When 1 < p <∞, maps f in W1/p,p((0,1);S1) have W1/p,p phases φ, but the W1/p,pseminorm of φ is not controlled by the one of f . Lack of control is illustrated by “the kink”: f = eıφ, where the phase φ moves quickly from 0 to 2π. A similar situation occurs for maps f : S1 → S1, with Moebius maps playing the role of kinks. We prove that this is the only loss of control mechanism: each map f : S1 ...

Recursion or self-reference is a key feature of contemporary research and writing in semiotics. The paper commences by focusing on the role of recursion in poststructuralism. It is suggested that much of what passes for recursion in this field is in fact not recursive all the way down. After the paradoxical meaning of radical recursion is adumbrated, topology is employed to provide some example...

Cost complementarities arise from synergies in the production of heterogeneous goods. It is shown that synergies can be accounted for in terms of shared public inputs (roughly) if and only if synergies decrease as the scope of production increases. This case of ‘‘substitutive’’ synergies is argued to be typical. The key technical tool is a novel interpretation of conjugate Moebius inversion in ...

In this paper, we prove that all but one of the components transfer digraph D? m needed for enumeration 2-factors in rectangular, thick cylinder and Moebius strip grid graphs fixed width (m ? N) are bipartite digraphs their orders could be expressed term binomial coefficients. addition, set vertices each component consists binary m-words which difference numbers zeros odd even positions is cons...