Miracle-dz/UniFAR-FTUs huggingface dataset:
Two notes on metric geometry

If IL, f d1L = 1, is a signed Borel measure on the unit ball in E3, it is shown that sup, f f [P qjd1L(p)dL. (q) = 2 with no extremal measure existing. Also, a class of simplices which generalizes the notion of acute triangle is studied. The results are applied to prove inequalities for determinants of the Cayley-Menger type. 1. A counterexample. In this article ,u will always denote a signed Borel measure, concentrated on a compact set K in Euclidean space, which satisfies Jd,u = 1. Let I(,i) denote the integral JfIp ql dM(p) d (q). It was shown in [1] and [2] that if K c E", then there is a constant bn such that sup, I ( IL) < bn (diameter of K). It was conjectured that an extremal measure ,uo would always exist so that I( ILO) = sup ,I( ,u). This conjecture was known to be true in case K was a finite set or the surface of a ball. However, we now show that an integral formula developed in t2], together with Archimedes' beautiful theorem on zonal areas, allows us to construct a counterexample when K is a solid ball in EV. Let us assume that the ball K has radius 1, and let N be a large positive number. Place a uniform measure of total mass N on the surface of K, and place a uniform negative measure of total mass I N on the surface of the concentric ball of radius 1 N . The measure MN is defined to be the sum of these two uniform measures. A key observation is that if t1 and t2 are two parallel planes which both cut the ball of radius 1 N 1, then MN assigns measure zero to the portion of K between t1 and t2. This follows from Archimedes' theorem. Let T be the usual invariant measure on the planes of E3 such tha-t the measure of the set of planes which cut a line segment is the length of the segment. We shall use without proof the fact that the measure of the set of planes in E3 which cut a ball of radius R is 4R. If t is a plane which cuts K, let A, and B, be the portions of K lying in the respective open half-spaces determined by t. In [2] it was established that (1) I(,l) = 2f I(A,)I(B,) dT(t). Also, it was shown that for almost all t, ,u(A,) + ,u(B,) = 1, and hence for almost all t,_ ,(A,) u(B,) < Received by the editors September 20, 1976. AMS (MOS) subject classifications (1970). Primary 52A50.
The gonality conjecture for curves on certain toric surfaces

The gonality is one of important invariants in the study of li near systems on curves. The gonality conjecture which was posed by Green and Lazarsfeld predicts that we can read off the gonality of a curve from any one line bundle of sufficiently large degree on the curve. This conjecture had been proved for curves on Hirzebruch surfaces by Aprodu. In this artlcle, we will extend this resu lt for curves on certain toric surfaces.
Adaptive level set image segmentation using the Mumford and Shah functional

This paper proposes an adaptive 2-phase level set image segmentation algorithm to improve the original level set-based piecewise constant Mumford-Shah model. With the introduction of a multiplicative gain field, the model is adaptive to intensity inhomogeneity, thus tending to obtain the actual boundaries of the objects, as well as a property-seeking and -driven classification algorithm.
Just-in-time control of time-varying discrete event dynamic systems in (max,+) algebra

We deal with timed event graphs whose holding times associated with places are variable. Defining a first-in-first-out functioning rule, we show that such graphs can be linearly described in (max,+) algebra. Moreover, this linear representation allows extending the just-in-time control synthesis existing for timed event graphs with constant holding times. An example is proposed in order to illustrate how the approach can be applied as a just-in-time strategy for production lines.
Galactic evolution and cosmology - Probing the cosmological deceleration parameter

Les relations deplacements vers le rouge avec la magnitude et la couleur, le denombrement galactique, la distribution en deplacement vers le rouge des galaxies et la lumiere de fond extragalactique sont calcules en tenant compte de l'evolution galactique pour differentes valeurs du parametre de deceleration cosmologique et du deplacement vers le rouge de la formation des galaxies
Is it possible to change the classroom activities in which we delegate the process of connecting mathematics with reality?

