Normal Forms for Nonautonomous Differential Equations

We extend Henry Poincarés normal form theory for autonomous differential equations x=f(x) to nonautonomous differential equations x=f(t, x). Poincarés nonresonance condition λ_j−∑ⁿ_i=1 ?_iλ_i≠0 for eigenvalues is generalized to the new nonresonance condition λ_j∩∑ⁿ_i=1 ?_iλ_i=∅ for spectral intervals.     

Meso-[2.2]paracyclophanyltriphenylporphyrin: A simple representative of cyclophanylporphyrins

(R + S)Meso-[2.2]Paracyclophanyltriphenylporphyrin 3 , a member of a novel class of cyclophanylporphyrins, was obtained and characterized by spectroscopic and electrochemical methods. Compared to meso-tetra[2.2]paracyclophanylporphyrin 1, it represents a simplified structure designed for the investigation of electronic interactions between the [2.2]paracyclophane moiety and porphyrin core and for use in metallation reactions.     

Stereochemical applications of potential energy calculations : Part V. Conformational studies of some 1,1,2-trisubstituted ethanes by the molecular mechanics method (MM2)

The conformational distribution of some 1,1,2-trisubstituted ethanes was studied by the molecular mechanics method. An overall satisfactory correlation with experimental data is obtained, especially when these refer to experimental conditions excluding possible dimerization.