Miracle-dz/UniFAR-FTUs huggingface dataset:
On computing logarithms on elliptic curves

We consider the problem of solving an exponential equation over a cyclic subgroup of order m of the group E of points of an elliptic curve over the finite field Fq. We prove that if Fifl is a minimal extension of Fq such that the subgroup of the points rational over Fq[ of the group E contains a subgroup isomorphic to Z Im x Z /m, then the complexity of solving the equation mentioned above is no greater than the complexity of computing logarithms in the field F(n or the complexity of O(ln m) arithmetic operations in that field. Thus, the computing of logarithms on elliptic curves is reduced to the computing of logarithms in a finite field. By a different approach, this result was obtained by Menezes, Okamoto, and Vanstone. 1. We consider an exponential equation in the group of points of an elliptic curve over the finite field Fq. The field Fq consists of q elements. Let F be a certain extension of the initial field Fq. Let a( e F^ i = 1, .,6, be such that the curve y + a\xy + <23y = x + a2x = a4x + a6 (1) has no singularities, then the points (x, y), x, y e F, satisfying equation (\), together vAth the infinite point ? „ form a commutative group which we denote by E/F. It is known that if F is a finite field of order q\ , then the order N(II of the group E/F satisfies the inequality
Weight spaces and irreducible representations of simple Lie algebras.

sentation of L admitting y j 3C as a weight function. In this paper we make a further study of the relationship between the representations of L and their weight spaces. 1. Weight spaces of irreducible representations. It is well known that there exists a one-one correspondence between the representations of L and those of U which preserves irreducibility. Throughout this paper we will not distinguish between a representation of L and its unique extension to U. Definition 1. Let (p, V) be a representation of L. Then for each linear functional X£3C*, the dual linear space of the Cartan subalgebra, we define Fx = {vE V\p(H)v = \(H)v (yn E 3d)}. Also we denote by [p:X] the dimension of the subspace 7\. If, in particular, [p:X] >0 we call X a weight function of the representation p and V\ the corresponding weight space. It is clear from the definitions of Q and 7\ that for any element cEQ, p(c) maps V\ into V\. Definition 2. Let (p, V) be a representation of L and X£3C*. Then we define a representation (n(p, X), Fx) of C by setting ri{p, X) (c) =p(c)| 7x for all cGC. Lemma 1. If (p, V) is an irreducible representation of L and X£3C* such that [p:X]>0 then (rj(p, X), 7x) is a nontrivial, irreducible representation of 6.
Mendenhall's studies of word-length distribution in the works of Shakespeare and Bacon

SUMMARY In 1901 T. C. Mendenhall, in one of the earliest studies of its kind, concluded that the frequency distribution of words of different length in the works of Shakespeare were so consistently different from those of Bacon, that it was very unlikely that works attributed to the former could have been written by the latter. It is here shown that in the writings of Sir Philip Sidney, a contemporary of the above, the differences in word-length distribution between his prose and his verse are very close indeed to those found between Bacon's prose and Shakespeare's verse. Thus the differences that Mendenhall found can be more simply explained by a difference of literary presentation. Mendenhall was misled in his conclusions by classifying Shakespeare's plays as 'prose'.
Various atomic structures of monolayer silicene fabricated on Ag(111)

Silicene, a monolayer of silicon atoms arranged in honeycomb lattices, can be synthesized on the Ag(111) surface, where it forms several superstructures with different buckling patterns and periodicity. Using scanning tunneling microscopy (STM), we obtained high-resolution images of silicene grown on Ag(111) and revealed its five phases, i.e., 4 × 4 − α, 4 × 4 − β, 13 × 13 ? > − α, 13 × 13 ? > − β and 13 × 13 ? > − γ, some observed for the first time. For each of the phases, we have determined its atomic structure by comparing the atomic-resolution STM images with theoretical simulation results previously reported. We thus eliminate the contradictions of previous studies on the structural models of various silicene phases supported by the Ag(111) surface.
Did Weierstrass’s differential calculus have a limit-avoiding character? His definition of a limit in ϵ – δ style

