SavedAdd your journal

Journals / Turkish Journal of Mathematics and Computer Science / 2019 / Cilt: 11 - Sayı: -

Abstract Omega Algebra that Subsumes Tropical Min and Max Plus Algebras

Cenap özel
Syed Khalid Nauman
Hanifa Zekraoui
Pages
1–10
Publication Date
2022-11-05
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

As applications, symmetrized omega algebras are constructed and matrices with basicoperations and some topological distances over them are defined.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper abstract omega algebra is introduced and the definition is modeled in such a way that itsubsumes almost all so called tropical min and max plus algebras.
📊
Key Findings & Data:Concrete examples of distinct nature of thesealgebras are presented.
💡
Conclusion & Impact:As applications, symmetrized omega algebras are constructed and matrices with basicoperations and some topological distances over them are defined.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper abstract omega algebra is introduced and the definition is modeled in such a way that itsubsumes almost all so called tropical min and max plus algebras. Concrete examples of distinct nature of thesealgebras are presented. As applications, symmetrized omega algebras are constructed and matrices with basicoperations and some topological distances over them are defined.

🔖

Cite This Article

özel, C., Nauman, S. K., Zekraoui, H. (2022). Abstract Omega Algebra that Subsumes Tropical Min and Max Plus Algebras. Turkish Journal of Mathematics and Computer Science, Cilt: 11 - Sayı: -, 1–10. https://ajindex.com/articles/609121

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (7)

  1. Giraudet, M., Leloup, G., Lucas, F., First order theory of cyclically ordered groups, hal-00879429
  2. Litvinov, G.L., The Maslov dequantization, idempotent and tropical mathematics: a brief introduction, Journal of Mathematical Sciences, 140(2007), 426–444
  3. Maclagan, D., Sturmfels, B., Introduction to Tropical Geometry, Graduate Studies in Mathematics, Vol 161, American Mathematical Society, 2015
  4. Ozel, C., Piekosz, A., Wajch, E., Zekraoui, H., The minimizing vector theorem in symmetrized max-plus algebra, Journal of convex analysis, 26(2)(2019), 661–686
  5. Pin, J. E., Tropical Semirings, Idempotency (Bristol, 1994), 50–69, Publ. Newton Inst., Vol. 11, Cambridge Univ. Press, Cambridge, 1998
  6. Simon, I., Recognizable sets with multiplicities in the tropical semiring, pages 107–120 in Mathematical Foundations of Computer Science (Carlsbad, 1988), Lecture Notes in Computer Science, Vol. 324, Springer, Berlin, 1988
  7. Swierczkowski, S., On cyclically ordered groups, Fundamenta Mathematicae, 47(1959) 161–166.