ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper we study couples of finite separable extensions of the function field $\mathbb{F}_q(T)$ which are arithmetically equivalent, i.e. such that prime ideals of $\mathbb{F}_q[T]$ decompose with the same inertia degrees in the two fields, up to finitely many exceptions. In the first part of this work, we extend previous results by Cornelissen, Kontogeorgis and Van der Zalm to the case of non-geometric extensions of $\mathbb{F}_q(T)$, which are fields such that their field of constants may be bigger than $\mathbb{F}_q$. In the second part, we explicitly produce examples of non-geometric extensions of $\mathbb{F}_2(T)$ which are equivalent and non-isomorphic over $\mathbb{F}_2(T)$ and non-equivalent over $\mathbb{F}_4(T)$, solving a particular Inverse Galois Problem.
Given a suitable action on a complex projective variety X of a non-reductive affine algebraic group H, this paper considers how to choose a reductive group G containing H and a projective completion of G x_H X which is a reductive envelope in the sense of math.AG/0703131. In particular it studies the family of examples given by moduli spaces of hypersurfaces in the weighted projective plane P(1,1,2) obtained as quotients by linear actions of the (non-reductive) automorphism group of P(1,1,2).
High spatial resolution observations in the 1 to 3.5 micron region of the Galactic Center source known historically as IRS 13 are presented. They include ground-based adaptive optics images in the H, Kp (2.12/0.4 micron) and L bands, NICMOS data in filters between 1.1 and 2.2 micron, and integral field spectroscopic data from BEAR, an Imaging FTS, in the HeI 2.06 micron and the Br$\gamma$ line regions. Analysis of all these data provides a completely new picture of the main component, IRS 13E, which appears as a cluster of seven individual stars within a projected diameter of ~0.5'' (0.02 pc). The brightest sources, 13E1, 13E2, 13E3 (a binary), and 13E4, are all massive stars, 13E1 a blue object, with no detected emission line while 13E2 and 13E4 are high-mass emission line stars. 13E2 is at the WR stage and 13E4 a massive O-type star. 13E3A and B are extremely red objects, proposed as other examples of dusty WR stars. All these sources have a common westward proper motion. 13E5, is a red source similar to 13E3A/B. This concentration of comoving massive hot stars, IRS 13E, is proposed as the remaining core of a massive star cluster, which could harbor an intermediate-mass black hole (IMBH) of ~1300 M_sol. This detection plays in favor of a scenario in which the helium stars and the other hot stars in the central pc originate from the stripping of a massive cluster formed several tens of pc from the center. The detection of a discrete X-ray emission (Baganoff et al. 2003) at the IRS~13 position is examined in this context.
During nuclear fission, a heavy nucleus splits into two rotating fragments. The associated angular momentum is large, yet the mechanism of its generation and its dependence on the mass of fragments remain poorly understood. In this Letter, we provide the first microscopic calculations of angular momentum distributions in fission fragments for a wide range of fragment masses. For the benchmark case of $^{239}$Pu($n_{\text{th}}$,f), we find that the angular momentum of the fragments is largely determined by the nuclear shell structure and deformation, and that the heavy fragments therefore typically carry less angular momentum than their light partners. We use the fission model $\tt{FREYA}$ to simulate the emission of neutrons and photons from the fragments. The dependence of the angular momenta on fragment mass after the emission of neutrons and statistical photons is linear for the heavy fragments and either constant or weakly linear for the light fragments, consistent with the universal sawtooth pattern suggested by recent experimental data. Finally, we observe that using microscopic angular momentum distributions modifies the number of emitted photons significantly.
The initial growth of MnBi on MnAs terminated (GaMn)As is studied by means of synchrotron based photoelectron spectroscopy. From analysis of surface core level shifts we conclude that a continued epitaxial MnBi layer is formed, in which the MnAs/MnBi interface occurs between As and Bi atomic planes. The well defined 1x2 surface reconstruction of the MnAs surface in preserved for up to 2 ML of MnBi before clear surface degradation occurs.
