The notion of the ‘mathematical impossibility’ of group decision making is founded on errors in microeconomics, game theory, and related disciplines. We highlight mathematical errors that have been committed by von Neumann and Morgenstern, Pareto, Hicks, Samuelson, and Debreu which have been propagated throughout the social sciences. 1 Applicability of Mathematical Operations 1.1 Mathematical S...

Let $X$ be an infinite set, equipped with a topology $tau$. In this paper we studied the relationship between $tau$, and ultrafilters on $X$. We can discovered, among other thing, some relations of the Robinson's compactness theorem, continuity and the separation axioms. It is important also, aspects of communication between mathematical concepts.

In this research, the activity of MnO, produced during steel making in aluminate-rich slags, was investigated. According to thermodynamic equations and mathematical calculation, a series of relations was obtained for evaluation of oxide activity using Masson’s theory. The obtained relations were solved according to Levenberg- Marquardt method and using Matlab software. The results were correlat...

It is well known fact that binary relations are generalized mathematical functions. Contrary to functions from domain to range, binary relations may assign to each element of domain two or more elements of range. Some basic operations on functions such as the inverse and composition are applicable to binary relations as well. Depending on the domain or range or both are fuzzy value fuzzy set, i...

Recent work has shown that undergraduates at a major public university demonstrate implicit understanding of inverse relations between multiplication problems with fractions, as evidenced by the fact that solving one problem facilitates solving its inverse. The present study investigated whether such implicit understanding of mathematical relations is related to overall math ability. We found t...

We use the technique of interactive theorem proving to develop the theory and an enumeration technique for finite idempotent relations. Starting from a short mathematical characterization of finite idempotents defined and proved in Isabelle/HOL, we derive first an iterative procedure to generate all instances of idempotents over a finite set. From there, we develop a more precise theoretical ch...

Most ontology development environments (ODEs) are term oriented and take a frame-based view of the information in an ontology about a given term. Even tools, such as Protégé 4, designed for axiom oriented development preserve the frame-based view as the central mode of interaction with the ontology. The frame-based approach has a number of advantages—most prominently that it is comfortable to p...