ShantanuT01/DACTYL-Pretraining huggingface dataset:
This paper deals with the Nash problem, which claims that there are as many families of arcs on a singular germ of surface $U$ as there are essential components of the exceptional divisor in the desingularisation of this singularity. Let $\mathcal{H}=\bigcup \bar{N_\alpha}$ be a particular decomposition of the set of arcs on $U$, described later on. We give two new conditions to insure that $\bar{N_\alpha}\not \subset \bar{N_\beta}$, $\alpha \not = \beta$; more precisely,for the first one, we claim that if there exists $f \in {\mathcal{O}}_{U}$ such that $ord_{E_\alpha}(f)<ord_{E_\beta}(f)$, where $E_\alpha, E_\beta$ are exceptional divisors of the desingularisation, then $\bar{N_\alpha}\not \subset \bar{N_\beta}$. The second condition, used when the singularity is rational and of surface, is the following:let $(S,s)$ et $(S',s')$ be two rational surface singularities so that there exist a dominant and birational morphism $\pi$ from $(S,s)$ to $(S',s')$;then,let $E_\alpha, E_\beta$ be two essential components of the exceptional divisors in the minimal desingularisation of $(S,s)$, such that their image by $\pi$, $E'_\alpha$ and $E'_\beta$, are exceptional divisor for $(S',s')$; if $\bar{N'_\alpha}(S',s')\not \subset \bar{N'_\beta}(S',s')$ then $\bar{N_\alpha}(S,s)\not \subset \bar{N_\beta}(S,s)$. These two conditions are simple, but it allows us to prove quite directly the conjecture for the rational minimal surface singularities, using the decomposition of minimal suface singularities into cyclic quotient singularities of type $A_n$. A proof of the conjecture for these singularities has already been given by Ana Reguera.
We describe a new approach to the definition of the moduli functor of stable varieties. While there is wide agreement as to what classes of varieties should appear, the notion of a family of stable surfaces is quite subtle, as key numerical invariants may fail to be constant in flat families. Our approach is to add natural stack structure to stable varieties. For example, given a canonical model we take the global-quotient stack structure arising from its realization as Proj of the canonical ring. Deformations of the stack structure preserve key numerical invariants of the stable variety, including the top self-intersection of the canonical divisor. This approach yields a transparent construction of the moduli stack of stable varieties as a global quotient of a suitable Hilbert scheme of weighted projective stacks.
The stability of antiferromagnetic long-range order against quenched disorder is considered. A simple model of an antiferromagnet with a spatially varying Neel temperature is shown to possess a nontrivial fixed point corresponding to long-range order that is stable unless either the order parameter or the spatial dimensionality exceeds a critical value. The instability of this fixed point corresponds to the system entering a random-singlet phase. The stabilization of long-range order is due to quantum fluctuations, whose role in determining the phase diagram is discussed.
We report precise measurements and quantitative data analysis on the low-temperature resistivity of several ferromagnetic manganite films. We clearly show that there exists a T^{4.5} term in low-temperature resistivity, and that this term is in quantitative agreement with the quantum theory of two-magnon scattering for half metallic ferromagnets. Our present results provide the first bulk experimental evidence of half-metallic ferromagnetism in doped manganites.
In this short note, we show that K-semistable Fano manifolds with the smallest alpha invariant are projective spaces. Singular cases are also investigated.
We review the issue of steady spherically symmetric accretion onto a renormalization group improved Schwarzschild space-time which is solution to an asymptotically safe theory (AS) containing high-derivative terms. We use a Hamiltonian dynamical system approach for the analysis of the accretion of four types of isothermal test fluids: ultra-stiff fluid, ultra-relativistic fluid, radiation fluid, and sub-relativistic fluid. An important outcome of our study is that, contrary to what claimed in a recent work, there exist physical solutions for the accretion of an ultra-relativistic fluid in AS which include subsonic, supersonic and transonic regimes. We also study quantum corrections to the known stability of the accretion in general relativity (GR). To this end we use a perturbative procedure based on the continuity equation with the mass accretion rate being the perturbed quantity. Two classes of perturbations are studied: standing waves and travelling waves. We find that quantum gravity effects either enhance or diminish the stability of the accretion depending on the type of test fluid and depending on the radial distance to the central object.
