The maximal class with respect to maximums for the family of upper semicontinuous strong Świca¸tkowski functions

The main goal of this paper is to characterize the maximal class with respect to maximums for the family of upper semicontinuous strong ?wi?atkowski functions.     

Connections between connected topological spaces on the set of positive integers

In this paper we introduce a connected topology T on the set ? of positive integers whose base consists of all arithmetic progressions connected in Golomb’s topology. It turns out that all arithmetic progressions which are connected in the topology T form a basis for Golomb’s topology. Further we examine connectedness of arithmetic progressions in the division topology T′ on ? which was defined by Rizza in 1993. Immediate consequences of these studies are results concerning local connectedness of the topological spaces (?, T) and (?, T′).     

Prediction of liquid-liquid flow in an SMX static mixer using large eddy simulations

The main purpose of the paper is to apply the large eddy simulations (LES) technique and to verify its use as a predicting tool for turbulent liquid-liquid flow in an SMX static mixer. LES modeling was carried out using the Smagorinsky-Lilly model of the turbulent subgrid viscosity for the Reynolds number of 5000 and 10000. The continuous phase was water and the dispersed phase was silicon oil. The investigation covers the effects of the density ratio between the phases. Three different cases of liquid densities were considered. The dispersed phase concentration distribution in the mixer cross-sections was compared with the corresponding time averaged results obtained formerly for the same configuration in a steady-state simulation using the standard RANS approach with the k-ɛ model. The dependency of the standard deviation of the dispersed phase concentration on the distance from the mixer inlet and the impact of the centrifugal force on the phase concentration distribution were investigated. The presented results for the SMX static mixer confirm conclusions of previous studies by Jaworski et al. (2006) obtained for a Kenics static mixer and show less a pronounced influence of the centrifugal force on the phase concentration distribution of the LES results in comparison to the RANS case.     

Segregation into Layers: A General Problem for Structural Instability under Pressure,Exemplified by SnH4

When a molecular compound is thermodynamically unstable (but kinetically persistent) with respect to the elements, structures that contain segregated layers of the elements may be favored at moderate pressures, as a compromise between the potential stability of novel electronic configurations and decomposition into the elements (or other stable compounds). We use stannane, SnH₄, to approach this quite general problem theoretically, since the heat of formation of SnH₄ is so positive. Our ground‐state DFT searches for optimal structures begin with slabs formed from 1–4 layers of tin atoms in the β‐Sn and bcc configurations, and also slabs of molecular hydrogen or hydrogen atoms, preserving the overall SnH₄ stoichiometry. As argued, segregated layers are an important structural feature in the lower‐ and moderate‐pressure regime (0 and 50 GPa). By 140 GPa (V/V₀=0.21) the coordination of tin and hydrogen increases and the slabs disappear, as judged from the optimized structures.     

Investigation into factors influencing stereoselectivity in the reactions of heterocycles with donor-acceptor-substituted rhodium carbenoids

Rhodium-catalyzed decomposition of aryldiazoacetates in the presence of pyrroles or furans results in mono- or biscyclopropanation of the heterocycle, but with opposite enantioinduction. In the absence of sterically encumbering groups, the cyclopropanation of furan occurs with initial bond formation at the 2-position. If this pathway is sterically blocked, cyclopropanation can occur with initial bond formation at the 3-position of the furan ring; in this case, the cyclopropanation reaction takes place on the opposite face of the heterocycle, and the opposite enantioinduction is observed. Upon extension of this methodology to benzofurans, a highly enantioselective monocyclopropanation reaction occurs to furnish a product derived from initial bond formation at the 2-position of the benzofuran. When this reaction pathway is inhibited by sterically encumbering substituents on the benzofuran, no cyclopropanation of the furan ring is observed, and instead, double cyclopropanation of the benzene ring occurs. Double cyclopropanation of the benzene ring was also observed in reactions with indoles.     

How does the type of counterion influence the polymerization rate and thermal properties of tailored choline-based linear- and star-shaped poly(ionic liquid)s PILs?

The synthesis of tailored [2-(methacryloyloxy)ethyl]-trimethylammonium chloride (ChMA/Cl⁻) and bis(trifluoromethanesulfonate) imide (ChMA/NTf₂⁻)-based ionic homopolymers by sustainable activators generated by electron transfer atom transfer radical polymerization (ATRP) method has been demonstrated. Linear and four-arm star-shaped macromolecules were obtained with the use of two synthetic strategies: (a) direct polymerization of ionic monomers with counterions differing in hydrophilicity (prepolymerization) and (2) modification by ion exchange from Cl⁻ to NTf₂⁻ (postpolymerization) using both classical ATRP initiator and pentaerythritol-based initiator. The effect of counterions on the polymerization kinetics and the physicochemical and thermodynamical properties of resulted poly(ionic liquid)s (PILs) has been investigated. Results showed that polymerizations of ChMA/NTf₂⁻ proceeded with higher rate in comparison to ChMA/Cl⁻ one independently on the predetermined topologies (linear and four-arm star-shaped). From thermodynamical point of view, the glass transition temperature T_g increased with molecular weight M_n for linear- and star-shaped PILs for both types of counterion. In addition, star-shaped polymers of comparable M_n to linear ones were characterized by slightly higher T_g values. The resulting polyelectrolytes, after modification via exchange of Cl⁻ anions to NTf₂⁻ ones were characterized by much higher T_g in comparison to those produced by direct polymerization of ionic monomer, indicating the crucial role of postpolymerization modification on thermodynamical properties of PILs. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 2681–2691