Miracle-dz/UniFAR-FTUs huggingface dataset:
The power spectrum of interplanetary Alfvénic fluctuations: Derivation of the governing equation and its solution

A model is presented to explain the radial evolution of the power spectra of interplanetary Alfvenic fluctuations found by Bavassano et al. (1982a) based on the magnetic field data of Helios 1 and 2. It is assumed in this model that Alfvenic fluctuations represent an asymmetric state of MHD turbulence in which most of the fluctuations are in the Alfvenic wave mode propagating outward from the sun, with a small part of the fluctuations in the wave mode propagating inward. There is weak nonlinear interaction between the two modes. It is also assumed that the turbulence will not become dissociated from the sources that create the waves propagating inward and that the weak nonlinear interaction will remain between 0.3 AU and 1 AU. The nonlinear interaction results in an energy cascading process. Both the effects of the cascading process and the effects of the slow variation of the solar wind on the outward propagating waves determine the radial evolution of the power spectra. Starting with the magnetohydrodynamic equations and deriving the equations governing fluctuations and correlation moments, we finally get an equation which describes the power spectrum. We present an analytic solution. The radial evolution of the power spectra of the fluctuations given by the analytical solution, from 0.29 AU to 0.87 AU, is in agreement with the observation of Helios 1 and 2 in the following aspects: (1) The spectral slope increases (in absolute value) for the frequency range lower than 2.5×10−3 Hz while the slope remains almost unchanged for the frequency range higher than 10−1.5 Hz. (2) The radial gradient of the power spectrum densities increases with increasing frequency. The dissipation length remains nearly unchanged for the frequency range f ≥ 10−2 Hz. (3) The radial variation of 〈b²〉 is approximately r−3.56. (4) The ratio of 〈b²〉/Bo² is nearly a constant.
Dual Standard Monomial Theoretic Basis and Canonical Basis for Type A

Let U− q (g) be the negative part of the quantized universal enveloping algebra constructed from a Cartan matrix associated to a complex semisimple Lie algebra g. Let λ be a dominant integral weight and V (λ) the irreducible U− q (g)-module with highest weight λ. There is on the one hand the canonical basis for U− q (g) [4, 12, 13] and on the other the standard monomial theoretic basis for the dual of V (λ) [7, 8, 11]. It is natural to ask if there is any relationship between these two bases. To quote Littelmann [11, page 552], “ . the properties of the path basis suggest that the transformation matrix should be upper triangular . ”. It is the purpose of this note to prove that such is indeed the case when the Cartan matrix is of type A. As to other types, we have nothing to say.
Exchange optics in Gd-doped EuO

This paper is concerned with magneto-optical properties of EuO single crystals, doped with up to 5-at. % Gd. The optical absorption and the Faraday rotation have been measured above and below the magnetic-ordering temperatures and in various magnetic fields. In addition the reflectivity between 13 eV and 250 \ensuremath{\mu}m has been observed and the Curie temperature has been determined. The measurements permit the evaluation of the magnetic short-and long-range order. The exchange interaction between free electrons and $4f$ spins can be determined and is found to decrease with increasing doping. The analysis of the optical data permits the derivation of the carrier concentration, their mobility, and temperature dependence. The carrier concentration shows an exchange-induced ionization near ${T}_{C}$ for nondegenerate samples and the mobility has a sharp minimum at ${T}_{C}$. The transport parameters also reflect the fact that the electron-$4f$-spin interaction decreases with increasing Gd concentration, probably owing to electrostatic-shielding effects.
On the effectivity of spectra representing motivic cohomology theories

Let k be an infinite perfect field. We provide a general criterion for a spectrum in the stable homotopy category over k to be effective, i.e. to be in the localizing subcategory generated by the suspension spectra of smooth schemes. As a consequence, we show that two recent versions of generalized motivic cohomology theories coincide.
Indivisibility of Heegner points in the multiplicative case

