pairs of keypoints between images. For this purpose, we use a certain level of tolerance between values of descriptors, as values of feature descriptors are almost never equal but similar between different images. After that, the method compares the structure of rotation and location of interest points in one image with the point structure in other images. Thus, we were able to find similar areas in images and determine the level of similarity between them, even when images contain different scenes.
High Energy Cosmic Rays (C.R.) versus Neutrino and Neutralino induced Air-Shower maybe tested at Horizons by their muons, gamma and Cerenkov blazing signals. Inclined and Horizontal C.R. Showers (70-90 zenith angle) produce secondary (gamma, e+, e-) mostly suppressed by high column atmosphere depth. Earliest shower Cherenkov photons are diluted by large distances and by air opacity, while secondary penetrating muons and their successive decay into electrons and gamma, may revive additional Cerenkov lights. GeVs gamma telescopes at the top of the mountains or in Space may detect at horizons PeVs up to EeV C.R. and their secondaries. Details on arrival angle and column depth, shower shape, timing signature of photon flash intensity, may inform us on the altitude interaction and primary UHECR composition. Below the horizons, at zenith angle among copious single albedo muons, rare up-going showers traced by muon bundles would give evidence of rare tau Earth-Skimming neutrinos, at EeVs energies. Their rate may be comparable with 6.3 PeVs anti-neutrino electron induced air-shower (mostly hadronic) originated above and also below horizons, in interposed atmosphere by W resonance at Glashow peak. Additional and complementary UHE SUSY neutralinos at tens PeVs-EeV energy may blaze, by its characteristic electromagnetic signature. Their secondary shower blazing Cerenkov lights and distances might be disentangled from UHECR by Stereoscopic Telescopes such as Magic ones or Hess array experiment. The horizontal detection sensitivity of Magic in the present set up (if totally devoted to the Horizons Shower search) maybe already be comparable to AMANDA underground neutrino detector at PeVs energies.
Magnetic transition phenomena in cubic chiral antiferromagnet EuPtSi with $T_{\rm N}$=4.0~K were investigated by means of single crystal neutron diffraction. At 0.3~K in the ground state, magnetic peaks emerge at positions represented by an ordering vector ${q}_{1}$=$(0.2, 0.3, 0)$ and its cyclic permutation. Upon heating, an additional magnetic peak splitting with hysteresis was uncovered at around $T^*_{\rm N}{\sim}$2.5~K, indicating the presence of a first-order commensurate-incommensurate transition with ${q}^*_{1}$=$(0.2, 0.3, {\delta})$ (${\delta}_{\rm max}{\simeq}$0.04) at $T^*_{\rm N}$. A half-polarized neutron scattering experiment for polarization parallel to the scattering vector revealed that polarization antiparallel to the scattering vector has stronger intensity in both magnetic phases. This feature clarifies the single chiral character of the helical structure with moments lying perpendicular to the ordering vector in both ordered states. Under a vertical magnetic field of 1.2~T for ${B}{\parallel}$[1,1,1] at 1.9~K entering into the so-called $A$ phase, magnetic peaks form characteristic hexagonal patterns in the equatorial scattering plane around nuclear peaks. An ordering vector ${q}_{A}{\simeq}({\pm}0.09, {\pm}0.20, {\mp}0.28)$ of the $A$-phase has similar periodic length as $q_{1}$, and could be the hallmark of a formation of skyrmion lattice in EuPtSi.
The asymptotic time derivative of the total dipole signal is proposed as an useful observable to investigate on Isospin equilibration phenomenon in multi-fragmentation processes. The study has been developed to describe charge/mass equilibration processes involving the gas and liquid "phases" of the total system formed during the early stage of a collision. General properties of this observable and the links with others isospin dependent phenomena are discussed. In particular, the $^{40}Cl+^{28}Si$ system at 40 MeV/nucleon is investigated by means of semiclassical microscopic many-body calculations based on the CoMD-II model. The study of the dynamical many-body correlations produced by the model also shows how the proposed observable is rather sensitive to different parameterizations of the isospin dependent interaction.
The purpose of this paper is twofold. First, we use a classical method to establish Gaussian bounds of the fundamental matrix of a generalized parabolic Lam\'{e} system with only bounded and measurable coefficients. Second, we derive a maximal $L^1$ regularity result for the abstract Cauchy problem associated with a composite operator. In a concrete example, we also obtain maximal $L^1$ regularity for the Lam\'{e} system, from which it follows that the Lipschitz seminorm of the solutions to the Lam\'{e} system is globally $L^1$-in-time integrable. As an application, we use a Lagrangian approach to prove a global-in-time well-posedness result for a viscous pressureless flow provided that the initial velocity satisfies a scaling-invariant smallness condition. The method established in this paper might be a powerful tool for studying many issues arising from viscous fluids with truly variable densities.
