Variational principles for self-adjoint operator functions arising from second-order systems

Variational principles are proved for self-adjoint operator functions arising from variational evolution equations of the form $$\langle\ddot{z}(t),y \rangle + \mathfrak{d}[\dot{z} (t), y] + \mathfrak{a}_0 [z(t),y] = 0.$$ Here $\mathfrak{a}_0$ and $\mathfrak{d}$ are densely defined, symmetric and positive sesquilinear forms on a Hilbert space $H$. We associate with the variational evolution equation an equivalent Cauchy problem corresponding to a block operator matrix $\mathcal{A}$, the forms $$\mathfrak{t}(\lambda)[x,y] := \lambda^2\langle x,y\rangle + \lambda\mathfrak{d}[x,y] + \mathfrak{a}_0[x,y],$$ where $\lambda\in \mathbb C$ and $x,y$ are in the domain of the form $\mathfrak{a}_0$, and a corresponding operator family $T(\lambda)$. Using form methods we define a generalized Rayleigh functional and characterize the eigenvalues above the essential spectrum of $\mathcal{A}$ by a min-max and a max-min variational principle. The obtained results are illustrated with a damped beam equation.Comment: to appear in Operators and Matrice

Viewpoints: Hindu-Christian Dialogue in Austria/Vienna as a Typical Example for Interreligious Dialogue

According to the Indian Embassy at present 4800 people from India live in Austria. Among them are approximately 1000 Hindus. Most of the Hindus live in Vienna. Hinduism does not belong to the religious communities -- like Islam or Buddhism -- which are acknowledged by the Austrian State. Therefore Hindu children, who visit Austrian schools, are registered with the notice no religion. In Austria Hindus represent a very small minority. Nevertheless several institutions and organisations are occupied with Hindu-Christian dialogue in quite different ways

Measuring the Overall Complexity of Graphical and Textual IEC 61131-3 Control Software

Software implements a significant proportion of functionality in factory automation. Thus, efficient development and the reuse of software parts, so-called units, enhance competitiveness. Thereby, complex control software units are more difficult to understand, leading to increased development, testing and maintenance costs. However, measuring complexity is challenging due to many different, subjective views on the topic. This paper compares different complexity definitions from literature and considers with a qualitative questionnaire study the complexity perception of domain experts, who confirm the importance of objective measures to compare complexity. The paper proposes a set of metrics that measure various classes of software complexity to identify the most complex software units as a prerequisite for refactoring. The metrics include complexity caused by size, data structure, control flow, information flow and lexical structure. Unlike most literature approaches, the metrics are compliant with graphical and textual languages from the IEC 61131-3 standard. Further, a concept for interpreting the metric results is presented. A comprehensive evaluation with industrial software from two German plant manufacturers validates the metrics' suitability to measure complexity.Comment: 8 pages, https://ieeexplore.ieee.org/abstract/document/9444196

Multidisciplinary Late Effects Clinics for Childhood Cancer Survivors in Germany - a Two-Center Study

Background: Childhood cancer survivors are at risk for therapy-related sequelae and, therefore, require long-term follow-up. At 2 university hospitals in Germany collaborative multidisciplinary late effects clinics were installed to provide specialized care and to evaluate the current health status of these patients in a clinical setting. Patients andMethods: Every patient who visited the late effects clinics at the university hospital in Lübeck and Erlangen over a period of 3 years and met the inclusion criteria was included in the study. Patients' characteristics as well as cancer diagnosis, treatment related factors and the prevalence of chronic health conditions were assessed. Results: 220 patients attended the late effects clinics during the observation period. The median follow-up period was 16 years (range 5-45 years). In total over 64% of the patients were affected by at least 1 chronic health condition, including endocrine disruptions in 19.1% of the patients. Moreover, secondary neoplasms occurred in 9.1% of the study participants. Conclusion: German childhood cancer survivors are affected by multiple therapy-related sequelae. A comprehensive network of late effects clinics should be established to ensure specialized and risk-adapted care for every childhood cancer survivor in Germany

Permafrost thaw subsidence of Siberian yedoma: field measurements and TerraSAR-X interferometry

