Thermodynamic analysis of liquid In–Sn alloys using Oelsen calorimetry

The results of calorimetric investigations of liquid In–Sn alloys using Oelsen calorimetry are presented in this article. Based on obtained enthalpy space diagram and enthalpy isotherm diagram, thermodynamic parameters for the liquid In–Sn alloys, including mixing and excess integral and partial molar quantities at temperature of 600 K, have been determined and compared with available literature data.     

The Drazin invertibility of the difference and the sum of two idempotent operators

In this note, some equivalents are established of the Drazin invertibility of differences and sums of idempotent operators on a Hilbert space.     

Ultrasound‐Assisted Synthesis of 3‐(Arylamino)‐1‐ferrocenylpropan‐1‐ones

A successful aza‐Michael addition of arylamines to a conjugated enone, acryloylferrocene, has been achieved by ultrasonic irradiation of the mixture of these reactants and the catalyst, i.e., montmorillonite K‐10. This solvent‐free reaction, yielding ferrocene containing Mannich bases, 3‐(arylamino)‐1‐ferrocenylpropan‐1‐ones, considered as valuable precursors in organic synthesis, has been performed by using a simple ultrasonic cleaner. Among 17 synthesized β‐amino ketones, three were new ones, and these were fully characterized by spectroscopic means. X‐Ray crystallographic analysis of three of these crystalline products enabled the insight into the conformational details of these compounds. All compounds were evaluated for their antibacterial activities against six Gram‐positive and five Gram‐negative strains in a microdilution assay. The observed promising antibacterial activity (with a MIC value of 25 μg/ml (ca. 0.07 μmol/ml) as the best result for almost all tested compounds against Micrococcus flavus) seems not only to be compound but also bacterial species‐specific.     

A new polymorph of 1‐ferrocenyl‐3‐(3‐nitroanilino)propan‐1‐one

Recrystallization of the title compound, [Fe(C₅H₅)(C₁₄H₁₃N₂O₃)], from a mixture of n‐hexane and dichloromethane gave the new polymorph, denoted (I), which crystallizes in the same space group (P) as the previously reported structure, denoted (II). The Fe—C distances in (I) range from 2.015 (3) to 2.048 (2) Å and the average value of the C—C bond lengths in the two cyclopentadienyl (Cp) rings is 1.403 (13) Å. As indicated by the smallest C—Cg1—Cg2—C torsion angle of 1.4° (Cg1 and Cg2 are the centroids of the two Cp rings), the orientation of the Cp rings in (I) is more eclipsed than in the case of (II), for which the value was 15.3°. Despite the pronounced conformational similarity between (I) and (II), the formation of self‐complementary N—H...O hydrogen‐bonded dimers represents the only structural motif common to the two polymorphs. In the extended structure, molecules of (I) utilize C—H...O hydrogen bonds and, unlike (II), an extensive set of intermolecular C—H...π interactions. Fingerprint plots based on Hirshfeld surfaces are used to compare the packing of the two polymorphs.     

Additive property of Drazin invertibility of elements in a ring

In this article, we investigate additive properties on the Drazin inverse of elements in rings. Under the commutative condition of ab?=?ba, we show that a?+?b is Drazin invertible if and only if 1?+?a ^D b is Drazin invertible. Not only the explicit representations of the Drazin inverse (a?+?b) ^D in terms of a, a ^D , b and b ^D , but also (1?+?a ^D b) ^D is given. Further, the same property is inherited by the generalized Drazin invertibility in a Banach algebra and is extended to bounded linear operators.