We first enumerate a generalization of domino towers that was proposed by Tricia M. Brown (J. Integer Seq. 20 (2017)), which we call S-omino towers. We establish equations that the generating function must satisfy and then apply the Lagrange inversion formula to find a closed formula for the number of towers. We also show a connection to generalized Dyck paths and provide an explicit bijection. Finally, we consider the set of row-convex k-omino towers, introduced by Brown, and calculate an exact generating function.
Using the motion of accreting particles onto halos in cosmological $N$-body simulations, we study the radial phase-space structures of cold dark matter (CDM) halos. In CDM cosmology, formation of virialized halos generically produces radial caustics, followed by multi-stream flows of accreted dark matter inside the halos. In particular, the radius of the outermost caustic called the splashback radius exhibits a sharp drop in the slope of the density profile. Here, we focus on the multi-stream structure of CDM halos inside the splashback radius. To analyze this, we use and extend the SPARTA algorithm developed by Diemer. By tracking the particle trajectories accreting onto the halos, we count their number of apocenter passages, which is then used to reveal the multi-stream flows of the dark matter particles. The resultant multi-stream structure in radial phase space is compared with the prediction of the self-similar solution by Fillmore & Goldreich for each halo. We find that $\sim30\%$ of the simulated halos satisfy our criteria to be regarded as being well fitted to the self-similar solution. The fitting parameters in the self-similar solution characterizes physical properties of the halos, including the mass accretion rate and the size of the outermost caustic (i.e., the splashback radius). We discuss in detail the correlation of these fitting parameters and other measures directly extracted from the $N$-body simulation.
We describe the Lie algebra deformations of D=4 Maxwell superalgebra that was recently introduced as the symmetry algebra of a kappa-symmetric massless superparticle in a supersymmetric constant electromagnetic background. Further we introduce the D=3 Maxwell superalgebra and present all its possible deformations. Finally the deformed superalgebras are used to derive via a contraction procedure the complete set of Casimir operators for D=4 and D=3 Maxwell superalgebras.
This paper has been withdrawn by the author, because it is now part of an enlarged version entitled "Time functions as utilities" arXiv:0909.0890
We report on magnetic properties of cubic compound Cu3TeO6 studied by $ac$ and $dc$ susceptibility and neutron powder diffraction for the first time. A novel magnetic lattice, three dimensional spin web, composed of almost planar regular hexagons of Cu2+, S =1/2 spins, defines the properties of Cu3TeO6. The behavior of the magnetic susceptibility in the paramagnetic state at approximately 170 K is suggestive for a competition between local anisotropies of Cu2+ hexagons. The resulting frustration is weaker than the antiferromagnetic nearest-neighbor interaction which leads to a collinear (or slightly canted) spin arrangement (k=0,0,0) and formation of magnetic domains below TN=61 K.
We give an elementary and self-contained introduction to pairings on elliptic curves over finite fields. For the first time in the literature, the three different definitions of the Weil pairing are stated correctly and proved to be equivalent using Weil reciprocity. Pairings with shorter loops, such as the ate, ate$_i$, R-ate and optimal pairings, together with their twisted variants, are presented with proofs of their bilinearity and non-degeneracy. Finally, we review different types of pairings in a cryptographic context. This article can be seen as an update chapter to A. Enge, Elliptic Curves and Their Applications to Cryptography - An Introduction, Kluwer Academic Publishers 1999.
For any conical symplectic resolution, we give a conjecture relating the intersection cohomology of the singular cone to the quantum cohomology of its resolution. We prove this conjecture for hypertoric varieties, recovering the ring structure on hypertoric intersection cohomology that was originally constructed by Braden and the second author.
The potential for application of magnetic skyrmions in high density storage devices provides a strong drive to investigate and exploit their stability and manipulability. Through a three-dimensional micromagnetic hysteresis study, we investigate the question of existence of skyrmions in cylindrical nanostructures of variable thickness. We quantify the applied field and thickness dependence of skyrmion states, and show that these states can be accessed through relevant practical hysteresis loop measurement protocols. As skyrmionic states have yet to be observed experimentally in confined helimagnetic geometries, our work opens prospects for developing viable hysteresis process-based methodologies to access and observe skyrmionic states.
