Structure and bonding of lanthanide dinitrogen complexes,Ln(N2)1-8

Lanthanide dinitrogen complexes, Ln(N₂) _x (x = 1-8), were investigated by Density Functional Theory computations using the B3LYP exchange-correlation functional in conjunction with quasirelativistic pseudopotentials for Ln. After a recent study on the lanthanum complexes (A. Kovács, Structural Chemistry 2018 , 29, 1825), the present study aimed to probe the changes upon variously filled 4f subshells of Ln on the structures, stabilities, and bonding properties in related complexes of Nd, Ho, and Lu. The bonding properties were assessed on the basis of natural atomic charges, Ln valence orbital populations, and analysis of bonding molecular orbitals.     

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.     

Biodistribution study of free and microencapsulated 6‐methylcoumarin in Wistar rats by HPLC

A sensitive, specific and reproducible HPLC method has been developed and validated for the quantitative determination of 6‐methylcoumarin (6MC) in plasma and other tissues in Wistar rats. A C₁₈ column was used with UV detection at 321 nm and a gradient system consisting of methanol‐deionized water was used as mobile phase. The retention time for 6MC was 14.921 min and no interfering peaks were observed for any of the matrices. Linear relationships (r² > 0.997) were obtained between the peak height ratios and the corresponding biological sample concentrations over the range 0.4–12.8 µg/mL. Precision and accuracy were evaluated; the coefficient of variation and the relative error for all of the organs were <2 and 7%, respectively. The limit of quantitation was 0.20 µg/mL for the heart and 0.30 µg/mL for the other tissues evaluated. This HPLC method was successfully used in the determination of 6MC in the biodistribution study after administration of 200 mg/kg of both 6MC‐free and 6MC‐loaded polymeric microparticles. In this study, extensive 6MC was found, in both free and microencapsulated forms, in all the organs tested. The 6MC‐free showed a range of between 1.7 and 11.5 µg/g, while the microencapsulated 6MC showed concentrations of between 6.35 and 17.7 µg/g, suggesting that 6MC improved absorption rate. Copyright © 2014 John Wiley & Sons, Ltd.