Continuous on rays solutions of an equation of the Go?a?b-Schinzel type

Let X be a real linear space. We characterize continuous on rays solutions f,g:X→R of the equation f(x+g(x)y)=f(x)f(y). Our result refers to papers of J. Chudziak (2006) [14] and J. Brzd?k (2003) [11].     

More about complements of quasi-uniformities

We continue our investigations on the lattice (q(X),⊆) of quasi-uniformities on a set X. Improving on earlier results, we show that the Pervin quasi-uniformity (resp. the well-monotone quasi-uniformity) of an infinite topological T₁-space X does not have a complement in (q(X),⊆). We also establish that a hereditarily precompact quasi-uniformity inducing the discrete topology on an infinite set X does not have a complement in (q(X),⊆).     

Reactions of group 13 metal trialkyls with oxamides

Alkyl aluminum-, gallium-, and indium oxamidates Me₄Al₂(dpoa) (1), Me₄Al₂(dboa) (2), Me₄Ga₂(dpoa) (3), Me₄Ga₂(dboa) (4), ^tBu₄Ga₂(dpoa) (5) and Me₄In₂(dboa) (6) (dpoa-H₂ = N,N′-diphenyloxamide, dboa-H₂ = N,N′-di-tert-butyloxamide) have been prepared and characterized. Compounds 1-3, 5 and 6 exist in the form of isomers a only, with a skeleton framework of the molecules consisting of two almost flat, coplanar and fused MNOC₂ (M = Al, Ga, In) heterocyclic rings. Depending on the reaction conditions, the compound 4 was obtained as the isomer 4a or as the mixture of two isomers 4a and 4b. Molecular structures of the compounds 1a-6a have been determined by X-ray crystallography. A structure of the isomer 4b was proposed on the basis of NMR spectroscopy. A skeleton framework of the 4b molecule consists of two fused different cycles, GaO₂C₂ and GaN₂C₂.     

Functionalized Organotin‐Chalcogenide Complexes That Exhibit Defect Heterocubane Scaffolds: Formation,Synthesis, and Characterization

The synthesis of new functionalized organotin‐chalcogenide complexes was achieved by systematic optimization of the reaction conditions. The structures of compounds [(R^{1, 2}Sn)₃S₄Cl] ( 1 , 2 ), [((R²Sn)₂SnS₄)₂(μ‐S)₂] ( 3 ), [(R^{1, 2}Sn)₃Se₄][SnCl₃] ( 4, 5 ), and [Li(thf)_n][(R³Sn)(HR³Sn)₂Se₄Cl] ( 6 ), in which R¹=CMe₂CH₂C(O)Me, R²=CMe₂CH₂C(NNH₂)Me, and R³=CH₂CH₂COO, are based on defect heterocubane scaffolds, as shown by X‐ray diffraction, ¹¹⁹Sn NMR spectroscopy, and ESI mass spectrometry analyses. Compounds 4 , 5 , and 6 constitute the first examples of defect heterocubane‐type metal‐chalcogenide complexes that are comprised of selenide ligands. Comprehensive DFT calculations prompted us to search for the formal intermediates [(R¹SnCl₂)₂(μ‐S)] ( 7 ) and [(R¹SnCl)₂(μ‐S)₂] ( 8 ), which were isolated and helped to understand the stepwise formation of compounds 1 – 6 .     

Poly(ethylene glycol)/β-cyclodextrin covalent gel networks: host matrices for studying radical processes in plant extract–riboflavin systems following UV irradiation

Finding new, biocompatible matrices that allow us to model the generation of free radicals is of utmost importance for balancing the harmful and beneficial effects of the latter. In this respect, we report here the simultaneous encapsulation of the radical source and the antioxidant agent in a polyethylene glycol/β-cyclodextrin (PEG/β-CD) covalent gel network. We used electron paramagnetic resonance spectroscopy to evaluate the scavenging action of plant extracts (purple loosestrife, comfrey, milfoil, horsetail, thyme, carob, green coffee) embedded in PEG/β-CD gels. Free radicals were generated in situ by UV irradiation of riboflavin co-embedded in the gels. Prior to this, the extracts were characterized in what concerns their antioxidant activity, and their major polyphenolic constituents were quantified by liquid chromatography-electrospray ionization-tandem mass spectrometry. Purple loosestrife showed the highest antioxidant capacity, followed by comfrey and milfoil. Using the 5,5-dimethyl-1-pyrroline N-oxide spin trap, we have demonstrated that the gel-embedded extracts effectively scavenge the reactive carbon-centered free radicals generated in gel. The PEG/β-CD gels have been shown to be a valuable alternative matrix for the encapsulation of plant active principles having antioxidant activity. Moreover, co-encapsulation of the radical source transforms these gels into a controlled environment in which free radical processes can be tailored.     

Polar Diketopyrrolopyrrole‐Imidazolium Salts as Selective Probes for Staining Mitochondria in Two‐Photon Fluorescence Microscopy

Three rationally designed polar derivatives of diketopyrrolopyrrole consisting of 1,3‐dimethylimidazolium cationic units and benzene, thiophene, or furan rings as π spacers were synthesized and thoroughly studied. The obtained salts are soluble in polar organic solvents and show satisfactory solubility in water, which makes them suitable for the applications in bioimaging. Photophysical measurements revealed that the obtained derivatives are characterized by strong absorption and good fluorescence quantum yields. The corresponding two‐photon properties were also examined and showed that the synthesized salts exhibit large two‐photon absorption cross‐sections reaching 4000 GM (GM=Goeppert‐Mayer unit, 1 GM=10^?50 cm⁴ s photon^?1) and very high two‐photon brightness values exceeding 2000 GM. It was demonstrated that these salts can be safely applied in two‐photon fluorescence microscopy for selective staining of mitochondria in living cells.     

Parabolic flow on metric measure spaces

We present parabolic equations on metric measure spaces. We prove existence and uniqueness of solutions. Under some assumptions the existence of global in time solution is proved. Moreover, regularity and qualitative property of the solutions are shown.     

Modular and Versatile Trans-Encoded Genetic Switches

Current bacterial RNA switches suffer from lack of versatile inputs and are difficult to engineer. We present versatile and modular RNA switches that are trans-encoded and based on tRNA-mimicking structures (TMSs). These switches provide a high degree of freedom for reengineering and can thus be designed to accept a wide range of inputs, including RNA, small molecules, and proteins. This powerful approach enables control of the translation of protein expression from plasmid and genome DNA.