On a frequency function approach to the unique continuation principle

In this survey we discuss the frequency function method so as to study the problem of unique continuation for elliptic partial differential equations. The methods used in the note were mainly introduced by Garofalo and Lin.     

Use of copper-coated fiber as a tunable optical time-delay line in precise timing systems

In this paper we present a novel, time-delay approach using a copper-coated fiber. Piezo optical-fiber stretchers and temperature-controlled fiber spools are normally used for a conventional time-delay lines. A copper-coated fiber preserves the performance of a standard single-mode optical fiber, while at the same time acting as an electrical wire, which can be effectively heated by applying an electrical current. As a result of the significant temperature change, the signal (group) delay can be properly adjusted and controlled. Compared to piezo optical-fiber stretchers and temperature-controlled fiber spools, much shorter lengths of fiber are required and a faster response time can be achieved. This paper also proposes a simple, lumped thermal model and thus a copper-coated fiber can be included in the heat-transfer and response-time calculations of a realistic system that involves surrounding elements (e.g., heatsinks).     

Hydroxylammonium 5‐Nitriminotetrazolates

The hydroxylammonium salts of monodeprotonated 5‐nitriminotetrazole ( 4 ), double deprotonated 5‐nitriminotetrazole ( 5 ), 1‐methyl‐5‐nitriminotetrazole ( 6 ), and 2‐methyl‐5‐nitraminotetrazole ( 7 ) have been prepared in high yield from the corresponding 5‐nitriminotetrazoles as free acids and an aqueous solution of hydroxylamine or the metathesis reactions of hydroxylammonium hydrochloride with the silver salt of the corresponding nitriminotetrazole, respectively. The energetic salts 4 – 7 were fully characterized by single‐crystal X‐ray diffraction ( 4 – 6 ), NMR spectroscopy, IR‐ and Raman spectroscopy as well as DSC measurements. The sensitivities towards impact, friction and electrical discharge were determined. In addition, several detonation parameters (e.g. heat of explosion, detonation velocity) were computed by the EXPLO5.04 computer code based on calculated (CBS‐4M) heats of formation and X‐ray densities.     

Atomic force microscopy reveals bistable configurations of dibenzo[a,h]thianthrene and their interconversion pathway

We investigated dibenzo[a,h]thianthrene molecules adsorbed on ultrathin layers of NaCl using a combined low-temperature scanning tunneling and atomic force microscope. Two stable configurations exist corresponding to different isomers of free nonplanar molecules. By means of excitations from inelastic electron tunneling we can switch between both configurations. Atomic force microscopy with submolecular resolution allows unambiguous determination of the molecular geometry, and the pathway of the interconversion of the isomers. Our investigations also shed new light on contrast mechanisms in scanning tunneling microscopy.     

Direct detection of Δ9-tetrahydrocannabinol in aqueous samples using a homogeneous increasing fluorescence immunoassay (HiFi)

The detection of the major active component of cannabis, Δ9-tetrahydrocannabinol (THC), becomes increasingly relevant due to its widespread abuse. For control purposes, some easy-to-use, sensitive and inexpensive test methods are needed. We have developed a fluorescence immunoassay utilising THC–fluorescein conjugate as tracer. Fluorescence spectroscopy of the conjugate revealed an unusual property: The relatively weak fluorescence of a dilute tracer solution was increased by a factor of up to 5 after binding of a THC-specific antibody. Fluorescence lifetime measurements in aqueous solutions suggested two different tracer conformations both associated with quenching of fluorescein fluorescence by the intramolecular THC moiety. After antibody binding, the tracer enters a third conformation in which fluorescence quenching of fluorescein is completely suppressed. Utilising this property, we established a homogeneous competitive immunoassay (homogeneous increasing fluorescence immunoassay) with low detection limits. The test requires only two reagents, the new tracer molecule and an anti-THC antibody. A single test takes only 8 min. The dynamic detection range for THC is 0.5 to 20 ng/mL in buffer, with a limit of detection (LOD) of 0.5 ng/mL. The test also works in diluted saliva samples (1:10 dilution with buffer) with an LOD of 2 ng/mL and a dynamic range of 2–50 ng/mL.     

Synthesis,spectral characterization,electrochemical properties and antimicrobial screening of sulfur containing acylferrocenes

Several known and eight new sulfur containing acylferrocenes of the general formula FcCO(CH₂)_nSR (where Fc = ferrocenyl, n = 1 or 2 and R = alkyl, 4-bromobenzyl or 2,6-dichlorobenzyl group) were synthesized in order to test their in vitro antimicrobial activity against 11 bacterial and three fungal/yeast strains. It has been shown that only four of the 14 ketones are completely inactive at the tested dose, while the activities of the other ones were noteworthy. All new compounds were well characterized by IR and NMR spectral data, and their electrochemical properties were investigated by cyclic voltammetry. The X-ray crystal structures of two representative ketones are also presented.     

The influence of bending on the performance of flexible carbon black/polymer composite gas sensors

The performance of electronics on flexible substrates suffers under substrate bending leading to reduced device performance. In this article, we highlighted the influence of bending strain on a conductive polymer composite gas sensor and developed a model to investigate the influence of strain. We evaluated the strain influence on the resistance of a gas sensor with respect to sensitivity, filler content, cyclic loading, and electrode orientation. The sensitivity of gas sensors increased with decreasing tensile bending radii. The influence of strain was dominant for gas sensors with less carbon black concentration. Cyclic bending tests showed a decrease of sensor resistance versus time and a plastic deformation. A sensor geometry orientations effect to reduce the sensitivity to bending strain was achieved by aligning the electrode fingers parallel to the strain. A model was successfully implemented to simulate strain influences inside the polymer incorporating the Poisson ratio. We suggest a concept to achieve a strain insensitive gas sensor by creating an orientation between single particles inside the composite. Implementing this results into existing gas sensors will improve the measurement quality and reliability of sensors on flexible substrates. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2013     

One-loop photon–photon scattering in a thermal,deconfining SU(2) Yang–Mills plasma

For a deconfining thermal SU(2) Yang–Mills plasma we discuss the role of (anti)calorons in introducing non-thermal behavior effectively described in terms of Planck’s quantum of action ?$?$. This non-thermality cancels exactly between the ground-state estimate and its free quasiparticle excitations. Kinematic constraints in 4-vertex scattering and the counting of radial loop variables versus the number of independent constraints on them are re-visited. Next, we consider thermal 2→2$2\to 2$ one-loop scattering of the modes remaining massless upon the (anti)caloron induced adjoint Higgs mechanism (thermal ground state after spatial coarse graining). Starting with stringent analytical arguments, we are able to exclude the contribution to photon–photon scattering from diagrams containing at least one three-vertex and, in a next step, a vast majority of all possible configurations involving two four-vertices. By numerical analysis we show that the remaining contribution of the overall S channel is severely suppressed compared those of the T and U channels, meaning that the creation of a pair of massive vector modes by a pair of photons and vice versa practically does not occur in the Yang–Mills plasma. For the T and U channels the domain of loop integration represents less than 10⁻⁷$10^{-7}$ times the volume of the unconstrained integration region. The thus introduced photon–photon correlation should affect the Cosmic Microwave Background’s polarization at low redshift. An adaption of the here-developed methods to the analysis of irreducible bubble diagrams could prove the conjecture of hep-th/0609033 on the termination of the loop expansion of thermodynamical quantities at a finite irreducible order.