A unified approach to embedding theorems for Sobolev type spaces of vector-valued functions, defined via their symmetric gradient, is proposed. The in question are built upon general rearrangement-invariant norms. Optimal target the relevant embeddings determined within class all spaces. In particular, gradient into shown be equivalent corresponding full same sharp condition uniformly continuou...

Triangular norms, or t-norms for short, play an important role for the semantics of fuzzy logics. Although an enormous number of examples and a remarkable number of construction methods for this kind of operation has been established, a uniform approach is still outstanding. This paper is devoted to a specific algebraic-geometrical framework within which t-norms, up to isomorphism, can be descr...

We consider two spacelike separated Dirac particles and construct five invariants under the spinor representations of local proper orthochronous Lorentz groups. All constructed are identically zero for product states. The behaviour unitary evolutions that act unitarily on any subspace with fixed particle momenta is studied. have invariant absolute values such subspaces if generated by zero-mass...

We study the local asymptotics at edge for particle systems arising from: (i) eigenvalues of sums unitarily invariant random Hermitian matrices and (ii) signatures corresponding to decompositions tensor products representations unitary group. Our method treats these two models in parallel, is based on new formulas observables described terms a special family lifts, which we call supersymmetric ...

Abstract We study a quantum analogue of the 2-Wasserstein distance as measure proximity on set ? N density matrices dimension N . show that such (semi-)distances do not induce Riemannian metrics tangent bundle ...

Contour lines totally fix the structure of leftcontinuous t-norms. For each t-norm, these contour lines are determined by the corresponding residual implicator. Most properties involving residual implicators can now easily be translated into properties involving contour lines. As the portation law expresses associativity, we dispose of a powerful tool for constructing left-continuous t-norms. I...

This contribution reviews the external and the internal representations of linear time-invariant systems. This is done both in the time and the frequency domains. The realization problem is then discussed. Given the importance of norms in robust control and model reduction, the final part of this contribution is dedicated to the definition and computation of various norms. Again, the interplay ...

The free convolution ⊞ is the binary operation on the set of probability measures on the real line which allows to deduce, from the individual spectral distributions, the spectral distribution of a sum of independent unitarily invariant square random matrices or of a sum of free operators in a non commutative probability space. In the same way, the rectangular free convolution ⊞ λ allows to ded...