Some singular value and unitarily invariant norm inequalities for Hilbert space operators

In this paper, we prove some singular value inequalities for sum and product of operators. Also, we obtain several generalizations of recent inequalities. Moreover, as applications we establish some unitarily invariant norm and trace inequalities for operators which provide refinements of previous results.     

Preparation of photocatalytic ZnO nanoparticles and application in photochemical degradation of betamethasone sodium phosphate using taguchi approach

In this study, ZnO nanoparticles were prepared by a sol-gel method for the first time. Taguchi method was used to identify the several factors that may affect degradation percentage of betamethasone sodium phosphate in wastewater in UV/K₂S₂O₈/nano-ZnO system. Our experimental design consisted of testing five factors, i.e., dosage of K₂S₂O₈, concentration of betamethasone sodium phosphate, amount of ZnO, irradiation time and initial pH. With four levels of each factor tested. It was found that, optimum parameters are irradiation time, 180 min; pH 9.0; betamethasone sodium phosphate, 30 mg/L; amount of ZnO, 13 mg; K₂S₂O₈, 1 mM. The percentage contribution of each factor was determined by the analysis of variance (ANOVA). The results showed that irradiation time; pH; amount of ZnO; drug concentration and dosage of K₂S₂O₈ contributed by 46.73, 28.56, 11.56, 6.70, and 6.44%, respectively. Finally, the kinetics process was studied and the photodegradation rate of betamethasone sodium phosphate was found to obey pseudo-first-order kinetics equation represented by the Langmuir-Hinshelwood model.     

Solid Particle Distribution in Centrifugal Impeller Contactors

The recently developed centrifugal impeller is examined to investigate the solid–liquid mixing in a mechanically agitated contactor. Using the sample withdrawal method, the effects of impeller geometrical parameters, impeller rotational speed (200–700 rpm), solid particle size (500–1100 µm), and solid loading (2–10 vol%) on the degree of homogeneity are studied. The axial and the radial solid concentration profiles and the minimum impeller speed for the complete homogenization are also determined. In comparison with a widely used propeller impeller, considerably higher homogeneity values in lower impeller speeds are obtained (90% homogeneity against 16% homogeneity at 200 rpm at the same conditions). Having also lower power consumption makes this a superior impeller in solid–liquid mixing processes especially in shear-sensitive systems.      

Synthesis and Characterization of Organosoluble Poly(imide-ether)s with Bulky 2,3-Diaryl Imidazole Moiety: Study Physical,Thermal and Optical Properties

Two new symmetrical diamines were designed and synthesized having different functional groups such as a pair of phenyl ether linkages, 2,3-diaryl substituted imidazole rings and CF₃ groups as pendant, and characterized by FT-IR, ¹H and ¹³C-NMR spectroscopy and elemental analysis. A series of new fluorescent poly(imide-ether)s (PIEs) was prepared by polymerization of the diamines with commercial tetracarboxylic dianhydrides such as pyromellitic dianhydride and 3,3′,4,4′-benzophenone tetracarboxylic dianhydride. The resulting PIEs were amorphous and had intrinsic viscosity [η] in the range of 0.42–0.51 dL/g. The weight average molecular weights (Mw) of these polymers were measured by GPC and were in the range of 28658–35595 g/mol with molecular weight distribution (MWD) of 2.12–2.27. These polymers were readily soluble in a variety of organic solvents and formed low-colored and flexible thin films with cut-off wavelength (λ₀) in the range of 385–420 nm, and all PIEs films exhibited high optical transparency. They also possessed good thermal stability with 10% weight loss temperatures (T_10%) in the range 486–537°C in N₂. The glass transition temperatures (T_g) of PIEs are in the range 251–324°C. These polymers showed fluorescence emission in film and in solution at 459–476 nm with the quantum yields in the range 4–12%.     

A quick and green ionic liquid-mediated approach for the synthesis of high-performance, organosoluble and thermally stable polyimides

Three diamine monomers with different derivatives of imidazole heterocyclic ring and meta-linked aryl ethers were synthesized and used in polycodensation reaction with various commercial dianhydrides for preparation of a series of novel poly(ether-imide) (PEI)s. The polycodensation reactions were carried out by using conventional method and in a green medium of ionic liquid (IL) without using NMP-pyridine-acetic anhydride. The PEIs were obtained in good yields (80% 96%) with moderate viscosity (0.48 0.66 dL/g) in a shorter reaction time (10 h) in IL as compared with the conventional method (36 h). All of the polymers were amorphous in nature, showed excellent solubility in amide-type polar aprotic solvents with ability to form tough and flexible films, and excellent thermal stability with Tgs in the range of 212 340 ℃ and 10% weight loss temperature (T10) up to 570℃ in N 2 and 528 ℃ in air.     

The photocatalytic degradation of cationic surfactant from wastewater in the presence of nano-zinc oxide using Taguchi method

The photocatalytic degradation of cetyl pyridinium chloride (CPC) has been investigated in aqueous phase using ultraviolet (UV) and ZnO nanopowder. Kinetic analysis showed that the extent of surfactant photocatalytic degradation can be fitted with pseudo-first-order model and photochemical elimination of CPC could be studied by Taguchi method. Our experimental design was based on testing five factors, i.e., dosage of K₂S₂O₈, concentration of CPC, amount of ZnO, irradiation time and initial pH. Each factor was tested at four levels. The optimum parameters were found to be pH 5.0; amount of ZnO 11 mg; K₂S₂O₈ 3 mM; CPC 10 mg/L; irradiation time, 8 h.