We characterize those regular continuous frames for which the least compactification is a perfect compactification. Perfect compactifications are those compactifications of frames for which the right adjoint of the compactification map preserves disjoint binary joins. Essential to our characterization is the construction of the frame analog of the twopoint compactification of a locally compact ...

Qualitative Process theory provides a formal representation for human-like models of continuous processes. Prior research mapped qualitative process elements onto English language constructions, but did not connect the representations to existing frame semantic resources. Here we identify and classify QP language constituents through their instantiation in FrameNet frames to provide a unified s...

Abstract Continuous frames and tensor products are important topics in theoretical physics. This paper combines those concepts. We derive fundamental properties of continuous for product Hilbert spaces. includes, example, the consistency property, i.e. preservation frame property under product, description canonical dual tensors by on space level. show full characterization all systems a given ...

In recent years directional multiscale transformations like the curveletor shearlet transformation have gained considerable attention. The reason for this is that these transforms are unlike more traditional transforms like wavelets able to efficiently handle data with features along edges. The main result confirming this property for shearlets is contained in [21] where it is shown that for ve...

0

Qualitative Process theory provides a formal representation for human-like models of continuous processes. However, qualitative reasoning systems frequently rely on hand-made models which inhibits expansion into new domains. A representation that unifies QP theory with natural language expressions would allow these systems to expand their models by reading and interaction, thus greatly increasi...

This paper addresses the natural question: “How should frames be compared?” We answer this question by quantifying the overcompleteness of all frames with the same index set. We introduce the concept of a frame measure function: a function which maps each frame to a continuous function. The comparison of these functions induces an equivalence and partial order that allows for a meaningful compa...