Displaying similar documents to “Max-min interval systems of linear equations with bounded solution”

On an algorithm for testing T4 solvability of max-plus interval systems

Helena Myšková (2012)

Kybernetika

Similarity:

In this paper, we shall deal with the solvability of interval systems of linear equations in max-plus algebra. Max-plus algebra is an algebraic structure in which classical addition and multiplication are replaced by ⊕ and ⊗ , where a ⊕ b = max { a , b } , a ⊗ b = a + b . The notation 𝔸 ⊗ x = 𝕓 represents an interval system of linear equations, where 𝔸 = [ b ¯ , A ¯ ] and 𝕓 = [ b ̲ , b ¯ ] are given interval matrix and interval vector, respectively. We can define several types of solvability of interval systems. In this paper, we define the T4 solvability and...

Inessentiality with respect to subspaces

Michael Levin (1995)

Fundamenta Mathematicae

Similarity:

Let X be a compactum and let A = ( A i , B i ) : i = 1 , 2 , . . . be a countable family of pairs of disjoint subsets of X. Then A is said to be essential on Y ⊂ X if for every closed F i separating A i and B i the intersection ( ∩ F i ) ∩ Y is not empty. So A is inessential on Y if there exist closed F i separating A i and B i such that ∩ F i does not intersect Y. Properties of inessentiality are studied and applied to prove:  Theorem. For every countable family of pairs of disjoint open subsets of a compactum X there exists an open set G ∩ X on...

Entropy and growth of expanding periodic orbits for one-dimensional maps

A. Katok, A. Mezhirov (1998)

Fundamenta Mathematicae

Similarity:

Let f be a continuous map of the circle S 1 or the interval I into itself, piecewise C 1 , piecewise monotone with finitely many intervals of monotonicity and having positive entropy h. For any ε > 0 we prove the existence of at least e ( h - ε ) n k periodic points of period n k with large derivative along the period, | ( f n k ) ' | > e ( h - ε ) n k for some subsequence n k of natural numbers. For a strictly monotone map f without critical points we show the existence of at least ( 1 - ε ) e h n such points.

An iterative algorithm for testing solvability of max-min interval systems

Helena Myšková (2012)

Kybernetika

Similarity:

This paper is dealing with solvability of interval systems of linear equations in max-min algebra. Max-min algebra is the algebraic structure in which classical addition and multiplication are replaced by ⊕ and ⊗ , where a ⊕ b = max { a , b } , a ⊗ b = min { a , b } . The notation 𝔸 ⊗ x = 𝕓 represents an interval system of linear equations, where 𝔸 = [ A ̲ , A ¯ ] and 𝕓 = [ b ̲ , b ¯ ] are given interval matrix and interval vector, respectively. We can define several types of solvability of interval systems. In this paper, we define the T4 and T5 solvability and give...

Analytic determinacy and 0# A forcing-free proof of Harrington’s theorem

Ramez Sami (1999)

Fundamenta Mathematicae

Similarity:

We prove the following theorem: Given a⊆ω and 1 ≤ α < ω 1 C K , if for some η < ℵ 1 and all u ∈ WO of length η, a is Σ α 0 ( u ) , then a is Σ α 0 . We use this result to give a new, forcing-free, proof of Leo Harrington’s theorem: Σ 1 1 -Turing-determinacy implies the existence of 0 .

Intersection topologies with respect to separable GO-spaces and the countable ordinals

M. Jones (1995)

Fundamenta Mathematicae

Similarity:

Given two topologies, T 1 and T 2 , on the same set X, the intersection topologywith respect to T 1 and T 2 is the topology with basis U 1 ∩ U 2 : U 1 ∈ T 1 , U 2 ∈ T 2 . Equivalently, T is the join of T 1 and T 2 in the lattice of topologies on the set X. Following the work of Reed concerning intersection topologies with respect to the real line and the countable ordinals, Kunen made an extensive investigation of normality, perfectness and ω 1 -compactness in this class of topologies. We demonstrate that the majority of his results...

On B 2 k -sequences

Martin Helm (1993)

Acta Arithmetica

Similarity:

Introduction. An old conjecture of P. Erdős repeated many times with a prize offer states that the counting function A(n) of a B r -sequence A satisfies l i m i n f n → ∞ ( A ( n ) / ( n 1 / r ) ) = 0 . The conjecture was proved for r=2 by P. Erdős himself (see [5]) and in the cases r=4 and r=6 by J. C. M. Nash in [4] and by Xing-De Jia in [2] respectively. A very interesting proof of the conjecture in the case of all even r=2k by Xing-De Jia is to appear in the Journal of Number Theory [3]. Here we present a different, very short proof...