Miracle-dz/UniFAR-FTUs huggingface dataset:
Sharp local embedding inequalities

In this paper we establish local versions of the Onofri and sharp Sobolev inequalities. Such local inequalities enable us to give a more direct and simpler proof of the Onofri inequality on 𝕊2, as well as an alternative proof of sharp Sobolev inequalities on 𝕊n (for n ≥ 3). © 2005 Wiley Periodicals, Inc.
The existence and shapes of dust lanes in galactic bars

I study the flow of gas in and around the bars or ovals of model barred galaxies and show that it is intimately linked to the properties of the periodic orbits. Simulations show that the density of the gas in and around the bar region is low, except for the centre and two narrow lanes which are the loci of shocks. Such shocks form if the x 1 periodic orbits have either loops or large curvature values at their apocentres. The form of the shock loci depends on a number of parameters characterizing the bar and disc potentials. In order for shocks to be offset from the bar major axis towards its leading side, the x 2 and x 3 families must not only exist but also cover a sufficient extent along the bar major axis
Meeting Report: Solar Energetic Particle Measurements Intercalibration Workshop, 11 April 2014, Boulder, Colorado

Following the conclusion of the 2014 Space Weather Week in Boulder, Colorado, the NOAA National Geophysical Data Center and Space Weather Prediction Center cohosted a 1 day workshop on the intercalibration of solar energetic particle (SEP) measurements. The overall purpose of this workshop was to discuss the intercalibration of SEP measurements from different instruments and different spacecraft, to foster new cooperative intercalibration efforts, and to identify a path forward for establishing a set of intercalibration guidelines. The detailed objectives of this workshop were described by Rodriguez and Onsager [2014]. Ten talks were given at the workshop (available at ftp://ftp.ngdc.noaa.gov/STP/publications/spe_intercal/), interspersed with extensive discussions. One outcome of these discussions is a recommendation that a set of guidelines be drafted for the on-orbit cross comparison of solar energetic particle measurements, similar to the ﬁ rst optical calibration guidelines developed for the Global Space-based Inter-Calibration System (GSICS) of the World Meteorological Organization (WMO) and the Coordination Group for Meteorological Satellites [ Datla et al . , 2009]. These guidelines should address the following questions:
Consistency of Procrustes Estimators

Lele has shown that the Procrustes estimator of form is inconsistent and raised the question about the consistency of the Procrustes estimator of shape. In this paper the consistency of estimators of form and shape is studied under various assumptions. In particular, it is shown that the Procrustes estimator of shape is consistent under the assumption of an isotropic error distribution and that consistency breaks down if the assumption of isotropy is relaxed. The relevance of these results for practical shape analysis is discussed. As a by‐product, some new results are derived for the offset uniform distribution from directional data.
SU(n)-CHERN–SIMONS INVARIANTS OF SEIFERT FIBERED 3-MANIFOLDS

We derive the formula for the Chern–Simons invariants of irrreducible SU(n)-flat connections on the Seifert fibered 3-manifolds. As an example, we calculate the values explicitly for the Seifert fibered 3-manifold S3/Γ, where Γ is a finite subgroup of SU(2).
Mixed convective/dynamic roll vortices and their effects on initial wind and temperature profiles

Abstract The onset and development of both dynamically and convectively forced boundary-layer rolls are studied with linear and nonlinear analyses of a truncated spectral model of shallow Boussinesq flow. Emphasis is given here on the energetics of the dominant roll modes, on the magnitudes of the roll-induced modifications of the initial basic-state wind and temperature profiles, and on the sensitivity of the linear stability results to the use of modified profiles as basic states. It is demonstrated that the roll circulations can produce substantial changes to the cross-roll component of the initial wind profile and that significant changes in orientation angle estimates can result from use of a roll-modified profile in the stability analysis. These results demonstrate that roll contributions must be removed from observed background wind profiles before using them to investigate the mechanisms underlying actual secondary flows in the boundary layer. The model is developed quite generally to accept arbit.
The effects of illuminance, color temperature and color rendering index of light sources upon comfortable visual environments

