Miracle-dz/UniFAR-FTUs huggingface dataset:
Variational integrator for the rotating shallow‐water equations on the sphere

We develop a variational integrator for the shallow‐water equations on a rotating sphere. The variational integrator is built around a discretization of the continuous Euler–Poincaré reduction framework for Eulerian hydrodynamics. We describe the discretization of the continuous Euler–Poincaré equations on arbitrary simplicial meshes. Standard numerical tests are carried out to verify the accuracy and excellent conservational properties of the discrete variational integrator.
The FIRST bright QSO survey

The FIRST radio survey provides a new resource for constructing a large quasar sample. With source positions accurate to better than 1{double_prime} and a point source sensitivity limit of 1 mJy, it reaches 50 times deeper than previous radio catalogs. We report here on the results of the pilot phase for a FIRST Bright Quasar Survey (FBQS). Based on matching the radio catalog from the initial 300 deg{sup 2} of FIRST coverage with the optical catalog from the Automated Plate Machine (APM) digitization of Palomar Sky Survey plates, we have defined a sample of 219 quasar candidates brighter than {ital E} = 17.50. We have obtained optical spectroscopy for 151 of these and classified 25 others from the literature, yielding 69 quasars or Seyfert 1 galaxies, of which 51 are new identifications. The brightest new quasar has an {ital E} magnitude of 14.6 and {ital z} = 0.91; four others are brighter than {ital E} = 16. The redshifts range from {ital z} = 0.12 to 3.42. Half of the detected objects are radio quiet with {ital L}{sub 21-cm}{lt}10{sup 32.5} ergs/s. We use the results of this pilot survey to establish criteria for the FBQS that will produce a quasarmore » search program which will be 70{percent} efficient and 95{percent} complete to a 21-cm flux density limit of 1.0 mJy. {copyright} {ital 1996 American Astronomical Society. }« less
Detection of entanglement with few local measurements

We introduce a general method for the experimental detection of entanglement by performing only few local measurements, assuming some prior knowledge of the density matrix. The idea is based on the minimal decomposition of witness operators into a pseudomixture of local operators. We discuss an experimentally relevant case of two qubits, and show an example how bound entanglement can be detected with few local measurements.
Monitoring squeezed collective modes of a one-dimensional Bose gas after an interaction quench using density-ripple analysis

We investigate the out-of-equilibrium dynamics following a sudden quench of the interaction strength, in a one-dimensional quasi-condensate trapped at the surface of an atom chip. Within a linearized approximation, the system is described by independent collective modes and the quench squeezes the phase space distribution of each mode, leading to a subsequent breathing of each quadrature. We show that the collective modes are resolved by the power spectrum of density ripples which appear after a short time of flight. This allows us to experimentally probe the expected breathing phenomenon. Our results are in good agreement with theoretical predictions which take the longitudinal harmonic confinement into account.
Subgroup posets, Bredon cohomology and equivariant Euler characteristics

For a discrete group $\Gamma$ satisfying some finiteness conditions we give a Bredon projective resolution of the trivial module in terms of projective covers of the chain complex associated to certain posets of subgroups. We use this to give new results on dimensions of $E\gamma$ and to reprove that for virtually solvable groups, $\underline{\cd}\Gamma=\vcd\Gamma$. We also deduce a formula to compute the Euler class of $E\gamma$ for $\Gamma$ virtually solvable of type $\FP_\infty$ and use it to compute orbifold Euler characteristics.
Castelnuovo–Mumford Regularity and Cohomological Dimension

Let be a standard graded ring, be the irrelevant ideal of R and 𝔞0 be an ideal of R 0. In this paper, as a generalization of the concept of Castelnouvo–Mumford regularity reg(M) of a finitely generated graded R-module M, we define the regularity of M with respect to 𝔞0 + R +, say reg𝔞0 + R + (M). We also study some relations of this new invariant with the classic one. To this end, we need to consider the cohomological dimension of some finitely generated R 0-modules. Also, we will express reg𝔞0 + R + (M) in terms of some invariants of the minimal graded free resolution of M and see that in a special case this invariant is independent of the choice of 𝔞0.
Autonomous limit of the 4-dimensional Painlevé-type equations and degeneration of curves of genus two

