Our purpose is to understand the mechanism through which pH affects the competition between base-induced elimination and substitution. To this end, we have quantum chemically investigated the competition between elimination and substitution pathways in H2O+C2H5OH2 (+) and OH(-)+C2H5OH, that is, two related model systems that represent, in a generic manner, the same reaction under acidic and bas...

A discrete Fourier analysis on the dodecahedron is studied, from which results on a tetrahedron is deduced by invariance. The results include Fourier analysis in trigonometric functions, interpolation and cubature formulas on these domains. In particular, a trigonometric Lagrange interpolation on the tetrahedron is shown to satisfy an explicit compact formula and the Lebesgue constant of the in...

A DNA tetrahedron is employed for efficient delivery of doxorubicin into drug-resistant breast cancer cells. The drug delivered with the DNA nanoconstruct is considerably cytotoxic, whereas free doxorubicin is virtually non-cytotoxic for the drug-resistant cells. Thus, the DNA tetrahedron, made of the inherently natural and biocompatible material, can be a good candidate for the drug carrier to...

The Sierpinski tetrahedron is two-dimensional with respect to fractal dimensions though it is realized in threedimensional space, and it has square projections in three orthogonal directions. We study its generalizations and present two-dimensional fractals with many square projections. One is generated from a hexagonal bipyramid which has square projections not in three but in six directions. ...

The retro-ene reaction is a common reaction of metastable immonium ions, leading to the expulsion of an alkene molecule. The kinetic energy release that accompanies this reaction decreases with alkyl substitution on the γ-carbon of the immonium ion. A number of authors have taken this result to indicate that the retro-ene reaction proceeds in a non-concerted manner via a carbocation intermediat...