Integral Representations of the Large and Little Schröder Numbers

In the paper, the authors establish several integral representations for the generating functions of the large and little Schröder numbers and for the large and little Schröder numbers.     

Mesoscopic Modeling of Capillarity-Induced Two-Phase Transport in a Microfluidic Porous Structure

Mesoscopic modeling at the pore scale offers great promise in exploring the underlying structure transport performance of flow through porous media. The present work studies the fluid flow subjected to capillarity-induced resonance in porous media characterized by different porous structure and wettability. The effects of porosity and wettability on the displacement behavior of the fluid flow through porous media are discussed. The results are presented in the form of temporal evolution of percentage saturation and displacement of the fluid front through porous media. The present study reveals that the vibration in the form of acoustic excitation could be significant in the mobilization of fluid through the porous media. The dependence of displacement of the fluid on physicochemical parameters like wettability of the surface, frequency along with the porosity is analyzed. It was observed that the mean displacement of the fluid is more in the case of invading fluid with wetting phase where the driving force strength is not so dominant.     

Three-term polynomial progressions in subsets of finite fields

We prove that the group of diffeomorphisms of the interval [0, 1] contains surface groups whose action on (0, 1) has no global fix point and such that only countably many points of the interval (0, 1) have non-trivial stabiliser.     

Conversion of Methanol to Aromatic-Rich Gasoline over High-Efficiency Bifunctional Catalysts: Green Synthesis of GaZSM-5 Zeolites via Dry-Gel Conversion Strategy

Russian Journal of Applied Chemistry - Nanoscale ZSM-5 (AlZ5-D) and Ga-substituted ZSM-5 zeolites ((Al,Ga)Z5-D and GaZ5-D) were synthesized by a green dry-gel conversion strategy. For comparison,...     

Strategies for Improving the Catalytic Performance of 2D Covalent Organic Frameworks for Hydrogen Evolution and Oxygen Evolution Reactions

Hydrogen evolution reaction (HER) and oxygen evolution reaction (OER) have been deemed as clean and sustainable strategies to solve the energy crisis and environmental problems. Various catalysts have been developed to promote the process of HER and OER. Among them, two-dimensional covalent organic frameworks (2D COFs) have received great attention due to their diverse and designable structure. In this minireview, we mainly summarize the diverse linkages of 2D COFs and strategies for enhancing the catalytic performance of 2D COFs for HER and OER, such as introducing active building blocks, metal ions and tailored linkages. Furthermore, a brief outlook for the development directions of COFs in the field of HER and OER is provided, expecting to stimulate new opportunities in future research.     

Montmorillonite KSF-Catalyzed Synthesis of 2,2′-(Arylmethylene)bis(3-hydroxy-5,5-dimethylcyclohex-2-en-1-ones) for the Functionalization of MCM-41 Silica Nanoparticles

Russian Journal of Organic Chemistry - A green protocol has been developed for the preparation of 2,2′-(arylmethylene)bis(3-hydroxy-5,5-dimethylcyclohex-2-en-1-ones) following the...