New Methods for the Synthesis of Imidazoline-N-Oxides

Δ³-lmidazoline-3-oxides were prepared by the reaction of corresponding aromatic Schiff bases with syn-2-bromoacetophenone oxime. 5,6-Dihydro-4H-1,2,5-oxadiazines were isolated as byproduct in some instances.     

Two‐dimensional MHD solver by fluctuation splitting and dual time stepping

Numerical solutions of 2D magneto‐hydrodynamic (MHD) equations by means of a fluctuation splitting (FS) scheme (with a new wave model and dual time stepping technique) is presented. The FS scheme, essentially based on the model explained in Proceedings of the Tenth International Conference, vol. 10, Swansea, 21–25 July 1997; Godunov Symposium, University of Michigan, Ann Arbor, 1–2 May 1997; Physics Symposium, Alanya, Turkey, 27–31 October 1998; J. Comput. Phys. 1999; 153 :437–466; Ph.D. Thesis, University of Marmara, Istanbul, Turkey, 2000), was extended to include gravitational source effects, limiters to limit oscillations, high order time accuracy through multistage Runge–Kutta steps, and a dual time stepping scheme to drive magnetic field divergence to zero during iterations. The numerical results show that with the new wave model called MHD‐B along with its embedded numerical dissipation, correct limiting viscosity solution has been recovered and that it can safely be used in order to investigate steady or time dependent magnetized or neutral compressible flows in two dimensions. Copyright © 2006 John Wiley & Sons, Ltd.     

An investigation into the biocidal effect of high voltage AC/DC atmospheric corona discharges on bacteria,yeasts, fungi and algae

A newly developed, low cost plasma system that works at atmospheric pressure and operates with both DC or AC high voltage power supplies was presented. This system was tested for its biocidal effect on a wide range of micro-organisms in water. Optimal killing parameters such as time, temperature and AC and DC high voltage power levels were tested for bacteria (Escherichia coli, Staphylococcus aureus, Pseudomonas aeruginosa, Streptococcus mutans, Bacillus subtilis), yeast (Candida albicans), fungi (Aspergillus niger) and green algae. Results show this system to have a very efficient biocidal effect on most bacteria, algae and fungi in water.     

Inequalities for the inverses of the polygamma functions

We provide an elementary proof of the left-hand side of the following inequality and give a new upper bound for it.

$$\begin{aligned} \bigg [\frac{n!}{x-(x^{-1/n}+\alpha )^{-n}}\bigg ]^{\frac{1}{n+1}}&<((-1)^{n-1}\psi ^{(n)})^{-1}(x) \\&<\bigg [\frac{n!}{x-(x^{-1/n}+\beta )^{-n}}\bigg ]^{\frac{1}{n+1}}, \end{aligned}$$

where \(\alpha =[(n-1)!]^{-1/n}\) and \(\beta =[n!\zeta (n+1)]^{-1/n}\), which was proved in Batir (J Math Anal Appl 328:452–465, 2007), and we prove the following inequalities for the inverse of the digamma function \(\psi \).

$$\begin{aligned} \frac{1}{\log (1+e^{-x})}<\psi ^{-1}(x)< e^{x}+\frac{1}{2}, \quad x\in \mathbb {R}. \end{aligned}$$

The proofs are based on nice applications of the mean value theorem for differentiation and elementary properties of the polygamma functions.

     

Synthesis and Ring Opening Reactions of Tetrahydroimidazo[1,5- b ][1,2,4]oxadiazol-2(1 H )-thiones

1,3-Dipolar cycloaddition of imidazoline 3-oxides 1 with methylisothiocyanate proceeds regio- and diastereoselectively to give tetrahydroimidazo[1,5- b ][1,2,4]oxadiazol-2(1 H )-thiones 3 in high yields. The cis configuration of the adducts were proved by our double cis elimination test as well as by NOESY experiments. The imidazooxadiazol-2-thiones 3a-e were treated with concentrated HCl in ethanol at 50°;C to give the corresponding 4 H -[1,2,4]oxadiazole-5-thione only in the cases where the substituent at C-6 is an aryl.     

Cycloaddition of Acyclic Nitrones with Phenyl Isocyanate: Synthesis and Ring‐Opening Reactions of 1,2,4‐Oxadiazolidin‐5‐ones

The cycloaddition of nitrones with unsubstituted or electron‐donating substituents on the C‐phenyl 1a,c,f with phenyl isocyanate proceeds smoothly for a short time with high yields to give the corresponding 1,2,4‐oxadiazolidinone 2, and 1b,d,e with electron‐withdrawing substituents gave the corresponding oxadiazolidinone in moderate yields after prolonged heating. Oxadiazolidinones 2a,c,f undergo diethylamine‐induced fragmentation for a short time to give the corresponding Schiff bases, and oxadiazolidinones 2b,d,e remain unchanged in these conditions. Prolonged heating of 2d,e in the presence of diethylamine led to complex mixtures. In the case of 2b the corresponding amidine was the main product of the reaction.     

Novel Methods for the Synthesis of 4‐Arylisoquinolinium Perchlorates and 4‐Arylisoquinolin‐1‐ones

2‐Benzylamino‐1‐phenyl‐ethanones 1 were converted to the corresponding isoquinolinium perchlorates 2 in high yields using 70% HClO₄‐FeCl₃ mixture as a cyclization and oxidation reagent. A mild and high yielding method for the oxidation of perchlorates 2 to isoquinolin‐1‐ones 3 involving the treatment of 2 with KOH and K₃[Fe(CN)₆] in THF‐H₂O two‐phase system at room temperature was developed. Compounds 2a–g were shown to be disproportionate to 3 and the corresponding 1,2‐dihydroisoquinoline 4 in the presence of base, which in turn is oxidized by K₃[Fe(CN)₆] to 2.