For certain elliptic curves $E$ over $\mathbb{Q}$ with multiplicative reduction at a prime $p\geq 5$, we prove the $p$-indivisibility of the derived Heegner classes defined with respect to an imaginary quadratic field $K$, as conjectured by Kolyvagin. The conditions on $E$ include that $E[p]$ be irreducible and not finite at $p$ and that $p$ split in the imaginary quadratic field $K$, along with certain $p$-indivisibility conditions on various Tamagawa factors. The proof extends the arguments of the second author for the case where $E$ has good ordinary reduction at~$p$.
Staircases to Analytic Sum-Sides for Many New Integer Partition Identities of Rogers-Ramanujan Type

We utilize the technique of staircases and jagged partitions to provide analytic sum-sides to some old and new partition identities of Rogers-Ramanujan type. Firstly, we conjecture a class of new partition identities related to the principally specialized characters of certain level $2$ modules for the affine Lie algebra $A_9^{(2)}$. Secondly, we provide analytic sum-sides to some earlier conjectures of the authors. Next, we use these analytic sum-sides to discover a number of further generalizations. Lastly, we apply this technique to the well-known Capparelli identities and present analytic sum-sides which we believe to be new. All of the new conjectures presented in this article are supported by a strong mathematical evidence.
The 13–14 December 2001 IMPROVE-2 Event. Part I: Synoptic and Mesoscale Evolution and Comparison with a Mesoscale Model Simulation

Abstract This paper describes the large-scale synoptic and mesoscale features of a major precipitation event that affected the second Improvement of Microphysical Parameterization through Observational Verification Experiment (IMPROVE-2) study area on 13–14 December 2001. The fifth-generation Pennsylvania State University–NCAR Mesoscale Model (MM5) was used to simulate both the synoptic and mesoscale features of the storm. Extensive model verification was performed utilizing the wealth of observational assets available during the experiment, including in situ aircraft measurements, radiosondes, radar data, and surface observations. The 13–14 December 2001 storm system was characterized by strong low-level cross-barrier flow, heavy precipitation, and the passage of an intense baroclinic zone. The model realistically simulated the three-dimensional thermodynamic and kinematic fields, the forward-tilted vertical structure of the baroclinic zone, and the associated major precipitation band. Deficiencies in th.
The Role of Atmospheric Transport for El Niño‐Southern Oscillation Teleconnections

The El Niño‐Southern Oscillation (ENSO) is one of Earth's main modes of climate variability, having huge impacts on weather, agriculture, and people worldwide. Although these impacts and teleconnections have been studied for decades, the role of atmospheric transport is not completely understood. We analyze the atmospheric transport outgoing from the Equatorial Pacific with the Lagrangian particle dispersion model FLEXPART driven by reanalysis data. Our results demonstrate the interocean‐basin exchange via the atmosphere: anomalously energetic air from the ENSO region mainly remains within the Tropics and Subtropics, while more air is transported toward the east during El Niño. Transport of anomalous moist air can directly be linked to several observed teleconnections, for example, droughts in the Amazon Basin and precipitation in Southeastern U.S. during El Niño. These results show that atmospheric transport plays a role in several ENSO teleconnections.
Destabilizing COXIV in Müller Glia Increases Retinal Glycolysis and Alters Scotopic Electroretinogram

Müller glia (MG), the principal glial cell of the retina, have a metabolism that defies categorization into glycolytic versus oxidative. We showed that MG mount a strong hypoxia response to ocular hypertension, raising the question of their relative reliance on mitochondria for function. To explore the role of oxidative phosphorylation (OXPHOS) in MG energy production in vivo, we generated and characterized adult mice in which MG have impaired cytochrome c oxidase (COXIV) activity through knockout of the COXIV constituent COX10. Histochemistry and protein analysis showed that COXIV protein levels were significantly lower in knockout mouse retina compared to control. Loss of COXIV activity in MG did not induce structural abnormalities, though oxidative stress was increased. Electroretinography assessment showed that knocking out COX10 significantly impaired scotopic a- and b-wave responses. Inhibiting mitochondrial respiration in MG also altered the retinal glycolytic profile. However, blocking OXPHOS in MG did not significantly exacerbate retinal ganglion cell (RGC) loss or photopic negative response after ocular hypertension (OHT). These results suggest that MG were able to compensate for reduced COXIV stability by maintaining fundamental processes, but changes in retinal physiology and metabolism-associated proteins indicate subtle changes in MG function.
Some approximations to L p -statistics of kernel density estimators