— In recent studies, 4-dimensional analogs of the Painlevï¿1⁄2 equations were listed and there are 40 types. The aim of the present paper is to geometrically characterize these 40 Painlevï¿1⁄2-type equations. For this purpose, we study the autonomous limit of these equations and degeneration of their spectral curves. The spectral curves are 2-parameter families of genus two curves and their generic degeneration are one of the types classified by Namikawa and Ueno. Liu’s algorithm enables us to find the degeneration types of the spectral curves for our 40 types of integrable systems. This result is analogous to the following fact; the families of the spectral curves of the autonomous 2-dimensional Painlevï¿1⁄2 equations PI, PII, PIV, P8 III , P D7 III , P D6 III , PV and PVI define elliptic surfaces with the singular fiber at H = ∞ of the Dynkin types E 8 , E (1) 7 , E (1) 6 , D (1) 8 , D (1) 7 , D (1) 6 , D (1) 5 and D (1) 4 , respectively.
Uncertainty principle and geometry of the infinite Grassmann manifold

We study the pairs of projections $$ P_If=\chi_If ,\ \ Q_Jf= \left(\chi_J \hat{f}\right)\check{\ } , \ \ f\in L^2(\mathbb{R}^n), $$ where $I, J\subset \mathbb{R}^n$ are sets of finite Lebesgue measure, $\chi_I, \chi_J$ denote the corresponding characteristic functions and $\hat{\ } , \check{\ }$ denote the Fourier-Plancherel transformation $L^2(\mathbb{R}^n)\to L^2(\mathbb{R}^n)$ and its inverse. These pairs of projections have been widely studied by several authors in connection with the mathematical formulation of Heisenberg's uncertainty principle. Our study is done from a differential geometric point of view. We apply known results on the Finsler geometry of the Grassmann manifold ${\cal P}({\cal H})$ of a Hilbert space ${\cal H}$ to establish that there exists a unique minimal geodesic of ${\cal P}({\cal H})$, which is a curve of the form $$ \delta(t)=e^{itX_{I,J}}P_Ie^{-itX_{I,J}} $$ which joins $P_I$ and $Q_J$ and has length $\pi/2$. As a consequence we obtain that if $H$ is the logarithm of the Fourier-Plancherel map, then $$ \|[H,P_I]\|\ge \pi/2. $$ The spectrum of $X_{I,J}$ is denumerable and symmetric with respect to the origin, it has a smallest positive eigenvalue $\gamma(X_{I,J})$ which satisfies $$ \cos(\gamma(X_{I,J}))=\|P_IQ_J\|. $$
Magnetohydrodynamics in full general relativity: Formulation and tests

A new implementation for magnetohydrodynamics (MHD) simulations in full general relativity (involving dynamical spacetimes) is presented. In our implementation, Einstein's evolution equations are evolved by a Baumgarte-Shapiro-Shibata-Nakamura formalism, MHD equations by a high-resolution central scheme, and induction equation by a constraint transport method. We perform numerical simulations for standard test problems in relativistic MHD, including special relativistic magnetized shocks, general relativistic magnetized Bondi flow in stationary spacetime, and a long-term evolution for self-gravitating system composed of a neutron star and a magnetized disk in full general relativity. In the final test, we illustrate that our implementation can follow winding-up of the magnetic field lines of magnetized and differentially rotating accretion disks around a compact object until saturation, after which magnetically driven wind and angular momentum transport inside the disk turn on.
Low-area Floer theory and non-displaceability

We introduce a new version of Floer theory of a non-monotone Lagrangian submanifold which only uses least area holomorphic disks with boundary on it. We use this theory to prove non-displaceability theorems about continuous families of Lagrangian tori in the complex projective plane and other del Pezzo surfaces.
The Erdős–Moser Sum-free Set Problem

Abstract We show that there is an absolute $c>0$ such that if $A$ is a finite set of integers, then there is a set $S\subset A$ of size at least $\log ^{1+c}|A|$ such that the restricted sumset $\{s+s^{\prime }:s,s^{\prime }\in S\text{ and }s\neq s^{\prime }\}$ is disjoint from $A$. (The logarithm here is to base $3$.)
Quantum backreaction on classical dynamics

Motivated by various systems in which quantum effects occur in classical backgrounds, we consider the dynamics of a classical particle as described by a coherent state that is coupled to a quantum bath via bi-quadratic interactions. We evaluate the resulting quantum dissipation of the motion of the classical particle. We also find classical initial conditions for the bath that effectively lead to the same dissipation as that due to quantum effects, possibly providing a way to approximately account for quantum backreaction within a classical analysis.
Gliese 569B: A Young Multiple Brown Dwarf System?