We consider the weighted parabolic problem of the type \begin{equation*} \begin{split} \left\{\begin{array}{ll} u_t-\mathrm{div}(\omega_2(x)|\nabla u|^{p-2} \nabla u )= \lambda \omega_1(x) |u|^{p-2}u,& x\in\Omega, u(x,0)=f(x),& x\in\Omega, u(x,t)=0,& x\in\partial\Omega,\ t>0, \end{array}\right. \end{split} \end{equation*} for quite a general class of possibly unbounded weights $ \omega_1,\omega_2$ satisfying the Hardy-type inequality. We prove existence of a global weak solution in the weighted Sobolev spaces provided that $\lambda$ is smaller than the optimal constant in the inequality.
This paper concerns the time growth of the highest-order energy of the systems of incompressible isotropic elastodynamics in two space dimensions. The global well-posedness of smooth solutions near equilibrium was first obtained by Lei [31] where the highest-order generalized energy may have certain growth in time. We improve above result and show that the highest-order generalized energy is uniformly bounded for all the time. The two dimensional incompressible elastodynamics is a system of nonlocal quasilinear wave equations where the unknowns decay as $\langle t\rangle^{-\frac12}$. This suggests the problem is supercritical in the sense that the decay rate is far from integrable. Surprisingly, we showed that in the highest-order energy estimate, the temporal decay can be strongly enhanced to be subcritical $\langle t \rangle^{-\frac54}$. The analysis is based on the ghost weight energy method by Alinhac [5], the inherent strong null structure by Lei [31] and the inherent div-curl structure of the system.
Mechanical behaviors of bulk metallic glasses (BMGs) including heterogeneous and homogeneous deformation are interpreted by phenomenological shear transformation zones (STZs) model. Currently, information about STZs, i.e. size and density, is only extracted by fitting model equation to the data obtained from macroscopic mechanical tests. This is inadequate since structural features of STZs theory cannot be assessed. Here, we develop anisotropic pair distribution function (PDF) method for directly characterizing mechanical response of deformation defects. Our results reveal the physical picture of deformation defects in BMGs and also provide direct experimental observation of a link between mechanical deformation and intrinsic properties of deformation defects in BMGs.
What is the true order of growth of torsion in the cohomology of an arithmetic group? Let $D$ be a quaternion over an imaginary quadratic field $F.$ Let $E/F$ be a cyclic Galois extension with $\mathrm{Gal}(E/F) = \langle \sigma \rangle.$ We prove lower bounds for "the Lefschetz number of $\sigma$ acting on torsion cohomology" of certain Galois-stable arithmetic subgroups of $D_E^\times.$ For these same subgroups, we unconditionally prove a would-be-numerical consequence of the existence of a hypothetical base change map for torsion cohomology.
We adapt the transfer matrix ($\T$-matrix) method originally designed for one-dimensional quantum mechanical problems to solve the circularly symmetric two-dimensional problem of graphene quantum dots. In similarity to one-dimensional problems, we show that the generalized $\T$-matrix contains rich information about the physical properties of these quantum dots. In particular, it is shown that the spectral equations for bound states as well as quasi-bound states of a circular graphene quantum dot and related quantities such as the local density of states and the scattering coefficients are all expressed exactly in terms of the $\T$-matrix for the radial confinement potential. As an example, we use the developed formalism to analyse physical aspects of a graphene quantum dot induced by a trapezoidal radial potential. Among the obtained results, it is in particular suggested that the thermal fluctuations and electrostatic disorders may appear as an obstacle to controlling the valley polarization of Dirac electrons.
Relativistic mean field theory with the NL3 force is used for producing potential energy surfaces (PES) for series of isotopes suggested as exhibiting critical point symmetries. Relatively flat PES are obtained for nuclei showing the E(5) symmetry, while in nuclei corresponding to the X(5) case, PES with a bump are obtained. The PES corresponding to the Pt chain of isotopes suggest a transition from prolate to oblate shapes at 186-Pt.
Density functional calculations of the electronic structure of the complex hydride NaAlH4 and the reference systems NaH and AlH3 are reported. We find a substantially ionic electronic structure for NaAlH4, which emphasizes the importance of solid state effects in this material. The relaxed hydrogen positions in NaAlH4 are in good agreement with recent experiment. The electronic structure of AlH3 is also ionic. Implications for the binding of complex hydrides are discussed.
