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 ...

(including the generalized coupled Sylvester matrix equations as special cases) have numerous applications in control and system theory. In this paper, an iterative algorithm is constructed to solve the general coupled matrix equations and their optimal approximation problem over generalized reflexive matrix solution (X1,X2, . . . ,Xq). When the general coupled matrix equations are consistent o...

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...

in some quality control applications, the quality of a process or a product is described by the relationship between a response variable and one or more explanatory variables, called a profile. moreover, in most practical applications, the qualitative characteristic of a product/service is vague, uncertain and linguistic and cannot be precisely stated. the purpose of this paper is to propose a ...

The spectrum of a graph is the family of eigenvalues of its (0, 1) adjacency matrix.A simple graph is reflexive if its second largest eigenvalue 2 does not exceed 2. The graphic property 2 2 is a hereditary one, i.e. every induced subgraph of a reflexive graph preserves this property and that is why reflexive graphs are usually represented through maximal graphs. Cacti, or treelike graphs, are ...

Rough set theory was proposed by Pawlak [1] as a mathematical tool to handle imprecision and uncertainty in data analysis. It has been successfully applied tomachine learning, intelligent systems, inductive reasoning, pattern recognition, mereology, image processing, signal analysis, knowledge discovery, decision analysis, expert systems, and many other fields [2–5]. The basic structure of roug...