The temperature dependence of hydrogen (H) desorption from Si(100) H-terminated surfaces by a scanning tunneling microscope (STM) is reported for negative sample bias. It is found that the STM induced H desorption rate ($R$) decreases several orders of magnitude when the substrate temperature is increased from 300 K to 610 K. This is most noticeable at a bias voltage of -7 V where $R$ decreases by a factor of ~200 for a temperature change of 80 K, whilst it only decreases by a factor of ~3 at -5 V upon the same temperature change. The experimental data can be explained by desorption due to vibrational heating by inelastic scattering via a hole resonance. This theory predicts a weak suppression of desorption with increasing temperature due to a decreasing vibrational lifetime, and a strong bias dependent suppression due to a temperature dependent lifetime of the hole resonance.
Bose-Einstein correlations in relativistic heavy ion collisions and their dependence on the freeze-out condition in hydrodynamic models is compared to time-like freeze-out, where particles are emitted away only from the surface, i.e. space- vs. time-like freeze-out. The corresponding HBT radii are calculated for the two models emphasizing the difference in the outward HBT radius.
In this article, we consider eigenfunctions $u$ of the bi-harmonic operator, i.e.,   $\triangle^2u=\lambda^2u$ on $\Omega$ with some homogeneous linear boundary conditions. We assume that $\Omega\subseteq\mathbb{R}^n$ ($n\geq2$) is a $C^{\infty}$ bounded domain, $\partial\Omega$ is piecewise analytic and $\partial\Omega$ is analytic except a set $\Gamma\subseteq\partial\Omega$ which is a finite union of some compact $(n-2)$ dimensional submanifolds of $\partial\Omega$. The main result of this paper is that the measure upper bounds of the nodal sets of the eigenfunctions is controlled by $\sqrt{\lambda}$. We first define a frequency function and a doubling index related to these eigenfunctions. With the help of establishing the monotonicity formula, doubling conditions and various a priori estimates, we obtain that the $(n-1)$ dimensional Hausdorff measures of nodal sets of these eigenfunctions in a ball are controlled by the frequency function and $\sqrt{\lambda}$. In order to further control the frequency function with $\sqrt{\lambda}$, we first establish the relationship between the frequency function and the doubling index, and then separate the domain $\Omega$ into two parts: a domain away from $\Gamma$ and a domain near $\Gamma$, and develop iteration arguments to deal with the two cases respectively.
The dynamic and static critical behaviors of driven and equilibrium lattice gas models are studied in two spatial dimensions. We show that in the short-time regime immediately following a critical quench, the dynamics of the transverse order parameters, auto-correlations, and Binder cumulant are consistent with the prediction of a Gaussian, $i.e.,$ non-interacting, effective theory, both for the equilibrium lattice gas and its nonequilibrium counterparts. Such a "super-universal" behavior is observed only at short times after a critical quench, while the various models display their distinct behaviors in the stationary states, described by the corresponding, known universality classes.
We present the whole set of equations with regularity and matching conditions required for the description of physically meaningful stationary cylindrically symmmetric distributions of matter, smoothly matched to Lewis vacuum spacetime. A specific example is given. The electric and magnetic parts of the Weyl tensor are calculated, and it is shown that purely electric solutions are necessarily static. Then, it is shown that no conformally flat stationary cylindrical fluid exits, satisfying regularity and matching conditions.
We investigate the photoproduction of $\rho$ mesons in ultraperipheral heavy ion collisions at RHIC and LHC energies in the dipole approach and within two phenomenological models based on the the Color Glass Condensate (CGC) formalism. We estimate the integrated cross section and rapidity distribution for meson production and compare our predictions with the data from the STAR collaboration. In particular, we demonstrate that the total cross section at RHIC is strongly dependent on the energy behavior of the dipole-target cross section at low energies, which is not well determined in the dipole approach. In contrast, the predictions at midrapidities at RHIC and in the full rapidity at LHC are under theoretical control and can be used to test the QCD dynamics at high energies.