The gold-assisted exfoliation is a very effective method to produce large-area ($cm^2$-scale) membranes of molybdenum disulfide ($MoS_2$) for electronics. However, the strong $MoS_2/Au$ interaction, beneficial for the exfoliation process, has a strong impact on the vibrational and light emission properties of $MoS_2$. Here, we report an atomic force microscopy (AFM), micro-Raman ($\mu-R$) and micro-Photoluminescence ($\mu-PL$) investigation of $MoS_2$ with variable thickness exfoliated on Au and subsequently transferred on an $Al_2O_3/Si$ substrate. The $E_{2g}$ - $A_{1g}$ vibrational modes separation $\Delta\mu$ (typically used to estimate $MoS_2$ thickness) exhibits an anomalous large value ($\Delta\mu=21.2 cm^{-1}$) for monolayer (1L) $MoS_2$ on Au as compared to the typical one ($\Delta\mu=18.5 cm^{-1}$) measured on 1L $MoS_2$ on $Al_2O_3/Si$. Such substrate-related differences, explained in terms of tensile strain and p-type doping arising from the $MoS_2/Au$ interaction, were found to gradually decrease while increasing the number of $MoS_2$ layers. Furthermore, $\mu-PL$ spectra for 1L $MoS_2$ on Au exhibit a strong quenching and an overall red-shift of the main emission peak at 1.79 eV, compared to the 1.84 eV peak for 1L $MoS_2$ on $Al_2O_3$. After PL spectra deconvolution, such red shift was explained in terms of a higher trion/exciton intensity ratio, probably due to the higher polarizability of the metal substrate, as well as to the smaller equilibrium distance at $MoS_2/Au$ interface.
We report results of 6.7 GHz methanol maser monitoring of 139 star-forming sites with the Torun 32 m radio telescope from June 2009 to February 2013. The targets were observed at least once a month, with higher cadences of 2-4 measurements per week for circumpolar objects. Nearly 80 percent of the sources display variability greater than 10 per cent on a time-scale between a week and a few years but about three quarters of the sample have only 1-3 spectral features which vary significantly. Irregular intensity fluctuation is the dominant type of variability and only nine objects show evidence for cyclic variations with periods of 120 to 416 d. Synchronised and anti-correlated variations of maser features are detected in four sources with a disc-like morphology. Rapid and high amplitude bursts of individual features are seen on 3-5 occasions in five sources. Long (>50 d to 20 months) lasting bursts are observed mostly for individual or groups of features in 19 sources and only one source experienced a remarkable global flare. A few flaring features display a strong anti-correlation between intensity and line-width that is expected for unsaturated amplification. There is a weak anti-correlation between the maser feature luminosity and variability measure, i.e. maser features with low luminosity tend to be more variable than those with high luminosity. The analysis of the spectral energy distribution and continuum radio emission reveals that the variability of the maser features increases when the bolometric luminosity and Lyman flux of the exciting object decreases. Our results support the concept of a major role for infrared pumping photons in triggering outburst activity of maser emission.
An electron-positron layer can cover the surface of a bare strange star (SS), the electric field in which can excite the vacuum and drive a pair wind by taking away the heat of the star. In order to investigate the pair emission ability of a proto-SS, we establish a toy model to describe its early thermal evolution, where the initial trapping of neutrinos is specially taken into account. It is found that the early cooling of the SS is dominated by the neutrino diffusion rather than the conventional Urca processes, which leads to the appearance of an initial temperature plateau. During this plateau phase, the surface e^{+-} pair emission can keep a constant luminosity of 10^{48}-10^{50} erg s^{-1} for about a few to a few tens of seconds, which is dependent on the value of the initial temperature. The total energy released through this e^{+-} wind can reach as high as 10^{51} erg. In principle, this pair wind could be responsible for the prompt emission or extended emission of some gamma-ray bursts.
