ShantanuT01/DACTYL-Pretraining huggingface dataset:
By a theorem of Wahl, for canonically embedded curves which are hyperplane sections of K3 surfaces, the first gaussian map is not surjective. In this paper we prove that if C is a general hyperplane section of high genus (greater than 280) of a general polarized K3 surface, then the second gaussian map of C is surjective. The resulting bound for the genus g of a general curve with surjective second gaussian map is decreased to g >152.
It was proved by Ginzburg and Mirkovic-Vilonen that the $G(O)$-equivariant perverse sheaves on the affine grassmannian of a connected reductive group $G$ form a tensor category equivalent to the tensor category of finite dimensional representations of the dual group $G^\vee$. The proof use the Tannakian formalism. The purpose of this paper is to construct explicitely the action of $G^\vee$ on the global cohomology of a perverse sheaf.
Let X be a smooth projective hypersurface. In this note we show that any six generated arithmetically Cohen-Macaulay vector bundle over X splits if dim X >= 6.
The toy model of a particle on a vertical rotating circle in the presence of uniform gravitational/ magnetic fields is explored in detail. After an analysis of the classical mechanics of the problem we then discuss the quantum mechanics from both exact and semi--classical standpoints. Exact solutions of the Schrodinger equation are obtained in some cases by diverse methods. Instantons, bounces are constructed and semi-classical, leading order tunneling amplitudes/decay rates are written down. We also investigate qualitatively the nature of small oscillations about the kink/bounce solutions. Finally, the connections of these toy examples with field theoretic and statistical mechanical models of relevance are pointed out.
Spin wave theory is applied to a quantum antiferromagnetic XXZ model on a triangle lattice in the presence of an in-plane magnetic field. The effect of the field is found to enhance the quantum fluctuation and to reduce the sublattice magnetization at the intermediate field strength in the anisotropic case. The possible implication to the field driven quantum phase transition from a spin solid to a spin liquid is discussed.
We consider a family of continued fraction expansions of any number in the unit closed interval $[0,1]$ whose digits are differences of consecutive non-positive integer powers of an integer $m \geq 2$. For this expansion, we apply the method of Rockett and Sz\"usz from [6] and obtained the solution of its Gauss-Kuzmin type problem.
We study two different actions on the moduli spaces of logarithmic connections over smooth complex projective curves. Firstly, we establish a dictionary between logarithmic orbifold connections and parabolic logarithmic connections over the quotient curve. Secondly, we prove that fixed points on the moduli space of connections under the action of finite order line bundles are exactly the push-forward of logarithmic connections on a certain unramified Galois cover of the base curve. In the coprime case, this action of finite order line bundles on the moduli space is cohomologically trivial.
This paper is a sequel to arXiv:1209.5550 where the notion of mixed Frobenius structure (MFS) was introduced as a generalization of the structure of a Frobenius manifold. Roughly speaking, the MFS is defined by replacing a metric of the Frobenius manifold with a filtration on the tangent bundle equipped with metrics on its graded quotients. The purpose of the current paper is to construct a MFS on the cohomology of a smooth projective variety whose multiplication is the non-equivariant limit of the quantum product twisted by a concave vector bundle. We show that such a MFS is naturally obtained as the non-equivariant limit of the Frobenius structure in the equivariant setting.
In this paper we study the Fourier coefficients of theta functions attached to Dirichlet characters at cusps other than infinity. The method is based on expressing them in terms of explicit elements of the adelic Schwartz space and studying the action of the adelic metaplectic group on these elements. We derive explicit formulae for the Fourier coefficients at all cusps. For the sake of simplicity, some restrictions are placed on the Dirichlet characters considered.
In this article, we consider the stochastic heat equation $du=(\Delta u+f(t,x))dt+ \sum_{k=1}^{\infty} g^{k}(t,x) \delta \beta_t^k, t \in [0,T]$, with random coefficients $f$ and $g^k$, driven by a sequence $(\beta^k)_k$ of i.i.d. fractional Brownian motions of index $H>1/2$. Using the Malliavin calculus techniques and a $p$-th moment maximal inequality for the infinite sum of Skorohod integrals with respect to $(\beta^k)_k$, we prove that the equation has a unique solution (in a Banach space of summability exponent $p \geq 2$), and this solution is H\"older continuous in both time and space.
