Energy corrections of the two dimensional Dunkl harmonic oscillator in the Non-Commutative phase-space

In this paper, we examine the harmonic oscillator problem in non-commutative phase space (NCPS) by using the Dunkl derivative instead of the habitual one. After defining the Hamilton operator, we use the perturbation method to derive the binding energy eigenvalues. We find eigenfunctions that correspond to these eigenvalues in terms of the Laguerre functions. We observe that the Dunkl-Harmonic Oscillator (DHO) in the NCPS differs from the ordinary one in the context of providing additional information on the even and odd parities. Therefore, we conclude that working with the Dunkl operator could be more appropriate because of its rich content.Comment: 7 page

Enzymatic oligomerization and polymerization of arylamines: state of the art and perspectives

The literature concerning the oxidative oligomerization and polymerization of various arylamines, e.g., aniline, substituted anilines, aminonaphthalene and its derivatives, catalyzed by oxidoreductases, such as laccases and peroxidases, in aqueous, organic, and mixed aqueous organic monophasic or biphasic media, is reviewed. An overview of template-free as well as template-assisted enzymatic syntheses of oligomers and polymers of arylamines is given. Special attention is paid to mechanistic aspects of these biocatalytic processes. Because of the nontoxicity of oxidoreductases and their high catalytic efficiency, as well as high selectivity of enzymatic oligomerizations/polymerizations under mild conditions-using mainly water as a solvent and often resulting in minimal byproduct formation-enzymatic oligomerizations and polymerizations of arylamines are environmentally friendly and significantly contribute to a "green'' chemistry of conducting and redox-active oligomers and polymers. Current and potential future applications of enzymatic polymerization processes and enzymatically synthesized oligo/polyarylamines are discussed