Spectral properties of the Dirichlet-to-Neumann operator for exterior Helmholtz problem and its applications to scattering theory

We prove that the Dirichlet-to-Neumann operator (DtN) has no spectrum in the lower half of the complex plane. We find several application of this fact in scattering by obstacles with impedance boundary conditions. In particular, we find an upper bound for the gradient of the scattering amplitude and for the total cross section. We justify numerical approximations by providing bounds on difference between theoretical and approximated solutions without using any a priory unknown constants

Invisibility in billiards

The question of invisibility for bodies with mirror surface is studied in the framework of geometrical optics. We construct bodies that are invisible/have zero resistance in two mutually orthogonal directions, and prove that there do not exist bodies which are invisible/have zero resistance in all possible directions of incidence

Resonance regimes of scattering by small bodies with impedance boundary conditions

The paper concerns scattering of plane waves by a bounded obstacle with complex valued impedance boundary conditions. We study the spectrum of the Neumann-to-Dirichlet operator for small wave numbers and long wave asymptotic behavior of the solutions of the scattering problem. The study includes the case when $k=0$ is an eigenvalue or a resonance. The transformation from the impedance to the Dirichlet boundary condition as impedance grows is described. A relation between poles and zeroes of the scattering matrix in the non-self adjoint case is established. The results are applied to a problem of scattering by an obstacle with a springy coating. The paper describes the dependence of the impedance on the properties of the material, that is on forces due to the deviation of the boundary of the obstacle from the equilibrium position

Structural insights into thrombolytic activity of destabilase from medicinal leech

Destabilase from the medical leech Hirudo medicinalis belongs to the family of i-type lysozymes. It has two different enzymatic activities: microbial cell walls destruction (muramidase activity), and dissolution of the stabilized fibrin (isopeptidase activity). Both activities are known to be inhibited by sodium chloride at near physiological concentrations, but the structural basis remains unknown. Here we present two crystal structures of destabilase, including a 1.1 Å-resolution structure in complex with sodium ion. Our structures reveal the location of sodium ion between Glu34/Asp46 residues, which were previously recognized as a glycosidase active site. While sodium coordination with these amino acids may explain inhibition of the muramidase activity, its influence on previously suggested Ser49/Lys58 isopeptidase activity dyad is unclear. We revise the Ser49/Lys58 hypothesis and compare sequences of i-type lysozymes with confirmed destabilase activity. We suggest that the general base for the isopeptidase activity is His112 rather than Lys58. pKa calculations of these amino acids, assessed through the 1 μs molecular dynamics simulation, confirm the hypothesis. Our findings highlight the ambiguity of destabilase catalytic residues identification and build foundations for further research of structure–activity relationship of isopeptidase activity as well as structure-based protein design for potential anticoagulant drug development.</p

How Do Microbial Pathogens Make CENs?

This article does not have an abstract

Fluorescent Discrimination between Traces of Chemical Warfare Agents and Their Mimics

An array of fluorogenic probes is able to discriminate between nerve agents, sarin, soman, tabun, VX and their mimics, in water or organic solvent, by qualitative fluorescence patterns and quantitative multivariate analysis, thus making the system suitable for the inthe- field detection of traces of chemical warfare agents as well as to differentiate between the real nerve agents and other related compounds.Ministerio de Economía y Competitividad, Spain (Project CTQ2012- 31611), Junta de Castilla y León, Consejería de Educación y Cultura y Fondo Social Europeo (Project BU246A12-1), the European Commission, Seventh Framework Programme (Project SNIFFER FP7-SEC-2012-312411) and the Swedish Ministry of Defence (no. A403913