In the 1820s, Cauchy founded his calculus on his original limit concept and developed his theory by using inequalities, but he did not apply these inequalities consistently to all parts of his theory. In contrast, Weierstrass consistently developed his 1861 lectures on differential calculus in terms of epsilonics. His lectures were not based on Cauchy’s limit and are distinguished by their limit-avoiding character. Dugac’s partial publication of the 1861 lectures makes these differences clear. But in the unpublished portions of the lectures, Weierstrass actually defined his limit in terms of inequalities. Weierstrass’s limit was a prototype of the modern limit but did not serve as a foundation of his calculus theory. For this reason, he did not provide the basic structure for the modern style analysis. Thus it was Dini’s 1878 textbook that introduced the definition of a limit in terms of inequalities.
Turbulent drag reduction in a closed flow system: Boundary layer versus bulk effects

We present an experimental study of drag reduction by polymer additives in a closed turbulent flow with a zero mean velocity at large Reynolds numbers. The study is performed using two different forcing schemes: a smooth forcing, for which the fluid is brought into movement through viscous boundary layers, and a very rough forcing where the fluid is stirred inertially by baffles. For a polymer solution of 30 wppm, a steady drag reduction is only observed for the smooth forcing. In the other case, absolutely no decrease of the turbulent energy dissipation is observed. When drag reduction is observed, the turbulent intensity in the bulk is unaltered upon addition of the polymer. This result demonstrates that, in our experimental system, the reduction of the energy dissipation does not only occur mainly in the boundary layers (as is well known for a long time), but takes place solely in the boundary layers. We also study heterogeneous drag reduction by local injection of a concentrated polymer solution. Duri.
Waterbells and Liquid Sheets

AbstractWaterbells result from the impact of a low-viscosity liquid jet (diameter D0, velocity U0) on a solid surface (characteristic length Di) of similar size (Di ∼ D0). Their stationary shape mainly results from the equilibrium between inertia and surface tension. When closed, this shape becomes sensitive to the pressure difference that occurs across the sheet and the bell can become unstable or exhibit stationary cusps. We first review the work done on the shape and stability of waterbells, and then address the case of “special bells,” like swirling bells, polygonal bells, and reverse bells. Finally, we discuss the singular limit of the “flat bell” or liquid sheet.
Daytime Cloud Overlap Detection from AVHRR and VIIRS

Abstract Two algorithms for detecting multilayered cloud systems with satellite data are presented. The first algorithm utilizes data in the 0.65-, 11-, and 12-μm regions of the spectrum that are available on the Advanced Very High Resolution Radiometer (AVHRR). The second algorithm incorporates two different techniques to detect cloud overlap: the same technique used in the first algorithm and an additional series of spectral tests that now include data from the 1.38- and 1.65-μm near-infrared regions that are available on the Moderate Resolution Imaging Spectroradiometer (MODIS) and will be available on the Visible/Infrared Imager/Radiometer Suite (VIIRS). VIIRS is the imager that will replace the AVHRR on the next generation of polar-orbiting satellites. Both algorithms were derived assuming that a scene with cloud overlap consists of a semitransparent ice cloud that overlaps a cloud composed of liquid water droplets. Each algorithm was tested on three different MODIS scenes. In all three cases, the se.
Dielectric resonator: cavity-enhanced optical manipulation in the near field

In the following paper we explore the dynamics of single colloidal particles and particle aggregates in a counterpropagating cavity-enhanced evanescent wave optical trap. For this study we make use of Fabry-Perot like cavity modes generated in a prism-coupled resonant dielectric waveguide. The advantage of using this type of optical structure is that there is an enhancement in the electric field of the evanescent at the sample surface that may be used to achieve greater coupling to colloidal particles for the purposes of optical micromanipulation. We demonstrate an order of magnitude increase in the optical forces acting on micrometer sized colloidal particles using cavity enhanced evanescent waves, compared with evanescent wave produced by conventional prism-coupling techniques. The combination of the enhanced optical interaction and the wide area illumination provided by the prism coupler makes it an ideal geometry for studying the collective dynamics of many particles over a large area. We study the different type of ordering observed when particles of different sizes are accumulated at the centre of this novel optical trap. We find that for large particles sizes (greater than 2μm), colloid dynamics are primarily driven by thermodynamics, whilst for smaller particles, in the range of 200-600nm, particles ordering is dictated by optical-matter interactions. We suggest a qualitative model for the observed optically induced ordering occurs and discuss how these results tie in with existing demonstrations of twodimensional optical binding.
Two-parameter asymptotic approximations in the analysis of a thin solid fixed on a small part of its boundary

