Neighborhood spaces, pretopological spaces, and closure spaces are topological space generalizations which can be characterized by means of their associated interior (or closure) operators. The category NBD of neighborhood spaces and continuous maps contains PRTOP as a bicoreflective subcategory and CLS as a bireflective subcategory, whereas TOP is bireflectively embedded in PRTOP and bicorefle...

For an (n − 1)-Auslander algebra Λ with global dimension n ≥ 2, we show that if Λ admits a trivial maximal (n − 1)-orthogonal subcategory of modΛ, then Λ is of finite representation type and the projective dimension or injective dimension of any indecomposable module in modΛ is at most n − 1. As a result, we have that for an Auslander algebra Λ with global dimension 2, if Λ admits a trivial max...

CATEGORY →subcategory m:m: → VALUE CATEGORY ONE TO MANY ENUMERATED TYPE permitted-value: String m:m the range (m:1)

Let D be a triangulated category with a cluster tilting subcategory U . The quotient category D/U is abelian; suppose that it has finite global dimension. We show that projection from D to D/U sends cluster tilting subcategories of D to support tilting subcategories of D/U , and that, in turn, support tilting subcategories of D/U can be lifted uniquely to weak cluster tilting subcategories of D.

We report on two experiments designed to examine how the similarity of retrieval-practised and not-retrieval-practised items influences the amount of retrieval-induced forgetting. Participants studied categorised item lists with each category consisting of exemplars from two different semantic subcategories. Using both the retrieval practice paradigm (Experiment 1) and the output interference p...

Stimuli that capture the central tendency of presented exemplars are often preferred-a phenomenon also known as the classic beauty-in-averageness effect. However, recent studies have shown that this effect can reverse under certain conditions. We propose that a key variable for such ugliness-in-averageness effects is the category structure of the presented exemplars. When exemplars cluster into...

Given a variety of algebras V, we study categories of algebras in V with a compatible structure of uniform space. The lattice of compatible uniformities of an algebra, Unif A, can be considered a generalization of the lattice of congruences ConA. Mal’cev properties of V influence the structure of Unif A, much as they do that of ConA. The category V[CHUnif] of complete, Hausdorff such algebras i...

We investigate the conditions under which least bisimulations exist with respect to set inclusion. In particular, we describe a natural way to remove redundant pairs from a given bisimulation. We then introduce the conciseness property on process graphs, which characterizes the existence of least bisimulations under the aforementioned method. Subsequently, we consider the category of process gr...

We present a partial Max-SAT solver QMaxSAT which uses CNF encoding of Boolean cardinality constraints. The old version 0.1 was obtained by adapting a CDCL based SAT solver MiniSat to manage cardinality constraints. It was placed first in the industrial subcategory and second in the crafted subcategory of partial Max-SAT category of the 2010 Max-SAT Evaluation. The new version 0.2 is obtained b...