This article presents two approximations to the error quantity , where f n is the kernel density estimate of the underlying density f and μ is a measure on the Borel sets of ℜ. The first method proposes the easier-to-compute sum representation . We study the difference |J n (p)−I n (p)| in terms of its rates of convergence to zero. A central limit theorem for J n (p) will then follow immediately. Our second approximation is based on a bootstrap version of I n (p). Using a recent result of [Csörgő, M. , Horvath, L. and Kokoszka, P., 2000, Approximations for bootstrapped empirical processes. Proceedings of the American Mathematical Society, 128, 2457–2464. ] on approximations of bootstrap empirical processes, we establish both conditional and unconditional bootstrap central limit theorems. The focus of the article is on the important case where the measure μ is either the Lebesgue measure or the measure with density f. For the bootstrap, the more general case where dμ(t) = w(t)d t, w(t)>0 will also be briefly addressed.
Spectral gaps and abelian covers of convex co-compact surfaces

Given a convex co-compact hyperbolic surface $X=\Gamma\backslash \mathbb{H}^2$, we investigate the resonance spectrum $\mathcal{R}_j$ of the laplacian $\Delta_j$ on large finite abelian covers $X=\Gamma_j\backslash \mathbb{H}^2$, where $\Gamma_j$ is a finite index normal subgroup of $\Gamma$. Let $\delta$ be the Hausdorff dimension of the limit set of $\Gamma$. We show that there exists an $\varepsilon>0$, such that for all $j$, resonances $\mathcal{R}_j$ in $\{ \delta-\varepsilon< \mathrm{Re}(s) \leq \delta \}$ are all real and satisfy a Weyl law given by the degree of the cover i.e. $\vert \Gamma/ \Gamma_j\vert$. In particular, we prove that for large imaginary parts, there is a uniform resonance gap, obtained through uniform Dolgopyat estimates for transfer operators. One of the new ingredients of the proof is the decay of oscillatory integrals with respect to Patterson-Sulivan measures, obtained recently by Bourgain-Dyatlov arXiv:1704.02909 .
Thermal Methanol Observations of the Outflow from the G31.41+0.31 Hot Molecular Core

The G31.41+0.31 region hosts one of the most prominent hot molecular cores known. Coincident with the hot molecular core is an outflow whose orientation has been controversial. We report VLA-C observations of thermal methanol (70–61 A+, 44 GHz) toward the position of the G31.41+0.31 hot molecular core. Our goals are to clarify the orientation of the outflow and to study the properties of a molecular outflow from a very young region of massive star formation. We confirm that the outflow is indeed associated with the hot molecular core. Our observations strongly suggest that the outflow is oriented in the northeast-southwest direction. The outflow is massive (≳15 M☉), with a dynamical time of the order of ~4 × 103 yr, and has a wide-angle bipolar morphology.
Communications in Mathematical Physics Integrable Boundary Interactions for Ruijsenaars ’ Difference Toda Chain

We endow Ruijsenaars’ open difference Toda chain with a one-sided boundary interaction of Askey–Wilson type and diagonalize the quantum Hamiltonian by means of deformed hyperoctahedral q-Whittaker functions that arise as a t = 0 degeneration of the Macdonald–Koornwinder multivariate Askey–Wilson polynomials. This immediately entails the quantum integrability, the bispectral dual system, and the n-particle scattering operator for the chain in question.
Cross-FCL: Toward a Cross-Edge Federated Continual Learning Framework in Mobile Edge Computing Systems

