A quasiperiodic word is, here, a finite or infinite word that can be obtained by concatenations or overlaps of a given finite word, called a quasiperiod of the whole word. For instance, aba is a quasiperiod of the Fibonacci word. It is an immediate observation that any quasiperiodic word contains an overlap. Thus its critical exponent is greater than 2. What is the minimal critical exponent of ...

A granular column is subjected to a small amplitude impact on its top. For a generalized power-law contact force between neighboring grains, numerical simulations show that the propagation of the impulse wave is controlled by dispersion. This leads quantitatively to a power-law decrease of the amplitude of the wave with depth. We find numerically the dependence of this power-law exponent on the...

In 1867, Syvlester noted that the Kronecker product of two Hadamard matrices is an Hadamard matrix. This gave a way to obtain an Hadamard matrix of exponent four from two of exponent two. Early last decade, Agayan and Sarukhanyan found a way to combine two Hadamard matrices of exponent two to obtain one of exponent three, and just last year Craigen, Seberry and Zhang discovered how to combine f...

We analyse the power spectra of avalanches in two classes of selforganized critical sandpile models, the Bak–Tang–Wiesenfeld model and the Manna model. We show that these decay with a 1/fα power law, where the exponent value α is significantly smaller than 2 and equals the scaling exponent relating the avalanche size to its duration. We discuss the basic ingredients behind this result, such as ...

|A new approach for getting upperbounds for the capacity and the error exponent of the Poisson channel is proposed. It is based on a new sphere{packing lowerbound for the error probability. Strong converse for the coding theorem is also established.