Realcompact subspaces

We show that every compact space of large enough size has a realcompact subspace of size κ, for κ?c. We also show that an uncountable realcompact space whose pseudocharacter is at most ω₁, has a realcompact subspaces of size ω₁, thus, by continuum hypothesis, every uncountable realcompact space has realcompact subspace of size ω₁.     

A high-order Monte Carlo algorithm for the direct simulation of Boltzmann equation

A high-order algorithm of the direct simulation Monte Carlo (DSMC) method, H-DSMC, has been developed to simulate rarefied flow regimes. The mth order Taylor series expansion has been employed to obtain a more generalized form of the time discretization for the collision part of Boltzmann equation. In the purposed algorithm, the higher order collision terms are introduced as well as higher order terms in the time step of the probabilistic coefficients. These newly implemented higher order terms improve the accuracy and efficiency of the solution and enhance the convergence rate quite significantly. Comparison between results of the classic DSMC method and the H-DSMC method shows the promising performance of the introduced technique.     

Copper (II) Nitrate-Silica Gel Mediated Regeneration of Carbonyl Compounds from Oximes Under Microwave Irradiation

Cu(NO₃)₂ supported on silica gel can be used as an effective and mild oxidizing agent for the direct conversion of oximes to carbonyl compounds under microwave irradiation in good yield.     

Sol–gel preparation and characterization of Ag and Mg co-doped nano TiO<Subscript>2</Subscript>: efficient photocatalytic degradation of C.I. Acid Red 27

In this study, we successfully prepared pure, mono-doped, and Ag, Mg co-doped TiO₂ nanoparticles using the sol–gel method, with titanium tetraisopropoxide as the Ti source. The prepared samples were characterized by X-ray powder diffraction (XRD), specific surface area and porosity (BET and BJH) measurement, scanning electron microscopy, transmission electron microscopy, X-ray photoelectron spectroscopy, photoluminescence, and energy dispersive X-ray spectroscopy techniques. The XRD data showed that the prepared nanoparticles had the same crystals structures as the pure TiO₂. Also, DRS results indicated that the band gap of co-doped photocatalyst was smaller than that of the monometallic and undoped TiO₂ and that there was a shift in the absorption band towards the visible light region. Furthermore, the photocatalytic activity of the prepared catalysts was evaluated by the degradation of C.I. Acid Red 27 in aqueous solution under visible light irradiation. The results showed that Ag (0.08 mol%), Mg (0.2 mol%) co-doped TiO₂ had the highest photoactivity among all samples under visible light. It was concluded that co-doping of the Ag and Mg can significantly improve the photocatalytic activity of the prepared photocatalysts, due to the efficient inhibition of the recombination of photogenerated electron–hole pairs. The optimum calcination temperature and time were 450 °C and 3 h, respectively.     

Switchable selectivity during oxidation of anilines in a ball mill

A solvent-free method for the direct oxidation of anilines to the corresponding azo and azoxy homocoupling products by using a planetary ball mill was developed. Various oxidants and grinding auxiliaries were tested and a variety of substituted anilines were investigated. It was possible to form chemoselectively either azo, azoxy, or the nitro compounds from reaction of aromatic anilines. The selectivity of the solvent-free reaction is switchable by applying a combination of oxidant and grinding auxiliary. Furthermore, a comparison with other methods of energy input (microwave, classical heating, and ultrasound) highlighted the advantages of the ball mill approach and its high energy efficiency.     

Spectrofluorimetric Determination of Nickel (ΙΙ) with Murexide

A very sensitive and selective spectrofluorimetric method has been developed for nickel (ΙΙ) determination in environmental samples. The method is based on measuring the decrease in fluorescence intensity of murexide after nickel (ΙΙ) binding. The intensity of the fluorescence emission peak was measured at ex/em 345/431 nm in several solutions with pH interval 3.0–7.0. The fluorescence intensity decrease was found to be linear in the concentration range of 0.007 mg.L^?1 to 0.1 mg.L^?1 and 0.1 mg.L^?1 to 20 mg.L^?1 of nickel (ΙΙ) by using 10^?4 M murexide at pH 3. The detection limit was found 0.004 mg.L^?1. Relatively large excesses of over 20 cations and anions do not interfere. The method was successfully applied to the analysis of nickel (ΙΙ) in sea, rain and ground water. This method is very precise and accurate (R.S.D.?=?0.42 % for the determination of 0.05 mg.L?¹ nickel in 10 replicates).     

Oxidation of Primary Aromatic Amines under Irradiation with Ultrasound and/or Microwaves

The oxidation of primary aromatic amines, p-methylaniline, p-ethylaniline and p-chloroaniline to the corresponding azo- and azoxy-compounds has been observed in ultrasound and/or microwaves systems. The individual irradiation of microwaves and its simultaneous irradiation with ultrasound obviously elevate the conversion of amines, as compared with the individual irradiation of ultrasound and the heating in a plain water bath. However, the formation of formamidine resulted in poor selectivity toward azo and azoxy products in the presence of dimethylformamide (DMF).