Closed-form solutions of general second order linear recurrences and applications

Two closed-form solutions of a general second order linear recurrence with variable coefficients are established. The first form is combinatorial in nature and is derived through the use of a set which counts the number of elements which are two units apart. The second form is closely related to continued fractions and is derived through the use of continued fraction-like relation. Several applications including a number of verifications of conjectures produced from the Ramanujan Machine are worked out, which illustrate its versatility in this respect.     

Essential closures and supports of multivariate copulas

We generalize the notion of essential closures and use them to formulate a geometric necessary condition for a set to be the support of a multivariate copula. Furthermore, in some special cases, we derive an explicit formula of the support in terms of essential closures and obtain a stronger necessary condition.     

Luminescent lanthanide coordination polymers with transformative energy transfer processes for physical and chemical sensing applications

The photophysical process of lanthanide(III) ion is based on the 4f-4f transition, which is the Laporte forbidden with narrow emission band and long emission lifetime. The 4f-4f emission process is affected by introducing aromatic organic ligands. In this review, recent progress of one-, two-, and three-dimensional polymer-typed lanthanide complexes, luminescent lanthanide coordination polymers, are focused for physical and chemical sensing applications. Their changeable luminescence depended on the physical and chemical environments come from the energy transfer between lanthanide(III) ions and aromatic organic ligands. The characteristic physical (temperature, pressure, pH and mechanical force) and chemical (adsorption of metal ions and molecules) sensitive luminescence of lanthanide coordination polymers are useful for future sensing applications.     

Influence of β-cyclodextrin complexation on photochemistry of bisphenols in aqueous solutions

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Mechanics of atoms interacting with a carbon nanotorus: optimal configuration and oscillation behaviour

In this paper, we investigate a carbon nanotorus as a caged molecular structure interacting with an atom. Assuming that the atom is located along the central axis perpendicular to the torus, the interaction energy of the system is determined using the continuum approximation together with the Lennard-Jones potential. This approach avoids the intensive computational calculations that are involved in other modelling approaches. Numerical results are presented in terms of dimensionless variables. The results show that the optimal major radius of the torus has a linear relationship with its minor radius when the atom is symmetrically situated along the torus axis. When the atom is offset from this axis, the minimum energy location shifts away from the centre as the ratio of the major and minor radii exceeds the value of 0.90. Finally, the oscillatory behaviour for the carbon atom is investigated. Our findings predict a novel nano-oscillator which can produce frequencies in the gigahertz range.     

Fabrication of a Nitrate Selective Electrode for Determination of Nitrate in Fertilizers by Using Flow Injection Analysis System

A nitrate ion selective electrode (nitrate-ISE) based on pyrrole modification on a common pencil lead was proposed. The lab-made nitrate-ISE was easily constructed by pyrrole polymerization with nitrate ion as the dopant using cyclic voltammetry. The fabricated nitrate-ISE was then coupled with flow injection analysis (FIA) for an automatic system. The flow potentiometry provided working range of 1x10^-4 to 4x10^-3 mol L^-1 of nitrate and allowed sample throughput up to 50 samples h^-1. Linear regression analysis showed good agreement (r²=0.9961) with Nernstian response. This system was applied to determine nitrate-nitrogen (nitrate-N) in fertilizer samples.     

Band gap engineering in silicene: A theoretical study of density functional tight-binding theory

In this work, we performed first principles calculations based on self-consistent charge density functional tight-binding to investigate different mechanisms of band gap tuning of silicene. We optimized structures of silicene sheet, functionalized silicene with H, CH₃ and F groups and nanoribbons with the edge of zigzag and armchair. Then we calculated electronic properties of silicene, functionalized silicene under uniaxial elastic strain, silicene nanoribbons and silicene under external electrical fields. It is found that the bond length and buckling value for relaxed silicene is agreeable with experimental and other theoretical values. Our results show that the band gap opens by functionalization of silicene. Also, we found that the direct band gap at K point for silicene changed to the direct band gap at the gamma point. Also, the functionalized silicene band gap decrease with increasing of the strain. For all sizes of the zigzag silicene nanoribbons, the band gap is near zero, while an oscillating decay occurs for the band gap of the armchair nanoribbons with increasing the nanoribbons width. At finally, it can be seen that the external electric field can open the band gap of silicene. We found that by increasing the electric field magnitude the band gap increases.     

Ocimum basilicum seed mucilage reinforced with montmorillonite for preparation of bionanocomposite film for food packaging applications

Use of nanocomposites is a well-established approach in enhancing the mechanical and barrier properties of bionanocomposite film for food packaging applications. The seed mucilage of Ocimum basilicum was employed for the preparation of bionanocomposite films with montmorillonite (MMT) as nanofiller. The films were prepared by solvent-casting method at varied solution pH (1, 3, 5 and 9) and MMT loading (1%, 3%, 5%, 10%, 15% and 20%). The films were characterized for physical, mechanical and barrier properties in addition to microstructure and X-ray diffraction pattern. XRD analysis revealed the exfoliated dispersion of MMT at pH 9, confirming its effective interaction with the bionanocomposite film. Maximum film tensile strength was achieved at a lower MMT load of 5%. Water vapour permeability reduced with increase in MMT loading up to 5%, followed by an increase at higher MMT loadings. Film formed at pH 9 showed tensile strength of 17.3 ± 0.33 MPa and reduced water vapour permeability (WVP) of 0.21 g mm.m⁻².hr⁻¹.kPa⁻¹.