Combinatorics of Pisot Substitutions

Siirretty Doriast

Automata and Differentiable Words

We exhibit the construction of a deterministic automaton that, given k > 0, recognizes the (regular) language of k-differentiable words. Our approach follows a scheme of Crochemore et al. based on minimal forbidden words. We extend this construction to the case of C\infinity-words, i.e., words differentiable arbitrary many times. We thus obtain an infinite automaton for representing the set of C\infinity-words. We derive a classification of C\infinity-words induced by the structure of the automaton. Then, we introduce a new framework for dealing with \infinity-words, based on a three letter alphabet. This allows us to define a compacted version of the automaton, that we use to prove that every C\infinity-word admits a repetition in C\infinity whose length is polynomially bounded.Comment: Accepted for publicatio

Mathematical Methods in Quantum Chemistry

The field of quantum chemistry is concerned with the modelling and simulation of the behaviour of molecular systems on the basis of the fundamental equations of quantum mechanics. Since these equations exhibit an extreme case of the curse of dimensionality (the Schrödinger equation for N electrons being a partial differential equation on R3N ), the quantum-chemical simulation of even moderate-size molecules already requires highly sophisticated model-reduction, approximation, and simulation techniques. The workshop brought together selected quantum chemists and physicists, and the growing community of mathematicians working in the area, to report and discuss recent advances on topics such as coupled-cluster theory, direct approximation schemes in full configuration-interaction (FCI) theory, interacting Green’s functions, foundations and computational aspects of densityfunctional theory (DFT), low-rank tensor methods, quantum chemistry in the presence of a strong magnetic field, and multiscale coupling of quantum simulations

Experimental and theoretical aspects of quantum chaos in Rydberg atoms in strong fields

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 1996.Includes bibliographical references (leaves 239-252).by Hong Jiao.Ph.D