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.     

Maximal Subrings and Covering Numbers of Finite Semisimple Rings

We classify the maximal subrings of the ring of n×n matrices over a finite field, and show that these subrings may be divided into three types. We also describe all of the maximal subrings of a finite semisimple ring, and categorize them into two classes. As an application of these results, we calculate the covering number of a finite semisimple ring.     

New Effects in the Poly-N-Vinylcaprolactam/Titanium(IV) Oxides Nanocomposite System and Their Nature

Nanocomposites based on poly-N-vinylcaprolactam (PVC), characterized by different drying temperatures of aqueous PVC solution at 25°С (PVC25) and 40°С (PVC40), with titanium(IV) oxide nanoparticles (TONs) (η-phase (TP: TiO_{2 – x} · mH₂O) with a superstructure to the anatase structure and ordered solid solution with partial replacement of oxygen atoms in the η-phase with peroxo group O ₂ ^2– (PP: TiO _x (O₂)_{2 – x} · nH₂O)) have been obtained for the first time and characterized by X-ray diffraction and IR spectroscopy. It is found that a common feature of TP/PVC and PP/PVC obtained by dry mixing and grinding is the decrease in the number of water molecules for TP and PP in the interlayer space of the structure and their attachment to the PVC amide groups; the differences are related to the specificity of PVC behavior in these systems: mechanodestruction of PVC in PP/PVC40 and different numbers of water molecules in PVC25 and PVC40.     

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.