Dynamics of a family of transcendental meromorphic functions having rational Schwarzian derivative

In the present paper, a class F of critically finite transcendental meromorphic functions having rational Schwarzian derivative is introduced and the dynamics of functions in one parameter family is investigated. It is found that there exist two parameter values λ^∗=?(0)>0 and , where and is the real root of ?^′(x)=0, such that the Fatou sets of fλ(z) for λ=λ^∗ and λ=λ∗∗ contain parabolic domains. A computationally useful characterization of the Julia set of the function fλ(z) as the complement of the basin of attraction of an attracting real fixed point of fλ(z) is established and applied for the generation of the images of the Julia sets of fλ(z). Further, it is observed that the Julia set of fλ∈K explodes to whole complex plane for λ>λ∗∗. Finally, our results found in the present paper are compared with the recent results on dynamics of one parameter families λtanz, [R.L. Devaney, L. Keen, Dynamics of meromorphic maps: Maps with polynomial Schwarzian derivative, Ann. Sci. École Norm. Sup. 22 (4) (1989) 55-79; L. Keen, J. Kotus, Dynamics of the family λtan(z), Conform. Geom. Dynam. 1 (1997) 28-57; G.M. Stallard, The Hausdorff dimension of Julia sets of meromorphic functions, J. London Math. Soc. 49 (1994) 281-295] and , λ>0 [G.P. Kapoor, M. Guru Prem Prasad, Dynamics of : The Julia set and bifurcation, Ergodic Theory Dynam. Systems 18 (1998) 1363-1383].     

Facile, Selective, and Regiocontrolled Synthesis of Oxazolines and Oxazoles Mediated by ZnI(2) and FeCl(3)

An expedient method for a direct approach to the selective and regiocontrolled synthesis of 2-oxazolines and 2-oxazoles mediated by ZnI(2) and FeCl(3) is described. A Lewis acid promoted cyclization of acetylenic amide with various functionalities was well tolerated to give 2-oxazolines and 2-oxazoles in good to excellent yields under mild reaction conditions.     

Some new organotin(IV), aluminium(III)-μ-oxoisopropoxides and their benzoylacetone derivatives

The first organotin(IV), aluminium(III)-μ-oxoisoprovides of the type [R₃SnOA](OⁱPr)₂] (R = Me or Ph) have been made by heating of trimethyl- or triphenyl-tin acetate with aluminium isopropoxide. The reactions of these μ-oxoisopropoxides with benzoylacetone in 1:1 and 1:2 molar ratios yielded the compounds of the type [R₃SnOAl(OⁱPr)(bzac)] and [R₃SnOAl(bzac)₂] (where R = Me or Ph and BZAC = deprotonated benzoylacetone), respectively.     

Analysis of bacterial strains with pyrolysis-gas chromatography/differential mobility spectrometry

Eight vegetative bacterial strains and two spores were characterized by pyrolysis-gas chromatography with differential mobility spectrometry (py-GC/DMS) yielding topographic plots of ion intensity, retention time, and compensation voltage simultaneously for ions in positive and negative polarity. Biomarkers were found in the pyrolysate at characteristic retention times and compensation voltages and were confirmed by standard addition with GC/MS analyses providing discrimination between Gram negative and Gram positive bacterial types, but no recognition of individual strains within the Gram negative bacteria. Principal component analysis was applied using two dimensional data sets of ion intensity versus retention time at five compensation voltages including the reactant ion peaks all in positive and negative ion polarity. Clustering was observed with compensation voltage (CV) chromatograms associated with ion separation in the DMS detector and little or no clustering was observed with the reactant ion peaks or CV chromatograms where ion separation is poor. Consistent clustering of Gram positive B. odysseyi and Gram negative E. coli in both positive and negative polarities with the reactant ion peak chromatograms and key CV chromatograms suggests common but unknown common chemical compositions in the pyrolysate.     

