We establish a framework for oracle identification problems in the continuous variable setting, where the stated problem necessarily is the same as in the discrete variable case, and continuous variables are manifested through a continuous representation in an infinite-dimensional Hilbert space. We apply this formalism to the Deutsch-Jozsa problem and show that, due to an uncertainty relation b...

This third and last part of a series of position papers on triangular norms (for Parts I and II see [25, 26]) presents the representation of continuous Archimedean t-norms by means of additive generators, and the representation of continuous t-norms by means of ordinal sums with Archimedean summands, both with full proofs. Finally some consequences of these representation theorems in the contex...

A representation of continuous and prime-continuous lattices via formal topology is found. This representation stems from special examples of formal topologies in constructive analysis that give rise to the definition of the classes of locally Stone and locally Scott formal topologies. As an application, a representation theorem for locally compact spaces is obtained.

In this paper we introduce a basic representation for the confluent Cherednik algebras HV, HIII, H7 III and H D8 III defined in arXiv:1307.6140. To prove faithfulness of this basic representation, we introduce the non-symmetric versions of the continuous dual qHahn, Al-Salam–Chihara, continuous big q-Hermite and continuous q-Hermite polynomials.