Bitangential interpolation in generalized Schur classes

Bitangential interpolation problems in the class of matrix valued functions in the generalized Schur class are considered in both the open unit disc and the open right half plane, including problems in which the solutions is not assumed to be holomorphic at the interpolation points. Linear fractional representations of the set of solutions to these problems are presented for invertible and singular Hermitian Pick matrices. These representations make use of a description of the ranges of linear fractional transformations with suitably chosen domains that was developed in a previous paper.Comment: Second version, corrected typos, changed subsection 5.6, 47 page

Column reduced rational matrix functions with given null-pole data in the complex plane

AbstractExplicit formulas are given for rational matrix functions which have a prescribed null-pole structure in the complex plane and are column reduced at infinity. A full parametrization of such functions is obtained. The results are specified and developed further for matrix polynomials

Convergence to equilibrium for the discrete coagulation-fragmentation equations with detailed balance

Under the condition of detailed balance and some additional restrictions on the size of the coefficients, we identify the equilibrium distribution to which solutions of the discrete coagulation-fragmentation system of equations converge for large times, thus showing that there is a critical mass which marks a change in the behavior of the solutions. This was previously known only for particular cases as the generalized Becker-D\"oring equations. Our proof is based on an inequality between the entropy and the entropy production which also gives some information on the rate of convergence to equilibrium for solutions under the critical mass.Comment: 28 page

Regularity and mass conservation for discrete coagulation-fragmentation equations with diffusion

We present a new a-priori estimate for discrete coagulation-fragmentation systems with size-dependent diffusion within a bounded, regular domain confined by homogeneous Neumann boundary conditions. Following from a duality argument, this a-priori estimate provides a global $L^2$ bound on the mass density and was previously used, for instance, in the context of reaction-diffusion equations. In this paper we demonstrate two lines of applications for such an estimate: On the one hand, it enables to simplify parts of the known existence theory and allows to show existence of solutions for generalised models involving collision-induced, quadratic fragmentation terms for which the previous existence theory seems difficult to apply. On the other hand and most prominently, it proves mass conservation (and thus the absence of gelation) for almost all the coagulation coefficients for which mass conservation is known to hold true in the space homogeneous case.Comment: 24 page

Predicting death and readmission after intensive care discharge

Background: Despite initial recovery from critical illness, many patients deteriorate after discharge from the intensive care unit (ICU). We examined prospectively collected data in an attempt to identify patients at risk of readmission or death after intensive care discharge. Methods: This was a secondary analysis of clinical audit data from patients discharged alive from a mixed medical and surgical (non-cardiac) ICU. Results: Four hundred and seventy-five patients (11.2%) died in hospital after discharge from the ICU. Increasing age, time in hospital before intensive care admission, Acute Physiology and Chronic Health Evaluation II (APACHE II) score, and discharge Therapeutic Intervention Scoring System (TISS) score were independent risk factors for death after intensive care discharge. Three hundred and eighty-five patients (8.8%) were readmitted to intensive care during the same hospital admission. Increasing age, time in hospital before intensive care, APACHE II score, and discharge to a high dependency unit were independent risk factors for readmission. One hundred and forty-three patients (3.3%) were readmitted within 48 h of intensive care discharge. APACHE II scores and discharge to a high dependency or other ICU were independent risk factors for early readmission. The overall discriminant ability of our models was moderate with only marginal benefit over the APACHE II scores alone. Conclusions: We identified risk factors associated with death and readmission to intensive care. It was not possible to produce a definitive model based on these risk factors for predicting death or readmission in an individual patient.Not peer reviewedAuthor versio

A lattice calculation of vector meson couplings to the vector and tensor currents using chirally improved fermions

We present a quenched lattice calculation of $f_V^\perp/f_V$, the coupling of vector mesons to the tensor current normalized by the vector meson decay constant. The chirally improved lattice Dirac operator, which allows us to reach small quark masses, is used. We put emphasis on analyzing the quark mass dependence of $f_V^\perp/f_V$ and find only a rather weak dependence. Our results at the $\rho$ and $\phi$ masses agree well with QCD sum rule calculations and those from previous lattice studies.Comment: 6 pages, 3 figures, one sentence remove