We consider partially observable Markov decision processes with finite or countably infinite (core) state and observation spaces and finite action set. Following a standard approach, an equivalent completely observed problem is formulated, with the same finite action set but with an uncountable state space, namely the space of probability distributions on the original core state space. By devel...

Let B be a σ–unital C–algebra. We show that every strongly continuous E0–semigroup on the algebra of adjointable operators on a full Hilbert B–module E gives rise to a full continuous product system of correspondences over B. We show that every full continuous product system of correspondences over B arises in that way. If the product system is countably generated, then E can be chosen countabl...

According to a Received View, relativistic quantum field theories (RQFTs) do not admit particle interpretations. This view requires that particles be localizable and countable, and that these characteristics be given mathematical expression in the forms of local and unique total number operators. Various results (the Reeh-Schlieder theorem, the Unruh Effect, Haag’s theorem) then indicate that f...

Abstract The distinction between abstract and concrete concepts is fundamental to cognitive linguistics science. This commonly operationalized through concreteness ratings based on the aggregated judgments of many people. What often overlooked in experimental studies using this operationalization that are attributed words , not directly. In paper we explore relationship linguistic properties En...

This paper proposes an efficient approach for the plane segmentation of indoor and corridor scenes. Specifically, proposed method first uses voxels to pre-segment scene establishes topological relationship between neighboring voxels. The voxel normal vectors are projected onto surface a Gaussian sphere based on corresponding directions achieve fast grouping using variant K-means approach. To im...

In this paper, I offer a Radical Constructon Grammar analysis of some aspects of countability in English. Radical Construction Grammar (Croft 1999, 2000, 2001, MS) shares with other construction grammars the assumption that all grammatical knowledge can be represented uniformly as a network of constructions, where ‘construction’ is taken to describe form-meaning pairings of grammatical structur...

In spacetime physics, we frequently need to consider a set of all spaces (‘universes’) as a whole. In particular, the concept of ‘closeness’ between spaces is essential. However there has been no established mathematical theory so far which deals with a space of spaces in a suitable manner for spacetime physics. Based on the scheme of the spectral representation of geometry, we construct a spac...

This paper examines the significance of the schematic domain of BOUNDEDNESS in adjectives. It is proposed that boundedness in adjectives is a fundamental characteristic associated with gradability. Cross-categorial correspondences are made to nouns and verbs, where boundedness is a feature of countability and aktionsart respectively. Two basic types of gradable adjectives are distinguished: tho...