We describe the Multi-Epoch Nearby Cluster Survey (MENeaCS), designed to measure the cluster Type Ia supernova (SN Ia) rate in a sample of 57 X-ray selected galaxy clusters, with redshifts of 0.05 < z < 0.15. Utilizing our real time analysis pipeline, we spectroscopically confirmed twenty-three cluster SN Ia, four of which were intracluster events. Using our deep CFHT/Megacam imaging, we measured total stellar luminosities in each of our galaxy clusters, and we performed detailed supernova detection efficiency simulations. Bringing these ingredients together, we measure an overall cluster SN Ia rate within R_{200} (1 Mpc) of 0.042^{+0.012}_{-0.010}^{+0.010}_{-0.008} SNuM (0.049^{+0.016}_{-0.014}^{+0.005}_{-0.004} SNuM) and a SN Ia rate within red sequence galaxies of 0.041^{+0.015}_{-0.015}^{+0.005}_{-0.010} SNuM (0.041^{+0.019}_{-0.015}^{+0.005}_{-0.004} SNuM). The red sequence SN Ia rate is consistent with published rates in early type/elliptical galaxies in the `field'. Using our red sequence SN Ia rate, and other cluster SNe measurements in early type galaxies up to $z\sim1$, we derive the late time (>2 Gyr) delay time distribution (DTD) of SN Ia assuming a cluster early type galaxy star formation epoch of z_f=3. Assuming a power law form for the DTD, \Psi(t)\propto t^s, we find s=-1.62\pm0.54. This result is consistent with predictions for the double degenerate SN Ia progenitor scenario (s\sim-1), and is also in line with recent calculations for the double detonation explosion mechanism (s\sim-2). The most recent calculations of the single degenerate scenario delay time distribution predicts an order of magnitude drop off in SN Ia rate \sim 6-7 Gyr after stellar formation, and the observed cluster rates cannot rule this out.
Ground level events (GLEs) occupy the high-energy end of gradual solar energetic particle (SEP) events. They are associated with coronal mass ejections (CMEs) and solar flares, but we still do not clearly understand the special conditions that produce these rare events. During Solar Cycle 23, a total of 16 GLEs were registered, using ground-based neutron monitor data. We first ask if these GLEs are clearly distinguishable from other SEP events observed from space. Setting aside possible difficulties in identifying all GLEs consistently, we then try to find observables which may unmistakably isolate these GLEs by studying the basic properties of the associated eruptions and the active regions (ARs) that produced them. It is found that neither the magnitudes of the CMEs and flares nor the complexities of the ARs give sufficient conditions for GLEs. It is possible to find CMEs, flares or ARs that are not associated with GLEs but that have more extreme properties than those associated with GLEs. We also try to evaluate the importance of magnetic field connection of the AR with Earth on the detection of GLEs and their onset times. Using the potential field source surface (PFSS) model, a half of the GLEs are found to be well-connected. However, the GLE onset time with respect to the onset of the associated flare and CME does not strongly depend on how well-connected the AR is. The GLE onset behavior may be largely determined by when and where the CME-driven shock develops. We could not relate the shocks responsible for the onsets of past GLEs with features in solar images, but the combined data from the Solar TErrestrial RElations Observatory (STEREO) and the Solar Dynamics Observatory (SDO) have the potential to change this for GLEs that may occur in the rising phase of Solar Cycle 24.
We investigate the behavior of vector bundles of conformal blocks for $sp_{2\ell}$ at level one on $\bar{M}_{0,n}$. We show their first Chern classes are equivalent to conformal blocks divisors for $sl_2$ at level $\ell$ if and only if the corresponding vector bundles have rank one or zero, and all become equal when the Lie algebra $\ell$ is large enough. As a consequence of these results, we conclude the cone generated by these divisors is polyhedral.
An $\{r,s\}$-leaper is a generalized knight that can jump from $(x,y)$ to $(x\pm r,y\pm s)$ or $(x\pm s,y\pm r)$ on a rectangular grid. The graph of an $\{r,s\}$-leaper on an $m\times n$ board is the set of $mn$~vertices $(x,y)$ for $0\leq x<m$ and $0\leq y<n$, with an edge between vertices that are one $\{r,s\}$-leaper move apart. We call $x$ the {\it rank} and $y$ the {\it file} of board position $(x,y)$. George~P. Jelliss raised several interesting questions about these graphs, and established some of their fundamental properties. The purpose of this paper is to characterize when the graphs are connected, for arbitrary~$r$ and~$s$, and to determine the smallest boards with Hamiltonian circuits when $s=r+1$ or $r=1$.
