Dichotomous Hamiltonians with Unbounded Entries and Solutions of Riccati Equations

An operator Riccati equation from systems theory is considered in the case that all entries of the associated Hamiltonian are unbounded. Using a certain dichotomy property of the Hamiltonian and its symmetry with respect to two different indefinite inner products, we prove the existence of nonnegative and nonpositive solutions of the Riccati equation. Moreover, conditions for the boundedness and uniqueness of these solutions are established.Comment: 31 pages, 3 figures; proof of uniqueness of solutions added; to appear in Journal of Evolution Equation

Eigenvalue estimates for non-selfadjoint Dirac operators on the real line

We show that the non-embedded eigenvalues of the Dirac operator on the real line with non-Hermitian potential $V$ lie in the disjoint union of two disks in the right and left half plane, respectively, provided that the $L^1-norm$ of $V$ is bounded from above by the speed of light times the reduced Planck constant. An analogous result for the Schr\"odinger operator, originally proved by Abramov, Aslanyan and Davies, emerges in the nonrelativistic limit. For massless Dirac operators, the condition on $V$ implies the absence of nonreal eigenvalues. Our results are further generalized to potentials with slower decay at infinity. As an application, we determine bounds on resonances and embedded eigenvalues of Dirac operators with Hermitian dilation-analytic potentials

Revisiting the anatomy of the right ventricle in the light of knowledge of its development

Controversies continue regarding several aspects of the anatomy of the morphologically right ventricle. There is disagreement as to whether the ventricle should be assessed in bipartite or tripartite fashion, and the number of leaflets to be found in the tricuspid valve. In particular, there is no agreement as to whether a muscular outlet septum is present in the normally constructed heart, nor how many septal components are to be found during normal development. Resolving these issues is of potential significance to those investigating and treating children with congenitally malformed hearts. With all these issues in mind, we have revisited our own experience in investigating the development and morphology of the normal right ventricle. To assess development, we have examined a large number of datasets, prepared by both standard and episcopic microscopy, from human and murine embryos. In terms of gross anatomy, we have compared dissections of normal autopsied hearts with virtual dissections of datasets prepared using computed tomography. Our developmental and postnatal studies, taken together, confirm that the ventricle is best assessed in tripartite fashion, with the three parts representing its inlet, apical trabecular, and outlet components. The ventricular septum, however, has only muscular and membranous components. The muscular part incorporates a small component derived from the muscularised fused proximal outflow cushions, but this part cannot be distinguished from the much larger part that is incorporated within the free-standing muscular infundibular sleeve. We confirm that the tricuspid valve itself has three components, which are located inferiorly, septally, and antero-superiorly.<br/

Gephyrin, the enigmatic organizer at GABAergic synapses

GABAA receptors are clustered at synaptic sites to achieve a high density of postsynaptic receptors opposite the input axonal terminals. This allows for an efficient propagation of GABA mediated signals, which mostly result in neuronal inhibition. A key organizer for inhibitory synaptic receptors is the 93 kDa protein gephyrin that forms oligomeric superstructures beneath the synaptic area. Gephyrin has long been known to be directly associated with glycine receptor β subunits that mediate synaptic inhibition in the spinal cord. Recently, synaptic GABAA receptors have also been shown to directly interact with gephyrin and interaction sites have been identified and mapped within the intracellular loops of the GABAA receptor α1, α2, and α3 subunits. Gephyrin-binding to GABAA receptors seems to be at least one order of magnitude weaker than to glycine receptors (GlyRs) and most probably is regulated by phosphorylation. Gephyrin not only has a structural function at synaptic sites, but also plays a crucial role in synaptic dynamics and is a platform for multiple protein-protein interactions, bringing receptors, cytoskeletal proteins and downstream signaling proteins into close spatial proximity

Revisiting the anatomy of the right ventricle in the light of knowledge of its development

Controversies continue regarding several aspects of the anatomy of the morphologically right ventricle. There is disagreement as to whether the ventricle should be assessed in bipartite or tripartite fashion, and the number of leaflets to be found in the tricuspid valve. In particular, there is no agreement as to whether a muscular outlet septum is present in the normally constructed heart, nor how many septal components are to be found during normal development. Resolving these issues is of potential significance to those investigating and treating children with congenitally malformed hearts. With all these issues in mind, we have revisited our own experience in investigating the development and morphology of the normal right ventricle. To assess development, we have examined a large number of datasets, prepared by both standard and episcopic microscopy, from human and murine embryos. In terms of gross anatomy, we have compared dissections of normal autopsied hearts with virtual dissections of datasets prepared using computed tomography. Our developmental and postnatal studies, taken together, confirm that the ventricle is best assessed in tripartite fashion, with the three parts representing its inlet, apical trabecular, and outlet components. The ventricular septum, however, has only muscular and membranous components. The muscular part incorporates a small component derived from the muscularised fused proximal outflow cushions, but this part cannot be distinguished from the much larger part that is incorporated within the free-standing muscular infundibular sleeve. We confirm that the tricuspid valve itself has three components, which are located inferiorly, septally, and antero-superiorly.<br/

Testbed for the Pellet Launching System for JT-60SA

As part of the European contribution to the large size superconducting tokamak project JT-60SA, a new Pellet Launching System (PLS) is designed and built. The aims of the PLS are to provide efficient fuelling to the plasma and to control and mitigate Edge Localised Modes (ELMs). Two pellet sources, one for fuelling pellets, one for pacing pellets, are delivering pellets to a centrifuge launcher. The centrifuge enables precise launch of pellets according to already proven control schemes. Furthermore, this system opens a way towards a test bed for the EU-DEMO fuelling system. The new PLS has to be completed and commissioned first at the IPP Garching pellet lab and then to be shipped to QST Naka site after having demonstrated its performance. This dedicated test bed has been set up, providing suitable vacuum conditions to operate the PLS in similar conditions (except magnetic field and radiation). Maximum hydrogen throughput is about 400 mbar·L/s per pellet source. Safety issues must be considered for hydrogen inventory of pellet sources (∼100 bar·L each). In a first step, the pellet sources will be put on a test vessel providing inherent safety by a huge volume (10 m³) which makes sure that the hydrogen concentration is below 1% under all circumstances. A hydrogen safety survey prior to assembly confirmed the concept to be followed by an assessment after the installation in order to get the required license for operation. The PLS as a whole, for the time being equipped with two pellet sources, is to be certified according to explosion prevention rules (ATEX) as a product to be shipped to Naka site. To obtain this, an appropriate declaration of explosion zones inside the vacuum system and the use of suitable and certified equipment is mandatory. Such, the integration of this system can be planned and assessed on a clear technical and regulatory basis