Federated Learning (FL) in mobile edge computing (MEC) systems has recently been studied extensively. In ubiquitous environments, there are usually cross-edge devices that learn a series of tasks across multiple independent edge FL systems. Due to the differences in the scenarios and tasks of different FL systems, cross-edge devices will forget past tasks after learning new tasks, which is unacceptable for devices that pay system costs to participate in FL. Continual learning (CL) is a viable solution to this problem, which aims to train a model to learn a series of tasks without forgetting old knowledge. Currently, there is no work to investigate the problem of CL in a cross-edge FL scenario. In this paper, we propose Cross-FCL, a Cross-edge Federated Continual Learning framework. Specifically, it enables devices to retain the knowledge learned in the past when participating in new task training through a parameter decomposition based FCL model. Then various cross-edge strategies are introduced, including biased global aggregation and local optimization, to trade off memory and adaptation. We conducted experiments on a real-world dataset and other public datasets. Extensive experiments demonstrate that Cross-FCL achieves best accuracy on IID and highly non-IID tasks with a low storage cost compared to other baselines.
Baroclinic Instability in the Venus Atmosphere

Abstract A three-dimensional, spherical, primitive equation eigenvalue model is used to investigate the baroclinic stability properties of the wind and temperature fields in the Venus atmosphere as measured by Pioneer Venus. It is found that baroclinic instability occurs in the region of the middle cloud deck. The most unstable modes have growth times less than eight days and are vertically confined to the region near the middle cloud layer. The most unstable baroclinic mode at zonal wavenumber 2 has characteristics similar to those observed for the high latitude rotating dipole thermal feature. Certain planetary scale baroclinic modes can penetrate to relatively high altitudes under the right circumstances, and may therefore explain some of the wave features observed between 60 and 90 km. For example, thermal oscillations with periods between four and seven days occurring at middle latitudes have characteristics which appear to be consistent with computed properties of planetary scale baroclinic modes.
Merging exchangeable occupancy models: $\mathcal{M}^{(a)}$- models and relation with the maximum entropy principle

In this paper a new transformation of occupancy models, called merging, is introduced. In particular, it will be studied the effect of merging on a class of occupancy models that was recently introduced in Collet et al (2013). These results have an interesting interpretation in the so-called entropy maximization inference. The last part of the paper is devoted to highlight the impact of our findings in this research area.
Quasi-Symmetries of Determinantal Point Processes

The main result of this paper is that determinantal point processes on the real line corresponding to projection operators with integrable kernels are quasi-invariant, in the continuous case, under the group of diffeomorphisms with compact support (Theorem 1.4); in the discrete case, under the group of all finite permutations of the phase space (Theorem 1.6). The Radon-Nikodym derivative is computed explicitly and is given by a regularized multiplicative functional. Theorem 1.4 applies, in particular, to the sine-process, as well as to determinantal point processes with the Bessel and the Airy kernels; Theorem 1.6 to the discrete sine-process and the Gamma kernel process. The paper answers a question of Grigori Olshanski.
Simulation of self‐propelled anguilliform swimming by local domain‐free discretization method

The local domain‐free discretization method is extended in this work to simulate fluid–structure interaction problems, the class of which is exemplified by the self‐propelled anguilliform swimming of deforming bodies in a fluid medium. Given the deformation of the fish body in its own reference frame, the translational and rotational motions of the body governed by Newton's Law are solved together with the surrounding flow field governed by Navier–Stokes equations. When the body is deforming and moving, no mesh regeneration is required in the computation. The loose coupling strategy is employed to simulate the fluid–structure interaction involved in the self‐propelled swimming. The local domain‐free discretization method and an efficient algorithm for classifying the Eulerian mesh points are described in brief. To validate the fluid–structure interaction solver, we simulate the ‘lock‐in’ phenomena associated with the vortex‐induced vibrations of an elastically mounted cylinder. Finally, we demonstrate applications of the method to two‐dimensional and three‐dimensional anguilliform‐swimming fish. The kinematics and dynamics associated with the center of mass are shown and the rotational movement is also presented via the angular position of the body axis. The wake structure is visualized in terms of vorticity contours. All the obtained numerical results show good agreement with available data in the literature. Copyright © 2011 John Wiley & Sons, Ltd.
Orbit equivalence and classification of weak solenoids

