‎In this article we discuss examples of fractal $omega$-operads‎. ‎Thus we show that there is an $omega$-operadic approach to explain existence of‎ ‎the globular set of globular setsfootnote{Globular sets are also called $omega$-graphs by the French School.}‎, ‎the reflexive globular set of reflexive globular sets‎, ‎the $omega$-magma of $omega$-magmas‎, ‎and also the reflexive $omega$-magma ...

It is well known that the Chern classes ci of a rank n vector bundle on P N , generated by global sections, are non-negative if i ≤ n and vanish otherwise. This paper deals with the following question: does the above result hold for the wider class of reflexive sheaves? We show that the Chern numbers ci with i ≥ 4 can be arbitrarily negative for reflexive sheaves of any rank; on the contrary fo...

Extended Abstract Representations of the lower and upper approximations of a set in the context of an approximation space as modal operators in the first order language of modal logics, are quite natural and widely familiar now to the rough-set community. According to the perception of an observer, objects of a universe (of discourse) are clustered. These are the basic information granules (or ...

The quotient space theory based on fuzzy tolerance relation is put forward to solve the problem of clustering in this paper. The similarity matrix does not always satisfy ultrametric inequality, theoretically and practically. We give the method to construct the hierarchical quotient space chain if the similarity matrix is only reflexive and symmetric. We consider not only the subset of data (cl...

The association between hyperstructures and binary relations had been intensively studied 5,6,10,11,2,4,20 . Chvalina 5,6 and Hort 2 use ordered structures for the construction of semigroups and hypergroups. Rosenberg 4 associated with any binary relation of full domain, a hypergroupoid and found conditions on , such that is a hypergroup. Corsini and Leoreanu 16 study hypergroups and binary rel...

E cannot always use the classical methods to solve complicated problems in economics, engineering, social sciences, medical sciences etc. because different types of uncertainties are present in these theories. These days so many theories are available to deal with such type of uncertainties, such as, theory of fuzzy sets [1], theory of intuitionistic fuzzy sets [2], [3], theory of vague sets [4...

Let X be a compact Hausdorff space and let H be a separable Hilbert space. We prove that the group of all order automorphisms of the C∗-algebra C(X)⊗ B(H) is algebraically reflexive.

Smarandache initiated neutrosophic sets (NSs) which can be used as a mathematical tool for dealing with indeterminate and inconsistent information. In order to apply NSs conveniently, single valued neutrosophic sets (SVNSs) were proposed by Wang et al. In this paper, we propose single valued neutrosophic relations (SVNRs) and study their properties. The notions of anti-reflexive kernel, symmetr...

We study rules A ⇒ B describing attribute dependencies in tables over domains with similarity relations. A ⇒ B reads “for any two table rows: similar values of attributes from A imply similar values of attributes from B”. The rules generalize ordinary functional dependencies in that they allow for processing of similarity of attribute values. Similarity is modeled by reflexive and symmetric fuz...

Standard Dutch and German have two reflexive forms: a weak form (zich in Dutch and sich in German) and a strong form (zichzelf in Dutch and sich selbst in German). The choice between the two reflexive forms in Dutch has been explained by the selectional restrictions of the verb, distinguishing between three verb classes: inherently reflexive verbs, accidentally reflexive verbs and transitive ve...