Formation of Supramolecular Nanostructures through in Situ Self-Assembly and Post-Assembly Modification of a Biocatalytically Constructed Dipeptide Hydrazide**

Aqueous self-assembly of short peptides has attracted growing attention for the construction of supramolecular materials for various bioapplications. Herein, we describe how the thermolysin-assisted biocatalytic construction of a dipeptide hydrazide from an N-protected amino acid and an amino acid hydrazide leads to the formation of thermally stable supramolecular hydrogels. In addition, we demonstrate the post-assembly modification of the supramolecular architectures constructed in situ tethering hydrazide groups as a chemical handle by means of fluorescence imaging.     

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.     

Vacuum‐driven fluid manipulation by a piezoelectric diaphragm micropump for microfluidic droplet generation with a rapid system response time

Recently, we developed a convenient microfluidic droplet generation device based on vacuum‐driven fluid manipulation with a piezoelectric diaphragm micropump. In the present study built on our previous work, we investigate the influence of settings applied to the piezoelectric pump, such as peak‐to‐peak drive voltage (V_p‐p) and wave frequency, on droplet generation characteristics. Stepwise adjustments to the drive voltage in ±10‐V_p‐p increments over the range of 200?250 V_p‐p during droplet creation revealed that the droplet generation rate could be reproducibly controlled at a specific drive voltage. The droplet generation rate switched within <0.5 s after the input of a new voltage. Although the droplet generation rate depended on the drive voltage, this setting had almost no influence on droplet size. The frequency over the selected range (50?60 Hz) did not markedly influence the droplet generation rate or droplet size. We show that the current fluid manipulation system can be conveniently used for both droplet generation and for rapid droplet reading, which is required in many microfluidic‐based applications.