We establish a dichotomy for the rate of decay Cesàro averages correlations sufficiently regular functions typical interval exchange transformations (IET) which are not rigid rotations (for weak mixing had been previously established in works Katok–Stepin, Veech, and Avila–Forni). show that is either logarithmic or polynomial, according to whether IET rotation class (i.e., it can be obtained as...

Martensitic transformations are diffusionless solid-to-solid phase transformations characterized by a rapid change of crystal structure, observed in metals, alloys, ceramics, and proteins. They come in two widely different classes. In steels, the transformation microstructure induced by quenching remains essentially unchanged upon subsequent loading or heating; the transformation is not reversi...

This paper continues the development of a simplicial theory of weak ω-categories, by studying categories which are enriched in weak complicial sets. These complicial Gray-categories generalise both the Kan complex enriched categories of homotopy theory and the 3-categorical Gray-categories of weak 3-category theory. We derive a simplicial nerve construction, which is closely related to Cordier ...

We consider a higher-derivative generalization of disformal transformations in $D$-dimensional spacetime and clarify the conditions under which they form group with respect to matrix product functional composition. These allow us systematically construct inverse transformation fully covariant manner. Applying invertible generalized known ghost-free scalar-tensor theories, we obtain novel class ...