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.     

Mononuclear and Dinuclear Copper Complexes of Tridentate Redox-active Ligands with Tunable H-bonding Donors: Structure,Spectroscopy and H+/e− Reactivity

In this research article, we describe the synthesis and characterization of mononuclear and dinuclear Cu complexes bound by a family of tridentate redox-active ligands with tunable H-bonding donors. The mononuclear Cu-anion complexes were oxidized to the corresponding “high-valent” intermediates by oxidation of the redox-active ligand. These species were capable of oxidizing phenols with weak O−H bonds via H-atom abstraction. Thermodynamic analysis of the H-atom abstractions, which included reduction potential measurements, pK_a determination and kinetic studies, revealed that modification of the anion coordinated to the Cu and changes in the H-bonding donor did not lead to major differences in the reactivity of the “high-valent” CuY complexes (Y: hydroxide, phenolate and acetate), which indicated that the tridentate ligand scaffold acts as the H⁺ and e⁻ acceptor.