We consider three aspects of avoiding large squares in infinite binary words. First, we construct an infinite binary word avoiding both cubes xxx and squares yy with |y| ≥ 4; our construction is somewhat simpler than the original construction of Dekking. Second, we construct an infinite binary word avoiding all squares except 0, 1, and (01); our construction is somewhat simpler than the origina...

While the classical account of the linear continuum takes it to be a totality of points, which are its ultimate parts, Aristotle conceives of it as continuous and infinitely divisible, without ultimate parts. A formal account of this conception can be given employing a theory of quantification for nonatomic domains and a theory of region-based topology.

In this comment, I extend Cavalcanti and Nosal’s (2010) framework to include the case of perfectly divisible money and unrestricted money holdings. I show that when trade takes place in Walrasian markets, counterfeits circulate and the Friedman rule is still optimal.

In this correspondence we determine an upper bound on the error recovery time of a decision feedback equalizer (DFE) operating on a high signal to noise ratio channel of exponential impulse response to be used for binary transmission. This bound is related to the channel time constant and we show that exponential impulse response channels form a favourable class of channels with regard to DFE e...

Let P be a hereditary property of words, i.e., an infinite class of finite words such that every subword (block) of a word belonging to P is also in P . Extending the classical Morse-Hedlund theorem, we show that either P contains at least n+1 words of length n for every n or, for some N , it contains at most N words of length n for every n. More importantly, we prove the following quantitative...