Finite-order meromorphic solutions and the discrete Painleve equations

Let w(z) be a finite-order meromorphic solution of the second-order difference equation w(z+1)+w(z-1) = R(z,w(z)) (eqn 1) where R(z,w(z)) is rational in w(z) and meromorphic in z. Then either w(z) satisfies a difference linear or Riccati equation or else equation (1) can be transformed to one of a list of canonical difference equations. This list consists of all known difference Painleve equation of the form (1), together with their autonomous versions. This suggests that the existence of finite-order meromorphic solutions is a good detector of integrable difference equations.Comment: 34 page

Difference analogue of the Lemma on the Logarithmic Derivative with applications to difference equations

The Lemma on the Logarithmic Derivative of a meromorphic function has many applications in the study of meromorphic functions and ordinary differential equations. In this paper, a difference analogue of the Logarithmic Derivative Lemma is presented and then applied to prove a number of results on meromorphic solutions of complex difference equations. These results include a difference analogue of the Clunie Lemma, as well as other results on the value distribution of solutions.Comment: 12 pages. To appear in the Journal of Mathematical Analysis and Application

Nevanlinna theory for the difference operator

Certain estimates involving the derivative $f\mapsto f'$ of a meromorphic function play key roles in the construction and applications of classical Nevanlinna theory. The purpose of this study is to extend the usual Nevanlinna theory to a theory for the exact difference $f\mapsto \Delta f=f(z+c)-f(z)$. An $a$-point of a meromorphic function $f$ is said to be $c$-paired at z\in\C if $f(z)=a=f(z+c)$ for a fixed constant c\in\C. In this paper the distribution of paired points of finite-order meromorphic functions is studied. One of the main results is an analogue of the second main theorem of Nevanlinna theory, where the usual ramification term is replaced by a quantity expressed in terms of the number of paired points of $f$. Corollaries of the theorem include analogues of the Nevanlinna defect relation, Picard's theorem and Nevanlinna's five value theorem. Applications to difference equations are discussed, and a number of examples illustrating the use and sharpness of the results are given.Comment: 19 page

Ternary nucleation of H_2SO_4, NH_3 and H_2O

A classical theory of the ternary homogeneous nucleation of sulfuric acid—ammonia—water is presented. For NH3 mixing ratios exceeding 1 ppt, the presence of ammonia enhances the binary (sulfuric acid—water) nucleation rate by several orders of magnitude. However, the limiting component for ternary nucleation—as for binary nucleation—is sulfuric acid. The sulfuric acid concentration needed for significant ternary nucleation is several orders of magnitude below that required in binary case

Value Efficiency Analysis of Academic Research [Updated 19 August 1998]

We propose a systematic approach to analyzing academic research performance at universities and research institutes. The analysis of research performance based on a set of (abstract) criteria which are relevant from the decision maker's point of view. The scales for these criteria are defined by means of concrete indicators. All indicators, are, however, not necessarily quantitative. Qualitative information is quantified using appropriate analytical tools. Once the criteria and indicators have been agreed upon and quantified, data on the research units is collected and a Value Efficiency Analysis is performed. The efficiency of research units is defined in the spirit of Data Envelopment Analysis (DEA), complemented with a decision makers (Rector in the European university system) preference information. This information is obtained by asking the decision maker to locate a point on the efficient frontier having the most preferred input and output values. Our approach and the accompanying Decision Support System enables a university to allocate resources more efficiently for its research units. Using data from the Helsinki School of Economics, we describe how our approach can be used

Investigating magnetic activity in very stable stellar magnetic fields: long-term photometric and spectroscopic study of the fully convective M4 dwarf V374 Peg

The ultrafast-rotating ($P_\mathrm{rot}\approx0.44 d$) fully convective single M4 dwarf V374 Peg is a well-known laboratory for studying intense stellar activity in a stable magnetic topology. As an observable proxy for the stellar magnetic field, we study the stability of the light curve, and thus the spot configuration. We also measure the occurrence rate of flares and coronal mass ejections (CMEs). We analyse spectroscopic observations, $BV(RI)_C$ photometry covering 5 years, and additional $R_C$ photometry that expands the temporal base over 16 years. The light curve suggests an almost rigid-body rotation, and a spot configuration that is stable over about 16 years, confirming the previous indications of a very stable magnetic field. We observed small changes on a nightly timescale, and frequent flaring, including a possible sympathetic flare. The strongest flares seem to be more concentrated around the phase where the light curve indicates a smaller active region. Spectral data suggest a complex CME with falling-back and re-ejected material, with a maximal projected velocity of $\approx$675km/s. We observed a CME rate much lower than expected from extrapolations of the solar flare-CME relation to active stars.Comment: 15 figures, 4 tables, accepted for publication in A&

