Unfamiliar Aspects of Bäcklund Transformations and an Associated Degasperis–Procesi Equation

We summarize the results of our recent work on Bäcklund transformations (BTs), particularly focusing on the relation between BTs and infinitesimal symmetries. We present a BT for an associated Degasperis–Procesi (aDP) equation and its superposition principle and investigate the solutions generated by applying this BT. Following our general methodology, we use the superposition principle of the BT to generate the infinitesimal symmetries of the aDP equation.     

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.     

Influence of Polarity and Activation Energy in Microwave–Assisted Organic Synthesis (MAOS)

The aim of this work was to determine the parameters that have decisive roles in microwave-assisted reactions and to develop a model, using computational chemistry, to predict a priori the type of reactions that can be improved under microwaves. For this purpose, a computational study was carried out on a variety of reactions, which have been reported to be improved under microwave irradiation. This comprises six types of reactions. The outcomes obtained in this study indicate that the most influential parameters are activation energy, enthalpy, and the polarity of all the species that participate. In addition to this, in most cases, slower reacting systems observe a much greater improvement under microwave irradiation. Furthermore, for these reactions, the presence of a polar component in the reaction (solvent, reagent, susceptor, etc.) is necessary for strong coupling with the electromagnetic radiation. We also quantified that an activation energy of 20–30 kcal mol⁻¹ and a polarity (μ) between 7–20 D of the species involved in the process is required to obtain significant improvements under microwave irradiation.     

Synthesis,spectral investigation and development of tetrahedral copper(II) complexes as artificial metallonucleases and antimalarial agents

Seven new copper(II) complexes of type [Cu(A)(L)]?H₂O (A = sparfloxacin, ciprofloxacin, levofloxacin, gatifloxacin, pefloxacin, ofloxacin, norfloxacin; L = 5‐[(3‐chlorophenyl)diazenyl]‐4‐hydroxy‐1,3‐thiazole‐2(3H)‐thione) were synthesized and characterized using elemental and thermogravimetric analyses, and electronic, electron paramagnetic resonance (EPR), Fourier transform infrared and liquid chromatography–mass spectroscopies. Tetrahedral geometry around copper is assigned in all complexes using EPR and electronic spectral analyses. All complexes were investigated for their interaction with herring sperm DNA utilizing absorption titration (K_b = 1.27–3.13 × 10⁵ M^?1) and hydrodynamic volume measurement studies. The studies suggest the classical intercalative mode of DNA binding. The cleavage reaction on pUC19 DNA was monitored by agarose gel electrophoresis. The results indicate that the Cu(II) complexes can more effectively promote the cleavage of plasmid DNA. The superoxide dismutase mimic activity of the complexes was evaluated by nitroblue tetrazolium assay, and the complexes catalysed the dismutation of superoxide at pH = 7.8 with IC₅₀ values in the range 0.597–0.900 μM. The complexes were screened for their in vitro antibacterial activity against five pathogenic bacteria. All the complexes are good cytotoxic agents and show LC₅₀ values ranging from 5.559 to 11.912 µg ml^?1. All newly synthesized Cu(II) complexes were also evaluated for their in vitro antimalarial activity against Plasmodium falciparum strain (IC₅₀ = 0.62–2.0 µg ml^?1). Copyright © 2015 John Wiley & Sons, Ltd.