Miracle-dz/UniFAR-FTUs huggingface dataset:
Small Area Estimation With Uncertain Random Effects

Random effects models play an important role in model-based small area estimation. Random effects account for any lack of fit of a regression model for the population means of small areas on a set of explanatory variables. In a recent article, Datta, Hall, and Mandal showed that if the random effects can be dispensed with via a suitable test, then the model parameters and the small area means may be estimated with substantially higher accuracy. The work of Datta, Hall, and Mandal is most useful when the number of small areas, m, is moderately large. For large m, the null hypothesis of no random effects will likely be rejected. Rejection of the null hypothesis is usually caused by a few large residuals signifying a departure of the direct estimator from the synthetic regression estimator. As a flexible alternative to the Fay–Herriot random effects model and the approach in Datta, Hall, and Mandal, in this article we consider a mixture model for random effects. It is reasonably expected that small areas with population means explained adequately by covariates have little model error, and the other areas with means not adequately explained by covariates will require a random component added to the regression model. This model is a useful alternative to the usual random effects model and the data determine the extent of lack of fit of the regression model for a particular small area, and include a random effect if needed. Unlike the Datta, Hall, and Mandal approach which recommends excluding random effects from all small areas if a test of null hypothesis of no random effects is not rejected, the present model is more flexible. We used this mixture model to estimate poverty ratios for 5–17-year-old-related children for the 50 U.S. states and Washington, DC. This application is motivated by the SAIPE project of the U.S. Census Bureau. We empirically evaluated the accuracy of the direct estimates and the estimates obtained from our mixture model and the Fay–Herriot random effects model. These empirical evaluations and a simulation study, in conjunction with a lower posterior variance of the new estimates, show that the new estimates are more accurate than both the frequentist and the Bayes estimates resulting from the standard Fay–Herriot model. Supplementary materials for this article are available online.
Electron spin resonance observation of trapped electron centers in atomic-layer-deposited hafnium oxide on Si

We observed two paramagnetic defects in thin films of HfO2 on silicon with electron spin resonance. Both appear after photoinjecting electrons into the dielectric. Strong spectroscopic evidence links one spectrum to an O2− defect. A second spectrum is likely due to an Hf+3 related defect.
Evaluation of cut-off frequencies of higher order modes in eccentric coaxial line

The paper presents a method of evaluation of the cut-off frequencies of higher order modes of transmission lines having eccentric annular cross-section using a combination of conformal transformation and the method of finite difference. The Laplacian operator appearing in the weighted Helmholtz equation resulting from the conformal transformation is represented as a five-point difference operator of unequal arm length along the two axes. The eigenvalues which give cut-off frequencies are evaluated from the characteristic equation expressed in terms of matrices obtained from a set of simultaneous equations satisfying the boundary conditions. Comparison of numerical data is presented.
EXPERIMENTAL AND MATHEMATICAL EVALUATION OF DYNAMIC BEHAVIOUR OF AN OIL-AIR COUPLING SHOCK ABSORBER

Abstract The physical mechanism of the actual shock absorber with multi-types of damping and non-linear stiffness through coupling the oil, air, rubber and spring by ingenious devices is systematically investigated. The experimental results of the key-model machine in multi-parameter coupling dynamic test show complex non-linearity dynamic characteristics. Based on this, the non-linear dynamic model for the shock absorber is presented by analysing the internal fluid dynamic phenomenon with respect to the shock absorber. Comparisons with experimental data confirm the validity of the model. Using the model, it is possible to evaluate the importance of different factors for designing the shock absorber.
Single ionization of helium by 730-eV electrons

We present fully differential measurements of 730-eV electron-impact single ionization of the ground state of helium with 205- or 100-eV outgoing electrons. Internormalized data are obtained for coplanar geometries with the fast electron detected at θA=6°, 9°, and 12°. The data are compared, where possible, with the corresponding data of Catoire et al. [J. Phys. B 39, 2827 (2006)] and the convergent close-coupling theory. An improved agreement is found between the present measurements and the theory.
The Formation of the Exponential Disk in Spiral Galaxies

