On the problem $Ax=\lambda Bx$ in max algebra: every system of intervals is a spectrum

Sergeĭ Sergeev

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Displaying similar documents to “On the problem $A x = λ B x$ in max algebra: every system of intervals is a spectrum”

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

Helena Myšková (2012)

Kybernetika

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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 $\oplus$ and $\otimes$ , where $a \oplus b = max {a, b}$ , $a \otimes b = a + b$ . The notation $𝔸 \otimes x = 𝕓$ represents an interval system of linear equations, where $𝔸 = [\bar{b}, \bar{A}]$ and $𝕓 = [\underset{̲}{b}, \bar{b}]$ 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...

Max-min interval systems of linear equations with bounded solution

Helena Myšková (2012)

Kybernetika

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Max-min algebra is an algebraic structure in which classical addition and multiplication are replaced by $\oplus$ and $\otimes$ , where $a \oplus b = max {a, b}, a \otimes b = min {a, b}$ . The notation $𝐀 \otimes 𝐱 = 𝐛$ represents an interval system of linear equations, where $𝐀 = [\underset{̲}{A}, \bar{A}]$ , $𝐛 = [\underset{̲}{b}, \bar{b}]$ are given interval matrix and interval vector, respectively, and a solution is from a given interval vector $𝐱 = [\underset{̲}{x}, \bar{x}]$ . We define six types of solvability of max-min interval systems with bounded solution and give necessary and sufficient conditions for them.

Ultimate boundedness results for solutions of certain third order nonlinear matrix differential equations

M. O. Omeike, A. U. Afuwape (2010)

Kragujevac Journal of Mathematics

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On ergodicity of some cylinder flows

Krzysztof Frączek (2000)

Fundamenta Mathematicae

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We study ergodicity of cylinder flows of the form $T_{f} : T \times ℝ \to T \times ℝ$ , $T_{f} (x, y) = (x + α, y + f (x))$ , where $f : T \to ℝ$ is a measurable cocycle with zero integral. We show a new class of smooth ergodic cocycles. Let k be a natural number and let f be a function such that $D^{k} f$ is piecewise absolutely continuous (but not continuous) with zero sum of jumps. We show that if the points of discontinuity of $D^{k} f$ have some good properties, then $T_{f}$ is ergodic. Moreover, there exists $ε_{f} > 0$ such that if $v : T \to ℝ$ is a function with zero integral such that $D^{k} v$ is of bounded...

Displaying similar documents to “On the problem A x = λ B x in max algebra: every system of intervals is a spectrum”

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

Max-min interval systems of linear equations with bounded solution

Ultimate boundedness results for solutions of certain third order nonlinear matrix differential equations

On ergodicity of some cylinder flows

Displaying similar documents to “On the problem $A x = λ B x$ in max algebra: every system of intervals is a spectrum”