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 evolution and future of influenza pandemic preparedness

The influenza virus is a global threat to human health causing unpredictable yet recurring pandemics, the last four emerging over the course of a hundred years. As our knowledge of influenza virus evolution, distribution, and transmission has increased, paths to pandemic preparedness have become apparent. In the 1950s, the World Health Organization (WHO) established a global influenza surveillance network that is now composed of institutions in 122 member states. This and other surveillance networks monitor circulating influenza strains in humans and animal reservoirs and are primed to detect influenza strains with pandemic potential. Both the United States Centers for Disease Control and Prevention and the WHO have also developed pandemic risk assessment tools that evaluate specific aspects of emerging influenza strains to develop a systematic process of determining research and funding priorities according to the risk of emergence and potential impact. Here, we review the history of influenza pandemic preparedness and the current state of preparedness, and we propose additional measures for improvement. We also comment on the intersection between the influenza pandemic preparedness network and the current SARS-CoV-2 crisis. We must continually evaluate and revise our risk assessment and pandemic preparedness plans and incorporate new information gathered from research and global crises.Subject terms: Influenza virus, Infectious diseases     

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.