We derive the superconformal index of the world-volume theory on M2-branes probing the cone over an arbitrary Sasaki-Einstein seven-manifold. The index is expressed in terms of the cohomology groups of the cone. We match our supergravity results with known results from gauge theory. Along the way we derive the spectrum of short Kaluza-Klein multiplets on generic Sasaki-Einstein seven-manifolds.
The Suzaku data of the highly variable magnetar 1E 1547.0$-$5408, obtained during the 2009 January activity, were reanalyzed. The 2.07 s pulsation of the 15--40 keV emission detected with the HXD was found to be phase modulated, with a period of $36.0^{+4.5}_{-2.5}$ ks and an amplitude of $0.52 \pm 0.14$ s. The modulation waveform is suggested to be more square-wave like rather than sinusoidal. While the effect was confirmed with the 10--14 keV XIS data, the modulation amplitude decreased towards lower energies, becoming consistent with 0 below 4 keV. After the case of 4U 0142+61, this makes the 2nd example of this kind of behavior detected from magnetars. The effect can be interpreted as a manifestation of free precession of this magnetar, which is suggested to be oblately deformed under the presence of strong toroidal field of $\sim 10^{16}$ G.
Criterion for the Riemann hypothesis found by B\'{a}ez-Duarte involves certain real coefficients $c_{k\text{}}$defined as alternating binomial sums. These coefficients can be effectively investigated using N\"{o}% rlund-Rice's integrals. Their behavior exhibits characteristic trend, due to trivial zeros of zeta, and fading oscillations, due to complex zeros. This method enables to calculate numerical values of $c_{k\text{}}$for large values of $k$, at least to $k=4\cdot 10^{8}$.   We give explicit expressions both for the trend and for the oscillations. The first tends to zero and is therefore, in view of the criterion, irrelevant for the Riemann hypothesis. The oscillations can be further decomposed into a series of harmonics with amplitudes diminishing quickly. Possible violation of the Riemann hypothesis would indicate that the amplitude of some high harmonic increases.
Disk and wind signatures are seen in the soft state of Galactic black holes, while the jet is seen in the hard state. Here we study the disk-wind connection in the $\rho$ class of variability in GRS 1915+105 using a joint NuSTAR-Chandra observation. The source shows 50 sec limit cycle oscillations. By including new information provided by the reflection spectrum, and using phase-resolved spectroscopy, we find that the change in the inner disk inferred from the blackbody emission is not matched by reflection measurements. The latter is almost constant, independent of the continuum model. The two radii are comparable only if the disk temperature color correction factor changes, an effect that could be due to the changing opacity of the disk caused by changes in metal abundances. The disk inclination is similar to that inferred from the jet axis, and oscillates by ~10 deg. The simultaneous Chandra data show the presence of two wind components with velocities between 500-5000 km/s, and possibly two more with velocities reaching 20,000 km/s (~0.06 c). The column densities are ~5e22 cm$^{-2}$. An upper limit to the wind response time of 2 sec is measured, implying a launch radius of <6e10 cm. The changes in wind velocity and absorbed flux require the geometry of the wind to change during the oscillations, constraining the wind to be launched from a distance of 290 - 1300 rg from the black hole. Both datasets support fundamental model predictions in which a bulge originates in the inner disk and moves outward as the instability progresses.
This paper deals with the long time behavior of solutions to a "fractional Fokker-Planck" equation of the form $\partial_t f = I[f] + \text{div}(xf)$ where the operator $I$ stands for a fractional Laplacian. We prove an exponential in time convergence towards equilibrium in new spaces. Indeed, such a result was already obtained in a $L^2$ space with a weight prescribed by the equilibrium in \cite{GI}. We improve this result obtaining the convergence in a $L^1$ space with a polynomial weight. To do that, we take advantage of the recent paper \cite{GMM} in which an abstract theory of enlargement of the functional space of the semigroup decay is developed.
