Visualising concordance

Concordance describes the agreement between m rankings of k objects. Despite the long history of measures of concordance and the recently revived interest in comparison of concordance (c.f. Legendre in J Agric Biol Environ Stat 10(2):226–245, 2005), the task of visualising concordance remained virtually unaddressed. We first show how to depict concordance by simply plotting raw data in parallel coordinates. Then we review further possibilities for depicting concordance using the recently developed plots of inter-rater variability in ordinal ratings (Nelson and Pepe in Stat Methods Med Res 9:475–496, 2000) and plots of correlation matrices (Trosset in J Comput Graph Stat 14(1):1–19, 2005). Next, we propose two novel concordance plots. The concordance bubble-plot is based on raw rank data, while the pin-cushion plot depicts rank differences in polar coordinates. We present visualisations of artificial and real-life datasets with different degree of concordance and identify strong and weak points of the proposed plots. In conclusion, we review some other work related to visualisation of concordance and discuss some other options for constructing novel concordance plots.     

SOME PROPERTIES OF MULTIPLE TAYLOR SERIES AND RANDOM TAYLOR SERIES

Some polar coordinates are used to determine the domain and the ball of convergence of a multiple Taylor series. In this domain and in this ball the series converges, converges absolutely and converges uniformly on any compact set. Growth and other properties of the series may also be studied. For some random multiple Taylor series there are some corresponding properties.     

Exact Harmonic Metric for a Uniformly Moving Schwarzschild Black Hole

The harmonic metric for Schwarzschild black hole with a uniform velocity is presented. In the limit of weak field and low velocity, this metric reduces to the post-Newtonian approximation for one moving point mass. As an application, we derive the dynamics of particle and photon in the weak-field limit for the moving Schwarzschild black hole with an arbitrary velocity. It is found that the relativistic motion of gravitational source can induce an additional centripetal force on the test particle, which may be comparable to or even larger than the conventional Newtonian gravitational force.     

Reflectionless truncation of target area for axially symmetric anisotropic elasticity

This paper presents an approach to numerical simulation of seismic wave propagation in anisotropic elastic media in cylindrical coordinates by means of conservative finite difference scheme on staggered grids. An original low cost domain distension based on Optimal Grids is proposed to restrict computational domain.     

Crystal shapes of cubic mesophases in pure and mixed carboxylic acids observed by optical microscopy

Two different cubic phases in pure (Ia3d cubic space group) and mixed (Im3m cubic space group) thermotropic carboxylic acids are observed by optical microscopy. In unpolarized light, the presence of the cubic phases is identified unambiguously by the observation of facetted single crystals with highly symmetrical shapes. The observed crystal habits are growth shapes, rather than equilibrium shapes. The facetting is described, both at the interfaces with air and with the isotropic liquid phase. The facets correspond to various reticular planes that are discussed in relation with crystallographic data.     

Fluorescence characteristics of Dy ions in calcium fluoroborate glasses

Calcium fluoroborate (CFB) glasses doped with different concentrations of trivalent dysprosium ions were prepared and investigated by the FTIR, optical absorption, photoluminescence and decay analysis. Free-ion Hamiltonian model and Judd-Ofelt theory have been used to analyze the energy level scheme and the spectral intensities of Dy³⁺ ions in CFB glasses. From the emission spectra it is observed that the samples emit intense light yellowish color which is nearer to white light. Chromaticity color coordinates have been calculated and the dominant emission wavelength has also been indicated. Decay curves of ⁴F_9/2 level for the samples with different concentrations have been analyzed using the Inokuti-Hirayama model and the energy transfer and non-radiative decay rates have been determined.     

Perturbation analysis for best approximation and the polar factor by subunitary matrices

This paper is a continuation and improvement over the results of Laszkiewicz and Zietak [BIT, 2006, 46: 345–366], studying perturbation analysis for polar decomposition. Some basic properties of best approximation subunitary matrices are investigated in detail. The perturbation bounds of the polar factor are also derived.      

A coupled-mode sound propagation model with complex effective depth

A coupled-mode sound propagation model with complex effective depth is presented,in order to involve the effect of branch line integral for acoustic field in a range-dependent waveguide.The equations of motion and continuity are used to obtain the coupled equations,which satisfy boundary conditions in the waveguide with varying topography and contain one coupling matrix.Meanwhile,the couplings between discrete and continuous spectrum are dealt with based on complex effective depth theory.Numerical simulations show that the accuracy of transmission loss is improved by the coupled mode model when eigenvalues of trapped modes are located near the branch point.The acoustic field in a non-horizontally stratified waveguide can be calculated efficiently and accurately by this model,and the energy corresponding to trapped modes,leaky modes and branch line integral can be considered adequately.     

On the origin of the anomalous ultraslow solvation dynamics in heterogeneous environments

Many recent experimental studies have reported a surprising ultraslow component (even >10 ns) in the solvation dynamics of a polar probe in an organized assembly, the origin of which is not understood at present. Here we propose two molecular mechanisms in explanation. The first one involves the motion of the ‘buried water’ molecules (both translation and rotation), accompanied by cooperative relaxation (‘local melting’) of several surfactant chains. An estimate of the time is obtained by using an effective Rouse chain model of chain dynamics, coupled with a mean first passage time calculation. The second explanation invokes self-diffusion of the (di)polar probe itself from a less polar to a more polar region. This may also involve cooperative motion of the surfactant chains in the hydrophobic core, if the probe has a sizeable distribution inside the core prior to excitation, or escape of the probe to the bulk from the surface of the self-assembly. The second mechanism should result in the narrowing of the full width of the emission spectrum with time, which has indeed been observed in recent experiments. It is argued that both the mechanisms may give rise to an ultraslow time constant and may be applicable to different experimental situations. The effectiveness of solvation as a dynamical probe in such complex systems has been discussed.