In the present experiment, the effects of illuminance upon comfortable visual environments of a room were examined by using a miniature room. The room was set to simulate an usual office. The light source was placed above the ceiling made of opaque acrylic plate. The room was lighted through the ceiling, using six kinds of lamps. Under various lighting conditions, subjects were required to rate the office according to the psy-cological method, which consisted of the " image " and " evaluation " tests. For each of the tests, the scale values obtained by the method of successive categories were subjected to principal components analysis. As the results of the analysis, four components were extracted for both the " image " and the "evaluation " tests accounting for 95(cid:631)(cid:631) and 90(cid:631)(cid:631) res-pectively. The canonical correlation analysis was, applied and indicated that the relation between two tests was very strong. In both tests, the first component closely related to illuminance, color temperature and color rendering, and strong depencence of the second component upon illuminance was found. The relationships between the scale values:of individual items. and illuminance were discussed.
Data assimilation in the FOAM operational short‐range ocean forecasting system: a description of the scheme and its impact

A detailed description of the data assimilation scheme used in the Forecasting Ocean Assimilation Model (FOAM) operational ocean forecasting system is presented. The theoretical basis for the scheme is an improved version of the analysis correction scheme, which includes information from previously assimilated data. The scheme requires the a priori specification of error covariance information for the background model field and the observations. The way in which these error covariances have been estimated is described and some examples are given. The FOAM system assimilates sea surface temperature, sea‐level anomaly, temperature profile, salinity profile and sea‐ice concentration data. Aspects of the scheme that are specific to each of these observation types are described.
A moment-generating function with application to the birnbaum-saunders distribution

The Birnbaum-Saunders distribution is a fatigue life distribution that was derived from a model assuming that failure is due to the development and growth of a dominant crack. This distribution has been shown to be applicable not only for fatigue analysis but also in other areas of engineering science. Because of its increasing use, it would be desirable to obtain expressions for the expected value of different powers of this distribution. In this article, the moment-generating function for the sinh-normal distribution is derived. It is shown that this moment-generating function can be used to obtain both integer and fractional moments for the Birnbaum-Saunders distribution. Thus it is now possible to obtain an expression for the expected value of the square root of a Birnbaum-Saunders random variable. A general expression for integer noncentral moments for the Birnbaum-Saunders distribution is derived using the moment-generating function of the sinh-normal distribution. Also included is an approximation .
Quantum Tori and the Structure of Elliptic Quasi-simple Lie Algebras

Abstract We study and classify those tame irreducible elliptic quasi-simple Lie algebras which are simply laced and of rankl⩾3. The first step is to identify the core of such an algebra up to central isogeny by identifying the coordinates. When the type isDorEthe coordinates are Laurent polynomials in ν variables, while for typeAthe coordinates can be any quantum torus in ν variables. The next step is to study the universal central extension as well as the derivation algebra of the core. These are related to the first Connes cyclic homology group of the coordinates. The final step is to use this information to give constructions of Lie algebras which we then prove yield representatives of all isomorphism classes of the above types of algebras.
The probability of winning break points in Grand Slam men's singles tennis

Abstract The probability of winning games of tennis has been modelled in terms of the probability of the server winning an individual point. These models are based on the assumptions of stationarity of the point and interdependence. Stationarity is the assumption that the outcome of tennis points is not influenced by the game score at the beginning of the point. The purpose of the current investigation was to compare the outcomes of tennis points during break points and non-break points using data from 528 men's singles tennis matches from all four Grand Slam tournaments in 2008 and 2009. The retrospective probability of the receiver winning a point was 0.42 ± 0.23 during break points which was significantly greater than the 0.38 ± 0.10 during non-break points (P < 0.001). This, in turn, led to players creating significantly more break points than expected (P < 0.001) and breaking serve more frequently than expected (P < 0.001) for the points won when receiving serve. This is evidence that stationarity cannot be assumed and that models of winning tennis games may need to be enhanced to address improved receiver performance during break points.
The X-ray structure of the 3C 295 cluster - A cooling flow at a redshift of 0.5

