Search Results (2)

The complementary dual of entropy has received significant attention in the literature. Due to the emergence of many generalizations and extensions of entropy, the need to generalize the complementary dual of uncertainty arose. This article develops the residual cumulative generalized fractional extropy as a generalization of the residual cumulative complementary dual of entropy. Many properties, including convergence, transformation, bounds, recurrence relations, and connections with other measures, are discussed. Moreover, the proposed measure’s order statistics and stochastic order are examined. Furthermore, the dynamic design of the measure, its properties, and its characterization are considered. Finally, nonparametric estimation via empirical residual cumulative generalized fractional extropy with an application to blood transfusion is performed. Full article

[Carbonatotetraamminecobalt(III)] permanganate monohydrate was synthesized first in the metathesis reaction of [Co(NH₃)₄CO₃]NO₃ and NaMnO₄ in aqueous solution. Its thermal dehydration at 100 °C resulted in phase-pure [Co(NH₃)₄CO₃]MnO₄ (compound 1). Compounds 1 and 2 (i.e., the hydrated form) were studied with IR, far-IR, and low-temperature Raman spectroscopies, and their vibrational modes were assigned. The lattice parameters were determined by powder X-ray diffraction (PXRD) and single crystal X-ray diffraction (SXRD) methods for the triclinic and orthorhombic compounds 1 and 2, respectively. The detailed structure of compound 2 was determined, and the role of hydrogen bonds in the structural motifs was clarified. UV studies on compounds 1 and 2 showed the distortion of the octahedral geometry of the complex cation during dehydration because of the partial loss of the hydrogen bonds between the crystal water and the ligands of the complex cation. The thermal decomposition consists of a solid phase quasi-intramolecular redox reaction between the ammonia ligands and permanganate anions with the formation of ammonia oxidation products (H₂O, NO, N₂O, and CO₂). The solid phase reaction product is amorphous cobalt manganese oxide containing ammonium, carbonate (and nitrate) anions. The temperature-controlled thermal decomposition of compound 2 in toluene at 110 °C showed that one of the decomposition intermediates is ammonium nitrate. The decomposition intermediates are transformed into Co_1.5Mn_1.5O₄ spinel with MnCo₂O₄ structure upon further heating. Solid compound 2 gave the spinel at 500 °C both in an inert and air atmosphere, whereas the sample pre-treated in toluene at 110 °C without and with the removal of ammonium nitrate by aqueous washing, gave the spinel already at 300 and 400 °C, respectively. The molten NH₄NO₃ is a medium to start spinel crystallization, but its decomposition stops further crystal growth of the spinel phase. By this procedure, the particle size of the spinel product as low as ~4.0 nm could be achieved for the treatments at 300 and 400 °C, and it increased only to 5.7 nm at 500 °C. The nano-sized mixed cobalt manganese oxides are potential candidates as Fischer-Tropsch catalysts. Full article