In permafrost active layer cycles of excess ice formation in winter and loss in summer result in seasonal vertical movements of the ground in both directions. Additionally, relatively uniform thawing of the ice-rich layer at the permafrost table, contributing to irreversible lowering of the surface, was reported for a number of Arctic locations. We use a simple method to quantify surface lowering (subsidence) and uplift in the Lena River Delta, Siberian Arctic, using more than 30 reference rods (fiberglass and metal) installed deeply in permafrost. We repeatedly measured the length of a rod part, which is emerged above the ground, in 2013-2017. Measurements show seasonal subsidence in a range from 0 to 4.6 cm (median: 1.6 cm; 8 measurements) in the cold summer of 2013 and from 0.8 to 8.6 cm (median: 4.8 cm; 31 measurements) in the warm summer of 2014. A pronounced multi-year subsidence of 9.3±5.7 cm was measured in the end of summer 2017 relative to the initial measurements in spring 2013. Additionally, we observed high spatial variability of subsidence even at the sub-meter scale. Differential Synthetic Aperture Radar Interferometry (DInSAR), most often used to measure ground displacement caused by tectonic or volcanic processes, is adapted now for the detection of subsidence in permafrost. Our study tests the viability of repeat pass (11 days) TerraSAR-X (TSX) data for the detection of thaw subsidence over the same study area. Due to TSX short wavelength and, therefore, shallow penetration depth, interferometry is strongly hampered by poor phase coherence. We built a stack of 11-day interferograms for the summer of 2013 where coherence of some single interferograms was on the edge of the acceptable. The stack showed only a minor subsidence with a mean of 0.3±0.3 cm over the studied area. Given the discrepancy between the DInSAR and field data we discuss the limitations of TSX data for an accurate representation of permafrost thaw subsidence

Synthesis and Biological Evaluation of a Novel Pentagastrin-Toxin Conjugate Designed for a Targeted Prodrug Mono-therapy of Cancer

A novel carbamate prodrug 2 containing a pentagastrin moiety was synthesized. 2 was designed as a detoxified analogue of the highly cytotoxic natural antibiotic duocarmycin SA (1) for the use in a targeted prodrug monotherapy of cancers expressing cholecystokinin (CCK-B)/gastrin receptors. The synthesis of prodrug 2 was performed using a palladium-catalyzed carbonylation of bromide 6, followed by a radical cyclisation to give the pharmacophoric unit 10, coupling of 10 to the DNA-binding subunit 15 and transformation of the resulting seco-drug 3b into the carbamate 2 via addition of a pentagastrin moiety

Trafficking defects and loss of ligand binding are the underlying causes of all reported DDR2 missense mutations found in SMED-SL patients

Spondylo-meta-epiphyseal dysplasia (SMED) with short limbs and abnormal calcifications (SMED-SL) is a rare, autosomal recessive human growth disorder, characterized by disproportionate short stature, short limbs, short broad fingers, abnormal metaphyses and epiphyses, platyspondyly and premature calcifications. Recently, three missense mutations and one splice-site mutation in the DDR2 gene were identified as causative genetic defects for SMED-SL, but the underlying cellular and biochemical mechanisms were not explored. Here we report a novel DDR2 missense mutation, c.337G>A (p.E113K), that causes SMED-SL in two siblings in the United Arab Emirates. Another DDR2 missense mutation, c.2254C>T (p.R752C), matching one of the previously reported SMED-SL mutations, was found in a second affected family. DDR2 is a plasma membrane receptor tyrosine kinase that functions as a collagen receptor. We expressed DDR2 constructs with the identified point mutations in human cell lines and evaluated their localization and functional properties. We found that all SMED-SL missense mutants were defective in collagen-induced receptor activation and that the three previously reported mutants (p.T713I, p.I726R and p.R752C) were retained in the endoplasmic reticulum. The novel mutant (p.E113K), in contrast, trafficked normally, like wild-type DDR2, but failed to bind collagen. This finding is in agreement with our recent structural data identifying Glu113 as an important amino acid in the DDR2 ligand-binding site. Our data thus demonstrate that SMED-SL can result from at least two different loss-of-function mechanisms: namely defects in DDR2 targeting to the plasma membrane or the loss of its ligand-binding activity