The nearby late M star Gliese 569B was recently found by adaptive optics imaging to be a double with separation ~1 AU. To explore the orbital motion and masses, we have undertaken a high-resolution (~0.″05) astrometric study. Images were obtained over 1.5 yr with bispectrum speckle interferometry at the 6.5 m Multiple Mirror Telescope (MMT) and 6 m Special Astrophysical Observatory telescope. Our data show motion corresponding to more than half the orbital period and constrain the total mass to be greater than 0.115 M☉, with a most probable value of 0.145 M☉. Higher masses cannot be excluded without more extended observations, but from statistical analysis we find an 80% probability that the total mass is less than 0.21 M☉. An infrared spectrum of the blended B double obtained with the MMT has been modeled as a blend of two different spectral types, chosen to be consistent with the measured J- and K-band brightness difference of a factor of ~2. The blended fit is not nearly as good as that to a pure M8.5+ template. Therefore, we hypothesize that the brighter component likely has two unresolved components with near equal masses, each the same as the fainter component. If Gl 569B is a triple, our dynamical limits suggest each component has a mass of 50 MJup. We infer an age for the system of 300 Myr from its kinematic motion, which places it as a member of the Ursa Major moving group. All the above parameters are consistent with the latest DUSTY evolution models for brown dwarfs.
Kondo effect in double quantum dots with interdot repulsion

We investigate a symmetrical double quantum dot system serially attached to the leads. The emphasis is on the numerical analysis of finite interdot tunneling in the presence of interdot repulsive capacitive coupling. The results reveal the competition between extended Kondo phases and local singlet phases in spin and charge degrees of freedom. The corresponding phase diagram is determined quantitatively.
The 2dF Galaxy Redshift Survey: stochastic relative biasing between galaxy populations

It is well known that the clustering of galaxies depends on galaxy type. Such relative bias complicates the inference of cosmological parameters from galaxy redshift surveys, and is a challenge to theories of galaxy formation and evolution. In this paper we perform a joint counts-in-cells analysis on galaxies in the 2dF Galaxy Redshift Survey, classified by both colour and spectral type, eta, as early- or late-type galaxies. We fit three different models of relative bias to the joint probability distribution of the cell counts, assuming Poisson sampling of the galaxy density field. We investigate the non-linearity and stochasticity of the relative bias, with cubic cells of side 10 less than or equal toLless than or equal to 45 Mpc (h= 0.7). Exact linear bias is ruled out with high significance on all scales. Power-law bias gives a better fit, but likelihood ratios prefer a bivariate lognormal distribution, with a non-zero 'stochasticity', i.e. scatter that may result from physical effects on galaxy formation other than those from the local density field. Using this model, we measure a correlation coefficient in log-density space (r(LN)) of 0.958 for cells of length L= 10 Mpc, increasing to 0.970 by L= 45 Mpc. This corresponds to a stochasticity sigma(b)/(b) over cap of 0.44 +/- 0.02 and 0.27 +/- 0.05, respectively. For smaller cells, the Poisson-sampled lognormal distribution presents an increasingly poor fit to the data, especially with regard to the fraction of completely empty cells. We compare these trends with the predictions of semi-analytic galaxy formation models: these match the data well in terms of the overall level of stochasticity, variation with scale and the fraction of empty cells.
An unbiased spectral line survey observation toward the low-mass star-forming region L1527

An unbiased spectral line survey toward a solar-type Class 0/I protostar, IRAS 04368+2557, in L1527 has been carried out in the 3 mm band with the Nobeyama 45 m telescope. L1527 is known as a warm carbon-chain chemistry (WCCC) source, which harbors abundant unsaturated organic species such as CnH (n = 3, 4, 5, …) in a warm and dense region near the protostar. The observation covers the frequency range from 80 to 116 GHz. A supplementary observation has also been conducted in the 70 GHz band to observe fundamental transitions of deuterated species. In total, 69 molecular species are identified, among which 27 species are carbon-chain species and their isomers, including their minor isotopologues. This spectral line survey provides us with a good template of the chemical composition of the WCCC source.
Lorentzian left invariant metrics on three dimensional unimodular Lie groups and their curvatures

