Relative Oscillation Theory, Weighted Zeros of the Wronskian, and the Spectral Shift Function

We develop an analog of classical oscillation theory for Sturm-Liouville operators which, rather than measuring the spectrum of one single operator, measures the difference between the spectra of two different operators. This is done by replacing zeros of solutions of one operator by weighted zeros of Wronskians of solutions of two different operators. In particular, we show that a Sturm-type comparison theorem still holds in this situation and demonstrate how this can be used to investigate the finiteness of eigenvalues in essential spectral gaps. Furthermore, the connection with Krein's spectral shift function is established.Comment: 26 page

Traits and stress: keys to identify community effects of low levels of toxicants in test systems

Community effects of low toxicant concentrations are obscured by a multitude of confounding factors. To resolve this issue for community test systems, we propose a trait-based approach to detect toxic effects. An experiment with outdoor stream mesocosms was established 2-years before contamination to allow the development of biotic interactions within the community. Following pulse contamination with the insecticide thiacloprid, communities were monitored for additional 2 years to observe long-term effects. Applying a priori ecotoxicological knowledge species were aggregated into trait-based groups that reflected stressor-specific vulnerability of populations to toxicant exposure. This reduces inter-replicate variation that is not related to toxicant effects and enables to better link exposure and effect. Species with low intrinsic sensitivity showed only transient effects at the highest thiacloprid concentration of 100 μg/l. Sensitive multivoltine species showed transient effects at 3.3 μg/l. Sensitive univoltine species were affected at 0.1 μg/l and did not recover during the year after contamination. Based on these results the new indicator SPEARmesocosm was calculated as the relative abundance of sensitive univoltine taxa. Long-term community effects of thiacloprid were detected at concentrations 1,000 times below those detected by the PRC (Principal Response Curve) approach. We also found that those species, characterised by the most vulnerable trait combination, that were stressed were affected more strongly by thiacloprid than non-stressed species. We conclude that the grouping of species according to toxicant-related traits enables identification and prediction of community response to low levels of toxicants and that additionally the environmental context determines species sensitivity to toxicants

On the structure of eigenfunctions corresponding to embedded eigenvalues of locally perturbed periodic graph operators

The article is devoted to the following question. Consider a periodic self-adjoint difference (differential) operator on a graph (quantum graph) G with a co-compact free action of the integer lattice Z^n. It is known that a local perturbation of the operator might embed an eigenvalue into the continuous spectrum (a feature uncommon for periodic elliptic operators of second order). In all known constructions of such examples, the corresponding eigenfunction is compactly supported. One wonders whether this must always be the case. The paper answers this question affirmatively. What is more surprising, one can estimate that the eigenmode must be localized not far away from the perturbation (in a neighborhood of the perturbation's support, the width of the neighborhood determined by the unperturbed operator only). The validity of this result requires the condition of irreducibility of the Fermi (Floquet) surface of the periodic operator, which is expected to be satisfied for instance for periodic Schroedinger operators.Comment: Submitted for publicatio

Trace Formulas for Schroedinger Operators in Connection with Scattering Theory for Finite-Gap Backgrounds

We investigate trace formulas for one-dimensional Schroedinger operators which are trace class perturbations of quasi-periodic finite-gap operators using Krein's spectral shift theory. In particular, we establish the conserved quantities for the solutions of the Korteweg-de Vries hierarchy in this class and relate them to the reflection coefficients via Abelian integrals on the underlying hyperelliptic Riemann surface.Comment: 14 page

Instability Control in Aircraft Automatic Control Systems

In general, an aircraft as a solid is described by a system of nonlinear non-stationary differential equations. This system includes the equations of motion of the center of mass, the equations of motion relative to the center of mass and kinematic equations

Do contaminants originating from state-of-the-art treated wastewater impact the ecological quality of surface waters?

Since the 1980s, advances in wastewater treatment technology have led to considerably improved surface water quality in the urban areas of many high income countries. However, trace concentrations of organic wastewater-associated contaminants may still pose a key environmental hazard impairing the ecological quality of surface waters. To identify key impact factors, we analyzed the effects of a wide range of anthropogenic and environmental variables on the aquatic macroinvertebrate community. We assessed ecological water quality at 26 sampling sites in four urban German lowland river systems with a 0–100% load of state-of-the-art biological activated sludge treated wastewater. The chemical analysis suite comprised 12 organic contaminants (five phosphor organic flame retardants, two musk fragrances, bisphenol A, nonylphenol, octylphenol, diethyltoluamide, terbutryn), 16 polycyclic aromatic hydrocarbons, and 12 heavy metals. Non-metric multidimensional scaling identified organic contaminants that are mainly wastewater-associated (i.e., phosphor organic flame retardants, musk fragrances, and diethyltoluamide) as a major impact variable on macroinvertebrate species composition. The structural degradation of streams was also identified as a significant factor. Multiple linear regression models revealed a significant impact of organic contaminants on invertebrate populations, in particular on Ephemeroptera, Plecoptera, and Trichoptera species. Spearman rank correlation analyses confirmed wastewater-associated organic contaminants as the most significant variable negatively impacting the biodiversity of sensitive macroinvertebrate species. In addition to increased aquatic pollution with organic contaminants, a greater wastewater fraction was accompanied by a slight decrease in oxygen concentration and an increase in salinity. This study highlights the importance of reducing the wastewater-associated impact on surface waters. For aquatic ecosystems in urban areas this would lead to: (i) improvement of the ecological integrity, (ii) reduction of biodiversity loss, and (iii) faster achievement of objectives of legislative requirements, e.g., the European Water Framework Directive

SELECTION OF TECHNOLOGICAL PARAMETERS FOR SYNTHESIS OF CUBIC ALUMINUM NITRIDE

The technological parameters of cubic aluminum nitride synthesis were studied. The effects of particle size, reaction temperature, reaction time on the synthesis of cubic AIN and the reaction mechanisms were analyzed. The basic methods of synthesis were classified and conditions determined. It is found that formation of metastable cubic phase is connected with supersaturation conditions

Evidence for Exotic J^{PC}=1^{-+} Meson Production in the Reaction pi- p --> eta pi- p at 18 GeV/c

Details of the analysis of the eta pi- system studied in the reaction pi^{-} p --> eta pi^{-} p at 18 GeV/c are given. Separate analyses for the 2 gamma and pi+ pi- pi0 decay modes of the eta are presented. An amplitude analysis of the data indicates the presence of interference between the a(2)(1320)- and a J^{PC}=1^{-+} wave between 1.2 and 1.6 GeV/c^2. The phase difference between these waves shows phase motion not attributable solely to the a(2)(1320)-. The data can be fitted by interference between the a(2)(1320)- and an exotic 1^{-+} resonance with M = 1370 +-16 +50 -30} MeV/c^2 and Gamma = 385 +- 40 +65 -105 MeV/c^2. Our results are compared with those of other experiments.Comment: 50 pages of text and 34 figure