The a priori Tan Theta Theorem for spectral subspaces

Let A be a self-adjoint operator on a separable Hilbert space H. Assume that the spectrum of A consists of two disjoint components s_0 and s_1 such that the set s_0 lies in a finite gap of the set s_1. Let V be a bounded self-adjoint operator on H off-diagonal with respect to the partition spec(A)=s_0 \cup s_1. It is known that if ||V||<\sqrt{2}d, where d=\dist(s_0,s_1), then the perturbation V does not close the gaps between s_0 and s_1 and the spectrum of the perturbed operator L=A+V consists of two isolated components s'_0 and s'_1 grown from s_0 and s_1, respectively. Furthermore, it is known that if V satisfies the stronger bound ||V||< d then the following sharp norm estimate holds: ||E_L(s'_0)-E_A(s_0)|| \leq sin(arctan(||V||/d)), where E_A(s_0) and E_L(s'_0) are the spectral projections of A and L associated with the spectral sets s_0 and s'_0, respectively. In the present work we prove that this estimate remains valid and sharp also for d \leq ||V||< \sqrt{2}d, which completely settles the issue.Comment: v3: some typos fixed; Examples adde

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

Attitudes of Student Teachers and Teachers Towards Integration: A Short Survey in Bavaria/Germany

The study focuses on attitudes of teachers and student teachers in the field of Special Education in Bavaria towards integration of children with disabilities in regular schools. The results show support for the idea of coeducation. The degree of agreement seems to be influenced by the subject in which people majored in during their studies. Fifty-eight point eight percent of the student teachers majoring in learning disabilities show general agreement, whereas only 37.2 % of the group majoring intellectual disabilities do. Most teachers in the field of Special Education (55.9 %) think integration has a positive impact on school development. 78.8 % (teachers) to 96.3 % (students majoring in intellectual disabilities) share the opinion that the coeducation of children would work well

Das mathematische Leistungsspektrum bei Schülerinnen und Schülern mit sonderpädagogischem Förderbedarft in der Sekundarstufe. Ein explorativer Querschnitt der fünften bis neunten Klassenstufe in Münchner Förderschulen

In der vorliegenden Studie wurden die Mathematikschulleistungen von 124 Schülerinnen und Schüler der 5. bis 9. Klasse aus drei Münchner Förderzentren untersucht. Ziel der Studie war es, das mathematische Leistungsspektrum der Schülerinnen und Schüler mit sonderpädagogischem Förderbedarf in der Sekundarstufe zu ermitteln. Das Spektrum der Schülerinnen und Schüler einer Klasse war dabei sehr heterogen. Generell festzustellen ist, dass die mathematischen Basiskompetenzen, also die Mengen-Zahlen-Kompetenzen und das Konventions- und Regelwissen, bei diesen Schülerinnen und Schüler der Sekundarstufe nicht ausreichend gesichert waren. Erwartungsgemäß waren die mathematischen Kompetenzen in den höheren Klassen weiter entwickelt als in den niedrigeren Jahrgangsstufen. Jedoch geben neben der Klassenstufe auch die Einschätzungen der Lehrerinnen und Lehrer bezüglich des Bedarfs nach individueller Unterstützung der Schülerinnen und Schüler sowie des Stands nach dem Regellehrplan der Schülerinnen und Schüler eine signifikante Varianzaufklärung auf die Schulleistung in Mathematik. Dies stellt eine heterogene Schülerschaft in der Sekundarstufe der Förderschulen dar und zeigt, dass eine Klassenbildung nach Schuljahren nicht zu leistungshomogenen Gruppen führt

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/

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/

The Early “Unnatural” History Following Surgical Repair of Ventricular Septal Defects

Introduction Surgical outcomes for simple ventricular septaldefects (VSD) have been excellent in the past three decades. Forthis project, the timing of resolution of left-sided dilation and mitralregurgitation (MR) following VSD repair was assessed. Methods Echocardiographic data surrounding surgery of 42 consecutivechildren who underwent surgical patch repair of a VSD werereviewed. The echocardiograms were reviewed up to a mean of 12months post-operatively (range 9 - 14 months). Quantitative dataindexed to body surface area including left atrial (LA) volume, mitralvalve annulus diameter, and left ventricular end-diastolic dimension(LVEDD) was analyzed. Results The majority of our pre-surgical cohort had only trace(44%) or no MR (31%), with a small proportion having mild (16%)or moderate MR (9%). No patients had moderate or greater MR followingrepair at follow-up. The median mitral valve annular Z-scorewas 1.8 (SD 1.6; range: -1.2 to 4.1) pre-operatively, improving to a 0.6(range: -1.7 to 2.4; p &lt; 0.001) at follow-up. LA dilation was present in70% of patients, with a median LA volume Z-score of 1.1 (range: -2.6to 15.5), decreasing to 13% median Z-score -1.2 (range: -3.5 to 2.9; p&lt; 0.001) at follow-up. LV dilation was present in 81% of pre-operativepatients with a median LVEDD Z-score of 3.0 (range: -2.0 to 7.9).There was significant improvement in qualitative assessment of LVenlargement (25%) with a median LVEDD Z-score of 0.5 (range:-2.1 to 2.9; p &lt; 0.001) at follow-up. Discharge echocardiogram wasperformed at a mean of 5.7 days (range: 3 - 12 days) following surgery. Conclusions Normalization of LA, mitral valve annulus, and LV sizeoccurred within the first three months in the majority of patients, withsignificant changes occurring within the first post-operative weekfollowing surgical repair for VSD

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