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′).     

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.     

Ion chromatography for the analysis of glyphosate and its selected metabolites. A review

Among all known compounds with herbicide activity glyphosate, has been the most commercially successful one. Currently, it is under evaluation because of its possible cancerogenic properties. However, the question is—if it is possible to completely withdraw it from use. Before it can happen, it is important to be sure of all its benefits and limitations, and this requires further detailed research. Due to the extent and prevalence of its use, glyphosate ends up in the environment and then in food and our bodies. There are several methods used for their determination. One of them is ion chromatography. Taking into account its advantages and disadvantages, as well as its rapid development, their importance in this field can be expected to increase in the near future. This paper summarizes the literature data from the past 22 years. The applications of ion chromatography in the determination of glyphosate in various types of environmental, food, and other samples are described. Moreover, the methods used so far are compared with the possibilities offered by ion chromatography, which main advantages and benefits are easy availability, low operating costs, green chemistry aspects, and suitable validation parameters.     

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.     

Disclosing the thermal behaviour,electrochemical and optical properties of synthetic Fe3(PO4)2(OH)2 materials

Journal of Thermal Analysis and Calorimetry - In this research paper, the thermal behaviour of the mixed valence iron oxides Fe3(PO4)2(OH)2 is presented in both air and vacuum atmosphere. The...