A significant fraction of the envelope of low- and intermediate-mass stars is unstable to convection, leading to sub-surface turbulent motion. Here, we consider and include the effects of turbulence pressure in our stellar evolution calculations. In search of an observational signature, we compare the fractional contribution of turbulent pressure to the observed macroturbulent velocities in stars at different evolutionary stages. We find a strong correlation between the two quantities, similar to what was previously found for massive OB stars. We therefore argue that turbulent pressure fluctuations of finite amplitude may excite high-order, high-angular degree stellar oscillations, which manifest themselves at the surface an additional broadening of the spectral lines, i.e., macroturbulence, across most of the HR diagram. When considering the locations in the HR diagram where we expect high-order oscillations to be excited by stochastic turbulent pressure fluctuations, we find a close match with the observational $\gamma$ Doradus instability strip, which indeed contains high-order, non-radial pulsators. We suggest that turbulent pressure fluctuations on a percentual level may contribute to the $\gamma$ Dor phenomenon, calling for more detailed theoretical modelling in this direction.
Radiative one-loop corrections to fermion pair production in $e^+e^-$ annihilation are calculated in the Minimal Supersymmetric Standard Model (MSSM). The size of the non-standard corrections is discussed for the process e^+e^- to mu^+mu^- and e^+e^- to hadrons at LEP2 energies and for e^+e^- to t tbar at a high energy e^+e^- collider. The relative difference between the predictions of the MSSM and the Standard Model is typically below 10%.
The regular Tur\'an number of a graph $F$, denoted by rex$(n,F)$, is the largest number of edges in a regular graph $G$ of order $n$ such that $G$ does not contain subgraphs isomorphic to $F$. Giving a partial answer to a recent problem raised by Gerbner et al. [arXiv:1909.04980] we prove that rex$(n,F)$ asymptotically equals the (classical) Tur\'an number whenever the chromatic number of $F$ is at least four; but it is substantially different for some 3-chromatic graphs $F$ if $n$ is odd.
We show that when the speed of control is bounded, there is a widely applicable minimal-time control problem for which a coherent feedback protocol is optimal, and is faster than all measurement-based feedback protocols, where the latter are defined in a strict sense. The superiority of the coherent protocol is due to the fact that it can exploit a geodesic path in Hilbert space, a path that measurement-based protocols cannot follow.
To probe the star-formation (SF) processes, we present results of an analysis of the molecular cloud G35.20$-$0.74 (hereafter MCG35.2) using multi-frequency observations. The MCG35.2 is depicted in a velocity range of 30-40 km s$^{-1}$. An almost horseshoe-like structure embedded within the MCG35.2 is evident in the infrared and millimeter images and harbors the previously known sites, ultra-compact/hyper-compact G35.20$-$0.74N H\,{\sc ii} region, Ap2-1, and Mercer 14 at its base. The site, Ap2-1 is found to be excited by a radio spectral type of B0.5V star where the distribution of 20 cm and H$\alpha$ emission is surrounded by the extended molecular hydrogen emission. Using the {\it Herschel} 160-500 $\mu$m and photometric 1-24 $\mu$m data analysis, several embedded clumps and clusters of young stellar objects (YSOs) are investigated within the MCG35.2, revealing the SF activities. Majority of the YSOs clusters and massive clumps (500-4250 M$_{\odot}$) are seen toward the horseshoe-like structure. The position-velocity analysis of $^{13}$CO emission shows a blue-shifted peak (at 33 km s$^{-1}$) and a red-shifted peak (at 37 km s$^{-1}$) interconnected by lower intensity intermediated velocity emission, tracing a broad bridge feature. The presence of such broad bridge feature suggests the onset of a collision between molecular components in the MCG35.2. A noticeable change in the H-band starlight mean polarization angles has also been observed in the MCG35.2, probably tracing the interaction between molecular components. Taken together, it seems that the cloud-cloud collision process has influenced the birth of massive stars and YSOs clusters in the MCG35.2.
The discovery of multiple stellar populations in globular clusters raises fundamental questions concerning the formation and dynamical history of these systems. In a previous study aimed at exploring the formation of second-generation (SG) stars from the ejecta of first-generation (FG) AGB stars, and the subsequent dynamical evolution of the cluster, we showed that SG stars are expected to form in a dense subsystem concentrated in the inner regions of the FG cluster. In this paper we explore the implications of the structural properties of multiple-population clusters, and in particular the presence of the inner SG subsystem, for the disruption of binary stars. We quantify the enhancement of the binary disruption rate due to the presence of the central SG subsystem for a number of different initial conditions. Our calculations show that SG binaries, which are assumed to be more concentrated in the cluster inner regions, are disrupted at a substantially larger rate than FG binaries. Assuming a similar initial fraction of FG and SG binaries, our dynamical study indicates that the SG population is now expected to contain a significantly smaller binary fraction than the FG population.
