We work out the theory of fractional isomorphism graphons as a generalization to classical finite graphs. The is given in terms homomorphism densities trees and it characterized distributions on iterated degree measures, Markov operators, weak conditional expectation with respect invariant sub-σ-algebras certain quotients graphons.

This lecture introduces the Jordan canonical form of a matrix — we prove that every square matrix is equivalent to a (essentially) unique Jordan matrix and we give a method to derive the latter. We also introduce the notion of minimal polynomial and we point out how to obtain it from the Jordan canonical form. Finally, we make an encounter with companion matrices. 1 Jordan form and an applicati...

In this paper, we study and analyze the algebraic structure of the circular cone. We establish a new efficient spectral decomposition, set up the Jordan algebra associated with the circular cone, and prove that this algebra forms a Euclidean Jordan algebra with a certain inner product. We then show that the cone of squares of this Euclidean Jordan algebra is indeed the circular cone itself. The...

In this paper, the notion of fuzzy n-polygroups (Fn -polygroups) is introduced and some related properties are investigated. In this regards, the concepts of normal  F-subpolygroups and homomorphisms of Fn-polygroups are adopted. Also, the quotient of Fn-polygroups by defining regular relations are studied. Finally, the classical isomorphism theorems of groups are generalized to Fn-polygroups p...

background: the control of spread of hiv takes concerted efforts at both national and international levels. education is an important component of preventing the spread of hiv. this study aimed to assess the attitudes of parents, teachers and students towards informing children about hiv/aids, attitudes concerning 'proper' age to learn about hiv/aids, possible differences in attitudes relating ...