A mechanism for the formation of the exponential stellar disk distribution in spiral galaxies is proposed. It is assumed that the gas which falls in to form the disk behaves like an accretion disk which evolves on a viscous time scale t(v) and forms stars on a time scale t(star). It is demonstrated that if t(v) roughly equals t(star) the resulting stellar disk has an exponential distribution independent of the disk rotation law and of the assumed viscosity prescription. Why the viscous and star formation time scales might be related is briefly commented on. 15 references.
Modification of two-level-atom resonance fluorescence near a plasmonic nanostructure

Modification of the resonance fluorescence spectrum of a two-level atom driven by a monochromatic field in the close proximity of a plasmonic nanostructure (metal sphere) is studied in detail. It is shown that one can control this spectrum by varying several key parameters: (i) the radius of the nanosphere, (ii) polarization of the incident radiation, and (iii) the atom's location around the nanosphere (its radial coordinate and polar angle in the spherical coordinate system). These parameters affect the local field enhancement and the modification of the radiative decay rate of the atom interacting with the nanosphere, which leads to modification of the resonance fluorescence spectrum of the atom (e.g., frequency shift of the satellite lines in the Mollow-type triplet, widths of the lines, and the spectrum intensity) by contrast with that in free space. The permittivity of the metal the nanosphere is made of is also an additional parameter, which defines the nonradiative decay. The latter in combination with other parameters allows continuous control of the transition from resonance fluorescence enhancement to its quenching.
The spectrum (P ⋀ bo) −∞

There are spectra P−k constructed from stunted real projective spaces as in [1] such that H*(P−k) is the span in ℤ/2[x, x−1] of those xi with i ≥ −k. (All cohomology groups have ℤ/2-coefficients unless specified otherwise.) Using collapsing maps, these form an inverse system which is similar to those of Lin ([15], p. 451). It is a corollary of Lin's work that there is an equivalence of spectra where holim is the homotopy inverse limit ([3], ch. 5) and Ŝ–1 the 2-adic completion of a sphere spectrum. One may denote by this holim (P–κ), although one must constantly keep in mind that , but rather
On optimization techniques for solving nonlinear inverse problems

This paper considers optimization techniques for the solution of nonlinear inverse problems where the forward problems, like those encountered in electromagnetics, are modelled by differential equations. Such problems are often solved by utilizing a Gauss-Newton method in which the forward model constraints are implicitly incorporated. Variants of Newton's method which use second-derivative information are rarely employed because their perceived disadvantage in computational cost per step offsets their potential benefits of faster convergence. In this paper we show that, by formulating the inversion as a constrained or unconstrained optimization problem, and by employing sparse matrix techniques, we can carry out variants of sequential quadratic programming and the full Newton iteration with only a modest additional cost. By working with the differential equation explicitly we are able to relate the constrained and the unconstrained formulations and discuss the advantages of each. To make the comparisons meaningful we adopt the same global optimization strategy for all inversions. As an illustration, we focus upon a 1D electromagnetic (EM) example simulating a magnetotelluric survey. This problem is sufficiently rich that it illuminates most of the computational complexities that are prevalent in multi-source inverse problems and we therefore describe its solution process in detail. The numerical results illustrate that variants of Newton's method which utilize second-derivative information can produce a solution in fewer iterations and, in some cases where the data contain significant noise, requiring fewer floating point operations than Gauss-Newton techniques. Although further research is required, we believe that the variants proposed here will have a significant impact on developing practical solutions to large-scale 3D EM inverse problems.
Deconvolution of Directly Precipitating and Trap-Precipitating Electrons in Solar Flare Hard X-Rays. II. Compton Gamma Ray Observatory Data Analysis

