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.     

Electronic and optical properties of Sr3X2 (X=N,P, As,Sb and Bi) compounds: first principles study

ABSTRACT

Direct bandgap semiconductors are very essential to fulfil the demand for the advancement in optoelectronic devices. Therefore it is important to predict new potential candidates having such unique features. In current work, Sr₃X₂ (X=N, P, As, Sb and Bi) compounds have been reported for the first time by well trusted FP-APW+lo method. For the better prediction of the energy band gap, mBJ is used alongwith routine generalised gradient approximation (GGA). The results show small and direct energy band gaps at Γ-Γ symmetry points with magnitude in the range from 0.62?eV (Sr₃P₂) to zero energy band gap (Sr₃Bi₂). In partial density of state Sr-d state and X-p state are contributed in the band structure. The compounds show mostly covalent bonding nature. The frequecy dependent optical properties in the linear optical range are also investigated.