Let $f$ and $g$ be commuting meromorphic functions with finitely many poles. By studying the behaviour of Fatou components under this relation, we prove that have same Julia set whenever no simply connected fast-escaping wandering domains. combining a recent result Tsantaris', obtain strongest statement (to date) regarding sets functions. In order to highlight difference entire case, show trans...

Consider a financial market in which an agent trades with utility-induced restrictions on wealth. By introducing a general convex-analytic framework which includes the class of umbrella wedges in certain Riesz spaces (cf. Definition 2.2 and Remark 2.3) and faces of convex sets, consisting of probability measures (cf. Lemma 4.5 and Proposition 5.4), together with a duality theory for polar wedge...

We prove new results about the remarkable infinite simple groups introduced by Richard Thompson in the 1960s. We give a faithful representation in the Cuntz C⋆algebra. For the finitely presented simple group V we show that the word-length and the table size satisfy an n log n relation. We show that the word problem of V belongs to the parallel complexity class AC1 (a subclass of P), whereas the...

We prove that the multiparameter (product) space BMO of functions of bounded mean oscillation can be written as the intersection of finitely many dyadic product BMO spaces, with equivalent norms, generalizing the one-parameter result of T. Mei. We establish the analogous dyadic structure theorems for the space VMO of functions of vanishing mean oscillation, for Ap weights, for reverse-Hölder we...

Super symmetry is a type of matrix-based symmetry that extends the concept of total symmetry. Super symmetric functions are “even more symmetric” than totally symmetric functions. Even if a function is not super symmetric, the super symmetric transpose matrices can be used to detect partial super symmetries. These partial symmetries can be mixed arbitrarily with ordinary symmetric variable pair...

Earlier work by several authors has focused on defining Boolean function classes by means of functional equations. In [10], it was shown that the classes of Boolean functions definable by functional equations coincide with initial segments of the quasi-ordered set (Ω,≤) made of the set Ω of Boolean functions, suitably quasi-ordered. Furthermore, the classes defined by finitely many equations co...