Based on the deconvolution method developed in the first paper of this series, we present here the data analysis of 20-200 keV hard X-ray (HXR) data from the Burst and Transient Source Experiment (BATSE) on board the Compton Gamma Ray Observatory (CGRO) recorded during 103 solar flares in 1991-1995. These are all of the flares simultaneously observed by CGRO with high time resolution (64 ms) and by Yohkoh in flare mode. The deconvolution method takes the measured HXR count rates as function of energy and time, I(ε, t), and computes the following self-consistently: the electron injection function n(E, t), the directly precipitating electron flux nprec(E, t), the trapped-precipitating flux ntrap(E, t), the fraction of directly precipitating electrons (qprec), the electron time-of-flight distance (lTOF), and the electron density at the loss cone site of the trap (ne). We find that the electron time-of-flight distances (lTOF = 20.0 ± 7.3 Mm) inferred with the deconvolution method are fully consistent with those obtained earlier using a Fourier filter method. The trap electron densities (ne = 1010.96±0.57 cm-3) obtained from deconvolving the e-folding decay times of HXR pulses (according to the trap model of Melrose & Brown) are found to be statistically a factor of 1.5 lower than those inferred from cross-correlation delays. The fraction qprec of directly precipitating electrons, measured for the first time here, is found to have a mean (and standard deviation) of qprec = 0.42 ± 0.16. Based on this precipitation fraction, we infer loss cone angles of α0 ≈ 20°-70° and magnetic mirror ratios of R = Bloss/Binj ≈ 1.2 - 3 (with a median value of Rmedian = 1.6) between the loss cone site and injection/acceleration site, assuming an isotropic pitch angle distribution at the injection site. The TOF distances and mirror ratios constrain magnetic scale heights in flare loops to λB = 10-150 Mm. The fact that this two-component model (with free-streaming and trapped electrons) satisfactorily fits the energy-dependent time delays in virtually all flares provides strong evidence that electron time-of-flight differences and collisional scattering times dominate the observed HXR timing, while the injection of electrons appears to be synchronized (independent of energy) and does not reveal the timing of the acceleration process.
The evolution of short-period binary pulsars: a systematic study

We present evolutionary sequences for low-mass close binary systems in which a low-mass (1.0–1.5 M⊙) secondary star transfers mass to a neutron star. Roche lobe filling occurs when the secondary is a turn-off main-sequence star (having a small helium core). We assume loss of angular momentum owing to gravitational wave radiation and magnetic braking. We have found that the loss (and the mechanism of loss) of mass and angular momentum from the system is the main factor determining the value of the bifurcation period (Pbif). The bifurcation period separates the formation of the converging systems from the diverging systems. Variations in the initial chemical composition, and in the initial mass of the secondary, lead only to minor changes in Pbif. We have also investigated how changes in the chemical composition influence the initial orbital period (Pi) versus final orbital period (Pf) relation. The initial chemical composition has a more significant effect on this relation for shorter Pi than for longer Pi. We have found systematic differences for the Pf versus white dwarf mass relation for various chemical compositions. For converging systems, we have found that there is a boundary orbital period (Pb) such that if Pi < Pb, a system will evolve through the period gap (there are no low-mass X-ray binaries with orbital periods between one and three hours) with a Roche lobe overflowing secondary, but the accretion on to the neutron star is forbidden owing to the ‘propeller effect’. The systems will end their evolution as ultra-short period and very bright, low-mass X-ray binaries. If Pb < Pi < Pbif, then short orbital period millisecond binary pulsar systems will be formed.
Electrical Signals in Dynamically Stressed Ionic Crystals: A Dislocation Model

A summary of new and previously published data on shock‐induced electrical signals observed in nominally pure NaCl single crystals is presented. A dislocation dynamics model is developed to account for the microscopic origin of these signals. This model, although only qualitatively applied so far, is shown to be able to explain many of the interesting features of the observed data, notably the change of signal polarity at ∼10 and ∼110 kbar and the distinct signal profiles observed when the sample is shocked along different crystallographic directions. New experimental results for NaCl single crystals doped with Ca2+, Ba2+, Mg2+, and OH− impurity ions are also presented. These results are consistent with the predictions of the proposed dislocation dynamics model.
Problème de Skorohod multivoque

