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## Scholarly Works (324 results)

In 1957, N. G. de Bruijn showed that the symmetric group Sym(Ω) on an infinite set Ω contains a free subgroup on 2^{card(Ω)} generators, and proved a more general statement, a sample consequence of which is that for any group *A* of cardinality ≤ card(Ω), the group Sym(Ω) contains a coproduct of 2^{card(Ω)} copies of *A*, not only in the variety of all groups, but in any variety of groups to which *A* belongs. His key lemma is here generalized to an arbitrary variety of algebras **V**, and formulated as a statement about functors **Set** → **V**. From this one easily obtains analogs of the results stated above with "group" and Sym(Ω) replaced by "monoid" and the monoid Self(Ω) of endomaps of Ω, by "associative *K*-algebra" and the *K*-algebra End_{K}(*V*) of endomorphisms of a *K*-vector-space *V* with basis Ω, and by "lattice" and the lattice Equiv(Ω) of equivalence relations on Ω. It is also shown, extending another result from de Bruijn's 1957 paper, that each of Sym(Ω), Self(Ω) and End_{K}(*V*) contains a coproduct of 2^{card(Ω)} copies of itself.

That paper also gave an example of a group of cardinality 2^{card(Ω)} that was *not* embeddable in Sym(Ω), and R. McKenzie subsequently established a large class of such examples. Those results are shown here to be instances of a general property of the lattice of solution sets in Sym(Ω) of sets of equations with constants in Sym(Ω). Again, similar results - this time of varying strengths - are obtained for Self(Ω), End_{K}(*V*) and Equiv(Ω), and also for the monoid Rel(Ω), of binary relations on Ω.

Many open questions and areas for further investigation are noted.

There have been inconsistent findings in previous second language research on the effect of vocabulary glossing on reading comprehension (Davis, 1989; Jacobs, Dufon, & Fong, 1994; Johnson, 1982; Pak, 1986). The present study was undertaken to extend this body of research in two ways: (a) by including another set of second language learners, another text, and another set of vocabulary glosses, accompanied by rigorous experimental procedures; and, (b) by considering the possible interaction of other variables with glossing. These other variables were: psychological type, tolerance of ambiguity, proficiency, frequency of gloss use, perceived value of gloss use, and time on task.

Glossing can be situated in the context of recent work on the reading process (Eskey, 1988; Lesgold & Perfetti, 1981; Rumelhart, 1980; Stanovich, 1980) and learning strategies (Cohen, 1990; O'Malley & Chamot, 1990; Ojrford, 1990; Wenden, 1991). Glossing strengthens the bottom-up component of the reading process. The use of glossing is one of several possible repair strategies that readers can use when they recognize comprehension breakdowns.

One hundred sixteen U.S. college students enrolled in a third-semester Spanish course participated in the study. They were randomly assigned to one of two conditions, with half reading an unglossed Spanish text and half reading the same text accompanied by English glosses. After reading the text, participants were asked to write as much of the text as they could recall. Results showed a significant effect for glossing but no significant interactions between the treatment and any of the other variables. Suggestions are made as to the optimal use of vocabulary glosses.

Properties of several sorts of lattices of convex subsets of Rn are examined. The lattice of convex sets containing the origin turns out, for n > 1, to satisfy a set of identities strictly between those of the lattice of all convex subsets of Rn and the lattice of all convex subsets of Rn-1. The lattices of arbitrary, of open bounded, and of compact convex sets in Rn all satisfy the same identities, but the last of these is join-semidistributive, while for n > 1 the first two are not. The lattice of relatively convex subsets of a fixed set S subset of Rn satisfies some, but in general not all of the identities of the lattice of "genuine" convex subsets of Rn.

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