A statistical query rst manipulates source category data to build a target category in the form of a grouping relation and then performs statistical functions on the associated measurement data. In this paper, the attributes in a grouping relation are partitioned into pair-wise disjoint sets, each called a dimension. A grouping relation is said to be orthogonal if it is equal to the cross produ...

DEFINITION Indexing units refers to the granularity of information in the retrieval system’s index, which can be in principle any document part of a structured text, and as a consequence determines the possible units of retrieval. There are three basic approaches: The first approach is to index every potentially retrievable unit as a whole—the so-called element-based approach [13]. The second a...

We show that for every infinite cardinal number m there exist two totally ordered abelian groups whose free product in any nontrivial variety of lattice-ordered groups has a disjoint set of cardinality m. This answers problem 10.7 of [13] and extends the results in [12]. We further prove that for the variety of abelian lattice-ordered groups or the variety of all lattice-ordered groups, the fre...

In this paper, we introduce the concept of dynamical distance on a nuclear conguration space. We partition the nuclear conguration space into disjoint classes. This classification coincides with the classical partitioning of molecular systems via the concept of conjugacy of dynamical systems. It gives a quantitative criterion to distinguish dierent molecular structures.