The behavior of conformal maps of domains near convex boundary arcs

The behavior of the derivatives of conformal maps of the unit disk onto simply connected domains in the complex plane whose boundaries contain convex or concave attainable arcs, as well as the behavior of the derivatives of the inverse maps, is studied. It is proved that these derivatives exist and are bounded on the corresponding arcs and near them; a criterion for their continuity at points of these arcs is stated and proved.     

New rare-earth metal acyl pyrazolonates: Synthesis,crystals structures,and luminescence properties

Ligand 3-methyl-1-phenyl-4-stearoylpyrazol-5-one (HQ) is synthesized and used to obtain new complexes of rare-earth metals (Eu, Gd, and Tb) of the composition [Ln(Q)₃(H₂O)(EtOH)]. The crystal structure of the terbium complex is determined by X-ray diffraction analysis (CIF file CCDC 975286). In a molecule of the complex, three aliphatic fragments n-C₁₇H₃₅ are codirected, which results in the formation of layers bound according to the fastener-sticker principle. The molecules of the complex are joined by a hydrogen bond network involving the pyrazolone rings and oxygen atoms of the inner-sphere solvent molecules (H₂O and EtOH). The terbium complex is luminescent at room temperature, whereas the luminescence of the europium complex is very weak at room temperature and increases by 60 times at lowered temperatures. This makes it possible to consider these compounds as a new class of “luminescent thermometers.”     

Simple synthesis of 2‐amino‐4‐(het)aryl‐4,6‐dihydro‐1(3)(11)H‐[1,3,5]triazino[2,1‐b]quinazolin‐6‐ones

The 2‐amino‐4‐(het)aryl‐4,6‐dihydro‐1(3)(11)H‐[1,3,5]triazino[2,1‐b]quinazolin‐6‐ones were prepared readily by cyclocondensation of anthranilic acid derived 4‐oxo‐3,4‐dihydroquinazolinyl‐2‐guanidine with a variety of aldehydes. The structures of the compounds were confirmed by nmr spectroscopy, including 2D NOESY experiments.