Note on the Hochschild cohomology of Hopf–Galois extension

We generalize [4, Theorem 4.3] to the case of Hopf–Galois extension, by introducing the cotensor product of a comodule algebra and its opposite algebra, and then give some applications.     

Graph-Theoretical Method to the Existence of Stationary Distribution of Stochastic Coupled Systems

In this paper, by linking Fokker–Planck equations with stochastic coupled systems, a new method is provided to investigate the existence of a stationary distribution of stochastic coupled systems. Based on the graph theory and the Lyapunov method, an appropriate Lyapunov function associated with stationary Fokker–Planck equations is constructed. Moreover, a Lyapunov-type theorem and a coefficients-type criterion are obtained to guarantee the existence of a stationary distribution. Furthermore, theoretical results are applied to explore the existence of a stationary distribution of stochastic predator–prey models with dispersal and a sufficient criterion is presented correspondingly. Finally, a numerical example is given to illustrate the effectiveness of our results.     

Self-supported metal sulphide nanocrystals-assembled nanosheets on carbon paper as efficient counter electrodes for quantum-dot-sensitized solar cells

Developing efficient counter electrodes (CEs) and quantum dots made of earth-abundant and non-toxic elements is essential but still challenging for quantum dot-sensitized solar cells (QDSSCs). Here, we report a facile strategy to prepare self-supported and robust CoS₂ and NiS nanocrystals-assembled nanosheets directly grown on carbon paper (MSx NS@CP) as efficient counter electrodes for QDSSCs. Such CEs integrate the merits of fast electron transfer from interconnected conductive scaffold, efficient mass transfer from hierarchically vertical nanosheet on 3D open substrate, as well as abundant highly active catalytic sites from metal sulphide nanocrystal units. As a result, QDDSCs based on such CoS₂ NS@CP and NiS NS@CP CEs achieve a PCE of 8.88% and 7.53%, respectively. The detailed analyses suggest that CoS₂ NS@CP has the highest catalytic activity and shows the lowest charger transfer resistance, leading to the highest PCE. These findings may inspire the design and exploration of other self-supported efficient CEs by integrating highly active catalysts onto 3D conductive networks for efficient QDSSCs.     

Heat-Resistant Epoxy Polymers of Anhydride Curing

The interaction of UP-643 epoxy-novolac resin with isomethyltetrahydrophthalic anhydride in the presence of the catalysts (azo-compounds of different structure) is studied. Latency of the catalysts is found. The possibility is shown of creating epoxy binders with a long lifetime (10–40 days) at room temperatures, cured at increased temperature up to heat-resistant polymers.