On decrit la morphologie RX de l'amas 3c295. Toutes les donnees optiques et RX sont compatibles avec un modele d'equilibre hydrostatique, isotherme (γ=1,05±0,07) dont les parametres sont semblables a ceux des amas proches. Par comparaison, on montre que la constante de Huble est Ho≤20(+27,−9) kms −1 Mpc −1
Evaluation and Representation of the Theoretical Orientation Workspace of the Gough–Stewart Platform

The evaluation and representation of the orientation workspace of robotic manipulators is a challenging task. This work focuses on the determination of the theoretical orientation workspace of the Gough-Stewart platform with given leg length ranges [ρ min i , ρ max i ]. By use of the roll-pitch-yaw angles (Φ, θ, ψ), the theoretical orientation workspace at a prescribed position P 0 can be defined by up to 12 workspace surfaces. The defined orientation workspace is a closed region in the 3D orientation Cartesian space OΦθψ. As all rotations R(x, Φ), R(y, 0), and R(z, ψ) take place with respect to the fixed frame, any point of the defined orientation workspace provides a clear measure for the platform to, respectively, rotate in order around the (x,y,z) axes of the fixed frame. An algorithm is presented to compute the size (volume) of the theoretical orientation workspace and intersectional curves of the workspace surfaces. The defined theoretical orientation workspace can be applied to determine a singularity-free orientation workspace.
A Time‐Series IUE Archival Study of the White Dwarf in the Ultrashort‐Period Dwarf Nova WZ Sagittae

The IUE archive offers a series of far‐UV spectra of the ultrashort‐period dwarf nova WZ Sge over a long time baseline and hence the opportunity to monitor the ongoing accretion, the cooling of the white dwarf, and temporal variations in the line spectra. We have carried out a quantitative analysis of these spectra including model atmosphere simulations. We find an indicated cooling of the white dwarf by 5140 K from 20,510 to 15,370 K with a thermal e‐folding time of 690 days. This cooling rate is well represented by heating of the white dwarf by accretion of matter with angular momentum during the 1978 December outburst followed by subsequent cooling. We find that the abundance of carbon in the white dwarf photosphere is elevated above solar. This finding is consistent with the results of recent Hubble Space Telescope observations. We find marginal evidence that the C abundance was 6 times solar close to the outburst and 2 times solar in the most recent spectra obtained 13.7 years later. However, uncertainties in the abundances do not allow any definitive conclusion regarding temporal abundance variations. The origin of the elevated carbon abundance is discussed in terms of accretion and diffusion while arguments are presented which may rule out ordinary convective dredge‐up and dredge‐up due to forced convection associated with shear mixing.
Exact Three-Dimensional Estimation in Blind Super-Resolution via Convex Optimization

In this work, we propose a general mathematical framework for blind three-dimensional super-resolution theory that recovers the continuous shifts and the amplitudes in a mixture of unknown waveforms upon using the received signal. We prove that the three-dimensional shifts, the amplitudes, and the unknown waveforms can all be recovered precisely and with high probability via convex programming when the number of the observed samples obeys certain complexity bound. This exact recovery holds provided that the shifts are sufficiently separated and that the unknown waveforms lie in a common known low-dimensional subspace that satisfies certain assumptions.
The Mode III Crack Problem in Bonded Materials With a Nonhomogeneous Interfacial Zone

The mode 3 crack problem for two bonded homogeneous half planes was considered. The interfacial zone was modelled by a nonhomogeneous strip in such a way that the shear modulus is a continuous function throughout the composite medium and has discontinuous derivatives along the boundaries of the interfacial zone. The problem was formulated for cracks perpendicular to the nominal interface and was solved for various crack locations in and around the interfacial region. The asymptotic stress field near the tip of a crack terminating at an interface was examined and it was shown that, unlike the corresponding stress field in piecewise homogeneous materials, in this case the stresses have the standard square root singularity and their angular variation was identical to that of a crack in a homogeneous medium. With application to the subcritical crack growth process in mind, the results given include mostly the stress intensity factors for some typical crack geometries and various material combinations.
COMPARISON OF DRAG AND INERTIA COEFFICIENTS FOR A CIRCULAR CYLINDER IN RANDOM WAVES DERIVED FROM DIFFERENT METHODS