There are five unimodular simply connected three dimensional unimodular non abelian Lie groups: the nilpotent Lie group $\mathrm{Nil}$, the special unitary group $\mathrm{SU}(2)$, the universal covering group $\widetilde{\mathrm{PSL}}(2,\mathbb{R})$ of the special linear group, the solvable Lie group $\mathrm{Sol}$ and the universal covering group $\widetilde{\mathrm{E}_0}(2)$ of the connected component of the Euclidean group. For each $G$ among these Lie groups, we give explicitly the list of all Lorentzian left invariant metrics on $G$, up to un automorphism of $G$. Moreover, for any Lorentzian left invariant metric in this list we give its Ricci curvature, scalar curvature, the signature of the Ricci curvature and we exhibit some special features of these curvatures. Namely, we give all the metrics with constant curvature, semi-symmetric non locally symmetric metrics and the Ricci solitons.
Embedding simply connected 2-complexes in 3-space -- V. A refined Kuratowski-type characterisation

This paper is the last paper in a series of five papers. Building on earlier papers in this series, we prove an analogue of Kuratowski's characterisation of graph planarity for three dimensions. More precisely, a simply connected 2-dimensional simplicial complex embeds in 3-space if and only if it has no obstruction from an explicit list of obstructions. This list of obstructions is finite except for one infinite family.
Diagonalizable quartic Thue equations with negative discriminant

The Thue-Siegel method is applied to derive an upper bound for the number of solutions to Thue's equation $F(x,y) = 1$ where $F$ is a quartic diagonalizable form with negative discriminant. Computation is used in this argument to handle forms whose discriminant is small in absolute value. We then apply our results to bound the number of integral points on a certain family of elliptic curves.
Quantum speed limits and the maximal rate of quantum learning

The Bremermann-Bekenstein bound is a fundamental bound on the maximal rate with which information can be transmitted. However, its derivation relies on rather weak estimates and plausibility arguments, which make the application of the bound impractical in the laboratory. In this paper, we revisit the bound and extend its scope by explicitly accounting for the back action of quantum measurements and refined expressions of the quantum speed limit. Our result can be interpreted as an upper bound on the maximal rate of quantum learning, and we show that the Bremermann-Bekenstein bound follows as a particular limit. Our results are illustrated, by first deriving a tractable expression from time-dependent perturbation theory, and then evaluating the bound for two time-dependent systems -- the harmonic oscillator and the P\"oschl-Teller potential.
Enhancing children's participation in early childhood education with participatory pedagogy

Children’s participation in early childhood education has raised concern and discussion in the international researches lately. Young children have been considered to have lack of participation experiences in early education settings because of institutional policies, social understanding about childhood and perspectives of educators (Bae, 2009; Emilson & Folkesson, 2006; Smith, 2002). Focus of children as active agents of their own development through sociocultural learning paradigm the approach of participatory learning has been considered important in early childhood education and research (Berthelsen, Brownlee & Johansson, 2009). This approach of children’s learning views participation as a developing and dynamic cultural phenomenon. This research is focusing on the educators’ perspectives and the conceptions of children’s participation in everyday pedagogic practices and is based on a survey conducted in early childhood education in Metropolitan area of Helsinki in 2010. The survey was realized in the VKK-Metro development and research project funded by the Ministry of Social and Health affairs. The participants represented 1114 working teams from 350 kindergartens. The working teams included 3721 educators taking care of 19 907 children. The analytical framework of research is based on an abductive approach conducted with mixed methods. The findings indicate that children’s voice was considered important by educators. Also opportunities to make independent initiatives and choices were considered as a right and an item of learning and of developing of skills of participation. However children’s chances to participate in decision making process and pedagogical processes were weak because of challenges of children’s participation experienced by educators. These challenges were connected to both institutional issues, such as routines and adult-childratios, and professional skills and beliefs about children’s competence. According to findings of this research children’s participation is understood to include such aspects as having opportunities to have an influence in their learning and the culture of kindergartens, becoming respected and listened to by educators and having chances to practice responsibility and self-regulation. The role of educators as facilitators of children’s participation is found essential and the research builds knowledge of children’s participation through framework of participatory pedagogy in early education context. Through this framework the challenges of children’s participation could be reflected and a culture of developing participation built in co-operation between educators, children and political and social environment of early childhood education.
Borcherds–Bozec algebras, root multiplicities and the Schofield construction

