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

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

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

Image charge dynamics in time-dependent quantum transport

In this work we investigate the effects of the electron-electron interaction between a molecular junction and the metallic leads in time-dependent quantum transport. We employ the recently developed embedded Kadanoff-Baym method [Phys. Rev. B 80, 115107 (2009)] and show that the molecule-lead interaction changes substantially the transient and steady-state transport properties. We first show that the mean-field Hartree-Fock (HF) approximation does not capture the polarization effects responsible for the renormalization of the molecular levels neither in nor out of equilibrium. Furthermore, due to the time-local nature of the HF self-energy there exists a region in parameter space for which the system does not relax after the switch-on of a bias voltage. These and other artifacts of the HF approximation disappear when including correlations at the second-Born or GW levels. Both these approximations contain polarization diagrams which correctly account for the screening of the charged molecule. We find that by changing the molecule-lead interaction the ratio between the screening and relaxation time changes, an effect which must be properly taken into account in any realistic time-dependent simulation. Another important finding is that while in equilibrium the molecule-lead interaction is responsible for a reduction of the HOMO-LUMO gap and for a substantial redistribution of the spectral weight between the main spectral peaks and the induced satellite spectrum, in the biased system it can have the opposite effect, i.e., it sharpens the spectral peaks and opens the HOMO-LUMO gap.Comment: 18 pages, 26 figure

Growth of meromorphic solutions of delay differential equations

Necessary conditions are obtained for certain types of rational delay differential equations to admit a non-rational meromorphic solution of hyper-order less than one. The equations obtained include delay Painlev\'e equations and equations solved by elliptic functions

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

A search for flares and mass ejections on young late-type stars in the open cluster Blanco-1

We present a search for stellar activity (flares and mass ejections) in a sample of 28 stars in the young open cluster Blanco-1. We use optical spectra obtained with ESO's VIMOS multi-object spectrograph installed on the VLT. From the total observing time of $\sim$ 5 hours, we find four H$\alpha$ flares but no distinct indication of coronal mass ejections (CMEs) on the investigated dK-dM stars. Two flares show "dips" in their light-curves right before their impulsive phases which are similar to previous discoveries in photometric light-curves of active dMe stars. We estimate an upper limit of $<$4 CMEs per day per star and discuss this result with respect to a semi- empirical estimation of the CME rate of main-sequence stars. We find that we should have detected at least one CME per star with a mass of 1-15$\times10^{16}$ g depending on the star's X-ray luminosity, but the estimated H$\alpha$ fluxes associated with these masses are below the detection limit of our observations. We conclude that the parameter which mainly influences the detection of stellar CMEs using the method of Doppler-shifted emission caused by moving plasma is not the spectral resolution or velocity but the flux or mass of the CME.Comment: Accepted for publication in MNRAS, accepted 2014 June 10, received 2014 June 5, in original form 2014 March 24, 14 pages, 5 figure

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&

Towards zero-shot language modeling

Can we construct a neural language model which is inductively biased towards learning human language? Motivated by this question, we aim at constructing an informative prior for held-out languages on the task of character-level, open-vocabulary language modeling. We obtain this prior as the posterior over network weights conditioned on the data from a sample of training languages, which is approximated through Laplace’s method. Based on a large and diverse sample of languages, the use of our prior outperforms baseline models with an uninformative prior in both zero-shot and few-shot settings, showing that the prior is imbued with universal linguistic knowledge. Moreover, we harness broad language-specific information available for most languages of the world, i.e., features from typological databases, as distant supervision for held-out languages. We explore several language modeling conditioning techniques, including concatenation and meta-networks for parameter generation. They appear beneficial in the few-shot setting, but ineffective in the zero-shot setting. Since the paucity of even plain digital text affects the majority of the world’s languages, we hope that these insights will broaden the scope of applications for language technology