A Redox‐Confused Bismuth(I/III) Triamide with a T‐Shaped Planar Ground State

Reaction of a tethered triamine ligand with Bi(NMe₂)₃ gives a Bi triamide, for which a Bi^I electronic structure is shown to be most appropriate. The T‐shaped geometry at bismuth provides the first structural model for edge inversion in bismuthines and the only example of a planar geometry for pnictogen triamides. Analogous phosphorus compounds exhibit a distorted pyramidal geometry because of different Bi?N and P?N bond polarities. Although considerable Bi^I character is indicated for the title Bi triamide, it exhibits reactivity similar to Bi^III electrophiles, and expresses either a vacant or a filled p orbital at Bi, as evidenced by coordination of either pyridine N‐oxide or W(CO)₅. The product of the former shows evidence of coordination‐induced oxidation state change at bismuth.     

Alkene–Tetrazine Ligation for Imaging Cellular DNA

5‐Vinyl‐2′‐deoxyuridine (VdU) is the first reported metabolic probe for cellular DNA synthesis that can be visualized by using an inverse electron demand Diels–Alder reaction with a fluorescent tetrazine. VdU is incorporated by endogenous enzymes into the genomes of replicating cells, where it exhibits reduced genotoxicity compared to 5‐ethynyl‐2′‐deoxyuridine (EdU). The VdU–tetrazine ligation reaction is rapid (k≈0.02 M ^?1 s^?1) and chemically orthogonal to the alkyne–azide “click” reaction of EdU‐modified DNA. Alkene–tetrazine ligation reactions provide the first alternative to azide–alkyne click reactions for the bioorthogonal chemical labeling of nucleic acids in cells and facilitate time‐resolved, multicolor labeling of DNA synthesis.     

Total harmonic distortion analysis for direct methanol fuel cell anode

In this study, total harmonic distortion (THD) analysis is put forward to illustrate nonlinear behavior of direct methanol fuel cell (DMFC) anode. THD simulations by means of different methanol oxidation kinetics as well as its experimental validation are both carried out. It is shown that the THD model adopting a three-step methanol oxidation mechanism with Kauranen–Frumkin/Temkin kinetics can be used to illustrate the THD variation for DMFC anode qualitatively. The experimental THD response at the frequency range from 0.063 Hz to 0.4 Hz is identified as the reflection of the nonlinearity variation of those kinetic steps involving intermediates in the methanol oxidation. In such a frequency domain, THD value decrease monotonously with decreasing methanol concentration, which notices its accessibility on methanol concentration detection.     

Analyzing the sustainability of harvesting behavior and the relationship to personality traits in a simulated Lotka–Volterra biotope

For the analysis presented in this paper we use experiments to study human behavior in a simulation environment based on a simple Lotka–Volterra predator–prey ecology. The aim is to study the influence of different harvesting strategies and of certain personality traits derived from the Hamburg Personality Inventory (HPI) [Andresen, B., 2002. HPI – Hamburger Persönlichkeitsinventar. Hogrefe, Göttingen] on the outcome in terms of sustainability and economic performance.     

Approximation of conformal mappings by circle patterns

A circle pattern is a configuration of circles in the plane whose combinatorics is given by a planar graph G such that to each vertex of G corresponds a circle. If two vertices are connected by an edge in G, the corresponding circles intersect with an intersection angle in (0, π). Two sequences of circle patterns are employed to approximate a given conformal map g and its first derivative. For the domain of g we use embedded circle patterns where all circles have the same radius decreasing to 0 and with uniformly bounded intersection angles. The image circle pattern has the same combinatorics and intersection angles and is determined from boundary conditions (radii or angles) according to the values of g′ (|g′| or arg g′). For quasicrystallic circle patterns the convergence result is strengthened to C ^∞-convergence on compact subsets.