Separating sets by lower and upper semicontinuous functions with a closed graph

In this paper we characterize the pairs (A^?, A⁺) of disjoint subsets of perfectly normal topological space which can be separated by a lower and an upper semicontinuous function with a closed graph.     

Phytochemical profile and therapeutic potential of Viscum album L.

Viscum album L., the European mistletoe, is a common species from the Viscaceae family. This evergreen hemiparasitic shrub grows on various trees and contains diverse, biologically active substances. Its chemical composition may vary depending on the time of harvest, species of the host tree and the manufacturing process. Among well-described and most active phytochemicals identified in V. album are lectins and viscotoxins, which play substantial role in cancer treatment because of their apoptotic and cytotoxic effects. Another group of compounds found in mistletoe are phenolic acids, phenylpropanoids and flavonoids with antioxidant and anti-inflammatory activities, which decrease blood pressure. Other mistletoe components include, among others, triterpenes with cytotoxic and apoptotic properties, and phytosterols, oligo- and polysaccharides. Extracts from the plant, especially aqueous, are applied in traditional and official medicine, among others in treating hypertension or arthritis. Potentially, it can also be used as a hepatoprotective or a sedative drug.     

Hyperstability of general linear functional equation

Our purpose is to investigate criteria for hyperstability of linear type functional equations. We prove that a function satisfying the equation approximately in some sense, must be a solution of it. We give some conditions on coefficients of the functional equation and a control function which guarantee hyperstability. Moreover, we show how our outcomes may be used to check whether the particular functional equation is hyperstable. Some relevant examples of applications are presented.     

Molecular Weight Distribution in Living Polymerization Proceeding with Reshuffling of Polymer Segments due to Chain Transfer to Polymer with Chain Scission, 2. Monte Carlo Simulation of Polymer Reshuffling Proceeding with Disproportionation of Chain Functionalities

The method for analyzing the reshuffling of polymer segments developed previously has been extended to systems involving the disproportionation of chain functionalities. The effect of interchain exchange reactions of this type, leading to the redistribution of chain lengths and of the chain functionalities (redistribution of living and dead chain ends), was analyzed by means of the Monte Carlo simulations. In the systems, in which no propagation occurs (monomer concentration equal to zero), a set of polymer chains containing one living and one dead end was taken as an initial material. A series of simulations were performed for systems with differing molecular weight distributions of the starting macromolecules. Uniform (no chain length distribution polymer – all chains are of the same length), Poisson, and the most probable (geometric) distributions were taken into consideration. Although the molecular weight distributions (MWDs) of functionally different chains of the same polymer were different apart from the eventual equilibrium conditions, the overall MWD was very close to that observed in analogous systems without disproportionation. The same was observed concerning MWDs in modeled polymerization systems, in which reshuffling and disproportionation accompanied propagation. Consequently, a method of estimating the ratio of rate constants of propagation and reshuffling (i. e. k_p /k _tr) in the relevant polymerization systems, using the observed polydispersity indexes, was proposed. The extent of disproportionation can be evaluated from the determined relationships of the polydispersity index and of the monofunctional chains fraction as functions of the average number of chain transformations.     

Quantitative comparison of selectivities in the polymerization of cyclic esters

Chain transfer processes (k_tr) taking place in the polymerization (anionic and pseudoanionic) of cyclic esters (lactones) are reviewed. These reactions are mostly responsible for the departure of these systems from the fully controlled (living) polymerizations. The ratios of k_p/k_tr have been determined for a number of initiating systems and the structures of the growing species are related to their selectivity, expressed by k_p/k_tr. It has been shown that the less reactive and more sterically crowded active species polymerize more selectively.     

Tosylated glycerol carbonate, a versatile bis-electrophile to access new functionalized glycidol derivatives

The reactivity of tosylated glycerol carbonate 2 toward nucleophiles has been exploited to generate glycidol analogues protected with carbonate or carbamate groups. The activated glycerol 2 is a reasonable linking agent with thiol and alcohol nucleophiles and an excellent and selective one with primary amines, allowing efficient bis-functionalizations of glycerol.     

Modular access to heterocycles: methyl 3-aminobenzo[<Emphasis Type="Italic">b</Emphasis>]thiophene-2-carboxylate–thiourea linkage or pyrimidine-4-one-2-thione formation

Abstract  Modular conditions for the formation of thioureas or pyrimidine-4-one-2-thiones connected to the benzo[b]thiophene, benzene and indole structures were performed. A benzo[b]thiophene isothiocyanate derivative was used as a model to study the condensation with simple aromatic amines and amino-l-sorbose derivative. The construction of pyrimidine-4-one-2-thiones using basic conditions afforded efficiently new heterocyclic aromatics, which were further transformed using the alkylated sulfur as a leaving group in palladium-catalyzed cross-coupling reactions. Graphical abstract        

Deoligomerization by cocomplexation: syntheses and structures of aluminum-calcium alkoxides and aryloxides

Reactions of oligomeric "Ca(dbbfo)2" and Ca9(CH3OCH2CH2O)18(CH3OCH2CH2OH)2 with Al(CH3)3 in toluene gave tetranuclear heterobimetallic [Ca(mu-dbbfo){(mu-dbbfo)(mu-CH3)Al(CH3)2}]2 (71%) and polymeric Ca{(mu-CH3OCH2CH2O)(mu-CH3)Al(CH3)2}2 (86%). The latter can be obtained as monomeric THF adduct Ca{(mu-CH3OCH2CH2O)Al(CH3)3}2(THF)2 (78%) when a mixture of solvents is used. The results, including an initial L-lactide polymerization test, are discussed in the context of calcium alkoxo cluster degradation in solution.     

Sodium dithionite initiated addition of 1-bromo-1-chloro-2,2,2-trifluoroethane to allylaromatics: Facile synthesis of conjugated dienes substituted with terminal CF3 group

Sodium dithionite effectively promotes the addition of 1-bromo-1-chloro-2,2,2-trifluoroethane to the terminal double bond of allylbenzenes 1. The reactions proceeded in MeCN/H₂O to give a 3:1 mole ratio of diastereoisomers of 1-(2-bromo-4-chloro-5,5,5-trifluoropentyl)benzenes 2 as the main products together with small amounts of its reductive debromination products 3. Total yields of 2 and 3 were dependent on the nature of the aromatic ring substituents in 1. Treatment of adducts 2 with DBU in refluxing hexanes resulted in double dehydrohalogenation affording, in good yields, conjugated dienes 4 (1,1,1-trifluoro-5-phenyl-2,4-pentadienes) terminated with the CF₃ group at the one end and the phenyl group at the opposite end. These dienes were found to be sufficiently reactive to undergo Diels-Alder condensation with active dienophiles to give trifluoromethylated carbocycles. The reactions of CF₃CHClBr with allylheterocycles were less successful and lead to low yields of mixtures of hardly separable compounds or to polymeric resins.