We analyze environmental correlations using mark clustering statistics with the mock galaxy catalogue constructed by Muldrew et al. (Paper I). We find that mark correlation functions are able to detect even a small dependence of galaxy properties on the environment, quantified by the overdensity $1+\delta$, while such a small dependence would be difficult to detect by traditional methods. We then show that rank ordering the marks and using the rank as a weight is a simple way of comparing the correlation signals for different marks. With this we quantify to what extent fixed-aperture overdensities are sensitive to large-scale halo environments, nearest-neighbor overdensities are sensitive to small-scale environments within haloes, and colour is a better tracer of overdensity than is luminosity.
An examination of object recognition challenge leaderboards (ILSVRC, PASCAL-VOC) reveals that the top-performing classifiers typically exhibit small differences amongst themselves in terms of error rate/mAP. To better differentiate the top performers, additional criteria are required. Moreover, the (test) images, on which the performance scores are based, predominantly contain fully visible objects. Therefore, `harder' test images, mimicking the challenging conditions (e.g. occlusion) in which humans routinely recognize objects, need to be utilized for benchmarking. To address the concerns mentioned above, we make two contributions. First, we systematically vary the level of local object-part content, global detail and spatial context in images from PASCAL VOC 2010 to create a new benchmarking dataset dubbed PPSS-12. Second, we propose an object-part based benchmarking procedure which quantifies classifiers' robustness to a range of visibility and contextual settings. The benchmarking procedure relies on a semantic similarity measure that naturally addresses potential semantic granularity differences between the category labels in training and test datasets, thus eliminating manual mapping. We use our procedure on the PPSS-12 dataset to benchmark top-performing classifiers trained on the ILSVRC-2012 dataset. Our results show that the proposed benchmarking procedure enables additional differentiation among state-of-the-art object classifiers in terms of their ability to handle missing content and insufficient object detail. Given this capability for additional differentiation, our approach can potentially supplement existing benchmarking procedures used in object recognition challenge leaderboards.
We report structural and magnetic properties of multilayers composed of thin layers of the half metallic ferromagnetic Heusler compound Co2MnGe and layers of Au, Cr and the Heusler compound Cu2MnAl. The hysteresis loops measured at low temperatures reveal the existence of an exchange bias field HEB in all of these multilayers. For the [Co2MnGe/Au] multilayer system HEB is largest reaching up to 1 kOe at a temperature of 2 K. We characterize the exchange bias phenomenon in detail and show that it originates from a spin glass type of magnetic order for a thin interlayer at the interfaces. We discuss the results in the light of different models proposed for the explanation of the exchange bias effect.
We have studied the physical and chemical properties of 18 southern Red Midcourse Space Experiment Sources (RMSs), using archival data taken from the Atacama Pathfinder Experiment (APEX) Telescope Large Area Survey of the Galaxy, the Australia Telescope Compact Array, and the Millimeter Astronomy Legacy Team Survey at 90 GHz. Most of our sources have simple cometary/unresolved radio emissions at 4.8 and/or 8.6GHz. The large number of Lyman continuum fluxes (NL) indicates they are probably massive O- or early B-type star formation regions. Archival IRAS infrared data are used to estimate the dust temperature, which is about 30 K of our sources. Then, the H2 column densities and the volume-averaged H2 number densities are estimated using the 0.87 mm dust emissions. Large-scale infall and ionized accretions may be occurring in G345.4881+00.3148. We also attempt to characterize the chemical properties of these RMSs through molecular line (N2H+ (1-0) and HCO+ (1-0)) observations. Most of the detected N2H+ and HCO+ emissions match well with the dust emission, implying a close link to their chemical evolution in the RMSs. We found that the abundance of N2H+ is one order of magnitude lower than that in other surveys of infrared dark clouds, and a positive correlation between the abundances of N2H+ and HCO+. The fractional abundance of N2H+ with respect to H2 seems to decrease as a function of NL. These observed trends could be interpreted as an indication of enhanced destruction of N2H+, either by CO or through dissociative recombination with electrons produced by central UV photons.
