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Asymptotic Identity in Min-Plus Algebra: A Report on CPNS [PDF]

Computational and Mathematical Methods in Medicine, 2012
Network calculus is a theory initiated primarily in computer communication networks, especially in the aspect of real-time communications, where min-plus algebra plays a role. Cyber-physical networking systems (CPNSs) are recently developing fast and models in data flows as well as systems in CPNS are, accordingly, greatly desired.
Li M, Zhao W.
exaly   +5 more sources

A Min-Plus Algebra System Theory for Traffic Networks

Mathematics, 2023
In this article, we introduce a comprehensive system theory based on the min-plus algebra of 2×2 matrices of functions. This novel approach enables the algebraic construction of traffic networks and the analytical derivation of performance bounds for ...
Nadir Farhi
doaj   +4 more sources

Characteristic Min-Polynomial and Eigen Problem of a Matrix over Min-Plus Algebra

JTAM (Jurnal Teori dan Aplikasi Matematika), 2023
Let R_ε=R∪{-∞}, with R being a set of all real numbers. The algebraic structure (R_ε,⊕,⊗) is called max-plus algebra. The task of finding the eigenvalue and eigenvector is called the eigenproblem.
Sahmura Maula Al Maghribi, Siswanto Siswanto, Sutrima Sutrima   +2 more
doaj   +2 more sources

CRAMER’S RULE IN MIN-PLUS ALGEBRA

Barekeng
Cramer’s rule is one of a method for solving a system of linear equations in conventional algebra. The system of linear equation  can be solved using Cramer’s rule if .
Zakia Nur Ramadhani Putri, Siswanto Siswanto, Vika Yugi Kurniawan   +2 more
doaj   +2 more sources

Interval min-plus algebraic structure and matrices over interval min-plus algebra

Journal of Physics: Conference Series, 2020
Abstract Max-plus algebra is the set ℝ max
A R Awallia, null Siswanto, V Y Kurniawan   +2 more
exaly   +2 more sources

CRAMER’S RULE IN INTERVAL MIN-PLUS ALGEBRA

Barekeng
A min-plus algebra is a set ,  where  is the set of all real numbers, equipped with the minimum  and addition  operations. The system of linear equations  in min-plus algebra can be solved using Cramer's rule.
Siswanto Siswanto, Ade Safira Septiany
doaj   +2 more sources

Determining the Inverse of a Matrix over Min-Plus Algebra

JTAM (Jurnal Teori dan Aplikasi Matematika)
Linear algebra over the semiring  R_ε with ⊗ (plus) and ⨁ (maximum) operations which is known as max-plus algebra. One of the isomorphic with this algebra is a min-plus algebra.
Siswanto Siswanto, Anggrina Gusmizain
doaj   +2 more sources

PERMANENT AND DOMINANT OF MATRIX OVER INTERVAL MIN-PLUS ALGEBRA

Barekeng
A min-plus algebra is a set , where is the set of all real numbers equipped with two binary operations, namely minimum and addition . Every square matrix in min-plus algebra can always be calculated as a permanent and dominant matrix.
Ade Safira Septiany, Siswanto Siswanto, Vika Yugi Kurniawan   +2 more
doaj   +2 more sources

Independent [1, 2]-domination of grids via min-plus algebra

Electronic Notes in Discrete Mathematics, 2016
Abstract Domination of grids has been proved to be a demanding task and with the addition of independence it becomes more challenging. It is known that no grid with m , n ≥ 5 has a perfect code, that is an independent vertex set such that each vertex not in it has exactly one neighbor in that set. So it is interesting to study the existence
Maria Luz Puertas
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Characteristic Polynomial and Eigenproblem of Triangular Matrix over Interval Min-Plus Algebra

JTAM (Jurnal Teori dan Aplikasi Matematika)
A min-plus algebra is a linear algebra over the semiring R_ε', equipped with the operations “"⊕'=min" ” and “⊗=+”. In min-plus algebra, there is the concept of characteristic polynomial obtained from permanent of matrix.
Anita Dwi Rahmawati, Siswanto Siswanto, Supriyadi Wibowo   +2 more
doaj   +2 more sources