Miracle-dz/UniFAR-FTUs huggingface dataset:
How hard is the tensor rank

We investigate the computational complexity of tensor rank, a concept that plays fundamental role in different topics of modern applied mathematics. For tensors over any integral domain, we prove that the rank problem is polynomial time equivalent to solving a system of polynomial equations over this integral domain. Our result gives a complete description of the algorithmic complexity of tensor rank and allows one to solve several known open problems. In particular, the tensor rank over $\mathbb{Z}$ turns out to be undecidable, which answers the question posed by Gonzalez and Ja'Ja' in 1980. We generalize our result and prove that the symmetric rank admits a similar description of computational complexity as the one we give for usual rank. In particular, computing the symmetric rank of a rational tensor is shown to be NP-hard, which proves a recent conjecture of Hillar and Lim. As a byproduct of our approach, we get a similar characterization of the algorithmic complexity of the minimal rank matrix completion problem, which gives a complete answer to the question discussed in 1999 by Buss, Frandsen, and Shallit.
Effects of HDDR treatment conditions on magnetic properties of Nd‐Fe‐B anisotropic powders

It is reported that Nd‐Fe‐B magnetic powders prepared by utilizing the HDDR (hydrogenation, disproportionation, desorption, and recombination) phenomena exhibit high coercivity, and the addition of Co, Ga, and Zr induces magnetic anisotropy in these powders. HDDR phenomena are caused by the heat treatment in hydrogen (H treatment) and subsequently in vacuum (V treatment). Present works describe the effects of V‐treatment conditions on magnetic properties of Nd12.6Febal. CoxB6.0 (x=0–17.4) alloys. The powders V‐treated at lower temperature show lower remanence and no noticeable magnetic anisotropy. V treatment at higher temperature enhances remanence and increases the differences of remanence between the powders aligned with and without magnetic field. Higher values are obtained in Co added alloys. This result suggests that a selective grain growth of Nd2Fe14B grains during V treatment plays an important role for the inducement of magnetic anisotropy in HDDR‐treated powders. The temperature for complete rec.
Duals of Hardy-amalgam spaces $\mathcal{H}_{\mathrm{loc}}^{(q,p)}$ and Pseudo-differential operators

In this paper, we carry on with the study of the Hardy-Amalgam spaces $\mathcal{H}_{\mathrm{loc}}^{(q,p)}$ spaces introduced in \cite{AbFt}. We investigate their dual spaces and establish some results of boundedness of pseudo-differential operators in these spaces.
Drag coefficient of the weakly ionized plasma in the high Knudsen number regime

The drag force acting on a micron-sized polystyrene particle in the high Knudsen number regime is investigated. Analysis of the particle trajectories in stationary neutral argon gas environment suggests the damping time constant τ∝p−1.20±0.04 and Epstein drag force coefficient δ=1.40. The neutral drag coefficient is compared with the drag coefficient measurement in dust-free plasma. The phenomena of the reduced drag in weakly viscous and weakly ionized rf plasma are also observed in this report. It is shown that the slight changes in rf power and pressure would enhance the reduced drag effect, which suggests that there is an additional electrostatic force acting along the particle motion in the plasma.
A Systematic Review of Research on Sport Migration

Research on sport migration spans many disciplines and strands of inquiry, with some studies seeking to analyse the academic outputs. However, these studies sometimes are focused on certain specific contexts or offer only qualitative analysis. This present study aimed to analyse the literature on sport migration. Through a systematic review, we combined data from the articles to propose a classification of the sport migration research field. The results show that research in sport migration have focused on athletes who are mostly men, working in elite sports, and with attention to more globally practiced sports, such as football. Regarding migratory flows, they are often carried out from peripheral countries to central countries. Considering all advances in academic output on sport migration, this line of research needs to broaden, observing other dynamics involved, such as other migratory routes, groups of migrants, and social agents.
Fixed poles in transfer function equations

