Katsunori Kawamura1 College of Science and Engineering Ritsumeikan University, 1-1-1 Noji Higashi, Kusatsu, Shiga 525-8577,Japan Abstract We show that there exists a non-cocommutative comultiplication ∆φ and a counit ε on the direct sum of Cuntz algebras O∗ ≡ C⊕O2 ⊕O3 ⊕O4 ⊕ · · · . From ∆φ, ε and the standard algebraic structure, the C ∗-algebra O∗ is a bialgebra. Furthermore we show the follow...

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The uniform box product was introduced by Scott Williams in 2001, but very little was done with it until the recent (2010 and 2012) [B1], [H1] dissertations of Jocelyn Bell and Jeffrey Hankins. Their results had to do with two questions that Williams posed a decade earlier: whether the uniform box product of compact spaces is normal, and whether it is paracompact. Hankins answered the latter qu...

Given the prevalence of the use of rhetorical relations in the generation of text (Itovy, 1989; Moore and Paris, 1988; Scott and Souza, 1990), it is surprising how little work has actually been done on the grammatical realization of these relations. Most systems, based on Mann and Thompson's formulation of Rhetorical Structure Theory (Mann and Thompson, 1988), have adopted simplified solutions ...

An exact meet in a lattice is a special type of infimum characterized by, inter alia, distributing over finite joins. In frames, the requirement that a meet is preserved by all frame homomorphisms makes for a slightly stronger property. In this paper these concepts are studied systematically, starting with general lattices and proceeding through general frames to spatial ones, and finally to an...