This paper presents results from experimental works to investigate wave loading on a vertical circular cylinder in random wave conditions in a wave flume with different water depths . In-line force coefficients (drag and inertia coefficient) are estimated from the measured pressures on cylinder’s surface at different elevations along the length of the cylinder. The wave kinematics are estimated by using different wave theories. Methods of max-min and least-squares (simplified by fit on wave-by-wave basis) are applied to determine force coefficients.
Dynamics of chiral liquid crystals under applied shear

We simulate the alignment dynamics of cholesteric (chiral) rod-like liquid crystals by using a Landau-de Gennes (LdG) expression for microstructure evolution in response to flow. This study is motivated by recent advances in novel cholesteric nanorod dispersions. Prior work on the modelling of cholesterics has suffered from the restriction of helicity to only a single direction, often with a pre-imposed pitch, due to numerical difficulties. This has severely limited cholesteric modelling in regard to both accuracy and experimental relevance. Our simulations avoid this limitation. Relevant forces on rods include solvent-rod drag, nematic alignment, microstructure elasticity and chiral twist. Phase diagrams are developed to demonstrate the response of these systems to variations in chiral and flow forces. Our results indicate that for low shear rates, chiral and elastic forces prevent the rods from moving in response to flow. At high shear rates, the rods tumble and form unique transient structures (combinations of tumbling and cholesteric phases) as flow forces and chiral forces compete. Even if slight alignment is induced at the boundaries, the phase diagram substantially changes, chiefly by constraining the possible chiral phases. This work has immediate relevance to applications which exploit the optical properties of films solidified from cholesteric dispersions. Current address for Kyle S. Conatser: New Deal HS, New Deal, TX 79350, USA
Clebsch parameterization: Basic properties and remarks on its applications

The Clebsch parameterization (u=∇φ+α∇β) has advantages in elucidating structural properties of vector fields; for example, it helps formulating the Hamiltonian form of ideal fluid mechanics, representing topological constraints (Casimir invariants), integrating the Cauchy characteristics of vortex fields, etc. Because of its “nonlinear” formulation, however, there are some difficulties which must be carefully overcome. (1) It is not complete, i.e., for an arbitrary vector field u, we may fail to find three scalar fields (Clebsch parameters) φ, α, and β that satisfy u=∇φ+α∇β globally in space. (2) It is not uniquely determined, i.e., the map (u1,u2,u3)↦(φ,α,β) is not injective. A generalized form such that u=∇φ+∑j=1ναj∇βj is complete if ν=n−1 (n is the space dimension). However, when we need to control the boundary values of φ, αj, and βj (for example, to determine them uniquely), we have to set ν=n.
A multiple-scattering scheme for modelling surface wave propagation in isotropic and anisotropic three-dimensional structures

SUMMARY We present a method to model the propagation of surface waves in Cartesian structures showing isotropic and anisotropic 3-D heterogeneities. It is assumed that the background structure is laterally homogeneous and that the heterogeneities act as secondary sources, producing multiple scattering and coupling between the surface wave modes of the background structure. No far-field approximation is made, enabling in particular the heterogeneities to be located in the vicinity of the source or receiver. The heterogeneities may be strong and extended 3-D bodies or perturbations of layer boundaries. Several applications are presented, including comparison to an exact solution for a cylindrical heterogeneity. The multiple-scattering series is shown to converge for strong heterogeneities of 10 per cent in S-wave velocity over several wavelengths. We analyse the influence of anisotropy and show in particular that some elastic coefficients, which are non-zero in mantle structures with crystals oriented in a non-horizontal flow, are able to distort the surface wave polarizations strongly.
The International Journal of Biostatistics Relative Risk Estimation in Cluster Randomized Trials : A Comparison of Generalized Estimating Equation Methods

