A nonlinear superposition principle and multibump solutions of periodic Schrödinger equations

In an abstract setting we prove a nonlinear superposition principle for zeros of equivariant vector fields that are asymptotically additive in a well-defined sense. This result is used to obtain multibump solutions for two basic types of periodic stationary Schrödinger equations with superlinear nonlinearity. The nonlinear term may be of convolution type. If the superquadratic term in the energy functional is convex, our results also apply in certain cases if 0 is in a gap of the spectrum of the Schrödinger operator.     

Light extraction via leaky modes in organic light emitting devices

Display and illumination technology require light sources with angular independent emission behaviour. Conversely, a strongly angular dependent spectral emission can be desirable for other applications in information technology or spectroscopy. In order to elucidate the potential of organic light-emitting devices (OLEDs) for the latter fields, we performed experimental and numerical studies of the angular dependent emission characteristics of cavity like OLEDs. The light generated in the organic multilayer structure and guided in leaky modes was coupled out by a prism. Here, a semitransparent gold anode, acting as a hole injection layer, was used to enhance the coupling of leaky modes guided inside the OLED to external modes (Kretschmann configuration). The observed light emission was strongly angle dependent, with the spectral emission peak of the device shifting from a wavelength of 680 nm to 500 nm as the angle is varied between 20° and 70° with respect to the normal of the substrate plane. Also, the emitted light shows a high degree of polarization. The observed behaviour can be predicted quantitatively by simulations, which are based on the transfer matrix formalism.     

Vertex Algebras, Lie Algebras, and Superstrings

We construct Lie algebras from vertex superalgebras and study their structure. They are sometimes generalized Kac–Moody algebras. In some special cases we can calculate the multiplicities of the roots.     

On real Paley-Wiener theorems for certain integral transforms

We prove real Paley-Wiener theorems for the (inverse) Jacobi transform, characterising the space of L²-functions whose image under the Jacobi transform are (smooth) functions with compact support.     

Regioselective alkylation of guanine via diacyloxyglyoxal-N2-acetylguanine adduct to obtain 7-alkylguanine derivatives. Studies on alkylation of guanine I

The acylated guanine-glyoxal adduct (I) has been alkylated with 4-bromobutyl acetate and in the presence of sodium hydride the reaction was regioselective to give 7-alkylguanine.     

Prime Quasientropy and Quasichaos

We construct a prime symmetry relation for integers that is equivalent to Goldbach's conjecture and show that numerical computations of this prime symmetry property strongly resemble a chaotic sequence. We define and examine the notions of global and local prime quasientropies. Finally, we employ the fact that the prime number sequence satisfies the property of deterministic randomness to consider its utility for the field of quantum computation.     

A computationally efficient finite element model with perfectly matched layers applied to scattering from axially symmetric objects

A frequency-domain finite-element (FE) technique for computing the radiation and scattering from axially symmetric fluid-loaded structures subject to a nonsymmetric forcing field is presented. The Berenger perfectly matched layer (PML), applied directly at the fluid-structure interface, makes it possible to emulate the Sommerfeld radiation condition using FE meshes of minimal size. For those cases where the acoustic field is computed over a band of frequencies, the meshing process is simplified by the use of a wavelength-dependent rescaling of the PML coordinates. Quantitative geometry discretization guidelines are obtained from a priori estimates of small-scale structural wavelengths, which dominate the acoustic field at low to mid frequencies. One particularly useful feature of the PML is that it can be applied across the interface between different fluids. This makes it possible to use the present tool to solve problems where the radiating or scattering objects are located inside a layered fluid medium. The proposed technique is verified by comparison with analytical solutions and with validated numerical models. The solutions presented show close agreement for a set of test problems ranging from scattering to underwater propagation.     

Studies on the collision‐induced dissociation of adipoR agonists after electrospray ionization and their implementation in sports drug testing

AdipoR agonists are small, orally active molecules capable of mimicking the protein adiponectin, which represents an adipokine with antidiabetic and antiatherogenic effects. Two adiponectin receptors were reported in the literature referred to as adipoR1 and adipoR2. Activation of these receptors stimulates mitochondrial biogenesis and results in an improved oxidative metabolism (via adipoR1) and increased insulin sensitivity (via adipoR2). Hence, adipoR agonists are potentially performance enhancing substances and targets of proactive and preventive anti‐doping measures. In this study, two adipoR agonists termed AdipoRon and 112254 as well as two isotopically labeled internal standards (ISTDs) were synthesized in three‐step reactions. The products were fully characterized by nuclear magnetic resonance spectroscopy (NMR), mass spectrometry (MS) and density functional theory (DFT) computation. Collision‐induced dissociation pathways following electrospray ionization were suggested based on the determined elemental compositions of product ions, comparison to product ions derived from labeled analogs (ISTDs), H/D‐exchange experiments and the results of DFT calculations. The most abundant product ions were found at m/z 174, tentatively assigned to protonated 1‐benzyl‐1,2,3,4‐tetrahydropyridine for AdipoRon, and m/z 207, suggested as protonated 1‐(4‐methoxybenzyl)piperazine, for 112254. Notably, the loss of the heterocyclic ring (i.e. piperazine and piperidine, respectively) in a supposedly intramolecular elimination reaction was observed in both cases. A qualitative determination of both AdipoR agonists in human plasma was established and fully validated for doping control purposes. Validation items such as recovery (86–89%), specificity, linearity, lower limit of detection (1 ng/ml), intraday (3–18%) and interday (5–16%) precision as well as ion suppression or enhancement were determined. Based on these findings adipoR agonists can be implemented in sports drug testing procedures. Copyright © 2015 John Wiley & Sons, Ltd.