The purpose of this article is to discuss some new aspects the vector-valued metric space. idea an arbitrary binary relation along with well-known F contraction used demonstrate existence fixed points in context a complete space for both single- and multi-valued mappings. Utilizing relation, help contraction, work extends complements very recently established Perov-type fixed-point results lite...

This paper presents efficient algorithms for clone items detection in a binary relation. Best implementation of these algorithms has O(|J |.||M||) time complexity, with J corresponding to the set of items of the relation and ||M|| corresponding to the size of the relation. This result improves the previous algorithm given in [3] which is O(|J |.||M||). Clone items have been introduced by Medina...

In this paper, we define a binary relation for general collective choice situations, the needing relation, that captures one notion of dependence between alternatives with respect to inclusion in several popular solution concepts, including the top-cycle set, the uncovered set, the Banks set, and the minimal covering set. After defining the relation and relating it to a graph theoretical view o...

In this talk, we discuss the results of investigations that began with a solution to an open problem posed by Schwabhäuser and Szczerba regarding definability (without parameters) in the three dimensional Euclidean geometry of lines, asking whether intersection was definable from perpendicularity (two lines intersecting at a right angle). It is not. The result is a “new” 3-dimensional geometry ...

The Multi-Relational Boolean factor analysis is a method from the family of matrix decomposition methods which enables us analyze binary multi-relational data, i.e. binary data which are composed from many binary data tables interconnected via relation. In this paper we present a new Boolean matrix factorization algorithm for this kind of data, which use the new knowledge from the theory of the...

We study the finite satisfiability problem for the two-variable fragment of first-order logic extended with counting quantifiers (C) and interpreted over linearly ordered structures. We show that the problem is undecidable in the case of two linear orders (in the presence of two other binary symbols). In the case of one linear order it is NExpTime-complete, even in the presence of the successor...

Macroeconometric and …nancial researchers often use binary data constructed in a way that creates serial dependence. We show that this dependence can be allowed for if the binary states are treated as Markov processes. In addition, the methods of construction ensure that certain sequences are never observed in the constructed data. Together these features make it di¢ cult to utilize static and ...

We study the ordered set of rough sets determined by relations which are not necessarily reflexive, symmetric, or transitive. We show that for tolerances and transitive binary relations the set of rough sets is not necessarily even a semilattice. We also prove that the set of rough sets determined by a symmetric and transitive binary relation forms a complete Stone lattice. Furthermore, for the...

Manski (1997) and Manski and Pepper (2000) gave sharp bounds on causal effects under the assumptions of monotone treatment response (MTR) and monotone treatment selection (MTS). VanderWeele (2008) provided bounds for binary treatment under an assumption of monotone confounding (MC). We discuss the relation between MC and MTS and provide bounds under various combinations of these assumptions. We...