The classical algorithm for mining association rules is low efficiency. Generally there is high redundancy between gained rules. To solve these problems, a new algorithm of finding non-redundant association rules based on frequent concept sets was proposed. The Hasse graph of these concepts was generated on the basis of the FP-tree. Because of the restriction of the support most Hasse graphs ha...

Let F be a field of characteristic different from 2. The u-invariant and the Hasse number ũ of a field F are classical and important field invariants pertaining to quadratic forms. These invariants measure the suprema of dimensions of anisotropic forms over F that satisfy certain additional properties. We prove new relations between these invariants and we give a new characterization of fields ...

Hasse-Minkowski’s theorem asserts that a quadratic form over a number field k admits a nontrivial zero if it does over completions at all places of k. One could look for analogues of Hasse principle for function fields. Let k be a field of characteristic not 2 and Ω a set of discrete valuations of k. Let k̂v denote the completion of k at v. We say that k satisfies Hasse principle with respect to...

We construct an Enriques surface over Q with empty étale-Brauer set (and hence no rational points) for which there is no algebraic Brauer-Manin obstruction to the Hasse principle. In addition, if there is a transcendental obstruction on our Enriques surface, then we obtain a K3 surface that has a transcendental obstruction to the Hasse principle.

The u-invariant and the Hasse number ũ of a field F of characteristic not 2 are classical and important field invariants pertaining to quadratic forms. They measure the suprema of dimensions of anisotropic forms over F that satisfy certain additional properties. We prove new relations between these invariants and a new characterization of fields with finite Hasse number (resp. finite u-invarian...

The Hasse-Minkowski Theorem provides a characterization of the rational quadratic forms. What follows is a proof of the Hasse-Minkowski Theorem paraphrased from the book, Number Theory by Z.I. Borevich and I.R. Shafarevich [1]. Throughout this paper, some familiarity with the p-adic numbers and the Hilbert symbol is assumed and some basic facts about quadratic forms are stated without proof. Al...

Middendorf, M. and F. Pfeiffer, Weakly transitive orientations, Hasse diagrams and string graphs, Discrete Mathematics 111 (1993) 393-400. We introduce the notion of a weakly transitive orientation for graphs as a natural generalization of transitive orientations and give a characterization for weakly transitive orientations in terms of forbidden substructurs. As a corollary of this characteriz...

To represent concurrent behaviours one can use concepts originating from language theory, including traces and comtraces. Traces can express notions such as concurrency and causality, whereas comtraces can also capture weak causality and simultaneity. This paper is concerned with the development of efficient data structures and algorithms for manipulating comtraces. We introduce and investigate...

of adèlic points under the product topology? Can one count the points in X(k) of bounded height? In favourable circumstances, the Hardy–Littlewood circle method can systematically provide answers to all of these questions. The focus of this survey will be upon the first and most basic of these questions: when is X(k) 6= ∅ for a given variety X defined over k? In considering what the circle meth...