The geometric phase acquired by the vector states under an adiabatic evolution along a noncyclic path can be calculated correctly in any instantaneous basis of a Hamiltonian that varies in time due to a time-dependent classical field.
Brownian dynamics algorithms integrate numerically Langevin equations and allow to probe long time scales in simulations. A common requirement for such algorithms is that interactions in the system should vary little during an integration time step: therefore, computational efficiency worsens as the interactions become steeper. In the extreme case of hard-body interactions, standard numerical integrators become ill defined. Several approximate schemes have been invented to handle such cases with little emphasis on testing the correctness of the integration scheme. Starting from the two-body Smoluchowsky equation, we discuss a general method for the overdamped Brownian dynamics of hard-spheres, recently developed by one of us. We test the accuracy of the algorithm with the exact solution of the Smoluchowsky equation in the case of twobody collisions and in the low-density limit.
The first observations of the recently completed Wisconsin H-Alpha Mapper (WHAM) facility include a study of emission lines from high velocity clouds in the M, A, and C complexes, with most of the observations on the M I cloud. We present results including clear detections of H-alpha emission from all three complexes with intensities ranging from 0.06 R to 0.20 R. In every observed direction where there is significant high velocity H I gas seen in the 21 cm line we have found associated ionized hydrogen emitting the H-alpha line. The velocities of the H-alpha and 21 cm emission are well correlated in every case except one, but the intensities are not correlated. There is some evidence that the ionized gas producing the H-alpha emission envelopes the 21 cm emitting neutral gas but the H-alpha "halo", if present, is not large. If the H-alpha emission arises from the photoionization of the H I clouds, then the implied Lyman continuum flux F_{LC} at the location of the clouds ranges from 1.3 to 4.2 x 10^5 photons cm^{-2} s^{-1}. If, on the other hand, the ionization is due to a shock arising from the collision of the high-velocity gas with an ambient medium in the halo, then the density of the pre-shocked gas can be constrained. We have also detected the [S II] 6716 angstrom line from the M I cloud and have evidence that the [S II] to H-alpha ratio varies with location on the cloud.
Stochastic monotonicity is a well known partial order relation between probability measures defined on the same partially ordered set. Strassen Theorem establishes equivalence between stochastic monotonicity and the existence of a coupling compatible with respect to the partial order. We consider the case of a countable set and introduce the class of \emph{finitely decomposable flows} on a directed acyclic graph associated to the partial order. We show that a probability measure stochastically dominates another probability measure if and only if there exists a finitely decomposable flow having divergence given by the difference of the two measures. We illustrate the result with some examples. In fluid theory the Lagrangian description follows the trajectories of the particles while the Eulerian one observes the local flow. A coupling gives a Lagrangian description of the transference plan of mass while a flow gives an Eulerian one
Ratios of azimuthal angle correlations for Mueller-Navelet jets are compared in QCD and N = 4 SYM. Such observables are well suited to study the effects of Moebius invariance in the Regge limit. The role of the renormalization prescription and the size of conformal contributions is addressed, showing that the BLM procedure best reproduces the N = 4 SYM results.
We study supersymmetric and non-supersymmetric extremal black holes obtained in Type IIA string theory compactified on K3 X T^2, with duality group O(6,22,Z) X SL(2,Z). In the Cardy limit an internal circle combines with the AdS_2 component in the near horizon geometry to give a BTZ black hole whose entropy is given by the Cardy formula. We study black holes carrying D0-D4 and D0-D6 brane charges. We find, both in the supersymmetric and non-supersymmetric cases, that a generic set of charges cannot be brought to the Cardy limit using the duality symmetries. In the non-supersymmetric case, unlike the supersymmetric one, we find that when the charges are large, a small fractional change in them always allows the charges to be taken to the Cardy limit. These results could lead to a microscopic determination of the entropy for extremal non-supersymmetric black holes, including rotating cases like the extreme Kerr black hole in four dimensions.