In this paper we study the pole structure of the solutions $H(z)$, if any, of equations of the form $T(z) = H(z)G(z)$ or, dually, $T(z) = F(z)H(z)$, where $T(z)$ and $G(z)$, or $F(z)$, are given matrices of rational functions (multivariable transfer functions) over a field K. This study is motivated by various design problems in linear dynamical system theory (such as model matching or factorization problems), whose solutions are systems with an internal dynamics determined by the pole structure of $H(z)$. The methods we use are algebraic and module theoretic methods and the main tools are represented by the modules of the poles and of the zeros associated with a transfer function. The main result is a complete description of the “essential” pole structure which is common to all the solutions $H(z)$. This is given by means of a module whose invariant factors are explicitly computed in terms of fractional representations of the data $T(z)$ and $G(z)$ or $F(z)$. The essential pole structure is shown to cons.
Perpendicular Transport of Charged Particles in Composite Model Turbulence: Recovery of Diffusion

The computation of charged particle orbits in model turbulent magnetic fields is used to investigate the properties of particle transport in the directions perpendicular to the large-scale magnetic field. Recent results by Qin, Matthaeus, & Bieber demonstrate that parallel scattering suppresses perpendicular diffusion to a subdiffusive level when the turbulence lacks transverse structure. Here numerical computations are used to show that in turbulence in which there is substantial transverse structure, a second regime of diffusive transport can be established. In both the subdiffusion regime and this "second diffusion" regime, perpendicular transport is intrinsically nonlinear. The regime of second diffusion persists for long times and may therefore be of interest in astrophysical transport problems such as the scattering and solar modulation of cosmic rays.
Face mask use in the COVID-19 pandemic: a cross-sectional study

Objective : This study aimed to investigate face mask use among the population of the state of Rio de Janeiro during the COVID-19 pandemic. Method : This was an online cross-sectional study. Data were collected via social media using an online form to gather general information about the participants and administering the Brazilian Portuguese version of the Face Mask Use Scale. Mann-Whitney and Kruskal Wallis tests were used to compare the scores. All ethical aspects were considered. Results: 1,783 (100%) individuals participated. The mean score was 18.2 (SD=8.2), with items ranging between 6.0 and 30, placing the practice of mask use at 60.6%. When evaluating self-protection, the mean score was 9.5 (SD=4.0), and protection of others, 8.7 (SD=4.6), ranging between 3.0 and 15.0. Conclusion: The practice of wearing face masks was neglected by the population of this study, and their use was geared more at self-protection than at the protection of others.
Investigations of high mobility single crystal chemical vapor deposition diamond for radiotherapy photon beam monitoring

The intrinsic properties of diamond make this material theoretically very suitable for applications in medical physics. Until now ionization chambers have been fabricated from natural stones and are commercialized by PTW, but their fairly high costs and long delivery times have often limited their use in hospital. The properties of commercialized intrinsic polycrystalline diamond were investigated in the past by many groups. The results were not completely satisfactory due to the nature of the polycrystalline material itself. In contrast, the recent progresses in the growth of high mobility single crystal synthetic diamonds prepared by chemical vapor deposition (CVD) technique offer new alternatives. In the framework of the MAESTRO project (Methods and Advanced Treatments and Simulations for Radio Oncology), the CEA-LIST is studying the potentialities of synthetic diamond for new techniques of irradiation such as intensity modulated radiation therapy. In this paper, we present the growth and characteristi.
Development of electromagnetic cascading in the Sun's magnetic field

The study of particle cascading initiated by Extremely High Energy (EHE) photons in the Sun's magnetic field offers us an opportunity to study some processes of astrophysical importance in space. This opportunity has beenparticularly useful in investigating the photon content in the EHE cosmic ray spectrum. The processes of magnetic pair creation and photon splitting are the basic mechanisms taken into account in our Monte Carlo simulation code. Such processes have been simulated for primary photons in the magnetic field near the Sun to study the characteristics of the cascading of these extraordinary showers. Upon simulation, such cascading particles produced by primary photons with an energy ≥10 1 9 eV could be detected on the Earth's surface within a solid angle of 6.12 x 10 - 4 sr from the Sun's position. The characteristics of cascading initiated by photons in such a strong magnetic field near the Sun are discussed.
Numerical study of vortex shedding from a rotating cylinder immersed in a uniform flow field