The computational requirements posed by multi-dimensional simulations of type Ia supernovae make it difficult to incorporate complex nuclear networks to follow the release of nuclear energy along with the propagation of the flame. Instead, these codes usually model the flame and use simplified nuclear kinetics, with the goal of determining a sufficiently accurate rate of nuclear energy generation and, afterwards, post-processing the thermodynamic trajectories with a large nuclear network to obtain more reliable nuclear yields. In this work, I study the performance of simplified nuclear networks with respect to reproduction of the nuclear yields obtained with a one-dimensional supernova code equipped with a large nuclear network. I start by defining a strategy to follow the properties of matter in nuclear statistical equilibrium (NSE). I propose to use published tables of NSE properties, together with a careful interpolation routine. Short networks (iso7 and 13{\alpha}) are able to give an accurate yield of 56Ni, after post-processing, but can fail by order of magnitude in predicting the ejected mass of even mildly abundant species (> 0.001 solar masses). A network of 21 species reproduces the nucleosynthesis of the Chandrasekhar and sub-Chandrasekhar explosions studied here with average errors better than 20% for the whole set of stable elements and isotopes followed in the models.
Given a minimal model of an elliptic curve, $E/K$, over a finite extension, $K$, of ${\mathbb Q}_{p}$ for any rational prime, $p$, and any point $P \in E(K)$ of infinite order, we determine precisely $\min \left( v \left( \phi_{n}(P) \right), v \left( \psi_{n}^{2}(P) \right) \right)$, where $v$ is a normalised valuation on $K$ and $\phi_{n}(P)$ and $\psi_{n}(P)$ are polynomials arising from multiplication by $n$ for this model of the curve.
We model the infrared (IR) emission from the ring-like dust disk around the main-sequence (MS) star Epsilon Eridani, a young analog to our solar system, in terms of a porous dust model previously developed for the extended wedge-shaped disk around the MS star $\beta$ Pictoris and the sharply truncated ring-like disks around the Herbig Ae/Be stars HR 4796A and HD 141569A. It is shown that the porous dust model with a porosity of $\simali$90% is also successful in reproducing the IR to submillimeter dust emission spectral energy distribution as well as the 850$\mum$ flux radial profile of the dust ring around the more evolved MS star Epsilon Eridani. Predictions are made for future {\it SIRTF} observations which may allow a direct test of the porous dust model.
We consider a generalized Hubbard model with on-site and nearest-neighbour repulsions U and V respectively, and nearest-neighbour hopping for spin up (down) which depends on the total occupation n_b of spin down (up) electrons on both sites involved. The hopping parameters are t_{AA}, t_{AB} and t_{BB} for n_b=0,1,2 respectively. We briefly summarize results which support that the model exhibits s-wave superconductivity for certain parameters and extend them by studying the Berry phases. Using a generalized Hartree-Fock(HF) BCS decoupling of the two and three-body terms, we obtain that at half filling, for t_{AB}<t_{AA}=t_{BB} and sufficiently small U and V the model leads to triplet p-wave superconductivity for a simple cubic lattice in any dimension. In one dimension, the resulting phase diagram is compared with that obtained numerically using two quantized Berry phases (topological numbers) as order parameters. While this novel method supports the previous results, there are quantitative differences.
We develop a method to compute the Ekedahl-Oort type of a curve C over a field k of characteristic p (which is the isomorphism type of the p-kernel group scheme J[p], where J is the Jacobian of C). Part of our method is general, in that we introduce the new notion of a Hasse-Witt triple, which re-encodes in a useful way the information contained in the Dieudonne module of J[p]. For complete intersection curves we then give a simple method to compute this Hasse-Witt triple. An implementation of this method is available in Magma.
A multi-step setup for heavy-flavour studies in high-energy nucleus-nucleus (AA) collisions --- addressing within a comprehensive framework the initial Q-Qbar production, the propagation in the hot medium until decoupling and the final hadronization and decays --- is presented. The initial hard production of Q-Qbar pairs is simulated using the POWHEG pQCD event generator, interfaced with the PYTHIA parton shower. Outcomes of the calculations are compared to experimental data in pp collisions and are used as a validated benchmark for the study of medium effects. In the AA case, the propagation of the heavy quarks in the medium is described in a framework provided by the relativistic Langevin equation. For the latter, different choices of transport coefficients are explored (either provided by a perturbative calculation or extracted from lattice-QCD simulations) and the corresponding numerical results are compared to experimental data from RHIC and the LHC. In particular, outcomes for the nuclear modification factor R_AA and for the elliptic flow v_2 of D/B mesons, heavy-flavour electrons and non-prompt J/\psi's are displayed.