We consider a parabolic problem with degeneracy in the interior of the spatial domain and Neumann boundary conditions. In particular, we will focus on the well-posedness of the problem and on Carleman estimates for the associated adjoint problem. The novelty of the present paper is that for the first time it is considered a problem with an interior degeneracy and Neumann boundary conditions so that no previous result can be adapted to this situation. As a consequence new observability inequalities are established.
We consider the class $\mathcal{E}_t(Y)$ of Appell polynomials whose generating function is given by means of a real power $t$ of the moment generating function of a certain random variable $Y$. For such polynomials, we obtain explicit expressions depending on the moments of $Y$. It turns out that various kinds of generalizations of Bernoulli and Apostol-Euler polynomials belong to $\mathcal{E}_t(Y)$ and can be written and investigated in a unified way. In particular, explicit expression for such polynomials can be given in terms of suitable probabilistic generalizations of the Stirling numbers of the second kind.
We show that the coefficient array of a family of Chebyshev moments defines an involution in the group of Riordan arrays. We then extend this result to certain families of $d$-orthogonal polynomials.
In this work, the transition between diffusion-limited and ballistic aggregation models was revisited using a model in which biased random walks simulate the particle trajectories. The bias is controlled by a parameter $\lambda$, which assumes the value $\lambda=0$ (1) for ballistic (diffusion-limited) aggregation model. Patterns growing from a single seed were considered. In order to simulate large clusters, a new efficient algorithm was developed. For $\lambda \ne 0$, the patterns are fractal on the small length scales, but homogeneous on the large ones. We evaluated the mean density of particles $\bar{\rho}$ in the region defined by a circle of radius $r$ centered at the initial seed. As a function of $r$, $\bar{\rho}$ reaches the asymptotic value $\rho_0(\lambda)$ following a power law $\bar{\rho}=\rho_0+Ar^{-\gamma}$ with a universal exponent $\gamma=0.46(2)$, independent of $\lambda$. The asymptotic value has the behavior $\rho_0\sim|1-\lambda|^\beta$, where $\beta= 0.26(1)$. The characteristic crossover length that determines the transition from DLA- to BA-like scaling regimes is given by $\xi\sim|1-\lambda|^{-\nu}$, where $\nu=0.61(1)$, while the cluster mass at the crossover follows a power law $M_\xi\sim|1 -\lambda|^{-\alpha}$, where $\alpha=0.97(2)$. We deduce the scaling relations $\beta=\n u\gamma$ and $\beta=2\nu-\alpha$ between these exponents.
In this note we generalize Nori's definition of the fundamental group scheme from a rational point to an arbitrary base point so that when we take $X$ to be a field $k$ and the point to be $k\subseteq \bar{k}$ we still get a non trivial group scheme which is similar to the absolute Galois group ${\rm Gal}(\bar{k}/k)$. Then we try to understand the group scheme at various levels.
A new limit of pion form factor at very large $Q^2$ is obtained by using a pion wave function determined from an effective chiral field theory of mesons. It shows that when $Q^2>>(1.8GeV)^2$ the pion form factor reaches the asymptotic limit ${\alpha_s(Q^2)\over Q^2}$.
Solar prominence models used so far in the analysis of MHD waves in such structures are quite elementary. In this work, we calculate numerically magnetohydrostatic models in two-dimensional configurations under the presence of gravity. Our interest is in models that connect the magnetic field to the photosphere and include an overlying arcade. The method used here is based on a relaxation process and requires solving the time-dependent nonlinear ideal MHD equations. Once a prominence model is obtained, we investigate the properties of MHD waves superimposed on the structure. We concentrate on motions purely two-dimensional neglecting propagation in the ignorable direction. We demonstrate how by using different numerical tools we can determine the period of oscillation of stable waves. We find that vertical oscillations, linked to fast MHD waves, are always stable and have periods in the 4-10 min range. Longitudinal oscillations, related to slow magnetoacoustic-gravity waves, have longer periods in the range of 28-40 min. These longitudinal oscillations are strongly influenced by the gravity force and become unstable for short magnetic arcades.
We give a bijection between partially directed paths in the symmetric wedge y= +/-x and matchings, which sends north steps to nestings. This gives a bijective proof of a result of Prellberg et al. that was first discovered through the corresponding generating functions: the number of partially directed paths starting at the origin confined to the symmetric wedge y= +/-x with k north steps is equal to the number of matchings on [2n] with k nestings.