Planar elasticity problems are considered for thin domains fixed along a small part of the end region boundary. The analysis involves two small parameters: the normalized thickness of the body and the normalized length of the fixed part of the boundary. The aim of the paper is to derive an asymptotic approximation of the solution to a boundary-value problem in such a domain and, in particular, analyze the 'effective boundary conditions', which occur for the leading-order terms of the asymptotics. We include applications for problems of both anti-plane shear and plane strain elasticity.
The r-process and neutrino-heated supernova ejecta

As a neutron star is formed by the collapse of the iron core of a massive star, its Kelvin-Helmholtz evolution is characterized by the release of gravitational binding energy as neutrinos. The interaction of these neutrinos with heated material above the neutron star generates a hot bubble in an atmosphere that is nearly in hydrostatic equilibrium and heated, after approximately 10 s, to an entropy of S/N(sub AS)k greater than or approximately = 400. The neutron-to-proton ratio for material moving outward through this bubble is set by the balance between neutrino and antineutrino capture on nucleons. Because the electron antineutrino spectrum at this time is hotter than the electron neutrino spectrum, the bubble is neutron-rich (0.38 less than or approximately = Y(sub e) less than or approximately = 0.47). Previous work using a schematic model has shown that these conditions are well suited to the production of heavy elements by the r-process. In this paper we have advanced the numerical modeling of a 20 solar mass 'delayed' supernova explosion to the point that we can follow the detailed evolution of material moving through the bubble at the late times appropiate to r-process nucleosynthesis. The supernova model predicts a final kinetic energy for the ejecta of 1.5 x 10(exp 51) ergs and leaves behind a remnant with a baryon mass of 1.50 solar mass (and a gravitational mass of 1.445 solar mass). We follow the thermodynamic and compositional evolution of 40 trajectories in rho(t), T(t), Y(sub e)(t) for a logarithmic grid of mass elements for the last approximately = 0.03 solar mass to be ejected by the proto-neutron star down to the last less than 10(exp -6) solar mass of material expelled at up to approximately = 18 s after core collapse. We find that an excellent fit to the solar r-process abundance distribution is obtained with no adjustable parameters in the nucleosynthesis calculations. Moreover, the abundances are produced in the quantities required to account for the present Galactic abundances. However, at earlier times, this one-dimensional model ejects too much material with entropies S/N(sub A)k approximately 50 and Y(sub e) approximately 0.46. This leads to an acceptable over production of N = 50 nuclei, particularly Sr-88, Y-89, and Zr-90, relative to their solar abundances. We speculate on various means to avoid the early overproduction and/or ejection of N = 50 isotonic nuclei while still producing and ejecting the correct amount of r-process material.
Self‐consistent formulation for the evolution of ionospheric conductances at the ionospheric E region within the M‐I coupling scheme