Axisymmetric solitonic states (chiral skyrmions) have been predicted theoretically more than two decades ago. However, until recently they have been observed in a form of skyrmionic condensates (hexagonal lattices and other mesophases). In this paper we report experimental and theoretical investigations of isolated chiral skyrmions discovered in PdFe/Ir(111) bilayers two years ago (Science 341 , 636 (2013)). The results of spin-polarized scanning tunneling microscopy analyzed within the continuum and discrete models provide a consistent description of isolated skyrmions in thin layers. The existence region of chiral skyrmions is restricted by strip-out instabilities at low fields and a collapse at high fields. We demonstrate that the same equations describe axisymmetric localized states in all condensed matter systems with broken mirror symmetry, and thus our findings establish basic properties of isolated skyrmions common for chiral liquid crystals, different classes of noncentrosymmetric magnets, ferroelectrics, and multiferroics.
We study the evolution of a collection of individuals subject to Brownian diffusion, reproduction and disappearance. In particular, we focus on the case where the individuals are initially prepared at equilibrium within a confined geometry. Such systems are widespread in physics and biology and apply for instance to the study of neutron populations in nuclear reactors and the dynamics of bacterial colonies, only to name a few. The fluctuations affecting the number of individuals in space and time may lead to a strong patchiness, with particles clustered together. We show that the analysis of this peculiar behaviour can be rather easily carried out by resorting to a backward formalism based on the Green's function, which allows the key physical observables, namely, the particle concentration and the pair correlation function, to be explicitly derived.
It is expected that the realization of a convergent and long-term stable numerical code for the simulation of a black hole inspiral collision will depend greatly upon the construction of stable algorithms capable of handling smooth and, most likely, time dependent boundaries. After deriving single grid, energy conserving discretizations for axisymmetric systems containing the axis of symmetry, we present a new excision method for moving black holes using multiple overlapping coordinate patches, such that each boundary is fixed with respect to at least one coordinate system. This multiple coordinate structure eliminates all need for extrapolation, a commonly used procedure for moving boundaries in numerical relativity.   We demonstrate this excision method by evolving a massless Klein-Gordon scalar field around a boosted Schwarzschild black hole in axisymmetry. The excision boundary is defined by a spherical coordinate system co-moving with the black hole. Our numerical experiments indicate that arbitrarily high boost velocities can be used without observing any sign of instability.
We study exactly self-similar blow-up profiles fot the generalized De Gregorio model for the three-dimensional Euler equation: $w_t + auw_x = u_xw, \quad u_x = Hw$ We show that for any $\alpha \in (0, 1)$ such that $|a\alpha|$ is sufficiently small, there is an exactly self-similar $C^\alpha$ solution that blows up in finite time. This simultaneously improves on the result in \cite{ElJe} by removing the restriction $1/\alpha \in \mathbb Z$ and \cite{El-GhMa,ChHoHu}, which only deals with asymptotically self-similar blow-ups.
We exhibit the superHiggs effect in heterotic string theory by turning on a background NS-NS field and deforming the BRST operator consistent with superconformal invariance. The NS-NS field spontaneously breaks spacetime supersymmetry. We show how the gravitini and the physical dilatini gain mass by eating the would-be Goldstone fermions.
The phase shift a neutron interferometer caused by the gravitational field and the rotation of the earth is derived in a unified way from the standpoint of general relativity. General relativistic quantum interference effects in the slowly rotating braneworld as the Sagnac effect and phase shift effect of interfering particle in neutron interferometer are considered. It was found that in the case of the Sagnac effect the influence of brane parameter is becoming important due to the fact that the angular velocity of the locally non rotating observer must be larger than one in the Kerr space-time. In the case of neutron interferometry it is found that due to the presence of the parameter $Q^{*}$ an additional term in the phase shift of interfering particle emerges from the results of the recent experiments we have obtained upper limit for the tidal charge as $Q^{*}\lesssim 10^{7} \rm{cm}^{2}$. Finally, as an example, we apply the obtained results to the calculation of the (ultra-cold neutrons) energy level modification in the braneworld.
We study how the dimensional regularization works in the light-cone gauge string field theory. We show that it is not necessary to add a contact term to the string field theory action as a counter term in this regularization at least at the tree level. We also investigate the one-loop amplitudes of the bosonic theory in noncritical dimensions and show that they are modular invariant.
