Descripción: A procedure for the construction of balanced orthogonal nonseparable quincunx multiwavelets, having filters with good lowpass properties, is introduced. The matrix filter bank is viewed as the polyphase matrix of other filters, upon which the lowpass condition is imposed. The multiscaling functions obtained are plotted by means of the cascade algorithm. The process of transforming an image with these wavelets is outlined: formulae for analysis and synthesis are given, the first steps are illustrated with images, and the decomposition of the original image into two input images is addressed. Compression is achieved in a nonlinear process. Experimental results show that (i) the constructed multiwavelets having lowpass properties perform better than other nonseparable multiwavelets, (ii) the energy compaction in the fine detail subbands is greater for the multiwavelets than for the one-dimensional wavelets tried.

Descripción: The excited states of the double hydrogen bond in the adenine-thymine nucleotide base pair has been investigated in the semiempirical CNDO/S-CI approximation. Double-minimum potential curves are obtained for several nuclear configurations characterizing simultaneous tautomeric rearrangements of the NH⋯N and O⋯HN bonds. The energy profiles for the coupled movement of the hydrogen bonding show that the Watson-Crick configuration of the adenine-thymine base pair is the most stable for all of the excited states studied. Estimates are made within the WKB approximation of the tunneling rate and tunneling probability. The results indicate that increasing the energy of the excited states would increase the probability of double protonic transfer by tunnel effect and thus for irreversible mutation. A comparison of the composition of the potentials for the single movement of the protons with the double-minimum potential of the concerted movement shows that the potential is nonseparable. The shortcomings that follow from the WKB approximation as applied to the present problem are discussed. © 1981 American Chemical Society.