Differential equations with state-dependent piecewise constant argument

A new class of differential equations with state-dependent piecewise constant argument is introduced. It is an extension of systems with piecewise constant argument. Fundamental theoretical results for the equations—the existence and uniqueness of solutions, the existence of periodic solutions, and the stability of the zero solution—are obtained. Appropriate examples are constructed.     

Chitosan Macromolecules on a Substrate: Deposition from Solutions in sc CO2 and Reorganisation in Vapours

Specially pretreated chitosan macromolecules possess limited solubility in supercritical carbon dioxide. When deposited on mica substrate from such solutions they adopt somewhat extended conformation. The adsorbed macromolecules become mobile on the interface when exposed to water vapour as revealed by environmental scanning force microscopy. During the exposure in the presence of coadsorbed water layer the chitosan strands demonstrate slight tendency to adopt more compact but still two-dimensional conformation on the substrate.     

Quantitative generation of cation radicals and dications using aromatic oxidants: effect of added electrolyte on the redox potentials of aromatic electron donors

Redox titrations using robust aromatic oxidants allow for a quantitative analysis of redox and optical properties of organic electron donors in their oxidized states. Unlike spectroelectrochemistry, redox titrations can be performed without added electrolyte in relatively nonpolar solvents, affording quick access to the redox and optical properties of a given electron donor without the need of a complex electrochemical setup. However, the redox potentials obtained by the two methods are not the same. To establish the direction and magnitude of this discrepancy, we have performed a systematic case study using a set of tetraarylethylene donors and a tetrasubstituted hydroquinone ether cation radical (^THEO^+?) as a stable aromatic oxidant. We show that redox potentials (especially second and higher oxidation potentials) measured by electrochemical methods are systematically lower compared with the redox potentials obtained by redox titrations in the absence of electrolyte, because of the enhanced stabilization of dications and polycations by electrolyte. We have also uncovered that the smaller cation radicals (e.g., a para‐hydroquinone or ortho‐hydroquinone ether cation radicals) are much more effectively stabilized when compared with the cation radicals in which charge is delocalized over larger area (e.g., tetraarylethylene cation radicals) in the presence of electrolyte because of increased ionic strength of the solution. Copyright © 2015 John Wiley & Sons, Ltd.     

Quadratic helicities and the energy of magnetic fields

Two new nonlocal asymptotic invariants of magnetic fields frozen into a finite domain filled with an ideal liquid conducting medium are introduced. The velocity of variation of the invariants in a nonideal medium is estimated for magnetic fields described by the induction equation. The invariants are used to study the spectral characteristics of magnetic fields.     

Efficient newton–raphson/singular value decomposition-based optimization scheme with dynamically updated critical condition number for rapid convergence of weighted histogram analysis method equations

Selection of the successful optimization strategy is an essential part of solving numerous practical problems yet often is a nontrivial task, especially when a function to be optimized is multidimensional and involves statistical data. Here we propose a robust optimization scheme, referred to as NR/SVD-Cdyn, which is based on a combination of the Newton–Raphson (NR) method along with singular value decomposition (SVD), and demonstrate its performance by numerically solving a system of the weighted histogram analysis method equations. Our results show significant improvement over the direct iteration and conventional NR optimization methods. The proposed scheme is universal and could be used for solving various optimization problems in the field of computational chemistry such as parameter fitting for the methods of molecular mechanics and semiempirical quantum-mechanical methods. © 2019 Wiley Periodicals, Inc.     

Synthesis,molecular structure,conformation and biological activity of Ad-substituted N-aryl-tetraoxaspiroalkanes

An efficient method has been developed for the synthesis of 7′-arylspiro{adamantane-[2,3′]-(1′,2′,4′,5′,7′-tetraoxazocanes)} by the ring transformation reaction of spiro{adamantane-[2,3’]-(1′,2′,4′,5′,7′-pentaoxacane)} with arylamines in the presence of Sm(NO₃)₃·6H₂O as the catalyst. NMR signals of the synthesized compounds were assigned considering the conformation dynamics of the tetraoxazocane ring with two rigid peroxide bonds. The structures of some of the compounds were studied by X-ray diffraction. The thermal stability of single crystal was determined by DSC method. Compounds 7′-(2-methylphenyl)spiro{adamantane-[2,3′]-(1′,2′,4′,5′,7′-tetraoxazocane)} and 7′-(4-fluorophenyl)spiro{adamantane-[2,3′]-(1′,2′,4′,5′,7′-tetraoxazocane)} exhibited cytotoxicity towards cancer cells.