We introduce a category of noncommutative bundles. To establish geometry in this category we construct suitable noncommutative differential calculi on these bundles and study their basic properties. Furthermore we define the notion of a connection with respect to a differential calculus and consider questions of existence and uniqueness. At the end these constructions are applied to basic examp...

Considering the Euclidean Jordan algebra of the real symmetric matrices endowed with the Jordan product and the inner product given by the usual trace of matrices, we construct an alternating Schur series with an element of the Jordan frame associated to the adjacency matrix of a strongly regular graph. From this series we establish necessary conditions for the existence of strongly regular gra...

This paper one of the series of papers in which we lay down the foundations for design of trustworthy computing systems. We propose here a methodology to perform behavior-based intrusion detection on security protocols using fuzzy relational methods. Fuzzified Allen temporal algebra plays an important role in capturing the time dimension of concurrent activites of principals as well as of intru...

In this paper, for an arbitrary multiplicative functional f from the set of all upper triangular fuzzy matrices to the fuzzy algebra, we prove that there exist a multiplicative functional F and a functional G from the fuzzy algebra to the fuzzy algebra such that the image of an upper triangular fuzzy matrix under f can be represented as the product of all the images of its main diagonal element...

A systematic and exhaustive method based on the group structure of a unitary Lie algebra is proposed to generate an enormous number of quantum codes. With respect to the algebraic structure, the orthogonality condition, which is the central rule of generating quantum codes, is proved to be fully equivalent to the distinguishability of the elements in this structure. In addition, four types of q...

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An abstract is not available for this content so a preview has been provided. As you have access to content, full PDF via the ‘Save PDF’ action button.

An abstract is not available for this content so a preview has been provided. As you have access to content, full PDF via the ‘Save PDF’ action button.