Topological structures of complex belief systems

The concepts of substantive beliefs and derived beliefs are defined, a set of substantive beliefs S like open set and the neighborhood of an element substantive belief. A semantic operation of conjunction is defined with a structure of an Abelian group. Mathematical structures exist such as poset beliefs and join-semilattttice beliefs. A metric space of beliefs and the distance of belief depending on the believer are defined. The concepts of closed and opened ball are defined. S′ is defined as subgroup of the metric space of beliefs Σ and S′ is a totally limited set. The term s is defined (substantive belief) in terms of closing of S′. It is deduced that Σ is paracompact due to Stone's Theorem. The pseudometric space of beliefs is defined to show how the metric of the nonbelieving subject has a topological space like a nonmaterial abstract ideal space formed in the mind of the believing subject, fulfilling the conditions of Kuratowski axioms of closure. To establish patterns of materialization of beliefs we are going to consider that these have defined mathematical structures. This will allow us to understand better cultural processes of text, architecture, norms, and education that are forms or the materialization of an ideology. This materialization is the conversion by means of certain mathematical correspondences, of an abstract set whose elements are beliefs or ideas, in an impure set whose elements are material or energetic. Text is a materialization of ideology.

Experiences with free and open courses using on-line multimedia resources

This paper analyzes the learning experiences and opinions obtained from a group of undergraduate students in their interaction with several on-line multimedia resources included in a free on-line course about Computer Networks. These new educational resources employed are based on the Web2.0 approach such as blogs, videos and virtual labs which have been added in a web-site for distance self-learning.

Reductive Removal of the Pivaloyl Protecting Group from Tetrazoles by a Naphthalene-Catalyzed Lithiation Process

The reaction of various 1-pivaloyl-1H-tetrazoles with excess lithium and a catalytic amount of naphthalene (20 mol%) led, after treatment with methanol, to the corresponding free tetrazoles through reductive C–N bond cleavage. This methodology represents a reasonable alternative to other nonreductive protocols.

Indium-Mediated Cleavage of the Trityl Group from Protected 1H-Tetrazoles

On treatment with indium metal in MeOH–THF, trityl groups undergo reductive removal from 1H-protected tetrazoles (including aliphatic, aromatic, and heteroaromatic substituents), affording the corresponding free tetrazoles in excellent yields, without any decomposition of the tetrazole ring or reduction of any other group.