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.     

Crystallization of Poly(ethylene adipate) within γ-Phase Poly(vinylidene fluoride) Matrix

The effects of PEA on the γ-phase PVDF crystal structure and the crystallization of PEA within the pre-existing γ-phase PVDF spherulites have been investigated by optical microscopy(OM), infrared spectroscopy(IR) and scanning electron microscopy(SEM). The results demonstrate that the γ-phase PVDF spherulites consist of the lamellae exhibiting a highly curved scroll-like morphology and develop preferentially in PEA-rich blend. With increasing PEA concentration, the scroll diameter increases and the scrolls are better separated from each other. PEA crystallizes first in the interspherulitic region and transcrystalline layer develops. Subsequently, the transcrystalline layer of PEA continues to grow within the γ-phase PVDF spherulites, e.g., in the region between the scrolls, until impinging on other PEA transcrystalline layers or spherulites. The crystallization kinetics results indicate that the growth rate of PEA crystals in the intraspherulitic region of γ-phase PVDF shows a positive correlation with content of PEA, but a negative one with the crystallization temperature of γ-phase PVDF.     

A New Approach to Develop a Standardized Method for Simultaneous Analysis of Astragaloside IV and Formononetin in Radix Astragali by High-Performance Thin-Layer Chromatography

JPC – Journal of Planar Chromatography – Modern TLC - A new high-performance thin-layer chromatographic (HPTLC) method has been developed for the simultaneous estimation of...     

A Photoluminescent Ag10Cu6 Cluster Stablized by a PNNP Ligand and Phenylacetylides Selectively and Reversibly Senses Ammonia in Air and Water

A photoluminescent bimetallic cluster [Ag₁₀Cu₆(bdppthi)₂(C≡CPh)₁₂(MeOH)₂(H₂O)](ClO₄)₄ ( 1 , bdppthi=N,N’-bis(diphenylphosphanylmethyl)-tetrahydroimidazole} was synthesized from the PNNP type ligand bdppthi generated in-situ. Upon excitation at 365 nm, 1 exhibited strong phosphorescent emission at 630 nm, which was selectively quenched by NH₃ in air or water. The sensing of NH₃ was rapid and recoverable, with detection limits of 53 ppm (v/v) in N₂ and 21 μmol/L (0.36 ppm, w/w) for NH₃ ⋅ H₂O in water. Cluster 1 could potentially serve as a bifunctional chemical sensor for the efficient detection of ammonia in waste-gas and waste-water.     

Numerical Modeling of Momentum Dispersion in Porous Media Based on the Pore Scale Prevalence Hypothesis

Transport in Porous Media - A macroscopic model that accounts for the effect of momentum dispersion on flows in porous media is proposed. The model is based on the pore scale prevalence hypothesis...