In this work, we study minimal equicontinuous actions which are locally quasi-analytic. The first main result shows that for minimal equicontinuous actions which are locally quasi-analytic, continuous orbit equivalence of the actions implies return equivalence. This generalizes results of Cortez and Medynets, and of Li. The second main result is that if G is a finitely-generated, virtually nilpotent group, then every minimal equicontinuous action by G is locally quasi-analytic. As an application, we show that the homeomorphism type of a nil-solenoid is determined by the topological full group of its monodromy action.
The Opacity at High Temperatures due to Compton Scattering.

The contribution to the radiative opacity of matter arising from Compton scattering is obtained for the entire region in which degeneracy in the electron distribution may be neglected. This corresponds to temperatures up to about 125 kev (1 kev = 11605800 deg K) and densities up to roughly 10/sup -4/ g cm/sup -3/ at the highest temPeratures considered. It is found that, at temperatures for which the Klein-Nishina cross section should be used, parts of the scattering into and out of a beam of radiation do not cancel, as previously assumed. The result of this is to lower the opacity by about 13 per cent at kT = 20 kev and 37 per cent at kT = 125 kev. Although absorption resulting in pair-creation may be neglected at these temperatures, it is found that pair production is responsible in another way for a sharp rise in the opacity by increasing the density ( N) of electrons and positrons significantly at the highest temperatures considered. In fact, at kT = 125 kev, the value of N corresponding to thermal equilibrium is large and almost independent of the matter density (p), where p does not include the mass of the electrons andmore » positrons resulting from pair-creation. Hence, it is concluded that for kT > 125 kev, the average mean free path A/sub c/ = (pKc)/ sup -1/ is small and independent of p. On the other hand, for kT < 30 kev, one has the familiar situation that the Compton opacity (K) is small and independent of p. (auth)« less
Symmetric genuine Spherical Whittaker functions on the metaplectic double cover of GSp(2n,F)

Let F be a p-adic field of odd residual characteristic. Let G(n) and G`(n) be the metaplectic double covers of the general symplectic group and the symplectic group attached to the 2n dimensional symplectic space over F. Let T be a genuine, possibly reducible, unramified principal series representation of G(n). In these notes we give an explicit formulas for a spanning set for the space of Spherical Whittaker functions attached to T. For odd n, and generically for even n, this spanning set is a basis. The signicant property of this set is that each of its elements is unchanged under the action of the Weyl group of G`(n). If n is odd then each element in the set has an equivariant property that generalizes the uniqueness result of Gelbart, Howe and Piatetski-Shapiro proven for G(1). Using this symmetric set, we construct a family of reducible genuine unramified principal series representations which have more then one generic constituent. This family contains all the reducible genuine unramified principal series representations induced from a unitary data and exists only for n even.
What happens to segment durations at the end of a word

Coda consonant clusters of monosyllabic words were studied to determine what durational modifications occur at the segment level as a function of the number, the order, and the morphemic status of segments in the coda. We focused on the segment /s/ because it has the fewest constraints in terms of position in coda clusters, allowing reversals such as tax (/tae ks/) and task (/taesk/), and because /s/ can also be a separate morpheme, allowing us to compare segment durations for tax and tacks (/tae ks/). Preliminary results from four talkers reaffirm previous findings that segment durations decrease as the number of segments increases, although all segments do not decrease to the same extent. Our data also reaffirm previous claims that morphemic /s/ has a longer duration relative to the overall word duration than its nonmorphemic counterpart. In addition to these factors, position at the right‐edge boundary of a word seems to play a special role in determining the relative durations of segments within a coda c.