In common teaching practice the habit of connecting mathematics classroom activities with reality is still substantially delegated to wor(l)d problems. During recent decades, a growing body of empirical research has documented that the practice of word problem solving in school mathematics does not match this idea of mathematical modelling and mathematization. If we wish to construct ‘real problems arising from real experiences of the child’ following the spirit of these new suggestions, we have to make changes. On the one hand we have to replace the type of activity in which we delegate the process of creating an interplay between reality and mathematics by substituting the word problems with an activity of realistic mathematical modelling, i.e. of both real-world based and quantitatively constrained sense-making; and, on the other hand, to ask for a change in teacher beliefs; furthermore, a directed effort to change the classroom socio-math norms will be needed. This paper discusses some classroom activities that takes these factors into account.
Curvature characterization of certain bounded domains of holomorphy

In this note, we study the relation between the existence of a negatively curved complete hermitian metric on a complex manifold M and the product structure of (or contained in) M. We introduce the concept of geometric ranks and give a curvature characterization of the rank one manifolds, which generalizes the previous results of P. Yang and N. Mok (see below). In the proof, we used the old techniques of Yau's Schwartz lemma and Cheng-Yau's result on the existence of Kahler-Einstein metrics.
Asymptotic Solutions for Backscattering by Smooth 2D Surfaces

High-frequency asymptotic expansions of electric and magnetic fields are obtained at a perfectly conducting smooth 2D surface illuminated by a plane incident wave in two cases of TE and TM linear polarization. Diffraction corrections up to the second order of the inverse large parameter p = ak (where a is a curvature radius at the specularly reflected point, and k is a field wavenumber) to the geometrical optics fields, and specifically to their phases, backscattering cross-sections (HH and VV for TE and TM polarizations, correspondingly), as well as the polarization ratio HH/VV, are derived for the specular points of a general form. These general results are applied to backscattering from cylinders with conical section directrixes (circle, parabola, ellipse and hyperbola), and a number of new compact explicit equations are derived, especially for elliptic and hyperbolic cylinders illuminated at an arbitrary incidence angle relative to their axes of symmetry.
Modes of Interannual Tropical Ocean–Atmosphere Interaction—a Unified View. Part I: Numerical Results

Abstract Coupled ocean-atmosphere models exhibit a variety of forms of tropical interannual variability that may be understood as different flow regimes of the coupled system. The parameter dependence of the primary bifurcation is examined in a “stripped-down” version of the Zebiak and Cane model using the equatorial band approximation for the sea surface temperature (SST) equation as by Neelin. In Part I of this three-part series, numerical results are obtained for a conventional semispectral version; Parts II and III use an integral formulation to generate analytical results in simplifying limits. In the uncoupled case and in the fast-wave limit (where oceanic adjustment occurs fast compared to SST time scales), distinct sets of modes occur that are primarily related to the time scales of SST change (SST modes) and of oceanic adjustment (ocean-dynamics modes). Elsewhere in the parameter space, the leading modes are best characterized as mixed SST/ocean-dynamics modes; in particular, the continuous surfa.
Absence of the c / a anomaly in Zn under high pressure with a helium-pressure medium

A high-pressure powder x-ray diffraction experiment on Zn has been carried out at room temperature with He pressure-transmitting medium in order to achieve the best hydrostatic conditions. The anomaly in the volume-dependence of the $c/a$ axial ratio, which has been observed previously, can no longer be observed. Hence the anomaly is most probably induced by the nonhydrostaticity associated with the solidification of the methanol-ethanol-water pressure-transmitting medium used in the previous studies. The present results suggest reconsideration of the calculated $c/a$ anomaly based on the electronic topological transition.
STOCHASTIC VERSIONS OF ANOSOV'S AND NEISTADT'S THEOREMS ON AVERAGING

