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.     

Cyclometalated Iridium(III) Complexes Containing Semicarbazone Ligands: Synthesis,Characterization, Photophysical and Biological Studies

The synthesis, crystal structure, photophysical properties, and biological activity of the novel bis‐cyclometalated complexes [Ir(ptpy)₂(vnsc)] ( 2 ) and [Ir(ptpy)₂(acsc)] ( 3 ) [ptpy = 2‐(p‐tolyl)pyridinato, vnsc = vanillin semicarbazone, acsc = acetone semicarbazone] are described. The new compounds were prepared by the reaction of [{Ir(μ‐Cl)(ptpy)₂}₂] ( 1 ) with the corresponding semicarbazone ligands under basic conditions. The molecular structure of compound 3 was confirmed by a single‐crystal X‐ray diffraction study. The complex crystallized from chloroform as a mono‐ solvate in the orthorhombic space group Pcab with eight molecules in the unit cell.     

A Remarkably Simple Class of Imidazolium‐Based Lipids and Their Biological Properties

A series of imidazolium salts bearing two alkyl chains in the backbone of the imidazolium core were synthesized, resembling the structure of lipids. Their antibacterial activity and cytotoxicity were evaluated using Gram‐positive and Gram‐negative bacteria and eukaryotic cell lines including tumor cells. It is shown that the length of alkyl chains in the backbone is vital for the antibiofilm activities of these lipid‐mimicking components. In addition to their biological activity, their surface activity and their membrane interactions are shown by film balance and quartz crystal microbalance (QCM) measurements. The structure–activity relationship indicates that the distinctive chemical structure contributes considerably to the biological activities of this novel class of lipids.     

Branched Polymers via ROMP of Termimers

Today's olefin metathesis catalysts show high reactivity, selectivity, and functional group tolerance and allow the design of new syntheses of precisely functionalized polymers. Here the synthesis of a new end‐capping reagent is investigated allowing the introduction of a highly reactive activated ester end‐group at the polymer chain end as well as its prefunctionalization to directly introduce functional moieties. The versatility of this new end‐capping reagent is demonstrated by utilizing it to synthesize a so‐called termimer (a monomer with termination capabilities). Copolymerization of a norbornene derivative with the termimer leads to hyperbranched ring‐opening metathesis polymerization polymers as proven by gel permeation chromatography and MALDI‐ToF‐(matrix‐assisted laser desorption/ionization time of flight) mass spectrometry.

     

Spectral density estimates with partial symmetries and an application to Bahri–Lions-type results

We are concerned with the existence of infinitely many solutions for the problem \(-\Delta u=|u|^{p-2}u+f\) in \(\Omega \), \(u=u_0\) on \(\partial \Omega \), where \(\Omega \) is a bounded domain in \(\mathbb {R}^N\), \(N\ge 3\). This can be seen as a perturbation of the problem with \(f=0\) and \(u_0=0\), which is odd in u. If \(\Omega \) is invariant with respect to a closed strict subgroup of O(N), then we prove infinite existence for all functions f and \(u_0\) in certain spaces of invariant functions for a larger range of exponents p than known before. In order to achieve this, we prove Lieb–Cwikel–Rosenbljum-type bounds for invariant potentials on \(\Omega \), employing improved Sobolev embeddings for spaces of invariant functions.