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.     

Tween 20-stabilized gold nanoparticles combined with adenosine triphosphate-BODIPY conjugates for the fluorescence detection of adenosine with more than 1000-fold selectivity

This study describes the development of a simple, enzyme-free, label-free, sensitive, and selective system for detecting adenosine based on the use of Tween 20-stabilized gold nanoparticles (Tween 20-AuNPs) as an efficient fluorescence quencher for boron dipyrromethene-conjugated adenosine 5′-triphosphate (BODIPY-ATP) and as a recognition element for adenosine. BODIPY-ATP can interact with Tween 20-AuNPs through the coordination between the adenine group of BODIPY-ATP and Au atoms on the NP surface, thereby causing the fluorescence quenching of BODIPY-ATP through the nanometal surface energy transfer (NSET) effect. When adenosine attaches to the NP surface, the attached adenosine exhibits additional electrostatic attraction to BODIPY-ATP. As a result, the presence of adenosine enhances the efficiency of AuNPs in fluorescence quenching of BODIPY-ATP. The AuNP-induced fluorescence quenching of BODIPY-ATP progressively increased with an increase in the concentration of adenosine; the detection limit at a signal-to-noise ratio of 3 for adenosine was determined to be 60 nM. The selectivity of the proposed system was more than 1000-fold for adenosine over any adenosine analogs and other nucleotides. The proposed system combined with a phenylboronic acid-containing column was successfully applied to the determination of adenosine in urine.     

Fatigue life enhancement by irradiation of 12Cr1MoV steel with a Zr<Superscript>+</Superscript> ion beam. Mesoscale deformation and fracture

The structure and properties of 12Cr1MoV steel irradiated with a zirconium ion beam were studied by optical microscopy, scanning electron microscopy, and micro- and nanoindentation. It is shown that the modification covers the entire cross-section of the irradiated specimens to a depth of 1 mm. The data on irradiation-induced structural changes are used to interpret the changes in mechanical properties of the irradiated specimens under static and cyclic loading. Particular attention is given to analysis of strain estimation by the digital image correlation method.