In gaining word knowledge, children’s semantic representations are initially imprecise before becoming gradually refined. We developed and tested a framework for a digital receptive vocabulary assessment that captured varied levels of representation as children learn words. At pre-test and post-test, children selected one of four images to match a word’s meaning: a correct target, a conceptually-related foil, a thematically-related foil, and a phonologically-similar foil. We expected that selecting a conceptually related foil would indicate that the word is understood at a deeper level than selecting a phonologically similar foil. Indeed, selection of phonological foils decreased from pre- to post-test, while selection of more advanced thematic and conceptual foils increased. These results demonstrate that this assessment tool probed semantic knowledge that might be characterized as intermediate word knowledge. The current paper presents a novel and sensitive way to capture the incremental process of word learning. Applications for vocabulary interventions are discussed.

Size is an important antecedent of firm survival, and several studies theoretically sustain and empirically support a ‘liability of middleness’. Indeed, it is widely believed that companies should act strategically to either become large or remain small and occupy a niche position, because mid-sized firms face the strongest market selection pressures. This study challenges that logic in renewable natural resource industries. Measuring size as product-line scale and firm-level portfolio breadth, we argue that in industries characterized by cost competition, the lack of product differentiation, large capital investments, and sharp price oscillation, scale and breadth have a curvilinear effect on survival that favors mid-sized firms rather than penalizing them. An empirical analysis of the US pulp and paper (P&P) industry over the period 1970–2000 strongly supports our arguments. This study is particularly relevant for emerging economies, in which natural resource industries represent an important portion of the total economic activity.

We consider finite p-groups G in which every cyclic subgroup has at most p conjugates. We show that the derived subgroup of such a group has order at most p2. Further, if the stronger condition holds that all subgroups have at most p conjugates then the central factor group has order p4 at most.

Let K and L be lattices, and let ϕ be a homomorphism of K into L.Then ϕ induces a natural 0-preserving join-homomorphism of Con K into Con L.

Extending a result of Huhn, the authors proved that if D and E are finite distributive lattices and ψ is a 0-preserving join-homomorphism from D into E, then D and E can be represented as the congruence lattices of the finite lattices K and L, respectively, such that ψ is the natural 0-preserving join-homomorphism induced by a suitable homomorphism ϕ: K → L. Let m and n denote the number of join-irreducible elements of D and E, respectively, and let k = max (m, n). The lattice L constructed was of size O(22(n+m)) and of breadth n+m.

We prove that K and L can be constructed as ‘small’ lattices of size O(k5) and of breadth three.