[1] We formulate the evolution of ionospheric conductivity in the framework of 3-D M-I coupling. Two important physical processes are taken into account. One is the ionization process by precipitating mono-energetic particles, which are accelerated by parallel-potential drops in the auroral acceleration region. The other process reflects the fact that part of field-aligned current (FAC) carried by electrons is closed with a perpendicular ionic current. Here, whereas the electric current is divergence-free, the divergence of electron current is finite. Therefore, the ionospheric electron density changes, and so does the conductivity. If the energy of electron precipitation is below ∼10 eV, this second process plays an important role in plasma transportation, production, and evacuation processes. In this case the density variation does not extend in space at the perpendicular electron velocity, but it rather moves at the ion perpendicular velocity. If the energy of electron precipitation is above ∼1 keV, in contrast, the precipitation has a nonlinear effect on plasma evolution. That is, the propagation speed of the density variation increases with increasing upward-FAC density, and the propagation takes place in the direction of the converging current into the upward FAC region. The Cowling effect on the plasma evolution process is crucially important. Our formulation is more general than the previous studies and is not limited to certain geometries, current component or interaction modes between the ionosphere and magnetosphere. It is therefore better-suited for describing the self-organized M-I coupling system, which evolves with current systems, conductivity, and magnetospheric processes interacting with each other.
Helicity of magnetic clouds and their associated active regions

[1] In this work we relate the magnetic and topological parameters of twelve interplanetary magnetic clouds to associated solar active regions. We use a cylindrically symmetric constant-α force-free model to derive field line twist, total current, and total magnetic flux from in situ observations of magnetic clouds. We compare these properties with those of the associated solar active regions, which we infer from solar vector magnetograms. Our comparison of fluxes and currents reveals: (1) the total flux ratios ΦMC/ΦAR tend to be of order unity, (2) the total current ratios IMC/IAR are orders of magnitude smaller, and (3) there is a statistically significant proportionality between them. Our key findings in comparing total twists αL are that (1) the values of (αL)MC are typically an order of magnitude greater than those of (αL)AR and (2) there is no statistically significant sign or amplitude relationship between them. These findings compel us to believe that magnetic clouds associated with active region eruptions are formed by magnetic reconnection between these regions and their larger-scale surroundings, rather than simple eruption of preexisting structures in the corona or chromosphere.
2006 December 17 Long Duration Flare Observed with the Hinode EUV Imaging Spectrometer

A GOES C-class long-duration flare that occurred near the west limb on 2006 December 17 was observed with the Hinode EUV Imaging Spectrometer (EIS) in raster-scan observations. Cusp-shaped arcades are prominent in the spectroheliogram of the Ca XVII emission line at 192.86 angstrom. Spatial relationships between hot flare loops with a cusp apex and cool post flare loops with various temperatures are clearly shown in the EIS observations. We find an enhanced line broadening above the bright loop-top region in the Ca XVII observation. The Doppler observations of cooling post flare loops with coronal temperatures show both downflows and upflows along the loops, and these are interpreted as a part of siphon flows. Enhanced nonthermal line broadenings are identified at the top of the post flare loops.
Unsteady Sediment‐Transport Modeling

The standard one‐dimensional equations of unsteady sediment‐transport are examined, and multiple time (or length) scales are identified. The existence of multiple scales may lead to a singularly perturbed behavior that should be taken into account in any general numerical model. Previous models, which reduce the number of conservation equations solved simultaneously from three to two, are seen to be unable to satisfy exactly either a general boundary condition or a general initial condition. Implications for numerical modeling are explored. Numerical results for the model problem of sediment‐deposition upstream of a dam illustrate the analytical argument.
On the Predictability of Quasi-Geostrophic Flow: The Effects of Beta and Baroclinicity.

Abstract The equilibrium statistics and predictability properties of one- and two-layer quasi-geostrophic flow are examined with the aid of a numerical model. The effect of beta in one-layer flow is to slow the transfer of energy into larger scales and to increase the predictability. In two-layer flow, when beta is zero, energy caters the system via baroclinic instability of the mean Row at very large scales and most energy transfer is confined to low wavenumbers. When beta is non-zero, energy enters at higher wavenumber (in baroclinic modes mainly) before cascading preferentially to lower wavenumber zonal barotropic modes. The predictability of two-layer flow is not significantly altered by beta, because beta increases the range of wavenumber over which significant nonlinear energy transfer occurs. The predictability times of the long waves are found to be always larger than those of the short waves, even when the initial error is spread evenly acres wavenumbers. Reducing the mean baroclinicity increases.
Evaluating Participation in Cooperative Maneuvers among Connected and Automated Vehicles

