Synthesis and Characterization of 5‐Cyanotetrazolide‐Based Ionic Liquids

New salts based on imidazolium, pyrrolidinium, phosphonium, guanidinium, and ammonium cations together with the 5‐cyanotetrazolide anion [C₂N₅]^? are reported. Depending on the nature of cation–anion interactions, characterized by XRD, the ionic liquids (ILs) have a low viscosity and are liquid at room temperature or have higher melting temperatures. Thermogravimetric analysis, cyclic voltammetry, viscosimetry, and impedance spectroscopy display a thermal stability up to 230 °C, an electrochemical window of 4.5 V, a viscosity of 25 mPa s at 20 °C, and an ionic conductivity of 5.4 mS cm^?1 at 20 °C for the IL 1‐butyl‐1‐methylpyrrolidinium 5‐cyanotetrazolide [BMPyr][C₂N₅]. On the basis of these results, the synthesized compounds are promising electrolytes for lithium‐ion batteries.     

Generalized bases of finite groups

Archiv der Mathematik - Motivated by recent results on the minimal base of a permutation group, we introduce a new local invariant attached to arbitrary finite groups. More precisely, a subset...     

Smart Geodesic Tracing in GRworkbench

We have developed a new tool for numerical work in General Relativity: GRworkbench. We discuss how GRworkbench's implementation of a numerically-amenable analogue to Differential Geometry facilitates the development of robust and chart-independent numerical algorithms. We consider, as an example, geodesic tracing on two charts covering the exterior Schwarzschild space-time.     

Heteroclinic orbits between rotating waves of semilinear parabolic equations on the circle

We investigate heteroclinic orbits between equilibria and rotating waves for scalar semilinear parabolic reaction-advection-diffusion equations with periodic boundary conditions. Using zero number properties of the solutions and the phase shift equivariance of the equation, we establish a necessary and sufficient condition for the existence of a heteroclinic connection between any pair of hyperbolic equilibria or rotating waves.     

Solid-phase approach towards the synthesis of functionalized imidazo[1,2-b]pyrazol-2-ones

The solid-phase synthesis of a series of imidazo[1,2-b]pyrazol-2-ones, an interesting 5,5-fused ring system, based on diverse set of hydrazine acids and malanonitriles is described. The method involves formation of 5-aminopyrazoles on solid support and subsequent cyclizative cleavage off the resin. Compounds were obtained in acceptable to excellent yields and are suitable for biological evaluation without further purification.     

Poisson algebras associated to quasi-Hopf algebras

We define admissible quasi-Hopf quantized universal enveloping (QHQUE) algebras by ?-adic valuation conditions. We show that any QHQUE algebra is twist-equivalent to an admissible one. We prove a related statement: any associator is twist-equivalent to a Lie associator. We attach a quantized formal series algebra to each admissible QHQUE algebra and study the resulting Poisson algebras.