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.     

Setting local rank constraints by orthogonal projections for image resolution analysis: Application to the determination of a low dose pharmaceutical compound

Raman chemical imaging provides chemical and spatial information about pharmaceutical drug product. By using resolution methods on acquired spectra, the objective is to calculate pure spectra and distribution maps of image compounds. With multivariate curve resolution-alternating least squares, constraints are used to improve the performance of the resolution and to decrease the ambiguity linked to the final solution. Non negativity and spatial local rank constraints have been identified as the most powerful constraints to be used.     

Recent advances on the use of active anodes in environmental electrochemistry

Active anodes, especially those consisting of metal mixed oxides (MMOs) containing Ru and/or Ir oxides, have been applied in the treatment of wastewater, especially when chloride ions are present. Their characteristics continuously drive the study of applications of these materials, be they in the degradation of different organic molecules, the preparation of new electrode materials and in the association of various processes to increase pollutant removal. Thus, this brief review aims to present some of the recent advances in the application of active anode materials in environmental electrochemistry. Focussing on the 2018–2020 period, it is possible to note many applied studies, using commercially available materials, covering a wide range of target pollutants. Still other studies aim to modify the catalyst surfaces to increase the mineralization capacity, and the use of these anodes in the production of free chlorine species to mediate indirect organic reduction is observed.