1. Ordered Classes, Isotone Maps, and Length Functions 1 1.1. Isotone Maps and Artinian Ordered Classes 1 1.2. Length Functions 2 2. Euclidean Functions 3 2.1. Basic Definitions 3 2.2. Structure Theory of Principal Rings 4 2.3. Generalized Euclidean Functions 4 2.4. Isotone Euclidean Functions 5 2.5. The Bottom Euclidean Function and the Euclidean Order Type 6 2.6. The Localized Euclidean Funct...

We present and evaluate an automatic tool for extracting algebraic specifications from Java classes. Our tool maps a Java class to an algebraic signature and then uses the signature to generate a large number of terms. The tool evaluates these terms and based on the results of the evaluation, it proposes equations. Finally, the tool generalizes equations to axioms and eliminates many redundant ...

‎In this paper‎, ‎we introduce the notion of strongly $k-$spaces (with the weak (=finest) pre-topology generated by their strongly compact subsets)‎. ‎We characterize the strongly $k-$spaces and investigate the relationships between preclosedness‎, ‎locally strongly compactness‎, ‎pre-first countableness and being strongly $k-$space.

Associative learning theories offer one account of the way animals and humans assess the relationship between events and adapt their behavior according to resulting expectations. They assume knowledge about event relations is represented in associative networks, which consist of mental representations of cues and outcomes and the associative links that connect them. However, in human causal and...

following the recent work of the authors in development and numerical verification of a new kinematic approach of the limit analysis for surface footings on non-associative materials, a practical procedure is proposed to utilize the theory. it is known that both the peak friction angle and dilation angle depend on the sand density as well as the stress level, which was not the concern of the fo...