2,147 research outputs found
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 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
Nuclear Effects on the UHE Neutrino-Nucleon Deep Inelastic Scattering Cross Section
Using a recent parametrization of nuclear effects in parton distribution
functions we calculate the neutrino-nucleon cross section at energies relevant
for ultra high energy neutrino telescopes. The modification of the cross
section in comparison with the calculation using parton densities in free
nucleons is of the order of few per cent for the parameter range of interest in
neutrino telescopes (A=10 and E=10 GeV) and it reaches 20 % at the highest
energies (E=10 GeV) and for the largest nuclear size (A=190) considered.Comment: 7 pages, Latex, figures as 3 postscript file
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