Connected and automated vehicles will not only autonomously plan their motions but also use vehicle-to-vehicle communication to negotiate cooperative maneuvers. Via intent-sharing and joint decision-making, those vehicles will perform coordinated actions together. Up to now, studies on cooperative maneuvers mostly assumed participants always cooperate. This scenario is fair but unrealistic. In our contribution, we investigate how vehicles can assess cooperative maneuver requests to decide whether or not to participate in them. Our decision algorithm ensures safety and fairness while being independent of the underlying cooperative maneuver protocol. We show the algorithm’s feasibility in simulations. This paper is thus another step towards realizing cooperative maneuvers.
Crowdsourcing and monetization as a strategy to reduce vehicular greenhouse gases emissions

This paper presents a strategy to estimate and control vehicular greenhouse emissions by combining crowdsourcing and monetization. We assume that vehicle manufacturers must accomplish emission limits and can demonstrate it by collecting carbon credits which consist of emissions estimates received directly from vehicles’ onboard computers. Manufacturers then can trade these credits in a blockchain-based monetization platform, feeding a self-sustainable strategy that motivates more drivers to participate in crowdsourcing. We discuss the practical aspects and challenges of implementing this strategy and also implement a prototype consisting of a smartphone app, a cloud-based system to compute emissions estimates, and a blockchain-based platform to perform monetization. Experiments performed in two different scenarios attest to our idea’s feasibility.
Temperature-dependent bending rigidity of graphene

Both previous theoretical and experimental work showed that the bending rigidity of a liquid membrane decreases with increasing temperature. We demonstrate that the elastic energy forms for a solid membrane and a liquid membrane are identical under equal-biaxial stretching, implying the bending rigidity of a solid membrane should decrease with increasing temperature. We perform molecular dynamics simulations to study how thermal fluctuation affects the bending rigidity of graphene, and find that the bending rigidity decreases exponentially with increasing temperature. This is in contrast with recent atomistic Monte Carlo simulation result that the bending rigidity of graphene increases with increasing temperature.
CertainOdom: Uncertainty Weighted Multi-task Learning Model for LiDAR Odometry Estimation

As a basic and indispensable module, LiDAR odom-etry estimation is widely used in robotics. In recent years, learning-based modeling approaches for odometry estimation have been validated to be feasible. However, it is necessary to consider security factors as the highest priorities when we apply the learning-based model to certain high-risk real-world scenarios, such as autonomous driving. The odometry uncertainty estimation provides more valuable information for downstream tasks, such as route planning and navigation. In this paper, we propose an end-to-end neural network (namely CertainOdom) to solve odometry and uncertainty estimation tasks by applying multi-task learning. Instead of using the manually-tuned hyper-parameters, we employ the learnable uncertainties to weigh the balance between the error of translation and orientation in the loss function. We evaluate the estimated trajectory and uncertainty on KITTI dataset. We also compare the robustness against the traditional geometry-based methods on our artificially degraded KITTI LiDAR dataset. Extensive experimental results show that our model with uncertainty weighted loss achieves competitive performance in LiDAR odometry estimation. We also explain our uncertainties qualitatively and quantitatively.
Sandbox Integrated Gateway for the Discovery of Cybersecurity Vulnerabilities

Emails are widely used as a form of communication and sharing files in an organization. However, email is widely used by cybercriminals to spread malware and carrying out cyber-attacks. We implemented an open-source email gateway in conjunction with a security sandbox for securing emails against malicious attachments. The email gateway scans all incoming and outgoing emails and stops emails containing suspicious files. An automated python script would then send the suspected email to the sandboxing element through sandbox API for further analysis, while the script is used also for the prevention of duplicate results. Moreover, the mail server administrator receives notifications from the email gateway about suspicious attachments. If detected attachment is a true positive based on the sandbox analysis result, email is deleted, otherwise, the email is delivered to the recipient. The paper describes in an empirical way the steps followed during the implementation, results, and conclusions of our research.