FK Comae Berenices, King of Spin: The COCOA-PUFS Project

COCOA-PUFS is an energy-diverse, time-domain study of the ultra-fast spinning, heavily spotted, yellow giant FK Com (HD117555; G4 III). This single star is thought to be a recent binary merger, and is exceptionally active by measure of its intense ultraviolet and X-ray emissions, and proclivity to flare. COCOA-PUFS was carried out with Hubble Space Telescope in the UV (120-300 nm), using mainly its high-performance Cosmic Origins Spectrograph, but also high-precision Space Telescope Imaging Spectrograph; Chandra X-ray Observatory in the soft X-rays (0.5-10 keV), utilizing its High-Energy Transmission Grating Spectrometer; together with supporting photometry and spectropolarimetry in the visible from the ground. This is an introductory report on the project. FK Com displayed variability on a wide range of time scales, over all wavelengths, during the week-long main campaign, including a large X-ray flare; "super-rotational broadening" of the far-ultraviolet "hot-lines" (e.g., Si IV 139 nm (T~80,000 K) together with chromospheric Mg II 280 nm and C II 133 nm (10,000-30,000 K); large Doppler swings suggestive of bright regions alternately on advancing and retreating limbs of the star; and substantial redshifts of the epoch-average emission profiles. These behaviors paint a picture of a highly extended, dynamic, hot (10 MK) coronal magnetosphere around the star, threaded by cooler structures perhaps analogous to solar prominences, and replenished continually by surface activity and flares. Suppression of angular momentum loss by the confining magnetosphere could temporarily postpone the inevitable stellar spindown, thereby lengthening this highly volatile stage of coronal evolution.Comment: to be published in ApJ

Comparing apples and oranges: assessment of the relative video quality in the presence of different types of distortions

<p>Abstract</p> <p>Video quality assessment is essential for the performance analysis of visual communication applications. Objective metrics can be used for estimating the relative quality differences, but they typically give reliable results only if the compared videos contain similar types of quality distortion. However, video compression typically produces different kinds of visual artifacts than transmission errors. In this article, we focus on a novel subjective quality assessment method that is suitable for comparing different types of quality distortions. The proposed method has been used to evaluate how well different objective quality metrics estimate the relative subjective quality levels for content with different types of quality distortions. Our conclusion is that none of the studied objective metrics works reliably for assessing the co-impact of compression artifacts and transmission errors on the subjective quality. Nevertheless, we have observed that the objective metrics' tendency to either over- or underestimate the perceived impact of transmission errors has a high correlation with the spatial and temporal activity levels of the content. Therefore, our results can be useful for improving the performance of objective metrics in the presence of both source and channel distortions.</p

Statistical Properties of Galactic Starlight Polarization

We present a statistical analysis of Galactic interstellar polarization from the largest compilation available of starlight data. The data comprises ~ 9300 stars of which we have selected ~ 5500 for our analysis. We find a nearly linear growth of mean polarization degree with extinction. The amplitude of this correlation shows that interstellar grains are not fully aligned with the Galactic magnetic field, which can be interpreted as the effect of a large random component of the field. In agreement with earlier studies of more limited scope, we estimate the ratio of the uniform to the random plane-of-the-sky components of the magnetic field to be B_u/B_r = 0.8. Moreover, a clear correlation exists between polarization degree and polarization angle what provides evidence that the magnetic field geometry follows Galactic structures on large-scales. The angular power spectrum C_l of the starlight polarization degree for Galactic plane data (|b| < 10 deg) is consistent with a power-law, C_l ~ l^{-1.5} (where l ~ 180 deg/\theta is the multipole order), for all angular scales \theta > 10 arcmin. An investigation of sparse and inhomogeneous sampling of the data shows that the starlight data analyzed traces an underlying polarized continuum that has the same power spectrum slope, C_l ~ l^{-1.5}. Our findings suggest that starlight data can be safely used for the modeling of Galactic polarized continuum emission at other wavelengths.Comment: 31 pages, 11 figures. Minor corrections and some clarifications included. Matches version accepted for publication by the Astrophysical Journa

Challenges for evaluating process-based models of gas exchange at forest sites with fetches of various species

Physiologically-based (or process-based) models are commonly applied to describe plant responses mechanistically in dependence on environmental conditions. They are increasingly evaluated with eddy-covariance measurements that integrate carbon and water exchange of an area of several hectares (called the fetch). However, almost all models applied to date in such exercises have considered only the dominant tree species and neglected other species that contributed to the measured gas exchange rates-either in separate patches or in mixture. This decreases the transferability of the model from one site to another because the contributions from other species might be different. It is therefore a major challenge in modeling today to separate the measured gas exchanges by sources. In this study, a detailed physiologically-based biosphere model is applied that allows distinguishing between tree species in mixed forests, considering them as «vegetation cohorts» that interact with each other. The sensitivity of the model to different assumptions about how different tree species contribute to an integrated measurement of standscale gas exchange is investigated. The model exercise is carried out for a forest site in Finland with dominant Scots pine but presence of significant amounts of Norway spruce and birch. The results demonstrate that forest structure affects simulated gas exchange rates indicating a possible importance of considering differences in physiological properties at the species level. It is argued that the variation of stand structure within the range of eddy-covariance measurements should be better accounted for in models and that inventory measurements need to consider this variation