In this paper we introduce Calder\'on-Zygmund theory for singular stochastic integrals with operator-valued kernel. particular, prove $L^p$-extrapolation results under a H\"ormander condition on the Sparse domination and sharp weighted bounds are obtained Dini kernel, leading to version of solution $A_2$-conjecture. The applied obtain $p$-independence maximal $L^p$-regularity both in complex re...

Multiple twinning in cubic crystals is represented geometrically by a three-dimensional fractal and algebraically by a groupoid. In this groupoid, the variant crystals are the objects, the misorientations between the variants are the operations, and the Sigma3(n) operators are the different types of operations (expressed by sets of equivalent operations). A general formula gives the number of v...

We describe the embedding of the semantic notions and modal operators of a fir st-order temporal logic based on time intervals in a multivalued setting. Truth values will be realized as functions from time intervals to "ordinary" truth values like t and f . The main emphasis lies on the realization of the various modal operators contained in the temporal logic as operations on the functional tr...

In this paper we consider a mixed boundary value problem with nonhomogeneous, nonlinear differential operator (called double phase operator), convection term (a reaction depending on the gradient), three multivalued terms, and an implicit obstacle constraint. Under very general assumptions data, prove that solution set of such is nonempty (so there at least one solution) weakly compact. The pro...