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.     

The Effect of the Spacer of Bis(biurea) Ligands on the Structure of A2L3‐type (A=anion) Phosphate Complexes

By tuning the length and rigidity of the spacer of bis(biurea) ligands L, three structural motifs of the A₂L₃ complexes (A represents anion, here orthophosphate PO₄^3?), namely helicate, mesocate, and mono‐bridged motif, have been assembled by coordination of the ligand to phosphate anion. Crystal structure analysis indicated that in the three complexes, each of the phosphate ions is coordinated by twelve hydrogen bonds from six surrounding urea groups. The anion coordination properties in solution have also been studied. The results further demonstrate the coordination behavior of phosphate ion, which shows strong tendency for coordination saturation and geometrical preference, thus allowing for the assembly of novel anion coordination‐based structures as in transition‐metal complexes.     

Supramolecular Assembly of Aminoethylene‐Lipopeptide PMO Conjugates into RNA Splice‐Switching Nanomicelles

Phosphorodiamidate morpholino oligomers (PMOs) are oligonucleotide analogs that can be used for therapeutic modulation of pre‐mRNA splicing. Similar to other classes of nucleic acid‐based therapeutics, PMOs require delivery systems for efficient transport to the intracellular target sites. Here, artificial peptides based on the oligo(ethylenamino) acid succinyl‐tetraethylenpentamine (Stp), hydrophobic modifications, and an azide group are presented, which are used for strain‐promoted azide‐alkyne cycloaddition conjugation with splice‐switching PMOs. By systematically varying the lead structure and formulation, it is determined that the type of contained fatty acid and supramolecular assembly have a critical impact on the delivery efficacy. A compound containing linolenic acid with three cis double bonds exhibits the highest splice‐switching activity and significantly increases functional protein expression in pLuc/705 reporter cells in vitro and after local administration in vivo. Structural and mechanistic studies reveal that the lipopeptide PMO conjugates form nanoparticles, which accelerate cellular uptake and that the content of unsaturated fatty acids enhances endosomal escape. In an in vitro Duchenne muscular dystrophy exon skipping model using H2K‐mdx52 dystrophic skeletal myotubes, the highly potent PMO conjugates mediate significant splice‐switching at very low nanomolar concentrations. The presented aminoethylene‐lipopeptides are thus a promising platform for the generation of PMO‐therapeutics with a favorable activity/toxicity profile.