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X-simplicity of interval max-min matrices

Ján Plavka, Štefan Berežný (2018)

Kybernetika

A matrix A is said to have 𝐗 -simple image eigenspace if any eigenvector x belonging to the interval 𝐗 = { x : x ̲ x x ¯ } containing a constant vector is the unique solution of the system A y = x in 𝐗 . The main result of this paper is an extension of 𝐗 -simplicity to interval max-min matrix 𝐀 = { A : A ̲ A A ¯ } distinguishing two possibilities, that at least one matrix or all matrices from a given interval have 𝐗 -simple image eigenspace. 𝐗 -simplicity of interval matrices in max-min algebra are studied and equivalent conditions for interval...

Z specification of object oriented constraint programs.

Laurent Henocque (2004)

RACSAM

Object oriented constraint programs (OOCPs) emerge as a leading evolution of constraint programming and artificial intelligence, first applied to a range of industrial applications called configuration problems. The rich variety of technical approaches to solving configuration problems (CLP(FD), CC(FD), DCSP, Terminological systems, constraint programs with set variables, . . . ) is a source of difficulty. No universally accepted formal language exists for communicating about OOCPs, which makes...

Σ -Hamiltonian and Σ -regular algebraic structures

Ivan Chajda, Petr Emanovský (1996)

Mathematica Bohemica

The concept of a -closed subset was introduced in [1] for an algebraic structure = ( A , F , R ) of type and a set of open formulas of the first order language L ( ) . The set C ( ) of all -closed subsets of forms a complete lattice whose properties were investigated in [1] and [2]. An algebraic structure is called - hamiltonian, if every non-empty -closed subset of is a class (block) of some congruence on ; is called - regular, if = 𝔽 for every two , 𝔽 whenever they have a congruence class B C ( ) in common....

Σ -isomorphic algebraic structures

Ivan Chajda, Petr Emanovský (1995)

Mathematica Bohemica

For an algebraic structure = ( A , F , R ) or type and a set Σ of open formulas of the first order language L ( ) we introduce the concept of Σ -closed subsets of . The set Σ ( ) of all Σ -closed subsets forms a complete lattice. Algebraic structures , of type are called Σ -isomorphic if Σ ( ) Σ ( ) . Examples of such Σ -closed subsets are e.g. subalgebras of an algebra, ideals of a ring, ideals of a lattice, convex subsets of an ordered or quasiordered set etc. We study Σ -isomorphic algebraic structures in dependence on the...

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