Existence and non-existence of solution for semilinear elliptic equation with harmonic potential and Sobolev critical/supercritical nonlinearities

In this paper, we study the existence and non-existence of the positive solution to a semilinear elliptic equation with the harmonic potential and power type nonlinearity. First, we obtain non-existence result in three space dimension with the Sobolev critical nonlinearity. Next, we prove that there exists a global bifurcation branch with the Sobolev supercritical nonlinearity.     

Tridentate bipyrazole compounds with a side-arm as a new class of antitumor agents

Eight tridentate bipyrazole derivatives with different side arms have been prepared in one step and with good yields. The products were screened for their cytotoxic activity against three tumor cell lines—human breast cancer cell line MDA-MB231, human prostate cancer cell line PC3, and human colorectal cell line LoVo, by use of colorimetric MTT assay. Structure–activity relationships reflected the effect of substituted drugs. Among this series, two compounds had remarkable in-vitro antiproliferative activity against the LoVo cell line with IC50 values ranging from 2.6 to 2.7 μg ml^?1. All the compounds had suitable drug-like characteristics according to Lipinski’s rule.     

Sustainable and rapid preparation of nanosized Fe/Ni-pentlandite particles by mechanochemistry

In recent years, metal-rich sulfides of the pentlandite type (M₉S₈) have attracted considerable attention for energy storage applications. However, common synthetic routes towards pentlandites either involve energy intensive high temperature procedures or solvothermal methods with specialized precursors and non-sustainable organic solvents. Herein, we demonstrate that ball milling is a simple and efficient method to synthesize nanosized bimetallic pentlandite particles (Fe_4.5Ni_4.5S₈, Pn) with an average size of ca. 250 nm in a single synthetic step from elemental- or sulfidic mixtures. We herein highlight the effects of the milling ball quantity, precursor types and milling time on the product quality. Along this line, Raman spectroscopy as well as temperature/pressure monitoring during the milling processes provide valuable insights into mechanistic differences between the mechanochemical Pn-formation. By employing the obtained Pn-nanosized particles as cathodic electrocatalysts for water splitting in a zero-gap PEM electrolyzer we provide a comprehensive path for a potential sustainable future process involving non-noble metal catalysts.

A sustainable and rapid mechanochemical method for the preparation of bimetallic nanosized pentlandite particles as cathode material is developed and tested within zero-gap PEM cells.     

Ready Access to Anhydrous Anionic Lanthanide Acetates by Using Imidazolium Acetate Ionic Liquids as the Reaction Medium

Access to lanthanide acetate coordination compounds is challenged by the tendency of lanthanides to coordinate water and the plethora of acetate coordination modes. A straightforward, reproducible synthetic procedure by treating lanthanide chloride hydrates with defined ratios of the ionic liquid (IL) 1-ethyl-3-methylimidazolium acetate ([C₂mim][OAc]) has been developed. This reaction pathway leads to two isostructural crystalline anhydrous coordination complexes, the polymeric [C₂mim]_n[{Ln₂(OAc)₇}_n] and the dimeric [C₂mim]₂[Ln₂(OAc)₈], based on the ion size and the ratio of IL used. A reaction with an IL : Ln-salt ratio of 5 : 1, where Ln=Nd, Sm, and Gd, led exclusively to the polymer, whilst for the heaviest lanthanides (Dy−Lu) the dimer was observed. Reaction with Eu and Tb resulted in a mixture of both polymeric and dimeric forms. When the amount of IL and/or the size of the cation was increased, the reaction led to only the dimeric compound for all the lanthanide series. Crystallographic analyses of the resulting salts revealed three different types of metal-acetate coordination modes where η²μκ² is the most represented in both structure types.