Relative risks have become a popular measure of treatment effect for binary outcomes in randomized controlled trials (RCTs). Relative risks can be estimated directly using log binomial regression but the model may fail to converge. Alternative methods are available for estimating relative risks but these have generally only been evaluated for independent data. As some of these methods are now being applied in cluster RCTs, investigation of their performance in this context is needed. We compare log binomial regression and three alternative methods (expanded logistic regression, log Poisson regression and log normal regression) for estimating relative risks in cluster RCTs. Clustering is taken into account using generalized estimating equations (GEEs) with an independence or exchangeable working correlation structure. The results of our large simulation study show that the log binomial GEE generally performs well for clustered data but suffers from convergence problems, as expected. Both the log Poisson GEE and log normal GEE have advantages in certain settings in terms of type I error, bias and coverage. The expanded logistic GEE can perform poorly and is sensitive to the chosen working correlation structure. Conclusions about the effectiveness of treatment often differ depending on the method used, highlighting the need to pre-specify an analysis approach. We recommend pre-specifying that either the log Poisson GEE or log normal GEE will be used in the event that the log binomial GEE fails to converge.
Direct Numerical Simulation of Isothermal Wake: DNS Noise, Strong Anisotropy Turbulence, and Vortex Dislocation Generation Mechanism

The isothermal wake from a circular cylinder at Reynolds number Re = 300 is analyzed numerically by direct numerical simulation (DNS). The DNS noise, anisotropic turbulence, and vortex dislocation mechanism are elucidated as follows: The coordinates x, y, and z are the vertical direction, horizontal direction perpendicular to the cylinder axis, and direction along the cylinder axis, and the velocities u, v, and w are in the x, y, and z directions. 1. The DNS noise in velocity w along the cylinder axis arising in the DNS at Re = 100 was obtained by computation. The DNS noise was verified to have an amplitude of 1 × 10−8 times the amplitudes of the vertical velocity u and the horizontal velocity v, to be neither turbulent nor laminar, and to be the disorderly accumulated result of round-off errors. 2. The streaklines were obtained by DNS at Re = 300, the strong anisotropy in turbulence was determined by power spectrum density (PSD) and, employing these, the mechanism in the wake behavior is discussed. 3. The degree of turbulence anisotropy degree is extremely difficult to determine experimentally but can be shown to be possible by PSD of DNS data. This turbulence anisotropy in the z direction along the cylinder axis is extremely strong. 4. The velocities u and v are time-dependent laminar with extremely weak turbulence, but the velocity w is either turbulent or transitional. 5. The vortex dislocation mechanism can be explained reasonably and clearly by employing the strongly anisotropic turbulence. 6. Because only the velocity w has the turbulence with extremely strong anisotropy, the vortex spirals are clearly generated. By action of the strongly anisotropic turbulence on the vortex spiral, the vortex dislocation is formed.
Application of an extended IEM to multiple surface scattering and backscatter enhancement

In the late 1980s backscattering enhancement and strong depolarization of waves scattered from randomly rough Gaussian surfaces with large rms slopes were observed in optical and millimeter measurements. It was noted that backscattering enhancement was most prominent, when the surface rms slope was of the order of unity, a condition under which multiple surface scattering may dominate. In this study an extended IEM model which includes surface multiple scattering called integral equation model with multiple scattering (IEMM) is applied to interpret this phenomenon. According to this model the conditions for significant multiple surface scattering to occur are (1) the normalized surface height k/spl sigma/>1 and (2) the surface rms slope >0.5. In the analysis of multiple scattering from very rough surfaces it is found that there is a sharp but small peak in the specular direction also. This observation comes directly from the IEMM model and is partially confirmed by the data reported by Ishimaru. Further comparisons of IEMM with experimental data acquired from very rough surfaces show excellent agreements in bistatic scattering including backscattering enhancement.