In systems which combine slow and fast motions the averaging principle says that a good approximation of the slow motion can be obtained by averaging its parameters in fast variables. This setup arises, for instance, in perturbations of Hamiltonian systems where motions on constant energy manifolds are fast and across them are slow. When these perturbations are deterministic Anosov's theorem says that the averaging principle works except for a small in measure set of initial conditions while Neistadt's theorem gives error estimates in the case of perturbations of integrable Hamiltonian systems. These results are extended here to the case of fast and slow motions given by stochastic differential equations.
Using wavelets for data generation

Wavelets are proposed as a non-parametric data generation tool. The idea behind the suggested method is decomposition of data into its details and later reconstruction by summation of the details randomly to generate new data. A Haar wavelet is used because of its simplicity. The method is applied to annual and monthly streamflow series taken from Turkey and USA. It is found to give good results for non-skewed data, as well as in the presence of auto-correlation.
LIMIT ON STABLY TRAPPED PARTICLE FLUXES

Abstract : Whistler mode noise leads to electron pitch angle diffusion. Similarly, ion cyclotron noise couples to ions. This diffusion results in particle precipitation into the ionosphere and creates a pitch angle distribution of trapped particles which is unstable to further wave growth. Since excessive wave growth leads to rapid diffusion and particle loss, the requirement that the growth rate be limited to the rate at which wave energy is depleted by wave propagation allows a estimate of an upper limit to the trapped equatorial particle flux. Electron fluxes greater than 40 keV and proton fluxes greater than 120 keV observed on Explorers XIV and XII respectively obey this limit with occasional exceptions. Beyond L = 4, the fluxes are just below their limit, indicating that an unspecified acceleration source sufficient to keep the trapped particles near their precipitation limit exists. Limiting proton and electron fluxes are roughly equal, suggesting a partial explanation for the existence of larger densities of high energy protons than electrons. Observed electron pitch angle profiles correspond to a diffusion coefficient in agreement with observed lifetimes. The required equatorial whistler mode wide band noise intensity, 0.001 gamma is not obviously inconsistent with observations, and is consistent with the lifetime and limiting trapped particle intensity. (Author)
Self-trapping of low-energy infrared femtosecond beams in lithium niobate

In this paper we report self-trapping of subnanojoule femtosecond near-infrared beams in photonic-grade undoped bulk lithium niobate under application of an external dc electric field. We show that the phenomenon occurs thanks to the photorefractive effect induced by a weak second-harmonic component generated under large velocity mismatch. It offers a way to extend lithium niobate's photorefractive response to the near-infrared spectrum for peak intensity lower than 1 GW/cm{sup 2}, which is three orders of magnitude lower than reported in the literature.
Determination of anaerobic threshold

This report describes the estimation of the parameters for a model of ventilation (y) by human subjects as a two-segment linear function of oxygen uptake (x). Experimental data were supplied by R.L. Hughson of the Department of Kinesiology. The analysis of one of nine available sets of data is described in detail. Ce rapport decrit l'estimation de parametres associes a un modele de ventilation pulmonaire (y) par des sujets humains ou celle-ci est vue comme une fonction lineaire, segmentee en deux parties, de la prise d'oxygene (x). Les donnees ont ete fournies par le Dr. R.L. Hughson du departement de kinesiologie. L'analyse de l'un des neuf ensembles de donnees disponibles est decrite en detail.
THE SIMPLICIAL MODEL OF UNIVALENT FOUNDATIONS

In this paper, we construct and investigate a model of the Univalent Foundations of Mathematics in the category of simplicial sets. To this end, we rst give a new technique for constructing models of dependent type theory, using universes to obtain coherence. We then construct a (weakly) universal Kan bration, and use it to exhibit a model in simplicial sets. Lastly, we introduce the Univalence Axiom, in several equivalent formulations, and show that it holds in our model. As a corollary, we conclude that Univalent Foundations are at least as consistent as ZFC with two inaccessible cardinals.
Extracting microphysical impacts in large-eddy simulations of shallow convection

