On the discrete boundary value problem for anisotropic equation

In this paper we consider the discrete anisotropic boundary value problem using critical point theory. Firstly we apply the direct method of the calculus of variations and the mountain pass technique in order to reach the existence of at least one nontrivial solution. Secondly we derive some version of a discrete three critical point theorem which we apply in order to get the existence of at least two nontrivial solutions.     

High-pressure Nucleation of Low-Density Polymorphs**

New polymorphs β and γ of bis-3-nitrophenyl disulphide, crystallized above 0.3 GPa, are less dense than the ambient-pressure polymorph α. This counterintuitive density relation results from the high-entropy nucleation and subsequent kinetic crystallization. The work performed by pressure compensates the high entropy and temperature product, substantiated in varied conformers and increased chemical potential. Pressure-increased viscosity promotes the kinetic polymorphs, in accordance with empirical Ostwald's rule of stages. It contrasts to mechanochemical techniques, favouring high-density polymorphs.     

Bispalladium(II) Complexes of di-p-Pyrirubyrin Derivatives as Promising Near-Infrared Photoacoustic Dyes

The insertion of palladium(II) into di-p-pyrirubyrin results in mutually convertible bimetallic complexes. Post-synthetic functionalization of one of them yielded bispalladium(II) dioxo-di-p-pyrirubyrin and, after demetallation, dioxo-di-p-pyrirubyrin, introducing for the first time the α,β′-pyridin-2-one unit into the macrocyclic frame. Bispalladium(II) di-p-pyrirubyrin 6 , bispalladium(II) dioxo-di-p-pyrirubyrin 9 , and dioxo-di-p-pyrirubyrin 10 absorb and emit light around 1000 nm and are characterized by high photostability. Thus, they are promising candidates for near-infrared photoacoustic dyes, ideally targeting ( 9 ) the wavelength of Yb-based fiber lasers. The incorporation of an α,β′-pyridine moiety into expanded porphyrins opens a highly interesting area of research due to the attractive optical and coordination properties of the resulting molecules.     

A novel double-sampled square-wave voltammetric technique combined with quadruple-disk metallic-glassy carbon electronic tongue for isotonic beverages profiling

This work demonstrates that quadruple-disk electrodes with an innovative design, iridium-platinum, platinum-glassy carbon, and iridium-glassy carbon can effectively function as a single sensor and act as a voltammetric electronic tongue in food profiling. The key strategy used was a novel technique called double-sampled differential square-wave voltammetry (DSSWV), which increased the resolution and enabled extraction of the full, hidden information available in the measuring signals. Four clustering validity indices, namely the Calinski – Harabasz index, Davies – Bouldin index, Silhouette index and gap statistics were employed to select the optimal sensor and methodology for interpreting the current samples. The best expected results were obtained using an iridium-platinum electrode combined with overall cathodic potential modulation using the DSSWV technique. Principal component analysis and polar dendrogram confirmed the correct clustering of different isotonic beverages. However, it was also demonstrated that in some variants of measurement and signal interpretation, it was not possible to group the samples appropriately.