A numerical study is made of the unsteady two-dimensional, incompressible flow past an impulsively started translating and rotating circular cylinder. The Reynolds number (Re) and the rotating-to-translating speed ratio (α) are two controlled parameters, and the influence of their different combinations on vortex shedding from the cylinder is investigated by the numerical scheme sketched below. Associated with the streamfunction (ψ)-vorticity (ω) formulation of the Navier-Stokes equations, the Poisson equation for ψ is solved by a Fourier/finite-analytic, separation of variable approach. This approach allows one to attenuate the artificial far-field boundary, and also yields a global conditioning on the wall vorticity in response to the no-slip condition. As for the vorticity transport equation, spatial discretization is done by means of finite difference in which the convection terms are handled with the aid of an ENO (essentially non-oscillatory)-like data reconstruction process. Finally, the interior vorticity is updated by an explicit, second-order Runge-Kutta method. Present computations fall into two categories. One with Re = 10 3 and α < 3; the other with Re = 10 4 and α < 2
Airplane Measurements of Planetary Boundary Layer Structure

Abstract Measurements of air velocity and temperature from an airplane in the planetary boundary layer with strong surface heating are used to calculate vertical heat, momentum and energy fluxes, as well as spectral densities and probability distributions of velocity and temperature. Airplane traverses parallel to the wind are compared to crosswind traverses and a definite elongation of the heat transporting eddies, or thermals, parallel to the wind is observed. The terms in the turbulent kinetic energy balance equation (with the exception of the pressure fluctuation term) and the temperature variance balance equation are estimated. The turbulent kinetic energy dissipation is almost constant with height between the lowest flight level of 100 m above the surface, and the highest flight level of 1000 m, which is just below the top of the boundary layer, while the generation term due to the buoyancy force decreases and the divergence of the vertical transport of kinetic energy increases with height to mainta.
Beam shifts on reflection of electromagnetic radiation off anisotropic crystals at optic phonon frequencies

We discuss possible beam shifts on external reflection of electromagnetic radiation off an anisotropic crystal around its optic phonon frequencies. In certain situations, these displacements may oppose the energy flow within the crystal. We show examples for reflection off crystal quartz in various configurations. Displacements of the order of a wavelength should occur with significant reflected intensity.
Measurement of coincidence timing resolution with CdTe detectors

The coincidence timing resolution is a critical performance parameter to determine if direct gamma-ray detection by semiconductor detector material such as CdTe or CdZnTe may be suitable for use in positron emission tomography systems. We report experimental results of the coincidence timing resolution measured with a pair of 2 by 2 by 10 mm3 CdTe detectors irradiated by 511 keV gamma rays under conditions that allow good timing resolution and good energy resolution to be obtained simultaneously. The measured coincidence time resolutions ranged from 14 ns to 24 ns. We also found that the coincidence timing resolution was proportional to the signal rise time, and that both of these were proportional to the electron transit time.
On the Fourier coefficients of meromorphic Jacobi forms

In this paper, we describe the automorphic properties of the Fourier coefficients of meromorphic Jacobi forms. Extending results of Dabholkar, Murthy, and Zagier, and Bringmann and Folsom, we prove that the canonical Fourier coefficients of a meromorphic Jacobi form φ(z; τ) are the holomorphic parts of some (vector-valued) almost harmonic Maass forms. We also give a precise description of their completions, which turn out to be uniquely determined by the Laurent coefficients of φ at each pole, as well as some well-known real analytic functions, that appear for instance in the completion of Appell–Lerch sums.
Asymptotic analysis of nonselfadjoint operators generated by coupled Euler‐Bernoulli and Timoshenko beam model

