A bstract In four-dimensional axion electrodynamics, a Chern-Simons coupling of the form ?F ^ F leads to higher-group global symmetry between background gauge fields. At same time, such mixing Weak Gravity Conjectures for and field, so that charged excitations Conjecture-satisfying string will also satisfy Conjecture field. this paper, we argue these symmetries phenomenon are related one anothe...

We prove that for a dense G± of shift-invariant measures on AZ d , all d shifts have purely singular continuous spectrum and give a new proof that in the weak topology of measure preserving Zd transformations, a dense G± is generated by transformations with purely singular continuous spectrum. We also give new examples of smooth unitary cocycles over an irrational rotation which have purely sin...

We investigate the physical meaning of some of the texture zeros which appear in most of the Ansätze on leptonic masses and their mixing. It is shown that starting from arbitrary lepton mass matrices and making suitable weak basis transformations one can obtain some of these sets of zeros, which therefore have no physical content. We then analyse four-zero texture Ansätze where the charged lept...

A nonsingular transformation is said to be doubly ergodic if for all sets A and B of positive measure there exists an integer n > 0 such that (T n(A) \ A) > 0 and (T n(A) \ B) > 0. While double ergodicity is equivalent to weak mixing for nite measure-preserving transformations, we show that this is not the case for in nite measure preserving transformations. We show that all measure-preserving ...

Fulton and MacPherson introduced the notion of bivariant theories related to Riemann-Roch-theorems, especially in the context of singular spaces. This is powerful formalism, which is a simultaneous generalization of a pair of contravariant and covariant theories. Natural transformations of bivariant theories are called Grothendieck transformations, and these generalize a pair of ordinary natura...

We show that a typical interval exchange transformation is either weakly mixing or it is an irrational rotation. We also conclude that a typical translation flow on a surface of genus g ≥ 2 (with prescribed singularity types) is weakly mixing.

Except for a set of first category, all pairs of measure preserving transformations generate a dense subgroup of G, the group of all invertible measure preserving transformations of the unit interval when G has the weak topology. Consider G the group of invertible (Lebesgue) measure preserving transformations of the unit interval onto itself. On G, we put the weak topology (Halmos [2, pp. 61-67...

Model transformations play a cornerstone role with the emergence of Model Driven Engineering (MDE), where models are transformed from higher to lower levels of abstraction. Unfortunately, a quick and easy way to check the correctness of model transformations is still missing, which compromises their quality (and in turn, the quality of the target models generated from them). In this paper we pr...