We advocate a (Wilson) renormalization-group (RG) treatment of finite-temperature first-order phase transitions, in particular those driven by radiative corrections such as occur in the standard model, and other spontaneously-broken gauge theories. We introduce the scale-dependent coarse-grained free energy $S_\La[\phi]$ which we explicitly calculate, using the Wilson RG and a $(4-\ep)$-expansion, for a scalar toy model that shares many features of the gauged case. As argued by Langer and others, the dynamics of the phase transition are described by $S_\La[\phi]$ with $\La$ of order the bubble wall thickness, and {\it not} by the usual (RG-improved) finite-temperature effective action which is reproduced by $S_\La[\phi]$ for $\La\to 0$. We argue that for weakly first-order transitions (such as that in the standard model) the $(4-\ep)$-expansion is necessary to control an inevitable growth of the effective scale-dependent coupling towards the strong-coupling regime, and that diagrammatic resummation techniques are unlikely to be appropriate.
Planet formation has been known for many years to be tied to the spatial distribution of gas and dust in disks around young stars. To constrain planet formation models, imaging observations of protoplanetary disks are required. In this framework, we have undertaken a mid-infrared imaging survey of Herbig Ae stars, which are pre-main sequence stars of intermediate mass still surrounded by a large amount of circumstellar material. The observations were made at a wavelength of 20.5 $\mu$m with the CAMIRAS camera mounted at the Cassegrain focus of the Canada France Hawaii Telescope.   We report the observations of three stars, HD135344, CQTau and HD163296. The circumstellar material around the three objects is spatially resolved. The extensions feature a disk like shape. The images provide direct information on two key parameters of the disk : its inclination and its outer radius. The outer radius is found to be quite different from the one deduced from disk models only constrained by fitting the Spectral Energy Distribution of the object. Other parameters of the disk, such as flaring, dust mass have been deduced from fitting both the observed extension and the spectral energy distribution with sophisticated disk models.   Our results show how important imaging data are to tighten constraints on the disk model parameters.
We propose a non-commutative generalization of Beilinson's Conjecture on the regulator map from algebraic K-theory to Deligne cohomology of algebraic varieties over Q. We also check a baby case of the generalized conjecture, namely, the case of finite-dimensional associative algebras.
We show that in a certain, angle-averaged squeezed limit, the $N$-point function of matter is related to the response of the matter power spectrum to a long-wavelength density perturbation, $P^{-1}d^nP(k|\delta_L)/d\delta_L^n|_{\delta_L=0}$, with $n=N-2$. By performing N-body simulations with a homogeneous overdensity superimposed on a flat Friedmann-Robertson-Lema\^itre-Walker (FRLW) universe using the \emph{separate universe} approach, we obtain measurements of the nonlinear matter power spectrum response up to $n=3$, which is equivalent to measuring the fully nonlinear matter $3-$ to $5-$point function in this squeezed limit. The sub-percent to few percent accuracy of those measurements is unprecedented. We then test the hypothesis that nonlinear $N$-point functions at a given time are a function of the linear power spectrum at that time, which is predicted by standard perturbation theory (SPT) and its variants that are based on the ideal pressureless fluid equations. Specifically, we compare the responses computed from the separate universe simulations and simulations with a rescaled initial (linear) power spectrum amplitude. We find discrepancies of 10\% at $k\simeq 0.2 - 0.5 \,h\,{\rm Mpc}^{-1}$ for $5-$ to $3-$point functions at $z=0$. The discrepancy occurs at higher wavenumbers at $z=2$. Thus, SPT and its variants, carried out to arbitrarily high order, are guaranteed to fail to describe matter $N$-point functions ($N>2$) around that scale.
Using Langlands's {\it Beyond Endoscopy} idea and analytic number theory techniques, we study the Asai L-function associated to a real quadratic field $\mathbf{K}/\Q.$ If the Asai L-function associated to an automorphic form over $\mathbf{K}$ has a pole, then the form is a base change from $\Q$. We prove this and further prove the analytic continuation of the L-function. This is one of the first examples of using a trace formula to get such information. A hope of Langlands is that general L-functions can be studied via this method.
The gluon distribution f(x, k_t^2,mu^2), unintegrated over the transverse momentum k_t of the gluon, satisfies the angular-ordered CCFM equation which interlocks the dependence on the scale k_t with the scale \mu of the probe. We show how, to leading logarithmic accuracy, the equation can be simplified to a single scale problem. In particular we demonstrate how to determine the two-scale unintegrated distribution f(x,k_t^2,mu^2) from knowledge of the integrated gluon obtained from a unified scheme embodying both BFKL and DGLAP evolution.