Height in splittings of relatively hyperbolic groups

Geometriae Dedicata - Given a finite graph of relatively hyperbolic groups with its fundamental group relatively hyperbolic and edge groups quasi-isometrically embedded and relatively quasiconvex...     

Dual Fluorometric Detection of Fe3+ and Hg2+ Ions in an Aqueous Medium Using Carbon Quantum Dots as a “Turn-off” Fluorescence Sensor

The present study aimed to develop a carbon dots-based fluorescence (FL) sensor that can detect more than one pollutant simultaneously in the same aqueous solution. The carbon dots-based FL sensor has been prepared by employing a facile hydrothermal method using citric acid and ethylenediamine as precursors. The as-synthesized CDs displayed excellent hydrophilicity, good photostability and blue fluorescence under UV light. They have been used as an efficient “turn-off” FL sensor for dual sensing of Fe³⁺ and Hg²⁺ ions in an aqueous medium with high sensitivity and selectivity through a static quenching mechanism. The lowest limit of detection (LOD) for Fe³⁺ and Hg²⁺ ions was found to be 0.406 µM and 0.934 µM, respectively over the concentration range of 0-50 µM. Therefore, the present work provides an effective strategy to monitor the concentration of Fe³⁺ and Hg²⁺ ions simultaneously in an aqueous medium using environment-friendly CDs.

Graphical Abstract

     

Alkaline oxygen evolution: exploring synergy between fcc and hcp cobalt nanoparticles entrapped in N-doped graphene

Herein, we report a Mott-Schottky catalyst by entrapping cobalt nanoparticles inside the N-doped graphene shell (Co@NC). The Co@NC delivered excellent oxygen evolution activity with an overpotential of merely 248 mV at a current density of 10 mA cm^–2 with promising long-term stability. The importance of Co encapsulated in NC has further been demonstrated by synthesizing Co nanoparticles without NC shell. The synergy between the hexagonal close-packed (hcp) and face-centered cubic (fcc) Co plays a major role to improve the OER activity, whereas the NC shell optimizes the electronic structure, improves the electron conductivity, and offers a large number of active sites in Co@NC. The density functional theory calculations have revealed that the hcp Co has a dominant role in the surface reaction of electrocatalytic oxygen evolution, whereas the fcc phase induces the built-in electric field at the interfaces with N-doped graphene to accelerate the H⁺ ion transport.     

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.