In the current paper, we present a series of results on the asymptotic and spectral analysis of coupled Euler‐Bernoulli and Timoshenko beam model. The model is well‐known in the different branches of the engineering sciences, such as in mechanical and civil engineering (in modelling of responses of the suspended bridges to a strong wind), in aeronautical engineering (in predicting and suppressing flutter in aircraft wings, tails, and control surfaces), in engineering and practical aspects of the computer science (in suppressing bending‐torsional flutter of a new generation of hard disk drives, which is expected to pack high track densities (20,000+TPI) and rotate at very high speeds (25,000+RPM)), in medical science (in bio mechanical modelling of bloodcarrying vessels in the body, which are elastic and collapsible). The aforementioned mathematical model is governed by a system of two coupled differential equations and a two parameter family of boundary conditions representing the action of the self‐straining actuators. This linear hyperbolic system is equivalent to a single operator evolution equation in the energy space. That equation defines a semigroup of bounded operators and a dynamics generator of the semigroup is our main object of interest. We formulate and proof the following results: (a) the dynamics generator is a nonselfadjoint operator with compact resolvent from the class 𝔖p with p > 1; (b) precise spectral asymptotics for the two‐branch discrete spectrum; (c) a nonselfadjoint operator, which is the inverse of the dynamics generator, is a finite‐rank perturbation of a selfadjoint operator. The latter fact is crucial for the proof that the root vectors of the dynamics generator form a complete and minimal set. In our forthcoming paper, we will use the spectral results to prove that the dynamics generator is Riesz spectral, which will allow us to solve several boundary and distributed controllability problems via the spectral decomposition method. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Researching classrooms: complexity and chaos

This article presents a critical review of complexity theory in relation to educational research. The ‘analytical reductionist’ approach is one in which the educational researcher seeks to reduce complex wholes to particular factors and to identify correlations between them and desirable outcomes. Complexity theory shows how this approach in social research is both unreliable within its own terms of reference and misdirected. Complexity theory is characterised by a number of features. These include recognition that educational systems contain multiple variables. These connect in non‐linear and dynamic ways, i.e. where factors are seen to interact in a causal relationship the effects do not necessarily relate proportionally to the cause, and few factors may interact with many and many may interact with few. The crucial point of focus is on (a) the nature of the connections that are products of previous interactions reaching into the particular history of the organisation, and (b) the constitutive nature of.
Fast seeding of NTMs by sawtooth crashes in TCV and their preemption using ECRH

Many tokamaks have observed that sawteeth of sufficient duration may trigger neoclassical tearing modes (NTMs) that lead to plasma performance degradation. In this paper, TCV's ability to accurately control the period of individual sawteeth is exploited, using localized electron cyclotron resonance heating and current drive (ECRH and ECCD), to trigger NTMs under controlled conditions, providing an excellent environment for the study of the seeding of NTMs by sawtooth crashes. The TCV experiments show evidence of a fast formation of seed islands with poloidal/toroidal mode numbers m/n = 3/2 and 2/1 within a few tens of microseconds following the sawtooth crash. Crashes of sawteeth with a longer period duration are observed to generate larger seed islands but also increase the plasma stability to conventional tearing modes. While these two effects compete, the NTM stability is found to decrease with increasing sawtooth period. The seed island size can be reduced and, thereby, the NTM stability improved, by increasing the value of the safety factor q95. Alternatively, NTM stability can be increased by application of preemptive ECRH at the resonant surface of the NTM. Preemptive ECRH is found to enlarge the plasma operational domain by improving the conventional tearing stability and by reducing the coupling between the driving (m/n = 1/1 or 2/2) and the driven modes (m/n = 2/1 or 3/2), resulting in smaller sawtooth generated seed islands. The efficiency of preemptive ECRH increases when sufficient ECRH power is applied in a short time interval prior to the sawtooth crash.
A system of three quantum particles with point-like interactions