AbstractA simple methodology is proposed to extract impacts of cloud microphysics on macrophysical cloud-field properties in large-eddy simulations of shallow convection. These impacts are typically difficult to assess because of natural variability of the simulated cloud field. The idea is to use two sets of thermodynamic variables driven by different microphysical schemes or by a single scheme with different parameters as applied here. The first set is coupled to the dynamics as in the standard model, and the second set is applied diagnostically—that is, driven by the flow but without the feedback on the flow dynamics. Having the two schemes operating in the same flow pattern allows for extracting the impact with high confidence. For illustration, the method is applied to simulations of precipitating shallow convection applying a simple bulk representation of warm-rain processes. Because of natural variability, the traditional approach provides an uncertain estimate of the impact of cloud droplet concen.
Formation of an Intermediate Filament Driven by Small-scale Magnetic Reconnection

We present the formation process of a filament in NOAA active region 12765 from 2020 June 5 to 8, using observations from the New Vacuum Solar Telescope, the Solar Dynamics Observatory, and the Global Oscillation Network Group. We found that intermittent small-scale magnetic reconnection occurs at the northern part of the filament, and the small-scale magnetic reconnection shows the characteristics of the oscillatory reconnections. During the magnetic reconnection process, a large amount of material is continuously injected into the filament channel. Furthermore, there are bidirectional inflow and outflow, current sheets, and bright cusp-shaped structures. The velocities of the material injections range from 17 to 183 km s−1 with an average velocity of about 57 km s−1. A total of 53 material injections were found from 03:10 UT on 2020 June 5 to 00:10 UT on June 8. The total mass carried by the injection events is about 7.39 × 1014 g, and the total kinetic energy released through magnetic reconnection is approximately 3.09 × 1021 J. The projection area of the filament increased from less than 1 × 102 Mm2 to around 7 × 102 Mm2. We conclude that the filament is formed by direct material injection into the filament channel due to the small-scale magnetic reconnections.
Algebraic Properties of Beta and Gamma Distributions, and Applications

Three new properties are derived. The first one relates to the distribution ofUG+G? , where the three variables are independent,G,G? have gamma distributions andUis arbitrary; the second one concerns the case whereUhas a beta distribution, and the third one the case where 1/Uhas a beta distribution. These properties generalize the additivity of independent gamma distributions with the same scale parameter. Applications to Markov chains and to the stochastic equationX=(in law)U(X+C) are given. The last section shows how non-negative relationships may be transformed into new ones on the whole line. In particular, the limit distribution of a time series with random coefficients and Gaussian error terms is found.
Efficient star formation in the spiral arms of M51

The molecular, neutral, and ionized hydrogen distributions in the Sbc galaxy M51 (NGC 5194) are compared. To estimate H2 surface densities observations of the CO (J = 1 - 0) transition were made in 60 positions out to a radius of 155 arcsec. Extinction-corrected H-alpha intensities were used to compute the detailed massive star formation rates (MSFRs) in the disk. Estimates of the gas surface density, the MSFR, and the ratio of these quantities, MSFR/sigma(p), were then examined. The spiral arms were found to exhibit an excess gas density, measuring between 1.4 and 1.6 times the interarm values at 45 arcsec resolution. The total (arm and interarm) gas content and massive star formation rates in concentric annuli in the disk of M51 were computed. The two quantities fall off together with radius, yielding a relatively constant MSFR/sigma(p) with radius. This behavior is not explained by current models of star formation in galactic disks. 60 refs.
An Upper Limit on the Charge of the Black Hole Sgr A* from EHT Observations

