The discretized flow on domains of attraction: a structural stability result

It is well known that, for stepsize sufficiently small, compactattractors of ordinary differential equations persist underdiscretization. The present paper describes the structure ofthe discrete-time dynamical system obtained via discretizationon A(M_h)\M_h where M_h is the approximate attractor and A(M_h)is its domain of attraction. The existence of a smooth embeddinginto a continuous-time parallelizable flow is proved. The constructioncan be used to define sections for discretizations and can beinterpreted as a justification of the method of modified equations.     

The Properties and Activity of TiO2/beta‐SiC Nanocomposites in Organic Dyes Photodegradation

The TiO₂/beta‐SiC nanocomposites containing 0–25 wt. % of beta‐SiC were synthesized by the sol‐gel method and tested in the photodegradation of methylene blue and methyl orange water solutions. With the increase in SiC content, only a slight decrease in energy band gap was observed (3.19–3.12 eV), together with significant increase in the surface area of the catalysts (42.7–80.4 m² g^?1). In the synthesized material, the anatase phase of TiO₂ was present in the form of small agglomerates resulting from the mechanical mixing process. In the process conditions (catalyst concentration 0.5 g L^?1, initial dye concentration 100 ppm, light source 100 W UV‐Vis lamp), we have observed no signs of catalyst deactivation. The significantly higher photodegradation activity of methylene blue than methyl orange can be attributed to the preferable pH of the solution compared to pH_PZC and the cationic character of the first dye. In case of methyl orange, pH process conditions substantially limit the contact of the catalyst with the dye, as negatively charged surface of the catalysts repels the dissociated anionic dye molecules.     

Multiple Zeolite Structures from One Ionic Liquid Template

This study reports the use of 1‐butyl‐3‐methyl imidazolium methanesulfonate ionic liquid as a template in the synthesis of zeolites. It is found that the silicon source determines the formation of beta (BEA), mordenite framework inverted (MFI), or analcime (ANA) zeolites. Depending on this source, different preorganized complexes are obtained that drive the formation of the different zeolite structures. In the presence of ethanol, the ionic liquid form preorganized complexes that drive the formation of MFI. In its absence, BEA is obtained. Whereas, the large amount of sodium present when using sodium metasilicate leads to ANA formation. A molecular simulation study of the relative stability of the template‐framework system and location of the template provides further insight into the mechanism of synthesis.     

Hydrophosphonylation of chiral hexahydroquinoxalin-2(1H)-one derivatives as an effective route to new bicyclic compounds: Aminophosphonates,enamines and imines

A series of new aminophosphonate and phosphonic acid derivatives of hexahydroquinoxalin-2(1H)-ones and tetrahydroquinoxalin-2(1H)-ones were synthesised via hydrophosphonylation of the corresponding bicyclic imines with various dialkyl or diaryl H-phosphonates, H-phosphinates or H-phosphine oxides as phosphorus nucleophiles. The utility of the obtained compounds was demonstrated by their application as a source of phosphonate carbanion in the Horner-Wadsworth-Emmons (HWE) reaction leading to new bicyclic amines with an exocyclic, and unexpectedly, also endocyclic double bond depending on the structure of the aldehyde used.     

Dual template synthesis of a highly mesoporous SSZ-13 zeolite with improved stability in the methanol-to-olefins reaction

The dual template synthesis of zeolite SSZ-13 by use of trimethyl-adamantanammonium hydroxide and a diquaternary-ammonium mesoporogen induces considerable mesoporosity without impeding zeolite microporosity. The strongly improved accessibility of Br?nsted sites in mesoporous SSZ-13 increases its stability during application as an acid catalyst in the methanol-to-olefins reaction.     

Partial Methane Oxidation to Methanol on Ru-Porphyrins – on the Role of Non-Innocent Ligands and Spin Crossover

The partial oxidation reaction of CH₄ led to the formation of CH₃OH in the presence of Ru-porphyrin oxo complexes (denoted as POR, POR-O and POR-OH where in the case of the last two, oxygen atom and the OH group were attached to the active site, respectively), in which Ru was present on different oxidation states. The simulations were performed based on Density Functional Theory (DFT) with extended geometric and electronic structure analyses of each reaction step. Moreover, the reaction pathways were investigated in different spin states. The Spin Crossover (SCO) phenomenon was found to play an important role in the kinetics of the reaction in the presence of POR and POR-O. Harmonic Oscillator Model of Aromaticity (HOMA) index was applied for different spin states to estimate the aromaticity changes of the pyrrole rings in the Ru-porphyrin complexes. In order to characterize the nature of bonding, the Natural Bond Orbitals (NBO) analysis including the Wiberg Bond Index (WBI) and Natural Population Analysis (NPA) was carried out. Finally, the Non-Covalent Interactions (NCI) index was employed to gain insight into interactions between the components of the reaction. It was found that the non-covalent interactions cannot be neglected in the studied reaction paths.