Consider a quantum three-particle system consisting of two fermions of unit mass and another particle of mass interacting in a point-like manner with the fermions. Such systems are studied here using the theory of self-adjoint extensions of symmetric operators: the Hamiltonian of the system is constructed as an extension of the symmetric energy operator which is defined on the functions in that vanish whenever the position of the third particle coincides with the position of a fermion. To construct a natural family of extensions of , one must solve the problem of self-adjoint extensions for an auxiliary sequence of symmetric operators acting in . All the operators with even are self-adjoint, and for every odd there are two numbers such that is self-adjoint and lower semibounded for , and has deficiency indices for . When , every self-adjoint extension of which is invariant under rotations of is lower semibounded, but if , then it has an infinite sequence of eigenvalues of multiplicity such that as (the Thomas effect). It follows from the last fact that there is a sequence of bound states of with spectrum , where the numbers cluster at 0 (Efimov's effect). Bibliography: 19 titles.
Reduction of deterministic coupled atmosphere–ocean models to stochastic ocean models: a numerical case study of the Lorenz–Maas system

Our starting point is the Lorenz–Maas coupled atmosphere–ocean model which was proposed by van der Schrier and van Veen and couples the ocean model by Maas with the Lorenz-84 model of the atmosphere. This 6-dimensional model (3-dimensional slow ocean and 3-dimensional fast atmosphere) is, to the knowledge of the authors, the simplest atmosphere–ocean model presently available which is derived from first principles in a controlled manner. This paper is an extensive numerical case study of the model, thereby implementing ‘Hasselmann's program,’ i.e. applying the various mathematical techniques of reducing the fully coupled deterministic model to a deterministic or stochastic model for the ocean alone, namely to: • the (deterministic) ‘statistical model,’ using the method of averaging, • the ‘linear stochastic model,’ based on the central limit theorem for the error in averaging, • the ‘nonlinear stochastic model,’ also known as ‘Hasselmann's equation’. The long-term and bifurcation behaviour of these models are studied and compared. The general result is that in most situations the nonlinear stochastic model outperforms the other ones.
Physical conditions in the Orion Nebula and an assessment of its helium abundance

New long-slit spectrophotometric observations were obtained to redetermine the helium abundance of the Orion Nebula. The ionic ratio He(+)/H(+) is found to remain nearly constant at 0.088 {plus minus} 0.006. In the bright innermost region, the errors are largely systematic due to uncertainties in the reddening curve for Orion grains and deviations from case B emissivity. In the outer regions, the errors are dominated by statistical errors. Photoionization models are computed to determine the correction for the unobserved presence of neutral helium in regions where hydrogen is ionized. 114 refs.
Solar wind‐magnetosphere energy coupling efficiency and partitioning: HILDCAAs and preceding CIR storms during solar cycle 23

A quantitative study on the energetics of the solar wind‐magnetosphere‐ionosphere system during High‐Intensity, Long‐Duration, Continuous AE Activity (HILDCAA) events for solar cycle 23 (from 1995 through 2008) is presented. For all HILDCAAs, the average energy transferred to the magnetospheric/ionospheric system was ~6.3 ×1016 J, and the ram kinetic energy of the incident solar wind was ~7.1 ×1018 J. For individual HILDCAA events the coupling efficiency, defined as the ratio of the solar wind energy input to the solar wind kinetic energy, varied between 0.3% and 2.8%, with an average value of ~0.9%. The solar wind coupling efficiency for corotating interaction region (CIR)‐driven storms prior to the HILDCAA events was found to vary from ~1% to 5%, with an average value of ~2%. Both of these values are lower than the> 5% coupling efficiency noted for interplanetary coronal mass ejection (and sheath)‐driven magnetic storms. During HILDCAAs, ~67% of the solar wind energy input went into Joule heating, ~22% into auroral precipitation, and ~11% into the ring current energy. The CIR‐storm Joule heating (~49%) was noticeably less than that during HILDCAAs, while the ring current energies were comparable for the two. Joule dissipation was higher for HILDCAAs that followed CIR‐storms (88%) than for isolated HILDCAAs (~60%). Possible physical interpretations for the statistical results obtained in this paper are discussed.
A Spectral Gap Theorem in $SU(d)$

We establish the spectral gap property for dense subgroups of $SU(d)$ ($d\geq 2$), generated by finitely many elements with algebraic entries; this result was announced in [BG3]. The method of proof differs, in several crucial aspects, from that used in [BG] in the case of SU(2).