The Translation Invariant Massive Nelson Model: II. The Continuous Spectrum below the Two-Boson Threshold

In this paper we continue the study of the energy-momentum spectrum of a class of translation invariant, linearly coupled, and massive Hamiltonians from non-relativistic quantum field theory. The class contains the Hamiltonians of E. Nelson (J Math Phys 5:1190–1197, 1964) and H. Fröhlich (Adv Phys 3:325–362, 1954). In Møller (Ann Henri Poincaré 6:1091–1135, 2005; Rev Math Phys 18:485–517, 2006) one of us previously investigated the structure of the ground state mass shell and the bottom of the continuous energy-momentum spectrum. Here we study the continuous energy-momentum spectrum itself up to the two-boson threshold, the threshold for energetic support of two-boson scattering states. We prove that non-threshold embedded mass shells have finite multiplicity and can accumulate only at thresholds. We furthermore establish the non-existence of singular continuous energy-momentum spectrum. Our results hold true for all values of the particle-field coupling strength but only below the two-boson threshold. The proof revolves around the construction of a certain relative velocity vector field used to construct a conjugate operator in the sense of Mourre.     

Aquatic Ecotoxicity Testing of Nanoparticles—The Quest To Disclose Nanoparticle Effects

The number of products on the market containing engineered nanoparticles (ENPs) has increased significantly, and concerns have been raised regarding their ecotoxicological effects. Environmental safety assessments as well as relevant and reliable ecotoxicological data are required for the safe and sustainable use of ENPs. Although the number of publications on the ecotoxicological effects and uptake of ENPs is rapidly expanding, the applicability of the reported data for hazard assessment is questionable. A major knowledge gap is whether nanoparticle effects occur when test organisms are exposed to ENPs in aquatic test systems. Filling this gap is not straightforward, because of the broad range of ENPs and the different behavior of ENPs compared to “ordinary” (dissolved) chemicals in the ecotoxicity test systems. The risk of generating false negatives, and false positives, in the currently used tests is high, and in most cases difficult to assess. This Review outlines some of the pitfalls in the aquatic toxicity testing of ENPs which may lead to misinterpretation of test results. Response types are also proposed to reveal potential nanoparticle effects in the aquatic test organisms.     

Synthesis of functionalized, unsymmetrical 1,3,4,6-tetrasubstituted 2,5-diketopiperazines

A general and efficient method for the synthesis of unsymmetrical 1,3,4,6-tetrasubstituted 2,5-diketo- piperazines (DKPs) is described. Cyclization of N-amide alkylated dipeptide methyl esters, followed by alkylation, furnished the corresponding tetrasubstituted DKPs in good overall yields. The influence of steric hindrance in the alkylation reactions appeared to be of lesser importance as long as reactive alkylating agents were used. Furthermore, we have demonstrated the use of tetrasubstituted DKPs as a scaffold for further chemical manipulations to produce novel DKPs with desired properties.     

Identification and characterization of endonuclein binding proteins: evidence of modulatory effects on signal transduction and chaperone activity

Background  

We have previously identified endonuclein as a cell cycle regulated WD-repeat protein that is up-regulated in adenocarcinoma of the pancreas. Now, we aim to investigate its biomedical functions.     

Synthesis of substituted 2-cyanoarylboronic esters

The synthesis of substituted 2-cyanoarylboronic esters is described via lithiation/in situ trapping of the corresponding methoxy-, trifluoromethyl-, fluoro-, chloro-, and bromobenzonitriles. The crude arylboronic esters were obtained in high yields and purities and with good regioselectivities.     

Tuning quadratic nonlinear photonic crystal fibers for zero group-velocity mismatch

We consider an index-guiding silica photonic crystal fiber with a triangular hole pattern and a periodically poled quadratic nonlinearity. By tuning the pitch and the relative hole size, second-harmonic generation with zero group-velocity mismatch is found for any fundamental wavelength above 780 nm. The nonlinear strength is optimized when the fundamental has maximum confinement in the core. The conversion bandwidth allows for femtosecond-pulse conversion, and 4%-180%W(-1)cm(-2) relative efficiencies were found.     

All-silica nanofluidic devices for DNA-analysis fabricated by imprint of sol-gel silica with silicon stamp

We present a simple and cheap method for fabrication of silica nanofluidic devices for single-molecule studies. By imprinting sol-gel materials with a multi-level stamp comprising micro- and nanofeatures, channels of different depth are produced in a single process step. Calcination of the imprinted hybrid sol-gel material produces purely inorganic silica, which has very low autofluorescence and can be fusion bonded to a glass lid. Compared to top-down processing of fused silica or silicon substrates, imprint of sol-gel silica enables fabrication of high-quality nanofluidic devices without expensive high-vacuum lithography and etching techniques. The applicability of the fabricated device for single-molecule studies is demonstrated by measuring the extension of DNA molecules of different lengths confined in the nanochannels.     

On the stability of a polling system with an adaptive service mechanism

We consider a single-server cyclic polling system with three queues where the server follows an adaptive rule: if it finds one of queues empty in a given cycle, it decides not to visit that queue in the next cycle. In the case of limited service policies, we prove stability and instability results under some conditions which are sufficient but not necessary, in general. Then we discuss open problems with identifying the exact stability region for models with limited service disciplines: we conjecture that a necessary and sufficient condition for the stability may depend on the whole distributions of the primitive sequences, and illustrate that by examples. We conclude the paper with a section on the stability analysis of a polling system with either gated or exhaustive service disciplines.     

Point vortex models of bluff body wakes

Periodic point vortex configurations can be used as reduced-order models of vorticity-dominated wakes behind bluff bodies. The staggered Kármán street is considered the canonical representation of these vortex wakes. However, the streamline topology of this configuration is structurally unstable. Slight variations in the intervortex separations cause fluid to wind through the street, which has implications for transport and mixing in vortex wakes. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)