The second data release of the Gaia mission has revealed a very rich structure in local velocity space. In terms of in-plane motions, this rich structure is also seen as multiple ridges in the actions of the axisymmetric background potential of the Galaxy. These ridges are probably related to a combination of effects from ongoing phase-mixing and resonances from the spiral arms and the bar. We have recently developed a method to capture the behaviour of the stellar phase-space distribution function at a resonance, by re-expressing it in terms of a new set of canonical actions and angles variables valid in the resonant region. Here, by properly treating the distribution function at resonances, and by using a realistic model for a slowly rotating large Galactic bar with pattern speed 39 km/s/kpc, we show that no less than six ridges in local action space can be related to resonances with the bar. Two of these at low angular momentum correspond to the corotation resonance, and can be associated to the Hercules moving group in local velocity space. Another one at high angular momentum corresponds to the outer Lindblad resonance, and can tentatively be associated to the velocity structure seen as an arch at high azimuthal velocities in Gaia data. The other ridges are associated to the 3:1, 4:1 and 6:1 resonances. The latter can be associated to the so-called 'horn' of the local velocity distribution. While it is clear that effects from spiral arms and incomplete phase-mixing related to external perturbations also play a role in shaping the complex kinematics revealed by Gaia data, the present work demonstrates that, contrary to common misconceptions, the bar alone can create multiple prominent ridges in velocity and action space.
For two decades, two-dimensional carbon species, including graphene, have been the core of research in pursuing next-generation logic applications beyond the silicon technology. Yet the opening of a gap in a controllable range of doping, whilst keeping high conductance outside of this gapped state, has remained a grand challenge in them thus far. Here we show that, by bringing Bernal-stacked bilayer graphene in contact with an anti-ferromagnetic insulator CrOCl, a strong insulating behavior is observed in a wide range of positive total electron doping $n_\mathrm{tot}$ and effective displacement field $D_\mathrm{eff}$ at low temperatures. Transport measurements further prove that such an insulating phase can be well described by the picture of an inter-layer excitonic state in bilayer graphene owing to electron-hole interactions. The consequential over 1 $\mathrm{G\Omega}$ excitonic insulator can be readily killed by tuning $D_\mathrm{eff}$ and/or $n_\mathrm{tot}$, and the system recovers to a high mobility graphene with a sheet resistance of less than 100 $\mathrm{\Omega}$. It thus yields transistors with "ON-OFF" ratios reaching 10$^{7}$, and a CMOS-like graphene logic inverter is demonstrated. Our findings of the robust insulating phase in bilayer graphene may be a leap forward to fertilize the future carbon computing.
In this article we deal with the backward uniqueness property of the heat equation in conical domains in two spatial dimensions via Carleman inequality techniques. Using a microlocal interpretation of the pseudoconvexity condition, we improve the bounds of \v{S}ver\'ak and Li on the minimal angle in which the backward uniqueness property is displayed: We reach angles of slightly less than $95^{\circ}$. Via two-dimensional limiting Carleman weights we obtain the uniqueness of possible controls of the heat equation with lower order perturbations in conical domains with opening angles larger than $90^{\circ}$
Among several well-known transition metal-based compounds, the van der Waals (vdW) Fe3-xGeTe2 (FGT) magnet is a strong candidate for use in two-dimensional (2D) magnetic devices due to its strong perpendicular magnetic anisotropy, sizeable Curie temperature (TC ~ 154 K), and versatile magnetic character that is retained in the low-dimensional limit. While the TC remains far too low for practical applications, there has been a successful push toward improving it via external driving forces such as pressure, irradiation, and doping. Here we present experimental evidence of a novel room-temperature (RT) ferromagnetic phase induced by the electrochemical intercalation of common tetrabutylammonium cations (TBA+) into FGT bulk crystals. We obtained Curie temperatures as high as 350 K with chemical and physical stability of the intercalated compound. The temperature-dependent Raman measurements in combination with vdW-corrected ab initio calculations suggest that charge transfer (electron doping) upon intercalation could lead to the observation of RT ferromagnetism. This work demonstrates that molecular intercalation is a viable route in realizing high-temperature vdW magnets in an inexpensive and reliable manner.