On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators

We consider one-dimensional Schroedinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians in quantum mechanics, we study properties of the transformations in detail. We show that they can be expressed as the sum of the identity and an integral Hilbert-Schmidt operator. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive the similar self-adjoint operator and also find the associated "charge conjugation" operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem.Comment: 27 page

Euthanasia and other end-of-life decisions: a mortality follow-back study in Belgium

BACKGROUND: This study compares prevalence and types of medical end-of-life decisions between the Dutch-speaking and French-speaking communities of Belgium. This is the first nationwide study that can make these comparisons and the first measurement after implementation of the euthanasia law (2002). METHODS: We performed a mortality follow-back study in 2005-2006. Data were collected via the nationwide Sentinel Network of General Practitioners, an epidemiological surveillance system representative of all Belgian GPs.Weekly, all GPs reported the medical end-of-life decisions among all non-sudden deaths of patients in their practice. We compared the northern Dutch-speaking (60%) and southern French-speaking communities (40%) controlling for population differences. RESULTS: We analysed 1690 non-sudden deaths. An end-of-life decision with possible life-shortening effect was made in 50% of patients in the Dutch-speaking community and 41% of patients in the French-speaking community (OR 1.4; 95%CI, 1.2 to 1.8). Continuous deep sedation until death occurred in 8% and 15% respectively (OR 0.5; 95%CI, 0.4 to 0.7). Community differences regarding the prevalence of euthanasia or physician-assisted suicide were not significant.Community differences were more present among home/care home than among hospital deaths: non-treatment decisions with explicit life-shortening intention were made more often in the Dutch-speaking than in the French-speaking community settings (OR 2.2; 95%CI, 1.2 to 3.9); while continuous deep sedation occurred less often in the Dutch-speaking community settings (OR 0.5; 95%CI, 0.3 to 0.9). CONCLUSION: Even though legal and general healthcare systems are the same for the whole country, there are considerable variations between the communities in type and prevalence of certain end-of-life decisions, even after controlling for population difference

Rationale for the treatment of children with CCSK in the UMBRELLA SIOP-RTSG 2016 protocol

The International Society of Paediatric Oncology-Renal Tumour Study Group (SIOP-RTSG) has developed a new protocol for the diagnosis, treatment, and follow-up monitoring of childhood renal tumours-the UMBRELLA SIOP-RTSG 2016 protocol (the UMBRELLA protocol). This protocol has been designed to continue international collaboration in the treatment of childhood renal tumours and will be implemented in over 50 different countries. Clear cell sarcoma of the kidney, which is a rare paediatric renal tumour that most commonly occurs in childre

On Markov processes with decomposable pseudo-differential generators

The paper is devoted to the study of Markov processes in finite-dimensional convex cones (especially R d and ) with a decomposable generator, i.e. with a generator of the form where every A n acts as a multiplication operator by a positive, not necessarily bounded, continuous function a n (x) and where every ψ n generates a Lévy process, i.e. a process with i.i.d. increments in R d . The following problems are discussed: (i) existence and uniqueness of Markov or Feller processes with a given generator, (ii) continuous dependence of the process on the coefficients a n and the starting points, (iii) well posedness of the corresponding martingale problem, (iv) generalized solutions to the Dirichlet problem, (v) regularity of boundary points