Symmetry of zeros of Lerch zeta-function for equal parameters

For most values of parameters λ and α, the zeros of the Lerch zeta-function L(λ, α, s) are distributed very chaotically. In this paper, we consider the particular case of equal parameters L(λ, λ, s) and show by calculations that the nontrivial zeros either lie extremely close to the critical line σ = 1/2 or are distributed almost symmetrically with respect to the critical line. We also investigate this phenomenon theoretically.     

Evaluation of Redox Activity of Human Myocardium‐derived Mesenchymal Stem Cells by Scanning Electrochemical Microscopy

In this study the redox activity of human myocardium‐derived mesenchymal stem cells (hmMSC) were investigated by redox‐competition (RC‐SECM) and generation‐collection (GC‐SECM) modes of scanning electrochemical microscopy (SECM), using 2‐methylnaphthalene‐1,4‐dione (menadione, MD) as a redox mediator. The redox activity of human healthy and dilated hmMSCs was evaluated by measuring reduction of MD. Measurements were performed by approaching and retracting the UME from the surface of growing hmMSC cells. The current study shows that the RC‐SECM mode can be applied to investigate integrity of cell membranes, whereas the most promising results were observed by using the GC‐SECM mode and applying the Hill's equation for the calculation/fitting of dependencies of electrical current vs menadione concentration. The calculated apparent Michaelis constant (K_M) for the production of menadiol (MDH₂) in the pathological hmMSC cells was 14.4 folds higher compared to that of the healthy hmMSC revealing the lover redox activity of pathological cells. Moreover, the calculated Hill's coefficient n shows a negative cooperative binding between MD and healthy hmMSC and positive cooperative binding between MD and pathological hmMSC. It means that healthy hmMSC is of lower affinity to MD, which is also related to the better membrane integrity of healthy cells. Data of this study demonstrate that SECM can be applied to investigate intracellular redox and membrane changes ongoing in human dilated myocardium‐derived hmMSC in order to improve their functioning and further regenerative potential.     

Facilitating oxygen reduction by silver nanoparticles on lanthanum strontium ferrite cathode

Journal of Solid State Electrochemistry - Single-phase silver (Ag)-doped La0.85-xSr0.15AgxFeO3-δ (x = 0–0.05) materials (LSAF) were synthesized by wet synthesis route and...     

An Enantiopure Hydrogen‐Bonded Octameric Tube: Self‐Sorting and Guest‐Induced Rearrangement

The assembly of a discrete hydrogen‐bonded molecular tube from eight small identical monomers is reported. Tube assembly was accomplished by means of selective heterodimerization between isocytosine and ureidopyrimidinone hydrogen‐bonding motifs embedded in an enantiopure bicyclic building block, leading to the selective formation of an octameric supramolecular tube. Upon introduction of a fullerene guest molecule, the octameric tube rearranges into a tetrameric inclusion complex and the hydrogen‐bonding mode is switched. The dynamic behavior of the system is further explored in solvent‐ and guest‐responsive self‐sorting experiments.     

Mathematical Modelling of the Influence of Ultra‐micro Electrode Geometry on Approach Curves Registered by Scanning Electrochemical Microscopy

Scanning electrochemical microscopy (SECM) is an emerging electroanalytical sensing technique, used to investigate the electrochemical properties of the sample by ultra‐micro‐electrode(UME) scanning probe. UME signal usually is the current, which depends not only on the properties of the evaluated system but also on UME characteristics such as geometry. Variations of UME geometry can decrease accuracy of the measurement, and then correct analysis of the SECM data becomes almost impossible. In the present work, we studied the precision of measurements with three different the most frequent types of defected UME's ((i) recessed‐UME, (ii) outwarded‐UME, (iii) cone‐UME). Measurement results were compared with that obtained with not defected standard‐plane‐UME. Computational experiment was performed with SECM model using diffusion equations with non‐rectangular border conditions to calculate estimated currents for these three types of defected UMEs and to compare them with that for standard‐plane‐UME. In order to test the correctness of the model, computations for recessed‐UME model were compared with data of real‐recessed‐UME experiment.     

Belt-shaped π-systems: relating geometry to electronic structure in a six-porphyrin nanoring

Linear π-conjugated oligomers have been widely investigated, but the behavior of the corresponding cyclic oligomers is poorly understood, despite the recent synthesis of π-conjugated macrocycles such as [n]cycloparaphenylenes and cyclo[n]thiophenes. Here we present an efficient template-directed synthesis of a π-conjugated butadiyne-linked cyclic porphyrin hexamer directly from the monomer. Small-angle X-ray scattering data show that this nanoring is shape-persistent in solution, even without its template, whereas the linear porphyrin hexamer is relatively flexible. The crystal structure of the nanoring-template complex shows that most of the strain is localized in the acetylenes; the porphyrin units are slightly curved, but the zinc coordination sphere is undistorted. The electrochemistry, absorption, and fluorescence spectra indicate that the HOMO-LUMO gap of the nanoring is less than that of the linear hexamer and less than that of the corresponding polymer. The nanoring exhibits six one-electron reductions and six one-electron oxidations, most of which are well resolved. Ultrafast fluorescence anisotropy measurements show that absorption of light generates an excited state that is delocalized over the whole π-system within a time of less than 0.5 ps. The fluorescence spectrum is amazingly structured and red-shifted. A similar, but less dramatic, red-shift has been reported in the fluorescence spectra of cycloparaphenylenes and was attributed to a high exciton binding energy; however the exciton binding energy of the porphyrin nanoring is similar to those of linear oligomers. Quantum-chemical excited state calculations show that the fluorescence spectrum of the nanoring can be fully explained in terms of vibronic Herzberg-Teller (HT) intensity borrowing.