In th is p a p e r w e provide a state space approach for cons t ruc t ing convoIutiona1 codes of rate 1/72 a n d complexi ty 6, whose f ree d is tance is n(6 + l), the max ima l possible f ree dis tance.

We study the resonance phenomena for time periodic perturbations of a Hamiltonian H on the Hilbert space L(R). Here, resonances are characterized in terms of time behavior of the survival probability. Our approach uses the Floquet-Howland formalism combined with the results of L. Cattaneo, J.M. Graf and W. Hunziker on resonances for time independent perturbations.

In [23], Todorcevic gives a survey of basis problems in combinatorial set theory, listing nine theorems and six working conjectures — all in the presence of PFA — including the following three of interest to us here: Conjecture 1 (Todorcevic; [23]). If R is a binary relation, then either R ≤ א0 ·ω1 or [ω1]0 ≤ R. Conjecture 2 (Hajnal, Juhasz; [5]). If X is a regular Hausdorff space, then the fol...

In particular, let K be a framed knot in a closed oriented three-manifold Y . For a rational number r , let Yr .K/ be the manifold obtained by Dehn surgery along K with slope r . Two surgeries along K with distinct slopes r and r 0 are called equivalent if there exists an orientation-preserving homeomorphism of the complement of K taking one slope to the other; and they are called truly cosmeti...

The convergence of Fourier series of trigonometric functions is easy to see, but the same question for general functions is not simple to answer. We study the convergence of Fourier series in Lp spaces. This result gives us a criterion that determines whether certain partial differential equations have solutions or not.We will follow closely the ideas from Schlag and Muscalu’s Classical and Mul...