On prouve un resultat d'existence et d'unicite pour une generalisation (par introduction d'un operateur maximal monotone multivoque) du probleme de Skorohod (avec reflexion normale) deterministe associe a un convexe ferme D de R d . La formulation a partir des operateurs maximaux monotones multivoques permet de considerer des drifts singuliers explosant au bord du domaine. Cette approche multivoque clarifie la connexion entre probleme de Skorohod et semigroupes nonlineaires. En guise d'application, on considere ensuite le cas stochastique: les equations differentielles stochastiques multivoques sont ainsi revisitees. Par consequent, cette contribution fournit une nouvelle methode de construction de diffusions reflechies normalement possedant un coefficient de derive discontinu, explosif.
Time-domain electromagnetic energy in a frequency-dispersive left-handed medium

From Maxwell's equations and the Poynting theorem, the time-domain electric and magnetic energy densities are generally defined in the frequency-dispersive media based on the conservation of energy. As a consequence, a general definition of electric and magnetic energy is proposed. Comparing with existing formulations of electric and magnetic energy in frequency-dispersive media, the new definition is more reasonable and is valid in any case. Using the new definition and staring from the equation of motion, we have shown rigorously that the total energy density and the individual electric and magnetic energy densities are always positive in a realistic artificial left-handed medium (LHM) [R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001)], which obeys actually the Lorentz medium model, although such a LHM has negative permittivity and negative permeability simultaneously in a certain frequency range. We have also shown that the conservation of energy is not violated in LHM. The earlier conclusions can be easily extended to the Drude medium model and the cold plasma medium model. Through an exact analysis of a one-dimensional transient current source radiating in LHM, numerical results are given to demonstrate that the work done by source, the power flowing outwards a surface, and the electric and magnetic energy stored in a volume are all positive in the time domain.
Uniform Asymptotics for Orthogonal Polynomials with Exponential Weights—the Riemann–Hilbert Approach

Let Q(x) =q2mx2m+q2m−1x2m−1+⋯ be a polynomial of degree 2m with q2m > 0, and let {πn(x)}n≥1 be the sequence of monic polynomials orthogonal with respect to the weight w(x) =e−Q(x) on . Furthermore, let αn and βn denote the Mhaskar–Rakhmanov–Saff (MRS) numbers associated with Q(x). By using the Riemann–Hilbert approach, an asymptotic expansion is constructed for πn(cnz+dn), which holds uniformly for all z bounded away from (−∞, −1), where and .
On singular Sturm–Liouville boundary-value problems

We consider the existence of positive solutions for the boundary-value problem (q(t)ϕ(u′))′ + λf(t,u) = 0, r < t < R, au(r) − bϕ−1 (q(r))u′(r) = 0, cu(R) + dϕ−1(q(R))u′(R) = 0, where ϕ(u′) = |u′|p−2u′, p > 1, λ > 0, f is p-superlinear or p-sublinear at ∞ and is allowed to become −∞ at u = 0. Our results unify and extend many known results in the literature.
ON QUASISIMILARITY FOR LOG-HYPONORMAL OPERATORS

In this paper we show that the normal parts of quasisimilar log-hyponormal operators are unitarily equivalent. A Fuglede-Putnam type theorem for log-hyponormal operators is proved. Also, it is shown that a log-hyponormal operator that is quasisimilar to an isometry is unitary and that a log-hyponormal spectral operator is normal.
Derivation, implementation, and initial testing of a compressible wall‐layer model

Traditional wall functions have been used successfully for decades to decrease the computational cost for obtaining solutions to incompressible flows with equilibrium turbulence. However, these traditional, analytic wall functions are poorly suited for more complex flows. The present work describes an alternative approach named the ‘diffusion model’. The diffusion model is a subgrid model developed by Blottner and Bond that solves a system of ODEs in the near‐wall region instead of assuming an analytic profile. The diffusion model has previously been shown to reproduce profiles of various turbulence models through the log layer with fixed outer boundary conditions. This paper documents the implementation and the testing of the diffusion model fully coupled with a 3‐D Reynolds‐averaged Navier–Stokes (RANS) algorithm, using the Spalart–Allmaras model. The results indicate that the coupled algorithm is valid when the interface between diffusion model and the 3‐D RANS algorithm is below the outer edge of the log layer. Although the current work focuses on using steady 3‐D RANS outside of the log layer, modeling assumptions introduced in the current work could be used to derive a diffusion model for coupling with a large eddy simulation region. Published in 2010 by John Wiley & Sons, Ltd.
Exponential empirical likelihood is not Bartlett correctable