Synthesis of spiroindene-1,3-dione isothiazolines via a cascade michael/1,3-dipolar cycloaddition reaction of 1,3,4-oxathiazol-2-one and 2-arylidene-1,3-indandiones

The reaction of 1,3,4-oxathiazol-2-one derivative with 2-arylidene-1,3-indandione to furnish novel spiroindene-1,3-dione isothiazoline derivatives by Michael/1,3-dipolar [3+2]-cycloaddition reaction was investigated. The key 1,3-dipolar cycloaddition reaction step was examined in toluene solvent at reflux temperature to obtain mixture of two regioisomers (6a and 6b – 14a and 14b) and single isomers (15–20). The scope of this new reaction was demonstrated with many examples with high reactivity and yields.     

Transition metal complexes with bidentate ligands spanning trans-positions. XII. The preparation and properties of complexes trans-[MX2 (1)] and trans-[PtHCl (1)] (M = Ni,Pd and Pt; X = Cl and NCS; 1 = ditertiary phosphine)

Complexes [MX₂(1)] (M = Ni, Pd and Pt; X=Cl and NCS; 1 = 2,11-bis(dialkyl-[or diaryl]phosphinomethyl)benzo[c]phenanthrene; alkyl = cyclohexyl t-butyl; aryl = m-tolyl, p-anisyl and m-CF₃ C₆H₄) have been synthesized. An NMR. study of the t-butyl complexes provides evidence for a “fan-like” motion of the benzo[c]phenanthrene moiety over the plane of the complex.     

An Oxidant- and Organic Solvent-Resistant Alkaline Metalloprotease from Streptomyces olivochromogenes

Organic solvent- and detergent-resistant proteases are important from an industrial viewpoint. However, they have been less frequently reported and only few of them are from actinomycetes. A metalloprotease from Streptomyces olivochromogenes (SOMP) was purified by ion exchange with Poros HQ and gel filtration with Sepharose CL-6B. Apparent molecular mass of the enzyme was estimated to be 51 kDa by sodium dodecyl sulfate–polyacrylamide gel electrophoresis and gelatin zymography. The activity was optimum at pH 7.5 and 50 °C and stable between pH 7.0 and 10.0. SOMP was stable below 45 °C and Ca²⁺ increased its thermostability. Ca²⁺ enhanced while Co²⁺, Cu²⁺, Zn²⁺, Mn²⁺, and Fe²⁺ inhibited the activity. Ethylenediaminetetraacetic acid and ethylene glycol-bis (β-aminoethyl ether)-N,N,N′,N′-tetraacetic acid, but not phenylmethylsulfonyl fluoride, aprotinin, and pefabloc SC, significantly suppressed the activity, suggesting that it might be a metalloprotease. Importantly, it is highly resistant against various detergents, organic solvents, and oxidizing agents, and the activity is enhanced by H₂O₂. The enzyme could be a novel protease based on its origin and peculiar biochemical properties. It may be useful in biotechnological applications especially for organic solvent-based enzymatic synthesis.     

Reactions of trapped electrons in methanol-isopropanol glasses irradiated at 77 K

Trapped electron (e _T ^– ) reactivity in methanol-isopropanol glasses irradiated at 77 K has been studied as a function of trap-depth, the variation in the trap depth being achieved by varying the methanol:isopropanol ratio. Benzyl chloride and carbon disulfide have been used as scavengers. In the case of the glasses containing benzyl chloride, the observed yield of the benzyl radical has been correlated with the trapping efficiency of the matrix. The data has been interpreted with the aim of assessing the relative importance of tunnelling in the scavenging of electrons in low temperature glassy matrices.     

Preparation,X-ray crystallography,and thermolysis of phenylenediammonium dibromide salts

Phenylenediammonium dibromide (PDADBr) salts have been prepared and characterized by X-ray crystallography. The thermal decomposition of PDADBr has been studied by thermogravimetry (TG) and differential thermal analysis (DTA). Kinetic parameters have been evaluated using model fitting and isoconversional methods. The thermolytic pathways have also been suggested which involve proton transfer as a primary step to regenerate parent amine and HBr. Interaction between amine and HBr at higher temperature yields gaseous products.