The Event Horizon Telescope (EHT) recently released an image of the supermassive black hole Sgr A* showing an angular shadow diameter d sh = 48.7 ± 7 μas and Schwarzschild shadow deviation δ=−0.08−0.09+0.09(VLTI) , −0.04−0.10+0.09(Keck) using a black hole mass M=4.0−0.6+1.1×106M⊙ . The EHT image of Sgr A* is consistent with a Kerr black hole’s expected appearance, and the results directly prove the existence of a supermassive black hole at the center of the Milky Way. Here, we use the EHT observational results for Sgr A* to investigate the constraints on its charge with the aid of Kerr-like black holes, paying attention to three leading rotating models, namely Kerr–Newman, Horndeski, and hairy black holes. Modeling the supermassive black hole Sgr A* as these Kerr-like black holes, we observe that the EHT results for Sgr A* place stricter upper limits on the parameter space of Kerr–Newman and Horndeski black holes than those placed by the EHT results for M87*. A systematic bias analysis reveals that observational results from future EHT experiments will place more precise limits on the charge of the black hole Sgr A*. Thus, the Kerr-like black holes and Kerr black holes are indiscernible in a substantial region of the EHT-constrained parameter space; the claim is substantiated by our bias analysis.
Energy Meter Patch Resistance and Welding Spot Anomaly Detection Method Based on Machine Vision

Based on the problems, such as the difficulty of detecting and obtaining evidence of patch resistance replacement and welding spot anomaly in the current field of meter anomaly detection, a patch resistance and welding spot anomaly detection algorithm is proposed based on machine vision. The resistance anomaly detection algorithm combines the K-D tree and Ransac to complete the high-efficiency energy meter registration. It detects the suspected resistance abnormal area through the difference shadow method and then judges the resistance abnormal situation according to the resistance value recognized by the classification network. The welding spot anomaly detection algorithm enhances the feature of the image through saliency detection, then obtains the target information of the welding spot by segmentation, and finally determines the welding spot anomaly condition in combination with the connection domain analysis. Experimental results show that the precision of patch resistance anomaly of this method reaches 95.28%, and the detection time is about 1.52s; the precision of welding spot anomaly reaches 96.74%, and the detection time is about 0.74s. The method can meet the requirements of spot detection accuracy and speed and has good application value.
Gridded, locally calibrated, probabilistic temperature forecasts based on ensemble model output statistics

We propose a further refinement of the the non‐homogeneous Gaussian regression approach for temperature, which transforms the output of an ensemble prediction system into predictive Gaussian distributions at each location of interest. Model fitting is partly done within a regression framework using a penalized version of the least‐squares loss function. This is conceptually simpler than the original approach and at the same time is able to prevent overfitting. While calibration is initially performed at observation locations only, geostatistical methods are used to provide predictive distributions on the entire grid. The incorporation of land‐use information in this interpolation scheme further improves predictive performance, even though a simpler statistical model than in the original approach is used. The assessment of predictive performance and calibration is carried out with dynamical forecasts of 2 m temperatures by the COSMO‐DE‐EPS, an application of the COSMO (Consortium for Small‐scale Modeling) model system which covers Germany and neighbouring countries.
Nonlinear polymer-clad silicon slot waveguide modulator with a half wave voltage of 0.25 V

We report on an electro-optic modulator fabricated from a silicon slot waveguide and clad in a nonlinear polymer. In this geometry, the electrodes form parts of the waveguide, and the modulator driving voltage drops across a 120nm slot. As a result, a half wave voltage of 0.25V is achieved near 1550nm. This is one of the lowest values for any modulator obtained to date. As the nonlinear polymers are extremely resistive, our device also has the advantage of drawing almost no current, suggesting this type of modulator could operate at exceedingly low power.
Molecular cloud cores and bimodal star formation

The phenomenon of bimodal star formation is reviewed in the context of supercritical and subcritical states for molecular clouds that are supported against their self-gravitation by magnetic fields. The governing set of equations is derived subject to the quasi-static and axisymmetric approximations. The method of numerical solution and tests of the resultant computer code are outlined. The results of the evolutionary calculations are discussed, emphasizing time scales, masses, and typical sizes of modeled cores that can be compared with observations. For a fixed mass, it is found that the level or turbulent support determines whether a dense core forms or not. This is used to generalize the concept of a critical mass to account for the contributions of turbulence and thermal pressures to the support of a cloud. 72 refs.