Using the twisted denominator identity, we derive a closed form root multiplicity formula for all symmetrizable Borcherds–Bozec algebras and discuss its applications including the case of Monster Borcherds–Bozec algebra. In the second half of the paper, we provide the Schofield construction of symmetric Borcherds–Bozec algebras.
Spin Excitations in the Antiferromagnet NaNiO2

In NaNiO2 , Ni3+ ions form a quasi-two-dimensional triangular lattice of S=1/2 spins. The magnetic order observed below 20K has been described as an A type antiferromagnet with ferromagnetic layers weakly coupled antiferromagnetically. We studied the magnetic excitations with the electron spin resonance for frequencies 1 20cm-1 , in magnetic fields up to 14T . The bulk of the results are interpreted in terms of a phenomenological model involving biaxial anisotropy for the spins: a strong easy-plane term, and a weaker anisotropy within the plane
Local error estimates of the finite element method for an elliptic problem with a Dirac source term

The solutions of elliptic problems with a Dirac measure right‐hand side are not H 1 in dimension d ∈ { 2 , 3 } and therefore the convergence of the finite element solutions is suboptimal in the L 2 ‐norm. In this article, we address the numerical analysis of the finite element method for the Laplace equation with Dirac source term: we consider, in dimension 3, the Dirac measure along a curve and, in dimension 2, the punctual Dirac measure. The study of this problem is motivated by the use of the Dirac measure as a reduced model in physical problems, for which high accuracy of the finite element method at the singularity is not required. We show a quasioptimal convergence in the H s ‐norm, for s ≥ 1 on subdomains which exclude the singularity; in the particular case of Lagrange finite elements, an optimal convergence in H 1 ‐norm is shown on a family of quasiuniform meshes. Our results are obtained using local Nitsche and Schatz‐type error estimates, a weak version of Aubin‐Nitsche duality lemma and a discrete inf‐sup condition. These theoretical results are confirmed by numerical illustrations.
The atmospheric parameters of FGK stars using wavelet analysis of CORALIE spectra

Atmospheric properties of F-,G- and K-type stars can be measured by spectral model fitting. These methods require data with good signal-to-noise ratio and reliable continuum normalisation. This is particularly challenging for the spectra we have obtained with the CORALIE \'{e}chelle spectrograph for FGK stars with transiting M-dwarf companions. The spectra tend to have low signal-to-noise ratios, which makes it difficult to analyse them using existing methods. Our aim is to create a reliable automated spectral analysis routine to determine $T_{\rm eff}$, [Fe/H], $V \sin i$ from the CORALIE spectra of FGK stars. We use wavelet decomposition to distinguish between noise, continuum trends, and stellar spectral features in the CORALIE spectra. A subset of wavelet coefficients from the target spectrum are compared to those from a grid of models in a Bayesian framework to determine the posterior probability distributions of the atmospheric parameters. By testing our method using synthetic spectra we found that our method converges on the best fitting atmospheric parameters. We test the wavelet method on 20 FGK exoplanet host stars for which higher quality data have been independently analysed using equivalent width measurements. We find that we can determine $T_{\rm eff}$ to a precision of $85$K, [Fe/H] to a precision of 0.06 dex and $V \sin i$ to a precision of 1.35 kms$^{-1}$ for stars with $V \sin i$ $\geq$ 5 kms$^{-1}$. We find an offset in metallicity $\approx -$0.18 dex relative to the equivelent width fitting method. We can determine $\log g$ to a precision of $0.13$ dex but measurements are only reliable to confirm dwarf-like surface gravity. The wavelet method can be used to determine $T_{\rm eff}$, [Fe/H] and $V \sin i$ for FGK stars from \'{e}chelle spectra. We find that our method is self consistent, and robust for spectra with SNR$\gtrapprox 40$.