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.     

Enantiomeric Cyclic Peptides with Different Caco‐2 Permeability Suggest Carrier‐Mediated Transport

Recently, oral absorption of cyclic hexapeptides was improved by N‐methylation of their backbone amides. However, the number and position of N‐methylations or of solvent exposed NHs did not correlate to intestinal permeability, measured in a Caco‐2 model. In this study, we investigate enantiomeric pairs of three polar and two lipophilic peptides to demonstrate the participation of carrier‐mediated transporters. As expected, all the enantiomeric peptides exhibited identical lipophilicity (logD_7.4) and passive transcellular permeability determined by the parallel artificial membrane permeability assay (PAMPA). However, the enantiomeric polar peptides exhibited different Caco‐2 permeability (P_app) in both directions a–b and b–a. The same trend was observed for one of the lipophilic peptide, whereas the second lipophilic enantiomer pair showed identical Caco‐2 permeability (within the errors). These findings provide the first evidence for the involvement of carrier‐mediated transport for peptides, especially for those of polar nature.     

Recent advances and challenges in the recovery and purification of cellular exosomes

Exosomes are nanovesicles secreted by most cellular types that carry important biochemical compounds throughout the body with different purposes, playing a preponderant role in cellular communication. Because of their structure, physicochemical properties and stability, recent studies are focusing in their use as nanocarriers for different therapeutic compounds for the treatment of different diseases ranging from cancer to Parkinson's disease. However, current bioseparation protocols and methodologies are selected based on the final exosome application or intended use and present both advantages and disadvantages when compared among them. In this context, this review aims to present the most important technologies available for exosome isolation while discussing their advantages and disadvantages and the possibilities of being combined with other strategies. This is critical since the development of novel exosome‐based therapeutic strategies will be constrained to the effectiveness and yield of the selected downstream purification methodologies for which a thorough understanding of the available technological resources is needed.