Using the rank of the Mordell-Weil group $E(\mathbb{Q})$ of an elliptic curve $E$ over $\mathbb{Q}$, we give a lower bound of the class number of the number field $\mathbb{Q}(E[p^n])$ generated by $p^n$-division points of $E$ when the curve $E$ does not possess a $p$-adic point of order $p$: $E(\mathbb{Q}_p)[p] =0$.
The study of stellar kinematic properties may provide hints on the formation and evolution of elliptical and lenticular galaxies. Although most previous studies have focused on the large scale of these galaxies, their central regions (scales of $\sim$ 100 pc) may contain important clues about their structure, such as kinematically decoupled cores. This is the fourth paper on a sample of 10 massive ($\sigma$ $>$ 200 km s$^{-1}$) and nearby ($d$ $<$ 31 Mpc) early-type galaxies, observed with the integral field unit of the Gemini South Multi Object Spectrograph. Here, we analyse the properties of the stellar kinematics in the circumnuclear region. We fitted the line-of-sight velocity distribution with a Gauss-Hermite function. In seven galaxies of the sample, we detected a rotation pattern in their radial velocity maps that are anti-correlated with $h_3$. We interpret this as stellar structures in rotation embedded in the bulges of the objects. Comparing the stellar kinematic results with the PCA Tomography results and also with the gas kinematic results of IC 5181, it seems that this object may have a non-axisymmetric potential at its centre. The velocity dispersion maps of four objects have a nuclear peak, which must correspond, in part, to unresolved stellar rotation. In NGC 1404, we detected a kinematic decoupled core with an extension of $\sim$ 200 pc. This galaxy also has a $\sigma$-drop in the centre, which may be related to both stellar components in counterrotation or with a kinematically cold star-forming region.
A scalar adjoint field is introduced as a spatial average over (anti)calorons in a thermalized SU(2) Yang-Mills theory. This field is associated with the thermal ground state in the deconfining phase and acts as a background for gauge fields of trivial topology. Without invoking detailed microscopic information we study the properties of the corresponding potential, and we discuss its thermodynamical implications. We also investigate the gluon condensate at finite temperature relating it to the adjoint scalar field.
The quiet Sun internetwork is permeated by weak and highly inclined magnetic fields whose physical properties, dynamics, and magnetic interactions are not fully understood. High spatial resolution magnetograms show them as discrete magnetic elements that appear/emerge and disappear/cancel continuously over the quiet Sun surface. The 4-m European Solar Telescope (EST) and the Advanced Technology Solar Telescope (ATST) will obtain two-dimensional, high cadence, high precision polarimetric measurements at the diffraction limit (30 km). Here, we compile the basic requirements for the observation of internetwork fields with EST and ATST (field of view, cadence, instrument configuration, etc). More specifically, we concentrate on the field-of-view requirements. To set them we analyze the proper motion of internetwork magnetic elements across the solar surface. We use 13 hours of magnetograms taken with the Hinode satellite to identify and track thousands of internetwork magnetic element in an isolated supergranular cell. We calculate the velocity components of each element and the mean distance they travel. The results show that, on average, magnetic elements in the interior of supergranular cells move toward the network. The radial velocity is observed to depend on the distance to the center of the supergranule. Internetwork magnetic elements travel 400 on average. These results suggest that ATST and EST should cover, at least, one supergranular cell to obtain a complete picture of the quiet Sun internetwork.
We find that in order to completely describe the spin transport, apart from spin current (or linear spin current), one has to introduce the angular spin current. The two spin currents respectively describe the translational and rotational motion of a spin. The definitions of these spin current densities are given and their physical properties are discussed. Both spin current densities appear naturally in the spin continuity equation. Moreover we predict that the angular spin current can also induce an electric field $\vec{E}$, and in particular $\vec{E}$ scales as $1/r^2$ at large distance $r$, whereas the $\vec{E}$ field generated from the linear spin current goes as $1/r^3$.
H-alpha emission from supernova remnants (SNRs) implies the existence of neutral hydrogens in the ambient medium. In the precursor of an SNR shock modified by cosmic rays (CRs), upstream plasmas are pushed by the CR pressure, but neutral particles are not, so that the relative velocity appears and some neutral particles become pickup ions by the charge exchange process in the precursor. We investigate how the pickup ions generated in the precursor affect the shock structure and the particle acceleration. If the CR pressure is larger than 20% of the shock ram pressure, the compression of the subshock becomes smaller than that without pickup ions because of the pressure of the pickup ions. Moreover, even if the shock is modified by CRs, the total compression ratio can be smaller than 4. In addition, the pickup ions play an important role for the injection into the particle acceleration. If the shock is a quasi-perpendicular shock and if the the multiply reflected ion acceleration occurs, the CR spectrum can be harder than that of the test particle diffusive shock acceleration below GeV.