Numerical simulation and convergence analysis for a system of nonlinear singularly perturbed differential equations arising in population dynamics

In this article, we consider a system of nonlinear singularly perturbed differential equations with two different parameters. To solve this system, we develop a weighted monotone hybrid scheme on a nonuniform mesh. The proposed scheme is a combination of the midpoint scheme and the upwind scheme involving the weight parameters. The weight parameters enable the method to switch automatically from the midpoint scheme to the upwind scheme as the nodal points start moving from the inner region to the outer region. The nonuniform mesh in particular the adaptive grid is constructed using the idea of equidistributing a positive monitor function involving the solution gradient. The method is shown to be second order convergent with respect to the small parameters. Numerical experiments are presented to show the robustness of the proposed scheme and indicate that the estimate is optimal.     

Perfluorocyclohexenyl aryl ether polymers via polycondensation of decafluorocyclohexene with bisphenols

A novel class of semifluorinated perfluorocyclohexenyl (PFCH) aryl ether homo/copolymers was successfully synthesized with high yield through the step‐growth polymerization of commercially available bisphenols and decafluorocyclohexene in the presence of a triethylamine base. The synthesized polymers exhibit variable thermal properties depending on the functional spacer group (R). PFCH aryl ether copolymers with random and alternating architectures were also prepared from versatile bis‐perfluorocyclohexenyl aryl ether monomers. The PFCH polymers show high thermal stabilities with a 5% decomposition temperature ranging from 359 to 444 °C in air and nitrogen atmosphere. These semifluorinated PFCH aromatic ether polymers contain intact enchained PFCH olefin moieties, making further reactions such as crosslinking and application specific functionalization possible. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 232–238     

Mechanistic aspects on molecular structure formation of polymeric networks from diisocyanates with amidine compounds

Polymeric networks are produced by step‐growth polyaddition and co‐polyaddition reactions of 1‐ethylimidazoline in combination with various diisocyanates. Five aromatic, two aliphatic diisocyanates and a polyurethane prepolymer are used as particular reactant in N,N‐dimethylformamide as solvent at room temperature. Obviously, 1‐ethylimidazoline can serve as trifunctional monomer, which enables a crosslinking reaction with diisocyanates. Molecular structure elements of the polymeric networks were studied by solid state 13C‐NMR spectroscopy revealing that detailed molecular structure formations are determined whether aromatic or aliphatic diisocyanates are used. Quantum chemical calculations were used as supporting method to elucidate the complex reaction cascades. Hence, it can be shown that beside 3:1 stoichiometric structures 2:1 based structures are formed as well. These structures are observed as kinetically controlled products only when aromatic diisocyanate monomers are used. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 977–985     

A simplified adaptive Cartesian grid system for solving the 2D shallow water equations

This paper presents a new simplified grid system that provides local refinement and dynamic adaptation for solving the 2D shallow water equations (SWEs). Local refinement is realized by simply specifying different subdivision levels to the cells on a background uniform coarse grid that covers the computational domain. On such a non‐uniform grid, the structured property of a regular Cartesian mesh is maintained and neighbor information is determined by simple algebraic relationships, i.e. data structure becomes unnecessary. Dynamic grid adaptation is achieved by changing the subdivision level of a background cell. Therefore, grid generation and adaptation is greatly simplified and straightforward to implement. The new adaptive grid‐based SWE solver is tested by applying it to simulate three idealized test cases and promising results are obtained. The new grid system offers a simplified alternative to the existing approaches for providing adaptive mesh refinement in computational fluid dynamics. Copyright © 2011 John Wiley & Sons, Ltd.     

Synthesis of oligo(spiroketal)s by polycondensation of silyl ethers derived from naturally occurring myo‐inositol with 1,4‐cyclohexanedione

Oligo(spiroketal)s (OSKs) were synthesized from myo‐inositol, a naturally occurring cyclic compound bearing six hydroxyl groups. The successful synthesis of OSKs was achieved using silyl ethers 2 derived from 1,4‐di‐O‐alkylated myo‐inositol 1 as monomers, which underwent polycondensation with 1,4‐cyclohexanedione (CHD) at 0 °C in the presence of trimethylsilyl triflate as a catalyst. Because of the irreversible nature of the condensation reaction of silyl ethers with ketones, the resulting OSKs 7 had higher molecular weights than previously reported OSKs that were obtained by polycondensation of tetraols 1 with CHD, where backward hydrolysis of the ketal functions occurred. In addition, another series of OSKs, 8, were synthesized using silyl ethers 3 derived from 2,5‐di‐O‐alkylated myo‐inositol 6 , which are more symmetric monomers than silyl ethers 2 . Silyl ethers 3 underwent efficient polycondensation with CHD, whereas tetraol 6 did not, demonstrating that the derivation of such tetraols into the corresponding silyl ethers is a powerful strategy to access OSKs. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 2407–2414     

A problem of determining a special spatial part of 3D memory kernel in an integro‐differential hyperbolic equation

The inverse problem of determining 2D spatial part of integral member kernel in integro‐differential wave equation is considered. It is supposed that the unknown function is a trigonometric polynomial with respect to the spatial variable y with coefficients continuous with respect to the variable x. Herein, the direct problem is represented by the initial‐boundary value problem for the half‐space x>0 with the zero initial Cauchy data and Neumann boundary condition as Dirac delta function concentrated on the boundary of the domain . Local existence and uniqueness theorem for the solution to the inverse problem is obtained.     

Synthesis and structure–property relationship of carbazole‐alt‐benzothiadiazole copolymers

A series of four π‐conjugated carbazole‐alt‐benzothiadiazole copolymers (PCBT) were prepared by Suzuki cross‐coupling reaction between synthesized dibromocarbazoles as electron‐rich subunits and 4,7‐bis(4,4,5,5‐tetramethyl‐1,3,2‐dioxaborolan‐2‐yl)?2,1,3‐benzothiadiazole as electron‐deficient subunits. The subunits were directly linked through 2,7‐ or 3,6‐ positions of the carbazole. In addition, the carbazole monomers have been N‐substituted by a branched or a linear side‐chain. The chemical structure of the copolymers and their precursors was confirmed by NMR and IR spectroscopies, and their molar masses were estimated by SEC. Thermal analysis under N₂ atmosphere showed no weight loss below 329°C, and no glass transition was observed in between 0 and 250°C. The band gaps of all PCBTs evaluated by optical spectroscopies and by cyclic voltammetry analysis were consistent with expectations and ranged between 2.2 and 2.3 eV. Finally, 2,7 and 3,6 linkages were shown to influence optical properties of PCBTs. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 2059–2068     

Triggering the Directional Selectivity of a Ring‐Closure Reaction Leads to Pyridoazacarbazoles with Anticancer Properties

We herein describe a facile and versatile synthetic route to the tetracyclic system of 6‐substituted 5,6‐dihydro‐11H‐pyrido[3,2‐i]‐1‐azacarbazoles with promising anticancer properties. These derivatives are built up by an elegant one‐step base‐catalyzed synthetic procedure from commercially available building blocks. One additional step provides the corresponding skeleton hitherto unknown in the literature. The possibility to synthesize a large library of compounds with various substitution patterns utilizing this method underlines the importance of this synthetic procedure.