We introduce two new hash-based index structures to index set-valued attributes. Both are able to support subset and superset queries. Analytical cost models for the new index structures as well as for the two existing index structures, sequential signature le and Russian Doll Tree, are presented and experimentally validated. Using the validated cost model, we express the performance of all fou...

Low carbon city is the direction of the development of city in the future. Firstly, this paper constructed the comprehensive evaluation index system of the low carbon economy city that including six primary indexes and 12 secondary indexes by summarizing the recent research of low-carbon connotation and low-carbon evaluation index. These indexes are low-carbon economy, low-carbon energy, low-ca...

A collection A of finite sets is closed under union if A, B ∈ A implies that A ∪ B ∈ A. The Union-Closed Sets Conjecture states that if A is a union-closed collection of sets, containing at least one non-empty set, then there is an element which belongs to at least half of the sets in A. We show that if q is the minimum cardinality of ∪A taken over all counterexamples A, then any counterexample...

We study countable saturation of metric reduced products and introduce continuous fields of metric structures indexed by locally compact, separable, completely metrizable spaces. Saturation of the reduced product depends both on the underlying index space and the model. By using the Gelfand–Naimark duality we conclude that the assertion “Stone–Čech remainder of the half-line has only trivial au...

In Chapter I, we exhibit a high strongly noncappable degree. Chapter II answers negatively the question whether a deep degree exists. It also shows a weak converse of this. Chapter III is devoted to index sets. We define a family of properties on hyperhypersimple sets and show that they yield index sets at each level of the hyperarithmetical hierarchy. We also classify the index set of quasimax...