In a recent paper, DiCiccio, Hall and Romano established that Owen's empirical likelihood is Bartlett correctable. This is an intriguing and perhaps surprising result and is the only nonparametric context in which Bartlett correctability is known to hold. An alternative, closely related nonparametric likelihood, referred to here as exponential empirical likelihood, may be constructed using Efron's method of nonparametric tilting. The purpose of this note is to show that exponential empirical likelihood is not Bartlett correctable.
Millimeter continuum observations of galactic center giant molecular cloud cores

Results are presented of observations of 1.3- and 0.8-mm continuum emission toward the cores of three Galactic center molecular clouds with ongoing massive star formation, Sagittarius B2, C, and D, which were made in order to study possible variations in the high-mass star formation rate per unit mass between the Galactic center and the disk. The luminosity-to-mass ratio, based on the mass estimates derived from the millimeter continuum emission, is used as a tracer of the high-mass star formation rate in GMC cores. The magnitude of errors involved in using millimeter continuum emission for determining the core mass is estimated through radiative transfer modeling. It is inferred from the present millimeter data, along with previously published far-infrared data, that the Sgr C and D cores are very similar in terms of mean dust optical depth and temperature. The luminosity-to-mass ratios derived for the Sgr C and D cores are found to be consistent with those of typical disk GMC cores with comparable far-infrared luminosities.
Self‐consistent study of a perpendicular collisionless and nonresistive shock

Particle dynamics and field behavior associated with a perpendicular collisionless supercritical and viscous shock are investigated by use of numerical simulation. A one‐dimensional, relativistic, fully electromagnetic and nonperiodic particle simulation code (for both electrons and ions) is used where self‐consistent space‐charge effects and induced effects are totally included. The principal field patterns of the shock (trailing wave train, ramp, and foot region) are studied in detail and are shown to have scale lengths mainly dictated by ion dynamics; the behavior of the corresponding plasma currents associated with the different field components is also presented. Ions are shown to suffer successive ‘‘acceleration–trapping–detrapping’’ at the shock front, and locally in the trailing wave train of the downstream region through combined effects of the electrostatic and magnetic fields. While detrapped, the reflected ions describe very large Larmor orbits and cause a ring distribution; a large rapid nonstochastic ion heating results from this ion gyration. This heating (resistivity‐free) is the main source of dissipation and is responsible for large field damping. Competitive effects such as particle stochasticity, particle trapping, wave damping, wave overtaking, and dispersion effects are shown to interact with each other and to affect the overall dissipation mechanism. Comparison with previous works is also discussed. Various Mach number situations are considered, leading to the definition of a transitory regime between subcritical and supercritical regimes and of a corresponding critical threshold of the electrostatic field. In contrast with the supercritical regime, the subcritical regime is characterized by a low density of trapped‐reflected ions, a broad ion distribution function with a weak tail, and a weak adiabatic bulk ion heating.
Mathematical Models in the Applied Sciences

Part I. Introduction: 1. Mathematical modelling Part II. Methods: 2. Non-dimensionalisation 3. Asymptotics 4. Perturbation methods Part III. Classical Models: 5. Heat transfer 6. Viscous flow 7. Solid mechanics 8. Electromagnetism Part IV. Continuum Models: 9. Enzyme kinetics 10. The Belousov-Zhabotinskii reaction 11. Spruce budworm infestations 12. Chemical reactors 13. Groundwater flow 14. Convection in a porous medium 15. River flow 16. One-dimensional two-phase flow Part V. Advanced Models: 17. Alloy solidification 18. Ice sheet dynamics 19. Chemosensory respiratory control 20. Frost heave in freezing soils References.